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;
63 tab
->bottom
.type
= isl_tab_undo_bottom
;
64 tab
->bottom
.next
= NULL
;
65 tab
->top
= &tab
->bottom
;
77 int isl_tab_extend_cons(struct isl_tab
*tab
, unsigned n_new
)
79 unsigned off
= 2 + tab
->M
;
84 if (tab
->max_con
< tab
->n_con
+ n_new
) {
85 struct isl_tab_var
*con
;
87 con
= isl_realloc_array(tab
->mat
->ctx
, tab
->con
,
88 struct isl_tab_var
, tab
->max_con
+ n_new
);
92 tab
->max_con
+= n_new
;
94 if (tab
->mat
->n_row
< tab
->n_row
+ n_new
) {
97 tab
->mat
= isl_mat_extend(tab
->mat
,
98 tab
->n_row
+ n_new
, off
+ tab
->n_col
);
101 row_var
= isl_realloc_array(tab
->mat
->ctx
, tab
->row_var
,
102 int, tab
->mat
->n_row
);
105 tab
->row_var
= row_var
;
107 enum isl_tab_row_sign
*s
;
108 s
= isl_realloc_array(tab
->mat
->ctx
, tab
->row_sign
,
109 enum isl_tab_row_sign
, tab
->mat
->n_row
);
118 /* Make room for at least n_new extra variables.
119 * Return -1 if anything went wrong.
121 int isl_tab_extend_vars(struct isl_tab
*tab
, unsigned n_new
)
123 struct isl_tab_var
*var
;
124 unsigned off
= 2 + tab
->M
;
126 if (tab
->max_var
< tab
->n_var
+ n_new
) {
127 var
= isl_realloc_array(tab
->mat
->ctx
, tab
->var
,
128 struct isl_tab_var
, tab
->n_var
+ n_new
);
132 tab
->max_var
+= n_new
;
135 if (tab
->mat
->n_col
< off
+ tab
->n_col
+ n_new
) {
138 tab
->mat
= isl_mat_extend(tab
->mat
,
139 tab
->mat
->n_row
, off
+ tab
->n_col
+ n_new
);
142 p
= isl_realloc_array(tab
->mat
->ctx
, tab
->col_var
,
143 int, tab
->n_col
+ n_new
);
152 struct isl_tab
*isl_tab_extend(struct isl_tab
*tab
, unsigned n_new
)
154 if (isl_tab_extend_cons(tab
, n_new
) >= 0)
161 static void free_undo(struct isl_tab
*tab
)
163 struct isl_tab_undo
*undo
, *next
;
165 for (undo
= tab
->top
; undo
&& undo
!= &tab
->bottom
; undo
= next
) {
172 void isl_tab_free(struct isl_tab
*tab
)
177 isl_mat_free(tab
->mat
);
178 isl_vec_free(tab
->dual
);
179 isl_basic_set_free(tab
->bset
);
185 isl_mat_free(tab
->samples
);
186 free(tab
->sample_index
);
187 isl_mat_free(tab
->basis
);
191 struct isl_tab
*isl_tab_dup(struct isl_tab
*tab
)
201 dup
= isl_calloc_type(tab
->ctx
, struct isl_tab
);
204 dup
->mat
= isl_mat_dup(tab
->mat
);
207 dup
->var
= isl_alloc_array(tab
->ctx
, struct isl_tab_var
, tab
->max_var
);
210 for (i
= 0; i
< tab
->n_var
; ++i
)
211 dup
->var
[i
] = tab
->var
[i
];
212 dup
->con
= isl_alloc_array(tab
->ctx
, struct isl_tab_var
, tab
->max_con
);
215 for (i
= 0; i
< tab
->n_con
; ++i
)
216 dup
->con
[i
] = tab
->con
[i
];
217 dup
->col_var
= isl_alloc_array(tab
->ctx
, int, tab
->mat
->n_col
- off
);
220 for (i
= 0; i
< tab
->n_col
; ++i
)
221 dup
->col_var
[i
] = tab
->col_var
[i
];
222 dup
->row_var
= isl_alloc_array(tab
->ctx
, int, tab
->mat
->n_row
);
225 for (i
= 0; i
< tab
->n_row
; ++i
)
226 dup
->row_var
[i
] = tab
->row_var
[i
];
228 dup
->row_sign
= isl_alloc_array(tab
->ctx
, enum isl_tab_row_sign
,
232 for (i
= 0; i
< tab
->n_row
; ++i
)
233 dup
->row_sign
[i
] = tab
->row_sign
[i
];
236 dup
->samples
= isl_mat_dup(tab
->samples
);
239 dup
->sample_index
= isl_alloc_array(tab
->mat
->ctx
, int,
240 tab
->samples
->n_row
);
241 if (!dup
->sample_index
)
243 dup
->n_sample
= tab
->n_sample
;
244 dup
->n_outside
= tab
->n_outside
;
246 dup
->n_row
= tab
->n_row
;
247 dup
->n_con
= tab
->n_con
;
248 dup
->n_eq
= tab
->n_eq
;
249 dup
->max_con
= tab
->max_con
;
250 dup
->n_col
= tab
->n_col
;
251 dup
->n_var
= tab
->n_var
;
252 dup
->max_var
= tab
->max_var
;
253 dup
->n_param
= tab
->n_param
;
254 dup
->n_div
= tab
->n_div
;
255 dup
->n_dead
= tab
->n_dead
;
256 dup
->n_redundant
= tab
->n_redundant
;
257 dup
->rational
= tab
->rational
;
258 dup
->empty
= tab
->empty
;
262 dup
->bottom
.type
= isl_tab_undo_bottom
;
263 dup
->bottom
.next
= NULL
;
264 dup
->top
= &dup
->bottom
;
266 dup
->n_zero
= tab
->n_zero
;
267 dup
->n_unbounded
= tab
->n_unbounded
;
268 dup
->basis
= isl_mat_dup(tab
->basis
);
276 /* Construct the coefficient matrix of the product tableau
278 * mat{1,2} is the coefficient matrix of tableau {1,2}
279 * row{1,2} is the number of rows in tableau {1,2}
280 * col{1,2} is the number of columns in tableau {1,2}
281 * off is the offset to the coefficient column (skipping the
282 * denominator, the constant term and the big parameter if any)
283 * r{1,2} is the number of redundant rows in tableau {1,2}
284 * d{1,2} is the number of dead columns in tableau {1,2}
286 * The order of the rows and columns in the result is as explained
287 * in isl_tab_product.
289 static struct isl_mat
*tab_mat_product(struct isl_mat
*mat1
,
290 struct isl_mat
*mat2
, unsigned row1
, unsigned row2
,
291 unsigned col1
, unsigned col2
,
292 unsigned off
, unsigned r1
, unsigned r2
, unsigned d1
, unsigned d2
)
295 struct isl_mat
*prod
;
298 prod
= isl_mat_alloc(mat1
->ctx
, mat1
->n_row
+ mat2
->n_row
,
302 for (i
= 0; i
< r1
; ++i
) {
303 isl_seq_cpy(prod
->row
[n
+ i
], mat1
->row
[i
], off
+ d1
);
304 isl_seq_clr(prod
->row
[n
+ i
] + off
+ d1
, d2
);
305 isl_seq_cpy(prod
->row
[n
+ i
] + off
+ d1
+ d2
,
306 mat1
->row
[i
] + off
+ d1
, col1
- d1
);
307 isl_seq_clr(prod
->row
[n
+ i
] + off
+ col1
+ d1
, col2
- d2
);
311 for (i
= 0; i
< r2
; ++i
) {
312 isl_seq_cpy(prod
->row
[n
+ i
], mat2
->row
[i
], off
);
313 isl_seq_clr(prod
->row
[n
+ i
] + off
, d1
);
314 isl_seq_cpy(prod
->row
[n
+ i
] + off
+ d1
,
315 mat2
->row
[i
] + off
, d2
);
316 isl_seq_clr(prod
->row
[n
+ i
] + off
+ d1
+ d2
, col1
- d1
);
317 isl_seq_cpy(prod
->row
[n
+ i
] + off
+ col1
+ d1
,
318 mat2
->row
[i
] + off
+ d2
, col2
- d2
);
322 for (i
= 0; i
< row1
- r1
; ++i
) {
323 isl_seq_cpy(prod
->row
[n
+ i
], mat1
->row
[r1
+ i
], off
+ d1
);
324 isl_seq_clr(prod
->row
[n
+ i
] + off
+ d1
, d2
);
325 isl_seq_cpy(prod
->row
[n
+ i
] + off
+ d1
+ d2
,
326 mat1
->row
[r1
+ i
] + off
+ d1
, col1
- d1
);
327 isl_seq_clr(prod
->row
[n
+ i
] + off
+ col1
+ d1
, col2
- d2
);
331 for (i
= 0; i
< row2
- r2
; ++i
) {
332 isl_seq_cpy(prod
->row
[n
+ i
], mat2
->row
[r2
+ i
], off
);
333 isl_seq_clr(prod
->row
[n
+ i
] + off
, d1
);
334 isl_seq_cpy(prod
->row
[n
+ i
] + off
+ d1
,
335 mat2
->row
[r2
+ i
] + off
, d2
);
336 isl_seq_clr(prod
->row
[n
+ i
] + off
+ d1
+ d2
, col1
- d1
);
337 isl_seq_cpy(prod
->row
[n
+ i
] + off
+ col1
+ d1
,
338 mat2
->row
[r2
+ i
] + off
+ d2
, col2
- d2
);
344 /* Update the row or column index of a variable that corresponds
345 * to a variable in the first input tableau.
347 static void update_index1(struct isl_tab_var
*var
,
348 unsigned r1
, unsigned r2
, unsigned d1
, unsigned d2
)
350 if (var
->index
== -1)
352 if (var
->is_row
&& var
->index
>= r1
)
354 if (!var
->is_row
&& var
->index
>= d1
)
358 /* Update the row or column index of a variable that corresponds
359 * to a variable in the second input tableau.
361 static void update_index2(struct isl_tab_var
*var
,
362 unsigned row1
, unsigned col1
,
363 unsigned r1
, unsigned r2
, unsigned d1
, unsigned d2
)
365 if (var
->index
== -1)
380 /* Create a tableau that represents the Cartesian product of the sets
381 * represented by tableaus tab1 and tab2.
382 * The order of the rows in the product is
383 * - redundant rows of tab1
384 * - redundant rows of tab2
385 * - non-redundant rows of tab1
386 * - non-redundant rows of tab2
387 * The order of the columns is
390 * - coefficient of big parameter, if any
391 * - dead columns of tab1
392 * - dead columns of tab2
393 * - live columns of tab1
394 * - live columns of tab2
395 * The order of the variables and the constraints is a concatenation
396 * of order in the two input tableaus.
398 struct isl_tab
*isl_tab_product(struct isl_tab
*tab1
, struct isl_tab
*tab2
)
401 struct isl_tab
*prod
;
403 unsigned r1
, r2
, d1
, d2
;
408 isl_assert(tab1
->mat
->ctx
, tab1
->M
== tab2
->M
, return NULL
);
409 isl_assert(tab1
->mat
->ctx
, tab1
->rational
== tab2
->rational
, return NULL
);
410 isl_assert(tab1
->mat
->ctx
, !tab1
->row_sign
, return NULL
);
411 isl_assert(tab1
->mat
->ctx
, !tab2
->row_sign
, return NULL
);
412 isl_assert(tab1
->mat
->ctx
, tab1
->n_param
== 0, return NULL
);
413 isl_assert(tab1
->mat
->ctx
, tab2
->n_param
== 0, return NULL
);
414 isl_assert(tab1
->mat
->ctx
, tab1
->n_div
== 0, return NULL
);
415 isl_assert(tab1
->mat
->ctx
, tab2
->n_div
== 0, return NULL
);
418 r1
= tab1
->n_redundant
;
419 r2
= tab2
->n_redundant
;
422 prod
= isl_calloc_type(tab1
->mat
->ctx
, struct isl_tab
);
425 prod
->mat
= tab_mat_product(tab1
->mat
, tab2
->mat
,
426 tab1
->n_row
, tab2
->n_row
,
427 tab1
->n_col
, tab2
->n_col
, off
, r1
, r2
, d1
, d2
);
430 prod
->var
= isl_alloc_array(tab1
->mat
->ctx
, struct isl_tab_var
,
431 tab1
->max_var
+ tab2
->max_var
);
434 for (i
= 0; i
< tab1
->n_var
; ++i
) {
435 prod
->var
[i
] = tab1
->var
[i
];
436 update_index1(&prod
->var
[i
], r1
, r2
, d1
, d2
);
438 for (i
= 0; i
< tab2
->n_var
; ++i
) {
439 prod
->var
[tab1
->n_var
+ i
] = tab2
->var
[i
];
440 update_index2(&prod
->var
[tab1
->n_var
+ i
],
441 tab1
->n_row
, tab1
->n_col
,
444 prod
->con
= isl_alloc_array(tab1
->mat
->ctx
, struct isl_tab_var
,
445 tab1
->max_con
+ tab2
->max_con
);
448 for (i
= 0; i
< tab1
->n_con
; ++i
) {
449 prod
->con
[i
] = tab1
->con
[i
];
450 update_index1(&prod
->con
[i
], r1
, r2
, d1
, d2
);
452 for (i
= 0; i
< tab2
->n_con
; ++i
) {
453 prod
->con
[tab1
->n_con
+ i
] = tab2
->con
[i
];
454 update_index2(&prod
->con
[tab1
->n_con
+ i
],
455 tab1
->n_row
, tab1
->n_col
,
458 prod
->col_var
= isl_alloc_array(tab1
->mat
->ctx
, int,
459 tab1
->n_col
+ tab2
->n_col
);
462 for (i
= 0; i
< tab1
->n_col
; ++i
) {
463 int pos
= i
< d1
? i
: i
+ d2
;
464 prod
->col_var
[pos
] = tab1
->col_var
[i
];
466 for (i
= 0; i
< tab2
->n_col
; ++i
) {
467 int pos
= i
< d2
? d1
+ i
: tab1
->n_col
+ i
;
468 int t
= tab2
->col_var
[i
];
473 prod
->col_var
[pos
] = t
;
475 prod
->row_var
= isl_alloc_array(tab1
->mat
->ctx
, int,
476 tab1
->mat
->n_row
+ tab2
->mat
->n_row
);
479 for (i
= 0; i
< tab1
->n_row
; ++i
) {
480 int pos
= i
< r1
? i
: i
+ r2
;
481 prod
->row_var
[pos
] = tab1
->row_var
[i
];
483 for (i
= 0; i
< tab2
->n_row
; ++i
) {
484 int pos
= i
< r2
? r1
+ i
: tab1
->n_row
+ i
;
485 int t
= tab2
->row_var
[i
];
490 prod
->row_var
[pos
] = t
;
492 prod
->samples
= NULL
;
493 prod
->sample_index
= NULL
;
494 prod
->n_row
= tab1
->n_row
+ tab2
->n_row
;
495 prod
->n_con
= tab1
->n_con
+ tab2
->n_con
;
497 prod
->max_con
= tab1
->max_con
+ tab2
->max_con
;
498 prod
->n_col
= tab1
->n_col
+ tab2
->n_col
;
499 prod
->n_var
= tab1
->n_var
+ tab2
->n_var
;
500 prod
->max_var
= tab1
->max_var
+ tab2
->max_var
;
503 prod
->n_dead
= tab1
->n_dead
+ tab2
->n_dead
;
504 prod
->n_redundant
= tab1
->n_redundant
+ tab2
->n_redundant
;
505 prod
->rational
= tab1
->rational
;
506 prod
->empty
= tab1
->empty
|| tab2
->empty
;
510 prod
->bottom
.type
= isl_tab_undo_bottom
;
511 prod
->bottom
.next
= NULL
;
512 prod
->top
= &prod
->bottom
;
515 prod
->n_unbounded
= 0;
524 static struct isl_tab_var
*var_from_index(struct isl_tab
*tab
, int i
)
529 return &tab
->con
[~i
];
532 struct isl_tab_var
*isl_tab_var_from_row(struct isl_tab
*tab
, int i
)
534 return var_from_index(tab
, tab
->row_var
[i
]);
537 static struct isl_tab_var
*var_from_col(struct isl_tab
*tab
, int i
)
539 return var_from_index(tab
, tab
->col_var
[i
]);
542 /* Check if there are any upper bounds on column variable "var",
543 * i.e., non-negative rows where var appears with a negative coefficient.
544 * Return 1 if there are no such bounds.
546 static int max_is_manifestly_unbounded(struct isl_tab
*tab
,
547 struct isl_tab_var
*var
)
550 unsigned off
= 2 + tab
->M
;
554 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
555 if (!isl_int_is_neg(tab
->mat
->row
[i
][off
+ var
->index
]))
557 if (isl_tab_var_from_row(tab
, i
)->is_nonneg
)
563 /* Check if there are any lower bounds on column variable "var",
564 * i.e., non-negative rows where var appears with a positive coefficient.
565 * Return 1 if there are no such bounds.
567 static int min_is_manifestly_unbounded(struct isl_tab
*tab
,
568 struct isl_tab_var
*var
)
571 unsigned off
= 2 + tab
->M
;
575 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
576 if (!isl_int_is_pos(tab
->mat
->row
[i
][off
+ var
->index
]))
578 if (isl_tab_var_from_row(tab
, i
)->is_nonneg
)
584 static int row_cmp(struct isl_tab
*tab
, int r1
, int r2
, int c
, isl_int t
)
586 unsigned off
= 2 + tab
->M
;
590 isl_int_mul(t
, tab
->mat
->row
[r1
][2], tab
->mat
->row
[r2
][off
+c
]);
591 isl_int_submul(t
, tab
->mat
->row
[r2
][2], tab
->mat
->row
[r1
][off
+c
]);
596 isl_int_mul(t
, tab
->mat
->row
[r1
][1], tab
->mat
->row
[r2
][off
+ c
]);
597 isl_int_submul(t
, tab
->mat
->row
[r2
][1], tab
->mat
->row
[r1
][off
+ c
]);
598 return isl_int_sgn(t
);
601 /* Given the index of a column "c", return the index of a row
602 * that can be used to pivot the column in, with either an increase
603 * (sgn > 0) or a decrease (sgn < 0) of the corresponding variable.
604 * If "var" is not NULL, then the row returned will be different from
605 * the one associated with "var".
607 * Each row in the tableau is of the form
609 * x_r = a_r0 + \sum_i a_ri x_i
611 * Only rows with x_r >= 0 and with the sign of a_ri opposite to "sgn"
612 * impose any limit on the increase or decrease in the value of x_c
613 * and this bound is equal to a_r0 / |a_rc|. We are therefore looking
614 * for the row with the smallest (most stringent) such bound.
615 * Note that the common denominator of each row drops out of the fraction.
616 * To check if row j has a smaller bound than row r, i.e.,
617 * a_j0 / |a_jc| < a_r0 / |a_rc| or a_j0 |a_rc| < a_r0 |a_jc|,
618 * we check if -sign(a_jc) (a_j0 a_rc - a_r0 a_jc) < 0,
619 * where -sign(a_jc) is equal to "sgn".
621 static int pivot_row(struct isl_tab
*tab
,
622 struct isl_tab_var
*var
, int sgn
, int c
)
626 unsigned off
= 2 + tab
->M
;
630 for (j
= tab
->n_redundant
; j
< tab
->n_row
; ++j
) {
631 if (var
&& j
== var
->index
)
633 if (!isl_tab_var_from_row(tab
, j
)->is_nonneg
)
635 if (sgn
* isl_int_sgn(tab
->mat
->row
[j
][off
+ c
]) >= 0)
641 tsgn
= sgn
* row_cmp(tab
, r
, j
, c
, t
);
642 if (tsgn
< 0 || (tsgn
== 0 &&
643 tab
->row_var
[j
] < tab
->row_var
[r
]))
650 /* Find a pivot (row and col) that will increase (sgn > 0) or decrease
651 * (sgn < 0) the value of row variable var.
652 * If not NULL, then skip_var is a row variable that should be ignored
653 * while looking for a pivot row. It is usually equal to var.
655 * As the given row in the tableau is of the form
657 * x_r = a_r0 + \sum_i a_ri x_i
659 * we need to find a column such that the sign of a_ri is equal to "sgn"
660 * (such that an increase in x_i will have the desired effect) or a
661 * column with a variable that may attain negative values.
662 * If a_ri is positive, then we need to move x_i in the same direction
663 * to obtain the desired effect. Otherwise, x_i has to move in the
664 * opposite direction.
666 static void find_pivot(struct isl_tab
*tab
,
667 struct isl_tab_var
*var
, struct isl_tab_var
*skip_var
,
668 int sgn
, int *row
, int *col
)
675 isl_assert(tab
->mat
->ctx
, var
->is_row
, return);
676 tr
= tab
->mat
->row
[var
->index
] + 2 + tab
->M
;
679 for (j
= tab
->n_dead
; j
< tab
->n_col
; ++j
) {
680 if (isl_int_is_zero(tr
[j
]))
682 if (isl_int_sgn(tr
[j
]) != sgn
&&
683 var_from_col(tab
, j
)->is_nonneg
)
685 if (c
< 0 || tab
->col_var
[j
] < tab
->col_var
[c
])
691 sgn
*= isl_int_sgn(tr
[c
]);
692 r
= pivot_row(tab
, skip_var
, sgn
, c
);
693 *row
= r
< 0 ? var
->index
: r
;
697 /* Return 1 if row "row" represents an obviously redundant inequality.
699 * - it represents an inequality or a variable
700 * - that is the sum of a non-negative sample value and a positive
701 * combination of zero or more non-negative variables.
703 int isl_tab_row_is_redundant(struct isl_tab
*tab
, int row
)
706 unsigned off
= 2 + tab
->M
;
708 if (tab
->row_var
[row
] < 0 && !isl_tab_var_from_row(tab
, row
)->is_nonneg
)
711 if (isl_int_is_neg(tab
->mat
->row
[row
][1]))
713 if (tab
->M
&& isl_int_is_neg(tab
->mat
->row
[row
][2]))
716 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
717 if (isl_int_is_zero(tab
->mat
->row
[row
][off
+ i
]))
719 if (isl_int_is_neg(tab
->mat
->row
[row
][off
+ i
]))
721 if (!var_from_col(tab
, i
)->is_nonneg
)
727 static void swap_rows(struct isl_tab
*tab
, int row1
, int row2
)
730 t
= tab
->row_var
[row1
];
731 tab
->row_var
[row1
] = tab
->row_var
[row2
];
732 tab
->row_var
[row2
] = t
;
733 isl_tab_var_from_row(tab
, row1
)->index
= row1
;
734 isl_tab_var_from_row(tab
, row2
)->index
= row2
;
735 tab
->mat
= isl_mat_swap_rows(tab
->mat
, row1
, row2
);
739 t
= tab
->row_sign
[row1
];
740 tab
->row_sign
[row1
] = tab
->row_sign
[row2
];
741 tab
->row_sign
[row2
] = t
;
744 static void push_union(struct isl_tab
*tab
,
745 enum isl_tab_undo_type type
, union isl_tab_undo_val u
)
747 struct isl_tab_undo
*undo
;
752 undo
= isl_alloc_type(tab
->mat
->ctx
, struct isl_tab_undo
);
760 undo
->next
= tab
->top
;
764 void isl_tab_push_var(struct isl_tab
*tab
,
765 enum isl_tab_undo_type type
, struct isl_tab_var
*var
)
767 union isl_tab_undo_val u
;
769 u
.var_index
= tab
->row_var
[var
->index
];
771 u
.var_index
= tab
->col_var
[var
->index
];
772 push_union(tab
, type
, u
);
775 void isl_tab_push(struct isl_tab
*tab
, enum isl_tab_undo_type type
)
777 union isl_tab_undo_val u
= { 0 };
778 push_union(tab
, type
, u
);
781 /* Push a record on the undo stack describing the current basic
782 * variables, so that the this state can be restored during rollback.
784 void isl_tab_push_basis(struct isl_tab
*tab
)
787 union isl_tab_undo_val u
;
789 u
.col_var
= isl_alloc_array(tab
->mat
->ctx
, int, tab
->n_col
);
795 for (i
= 0; i
< tab
->n_col
; ++i
)
796 u
.col_var
[i
] = tab
->col_var
[i
];
797 push_union(tab
, isl_tab_undo_saved_basis
, u
);
800 struct isl_tab
*isl_tab_init_samples(struct isl_tab
*tab
)
807 tab
->samples
= isl_mat_alloc(tab
->mat
->ctx
, 1, 1 + tab
->n_var
);
810 tab
->sample_index
= isl_alloc_array(tab
->mat
->ctx
, int, 1);
811 if (!tab
->sample_index
)
819 struct isl_tab
*isl_tab_add_sample(struct isl_tab
*tab
,
820 __isl_take isl_vec
*sample
)
825 if (tab
->n_sample
+ 1 > tab
->samples
->n_row
) {
826 int *t
= isl_realloc_array(tab
->mat
->ctx
,
827 tab
->sample_index
, int, tab
->n_sample
+ 1);
830 tab
->sample_index
= t
;
833 tab
->samples
= isl_mat_extend(tab
->samples
,
834 tab
->n_sample
+ 1, tab
->samples
->n_col
);
838 isl_seq_cpy(tab
->samples
->row
[tab
->n_sample
], sample
->el
, sample
->size
);
839 isl_vec_free(sample
);
840 tab
->sample_index
[tab
->n_sample
] = tab
->n_sample
;
845 isl_vec_free(sample
);
850 struct isl_tab
*isl_tab_drop_sample(struct isl_tab
*tab
, int s
)
852 if (s
!= tab
->n_outside
) {
853 int t
= tab
->sample_index
[tab
->n_outside
];
854 tab
->sample_index
[tab
->n_outside
] = tab
->sample_index
[s
];
855 tab
->sample_index
[s
] = t
;
856 isl_mat_swap_rows(tab
->samples
, tab
->n_outside
, s
);
859 isl_tab_push(tab
, isl_tab_undo_drop_sample
);
864 /* Record the current number of samples so that we can remove newer
865 * samples during a rollback.
867 void isl_tab_save_samples(struct isl_tab
*tab
)
869 union isl_tab_undo_val u
;
875 push_union(tab
, isl_tab_undo_saved_samples
, u
);
878 /* Mark row with index "row" as being redundant.
879 * If we may need to undo the operation or if the row represents
880 * a variable of the original problem, the row is kept,
881 * but no longer considered when looking for a pivot row.
882 * Otherwise, the row is simply removed.
884 * The row may be interchanged with some other row. If it
885 * is interchanged with a later row, return 1. Otherwise return 0.
886 * If the rows are checked in order in the calling function,
887 * then a return value of 1 means that the row with the given
888 * row number may now contain a different row that hasn't been checked yet.
890 int isl_tab_mark_redundant(struct isl_tab
*tab
, int row
)
892 struct isl_tab_var
*var
= isl_tab_var_from_row(tab
, row
);
893 var
->is_redundant
= 1;
894 isl_assert(tab
->mat
->ctx
, row
>= tab
->n_redundant
, return -1);
895 if (tab
->need_undo
|| tab
->row_var
[row
] >= 0) {
896 if (tab
->row_var
[row
] >= 0 && !var
->is_nonneg
) {
898 isl_tab_push_var(tab
, isl_tab_undo_nonneg
, var
);
900 if (row
!= tab
->n_redundant
)
901 swap_rows(tab
, row
, tab
->n_redundant
);
902 isl_tab_push_var(tab
, isl_tab_undo_redundant
, var
);
906 if (row
!= tab
->n_row
- 1)
907 swap_rows(tab
, row
, tab
->n_row
- 1);
908 isl_tab_var_from_row(tab
, tab
->n_row
- 1)->index
= -1;
914 struct isl_tab
*isl_tab_mark_empty(struct isl_tab
*tab
)
916 if (!tab
->empty
&& tab
->need_undo
)
917 isl_tab_push(tab
, isl_tab_undo_empty
);
922 /* Update the rows signs after a pivot of "row" and "col", with "row_sgn"
923 * the original sign of the pivot element.
924 * We only keep track of row signs during PILP solving and in this case
925 * we only pivot a row with negative sign (meaning the value is always
926 * non-positive) using a positive pivot element.
928 * For each row j, the new value of the parametric constant is equal to
930 * a_j0 - a_jc a_r0/a_rc
932 * where a_j0 is the original parametric constant, a_rc is the pivot element,
933 * a_r0 is the parametric constant of the pivot row and a_jc is the
934 * pivot column entry of the row j.
935 * Since a_r0 is non-positive and a_rc is positive, the sign of row j
936 * remains the same if a_jc has the same sign as the row j or if
937 * a_jc is zero. In all other cases, we reset the sign to "unknown".
939 static void update_row_sign(struct isl_tab
*tab
, int row
, int col
, int row_sgn
)
942 struct isl_mat
*mat
= tab
->mat
;
943 unsigned off
= 2 + tab
->M
;
948 if (tab
->row_sign
[row
] == 0)
950 isl_assert(mat
->ctx
, row_sgn
> 0, return);
951 isl_assert(mat
->ctx
, tab
->row_sign
[row
] == isl_tab_row_neg
, return);
952 tab
->row_sign
[row
] = isl_tab_row_pos
;
953 for (i
= 0; i
< tab
->n_row
; ++i
) {
957 s
= isl_int_sgn(mat
->row
[i
][off
+ col
]);
960 if (!tab
->row_sign
[i
])
962 if (s
< 0 && tab
->row_sign
[i
] == isl_tab_row_neg
)
964 if (s
> 0 && tab
->row_sign
[i
] == isl_tab_row_pos
)
966 tab
->row_sign
[i
] = isl_tab_row_unknown
;
970 /* Given a row number "row" and a column number "col", pivot the tableau
971 * such that the associated variables are interchanged.
972 * The given row in the tableau expresses
974 * x_r = a_r0 + \sum_i a_ri x_i
978 * x_c = 1/a_rc x_r - a_r0/a_rc + sum_{i \ne r} -a_ri/a_rc
980 * Substituting this equality into the other rows
982 * x_j = a_j0 + \sum_i a_ji x_i
984 * with a_jc \ne 0, we obtain
986 * 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
993 * where i is any other column and j is any other row,
994 * is therefore transformed into
996 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
997 * 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)
999 * The transformation is performed along the following steps
1001 * d_r/n_rc n_ri/n_rc
1004 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1007 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1008 * n_jc/(|n_rc| d_j) n_ji/(|n_rc| d_j)
1010 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1011 * n_jc/(|n_rc| d_j) (n_ji |n_rc|)/(|n_rc| d_j)
1013 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1014 * n_jc/(|n_rc| d_j) (n_ji |n_rc| - s(n_rc)n_jc n_ri)/(|n_rc| d_j)
1016 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1017 * 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)
1020 void isl_tab_pivot(struct isl_tab
*tab
, int row
, int col
)
1025 struct isl_mat
*mat
= tab
->mat
;
1026 struct isl_tab_var
*var
;
1027 unsigned off
= 2 + tab
->M
;
1029 isl_int_swap(mat
->row
[row
][0], mat
->row
[row
][off
+ col
]);
1030 sgn
= isl_int_sgn(mat
->row
[row
][0]);
1032 isl_int_neg(mat
->row
[row
][0], mat
->row
[row
][0]);
1033 isl_int_neg(mat
->row
[row
][off
+ col
], mat
->row
[row
][off
+ col
]);
1035 for (j
= 0; j
< off
- 1 + tab
->n_col
; ++j
) {
1036 if (j
== off
- 1 + col
)
1038 isl_int_neg(mat
->row
[row
][1 + j
], mat
->row
[row
][1 + j
]);
1040 if (!isl_int_is_one(mat
->row
[row
][0]))
1041 isl_seq_normalize(mat
->ctx
, mat
->row
[row
], off
+ tab
->n_col
);
1042 for (i
= 0; i
< tab
->n_row
; ++i
) {
1045 if (isl_int_is_zero(mat
->row
[i
][off
+ col
]))
1047 isl_int_mul(mat
->row
[i
][0], mat
->row
[i
][0], mat
->row
[row
][0]);
1048 for (j
= 0; j
< off
- 1 + tab
->n_col
; ++j
) {
1049 if (j
== off
- 1 + col
)
1051 isl_int_mul(mat
->row
[i
][1 + j
],
1052 mat
->row
[i
][1 + j
], mat
->row
[row
][0]);
1053 isl_int_addmul(mat
->row
[i
][1 + j
],
1054 mat
->row
[i
][off
+ col
], mat
->row
[row
][1 + j
]);
1056 isl_int_mul(mat
->row
[i
][off
+ col
],
1057 mat
->row
[i
][off
+ col
], mat
->row
[row
][off
+ col
]);
1058 if (!isl_int_is_one(mat
->row
[i
][0]))
1059 isl_seq_normalize(mat
->ctx
, mat
->row
[i
], off
+ tab
->n_col
);
1061 t
= tab
->row_var
[row
];
1062 tab
->row_var
[row
] = tab
->col_var
[col
];
1063 tab
->col_var
[col
] = t
;
1064 var
= isl_tab_var_from_row(tab
, row
);
1067 var
= var_from_col(tab
, col
);
1070 update_row_sign(tab
, row
, col
, sgn
);
1073 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1074 if (isl_int_is_zero(mat
->row
[i
][off
+ col
]))
1076 if (!isl_tab_var_from_row(tab
, i
)->frozen
&&
1077 isl_tab_row_is_redundant(tab
, i
))
1078 if (isl_tab_mark_redundant(tab
, i
))
1083 /* If "var" represents a column variable, then pivot is up (sgn > 0)
1084 * or down (sgn < 0) to a row. The variable is assumed not to be
1085 * unbounded in the specified direction.
1086 * If sgn = 0, then the variable is unbounded in both directions,
1087 * and we pivot with any row we can find.
1089 static void to_row(struct isl_tab
*tab
, struct isl_tab_var
*var
, int sign
)
1092 unsigned off
= 2 + tab
->M
;
1098 for (r
= tab
->n_redundant
; r
< tab
->n_row
; ++r
)
1099 if (!isl_int_is_zero(tab
->mat
->row
[r
][off
+var
->index
]))
1101 isl_assert(tab
->mat
->ctx
, r
< tab
->n_row
, return);
1103 r
= pivot_row(tab
, NULL
, sign
, var
->index
);
1104 isl_assert(tab
->mat
->ctx
, r
>= 0, return);
1107 isl_tab_pivot(tab
, r
, var
->index
);
1110 static void check_table(struct isl_tab
*tab
)
1116 for (i
= 0; i
< tab
->n_row
; ++i
) {
1117 if (!isl_tab_var_from_row(tab
, i
)->is_nonneg
)
1119 assert(!isl_int_is_neg(tab
->mat
->row
[i
][1]));
1123 /* Return the sign of the maximal value of "var".
1124 * If the sign is not negative, then on return from this function,
1125 * the sample value will also be non-negative.
1127 * If "var" is manifestly unbounded wrt positive values, we are done.
1128 * Otherwise, we pivot the variable up to a row if needed
1129 * Then we continue pivoting down until either
1130 * - no more down pivots can be performed
1131 * - the sample value is positive
1132 * - the variable is pivoted into a manifestly unbounded column
1134 static int sign_of_max(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1138 if (max_is_manifestly_unbounded(tab
, var
))
1140 to_row(tab
, var
, 1);
1141 while (!isl_int_is_pos(tab
->mat
->row
[var
->index
][1])) {
1142 find_pivot(tab
, var
, var
, 1, &row
, &col
);
1144 return isl_int_sgn(tab
->mat
->row
[var
->index
][1]);
1145 isl_tab_pivot(tab
, row
, col
);
1146 if (!var
->is_row
) /* manifestly unbounded */
1152 static int row_is_neg(struct isl_tab
*tab
, int row
)
1155 return isl_int_is_neg(tab
->mat
->row
[row
][1]);
1156 if (isl_int_is_pos(tab
->mat
->row
[row
][2]))
1158 if (isl_int_is_neg(tab
->mat
->row
[row
][2]))
1160 return isl_int_is_neg(tab
->mat
->row
[row
][1]);
1163 static int row_sgn(struct isl_tab
*tab
, int row
)
1166 return isl_int_sgn(tab
->mat
->row
[row
][1]);
1167 if (!isl_int_is_zero(tab
->mat
->row
[row
][2]))
1168 return isl_int_sgn(tab
->mat
->row
[row
][2]);
1170 return isl_int_sgn(tab
->mat
->row
[row
][1]);
1173 /* Perform pivots until the row variable "var" has a non-negative
1174 * sample value or until no more upward pivots can be performed.
1175 * Return the sign of the sample value after the pivots have been
1178 static int restore_row(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1182 while (row_is_neg(tab
, var
->index
)) {
1183 find_pivot(tab
, var
, var
, 1, &row
, &col
);
1186 isl_tab_pivot(tab
, row
, col
);
1187 if (!var
->is_row
) /* manifestly unbounded */
1190 return row_sgn(tab
, var
->index
);
1193 /* Perform pivots until we are sure that the row variable "var"
1194 * can attain non-negative values. After return from this
1195 * function, "var" is still a row variable, but its sample
1196 * value may not be non-negative, even if the function returns 1.
1198 static int at_least_zero(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1202 while (isl_int_is_neg(tab
->mat
->row
[var
->index
][1])) {
1203 find_pivot(tab
, var
, var
, 1, &row
, &col
);
1206 if (row
== var
->index
) /* manifestly unbounded */
1208 isl_tab_pivot(tab
, row
, col
);
1210 return !isl_int_is_neg(tab
->mat
->row
[var
->index
][1]);
1213 /* Return a negative value if "var" can attain negative values.
1214 * Return a non-negative value otherwise.
1216 * If "var" is manifestly unbounded wrt negative values, we are done.
1217 * Otherwise, if var is in a column, we can pivot it down to a row.
1218 * Then we continue pivoting down until either
1219 * - the pivot would result in a manifestly unbounded column
1220 * => we don't perform the pivot, but simply return -1
1221 * - no more down pivots can be performed
1222 * - the sample value is negative
1223 * If the sample value becomes negative and the variable is supposed
1224 * to be nonnegative, then we undo the last pivot.
1225 * However, if the last pivot has made the pivoting variable
1226 * obviously redundant, then it may have moved to another row.
1227 * In that case we look for upward pivots until we reach a non-negative
1230 static int sign_of_min(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1233 struct isl_tab_var
*pivot_var
= NULL
;
1235 if (min_is_manifestly_unbounded(tab
, var
))
1239 row
= pivot_row(tab
, NULL
, -1, col
);
1240 pivot_var
= var_from_col(tab
, col
);
1241 isl_tab_pivot(tab
, row
, col
);
1242 if (var
->is_redundant
)
1244 if (isl_int_is_neg(tab
->mat
->row
[var
->index
][1])) {
1245 if (var
->is_nonneg
) {
1246 if (!pivot_var
->is_redundant
&&
1247 pivot_var
->index
== row
)
1248 isl_tab_pivot(tab
, row
, col
);
1250 restore_row(tab
, var
);
1255 if (var
->is_redundant
)
1257 while (!isl_int_is_neg(tab
->mat
->row
[var
->index
][1])) {
1258 find_pivot(tab
, var
, var
, -1, &row
, &col
);
1259 if (row
== var
->index
)
1262 return isl_int_sgn(tab
->mat
->row
[var
->index
][1]);
1263 pivot_var
= var_from_col(tab
, col
);
1264 isl_tab_pivot(tab
, row
, col
);
1265 if (var
->is_redundant
)
1268 if (pivot_var
&& var
->is_nonneg
) {
1269 /* pivot back to non-negative value */
1270 if (!pivot_var
->is_redundant
&& pivot_var
->index
== row
)
1271 isl_tab_pivot(tab
, row
, col
);
1273 restore_row(tab
, var
);
1278 static int row_at_most_neg_one(struct isl_tab
*tab
, int row
)
1281 if (isl_int_is_pos(tab
->mat
->row
[row
][2]))
1283 if (isl_int_is_neg(tab
->mat
->row
[row
][2]))
1286 return isl_int_is_neg(tab
->mat
->row
[row
][1]) &&
1287 isl_int_abs_ge(tab
->mat
->row
[row
][1],
1288 tab
->mat
->row
[row
][0]);
1291 /* Return 1 if "var" can attain values <= -1.
1292 * Return 0 otherwise.
1294 * The sample value of "var" is assumed to be non-negative when the
1295 * the function is called and will be made non-negative again before
1296 * the function returns.
1298 int isl_tab_min_at_most_neg_one(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1301 struct isl_tab_var
*pivot_var
;
1303 if (min_is_manifestly_unbounded(tab
, var
))
1307 row
= pivot_row(tab
, NULL
, -1, col
);
1308 pivot_var
= var_from_col(tab
, col
);
1309 isl_tab_pivot(tab
, row
, col
);
1310 if (var
->is_redundant
)
1312 if (row_at_most_neg_one(tab
, var
->index
)) {
1313 if (var
->is_nonneg
) {
1314 if (!pivot_var
->is_redundant
&&
1315 pivot_var
->index
== row
)
1316 isl_tab_pivot(tab
, row
, col
);
1318 restore_row(tab
, var
);
1323 if (var
->is_redundant
)
1326 find_pivot(tab
, var
, var
, -1, &row
, &col
);
1327 if (row
== var
->index
)
1331 pivot_var
= var_from_col(tab
, col
);
1332 isl_tab_pivot(tab
, row
, col
);
1333 if (var
->is_redundant
)
1335 } while (!row_at_most_neg_one(tab
, var
->index
));
1336 if (var
->is_nonneg
) {
1337 /* pivot back to non-negative value */
1338 if (!pivot_var
->is_redundant
&& pivot_var
->index
== row
)
1339 isl_tab_pivot(tab
, row
, col
);
1340 restore_row(tab
, var
);
1345 /* Return 1 if "var" can attain values >= 1.
1346 * Return 0 otherwise.
1348 static int at_least_one(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1353 if (max_is_manifestly_unbounded(tab
, var
))
1355 to_row(tab
, var
, 1);
1356 r
= tab
->mat
->row
[var
->index
];
1357 while (isl_int_lt(r
[1], r
[0])) {
1358 find_pivot(tab
, var
, var
, 1, &row
, &col
);
1360 return isl_int_ge(r
[1], r
[0]);
1361 if (row
== var
->index
) /* manifestly unbounded */
1363 isl_tab_pivot(tab
, row
, col
);
1368 static void swap_cols(struct isl_tab
*tab
, int col1
, int col2
)
1371 unsigned off
= 2 + tab
->M
;
1372 t
= tab
->col_var
[col1
];
1373 tab
->col_var
[col1
] = tab
->col_var
[col2
];
1374 tab
->col_var
[col2
] = t
;
1375 var_from_col(tab
, col1
)->index
= col1
;
1376 var_from_col(tab
, col2
)->index
= col2
;
1377 tab
->mat
= isl_mat_swap_cols(tab
->mat
, off
+ col1
, off
+ col2
);
1380 /* Mark column with index "col" as representing a zero variable.
1381 * If we may need to undo the operation the column is kept,
1382 * but no longer considered.
1383 * Otherwise, the column is simply removed.
1385 * The column may be interchanged with some other column. If it
1386 * is interchanged with a later column, return 1. Otherwise return 0.
1387 * If the columns are checked in order in the calling function,
1388 * then a return value of 1 means that the column with the given
1389 * column number may now contain a different column that
1390 * hasn't been checked yet.
1392 int isl_tab_kill_col(struct isl_tab
*tab
, int col
)
1394 var_from_col(tab
, col
)->is_zero
= 1;
1395 if (tab
->need_undo
) {
1396 isl_tab_push_var(tab
, isl_tab_undo_zero
, var_from_col(tab
, col
));
1397 if (col
!= tab
->n_dead
)
1398 swap_cols(tab
, col
, tab
->n_dead
);
1402 if (col
!= tab
->n_col
- 1)
1403 swap_cols(tab
, col
, tab
->n_col
- 1);
1404 var_from_col(tab
, tab
->n_col
- 1)->index
= -1;
1410 /* Row variable "var" is non-negative and cannot attain any values
1411 * larger than zero. This means that the coefficients of the unrestricted
1412 * column variables are zero and that the coefficients of the non-negative
1413 * column variables are zero or negative.
1414 * Each of the non-negative variables with a negative coefficient can
1415 * then also be written as the negative sum of non-negative variables
1416 * and must therefore also be zero.
1418 static void close_row(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1421 struct isl_mat
*mat
= tab
->mat
;
1422 unsigned off
= 2 + tab
->M
;
1424 isl_assert(tab
->mat
->ctx
, var
->is_nonneg
, return);
1427 isl_tab_push_var(tab
, isl_tab_undo_zero
, var
);
1428 for (j
= tab
->n_dead
; j
< tab
->n_col
; ++j
) {
1429 if (isl_int_is_zero(mat
->row
[var
->index
][off
+ j
]))
1431 isl_assert(tab
->mat
->ctx
,
1432 isl_int_is_neg(mat
->row
[var
->index
][off
+ j
]), return);
1433 if (isl_tab_kill_col(tab
, j
))
1436 isl_tab_mark_redundant(tab
, var
->index
);
1439 /* Add a constraint to the tableau and allocate a row for it.
1440 * Return the index into the constraint array "con".
1442 int isl_tab_allocate_con(struct isl_tab
*tab
)
1446 isl_assert(tab
->mat
->ctx
, tab
->n_row
< tab
->mat
->n_row
, return -1);
1447 isl_assert(tab
->mat
->ctx
, tab
->n_con
< tab
->max_con
, return -1);
1450 tab
->con
[r
].index
= tab
->n_row
;
1451 tab
->con
[r
].is_row
= 1;
1452 tab
->con
[r
].is_nonneg
= 0;
1453 tab
->con
[r
].is_zero
= 0;
1454 tab
->con
[r
].is_redundant
= 0;
1455 tab
->con
[r
].frozen
= 0;
1456 tab
->con
[r
].negated
= 0;
1457 tab
->row_var
[tab
->n_row
] = ~r
;
1461 isl_tab_push_var(tab
, isl_tab_undo_allocate
, &tab
->con
[r
]);
1466 /* Add a variable to the tableau and allocate a column for it.
1467 * Return the index into the variable array "var".
1469 int isl_tab_allocate_var(struct isl_tab
*tab
)
1473 unsigned off
= 2 + tab
->M
;
1475 isl_assert(tab
->mat
->ctx
, tab
->n_col
< tab
->mat
->n_col
, return -1);
1476 isl_assert(tab
->mat
->ctx
, tab
->n_var
< tab
->max_var
, return -1);
1479 tab
->var
[r
].index
= tab
->n_col
;
1480 tab
->var
[r
].is_row
= 0;
1481 tab
->var
[r
].is_nonneg
= 0;
1482 tab
->var
[r
].is_zero
= 0;
1483 tab
->var
[r
].is_redundant
= 0;
1484 tab
->var
[r
].frozen
= 0;
1485 tab
->var
[r
].negated
= 0;
1486 tab
->col_var
[tab
->n_col
] = r
;
1488 for (i
= 0; i
< tab
->n_row
; ++i
)
1489 isl_int_set_si(tab
->mat
->row
[i
][off
+ tab
->n_col
], 0);
1493 isl_tab_push_var(tab
, isl_tab_undo_allocate
, &tab
->var
[r
]);
1498 /* Add a row to the tableau. The row is given as an affine combination
1499 * of the original variables and needs to be expressed in terms of the
1502 * We add each term in turn.
1503 * If r = n/d_r is the current sum and we need to add k x, then
1504 * if x is a column variable, we increase the numerator of
1505 * this column by k d_r
1506 * if x = f/d_x is a row variable, then the new representation of r is
1508 * n k f d_x/g n + d_r/g k f m/d_r n + m/d_g k f
1509 * --- + --- = ------------------- = -------------------
1510 * d_r d_r d_r d_x/g m
1512 * with g the gcd of d_r and d_x and m the lcm of d_r and d_x.
1514 int isl_tab_add_row(struct isl_tab
*tab
, isl_int
*line
)
1520 unsigned off
= 2 + tab
->M
;
1522 r
= isl_tab_allocate_con(tab
);
1528 row
= tab
->mat
->row
[tab
->con
[r
].index
];
1529 isl_int_set_si(row
[0], 1);
1530 isl_int_set(row
[1], line
[0]);
1531 isl_seq_clr(row
+ 2, tab
->M
+ tab
->n_col
);
1532 for (i
= 0; i
< tab
->n_var
; ++i
) {
1533 if (tab
->var
[i
].is_zero
)
1535 if (tab
->var
[i
].is_row
) {
1537 row
[0], tab
->mat
->row
[tab
->var
[i
].index
][0]);
1538 isl_int_swap(a
, row
[0]);
1539 isl_int_divexact(a
, row
[0], a
);
1541 row
[0], tab
->mat
->row
[tab
->var
[i
].index
][0]);
1542 isl_int_mul(b
, b
, line
[1 + i
]);
1543 isl_seq_combine(row
+ 1, a
, row
+ 1,
1544 b
, tab
->mat
->row
[tab
->var
[i
].index
] + 1,
1545 1 + tab
->M
+ tab
->n_col
);
1547 isl_int_addmul(row
[off
+ tab
->var
[i
].index
],
1548 line
[1 + i
], row
[0]);
1549 if (tab
->M
&& i
>= tab
->n_param
&& i
< tab
->n_var
- tab
->n_div
)
1550 isl_int_submul(row
[2], line
[1 + i
], row
[0]);
1552 isl_seq_normalize(tab
->mat
->ctx
, row
, off
+ tab
->n_col
);
1557 tab
->row_sign
[tab
->con
[r
].index
] = 0;
1562 static int drop_row(struct isl_tab
*tab
, int row
)
1564 isl_assert(tab
->mat
->ctx
, ~tab
->row_var
[row
] == tab
->n_con
- 1, return -1);
1565 if (row
!= tab
->n_row
- 1)
1566 swap_rows(tab
, row
, tab
->n_row
- 1);
1572 static int drop_col(struct isl_tab
*tab
, int col
)
1574 isl_assert(tab
->mat
->ctx
, tab
->col_var
[col
] == tab
->n_var
- 1, return -1);
1575 if (col
!= tab
->n_col
- 1)
1576 swap_cols(tab
, col
, tab
->n_col
- 1);
1582 /* Add inequality "ineq" and check if it conflicts with the
1583 * previously added constraints or if it is obviously redundant.
1585 struct isl_tab
*isl_tab_add_ineq(struct isl_tab
*tab
, isl_int
*ineq
)
1593 struct isl_basic_set
*bset
= tab
->bset
;
1595 isl_assert(tab
->mat
->ctx
, tab
->n_eq
== bset
->n_eq
, goto error
);
1596 isl_assert(tab
->mat
->ctx
,
1597 tab
->n_con
== bset
->n_eq
+ bset
->n_ineq
, goto error
);
1598 tab
->bset
= isl_basic_set_add_ineq(tab
->bset
, ineq
);
1599 isl_tab_push(tab
, isl_tab_undo_bset_ineq
);
1603 r
= isl_tab_add_row(tab
, ineq
);
1606 tab
->con
[r
].is_nonneg
= 1;
1607 isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]);
1608 if (isl_tab_row_is_redundant(tab
, tab
->con
[r
].index
)) {
1609 isl_tab_mark_redundant(tab
, tab
->con
[r
].index
);
1613 sgn
= restore_row(tab
, &tab
->con
[r
]);
1615 return isl_tab_mark_empty(tab
);
1616 if (tab
->con
[r
].is_row
&& isl_tab_row_is_redundant(tab
, tab
->con
[r
].index
))
1617 isl_tab_mark_redundant(tab
, tab
->con
[r
].index
);
1624 /* Pivot a non-negative variable down until it reaches the value zero
1625 * and then pivot the variable into a column position.
1627 static int to_col(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1631 unsigned off
= 2 + tab
->M
;
1636 while (isl_int_is_pos(tab
->mat
->row
[var
->index
][1])) {
1637 find_pivot(tab
, var
, NULL
, -1, &row
, &col
);
1638 isl_assert(tab
->mat
->ctx
, row
!= -1, return -1);
1639 isl_tab_pivot(tab
, row
, col
);
1644 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
)
1645 if (!isl_int_is_zero(tab
->mat
->row
[var
->index
][off
+ i
]))
1648 isl_assert(tab
->mat
->ctx
, i
< tab
->n_col
, return -1);
1649 isl_tab_pivot(tab
, var
->index
, i
);
1654 /* We assume Gaussian elimination has been performed on the equalities.
1655 * The equalities can therefore never conflict.
1656 * Adding the equalities is currently only really useful for a later call
1657 * to isl_tab_ineq_type.
1659 static struct isl_tab
*add_eq(struct isl_tab
*tab
, isl_int
*eq
)
1666 r
= isl_tab_add_row(tab
, eq
);
1670 r
= tab
->con
[r
].index
;
1671 i
= isl_seq_first_non_zero(tab
->mat
->row
[r
] + 2 + tab
->M
+ tab
->n_dead
,
1672 tab
->n_col
- tab
->n_dead
);
1673 isl_assert(tab
->mat
->ctx
, i
>= 0, goto error
);
1675 isl_tab_pivot(tab
, r
, i
);
1676 isl_tab_kill_col(tab
, i
);
1685 static int row_is_manifestly_zero(struct isl_tab
*tab
, int row
)
1687 unsigned off
= 2 + tab
->M
;
1689 if (!isl_int_is_zero(tab
->mat
->row
[row
][1]))
1691 if (tab
->M
&& !isl_int_is_zero(tab
->mat
->row
[row
][2]))
1693 return isl_seq_first_non_zero(tab
->mat
->row
[row
] + off
+ tab
->n_dead
,
1694 tab
->n_col
- tab
->n_dead
) == -1;
1697 /* Add an equality that is known to be valid for the given tableau.
1699 struct isl_tab
*isl_tab_add_valid_eq(struct isl_tab
*tab
, isl_int
*eq
)
1701 struct isl_tab_var
*var
;
1706 r
= isl_tab_add_row(tab
, eq
);
1712 if (row_is_manifestly_zero(tab
, r
)) {
1714 isl_tab_mark_redundant(tab
, r
);
1718 if (isl_int_is_neg(tab
->mat
->row
[r
][1])) {
1719 isl_seq_neg(tab
->mat
->row
[r
] + 1, tab
->mat
->row
[r
] + 1,
1724 if (to_col(tab
, var
) < 0)
1727 isl_tab_kill_col(tab
, var
->index
);
1735 static int add_zero_row(struct isl_tab
*tab
)
1740 r
= isl_tab_allocate_con(tab
);
1744 row
= tab
->mat
->row
[tab
->con
[r
].index
];
1745 isl_seq_clr(row
+ 1, 1 + tab
->M
+ tab
->n_col
);
1746 isl_int_set_si(row
[0], 1);
1751 /* Add equality "eq" and check if it conflicts with the
1752 * previously added constraints or if it is obviously redundant.
1754 struct isl_tab
*isl_tab_add_eq(struct isl_tab
*tab
, isl_int
*eq
)
1756 struct isl_tab_undo
*snap
= NULL
;
1757 struct isl_tab_var
*var
;
1764 isl_assert(tab
->mat
->ctx
, !tab
->M
, goto error
);
1767 snap
= isl_tab_snap(tab
);
1769 r
= isl_tab_add_row(tab
, eq
);
1775 if (row_is_manifestly_zero(tab
, row
)) {
1777 if (isl_tab_rollback(tab
, snap
) < 0)
1785 tab
->bset
= isl_basic_set_add_ineq(tab
->bset
, eq
);
1786 isl_tab_push(tab
, isl_tab_undo_bset_ineq
);
1787 isl_seq_neg(eq
, eq
, 1 + tab
->n_var
);
1788 tab
->bset
= isl_basic_set_add_ineq(tab
->bset
, eq
);
1789 isl_seq_neg(eq
, eq
, 1 + tab
->n_var
);
1790 isl_tab_push(tab
, isl_tab_undo_bset_ineq
);
1793 if (add_zero_row(tab
) < 0)
1797 sgn
= isl_int_sgn(tab
->mat
->row
[row
][1]);
1800 isl_seq_neg(tab
->mat
->row
[row
] + 1, tab
->mat
->row
[row
] + 1,
1806 if (sgn
< 0 && sign_of_max(tab
, var
) < 0)
1807 return isl_tab_mark_empty(tab
);
1810 if (to_col(tab
, var
) < 0)
1813 isl_tab_kill_col(tab
, var
->index
);
1821 struct isl_tab
*isl_tab_from_basic_map(struct isl_basic_map
*bmap
)
1824 struct isl_tab
*tab
;
1828 tab
= isl_tab_alloc(bmap
->ctx
,
1829 isl_basic_map_total_dim(bmap
) + bmap
->n_ineq
+ 1,
1830 isl_basic_map_total_dim(bmap
), 0);
1833 tab
->rational
= ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
);
1834 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
1835 return isl_tab_mark_empty(tab
);
1836 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
1837 tab
= add_eq(tab
, bmap
->eq
[i
]);
1841 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
1842 tab
= isl_tab_add_ineq(tab
, bmap
->ineq
[i
]);
1843 if (!tab
|| tab
->empty
)
1849 struct isl_tab
*isl_tab_from_basic_set(struct isl_basic_set
*bset
)
1851 return isl_tab_from_basic_map((struct isl_basic_map
*)bset
);
1854 /* Construct a tableau corresponding to the recession cone of "bset".
1856 struct isl_tab
*isl_tab_from_recession_cone(struct isl_basic_set
*bset
)
1860 struct isl_tab
*tab
;
1864 tab
= isl_tab_alloc(bset
->ctx
, bset
->n_eq
+ bset
->n_ineq
,
1865 isl_basic_set_total_dim(bset
), 0);
1868 tab
->rational
= ISL_F_ISSET(bset
, ISL_BASIC_SET_RATIONAL
);
1871 for (i
= 0; i
< bset
->n_eq
; ++i
) {
1872 isl_int_swap(bset
->eq
[i
][0], cst
);
1873 tab
= add_eq(tab
, bset
->eq
[i
]);
1874 isl_int_swap(bset
->eq
[i
][0], cst
);
1878 for (i
= 0; i
< bset
->n_ineq
; ++i
) {
1880 isl_int_swap(bset
->ineq
[i
][0], cst
);
1881 r
= isl_tab_add_row(tab
, bset
->ineq
[i
]);
1882 isl_int_swap(bset
->ineq
[i
][0], cst
);
1885 tab
->con
[r
].is_nonneg
= 1;
1886 isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]);
1897 /* Assuming "tab" is the tableau of a cone, check if the cone is
1898 * bounded, i.e., if it is empty or only contains the origin.
1900 int isl_tab_cone_is_bounded(struct isl_tab
*tab
)
1908 if (tab
->n_dead
== tab
->n_col
)
1912 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1913 struct isl_tab_var
*var
;
1914 var
= isl_tab_var_from_row(tab
, i
);
1915 if (!var
->is_nonneg
)
1917 if (sign_of_max(tab
, var
) != 0)
1919 close_row(tab
, var
);
1922 if (tab
->n_dead
== tab
->n_col
)
1924 if (i
== tab
->n_row
)
1929 int isl_tab_sample_is_integer(struct isl_tab
*tab
)
1936 for (i
= 0; i
< tab
->n_var
; ++i
) {
1938 if (!tab
->var
[i
].is_row
)
1940 row
= tab
->var
[i
].index
;
1941 if (!isl_int_is_divisible_by(tab
->mat
->row
[row
][1],
1942 tab
->mat
->row
[row
][0]))
1948 static struct isl_vec
*extract_integer_sample(struct isl_tab
*tab
)
1951 struct isl_vec
*vec
;
1953 vec
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_var
);
1957 isl_int_set_si(vec
->block
.data
[0], 1);
1958 for (i
= 0; i
< tab
->n_var
; ++i
) {
1959 if (!tab
->var
[i
].is_row
)
1960 isl_int_set_si(vec
->block
.data
[1 + i
], 0);
1962 int row
= tab
->var
[i
].index
;
1963 isl_int_divexact(vec
->block
.data
[1 + i
],
1964 tab
->mat
->row
[row
][1], tab
->mat
->row
[row
][0]);
1971 struct isl_vec
*isl_tab_get_sample_value(struct isl_tab
*tab
)
1974 struct isl_vec
*vec
;
1980 vec
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_var
);
1986 isl_int_set_si(vec
->block
.data
[0], 1);
1987 for (i
= 0; i
< tab
->n_var
; ++i
) {
1989 if (!tab
->var
[i
].is_row
) {
1990 isl_int_set_si(vec
->block
.data
[1 + i
], 0);
1993 row
= tab
->var
[i
].index
;
1994 isl_int_gcd(m
, vec
->block
.data
[0], tab
->mat
->row
[row
][0]);
1995 isl_int_divexact(m
, tab
->mat
->row
[row
][0], m
);
1996 isl_seq_scale(vec
->block
.data
, vec
->block
.data
, m
, 1 + i
);
1997 isl_int_divexact(m
, vec
->block
.data
[0], tab
->mat
->row
[row
][0]);
1998 isl_int_mul(vec
->block
.data
[1 + i
], m
, tab
->mat
->row
[row
][1]);
2000 vec
= isl_vec_normalize(vec
);
2006 /* Update "bmap" based on the results of the tableau "tab".
2007 * In particular, implicit equalities are made explicit, redundant constraints
2008 * are removed and if the sample value happens to be integer, it is stored
2009 * in "bmap" (unless "bmap" already had an integer sample).
2011 * The tableau is assumed to have been created from "bmap" using
2012 * isl_tab_from_basic_map.
2014 struct isl_basic_map
*isl_basic_map_update_from_tab(struct isl_basic_map
*bmap
,
2015 struct isl_tab
*tab
)
2027 bmap
= isl_basic_map_set_to_empty(bmap
);
2029 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
) {
2030 if (isl_tab_is_equality(tab
, n_eq
+ i
))
2031 isl_basic_map_inequality_to_equality(bmap
, i
);
2032 else if (isl_tab_is_redundant(tab
, n_eq
+ i
))
2033 isl_basic_map_drop_inequality(bmap
, i
);
2035 if (!tab
->rational
&&
2036 !bmap
->sample
&& isl_tab_sample_is_integer(tab
))
2037 bmap
->sample
= extract_integer_sample(tab
);
2041 struct isl_basic_set
*isl_basic_set_update_from_tab(struct isl_basic_set
*bset
,
2042 struct isl_tab
*tab
)
2044 return (struct isl_basic_set
*)isl_basic_map_update_from_tab(
2045 (struct isl_basic_map
*)bset
, tab
);
2048 /* Given a non-negative variable "var", add a new non-negative variable
2049 * that is the opposite of "var", ensuring that var can only attain the
2051 * If var = n/d is a row variable, then the new variable = -n/d.
2052 * If var is a column variables, then the new variable = -var.
2053 * If the new variable cannot attain non-negative values, then
2054 * the resulting tableau is empty.
2055 * Otherwise, we know the value will be zero and we close the row.
2057 static struct isl_tab
*cut_to_hyperplane(struct isl_tab
*tab
,
2058 struct isl_tab_var
*var
)
2063 unsigned off
= 2 + tab
->M
;
2067 isl_assert(tab
->mat
->ctx
, !var
->is_redundant
, goto error
);
2069 if (isl_tab_extend_cons(tab
, 1) < 0)
2073 tab
->con
[r
].index
= tab
->n_row
;
2074 tab
->con
[r
].is_row
= 1;
2075 tab
->con
[r
].is_nonneg
= 0;
2076 tab
->con
[r
].is_zero
= 0;
2077 tab
->con
[r
].is_redundant
= 0;
2078 tab
->con
[r
].frozen
= 0;
2079 tab
->con
[r
].negated
= 0;
2080 tab
->row_var
[tab
->n_row
] = ~r
;
2081 row
= tab
->mat
->row
[tab
->n_row
];
2084 isl_int_set(row
[0], tab
->mat
->row
[var
->index
][0]);
2085 isl_seq_neg(row
+ 1,
2086 tab
->mat
->row
[var
->index
] + 1, 1 + tab
->n_col
);
2088 isl_int_set_si(row
[0], 1);
2089 isl_seq_clr(row
+ 1, 1 + tab
->n_col
);
2090 isl_int_set_si(row
[off
+ var
->index
], -1);
2095 isl_tab_push_var(tab
, isl_tab_undo_allocate
, &tab
->con
[r
]);
2097 sgn
= sign_of_max(tab
, &tab
->con
[r
]);
2099 return isl_tab_mark_empty(tab
);
2100 tab
->con
[r
].is_nonneg
= 1;
2101 isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]);
2103 close_row(tab
, &tab
->con
[r
]);
2111 /* Given a tableau "tab" and an inequality constraint "con" of the tableau,
2112 * relax the inequality by one. That is, the inequality r >= 0 is replaced
2113 * by r' = r + 1 >= 0.
2114 * If r is a row variable, we simply increase the constant term by one
2115 * (taking into account the denominator).
2116 * If r is a column variable, then we need to modify each row that
2117 * refers to r = r' - 1 by substituting this equality, effectively
2118 * subtracting the coefficient of the column from the constant.
2120 struct isl_tab
*isl_tab_relax(struct isl_tab
*tab
, int con
)
2122 struct isl_tab_var
*var
;
2123 unsigned off
= 2 + tab
->M
;
2128 var
= &tab
->con
[con
];
2130 if (!var
->is_row
&& !max_is_manifestly_unbounded(tab
, var
))
2131 to_row(tab
, var
, 1);
2134 isl_int_add(tab
->mat
->row
[var
->index
][1],
2135 tab
->mat
->row
[var
->index
][1], tab
->mat
->row
[var
->index
][0]);
2139 for (i
= 0; i
< tab
->n_row
; ++i
) {
2140 if (isl_int_is_zero(tab
->mat
->row
[i
][off
+ var
->index
]))
2142 isl_int_sub(tab
->mat
->row
[i
][1], tab
->mat
->row
[i
][1],
2143 tab
->mat
->row
[i
][off
+ var
->index
]);
2148 isl_tab_push_var(tab
, isl_tab_undo_relax
, var
);
2153 struct isl_tab
*isl_tab_select_facet(struct isl_tab
*tab
, int con
)
2158 return cut_to_hyperplane(tab
, &tab
->con
[con
]);
2161 static int may_be_equality(struct isl_tab
*tab
, int row
)
2163 unsigned off
= 2 + tab
->M
;
2164 return (tab
->rational
? isl_int_is_zero(tab
->mat
->row
[row
][1])
2165 : isl_int_lt(tab
->mat
->row
[row
][1],
2166 tab
->mat
->row
[row
][0])) &&
2167 isl_seq_first_non_zero(tab
->mat
->row
[row
] + off
+ tab
->n_dead
,
2168 tab
->n_col
- tab
->n_dead
) != -1;
2171 /* Check for (near) equalities among the constraints.
2172 * A constraint is an equality if it is non-negative and if
2173 * its maximal value is either
2174 * - zero (in case of rational tableaus), or
2175 * - strictly less than 1 (in case of integer tableaus)
2177 * We first mark all non-redundant and non-dead variables that
2178 * are not frozen and not obviously not an equality.
2179 * Then we iterate over all marked variables if they can attain
2180 * any values larger than zero or at least one.
2181 * If the maximal value is zero, we mark any column variables
2182 * that appear in the row as being zero and mark the row as being redundant.
2183 * Otherwise, if the maximal value is strictly less than one (and the
2184 * tableau is integer), then we restrict the value to being zero
2185 * by adding an opposite non-negative variable.
2187 struct isl_tab
*isl_tab_detect_implicit_equalities(struct isl_tab
*tab
)
2196 if (tab
->n_dead
== tab
->n_col
)
2200 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
2201 struct isl_tab_var
*var
= isl_tab_var_from_row(tab
, i
);
2202 var
->marked
= !var
->frozen
&& var
->is_nonneg
&&
2203 may_be_equality(tab
, i
);
2207 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
2208 struct isl_tab_var
*var
= var_from_col(tab
, i
);
2209 var
->marked
= !var
->frozen
&& var
->is_nonneg
;
2214 struct isl_tab_var
*var
;
2215 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
2216 var
= isl_tab_var_from_row(tab
, i
);
2220 if (i
== tab
->n_row
) {
2221 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
2222 var
= var_from_col(tab
, i
);
2226 if (i
== tab
->n_col
)
2231 if (sign_of_max(tab
, var
) == 0)
2232 close_row(tab
, var
);
2233 else if (!tab
->rational
&& !at_least_one(tab
, var
)) {
2234 tab
= cut_to_hyperplane(tab
, var
);
2235 return isl_tab_detect_implicit_equalities(tab
);
2237 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
2238 var
= isl_tab_var_from_row(tab
, i
);
2241 if (may_be_equality(tab
, i
))
2251 /* Check for (near) redundant constraints.
2252 * A constraint is redundant if it is non-negative and if
2253 * its minimal value (temporarily ignoring the non-negativity) is either
2254 * - zero (in case of rational tableaus), or
2255 * - strictly larger than -1 (in case of integer tableaus)
2257 * We first mark all non-redundant and non-dead variables that
2258 * are not frozen and not obviously negatively unbounded.
2259 * Then we iterate over all marked variables if they can attain
2260 * any values smaller than zero or at most negative one.
2261 * If not, we mark the row as being redundant (assuming it hasn't
2262 * been detected as being obviously redundant in the mean time).
2264 struct isl_tab
*isl_tab_detect_redundant(struct isl_tab
*tab
)
2273 if (tab
->n_redundant
== tab
->n_row
)
2277 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
2278 struct isl_tab_var
*var
= isl_tab_var_from_row(tab
, i
);
2279 var
->marked
= !var
->frozen
&& var
->is_nonneg
;
2283 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
2284 struct isl_tab_var
*var
= var_from_col(tab
, i
);
2285 var
->marked
= !var
->frozen
&& var
->is_nonneg
&&
2286 !min_is_manifestly_unbounded(tab
, var
);
2291 struct isl_tab_var
*var
;
2292 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
2293 var
= isl_tab_var_from_row(tab
, i
);
2297 if (i
== tab
->n_row
) {
2298 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
2299 var
= var_from_col(tab
, i
);
2303 if (i
== tab
->n_col
)
2308 if ((tab
->rational
? (sign_of_min(tab
, var
) >= 0)
2309 : !isl_tab_min_at_most_neg_one(tab
, var
)) &&
2311 isl_tab_mark_redundant(tab
, var
->index
);
2312 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
2313 var
= var_from_col(tab
, i
);
2316 if (!min_is_manifestly_unbounded(tab
, var
))
2326 int isl_tab_is_equality(struct isl_tab
*tab
, int con
)
2333 if (tab
->con
[con
].is_zero
)
2335 if (tab
->con
[con
].is_redundant
)
2337 if (!tab
->con
[con
].is_row
)
2338 return tab
->con
[con
].index
< tab
->n_dead
;
2340 row
= tab
->con
[con
].index
;
2343 return isl_int_is_zero(tab
->mat
->row
[row
][1]) &&
2344 isl_seq_first_non_zero(tab
->mat
->row
[row
] + 2 + tab
->n_dead
,
2345 tab
->n_col
- tab
->n_dead
) == -1;
2348 /* Return the minimial value of the affine expression "f" with denominator
2349 * "denom" in *opt, *opt_denom, assuming the tableau is not empty and
2350 * the expression cannot attain arbitrarily small values.
2351 * If opt_denom is NULL, then *opt is rounded up to the nearest integer.
2352 * The return value reflects the nature of the result (empty, unbounded,
2353 * minmimal value returned in *opt).
2355 enum isl_lp_result
isl_tab_min(struct isl_tab
*tab
,
2356 isl_int
*f
, isl_int denom
, isl_int
*opt
, isl_int
*opt_denom
,
2360 enum isl_lp_result res
= isl_lp_ok
;
2361 struct isl_tab_var
*var
;
2362 struct isl_tab_undo
*snap
;
2365 return isl_lp_empty
;
2367 snap
= isl_tab_snap(tab
);
2368 r
= isl_tab_add_row(tab
, f
);
2370 return isl_lp_error
;
2372 isl_int_mul(tab
->mat
->row
[var
->index
][0],
2373 tab
->mat
->row
[var
->index
][0], denom
);
2376 find_pivot(tab
, var
, var
, -1, &row
, &col
);
2377 if (row
== var
->index
) {
2378 res
= isl_lp_unbounded
;
2383 isl_tab_pivot(tab
, row
, col
);
2385 if (ISL_FL_ISSET(flags
, ISL_TAB_SAVE_DUAL
)) {
2388 isl_vec_free(tab
->dual
);
2389 tab
->dual
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_con
);
2391 return isl_lp_error
;
2392 isl_int_set(tab
->dual
->el
[0], tab
->mat
->row
[var
->index
][0]);
2393 for (i
= 0; i
< tab
->n_con
; ++i
) {
2395 if (tab
->con
[i
].is_row
) {
2396 isl_int_set_si(tab
->dual
->el
[1 + i
], 0);
2399 pos
= 2 + tab
->M
+ tab
->con
[i
].index
;
2400 if (tab
->con
[i
].negated
)
2401 isl_int_neg(tab
->dual
->el
[1 + i
],
2402 tab
->mat
->row
[var
->index
][pos
]);
2404 isl_int_set(tab
->dual
->el
[1 + i
],
2405 tab
->mat
->row
[var
->index
][pos
]);
2408 if (opt
&& res
== isl_lp_ok
) {
2410 isl_int_set(*opt
, tab
->mat
->row
[var
->index
][1]);
2411 isl_int_set(*opt_denom
, tab
->mat
->row
[var
->index
][0]);
2413 isl_int_cdiv_q(*opt
, tab
->mat
->row
[var
->index
][1],
2414 tab
->mat
->row
[var
->index
][0]);
2416 if (isl_tab_rollback(tab
, snap
) < 0)
2417 return isl_lp_error
;
2421 int isl_tab_is_redundant(struct isl_tab
*tab
, int con
)
2425 if (tab
->con
[con
].is_zero
)
2427 if (tab
->con
[con
].is_redundant
)
2429 return tab
->con
[con
].is_row
&& tab
->con
[con
].index
< tab
->n_redundant
;
2432 /* Take a snapshot of the tableau that can be restored by s call to
2435 struct isl_tab_undo
*isl_tab_snap(struct isl_tab
*tab
)
2443 /* Undo the operation performed by isl_tab_relax.
2445 static void unrelax(struct isl_tab
*tab
, struct isl_tab_var
*var
)
2447 unsigned off
= 2 + tab
->M
;
2449 if (!var
->is_row
&& !max_is_manifestly_unbounded(tab
, var
))
2450 to_row(tab
, var
, 1);
2453 isl_int_sub(tab
->mat
->row
[var
->index
][1],
2454 tab
->mat
->row
[var
->index
][1], tab
->mat
->row
[var
->index
][0]);
2458 for (i
= 0; i
< tab
->n_row
; ++i
) {
2459 if (isl_int_is_zero(tab
->mat
->row
[i
][off
+ var
->index
]))
2461 isl_int_add(tab
->mat
->row
[i
][1], tab
->mat
->row
[i
][1],
2462 tab
->mat
->row
[i
][off
+ var
->index
]);
2468 static void perform_undo_var(struct isl_tab
*tab
, struct isl_tab_undo
*undo
)
2470 struct isl_tab_var
*var
= var_from_index(tab
, undo
->u
.var_index
);
2471 switch(undo
->type
) {
2472 case isl_tab_undo_nonneg
:
2475 case isl_tab_undo_redundant
:
2476 var
->is_redundant
= 0;
2479 case isl_tab_undo_zero
:
2484 case isl_tab_undo_allocate
:
2485 if (undo
->u
.var_index
>= 0) {
2486 isl_assert(tab
->mat
->ctx
, !var
->is_row
, return);
2487 drop_col(tab
, var
->index
);
2491 if (!max_is_manifestly_unbounded(tab
, var
))
2492 to_row(tab
, var
, 1);
2493 else if (!min_is_manifestly_unbounded(tab
, var
))
2494 to_row(tab
, var
, -1);
2496 to_row(tab
, var
, 0);
2498 drop_row(tab
, var
->index
);
2500 case isl_tab_undo_relax
:
2506 /* Restore the tableau to the state where the basic variables
2507 * are those in "col_var".
2508 * We first construct a list of variables that are currently in
2509 * the basis, but shouldn't. Then we iterate over all variables
2510 * that should be in the basis and for each one that is currently
2511 * not in the basis, we exchange it with one of the elements of the
2512 * list constructed before.
2513 * We can always find an appropriate variable to pivot with because
2514 * the current basis is mapped to the old basis by a non-singular
2515 * matrix and so we can never end up with a zero row.
2517 static int restore_basis(struct isl_tab
*tab
, int *col_var
)
2521 int *extra
= NULL
; /* current columns that contain bad stuff */
2522 unsigned off
= 2 + tab
->M
;
2524 extra
= isl_alloc_array(tab
->mat
->ctx
, int, tab
->n_col
);
2527 for (i
= 0; i
< tab
->n_col
; ++i
) {
2528 for (j
= 0; j
< tab
->n_col
; ++j
)
2529 if (tab
->col_var
[i
] == col_var
[j
])
2533 extra
[n_extra
++] = i
;
2535 for (i
= 0; i
< tab
->n_col
&& n_extra
> 0; ++i
) {
2536 struct isl_tab_var
*var
;
2539 for (j
= 0; j
< tab
->n_col
; ++j
)
2540 if (col_var
[i
] == tab
->col_var
[j
])
2544 var
= var_from_index(tab
, col_var
[i
]);
2546 for (j
= 0; j
< n_extra
; ++j
)
2547 if (!isl_int_is_zero(tab
->mat
->row
[row
][off
+extra
[j
]]))
2549 isl_assert(tab
->mat
->ctx
, j
< n_extra
, goto error
);
2550 isl_tab_pivot(tab
, row
, extra
[j
]);
2551 extra
[j
] = extra
[--n_extra
];
2563 /* Remove all samples with index n or greater, i.e., those samples
2564 * that were added since we saved this number of samples in
2565 * isl_tab_save_samples.
2567 static int drop_samples_since(struct isl_tab
*tab
, int n
)
2571 for (i
= tab
->n_sample
- 1; i
>= 0 && tab
->n_sample
> n
; --i
) {
2572 if (tab
->sample_index
[i
] < n
)
2575 if (i
!= tab
->n_sample
- 1) {
2576 int t
= tab
->sample_index
[tab
->n_sample
-1];
2577 tab
->sample_index
[tab
->n_sample
-1] = tab
->sample_index
[i
];
2578 tab
->sample_index
[i
] = t
;
2579 isl_mat_swap_rows(tab
->samples
, tab
->n_sample
-1, i
);
2585 static int perform_undo(struct isl_tab
*tab
, struct isl_tab_undo
*undo
)
2587 switch (undo
->type
) {
2588 case isl_tab_undo_empty
:
2591 case isl_tab_undo_nonneg
:
2592 case isl_tab_undo_redundant
:
2593 case isl_tab_undo_zero
:
2594 case isl_tab_undo_allocate
:
2595 case isl_tab_undo_relax
:
2596 perform_undo_var(tab
, undo
);
2598 case isl_tab_undo_bset_eq
:
2599 isl_basic_set_free_equality(tab
->bset
, 1);
2601 case isl_tab_undo_bset_ineq
:
2602 isl_basic_set_free_inequality(tab
->bset
, 1);
2604 case isl_tab_undo_bset_div
:
2605 isl_basic_set_free_div(tab
->bset
, 1);
2607 tab
->samples
->n_col
--;
2609 case isl_tab_undo_saved_basis
:
2610 if (restore_basis(tab
, undo
->u
.col_var
) < 0)
2613 case isl_tab_undo_drop_sample
:
2616 case isl_tab_undo_saved_samples
:
2617 drop_samples_since(tab
, undo
->u
.n
);
2620 isl_assert(tab
->mat
->ctx
, 0, return -1);
2625 /* Return the tableau to the state it was in when the snapshot "snap"
2628 int isl_tab_rollback(struct isl_tab
*tab
, struct isl_tab_undo
*snap
)
2630 struct isl_tab_undo
*undo
, *next
;
2636 for (undo
= tab
->top
; undo
&& undo
!= &tab
->bottom
; undo
= next
) {
2640 if (perform_undo(tab
, undo
) < 0) {
2654 /* The given row "row" represents an inequality violated by all
2655 * points in the tableau. Check for some special cases of such
2656 * separating constraints.
2657 * In particular, if the row has been reduced to the constant -1,
2658 * then we know the inequality is adjacent (but opposite) to
2659 * an equality in the tableau.
2660 * If the row has been reduced to r = -1 -r', with r' an inequality
2661 * of the tableau, then the inequality is adjacent (but opposite)
2662 * to the inequality r'.
2664 static enum isl_ineq_type
separation_type(struct isl_tab
*tab
, unsigned row
)
2667 unsigned off
= 2 + tab
->M
;
2670 return isl_ineq_separate
;
2672 if (!isl_int_is_one(tab
->mat
->row
[row
][0]))
2673 return isl_ineq_separate
;
2674 if (!isl_int_is_negone(tab
->mat
->row
[row
][1]))
2675 return isl_ineq_separate
;
2677 pos
= isl_seq_first_non_zero(tab
->mat
->row
[row
] + off
+ tab
->n_dead
,
2678 tab
->n_col
- tab
->n_dead
);
2680 return isl_ineq_adj_eq
;
2682 if (!isl_int_is_negone(tab
->mat
->row
[row
][off
+ tab
->n_dead
+ pos
]))
2683 return isl_ineq_separate
;
2685 pos
= isl_seq_first_non_zero(
2686 tab
->mat
->row
[row
] + off
+ tab
->n_dead
+ pos
+ 1,
2687 tab
->n_col
- tab
->n_dead
- pos
- 1);
2689 return pos
== -1 ? isl_ineq_adj_ineq
: isl_ineq_separate
;
2692 /* Check the effect of inequality "ineq" on the tableau "tab".
2694 * isl_ineq_redundant: satisfied by all points in the tableau
2695 * isl_ineq_separate: satisfied by no point in the tableau
2696 * isl_ineq_cut: satisfied by some by not all points
2697 * isl_ineq_adj_eq: adjacent to an equality
2698 * isl_ineq_adj_ineq: adjacent to an inequality.
2700 enum isl_ineq_type
isl_tab_ineq_type(struct isl_tab
*tab
, isl_int
*ineq
)
2702 enum isl_ineq_type type
= isl_ineq_error
;
2703 struct isl_tab_undo
*snap
= NULL
;
2708 return isl_ineq_error
;
2710 if (isl_tab_extend_cons(tab
, 1) < 0)
2711 return isl_ineq_error
;
2713 snap
= isl_tab_snap(tab
);
2715 con
= isl_tab_add_row(tab
, ineq
);
2719 row
= tab
->con
[con
].index
;
2720 if (isl_tab_row_is_redundant(tab
, row
))
2721 type
= isl_ineq_redundant
;
2722 else if (isl_int_is_neg(tab
->mat
->row
[row
][1]) &&
2724 isl_int_abs_ge(tab
->mat
->row
[row
][1],
2725 tab
->mat
->row
[row
][0]))) {
2726 if (at_least_zero(tab
, &tab
->con
[con
]))
2727 type
= isl_ineq_cut
;
2729 type
= separation_type(tab
, row
);
2730 } else if (tab
->rational
? (sign_of_min(tab
, &tab
->con
[con
]) < 0)
2731 : isl_tab_min_at_most_neg_one(tab
, &tab
->con
[con
]))
2732 type
= isl_ineq_cut
;
2734 type
= isl_ineq_redundant
;
2736 if (isl_tab_rollback(tab
, snap
))
2737 return isl_ineq_error
;
2740 isl_tab_rollback(tab
, snap
);
2741 return isl_ineq_error
;
2744 void isl_tab_dump(struct isl_tab
*tab
, FILE *out
, int indent
)
2750 fprintf(out
, "%*snull tab\n", indent
, "");
2753 fprintf(out
, "%*sn_redundant: %d, n_dead: %d", indent
, "",
2754 tab
->n_redundant
, tab
->n_dead
);
2756 fprintf(out
, ", rational");
2758 fprintf(out
, ", empty");
2760 fprintf(out
, "%*s[", indent
, "");
2761 for (i
= 0; i
< tab
->n_var
; ++i
) {
2763 fprintf(out
, (i
== tab
->n_param
||
2764 i
== tab
->n_var
- tab
->n_div
) ? "; "
2766 fprintf(out
, "%c%d%s", tab
->var
[i
].is_row
? 'r' : 'c',
2768 tab
->var
[i
].is_zero
? " [=0]" :
2769 tab
->var
[i
].is_redundant
? " [R]" : "");
2771 fprintf(out
, "]\n");
2772 fprintf(out
, "%*s[", indent
, "");
2773 for (i
= 0; i
< tab
->n_con
; ++i
) {
2776 fprintf(out
, "%c%d%s", tab
->con
[i
].is_row
? 'r' : 'c',
2778 tab
->con
[i
].is_zero
? " [=0]" :
2779 tab
->con
[i
].is_redundant
? " [R]" : "");
2781 fprintf(out
, "]\n");
2782 fprintf(out
, "%*s[", indent
, "");
2783 for (i
= 0; i
< tab
->n_row
; ++i
) {
2784 const char *sign
= "";
2787 if (tab
->row_sign
) {
2788 if (tab
->row_sign
[i
] == isl_tab_row_unknown
)
2790 else if (tab
->row_sign
[i
] == isl_tab_row_neg
)
2792 else if (tab
->row_sign
[i
] == isl_tab_row_pos
)
2797 fprintf(out
, "r%d: %d%s%s", i
, tab
->row_var
[i
],
2798 isl_tab_var_from_row(tab
, i
)->is_nonneg
? " [>=0]" : "", sign
);
2800 fprintf(out
, "]\n");
2801 fprintf(out
, "%*s[", indent
, "");
2802 for (i
= 0; i
< tab
->n_col
; ++i
) {
2805 fprintf(out
, "c%d: %d%s", i
, tab
->col_var
[i
],
2806 var_from_col(tab
, i
)->is_nonneg
? " [>=0]" : "");
2808 fprintf(out
, "]\n");
2809 r
= tab
->mat
->n_row
;
2810 tab
->mat
->n_row
= tab
->n_row
;
2811 c
= tab
->mat
->n_col
;
2812 tab
->mat
->n_col
= 2 + tab
->M
+ tab
->n_col
;
2813 isl_mat_dump(tab
->mat
, out
, indent
);
2814 tab
->mat
->n_row
= r
;
2815 tab
->mat
->n_col
= c
;
2817 isl_basic_set_dump(tab
->bset
, out
, indent
);