2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2010 INRIA Saclay
4 * Copyright 2016-2017 Sven Verdoolaege
6 * Use of this software is governed by the MIT license
8 * Written by Sven Verdoolaege, K.U.Leuven, Departement
9 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
10 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
11 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
14 #include <isl_ctx_private.h>
15 #include "isl_map_private.h"
18 #include "isl_sample.h"
19 #include <isl_mat_private.h>
20 #include <isl_vec_private.h>
21 #include <isl_aff_private.h>
22 #include <isl_constraint_private.h>
23 #include <isl_options_private.h>
24 #include <isl_config.h>
26 #include <bset_to_bmap.c>
29 * The implementation of parametric integer linear programming in this file
30 * was inspired by the paper "Parametric Integer Programming" and the
31 * report "Solving systems of affine (in)equalities" by Paul Feautrier
34 * The strategy used for obtaining a feasible solution is different
35 * from the one used in isl_tab.c. In particular, in isl_tab.c,
36 * upon finding a constraint that is not yet satisfied, we pivot
37 * in a row that increases the constant term of the row holding the
38 * constraint, making sure the sample solution remains feasible
39 * for all the constraints it already satisfied.
40 * Here, we always pivot in the row holding the constraint,
41 * choosing a column that induces the lexicographically smallest
42 * increment to the sample solution.
44 * By starting out from a sample value that is lexicographically
45 * smaller than any integer point in the problem space, the first
46 * feasible integer sample point we find will also be the lexicographically
47 * smallest. If all variables can be assumed to be non-negative,
48 * then the initial sample value may be chosen equal to zero.
49 * However, we will not make this assumption. Instead, we apply
50 * the "big parameter" trick. Any variable x is then not directly
51 * used in the tableau, but instead it is represented by another
52 * variable x' = M + x, where M is an arbitrarily large (positive)
53 * value. x' is therefore always non-negative, whatever the value of x.
54 * Taking as initial sample value x' = 0 corresponds to x = -M,
55 * which is always smaller than any possible value of x.
57 * The big parameter trick is used in the main tableau and
58 * also in the context tableau if isl_context_lex is used.
59 * In this case, each tableaus has its own big parameter.
60 * Before doing any real work, we check if all the parameters
61 * happen to be non-negative. If so, we drop the column corresponding
62 * to M from the initial context tableau.
63 * If isl_context_gbr is used, then the big parameter trick is only
64 * used in the main tableau.
68 struct isl_context_op
{
69 /* detect nonnegative parameters in context and mark them in tab */
70 struct isl_tab
*(*detect_nonnegative_parameters
)(
71 struct isl_context
*context
, struct isl_tab
*tab
);
72 /* return temporary reference to basic set representation of context */
73 struct isl_basic_set
*(*peek_basic_set
)(struct isl_context
*context
);
74 /* return temporary reference to tableau representation of context */
75 struct isl_tab
*(*peek_tab
)(struct isl_context
*context
);
76 /* add equality; check is 1 if eq may not be valid;
77 * update is 1 if we may want to call ineq_sign on context later.
79 void (*add_eq
)(struct isl_context
*context
, isl_int
*eq
,
80 int check
, int update
);
81 /* add inequality; check is 1 if ineq may not be valid;
82 * update is 1 if we may want to call ineq_sign on context later.
84 void (*add_ineq
)(struct isl_context
*context
, isl_int
*ineq
,
85 int check
, int update
);
86 /* check sign of ineq based on previous information.
87 * strict is 1 if saturation should be treated as a positive sign.
89 enum isl_tab_row_sign (*ineq_sign
)(struct isl_context
*context
,
90 isl_int
*ineq
, int strict
);
91 /* check if inequality maintains feasibility */
92 int (*test_ineq
)(struct isl_context
*context
, isl_int
*ineq
);
93 /* return index of a div that corresponds to "div" */
94 int (*get_div
)(struct isl_context
*context
, struct isl_tab
*tab
,
96 /* insert div "div" to context at "pos" and return non-negativity */
97 isl_bool (*insert_div
)(struct isl_context
*context
, int pos
,
98 __isl_keep isl_vec
*div
);
99 int (*detect_equalities
)(struct isl_context
*context
,
100 struct isl_tab
*tab
);
101 /* return row index of "best" split */
102 int (*best_split
)(struct isl_context
*context
, struct isl_tab
*tab
);
103 /* check if context has already been determined to be empty */
104 int (*is_empty
)(struct isl_context
*context
);
105 /* check if context is still usable */
106 int (*is_ok
)(struct isl_context
*context
);
107 /* save a copy/snapshot of context */
108 void *(*save
)(struct isl_context
*context
);
109 /* restore saved context */
110 void (*restore
)(struct isl_context
*context
, void *);
111 /* discard saved context */
112 void (*discard
)(void *);
113 /* invalidate context */
114 void (*invalidate
)(struct isl_context
*context
);
116 __isl_null
struct isl_context
*(*free
)(struct isl_context
*context
);
119 /* Shared parts of context representation.
121 * "n_unknown" is the number of final unknown integer divisions
122 * in the input domain.
125 struct isl_context_op
*op
;
129 struct isl_context_lex
{
130 struct isl_context context
;
134 /* A stack (linked list) of solutions of subtrees of the search space.
136 * "ma" describes the solution as a function of "dom".
137 * In particular, the domain space of "ma" is equal to the space of "dom".
139 * If "ma" is NULL, then there is no solution on "dom".
141 struct isl_partial_sol
{
143 struct isl_basic_set
*dom
;
146 struct isl_partial_sol
*next
;
150 struct isl_sol_callback
{
151 struct isl_tab_callback callback
;
155 /* isl_sol is an interface for constructing a solution to
156 * a parametric integer linear programming problem.
157 * Every time the algorithm reaches a state where a solution
158 * can be read off from the tableau, the function "add" is called
159 * on the isl_sol passed to find_solutions_main. In a state where
160 * the tableau is empty, "add_empty" is called instead.
161 * "free" is called to free the implementation specific fields, if any.
163 * "error" is set if some error has occurred. This flag invalidates
164 * the remainder of the data structure.
165 * If "rational" is set, then a rational optimization is being performed.
166 * "level" is the current level in the tree with nodes for each
167 * split in the context.
168 * If "max" is set, then a maximization problem is being solved, rather than
169 * a minimization problem, which means that the variables in the
170 * tableau have value "M - x" rather than "M + x".
171 * "n_out" is the number of output dimensions in the input.
172 * "space" is the space in which the solution (and also the input) lives.
174 * The context tableau is owned by isl_sol and is updated incrementally.
176 * There are currently three implementations of this interface,
177 * isl_sol_map, which simply collects the solutions in an isl_map
178 * and (optionally) the parts of the context where there is no solution
180 * isl_sol_pma, which collects an isl_pw_multi_aff instead, and
181 * isl_sol_for, which calls a user-defined function for each part of
191 struct isl_context
*context
;
192 struct isl_partial_sol
*partial
;
193 void (*add
)(struct isl_sol
*sol
,
194 __isl_take isl_basic_set
*dom
, __isl_take isl_multi_aff
*ma
);
195 void (*add_empty
)(struct isl_sol
*sol
, struct isl_basic_set
*bset
);
196 void (*free
)(struct isl_sol
*sol
);
197 struct isl_sol_callback dec_level
;
200 static void sol_free(struct isl_sol
*sol
)
202 struct isl_partial_sol
*partial
, *next
;
205 for (partial
= sol
->partial
; partial
; partial
= next
) {
206 next
= partial
->next
;
207 isl_basic_set_free(partial
->dom
);
208 isl_multi_aff_free(partial
->ma
);
211 isl_space_free(sol
->space
);
213 sol
->context
->op
->free(sol
->context
);
218 /* Push a partial solution represented by a domain and function "ma"
219 * onto the stack of partial solutions.
220 * If "ma" is NULL, then "dom" represents a part of the domain
223 static void sol_push_sol(struct isl_sol
*sol
,
224 __isl_take isl_basic_set
*dom
, __isl_take isl_multi_aff
*ma
)
226 struct isl_partial_sol
*partial
;
228 if (sol
->error
|| !dom
)
231 partial
= isl_alloc_type(dom
->ctx
, struct isl_partial_sol
);
235 partial
->level
= sol
->level
;
238 partial
->next
= sol
->partial
;
240 sol
->partial
= partial
;
244 isl_basic_set_free(dom
);
245 isl_multi_aff_free(ma
);
249 /* Check that the final columns of "M", starting at "first", are zero.
251 static isl_stat
check_final_columns_are_zero(__isl_keep isl_mat
*M
,
255 unsigned rows
, cols
, n
;
258 return isl_stat_error
;
259 rows
= isl_mat_rows(M
);
260 cols
= isl_mat_cols(M
);
262 for (i
= 0; i
< rows
; ++i
)
263 if (isl_seq_first_non_zero(M
->row
[i
] + first
, n
) != -1)
264 isl_die(isl_mat_get_ctx(M
), isl_error_internal
,
265 "final columns should be zero",
266 return isl_stat_error
);
270 /* Set the affine expressions in "ma" according to the rows in "M", which
271 * are defined over the local space "ls".
272 * The matrix "M" may have extra (zero) columns beyond the number
273 * of variables in "ls".
275 static __isl_give isl_multi_aff
*set_from_affine_matrix(
276 __isl_take isl_multi_aff
*ma
, __isl_take isl_local_space
*ls
,
277 __isl_take isl_mat
*M
)
282 if (!ma
|| !ls
|| !M
)
285 dim
= isl_local_space_dim(ls
, isl_dim_all
);
286 if (check_final_columns_are_zero(M
, 1 + dim
) < 0)
288 for (i
= 1; i
< M
->n_row
; ++i
) {
289 aff
= isl_aff_alloc(isl_local_space_copy(ls
));
291 isl_int_set(aff
->v
->el
[0], M
->row
[0][0]);
292 isl_seq_cpy(aff
->v
->el
+ 1, M
->row
[i
], 1 + dim
);
294 aff
= isl_aff_normalize(aff
);
295 ma
= isl_multi_aff_set_aff(ma
, i
- 1, aff
);
297 isl_local_space_free(ls
);
302 isl_local_space_free(ls
);
304 isl_multi_aff_free(ma
);
308 /* Push a partial solution represented by a domain and mapping M
309 * onto the stack of partial solutions.
311 * The affine matrix "M" maps the dimensions of the context
312 * to the output variables. Convert it into an isl_multi_aff and
313 * then call sol_push_sol.
315 * Note that the description of the initial context may have involved
316 * existentially quantified variables, in which case they also appear
317 * in "dom". These need to be removed before creating the affine
318 * expression because an affine expression cannot be defined in terms
319 * of existentially quantified variables without a known representation.
320 * Since newly added integer divisions are inserted before these
321 * existentially quantified variables, they are still in the final
322 * positions and the corresponding final columns of "M" are zero
323 * because align_context_divs adds the existentially quantified
324 * variables of the context to the main tableau without any constraints and
325 * any equality constraints that are added later on can only serve
326 * to eliminate these existentially quantified variables.
328 static void sol_push_sol_mat(struct isl_sol
*sol
,
329 __isl_take isl_basic_set
*dom
, __isl_take isl_mat
*M
)
335 n_div
= isl_basic_set_dim(dom
, isl_dim_div
);
336 n_known
= n_div
- sol
->context
->n_unknown
;
338 ma
= isl_multi_aff_alloc(isl_space_copy(sol
->space
));
339 ls
= isl_basic_set_get_local_space(dom
);
340 ls
= isl_local_space_drop_dims(ls
, isl_dim_div
,
341 n_known
, n_div
- n_known
);
342 ma
= set_from_affine_matrix(ma
, ls
, M
);
345 dom
= isl_basic_set_free(dom
);
346 sol_push_sol(sol
, dom
, ma
);
349 /* Pop one partial solution from the partial solution stack and
350 * pass it on to sol->add or sol->add_empty.
352 static void sol_pop_one(struct isl_sol
*sol
)
354 struct isl_partial_sol
*partial
;
356 partial
= sol
->partial
;
357 sol
->partial
= partial
->next
;
360 sol
->add(sol
, partial
->dom
, partial
->ma
);
362 sol
->add_empty(sol
, partial
->dom
);
366 /* Return a fresh copy of the domain represented by the context tableau.
368 static struct isl_basic_set
*sol_domain(struct isl_sol
*sol
)
370 struct isl_basic_set
*bset
;
375 bset
= isl_basic_set_dup(sol
->context
->op
->peek_basic_set(sol
->context
));
376 bset
= isl_basic_set_update_from_tab(bset
,
377 sol
->context
->op
->peek_tab(sol
->context
));
382 /* Check whether two partial solutions have the same affine expressions.
384 static isl_bool
same_solution(struct isl_partial_sol
*s1
,
385 struct isl_partial_sol
*s2
)
387 if (!s1
->ma
!= !s2
->ma
)
388 return isl_bool_false
;
390 return isl_bool_true
;
392 return isl_multi_aff_plain_is_equal(s1
->ma
, s2
->ma
);
395 /* Swap the initial two partial solutions in "sol".
399 * sol->partial = p1; p1->next = p2; p2->next = p3
403 * sol->partial = p2; p2->next = p1; p1->next = p3
405 static void swap_initial(struct isl_sol
*sol
)
407 struct isl_partial_sol
*partial
;
409 partial
= sol
->partial
;
410 sol
->partial
= partial
->next
;
411 partial
->next
= partial
->next
->next
;
412 sol
->partial
->next
= partial
;
415 /* Combine the initial two partial solution of "sol" into
416 * a partial solution with the current context domain of "sol" and
417 * the function description of the second partial solution in the list.
418 * The level of the new partial solution is set to the current level.
420 * That is, the first two partial solutions (D1,M1) and (D2,M2) are
421 * replaced by (D,M2), where D is the domain of "sol", which is assumed
422 * to be the union of D1 and D2, while M1 is assumed to be equal to M2
425 static isl_stat
combine_initial_into_second(struct isl_sol
*sol
)
427 struct isl_partial_sol
*partial
;
430 partial
= sol
->partial
;
432 bset
= sol_domain(sol
);
433 isl_basic_set_free(partial
->next
->dom
);
434 partial
->next
->dom
= bset
;
435 partial
->next
->level
= sol
->level
;
438 return isl_stat_error
;
440 sol
->partial
= partial
->next
;
441 isl_basic_set_free(partial
->dom
);
442 isl_multi_aff_free(partial
->ma
);
448 /* Are "ma1" and "ma2" equal to each other on "dom"?
450 * Combine "ma1" and "ma2" with "dom" and check if the results are the same.
451 * "dom" may have existentially quantified variables. Eliminate them first
452 * as otherwise they would have to be eliminated twice, in a more complicated
455 static isl_bool
equal_on_domain(__isl_keep isl_multi_aff
*ma1
,
456 __isl_keep isl_multi_aff
*ma2
, __isl_keep isl_basic_set
*dom
)
459 isl_pw_multi_aff
*pma1
, *pma2
;
462 set
= isl_basic_set_compute_divs(isl_basic_set_copy(dom
));
463 pma1
= isl_pw_multi_aff_alloc(isl_set_copy(set
),
464 isl_multi_aff_copy(ma1
));
465 pma2
= isl_pw_multi_aff_alloc(set
, isl_multi_aff_copy(ma2
));
466 equal
= isl_pw_multi_aff_is_equal(pma1
, pma2
);
467 isl_pw_multi_aff_free(pma1
);
468 isl_pw_multi_aff_free(pma2
);
473 /* The initial two partial solutions of "sol" are known to be at
475 * If they represent the same solution (on different parts of the domain),
476 * then combine them into a single solution at the current level.
477 * Otherwise, pop them both.
479 * Even if the two partial solution are not obviously the same,
480 * one may still be a simplification of the other over its own domain.
481 * Also check if the two sets of affine functions are equal when
482 * restricted to one of the domains. If so, combine the two
483 * using the set of affine functions on the other domain.
484 * That is, for two partial solutions (D1,M1) and (D2,M2),
485 * if M1 = M2 on D1, then the pair of partial solutions can
486 * be replaced by (D1+D2,M2) and similarly when M1 = M2 on D2.
488 static isl_stat
combine_initial_if_equal(struct isl_sol
*sol
)
490 struct isl_partial_sol
*partial
;
493 partial
= sol
->partial
;
495 same
= same_solution(partial
, partial
->next
);
497 return isl_stat_error
;
499 return combine_initial_into_second(sol
);
500 if (partial
->ma
&& partial
->next
->ma
) {
501 same
= equal_on_domain(partial
->ma
, partial
->next
->ma
,
504 return isl_stat_error
;
506 return combine_initial_into_second(sol
);
507 same
= equal_on_domain(partial
->ma
, partial
->next
->ma
,
511 return combine_initial_into_second(sol
);
521 /* Pop all solutions from the partial solution stack that were pushed onto
522 * the stack at levels that are deeper than the current level.
523 * If the two topmost elements on the stack have the same level
524 * and represent the same solution, then their domains are combined.
525 * This combined domain is the same as the current context domain
526 * as sol_pop is called each time we move back to a higher level.
527 * If the outer level (0) has been reached, then all partial solutions
528 * at the current level are also popped off.
530 static void sol_pop(struct isl_sol
*sol
)
532 struct isl_partial_sol
*partial
;
537 partial
= sol
->partial
;
541 if (partial
->level
== 0 && sol
->level
== 0) {
542 for (partial
= sol
->partial
; partial
; partial
= sol
->partial
)
547 if (partial
->level
<= sol
->level
)
550 if (partial
->next
&& partial
->next
->level
== partial
->level
) {
551 if (combine_initial_if_equal(sol
) < 0)
556 if (sol
->level
== 0) {
557 for (partial
= sol
->partial
; partial
; partial
= sol
->partial
)
563 error
: sol
->error
= 1;
566 static void sol_dec_level(struct isl_sol
*sol
)
576 static isl_stat
sol_dec_level_wrap(struct isl_tab_callback
*cb
)
578 struct isl_sol_callback
*callback
= (struct isl_sol_callback
*)cb
;
580 sol_dec_level(callback
->sol
);
582 return callback
->sol
->error
? isl_stat_error
: isl_stat_ok
;
585 /* Move down to next level and push callback onto context tableau
586 * to decrease the level again when it gets rolled back across
587 * the current state. That is, dec_level will be called with
588 * the context tableau in the same state as it is when inc_level
591 static void sol_inc_level(struct isl_sol
*sol
)
599 tab
= sol
->context
->op
->peek_tab(sol
->context
);
600 if (isl_tab_push_callback(tab
, &sol
->dec_level
.callback
) < 0)
604 static void scale_rows(struct isl_mat
*mat
, isl_int m
, int n_row
)
608 if (isl_int_is_one(m
))
611 for (i
= 0; i
< n_row
; ++i
)
612 isl_seq_scale(mat
->row
[i
], mat
->row
[i
], m
, mat
->n_col
);
615 /* Add the solution identified by the tableau and the context tableau.
617 * The layout of the variables is as follows.
618 * tab->n_var is equal to the total number of variables in the input
619 * map (including divs that were copied from the context)
620 * + the number of extra divs constructed
621 * Of these, the first tab->n_param and the last tab->n_div variables
622 * correspond to the variables in the context, i.e.,
623 * tab->n_param + tab->n_div = context_tab->n_var
624 * tab->n_param is equal to the number of parameters and input
625 * dimensions in the input map
626 * tab->n_div is equal to the number of divs in the context
628 * If there is no solution, then call add_empty with a basic set
629 * that corresponds to the context tableau. (If add_empty is NULL,
632 * If there is a solution, then first construct a matrix that maps
633 * all dimensions of the context to the output variables, i.e.,
634 * the output dimensions in the input map.
635 * The divs in the input map (if any) that do not correspond to any
636 * div in the context do not appear in the solution.
637 * The algorithm will make sure that they have an integer value,
638 * but these values themselves are of no interest.
639 * We have to be careful not to drop or rearrange any divs in the
640 * context because that would change the meaning of the matrix.
642 * To extract the value of the output variables, it should be noted
643 * that we always use a big parameter M in the main tableau and so
644 * the variable stored in this tableau is not an output variable x itself, but
645 * x' = M + x (in case of minimization)
647 * x' = M - x (in case of maximization)
648 * If x' appears in a column, then its optimal value is zero,
649 * which means that the optimal value of x is an unbounded number
650 * (-M for minimization and M for maximization).
651 * We currently assume that the output dimensions in the original map
652 * are bounded, so this cannot occur.
653 * Similarly, when x' appears in a row, then the coefficient of M in that
654 * row is necessarily 1.
655 * If the row in the tableau represents
656 * d x' = c + d M + e(y)
657 * then, in case of minimization, the corresponding row in the matrix
660 * with a d = m, the (updated) common denominator of the matrix.
661 * In case of maximization, the row will be
664 static void sol_add(struct isl_sol
*sol
, struct isl_tab
*tab
)
666 struct isl_basic_set
*bset
= NULL
;
667 struct isl_mat
*mat
= NULL
;
672 if (sol
->error
|| !tab
)
675 if (tab
->empty
&& !sol
->add_empty
)
677 if (sol
->context
->op
->is_empty(sol
->context
))
680 bset
= sol_domain(sol
);
683 sol_push_sol(sol
, bset
, NULL
);
689 mat
= isl_mat_alloc(tab
->mat
->ctx
, 1 + sol
->n_out
,
690 1 + tab
->n_param
+ tab
->n_div
);
696 isl_seq_clr(mat
->row
[0] + 1, mat
->n_col
- 1);
697 isl_int_set_si(mat
->row
[0][0], 1);
698 for (row
= 0; row
< sol
->n_out
; ++row
) {
699 int i
= tab
->n_param
+ row
;
702 isl_seq_clr(mat
->row
[1 + row
], mat
->n_col
);
703 if (!tab
->var
[i
].is_row
) {
705 isl_die(mat
->ctx
, isl_error_invalid
,
706 "unbounded optimum", goto error2
);
710 r
= tab
->var
[i
].index
;
712 isl_int_ne(tab
->mat
->row
[r
][2], tab
->mat
->row
[r
][0]))
713 isl_die(mat
->ctx
, isl_error_invalid
,
714 "unbounded optimum", goto error2
);
715 isl_int_gcd(m
, mat
->row
[0][0], tab
->mat
->row
[r
][0]);
716 isl_int_divexact(m
, tab
->mat
->row
[r
][0], m
);
717 scale_rows(mat
, m
, 1 + row
);
718 isl_int_divexact(m
, mat
->row
[0][0], tab
->mat
->row
[r
][0]);
719 isl_int_mul(mat
->row
[1 + row
][0], m
, tab
->mat
->row
[r
][1]);
720 for (j
= 0; j
< tab
->n_param
; ++j
) {
722 if (tab
->var
[j
].is_row
)
724 col
= tab
->var
[j
].index
;
725 isl_int_mul(mat
->row
[1 + row
][1 + j
], m
,
726 tab
->mat
->row
[r
][off
+ col
]);
728 for (j
= 0; j
< tab
->n_div
; ++j
) {
730 if (tab
->var
[tab
->n_var
- tab
->n_div
+j
].is_row
)
732 col
= tab
->var
[tab
->n_var
- tab
->n_div
+j
].index
;
733 isl_int_mul(mat
->row
[1 + row
][1 + tab
->n_param
+ j
], m
,
734 tab
->mat
->row
[r
][off
+ col
]);
737 isl_seq_neg(mat
->row
[1 + row
], mat
->row
[1 + row
],
743 sol_push_sol_mat(sol
, bset
, mat
);
748 isl_basic_set_free(bset
);
756 struct isl_set
*empty
;
759 static void sol_map_free(struct isl_sol
*sol
)
761 struct isl_sol_map
*sol_map
= (struct isl_sol_map
*) sol
;
762 isl_map_free(sol_map
->map
);
763 isl_set_free(sol_map
->empty
);
766 /* This function is called for parts of the context where there is
767 * no solution, with "bset" corresponding to the context tableau.
768 * Simply add the basic set to the set "empty".
770 static void sol_map_add_empty(struct isl_sol_map
*sol
,
771 struct isl_basic_set
*bset
)
773 if (!bset
|| !sol
->empty
)
776 sol
->empty
= isl_set_grow(sol
->empty
, 1);
777 bset
= isl_basic_set_simplify(bset
);
778 bset
= isl_basic_set_finalize(bset
);
779 sol
->empty
= isl_set_add_basic_set(sol
->empty
, isl_basic_set_copy(bset
));
782 isl_basic_set_free(bset
);
785 isl_basic_set_free(bset
);
789 static void sol_map_add_empty_wrap(struct isl_sol
*sol
,
790 struct isl_basic_set
*bset
)
792 sol_map_add_empty((struct isl_sol_map
*)sol
, bset
);
795 /* Given a basic set "dom" that represents the context and a tuple of
796 * affine expressions "ma" defined over this domain, construct a basic map
797 * that expresses this function on the domain.
799 static void sol_map_add(struct isl_sol_map
*sol
,
800 __isl_take isl_basic_set
*dom
, __isl_take isl_multi_aff
*ma
)
804 if (sol
->sol
.error
|| !dom
|| !ma
)
807 bmap
= isl_basic_map_from_multi_aff2(ma
, sol
->sol
.rational
);
808 bmap
= isl_basic_map_intersect_domain(bmap
, dom
);
809 sol
->map
= isl_map_grow(sol
->map
, 1);
810 sol
->map
= isl_map_add_basic_map(sol
->map
, bmap
);
815 isl_basic_set_free(dom
);
816 isl_multi_aff_free(ma
);
820 static void sol_map_add_wrap(struct isl_sol
*sol
,
821 __isl_take isl_basic_set
*dom
, __isl_take isl_multi_aff
*ma
)
823 sol_map_add((struct isl_sol_map
*)sol
, dom
, ma
);
827 /* Store the "parametric constant" of row "row" of tableau "tab" in "line",
828 * i.e., the constant term and the coefficients of all variables that
829 * appear in the context tableau.
830 * Note that the coefficient of the big parameter M is NOT copied.
831 * The context tableau may not have a big parameter and even when it
832 * does, it is a different big parameter.
834 static void get_row_parameter_line(struct isl_tab
*tab
, int row
, isl_int
*line
)
837 unsigned off
= 2 + tab
->M
;
839 isl_int_set(line
[0], tab
->mat
->row
[row
][1]);
840 for (i
= 0; i
< tab
->n_param
; ++i
) {
841 if (tab
->var
[i
].is_row
)
842 isl_int_set_si(line
[1 + i
], 0);
844 int col
= tab
->var
[i
].index
;
845 isl_int_set(line
[1 + i
], tab
->mat
->row
[row
][off
+ col
]);
848 for (i
= 0; i
< tab
->n_div
; ++i
) {
849 if (tab
->var
[tab
->n_var
- tab
->n_div
+ i
].is_row
)
850 isl_int_set_si(line
[1 + tab
->n_param
+ i
], 0);
852 int col
= tab
->var
[tab
->n_var
- tab
->n_div
+ i
].index
;
853 isl_int_set(line
[1 + tab
->n_param
+ i
],
854 tab
->mat
->row
[row
][off
+ col
]);
859 /* Check if rows "row1" and "row2" have identical "parametric constants",
860 * as explained above.
861 * In this case, we also insist that the coefficients of the big parameter
862 * be the same as the values of the constants will only be the same
863 * if these coefficients are also the same.
865 static int identical_parameter_line(struct isl_tab
*tab
, int row1
, int row2
)
868 unsigned off
= 2 + tab
->M
;
870 if (isl_int_ne(tab
->mat
->row
[row1
][1], tab
->mat
->row
[row2
][1]))
873 if (tab
->M
&& isl_int_ne(tab
->mat
->row
[row1
][2],
874 tab
->mat
->row
[row2
][2]))
877 for (i
= 0; i
< tab
->n_param
+ tab
->n_div
; ++i
) {
878 int pos
= i
< tab
->n_param
? i
:
879 tab
->n_var
- tab
->n_div
+ i
- tab
->n_param
;
882 if (tab
->var
[pos
].is_row
)
884 col
= tab
->var
[pos
].index
;
885 if (isl_int_ne(tab
->mat
->row
[row1
][off
+ col
],
886 tab
->mat
->row
[row2
][off
+ col
]))
892 /* Return an inequality that expresses that the "parametric constant"
893 * should be non-negative.
894 * This function is only called when the coefficient of the big parameter
897 static struct isl_vec
*get_row_parameter_ineq(struct isl_tab
*tab
, int row
)
899 struct isl_vec
*ineq
;
901 ineq
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_param
+ tab
->n_div
);
905 get_row_parameter_line(tab
, row
, ineq
->el
);
907 ineq
= isl_vec_normalize(ineq
);
912 /* Normalize a div expression of the form
914 * [(g*f(x) + c)/(g * m)]
916 * with c the constant term and f(x) the remaining coefficients, to
920 static void normalize_div(__isl_keep isl_vec
*div
)
922 isl_ctx
*ctx
= isl_vec_get_ctx(div
);
923 int len
= div
->size
- 2;
925 isl_seq_gcd(div
->el
+ 2, len
, &ctx
->normalize_gcd
);
926 isl_int_gcd(ctx
->normalize_gcd
, ctx
->normalize_gcd
, div
->el
[0]);
928 if (isl_int_is_one(ctx
->normalize_gcd
))
931 isl_int_divexact(div
->el
[0], div
->el
[0], ctx
->normalize_gcd
);
932 isl_int_fdiv_q(div
->el
[1], div
->el
[1], ctx
->normalize_gcd
);
933 isl_seq_scale_down(div
->el
+ 2, div
->el
+ 2, ctx
->normalize_gcd
, len
);
936 /* Return an integer division for use in a parametric cut based
938 * In particular, let the parametric constant of the row be
942 * where y_0 = 1, but none of the y_i corresponds to the big parameter M.
943 * The div returned is equal to
945 * floor(\sum_i {-a_i} y_i) = floor((\sum_i (-a_i mod d) y_i)/d)
947 static struct isl_vec
*get_row_parameter_div(struct isl_tab
*tab
, int row
)
951 div
= isl_vec_alloc(tab
->mat
->ctx
, 1 + 1 + tab
->n_param
+ tab
->n_div
);
955 isl_int_set(div
->el
[0], tab
->mat
->row
[row
][0]);
956 get_row_parameter_line(tab
, row
, div
->el
+ 1);
957 isl_seq_neg(div
->el
+ 1, div
->el
+ 1, div
->size
- 1);
959 isl_seq_fdiv_r(div
->el
+ 1, div
->el
+ 1, div
->el
[0], div
->size
- 1);
964 /* Return an integer division for use in transferring an integrality constraint
966 * In particular, let the parametric constant of the row be
970 * where y_0 = 1, but none of the y_i corresponds to the big parameter M.
971 * The the returned div is equal to
973 * floor(\sum_i {a_i} y_i) = floor((\sum_i (a_i mod d) y_i)/d)
975 static struct isl_vec
*get_row_split_div(struct isl_tab
*tab
, int row
)
979 div
= isl_vec_alloc(tab
->mat
->ctx
, 1 + 1 + tab
->n_param
+ tab
->n_div
);
983 isl_int_set(div
->el
[0], tab
->mat
->row
[row
][0]);
984 get_row_parameter_line(tab
, row
, div
->el
+ 1);
986 isl_seq_fdiv_r(div
->el
+ 1, div
->el
+ 1, div
->el
[0], div
->size
- 1);
991 /* Construct and return an inequality that expresses an upper bound
993 * In particular, if the div is given by
997 * then the inequality expresses
1001 static __isl_give isl_vec
*ineq_for_div(__isl_keep isl_basic_set
*bset
,
1006 struct isl_vec
*ineq
;
1011 total
= isl_basic_set_total_dim(bset
);
1012 div_pos
= 1 + total
- bset
->n_div
+ div
;
1014 ineq
= isl_vec_alloc(bset
->ctx
, 1 + total
);
1018 isl_seq_cpy(ineq
->el
, bset
->div
[div
] + 1, 1 + total
);
1019 isl_int_neg(ineq
->el
[div_pos
], bset
->div
[div
][0]);
1023 /* Given a row in the tableau and a div that was created
1024 * using get_row_split_div and that has been constrained to equality, i.e.,
1026 * d = floor(\sum_i {a_i} y_i) = \sum_i {a_i} y_i
1028 * replace the expression "\sum_i {a_i} y_i" in the row by d,
1029 * i.e., we subtract "\sum_i {a_i} y_i" and add 1 d.
1030 * The coefficients of the non-parameters in the tableau have been
1031 * verified to be integral. We can therefore simply replace coefficient b
1032 * by floor(b). For the coefficients of the parameters we have
1033 * floor(a_i) = a_i - {a_i}, while for the other coefficients, we have
1036 static struct isl_tab
*set_row_cst_to_div(struct isl_tab
*tab
, int row
, int div
)
1038 isl_seq_fdiv_q(tab
->mat
->row
[row
] + 1, tab
->mat
->row
[row
] + 1,
1039 tab
->mat
->row
[row
][0], 1 + tab
->M
+ tab
->n_col
);
1041 isl_int_set_si(tab
->mat
->row
[row
][0], 1);
1043 if (tab
->var
[tab
->n_var
- tab
->n_div
+ div
].is_row
) {
1044 int drow
= tab
->var
[tab
->n_var
- tab
->n_div
+ div
].index
;
1046 isl_assert(tab
->mat
->ctx
,
1047 isl_int_is_one(tab
->mat
->row
[drow
][0]), goto error
);
1048 isl_seq_combine(tab
->mat
->row
[row
] + 1,
1049 tab
->mat
->ctx
->one
, tab
->mat
->row
[row
] + 1,
1050 tab
->mat
->ctx
->one
, tab
->mat
->row
[drow
] + 1,
1051 1 + tab
->M
+ tab
->n_col
);
1053 int dcol
= tab
->var
[tab
->n_var
- tab
->n_div
+ div
].index
;
1055 isl_int_add_ui(tab
->mat
->row
[row
][2 + tab
->M
+ dcol
],
1056 tab
->mat
->row
[row
][2 + tab
->M
+ dcol
], 1);
1065 /* Check if the (parametric) constant of the given row is obviously
1066 * negative, meaning that we don't need to consult the context tableau.
1067 * If there is a big parameter and its coefficient is non-zero,
1068 * then this coefficient determines the outcome.
1069 * Otherwise, we check whether the constant is negative and
1070 * all non-zero coefficients of parameters are negative and
1071 * belong to non-negative parameters.
1073 static int is_obviously_neg(struct isl_tab
*tab
, int row
)
1077 unsigned off
= 2 + tab
->M
;
1080 if (isl_int_is_pos(tab
->mat
->row
[row
][2]))
1082 if (isl_int_is_neg(tab
->mat
->row
[row
][2]))
1086 if (isl_int_is_nonneg(tab
->mat
->row
[row
][1]))
1088 for (i
= 0; i
< tab
->n_param
; ++i
) {
1089 /* Eliminated parameter */
1090 if (tab
->var
[i
].is_row
)
1092 col
= tab
->var
[i
].index
;
1093 if (isl_int_is_zero(tab
->mat
->row
[row
][off
+ col
]))
1095 if (!tab
->var
[i
].is_nonneg
)
1097 if (isl_int_is_pos(tab
->mat
->row
[row
][off
+ col
]))
1100 for (i
= 0; i
< tab
->n_div
; ++i
) {
1101 if (tab
->var
[tab
->n_var
- tab
->n_div
+ i
].is_row
)
1103 col
= tab
->var
[tab
->n_var
- tab
->n_div
+ i
].index
;
1104 if (isl_int_is_zero(tab
->mat
->row
[row
][off
+ col
]))
1106 if (!tab
->var
[tab
->n_var
- tab
->n_div
+ i
].is_nonneg
)
1108 if (isl_int_is_pos(tab
->mat
->row
[row
][off
+ col
]))
1114 /* Check if the (parametric) constant of the given row is obviously
1115 * non-negative, meaning that we don't need to consult the context tableau.
1116 * If there is a big parameter and its coefficient is non-zero,
1117 * then this coefficient determines the outcome.
1118 * Otherwise, we check whether the constant is non-negative and
1119 * all non-zero coefficients of parameters are positive and
1120 * belong to non-negative parameters.
1122 static int is_obviously_nonneg(struct isl_tab
*tab
, int row
)
1126 unsigned off
= 2 + tab
->M
;
1129 if (isl_int_is_pos(tab
->mat
->row
[row
][2]))
1131 if (isl_int_is_neg(tab
->mat
->row
[row
][2]))
1135 if (isl_int_is_neg(tab
->mat
->row
[row
][1]))
1137 for (i
= 0; i
< tab
->n_param
; ++i
) {
1138 /* Eliminated parameter */
1139 if (tab
->var
[i
].is_row
)
1141 col
= tab
->var
[i
].index
;
1142 if (isl_int_is_zero(tab
->mat
->row
[row
][off
+ col
]))
1144 if (!tab
->var
[i
].is_nonneg
)
1146 if (isl_int_is_neg(tab
->mat
->row
[row
][off
+ col
]))
1149 for (i
= 0; i
< tab
->n_div
; ++i
) {
1150 if (tab
->var
[tab
->n_var
- tab
->n_div
+ i
].is_row
)
1152 col
= tab
->var
[tab
->n_var
- tab
->n_div
+ i
].index
;
1153 if (isl_int_is_zero(tab
->mat
->row
[row
][off
+ col
]))
1155 if (!tab
->var
[tab
->n_var
- tab
->n_div
+ i
].is_nonneg
)
1157 if (isl_int_is_neg(tab
->mat
->row
[row
][off
+ col
]))
1163 /* Given a row r and two columns, return the column that would
1164 * lead to the lexicographically smallest increment in the sample
1165 * solution when leaving the basis in favor of the row.
1166 * Pivoting with column c will increment the sample value by a non-negative
1167 * constant times a_{V,c}/a_{r,c}, with a_{V,c} the elements of column c
1168 * corresponding to the non-parametric variables.
1169 * If variable v appears in a column c_v, the a_{v,c} = 1 iff c = c_v,
1170 * with all other entries in this virtual row equal to zero.
1171 * If variable v appears in a row, then a_{v,c} is the element in column c
1174 * Let v be the first variable with a_{v,c1}/a_{r,c1} != a_{v,c2}/a_{r,c2}.
1175 * Then if a_{v,c1}/a_{r,c1} < a_{v,c2}/a_{r,c2}, i.e.,
1176 * a_{v,c2} a_{r,c1} - a_{v,c1} a_{r,c2} > 0, c1 results in the minimal
1177 * increment. Otherwise, it's c2.
1179 static int lexmin_col_pair(struct isl_tab
*tab
,
1180 int row
, int col1
, int col2
, isl_int tmp
)
1185 tr
= tab
->mat
->row
[row
] + 2 + tab
->M
;
1187 for (i
= tab
->n_param
; i
< tab
->n_var
- tab
->n_div
; ++i
) {
1191 if (!tab
->var
[i
].is_row
) {
1192 if (tab
->var
[i
].index
== col1
)
1194 if (tab
->var
[i
].index
== col2
)
1199 if (tab
->var
[i
].index
== row
)
1202 r
= tab
->mat
->row
[tab
->var
[i
].index
] + 2 + tab
->M
;
1203 s1
= isl_int_sgn(r
[col1
]);
1204 s2
= isl_int_sgn(r
[col2
]);
1205 if (s1
== 0 && s2
== 0)
1212 isl_int_mul(tmp
, r
[col2
], tr
[col1
]);
1213 isl_int_submul(tmp
, r
[col1
], tr
[col2
]);
1214 if (isl_int_is_pos(tmp
))
1216 if (isl_int_is_neg(tmp
))
1222 /* Does the index into the tab->var or tab->con array "index"
1223 * correspond to a variable in the context tableau?
1224 * In particular, it needs to be an index into the tab->var array and
1225 * it needs to refer to either one of the first tab->n_param variables or
1226 * one of the last tab->n_div variables.
1228 static int is_parameter_var(struct isl_tab
*tab
, int index
)
1232 if (index
< tab
->n_param
)
1234 if (index
>= tab
->n_var
- tab
->n_div
)
1239 /* Does column "col" of "tab" refer to a variable in the context tableau?
1241 static int col_is_parameter_var(struct isl_tab
*tab
, int col
)
1243 return is_parameter_var(tab
, tab
->col_var
[col
]);
1246 /* Does row "row" of "tab" refer to a variable in the context tableau?
1248 static int row_is_parameter_var(struct isl_tab
*tab
, int row
)
1250 return is_parameter_var(tab
, tab
->row_var
[row
]);
1253 /* Given a row in the tableau, find and return the column that would
1254 * result in the lexicographically smallest, but positive, increment
1255 * in the sample point.
1256 * If there is no such column, then return tab->n_col.
1257 * If anything goes wrong, return -1.
1259 static int lexmin_pivot_col(struct isl_tab
*tab
, int row
)
1262 int col
= tab
->n_col
;
1266 tr
= tab
->mat
->row
[row
] + 2 + tab
->M
;
1270 for (j
= tab
->n_dead
; j
< tab
->n_col
; ++j
) {
1271 if (col_is_parameter_var(tab
, j
))
1274 if (!isl_int_is_pos(tr
[j
]))
1277 if (col
== tab
->n_col
)
1280 col
= lexmin_col_pair(tab
, row
, col
, j
, tmp
);
1281 isl_assert(tab
->mat
->ctx
, col
>= 0, goto error
);
1291 /* Return the first known violated constraint, i.e., a non-negative
1292 * constraint that currently has an either obviously negative value
1293 * or a previously determined to be negative value.
1295 * If any constraint has a negative coefficient for the big parameter,
1296 * if any, then we return one of these first.
1298 static int first_neg(struct isl_tab
*tab
)
1303 for (row
= tab
->n_redundant
; row
< tab
->n_row
; ++row
) {
1304 if (!isl_tab_var_from_row(tab
, row
)->is_nonneg
)
1306 if (!isl_int_is_neg(tab
->mat
->row
[row
][2]))
1309 tab
->row_sign
[row
] = isl_tab_row_neg
;
1312 for (row
= tab
->n_redundant
; row
< tab
->n_row
; ++row
) {
1313 if (!isl_tab_var_from_row(tab
, row
)->is_nonneg
)
1315 if (tab
->row_sign
) {
1316 if (tab
->row_sign
[row
] == 0 &&
1317 is_obviously_neg(tab
, row
))
1318 tab
->row_sign
[row
] = isl_tab_row_neg
;
1319 if (tab
->row_sign
[row
] != isl_tab_row_neg
)
1321 } else if (!is_obviously_neg(tab
, row
))
1328 /* Check whether the invariant that all columns are lexico-positive
1329 * is satisfied. This function is not called from the current code
1330 * but is useful during debugging.
1332 static void check_lexpos(struct isl_tab
*tab
) __attribute__ ((unused
));
1333 static void check_lexpos(struct isl_tab
*tab
)
1335 unsigned off
= 2 + tab
->M
;
1340 for (col
= tab
->n_dead
; col
< tab
->n_col
; ++col
) {
1341 if (col_is_parameter_var(tab
, col
))
1343 for (var
= tab
->n_param
; var
< tab
->n_var
- tab
->n_div
; ++var
) {
1344 if (!tab
->var
[var
].is_row
) {
1345 if (tab
->var
[var
].index
== col
)
1350 row
= tab
->var
[var
].index
;
1351 if (isl_int_is_zero(tab
->mat
->row
[row
][off
+ col
]))
1353 if (isl_int_is_pos(tab
->mat
->row
[row
][off
+ col
]))
1355 fprintf(stderr
, "lexneg column %d (row %d)\n",
1358 if (var
>= tab
->n_var
- tab
->n_div
)
1359 fprintf(stderr
, "zero column %d\n", col
);
1363 /* Report to the caller that the given constraint is part of an encountered
1366 static int report_conflicting_constraint(struct isl_tab
*tab
, int con
)
1368 return tab
->conflict(con
, tab
->conflict_user
);
1371 /* Given a conflicting row in the tableau, report all constraints
1372 * involved in the row to the caller. That is, the row itself
1373 * (if it represents a constraint) and all constraint columns with
1374 * non-zero (and therefore negative) coefficients.
1376 static int report_conflict(struct isl_tab
*tab
, int row
)
1384 if (tab
->row_var
[row
] < 0 &&
1385 report_conflicting_constraint(tab
, ~tab
->row_var
[row
]) < 0)
1388 tr
= tab
->mat
->row
[row
] + 2 + tab
->M
;
1390 for (j
= tab
->n_dead
; j
< tab
->n_col
; ++j
) {
1391 if (col_is_parameter_var(tab
, j
))
1394 if (!isl_int_is_neg(tr
[j
]))
1397 if (tab
->col_var
[j
] < 0 &&
1398 report_conflicting_constraint(tab
, ~tab
->col_var
[j
]) < 0)
1405 /* Resolve all known or obviously violated constraints through pivoting.
1406 * In particular, as long as we can find any violated constraint, we
1407 * look for a pivoting column that would result in the lexicographically
1408 * smallest increment in the sample point. If there is no such column
1409 * then the tableau is infeasible.
1411 static int restore_lexmin(struct isl_tab
*tab
) WARN_UNUSED
;
1412 static int restore_lexmin(struct isl_tab
*tab
)
1420 while ((row
= first_neg(tab
)) != -1) {
1421 col
= lexmin_pivot_col(tab
, row
);
1422 if (col
>= tab
->n_col
) {
1423 if (report_conflict(tab
, row
) < 0)
1425 if (isl_tab_mark_empty(tab
) < 0)
1431 if (isl_tab_pivot(tab
, row
, col
) < 0)
1437 /* Given a row that represents an equality, look for an appropriate
1439 * In particular, if there are any non-zero coefficients among
1440 * the non-parameter variables, then we take the last of these
1441 * variables. Eliminating this variable in terms of the other
1442 * variables and/or parameters does not influence the property
1443 * that all column in the initial tableau are lexicographically
1444 * positive. The row corresponding to the eliminated variable
1445 * will only have non-zero entries below the diagonal of the
1446 * initial tableau. That is, we transform
1452 * If there is no such non-parameter variable, then we are dealing with
1453 * pure parameter equality and we pick any parameter with coefficient 1 or -1
1454 * for elimination. This will ensure that the eliminated parameter
1455 * always has an integer value whenever all the other parameters are integral.
1456 * If there is no such parameter then we return -1.
1458 static int last_var_col_or_int_par_col(struct isl_tab
*tab
, int row
)
1460 unsigned off
= 2 + tab
->M
;
1463 for (i
= tab
->n_var
- tab
->n_div
- 1; i
>= 0 && i
>= tab
->n_param
; --i
) {
1465 if (tab
->var
[i
].is_row
)
1467 col
= tab
->var
[i
].index
;
1468 if (col
<= tab
->n_dead
)
1470 if (!isl_int_is_zero(tab
->mat
->row
[row
][off
+ col
]))
1473 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
1474 if (isl_int_is_one(tab
->mat
->row
[row
][off
+ i
]))
1476 if (isl_int_is_negone(tab
->mat
->row
[row
][off
+ i
]))
1482 /* Add an equality that is known to be valid to the tableau.
1483 * We first check if we can eliminate a variable or a parameter.
1484 * If not, we add the equality as two inequalities.
1485 * In this case, the equality was a pure parameter equality and there
1486 * is no need to resolve any constraint violations.
1488 * This function assumes that at least two more rows and at least
1489 * two more elements in the constraint array are available in the tableau.
1491 static struct isl_tab
*add_lexmin_valid_eq(struct isl_tab
*tab
, isl_int
*eq
)
1498 r
= isl_tab_add_row(tab
, eq
);
1502 r
= tab
->con
[r
].index
;
1503 i
= last_var_col_or_int_par_col(tab
, r
);
1505 tab
->con
[r
].is_nonneg
= 1;
1506 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]) < 0)
1508 isl_seq_neg(eq
, eq
, 1 + tab
->n_var
);
1509 r
= isl_tab_add_row(tab
, eq
);
1512 tab
->con
[r
].is_nonneg
= 1;
1513 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]) < 0)
1516 if (isl_tab_pivot(tab
, r
, i
) < 0)
1518 if (isl_tab_kill_col(tab
, i
) < 0)
1529 /* Check if the given row is a pure constant.
1531 static int is_constant(struct isl_tab
*tab
, int row
)
1533 unsigned off
= 2 + tab
->M
;
1535 return isl_seq_first_non_zero(tab
->mat
->row
[row
] + off
+ tab
->n_dead
,
1536 tab
->n_col
- tab
->n_dead
) == -1;
1539 /* Add an equality that may or may not be valid to the tableau.
1540 * If the resulting row is a pure constant, then it must be zero.
1541 * Otherwise, the resulting tableau is empty.
1543 * If the row is not a pure constant, then we add two inequalities,
1544 * each time checking that they can be satisfied.
1545 * In the end we try to use one of the two constraints to eliminate
1548 * This function assumes that at least two more rows and at least
1549 * two more elements in the constraint array are available in the tableau.
1551 static int add_lexmin_eq(struct isl_tab
*tab
, isl_int
*eq
) WARN_UNUSED
;
1552 static int add_lexmin_eq(struct isl_tab
*tab
, isl_int
*eq
)
1556 struct isl_tab_undo
*snap
;
1560 snap
= isl_tab_snap(tab
);
1561 r1
= isl_tab_add_row(tab
, eq
);
1564 tab
->con
[r1
].is_nonneg
= 1;
1565 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r1
]) < 0)
1568 row
= tab
->con
[r1
].index
;
1569 if (is_constant(tab
, row
)) {
1570 if (!isl_int_is_zero(tab
->mat
->row
[row
][1]) ||
1571 (tab
->M
&& !isl_int_is_zero(tab
->mat
->row
[row
][2]))) {
1572 if (isl_tab_mark_empty(tab
) < 0)
1576 if (isl_tab_rollback(tab
, snap
) < 0)
1581 if (restore_lexmin(tab
) < 0)
1586 isl_seq_neg(eq
, eq
, 1 + tab
->n_var
);
1588 r2
= isl_tab_add_row(tab
, eq
);
1591 tab
->con
[r2
].is_nonneg
= 1;
1592 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r2
]) < 0)
1595 if (restore_lexmin(tab
) < 0)
1600 if (!tab
->con
[r1
].is_row
) {
1601 if (isl_tab_kill_col(tab
, tab
->con
[r1
].index
) < 0)
1603 } else if (!tab
->con
[r2
].is_row
) {
1604 if (isl_tab_kill_col(tab
, tab
->con
[r2
].index
) < 0)
1609 tab
->bmap
= isl_basic_map_add_ineq(tab
->bmap
, eq
);
1610 if (isl_tab_push(tab
, isl_tab_undo_bmap_ineq
) < 0)
1612 isl_seq_neg(eq
, eq
, 1 + tab
->n_var
);
1613 tab
->bmap
= isl_basic_map_add_ineq(tab
->bmap
, eq
);
1614 isl_seq_neg(eq
, eq
, 1 + tab
->n_var
);
1615 if (isl_tab_push(tab
, isl_tab_undo_bmap_ineq
) < 0)
1624 /* Add an inequality to the tableau, resolving violations using
1627 * This function assumes that at least one more row and at least
1628 * one more element in the constraint array are available in the tableau.
1630 static struct isl_tab
*add_lexmin_ineq(struct isl_tab
*tab
, isl_int
*ineq
)
1637 tab
->bmap
= isl_basic_map_add_ineq(tab
->bmap
, ineq
);
1638 if (isl_tab_push(tab
, isl_tab_undo_bmap_ineq
) < 0)
1643 r
= isl_tab_add_row(tab
, ineq
);
1646 tab
->con
[r
].is_nonneg
= 1;
1647 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]) < 0)
1649 if (isl_tab_row_is_redundant(tab
, tab
->con
[r
].index
)) {
1650 if (isl_tab_mark_redundant(tab
, tab
->con
[r
].index
) < 0)
1655 if (restore_lexmin(tab
) < 0)
1657 if (!tab
->empty
&& tab
->con
[r
].is_row
&&
1658 isl_tab_row_is_redundant(tab
, tab
->con
[r
].index
))
1659 if (isl_tab_mark_redundant(tab
, tab
->con
[r
].index
) < 0)
1667 /* Check if the coefficients of the parameters are all integral.
1669 static int integer_parameter(struct isl_tab
*tab
, int row
)
1673 unsigned off
= 2 + tab
->M
;
1675 for (i
= 0; i
< tab
->n_param
; ++i
) {
1676 /* Eliminated parameter */
1677 if (tab
->var
[i
].is_row
)
1679 col
= tab
->var
[i
].index
;
1680 if (!isl_int_is_divisible_by(tab
->mat
->row
[row
][off
+ col
],
1681 tab
->mat
->row
[row
][0]))
1684 for (i
= 0; i
< tab
->n_div
; ++i
) {
1685 if (tab
->var
[tab
->n_var
- tab
->n_div
+ i
].is_row
)
1687 col
= tab
->var
[tab
->n_var
- tab
->n_div
+ i
].index
;
1688 if (!isl_int_is_divisible_by(tab
->mat
->row
[row
][off
+ col
],
1689 tab
->mat
->row
[row
][0]))
1695 /* Check if the coefficients of the non-parameter variables are all integral.
1697 static int integer_variable(struct isl_tab
*tab
, int row
)
1700 unsigned off
= 2 + tab
->M
;
1702 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
1703 if (col_is_parameter_var(tab
, i
))
1705 if (!isl_int_is_divisible_by(tab
->mat
->row
[row
][off
+ i
],
1706 tab
->mat
->row
[row
][0]))
1712 /* Check if the constant term is integral.
1714 static int integer_constant(struct isl_tab
*tab
, int row
)
1716 return isl_int_is_divisible_by(tab
->mat
->row
[row
][1],
1717 tab
->mat
->row
[row
][0]);
1720 #define I_CST 1 << 0
1721 #define I_PAR 1 << 1
1722 #define I_VAR 1 << 2
1724 /* Check for next (non-parameter) variable after "var" (first if var == -1)
1725 * that is non-integer and therefore requires a cut and return
1726 * the index of the variable.
1727 * For parametric tableaus, there are three parts in a row,
1728 * the constant, the coefficients of the parameters and the rest.
1729 * For each part, we check whether the coefficients in that part
1730 * are all integral and if so, set the corresponding flag in *f.
1731 * If the constant and the parameter part are integral, then the
1732 * current sample value is integral and no cut is required
1733 * (irrespective of whether the variable part is integral).
1735 static int next_non_integer_var(struct isl_tab
*tab
, int var
, int *f
)
1737 var
= var
< 0 ? tab
->n_param
: var
+ 1;
1739 for (; var
< tab
->n_var
- tab
->n_div
; ++var
) {
1742 if (!tab
->var
[var
].is_row
)
1744 row
= tab
->var
[var
].index
;
1745 if (integer_constant(tab
, row
))
1746 ISL_FL_SET(flags
, I_CST
);
1747 if (integer_parameter(tab
, row
))
1748 ISL_FL_SET(flags
, I_PAR
);
1749 if (ISL_FL_ISSET(flags
, I_CST
) && ISL_FL_ISSET(flags
, I_PAR
))
1751 if (integer_variable(tab
, row
))
1752 ISL_FL_SET(flags
, I_VAR
);
1759 /* Check for first (non-parameter) variable that is non-integer and
1760 * therefore requires a cut and return the corresponding row.
1761 * For parametric tableaus, there are three parts in a row,
1762 * the constant, the coefficients of the parameters and the rest.
1763 * For each part, we check whether the coefficients in that part
1764 * are all integral and if so, set the corresponding flag in *f.
1765 * If the constant and the parameter part are integral, then the
1766 * current sample value is integral and no cut is required
1767 * (irrespective of whether the variable part is integral).
1769 static int first_non_integer_row(struct isl_tab
*tab
, int *f
)
1771 int var
= next_non_integer_var(tab
, -1, f
);
1773 return var
< 0 ? -1 : tab
->var
[var
].index
;
1776 /* Add a (non-parametric) cut to cut away the non-integral sample
1777 * value of the given row.
1779 * If the row is given by
1781 * m r = f + \sum_i a_i y_i
1785 * c = - {-f/m} + \sum_i {a_i/m} y_i >= 0
1787 * The big parameter, if any, is ignored, since it is assumed to be big
1788 * enough to be divisible by any integer.
1789 * If the tableau is actually a parametric tableau, then this function
1790 * is only called when all coefficients of the parameters are integral.
1791 * The cut therefore has zero coefficients for the parameters.
1793 * The current value is known to be negative, so row_sign, if it
1794 * exists, is set accordingly.
1796 * Return the row of the cut or -1.
1798 static int add_cut(struct isl_tab
*tab
, int row
)
1803 unsigned off
= 2 + tab
->M
;
1805 if (isl_tab_extend_cons(tab
, 1) < 0)
1807 r
= isl_tab_allocate_con(tab
);
1811 r_row
= tab
->mat
->row
[tab
->con
[r
].index
];
1812 isl_int_set(r_row
[0], tab
->mat
->row
[row
][0]);
1813 isl_int_neg(r_row
[1], tab
->mat
->row
[row
][1]);
1814 isl_int_fdiv_r(r_row
[1], r_row
[1], tab
->mat
->row
[row
][0]);
1815 isl_int_neg(r_row
[1], r_row
[1]);
1817 isl_int_set_si(r_row
[2], 0);
1818 for (i
= 0; i
< tab
->n_col
; ++i
)
1819 isl_int_fdiv_r(r_row
[off
+ i
],
1820 tab
->mat
->row
[row
][off
+ i
], tab
->mat
->row
[row
][0]);
1822 tab
->con
[r
].is_nonneg
= 1;
1823 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]) < 0)
1826 tab
->row_sign
[tab
->con
[r
].index
] = isl_tab_row_neg
;
1828 return tab
->con
[r
].index
;
1834 /* Given a non-parametric tableau, add cuts until an integer
1835 * sample point is obtained or until the tableau is determined
1836 * to be integer infeasible.
1837 * As long as there is any non-integer value in the sample point,
1838 * we add appropriate cuts, if possible, for each of these
1839 * non-integer values and then resolve the violated
1840 * cut constraints using restore_lexmin.
1841 * If one of the corresponding rows is equal to an integral
1842 * combination of variables/constraints plus a non-integral constant,
1843 * then there is no way to obtain an integer point and we return
1844 * a tableau that is marked empty.
1845 * The parameter cutting_strategy controls the strategy used when adding cuts
1846 * to remove non-integer points. CUT_ALL adds all possible cuts
1847 * before continuing the search. CUT_ONE adds only one cut at a time.
1849 static struct isl_tab
*cut_to_integer_lexmin(struct isl_tab
*tab
,
1850 int cutting_strategy
)
1861 while ((var
= next_non_integer_var(tab
, -1, &flags
)) != -1) {
1863 if (ISL_FL_ISSET(flags
, I_VAR
)) {
1864 if (isl_tab_mark_empty(tab
) < 0)
1868 row
= tab
->var
[var
].index
;
1869 row
= add_cut(tab
, row
);
1872 if (cutting_strategy
== CUT_ONE
)
1874 } while ((var
= next_non_integer_var(tab
, var
, &flags
)) != -1);
1875 if (restore_lexmin(tab
) < 0)
1886 /* Check whether all the currently active samples also satisfy the inequality
1887 * "ineq" (treated as an equality if eq is set).
1888 * Remove those samples that do not.
1890 static struct isl_tab
*check_samples(struct isl_tab
*tab
, isl_int
*ineq
, int eq
)
1898 isl_assert(tab
->mat
->ctx
, tab
->bmap
, goto error
);
1899 isl_assert(tab
->mat
->ctx
, tab
->samples
, goto error
);
1900 isl_assert(tab
->mat
->ctx
, tab
->samples
->n_col
== 1 + tab
->n_var
, goto error
);
1903 for (i
= tab
->n_outside
; i
< tab
->n_sample
; ++i
) {
1905 isl_seq_inner_product(ineq
, tab
->samples
->row
[i
],
1906 1 + tab
->n_var
, &v
);
1907 sgn
= isl_int_sgn(v
);
1908 if (eq
? (sgn
== 0) : (sgn
>= 0))
1910 tab
= isl_tab_drop_sample(tab
, i
);
1922 /* Check whether the sample value of the tableau is finite,
1923 * i.e., either the tableau does not use a big parameter, or
1924 * all values of the variables are equal to the big parameter plus
1925 * some constant. This constant is the actual sample value.
1927 static int sample_is_finite(struct isl_tab
*tab
)
1934 for (i
= 0; i
< tab
->n_var
; ++i
) {
1936 if (!tab
->var
[i
].is_row
)
1938 row
= tab
->var
[i
].index
;
1939 if (isl_int_ne(tab
->mat
->row
[row
][0], tab
->mat
->row
[row
][2]))
1945 /* Check if the context tableau of sol has any integer points.
1946 * Leave tab in empty state if no integer point can be found.
1947 * If an integer point can be found and if moreover it is finite,
1948 * then it is added to the list of sample values.
1950 * This function is only called when none of the currently active sample
1951 * values satisfies the most recently added constraint.
1953 static struct isl_tab
*check_integer_feasible(struct isl_tab
*tab
)
1955 struct isl_tab_undo
*snap
;
1960 snap
= isl_tab_snap(tab
);
1961 if (isl_tab_push_basis(tab
) < 0)
1964 tab
= cut_to_integer_lexmin(tab
, CUT_ALL
);
1968 if (!tab
->empty
&& sample_is_finite(tab
)) {
1969 struct isl_vec
*sample
;
1971 sample
= isl_tab_get_sample_value(tab
);
1973 if (isl_tab_add_sample(tab
, sample
) < 0)
1977 if (!tab
->empty
&& isl_tab_rollback(tab
, snap
) < 0)
1986 /* Check if any of the currently active sample values satisfies
1987 * the inequality "ineq" (an equality if eq is set).
1989 static int tab_has_valid_sample(struct isl_tab
*tab
, isl_int
*ineq
, int eq
)
1997 isl_assert(tab
->mat
->ctx
, tab
->bmap
, return -1);
1998 isl_assert(tab
->mat
->ctx
, tab
->samples
, return -1);
1999 isl_assert(tab
->mat
->ctx
, tab
->samples
->n_col
== 1 + tab
->n_var
, return -1);
2002 for (i
= tab
->n_outside
; i
< tab
->n_sample
; ++i
) {
2004 isl_seq_inner_product(ineq
, tab
->samples
->row
[i
],
2005 1 + tab
->n_var
, &v
);
2006 sgn
= isl_int_sgn(v
);
2007 if (eq
? (sgn
== 0) : (sgn
>= 0))
2012 return i
< tab
->n_sample
;
2015 /* Insert a div specified by "div" to the tableau "tab" at position "pos" and
2016 * return isl_bool_true if the div is obviously non-negative.
2018 static isl_bool
context_tab_insert_div(struct isl_tab
*tab
, int pos
,
2019 __isl_keep isl_vec
*div
,
2020 isl_stat (*add_ineq
)(void *user
, isl_int
*), void *user
)
2024 struct isl_mat
*samples
;
2027 r
= isl_tab_insert_div(tab
, pos
, div
, add_ineq
, user
);
2029 return isl_bool_error
;
2030 nonneg
= tab
->var
[r
].is_nonneg
;
2031 tab
->var
[r
].frozen
= 1;
2033 samples
= isl_mat_extend(tab
->samples
,
2034 tab
->n_sample
, 1 + tab
->n_var
);
2035 tab
->samples
= samples
;
2037 return isl_bool_error
;
2038 for (i
= tab
->n_outside
; i
< samples
->n_row
; ++i
) {
2039 isl_seq_inner_product(div
->el
+ 1, samples
->row
[i
],
2040 div
->size
- 1, &samples
->row
[i
][samples
->n_col
- 1]);
2041 isl_int_fdiv_q(samples
->row
[i
][samples
->n_col
- 1],
2042 samples
->row
[i
][samples
->n_col
- 1], div
->el
[0]);
2044 tab
->samples
= isl_mat_move_cols(tab
->samples
, 1 + pos
,
2045 1 + tab
->n_var
- 1, 1);
2047 return isl_bool_error
;
2052 /* Add a div specified by "div" to both the main tableau and
2053 * the context tableau. In case of the main tableau, we only
2054 * need to add an extra div. In the context tableau, we also
2055 * need to express the meaning of the div.
2056 * Return the index of the div or -1 if anything went wrong.
2058 * The new integer division is added before any unknown integer
2059 * divisions in the context to ensure that it does not get
2060 * equated to some linear combination involving unknown integer
2063 static int add_div(struct isl_tab
*tab
, struct isl_context
*context
,
2064 __isl_keep isl_vec
*div
)
2069 struct isl_tab
*context_tab
= context
->op
->peek_tab(context
);
2071 if (!tab
|| !context_tab
)
2074 pos
= context_tab
->n_var
- context
->n_unknown
;
2075 if ((nonneg
= context
->op
->insert_div(context
, pos
, div
)) < 0)
2078 if (!context
->op
->is_ok(context
))
2081 pos
= tab
->n_var
- context
->n_unknown
;
2082 if (isl_tab_extend_vars(tab
, 1) < 0)
2084 r
= isl_tab_insert_var(tab
, pos
);
2088 tab
->var
[r
].is_nonneg
= 1;
2089 tab
->var
[r
].frozen
= 1;
2092 return tab
->n_div
- 1 - context
->n_unknown
;
2094 context
->op
->invalidate(context
);
2098 static int find_div(struct isl_tab
*tab
, isl_int
*div
, isl_int denom
)
2101 unsigned total
= isl_basic_map_total_dim(tab
->bmap
);
2103 for (i
= 0; i
< tab
->bmap
->n_div
; ++i
) {
2104 if (isl_int_ne(tab
->bmap
->div
[i
][0], denom
))
2106 if (!isl_seq_eq(tab
->bmap
->div
[i
] + 1, div
, 1 + total
))
2113 /* Return the index of a div that corresponds to "div".
2114 * We first check if we already have such a div and if not, we create one.
2116 static int get_div(struct isl_tab
*tab
, struct isl_context
*context
,
2117 struct isl_vec
*div
)
2120 struct isl_tab
*context_tab
= context
->op
->peek_tab(context
);
2125 d
= find_div(context_tab
, div
->el
+ 1, div
->el
[0]);
2129 return add_div(tab
, context
, div
);
2132 /* Add a parametric cut to cut away the non-integral sample value
2134 * Let a_i be the coefficients of the constant term and the parameters
2135 * and let b_i be the coefficients of the variables or constraints
2136 * in basis of the tableau.
2137 * Let q be the div q = floor(\sum_i {-a_i} y_i).
2139 * The cut is expressed as
2141 * c = \sum_i -{-a_i} y_i + \sum_i {b_i} x_i + q >= 0
2143 * If q did not already exist in the context tableau, then it is added first.
2144 * If q is in a column of the main tableau then the "+ q" can be accomplished
2145 * by setting the corresponding entry to the denominator of the constraint.
2146 * If q happens to be in a row of the main tableau, then the corresponding
2147 * row needs to be added instead (taking care of the denominators).
2148 * Note that this is very unlikely, but perhaps not entirely impossible.
2150 * The current value of the cut is known to be negative (or at least
2151 * non-positive), so row_sign is set accordingly.
2153 * Return the row of the cut or -1.
2155 static int add_parametric_cut(struct isl_tab
*tab
, int row
,
2156 struct isl_context
*context
)
2158 struct isl_vec
*div
;
2165 unsigned off
= 2 + tab
->M
;
2170 div
= get_row_parameter_div(tab
, row
);
2174 n
= tab
->n_div
- context
->n_unknown
;
2175 d
= context
->op
->get_div(context
, tab
, div
);
2180 if (isl_tab_extend_cons(tab
, 1) < 0)
2182 r
= isl_tab_allocate_con(tab
);
2186 r_row
= tab
->mat
->row
[tab
->con
[r
].index
];
2187 isl_int_set(r_row
[0], tab
->mat
->row
[row
][0]);
2188 isl_int_neg(r_row
[1], tab
->mat
->row
[row
][1]);
2189 isl_int_fdiv_r(r_row
[1], r_row
[1], tab
->mat
->row
[row
][0]);
2190 isl_int_neg(r_row
[1], r_row
[1]);
2192 isl_int_set_si(r_row
[2], 0);
2193 for (i
= 0; i
< tab
->n_param
; ++i
) {
2194 if (tab
->var
[i
].is_row
)
2196 col
= tab
->var
[i
].index
;
2197 isl_int_neg(r_row
[off
+ col
], tab
->mat
->row
[row
][off
+ col
]);
2198 isl_int_fdiv_r(r_row
[off
+ col
], r_row
[off
+ col
],
2199 tab
->mat
->row
[row
][0]);
2200 isl_int_neg(r_row
[off
+ col
], r_row
[off
+ col
]);
2202 for (i
= 0; i
< tab
->n_div
; ++i
) {
2203 if (tab
->var
[tab
->n_var
- tab
->n_div
+ i
].is_row
)
2205 col
= tab
->var
[tab
->n_var
- tab
->n_div
+ i
].index
;
2206 isl_int_neg(r_row
[off
+ col
], tab
->mat
->row
[row
][off
+ col
]);
2207 isl_int_fdiv_r(r_row
[off
+ col
], r_row
[off
+ col
],
2208 tab
->mat
->row
[row
][0]);
2209 isl_int_neg(r_row
[off
+ col
], r_row
[off
+ col
]);
2211 for (i
= 0; i
< tab
->n_col
; ++i
) {
2212 if (tab
->col_var
[i
] >= 0 &&
2213 (tab
->col_var
[i
] < tab
->n_param
||
2214 tab
->col_var
[i
] >= tab
->n_var
- tab
->n_div
))
2216 isl_int_fdiv_r(r_row
[off
+ i
],
2217 tab
->mat
->row
[row
][off
+ i
], tab
->mat
->row
[row
][0]);
2219 if (tab
->var
[tab
->n_var
- tab
->n_div
+ d
].is_row
) {
2221 int d_row
= tab
->var
[tab
->n_var
- tab
->n_div
+ d
].index
;
2223 isl_int_gcd(gcd
, tab
->mat
->row
[d_row
][0], r_row
[0]);
2224 isl_int_divexact(r_row
[0], r_row
[0], gcd
);
2225 isl_int_divexact(gcd
, tab
->mat
->row
[d_row
][0], gcd
);
2226 isl_seq_combine(r_row
+ 1, gcd
, r_row
+ 1,
2227 r_row
[0], tab
->mat
->row
[d_row
] + 1,
2228 off
- 1 + tab
->n_col
);
2229 isl_int_mul(r_row
[0], r_row
[0], tab
->mat
->row
[d_row
][0]);
2232 col
= tab
->var
[tab
->n_var
- tab
->n_div
+ d
].index
;
2233 isl_int_set(r_row
[off
+ col
], tab
->mat
->row
[row
][0]);
2236 tab
->con
[r
].is_nonneg
= 1;
2237 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]) < 0)
2240 tab
->row_sign
[tab
->con
[r
].index
] = isl_tab_row_neg
;
2242 row
= tab
->con
[r
].index
;
2244 if (d
>= n
&& context
->op
->detect_equalities(context
, tab
) < 0)
2250 /* Construct a tableau for bmap that can be used for computing
2251 * the lexicographic minimum (or maximum) of bmap.
2252 * If not NULL, then dom is the domain where the minimum
2253 * should be computed. In this case, we set up a parametric
2254 * tableau with row signs (initialized to "unknown").
2255 * If M is set, then the tableau will use a big parameter.
2256 * If max is set, then a maximum should be computed instead of a minimum.
2257 * This means that for each variable x, the tableau will contain the variable
2258 * x' = M - x, rather than x' = M + x. This in turn means that the coefficient
2259 * of the variables in all constraints are negated prior to adding them
2262 static __isl_give
struct isl_tab
*tab_for_lexmin(__isl_keep isl_basic_map
*bmap
,
2263 __isl_keep isl_basic_set
*dom
, unsigned M
, int max
)
2266 struct isl_tab
*tab
;
2270 tab
= isl_tab_alloc(bmap
->ctx
, 2 * bmap
->n_eq
+ bmap
->n_ineq
+ 1,
2271 isl_basic_map_total_dim(bmap
), M
);
2275 tab
->rational
= ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
);
2277 tab
->n_param
= isl_basic_set_total_dim(dom
) - dom
->n_div
;
2278 tab
->n_div
= dom
->n_div
;
2279 tab
->row_sign
= isl_calloc_array(bmap
->ctx
,
2280 enum isl_tab_row_sign
, tab
->mat
->n_row
);
2281 if (tab
->mat
->n_row
&& !tab
->row_sign
)
2284 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
)) {
2285 if (isl_tab_mark_empty(tab
) < 0)
2290 for (i
= tab
->n_param
; i
< tab
->n_var
- tab
->n_div
; ++i
) {
2291 tab
->var
[i
].is_nonneg
= 1;
2292 tab
->var
[i
].frozen
= 1;
2294 o_var
= 1 + tab
->n_param
;
2295 n_var
= tab
->n_var
- tab
->n_param
- tab
->n_div
;
2296 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
2298 isl_seq_neg(bmap
->eq
[i
] + o_var
,
2299 bmap
->eq
[i
] + o_var
, n_var
);
2300 tab
= add_lexmin_valid_eq(tab
, bmap
->eq
[i
]);
2302 isl_seq_neg(bmap
->eq
[i
] + o_var
,
2303 bmap
->eq
[i
] + o_var
, n_var
);
2304 if (!tab
|| tab
->empty
)
2307 if (bmap
->n_eq
&& restore_lexmin(tab
) < 0)
2309 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
2311 isl_seq_neg(bmap
->ineq
[i
] + o_var
,
2312 bmap
->ineq
[i
] + o_var
, n_var
);
2313 tab
= add_lexmin_ineq(tab
, bmap
->ineq
[i
]);
2315 isl_seq_neg(bmap
->ineq
[i
] + o_var
,
2316 bmap
->ineq
[i
] + o_var
, n_var
);
2317 if (!tab
|| tab
->empty
)
2326 /* Given a main tableau where more than one row requires a split,
2327 * determine and return the "best" row to split on.
2329 * Given two rows in the main tableau, if the inequality corresponding
2330 * to the first row is redundant with respect to that of the second row
2331 * in the current tableau, then it is better to split on the second row,
2332 * since in the positive part, both rows will be positive.
2333 * (In the negative part a pivot will have to be performed and just about
2334 * anything can happen to the sign of the other row.)
2336 * As a simple heuristic, we therefore select the row that makes the most
2337 * of the other rows redundant.
2339 * Perhaps it would also be useful to look at the number of constraints
2340 * that conflict with any given constraint.
2342 * best is the best row so far (-1 when we have not found any row yet).
2343 * best_r is the number of other rows made redundant by row best.
2344 * When best is still -1, bset_r is meaningless, but it is initialized
2345 * to some arbitrary value (0) anyway. Without this redundant initialization
2346 * valgrind may warn about uninitialized memory accesses when isl
2347 * is compiled with some versions of gcc.
2349 static int best_split(struct isl_tab
*tab
, struct isl_tab
*context_tab
)
2351 struct isl_tab_undo
*snap
;
2357 if (isl_tab_extend_cons(context_tab
, 2) < 0)
2360 snap
= isl_tab_snap(context_tab
);
2362 for (split
= tab
->n_redundant
; split
< tab
->n_row
; ++split
) {
2363 struct isl_tab_undo
*snap2
;
2364 struct isl_vec
*ineq
= NULL
;
2368 if (!isl_tab_var_from_row(tab
, split
)->is_nonneg
)
2370 if (tab
->row_sign
[split
] != isl_tab_row_any
)
2373 ineq
= get_row_parameter_ineq(tab
, split
);
2376 ok
= isl_tab_add_ineq(context_tab
, ineq
->el
) >= 0;
2381 snap2
= isl_tab_snap(context_tab
);
2383 for (row
= tab
->n_redundant
; row
< tab
->n_row
; ++row
) {
2384 struct isl_tab_var
*var
;
2388 if (!isl_tab_var_from_row(tab
, row
)->is_nonneg
)
2390 if (tab
->row_sign
[row
] != isl_tab_row_any
)
2393 ineq
= get_row_parameter_ineq(tab
, row
);
2396 ok
= isl_tab_add_ineq(context_tab
, ineq
->el
) >= 0;
2400 var
= &context_tab
->con
[context_tab
->n_con
- 1];
2401 if (!context_tab
->empty
&&
2402 !isl_tab_min_at_most_neg_one(context_tab
, var
))
2404 if (isl_tab_rollback(context_tab
, snap2
) < 0)
2407 if (best
== -1 || r
> best_r
) {
2411 if (isl_tab_rollback(context_tab
, snap
) < 0)
2418 static struct isl_basic_set
*context_lex_peek_basic_set(
2419 struct isl_context
*context
)
2421 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2424 return isl_tab_peek_bset(clex
->tab
);
2427 static struct isl_tab
*context_lex_peek_tab(struct isl_context
*context
)
2429 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2433 static void context_lex_add_eq(struct isl_context
*context
, isl_int
*eq
,
2434 int check
, int update
)
2436 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2437 if (isl_tab_extend_cons(clex
->tab
, 2) < 0)
2439 if (add_lexmin_eq(clex
->tab
, eq
) < 0)
2442 int v
= tab_has_valid_sample(clex
->tab
, eq
, 1);
2446 clex
->tab
= check_integer_feasible(clex
->tab
);
2449 clex
->tab
= check_samples(clex
->tab
, eq
, 1);
2452 isl_tab_free(clex
->tab
);
2456 static void context_lex_add_ineq(struct isl_context
*context
, isl_int
*ineq
,
2457 int check
, int update
)
2459 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2460 if (isl_tab_extend_cons(clex
->tab
, 1) < 0)
2462 clex
->tab
= add_lexmin_ineq(clex
->tab
, ineq
);
2464 int v
= tab_has_valid_sample(clex
->tab
, ineq
, 0);
2468 clex
->tab
= check_integer_feasible(clex
->tab
);
2471 clex
->tab
= check_samples(clex
->tab
, ineq
, 0);
2474 isl_tab_free(clex
->tab
);
2478 static isl_stat
context_lex_add_ineq_wrap(void *user
, isl_int
*ineq
)
2480 struct isl_context
*context
= (struct isl_context
*)user
;
2481 context_lex_add_ineq(context
, ineq
, 0, 0);
2482 return context
->op
->is_ok(context
) ? isl_stat_ok
: isl_stat_error
;
2485 /* Check which signs can be obtained by "ineq" on all the currently
2486 * active sample values. See row_sign for more information.
2488 static enum isl_tab_row_sign
tab_ineq_sign(struct isl_tab
*tab
, isl_int
*ineq
,
2494 enum isl_tab_row_sign res
= isl_tab_row_unknown
;
2496 isl_assert(tab
->mat
->ctx
, tab
->samples
, return isl_tab_row_unknown
);
2497 isl_assert(tab
->mat
->ctx
, tab
->samples
->n_col
== 1 + tab
->n_var
,
2498 return isl_tab_row_unknown
);
2501 for (i
= tab
->n_outside
; i
< tab
->n_sample
; ++i
) {
2502 isl_seq_inner_product(tab
->samples
->row
[i
], ineq
,
2503 1 + tab
->n_var
, &tmp
);
2504 sgn
= isl_int_sgn(tmp
);
2505 if (sgn
> 0 || (sgn
== 0 && strict
)) {
2506 if (res
== isl_tab_row_unknown
)
2507 res
= isl_tab_row_pos
;
2508 if (res
== isl_tab_row_neg
)
2509 res
= isl_tab_row_any
;
2512 if (res
== isl_tab_row_unknown
)
2513 res
= isl_tab_row_neg
;
2514 if (res
== isl_tab_row_pos
)
2515 res
= isl_tab_row_any
;
2517 if (res
== isl_tab_row_any
)
2525 static enum isl_tab_row_sign
context_lex_ineq_sign(struct isl_context
*context
,
2526 isl_int
*ineq
, int strict
)
2528 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2529 return tab_ineq_sign(clex
->tab
, ineq
, strict
);
2532 /* Check whether "ineq" can be added to the tableau without rendering
2535 static int context_lex_test_ineq(struct isl_context
*context
, isl_int
*ineq
)
2537 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2538 struct isl_tab_undo
*snap
;
2544 if (isl_tab_extend_cons(clex
->tab
, 1) < 0)
2547 snap
= isl_tab_snap(clex
->tab
);
2548 if (isl_tab_push_basis(clex
->tab
) < 0)
2550 clex
->tab
= add_lexmin_ineq(clex
->tab
, ineq
);
2551 clex
->tab
= check_integer_feasible(clex
->tab
);
2554 feasible
= !clex
->tab
->empty
;
2555 if (isl_tab_rollback(clex
->tab
, snap
) < 0)
2561 static int context_lex_get_div(struct isl_context
*context
, struct isl_tab
*tab
,
2562 struct isl_vec
*div
)
2564 return get_div(tab
, context
, div
);
2567 /* Insert a div specified by "div" to the context tableau at position "pos" and
2568 * return isl_bool_true if the div is obviously non-negative.
2569 * context_tab_add_div will always return isl_bool_true, because all variables
2570 * in a isl_context_lex tableau are non-negative.
2571 * However, if we are using a big parameter in the context, then this only
2572 * reflects the non-negativity of the variable used to _encode_ the
2573 * div, i.e., div' = M + div, so we can't draw any conclusions.
2575 static isl_bool
context_lex_insert_div(struct isl_context
*context
, int pos
,
2576 __isl_keep isl_vec
*div
)
2578 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2580 nonneg
= context_tab_insert_div(clex
->tab
, pos
, div
,
2581 context_lex_add_ineq_wrap
, context
);
2583 return isl_bool_error
;
2585 return isl_bool_false
;
2589 static int context_lex_detect_equalities(struct isl_context
*context
,
2590 struct isl_tab
*tab
)
2595 static int context_lex_best_split(struct isl_context
*context
,
2596 struct isl_tab
*tab
)
2598 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2599 struct isl_tab_undo
*snap
;
2602 snap
= isl_tab_snap(clex
->tab
);
2603 if (isl_tab_push_basis(clex
->tab
) < 0)
2605 r
= best_split(tab
, clex
->tab
);
2607 if (r
>= 0 && isl_tab_rollback(clex
->tab
, snap
) < 0)
2613 static int context_lex_is_empty(struct isl_context
*context
)
2615 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2618 return clex
->tab
->empty
;
2621 static void *context_lex_save(struct isl_context
*context
)
2623 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2624 struct isl_tab_undo
*snap
;
2626 snap
= isl_tab_snap(clex
->tab
);
2627 if (isl_tab_push_basis(clex
->tab
) < 0)
2629 if (isl_tab_save_samples(clex
->tab
) < 0)
2635 static void context_lex_restore(struct isl_context
*context
, void *save
)
2637 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2638 if (isl_tab_rollback(clex
->tab
, (struct isl_tab_undo
*)save
) < 0) {
2639 isl_tab_free(clex
->tab
);
2644 static void context_lex_discard(void *save
)
2648 static int context_lex_is_ok(struct isl_context
*context
)
2650 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2654 /* For each variable in the context tableau, check if the variable can
2655 * only attain non-negative values. If so, mark the parameter as non-negative
2656 * in the main tableau. This allows for a more direct identification of some
2657 * cases of violated constraints.
2659 static struct isl_tab
*tab_detect_nonnegative_parameters(struct isl_tab
*tab
,
2660 struct isl_tab
*context_tab
)
2663 struct isl_tab_undo
*snap
;
2664 struct isl_vec
*ineq
= NULL
;
2665 struct isl_tab_var
*var
;
2668 if (context_tab
->n_var
== 0)
2671 ineq
= isl_vec_alloc(tab
->mat
->ctx
, 1 + context_tab
->n_var
);
2675 if (isl_tab_extend_cons(context_tab
, 1) < 0)
2678 snap
= isl_tab_snap(context_tab
);
2681 isl_seq_clr(ineq
->el
, ineq
->size
);
2682 for (i
= 0; i
< context_tab
->n_var
; ++i
) {
2683 isl_int_set_si(ineq
->el
[1 + i
], 1);
2684 if (isl_tab_add_ineq(context_tab
, ineq
->el
) < 0)
2686 var
= &context_tab
->con
[context_tab
->n_con
- 1];
2687 if (!context_tab
->empty
&&
2688 !isl_tab_min_at_most_neg_one(context_tab
, var
)) {
2690 if (i
>= tab
->n_param
)
2691 j
= i
- tab
->n_param
+ tab
->n_var
- tab
->n_div
;
2692 tab
->var
[j
].is_nonneg
= 1;
2695 isl_int_set_si(ineq
->el
[1 + i
], 0);
2696 if (isl_tab_rollback(context_tab
, snap
) < 0)
2700 if (context_tab
->M
&& n
== context_tab
->n_var
) {
2701 context_tab
->mat
= isl_mat_drop_cols(context_tab
->mat
, 2, 1);
2713 static struct isl_tab
*context_lex_detect_nonnegative_parameters(
2714 struct isl_context
*context
, struct isl_tab
*tab
)
2716 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2717 struct isl_tab_undo
*snap
;
2722 snap
= isl_tab_snap(clex
->tab
);
2723 if (isl_tab_push_basis(clex
->tab
) < 0)
2726 tab
= tab_detect_nonnegative_parameters(tab
, clex
->tab
);
2728 if (isl_tab_rollback(clex
->tab
, snap
) < 0)
2737 static void context_lex_invalidate(struct isl_context
*context
)
2739 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2740 isl_tab_free(clex
->tab
);
2744 static __isl_null
struct isl_context
*context_lex_free(
2745 struct isl_context
*context
)
2747 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2748 isl_tab_free(clex
->tab
);
2754 struct isl_context_op isl_context_lex_op
= {
2755 context_lex_detect_nonnegative_parameters
,
2756 context_lex_peek_basic_set
,
2757 context_lex_peek_tab
,
2759 context_lex_add_ineq
,
2760 context_lex_ineq_sign
,
2761 context_lex_test_ineq
,
2762 context_lex_get_div
,
2763 context_lex_insert_div
,
2764 context_lex_detect_equalities
,
2765 context_lex_best_split
,
2766 context_lex_is_empty
,
2769 context_lex_restore
,
2770 context_lex_discard
,
2771 context_lex_invalidate
,
2775 static struct isl_tab
*context_tab_for_lexmin(__isl_take isl_basic_set
*bset
)
2777 struct isl_tab
*tab
;
2781 tab
= tab_for_lexmin(bset_to_bmap(bset
), NULL
, 1, 0);
2782 if (isl_tab_track_bset(tab
, bset
) < 0)
2784 tab
= isl_tab_init_samples(tab
);
2791 static struct isl_context
*isl_context_lex_alloc(struct isl_basic_set
*dom
)
2793 struct isl_context_lex
*clex
;
2798 clex
= isl_alloc_type(dom
->ctx
, struct isl_context_lex
);
2802 clex
->context
.op
= &isl_context_lex_op
;
2804 clex
->tab
= context_tab_for_lexmin(isl_basic_set_copy(dom
));
2805 if (restore_lexmin(clex
->tab
) < 0)
2807 clex
->tab
= check_integer_feasible(clex
->tab
);
2811 return &clex
->context
;
2813 clex
->context
.op
->free(&clex
->context
);
2817 /* Representation of the context when using generalized basis reduction.
2819 * "shifted" contains the offsets of the unit hypercubes that lie inside the
2820 * context. Any rational point in "shifted" can therefore be rounded
2821 * up to an integer point in the context.
2822 * If the context is constrained by any equality, then "shifted" is not used
2823 * as it would be empty.
2825 struct isl_context_gbr
{
2826 struct isl_context context
;
2827 struct isl_tab
*tab
;
2828 struct isl_tab
*shifted
;
2829 struct isl_tab
*cone
;
2832 static struct isl_tab
*context_gbr_detect_nonnegative_parameters(
2833 struct isl_context
*context
, struct isl_tab
*tab
)
2835 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
2838 return tab_detect_nonnegative_parameters(tab
, cgbr
->tab
);
2841 static struct isl_basic_set
*context_gbr_peek_basic_set(
2842 struct isl_context
*context
)
2844 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
2847 return isl_tab_peek_bset(cgbr
->tab
);
2850 static struct isl_tab
*context_gbr_peek_tab(struct isl_context
*context
)
2852 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
2856 /* Initialize the "shifted" tableau of the context, which
2857 * contains the constraints of the original tableau shifted
2858 * by the sum of all negative coefficients. This ensures
2859 * that any rational point in the shifted tableau can
2860 * be rounded up to yield an integer point in the original tableau.
2862 static void gbr_init_shifted(struct isl_context_gbr
*cgbr
)
2865 struct isl_vec
*cst
;
2866 struct isl_basic_set
*bset
= isl_tab_peek_bset(cgbr
->tab
);
2867 unsigned dim
= isl_basic_set_total_dim(bset
);
2869 cst
= isl_vec_alloc(cgbr
->tab
->mat
->ctx
, bset
->n_ineq
);
2873 for (i
= 0; i
< bset
->n_ineq
; ++i
) {
2874 isl_int_set(cst
->el
[i
], bset
->ineq
[i
][0]);
2875 for (j
= 0; j
< dim
; ++j
) {
2876 if (!isl_int_is_neg(bset
->ineq
[i
][1 + j
]))
2878 isl_int_add(bset
->ineq
[i
][0], bset
->ineq
[i
][0],
2879 bset
->ineq
[i
][1 + j
]);
2883 cgbr
->shifted
= isl_tab_from_basic_set(bset
, 0);
2885 for (i
= 0; i
< bset
->n_ineq
; ++i
)
2886 isl_int_set(bset
->ineq
[i
][0], cst
->el
[i
]);
2891 /* Check if the shifted tableau is non-empty, and if so
2892 * use the sample point to construct an integer point
2893 * of the context tableau.
2895 static struct isl_vec
*gbr_get_shifted_sample(struct isl_context_gbr
*cgbr
)
2897 struct isl_vec
*sample
;
2900 gbr_init_shifted(cgbr
);
2903 if (cgbr
->shifted
->empty
)
2904 return isl_vec_alloc(cgbr
->tab
->mat
->ctx
, 0);
2906 sample
= isl_tab_get_sample_value(cgbr
->shifted
);
2907 sample
= isl_vec_ceil(sample
);
2912 static __isl_give isl_basic_set
*drop_constant_terms(
2913 __isl_take isl_basic_set
*bset
)
2920 for (i
= 0; i
< bset
->n_eq
; ++i
)
2921 isl_int_set_si(bset
->eq
[i
][0], 0);
2923 for (i
= 0; i
< bset
->n_ineq
; ++i
)
2924 isl_int_set_si(bset
->ineq
[i
][0], 0);
2929 static int use_shifted(struct isl_context_gbr
*cgbr
)
2933 return cgbr
->tab
->bmap
->n_eq
== 0 && cgbr
->tab
->bmap
->n_div
== 0;
2936 static struct isl_vec
*gbr_get_sample(struct isl_context_gbr
*cgbr
)
2938 struct isl_basic_set
*bset
;
2939 struct isl_basic_set
*cone
;
2941 if (isl_tab_sample_is_integer(cgbr
->tab
))
2942 return isl_tab_get_sample_value(cgbr
->tab
);
2944 if (use_shifted(cgbr
)) {
2945 struct isl_vec
*sample
;
2947 sample
= gbr_get_shifted_sample(cgbr
);
2948 if (!sample
|| sample
->size
> 0)
2951 isl_vec_free(sample
);
2955 bset
= isl_tab_peek_bset(cgbr
->tab
);
2956 cgbr
->cone
= isl_tab_from_recession_cone(bset
, 0);
2959 if (isl_tab_track_bset(cgbr
->cone
,
2960 isl_basic_set_copy(bset
)) < 0)
2963 if (isl_tab_detect_implicit_equalities(cgbr
->cone
) < 0)
2966 if (cgbr
->cone
->n_dead
== cgbr
->cone
->n_col
) {
2967 struct isl_vec
*sample
;
2968 struct isl_tab_undo
*snap
;
2970 if (cgbr
->tab
->basis
) {
2971 if (cgbr
->tab
->basis
->n_col
!= 1 + cgbr
->tab
->n_var
) {
2972 isl_mat_free(cgbr
->tab
->basis
);
2973 cgbr
->tab
->basis
= NULL
;
2975 cgbr
->tab
->n_zero
= 0;
2976 cgbr
->tab
->n_unbounded
= 0;
2979 snap
= isl_tab_snap(cgbr
->tab
);
2981 sample
= isl_tab_sample(cgbr
->tab
);
2983 if (!sample
|| isl_tab_rollback(cgbr
->tab
, snap
) < 0) {
2984 isl_vec_free(sample
);
2991 cone
= isl_basic_set_dup(isl_tab_peek_bset(cgbr
->cone
));
2992 cone
= drop_constant_terms(cone
);
2993 cone
= isl_basic_set_update_from_tab(cone
, cgbr
->cone
);
2994 cone
= isl_basic_set_underlying_set(cone
);
2995 cone
= isl_basic_set_gauss(cone
, NULL
);
2997 bset
= isl_basic_set_dup(isl_tab_peek_bset(cgbr
->tab
));
2998 bset
= isl_basic_set_update_from_tab(bset
, cgbr
->tab
);
2999 bset
= isl_basic_set_underlying_set(bset
);
3000 bset
= isl_basic_set_gauss(bset
, NULL
);
3002 return isl_basic_set_sample_with_cone(bset
, cone
);
3005 static void check_gbr_integer_feasible(struct isl_context_gbr
*cgbr
)
3007 struct isl_vec
*sample
;
3012 if (cgbr
->tab
->empty
)
3015 sample
= gbr_get_sample(cgbr
);
3019 if (sample
->size
== 0) {
3020 isl_vec_free(sample
);
3021 if (isl_tab_mark_empty(cgbr
->tab
) < 0)
3026 if (isl_tab_add_sample(cgbr
->tab
, sample
) < 0)
3031 isl_tab_free(cgbr
->tab
);
3035 static struct isl_tab
*add_gbr_eq(struct isl_tab
*tab
, isl_int
*eq
)
3040 if (isl_tab_extend_cons(tab
, 2) < 0)
3043 if (isl_tab_add_eq(tab
, eq
) < 0)
3052 /* Add the equality described by "eq" to the context.
3053 * If "check" is set, then we check if the context is empty after
3054 * adding the equality.
3055 * If "update" is set, then we check if the samples are still valid.
3057 * We do not explicitly add shifted copies of the equality to
3058 * cgbr->shifted since they would conflict with each other.
3059 * Instead, we directly mark cgbr->shifted empty.
3061 static void context_gbr_add_eq(struct isl_context
*context
, isl_int
*eq
,
3062 int check
, int update
)
3064 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3066 cgbr
->tab
= add_gbr_eq(cgbr
->tab
, eq
);
3068 if (cgbr
->shifted
&& !cgbr
->shifted
->empty
&& use_shifted(cgbr
)) {
3069 if (isl_tab_mark_empty(cgbr
->shifted
) < 0)
3073 if (cgbr
->cone
&& cgbr
->cone
->n_col
!= cgbr
->cone
->n_dead
) {
3074 if (isl_tab_extend_cons(cgbr
->cone
, 2) < 0)
3076 if (isl_tab_add_eq(cgbr
->cone
, eq
) < 0)
3081 int v
= tab_has_valid_sample(cgbr
->tab
, eq
, 1);
3085 check_gbr_integer_feasible(cgbr
);
3088 cgbr
->tab
= check_samples(cgbr
->tab
, eq
, 1);
3091 isl_tab_free(cgbr
->tab
);
3095 static void add_gbr_ineq(struct isl_context_gbr
*cgbr
, isl_int
*ineq
)
3100 if (isl_tab_extend_cons(cgbr
->tab
, 1) < 0)
3103 if (isl_tab_add_ineq(cgbr
->tab
, ineq
) < 0)
3106 if (cgbr
->shifted
&& !cgbr
->shifted
->empty
&& use_shifted(cgbr
)) {
3109 dim
= isl_basic_map_total_dim(cgbr
->tab
->bmap
);
3111 if (isl_tab_extend_cons(cgbr
->shifted
, 1) < 0)
3114 for (i
= 0; i
< dim
; ++i
) {
3115 if (!isl_int_is_neg(ineq
[1 + i
]))
3117 isl_int_add(ineq
[0], ineq
[0], ineq
[1 + i
]);
3120 if (isl_tab_add_ineq(cgbr
->shifted
, ineq
) < 0)
3123 for (i
= 0; i
< dim
; ++i
) {
3124 if (!isl_int_is_neg(ineq
[1 + i
]))
3126 isl_int_sub(ineq
[0], ineq
[0], ineq
[1 + i
]);
3130 if (cgbr
->cone
&& cgbr
->cone
->n_col
!= cgbr
->cone
->n_dead
) {
3131 if (isl_tab_extend_cons(cgbr
->cone
, 1) < 0)
3133 if (isl_tab_add_ineq(cgbr
->cone
, ineq
) < 0)
3139 isl_tab_free(cgbr
->tab
);
3143 static void context_gbr_add_ineq(struct isl_context
*context
, isl_int
*ineq
,
3144 int check
, int update
)
3146 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3148 add_gbr_ineq(cgbr
, ineq
);
3153 int v
= tab_has_valid_sample(cgbr
->tab
, ineq
, 0);
3157 check_gbr_integer_feasible(cgbr
);
3160 cgbr
->tab
= check_samples(cgbr
->tab
, ineq
, 0);
3163 isl_tab_free(cgbr
->tab
);
3167 static isl_stat
context_gbr_add_ineq_wrap(void *user
, isl_int
*ineq
)
3169 struct isl_context
*context
= (struct isl_context
*)user
;
3170 context_gbr_add_ineq(context
, ineq
, 0, 0);
3171 return context
->op
->is_ok(context
) ? isl_stat_ok
: isl_stat_error
;
3174 static enum isl_tab_row_sign
context_gbr_ineq_sign(struct isl_context
*context
,
3175 isl_int
*ineq
, int strict
)
3177 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3178 return tab_ineq_sign(cgbr
->tab
, ineq
, strict
);
3181 /* Check whether "ineq" can be added to the tableau without rendering
3184 static int context_gbr_test_ineq(struct isl_context
*context
, isl_int
*ineq
)
3186 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3187 struct isl_tab_undo
*snap
;
3188 struct isl_tab_undo
*shifted_snap
= NULL
;
3189 struct isl_tab_undo
*cone_snap
= NULL
;
3195 if (isl_tab_extend_cons(cgbr
->tab
, 1) < 0)
3198 snap
= isl_tab_snap(cgbr
->tab
);
3200 shifted_snap
= isl_tab_snap(cgbr
->shifted
);
3202 cone_snap
= isl_tab_snap(cgbr
->cone
);
3203 add_gbr_ineq(cgbr
, ineq
);
3204 check_gbr_integer_feasible(cgbr
);
3207 feasible
= !cgbr
->tab
->empty
;
3208 if (isl_tab_rollback(cgbr
->tab
, snap
) < 0)
3211 if (isl_tab_rollback(cgbr
->shifted
, shifted_snap
))
3213 } else if (cgbr
->shifted
) {
3214 isl_tab_free(cgbr
->shifted
);
3215 cgbr
->shifted
= NULL
;
3218 if (isl_tab_rollback(cgbr
->cone
, cone_snap
))
3220 } else if (cgbr
->cone
) {
3221 isl_tab_free(cgbr
->cone
);
3228 /* Return the column of the last of the variables associated to
3229 * a column that has a non-zero coefficient.
3230 * This function is called in a context where only coefficients
3231 * of parameters or divs can be non-zero.
3233 static int last_non_zero_var_col(struct isl_tab
*tab
, isl_int
*p
)
3238 if (tab
->n_var
== 0)
3241 for (i
= tab
->n_var
- 1; i
>= 0; --i
) {
3242 if (i
>= tab
->n_param
&& i
< tab
->n_var
- tab
->n_div
)
3244 if (tab
->var
[i
].is_row
)
3246 col
= tab
->var
[i
].index
;
3247 if (!isl_int_is_zero(p
[col
]))
3254 /* Look through all the recently added equalities in the context
3255 * to see if we can propagate any of them to the main tableau.
3257 * The newly added equalities in the context are encoded as pairs
3258 * of inequalities starting at inequality "first".
3260 * We tentatively add each of these equalities to the main tableau
3261 * and if this happens to result in a row with a final coefficient
3262 * that is one or negative one, we use it to kill a column
3263 * in the main tableau. Otherwise, we discard the tentatively
3265 * This tentative addition of equality constraints turns
3266 * on the undo facility of the tableau. Turn it off again
3267 * at the end, assuming it was turned off to begin with.
3269 * Return 0 on success and -1 on failure.
3271 static int propagate_equalities(struct isl_context_gbr
*cgbr
,
3272 struct isl_tab
*tab
, unsigned first
)
3275 struct isl_vec
*eq
= NULL
;
3276 isl_bool needs_undo
;
3278 needs_undo
= isl_tab_need_undo(tab
);
3281 eq
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_var
);
3285 if (isl_tab_extend_cons(tab
, (cgbr
->tab
->bmap
->n_ineq
- first
)/2) < 0)
3288 isl_seq_clr(eq
->el
+ 1 + tab
->n_param
,
3289 tab
->n_var
- tab
->n_param
- tab
->n_div
);
3290 for (i
= first
; i
< cgbr
->tab
->bmap
->n_ineq
; i
+= 2) {
3293 struct isl_tab_undo
*snap
;
3294 snap
= isl_tab_snap(tab
);
3296 isl_seq_cpy(eq
->el
, cgbr
->tab
->bmap
->ineq
[i
], 1 + tab
->n_param
);
3297 isl_seq_cpy(eq
->el
+ 1 + tab
->n_var
- tab
->n_div
,
3298 cgbr
->tab
->bmap
->ineq
[i
] + 1 + tab
->n_param
,
3301 r
= isl_tab_add_row(tab
, eq
->el
);
3304 r
= tab
->con
[r
].index
;
3305 j
= last_non_zero_var_col(tab
, tab
->mat
->row
[r
] + 2 + tab
->M
);
3306 if (j
< 0 || j
< tab
->n_dead
||
3307 !isl_int_is_one(tab
->mat
->row
[r
][0]) ||
3308 (!isl_int_is_one(tab
->mat
->row
[r
][2 + tab
->M
+ j
]) &&
3309 !isl_int_is_negone(tab
->mat
->row
[r
][2 + tab
->M
+ j
]))) {
3310 if (isl_tab_rollback(tab
, snap
) < 0)
3314 if (isl_tab_pivot(tab
, r
, j
) < 0)
3316 if (isl_tab_kill_col(tab
, j
) < 0)
3319 if (restore_lexmin(tab
) < 0)
3324 isl_tab_clear_undo(tab
);
3330 isl_tab_free(cgbr
->tab
);
3335 static int context_gbr_detect_equalities(struct isl_context
*context
,
3336 struct isl_tab
*tab
)
3338 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3342 struct isl_basic_set
*bset
= isl_tab_peek_bset(cgbr
->tab
);
3343 cgbr
->cone
= isl_tab_from_recession_cone(bset
, 0);
3346 if (isl_tab_track_bset(cgbr
->cone
,
3347 isl_basic_set_copy(bset
)) < 0)
3350 if (isl_tab_detect_implicit_equalities(cgbr
->cone
) < 0)
3353 n_ineq
= cgbr
->tab
->bmap
->n_ineq
;
3354 cgbr
->tab
= isl_tab_detect_equalities(cgbr
->tab
, cgbr
->cone
);
3357 if (cgbr
->tab
->bmap
->n_ineq
> n_ineq
&&
3358 propagate_equalities(cgbr
, tab
, n_ineq
) < 0)
3363 isl_tab_free(cgbr
->tab
);
3368 static int context_gbr_get_div(struct isl_context
*context
, struct isl_tab
*tab
,
3369 struct isl_vec
*div
)
3371 return get_div(tab
, context
, div
);
3374 static isl_bool
context_gbr_insert_div(struct isl_context
*context
, int pos
,
3375 __isl_keep isl_vec
*div
)
3377 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3379 int r
, n_div
, o_div
;
3381 n_div
= isl_basic_map_dim(cgbr
->cone
->bmap
, isl_dim_div
);
3382 o_div
= cgbr
->cone
->n_var
- n_div
;
3384 if (isl_tab_extend_cons(cgbr
->cone
, 3) < 0)
3385 return isl_bool_error
;
3386 if (isl_tab_extend_vars(cgbr
->cone
, 1) < 0)
3387 return isl_bool_error
;
3388 if ((r
= isl_tab_insert_var(cgbr
->cone
, pos
)) <0)
3389 return isl_bool_error
;
3391 cgbr
->cone
->bmap
= isl_basic_map_insert_div(cgbr
->cone
->bmap
,
3393 if (!cgbr
->cone
->bmap
)
3394 return isl_bool_error
;
3395 if (isl_tab_push_var(cgbr
->cone
, isl_tab_undo_bmap_div
,
3396 &cgbr
->cone
->var
[r
]) < 0)
3397 return isl_bool_error
;
3399 return context_tab_insert_div(cgbr
->tab
, pos
, div
,
3400 context_gbr_add_ineq_wrap
, context
);
3403 static int context_gbr_best_split(struct isl_context
*context
,
3404 struct isl_tab
*tab
)
3406 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3407 struct isl_tab_undo
*snap
;
3410 snap
= isl_tab_snap(cgbr
->tab
);
3411 r
= best_split(tab
, cgbr
->tab
);
3413 if (r
>= 0 && isl_tab_rollback(cgbr
->tab
, snap
) < 0)
3419 static int context_gbr_is_empty(struct isl_context
*context
)
3421 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3424 return cgbr
->tab
->empty
;
3427 struct isl_gbr_tab_undo
{
3428 struct isl_tab_undo
*tab_snap
;
3429 struct isl_tab_undo
*shifted_snap
;
3430 struct isl_tab_undo
*cone_snap
;
3433 static void *context_gbr_save(struct isl_context
*context
)
3435 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3436 struct isl_gbr_tab_undo
*snap
;
3441 snap
= isl_alloc_type(cgbr
->tab
->mat
->ctx
, struct isl_gbr_tab_undo
);
3445 snap
->tab_snap
= isl_tab_snap(cgbr
->tab
);
3446 if (isl_tab_save_samples(cgbr
->tab
) < 0)
3450 snap
->shifted_snap
= isl_tab_snap(cgbr
->shifted
);
3452 snap
->shifted_snap
= NULL
;
3455 snap
->cone_snap
= isl_tab_snap(cgbr
->cone
);
3457 snap
->cone_snap
= NULL
;
3465 static void context_gbr_restore(struct isl_context
*context
, void *save
)
3467 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3468 struct isl_gbr_tab_undo
*snap
= (struct isl_gbr_tab_undo
*)save
;
3471 if (isl_tab_rollback(cgbr
->tab
, snap
->tab_snap
) < 0)
3474 if (snap
->shifted_snap
) {
3475 if (isl_tab_rollback(cgbr
->shifted
, snap
->shifted_snap
) < 0)
3477 } else if (cgbr
->shifted
) {
3478 isl_tab_free(cgbr
->shifted
);
3479 cgbr
->shifted
= NULL
;
3482 if (snap
->cone_snap
) {
3483 if (isl_tab_rollback(cgbr
->cone
, snap
->cone_snap
) < 0)
3485 } else if (cgbr
->cone
) {
3486 isl_tab_free(cgbr
->cone
);
3495 isl_tab_free(cgbr
->tab
);
3499 static void context_gbr_discard(void *save
)
3501 struct isl_gbr_tab_undo
*snap
= (struct isl_gbr_tab_undo
*)save
;
3505 static int context_gbr_is_ok(struct isl_context
*context
)
3507 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3511 static void context_gbr_invalidate(struct isl_context
*context
)
3513 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3514 isl_tab_free(cgbr
->tab
);
3518 static __isl_null
struct isl_context
*context_gbr_free(
3519 struct isl_context
*context
)
3521 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3522 isl_tab_free(cgbr
->tab
);
3523 isl_tab_free(cgbr
->shifted
);
3524 isl_tab_free(cgbr
->cone
);
3530 struct isl_context_op isl_context_gbr_op
= {
3531 context_gbr_detect_nonnegative_parameters
,
3532 context_gbr_peek_basic_set
,
3533 context_gbr_peek_tab
,
3535 context_gbr_add_ineq
,
3536 context_gbr_ineq_sign
,
3537 context_gbr_test_ineq
,
3538 context_gbr_get_div
,
3539 context_gbr_insert_div
,
3540 context_gbr_detect_equalities
,
3541 context_gbr_best_split
,
3542 context_gbr_is_empty
,
3545 context_gbr_restore
,
3546 context_gbr_discard
,
3547 context_gbr_invalidate
,
3551 static struct isl_context
*isl_context_gbr_alloc(__isl_keep isl_basic_set
*dom
)
3553 struct isl_context_gbr
*cgbr
;
3558 cgbr
= isl_calloc_type(dom
->ctx
, struct isl_context_gbr
);
3562 cgbr
->context
.op
= &isl_context_gbr_op
;
3564 cgbr
->shifted
= NULL
;
3566 cgbr
->tab
= isl_tab_from_basic_set(dom
, 1);
3567 cgbr
->tab
= isl_tab_init_samples(cgbr
->tab
);
3570 check_gbr_integer_feasible(cgbr
);
3572 return &cgbr
->context
;
3574 cgbr
->context
.op
->free(&cgbr
->context
);
3578 /* Allocate a context corresponding to "dom".
3579 * The representation specific fields are initialized by
3580 * isl_context_lex_alloc or isl_context_gbr_alloc.
3581 * The shared "n_unknown" field is initialized to the number
3582 * of final unknown integer divisions in "dom".
3584 static struct isl_context
*isl_context_alloc(__isl_keep isl_basic_set
*dom
)
3586 struct isl_context
*context
;
3592 if (dom
->ctx
->opt
->context
== ISL_CONTEXT_LEXMIN
)
3593 context
= isl_context_lex_alloc(dom
);
3595 context
= isl_context_gbr_alloc(dom
);
3600 first
= isl_basic_set_first_unknown_div(dom
);
3602 return context
->op
->free(context
);
3603 context
->n_unknown
= isl_basic_set_dim(dom
, isl_dim_div
) - first
;
3608 /* Initialize some common fields of "sol", which keeps track
3609 * of the solution of an optimization problem on "bmap" over
3611 * If "max" is set, then a maximization problem is being solved, rather than
3612 * a minimization problem, which means that the variables in the
3613 * tableau have value "M - x" rather than "M + x".
3615 static isl_stat
sol_init(struct isl_sol
*sol
, __isl_keep isl_basic_map
*bmap
,
3616 __isl_keep isl_basic_set
*dom
, int max
)
3618 sol
->rational
= ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
);
3619 sol
->dec_level
.callback
.run
= &sol_dec_level_wrap
;
3620 sol
->dec_level
.sol
= sol
;
3622 sol
->n_out
= isl_basic_map_dim(bmap
, isl_dim_out
);
3623 sol
->space
= isl_basic_map_get_space(bmap
);
3625 sol
->context
= isl_context_alloc(dom
);
3626 if (!sol
->space
|| !sol
->context
)
3627 return isl_stat_error
;
3632 /* Construct an isl_sol_map structure for accumulating the solution.
3633 * If track_empty is set, then we also keep track of the parts
3634 * of the context where there is no solution.
3635 * If max is set, then we are solving a maximization, rather than
3636 * a minimization problem, which means that the variables in the
3637 * tableau have value "M - x" rather than "M + x".
3639 static struct isl_sol
*sol_map_init(__isl_keep isl_basic_map
*bmap
,
3640 __isl_take isl_basic_set
*dom
, int track_empty
, int max
)
3642 struct isl_sol_map
*sol_map
= NULL
;
3648 sol_map
= isl_calloc_type(bmap
->ctx
, struct isl_sol_map
);
3652 sol_map
->sol
.free
= &sol_map_free
;
3653 if (sol_init(&sol_map
->sol
, bmap
, dom
, max
) < 0)
3655 sol_map
->sol
.add
= &sol_map_add_wrap
;
3656 sol_map
->sol
.add_empty
= track_empty
? &sol_map_add_empty_wrap
: NULL
;
3657 space
= isl_space_copy(sol_map
->sol
.space
);
3658 sol_map
->map
= isl_map_alloc_space(space
, 1, ISL_MAP_DISJOINT
);
3663 sol_map
->empty
= isl_set_alloc_space(isl_basic_set_get_space(dom
),
3664 1, ISL_SET_DISJOINT
);
3665 if (!sol_map
->empty
)
3669 isl_basic_set_free(dom
);
3670 return &sol_map
->sol
;
3672 isl_basic_set_free(dom
);
3673 sol_free(&sol_map
->sol
);
3677 /* Check whether all coefficients of (non-parameter) variables
3678 * are non-positive, meaning that no pivots can be performed on the row.
3680 static int is_critical(struct isl_tab
*tab
, int row
)
3683 unsigned off
= 2 + tab
->M
;
3685 for (j
= tab
->n_dead
; j
< tab
->n_col
; ++j
) {
3686 if (col_is_parameter_var(tab
, j
))
3689 if (isl_int_is_pos(tab
->mat
->row
[row
][off
+ j
]))
3696 /* Check whether the inequality represented by vec is strict over the integers,
3697 * i.e., there are no integer values satisfying the constraint with
3698 * equality. This happens if the gcd of the coefficients is not a divisor
3699 * of the constant term. If so, scale the constraint down by the gcd
3700 * of the coefficients.
3702 static int is_strict(struct isl_vec
*vec
)
3708 isl_seq_gcd(vec
->el
+ 1, vec
->size
- 1, &gcd
);
3709 if (!isl_int_is_one(gcd
)) {
3710 strict
= !isl_int_is_divisible_by(vec
->el
[0], gcd
);
3711 isl_int_fdiv_q(vec
->el
[0], vec
->el
[0], gcd
);
3712 isl_seq_scale_down(vec
->el
+ 1, vec
->el
+ 1, gcd
, vec
->size
-1);
3719 /* Determine the sign of the given row of the main tableau.
3720 * The result is one of
3721 * isl_tab_row_pos: always non-negative; no pivot needed
3722 * isl_tab_row_neg: always non-positive; pivot
3723 * isl_tab_row_any: can be both positive and negative; split
3725 * We first handle some simple cases
3726 * - the row sign may be known already
3727 * - the row may be obviously non-negative
3728 * - the parametric constant may be equal to that of another row
3729 * for which we know the sign. This sign will be either "pos" or
3730 * "any". If it had been "neg" then we would have pivoted before.
3732 * If none of these cases hold, we check the value of the row for each
3733 * of the currently active samples. Based on the signs of these values
3734 * we make an initial determination of the sign of the row.
3736 * all zero -> unk(nown)
3737 * all non-negative -> pos
3738 * all non-positive -> neg
3739 * both negative and positive -> all
3741 * If we end up with "all", we are done.
3742 * Otherwise, we perform a check for positive and/or negative
3743 * values as follows.
3745 * samples neg unk pos
3751 * There is no special sign for "zero", because we can usually treat zero
3752 * as either non-negative or non-positive, whatever works out best.
3753 * However, if the row is "critical", meaning that pivoting is impossible
3754 * then we don't want to limp zero with the non-positive case, because
3755 * then we we would lose the solution for those values of the parameters
3756 * where the value of the row is zero. Instead, we treat 0 as non-negative
3757 * ensuring a split if the row can attain both zero and negative values.
3758 * The same happens when the original constraint was one that could not
3759 * be satisfied with equality by any integer values of the parameters.
3760 * In this case, we normalize the constraint, but then a value of zero
3761 * for the normalized constraint is actually a positive value for the
3762 * original constraint, so again we need to treat zero as non-negative.
3763 * In both these cases, we have the following decision tree instead:
3765 * all non-negative -> pos
3766 * all negative -> neg
3767 * both negative and non-negative -> all
3775 static enum isl_tab_row_sign
row_sign(struct isl_tab
*tab
,
3776 struct isl_sol
*sol
, int row
)
3778 struct isl_vec
*ineq
= NULL
;
3779 enum isl_tab_row_sign res
= isl_tab_row_unknown
;
3784 if (tab
->row_sign
[row
] != isl_tab_row_unknown
)
3785 return tab
->row_sign
[row
];
3786 if (is_obviously_nonneg(tab
, row
))
3787 return isl_tab_row_pos
;
3788 for (row2
= tab
->n_redundant
; row2
< tab
->n_row
; ++row2
) {
3789 if (tab
->row_sign
[row2
] == isl_tab_row_unknown
)
3791 if (identical_parameter_line(tab
, row
, row2
))
3792 return tab
->row_sign
[row2
];
3795 critical
= is_critical(tab
, row
);
3797 ineq
= get_row_parameter_ineq(tab
, row
);
3801 strict
= is_strict(ineq
);
3803 res
= sol
->context
->op
->ineq_sign(sol
->context
, ineq
->el
,
3804 critical
|| strict
);
3806 if (res
== isl_tab_row_unknown
|| res
== isl_tab_row_pos
) {
3807 /* test for negative values */
3809 isl_seq_neg(ineq
->el
, ineq
->el
, ineq
->size
);
3810 isl_int_sub_ui(ineq
->el
[0], ineq
->el
[0], 1);
3812 feasible
= sol
->context
->op
->test_ineq(sol
->context
, ineq
->el
);
3816 res
= isl_tab_row_pos
;
3818 res
= (res
== isl_tab_row_unknown
) ? isl_tab_row_neg
3820 if (res
== isl_tab_row_neg
) {
3821 isl_seq_neg(ineq
->el
, ineq
->el
, ineq
->size
);
3822 isl_int_sub_ui(ineq
->el
[0], ineq
->el
[0], 1);
3826 if (res
== isl_tab_row_neg
) {
3827 /* test for positive values */
3829 if (!critical
&& !strict
)
3830 isl_int_sub_ui(ineq
->el
[0], ineq
->el
[0], 1);
3832 feasible
= sol
->context
->op
->test_ineq(sol
->context
, ineq
->el
);
3836 res
= isl_tab_row_any
;
3843 return isl_tab_row_unknown
;
3846 static void find_solutions(struct isl_sol
*sol
, struct isl_tab
*tab
);
3848 /* Find solutions for values of the parameters that satisfy the given
3851 * We currently take a snapshot of the context tableau that is reset
3852 * when we return from this function, while we make a copy of the main
3853 * tableau, leaving the original main tableau untouched.
3854 * These are fairly arbitrary choices. Making a copy also of the context
3855 * tableau would obviate the need to undo any changes made to it later,
3856 * while taking a snapshot of the main tableau could reduce memory usage.
3857 * If we were to switch to taking a snapshot of the main tableau,
3858 * we would have to keep in mind that we need to save the row signs
3859 * and that we need to do this before saving the current basis
3860 * such that the basis has been restore before we restore the row signs.
3862 static void find_in_pos(struct isl_sol
*sol
, struct isl_tab
*tab
, isl_int
*ineq
)
3868 saved
= sol
->context
->op
->save(sol
->context
);
3870 tab
= isl_tab_dup(tab
);
3874 sol
->context
->op
->add_ineq(sol
->context
, ineq
, 0, 1);
3876 find_solutions(sol
, tab
);
3879 sol
->context
->op
->restore(sol
->context
, saved
);
3881 sol
->context
->op
->discard(saved
);
3887 /* Record the absence of solutions for those values of the parameters
3888 * that do not satisfy the given inequality with equality.
3890 static void no_sol_in_strict(struct isl_sol
*sol
,
3891 struct isl_tab
*tab
, struct isl_vec
*ineq
)
3896 if (!sol
->context
|| sol
->error
)
3898 saved
= sol
->context
->op
->save(sol
->context
);
3900 isl_int_sub_ui(ineq
->el
[0], ineq
->el
[0], 1);
3902 sol
->context
->op
->add_ineq(sol
->context
, ineq
->el
, 1, 0);
3911 isl_int_add_ui(ineq
->el
[0], ineq
->el
[0], 1);
3913 sol
->context
->op
->restore(sol
->context
, saved
);
3919 /* Reset all row variables that are marked to have a sign that may
3920 * be both positive and negative to have an unknown sign.
3922 static void reset_any_to_unknown(struct isl_tab
*tab
)
3926 for (row
= tab
->n_redundant
; row
< tab
->n_row
; ++row
) {
3927 if (!isl_tab_var_from_row(tab
, row
)->is_nonneg
)
3929 if (tab
->row_sign
[row
] == isl_tab_row_any
)
3930 tab
->row_sign
[row
] = isl_tab_row_unknown
;
3934 /* Compute the lexicographic minimum of the set represented by the main
3935 * tableau "tab" within the context "sol->context_tab".
3936 * On entry the sample value of the main tableau is lexicographically
3937 * less than or equal to this lexicographic minimum.
3938 * Pivots are performed until a feasible point is found, which is then
3939 * necessarily equal to the minimum, or until the tableau is found to
3940 * be infeasible. Some pivots may need to be performed for only some
3941 * feasible values of the context tableau. If so, the context tableau
3942 * is split into a part where the pivot is needed and a part where it is not.
3944 * Whenever we enter the main loop, the main tableau is such that no
3945 * "obvious" pivots need to be performed on it, where "obvious" means
3946 * that the given row can be seen to be negative without looking at
3947 * the context tableau. In particular, for non-parametric problems,
3948 * no pivots need to be performed on the main tableau.
3949 * The caller of find_solutions is responsible for making this property
3950 * hold prior to the first iteration of the loop, while restore_lexmin
3951 * is called before every other iteration.
3953 * Inside the main loop, we first examine the signs of the rows of
3954 * the main tableau within the context of the context tableau.
3955 * If we find a row that is always non-positive for all values of
3956 * the parameters satisfying the context tableau and negative for at
3957 * least one value of the parameters, we perform the appropriate pivot
3958 * and start over. An exception is the case where no pivot can be
3959 * performed on the row. In this case, we require that the sign of
3960 * the row is negative for all values of the parameters (rather than just
3961 * non-positive). This special case is handled inside row_sign, which
3962 * will say that the row can have any sign if it determines that it can
3963 * attain both negative and zero values.
3965 * If we can't find a row that always requires a pivot, but we can find
3966 * one or more rows that require a pivot for some values of the parameters
3967 * (i.e., the row can attain both positive and negative signs), then we split
3968 * the context tableau into two parts, one where we force the sign to be
3969 * non-negative and one where we force is to be negative.
3970 * The non-negative part is handled by a recursive call (through find_in_pos).
3971 * Upon returning from this call, we continue with the negative part and
3972 * perform the required pivot.
3974 * If no such rows can be found, all rows are non-negative and we have
3975 * found a (rational) feasible point. If we only wanted a rational point
3977 * Otherwise, we check if all values of the sample point of the tableau
3978 * are integral for the variables. If so, we have found the minimal
3979 * integral point and we are done.
3980 * If the sample point is not integral, then we need to make a distinction
3981 * based on whether the constant term is non-integral or the coefficients
3982 * of the parameters. Furthermore, in order to decide how to handle
3983 * the non-integrality, we also need to know whether the coefficients
3984 * of the other columns in the tableau are integral. This leads
3985 * to the following table. The first two rows do not correspond
3986 * to a non-integral sample point and are only mentioned for completeness.
3988 * constant parameters other
3991 * int int rat | -> no problem
3993 * rat int int -> fail
3995 * rat int rat -> cut
3998 * rat rat rat | -> parametric cut
4001 * rat rat int | -> split context
4003 * If the parametric constant is completely integral, then there is nothing
4004 * to be done. If the constant term is non-integral, but all the other
4005 * coefficient are integral, then there is nothing that can be done
4006 * and the tableau has no integral solution.
4007 * If, on the other hand, one or more of the other columns have rational
4008 * coefficients, but the parameter coefficients are all integral, then
4009 * we can perform a regular (non-parametric) cut.
4010 * Finally, if there is any parameter coefficient that is non-integral,
4011 * then we need to involve the context tableau. There are two cases here.
4012 * If at least one other column has a rational coefficient, then we
4013 * can perform a parametric cut in the main tableau by adding a new
4014 * integer division in the context tableau.
4015 * If all other columns have integral coefficients, then we need to
4016 * enforce that the rational combination of parameters (c + \sum a_i y_i)/m
4017 * is always integral. We do this by introducing an integer division
4018 * q = floor((c + \sum a_i y_i)/m) and stipulating that its argument should
4019 * always be integral in the context tableau, i.e., m q = c + \sum a_i y_i.
4020 * Since q is expressed in the tableau as
4021 * c + \sum a_i y_i - m q >= 0
4022 * -c - \sum a_i y_i + m q + m - 1 >= 0
4023 * it is sufficient to add the inequality
4024 * -c - \sum a_i y_i + m q >= 0
4025 * In the part of the context where this inequality does not hold, the
4026 * main tableau is marked as being empty.
4028 static void find_solutions(struct isl_sol
*sol
, struct isl_tab
*tab
)
4030 struct isl_context
*context
;
4033 if (!tab
|| sol
->error
)
4036 context
= sol
->context
;
4040 if (context
->op
->is_empty(context
))
4043 for (r
= 0; r
>= 0 && tab
&& !tab
->empty
; r
= restore_lexmin(tab
)) {
4046 enum isl_tab_row_sign sgn
;
4050 for (row
= tab
->n_redundant
; row
< tab
->n_row
; ++row
) {
4051 if (!isl_tab_var_from_row(tab
, row
)->is_nonneg
)
4053 sgn
= row_sign(tab
, sol
, row
);
4056 tab
->row_sign
[row
] = sgn
;
4057 if (sgn
== isl_tab_row_any
)
4059 if (sgn
== isl_tab_row_any
&& split
== -1)
4061 if (sgn
== isl_tab_row_neg
)
4064 if (row
< tab
->n_row
)
4067 struct isl_vec
*ineq
;
4069 split
= context
->op
->best_split(context
, tab
);
4072 ineq
= get_row_parameter_ineq(tab
, split
);
4076 reset_any_to_unknown(tab
);
4077 tab
->row_sign
[split
] = isl_tab_row_pos
;
4079 find_in_pos(sol
, tab
, ineq
->el
);
4080 tab
->row_sign
[split
] = isl_tab_row_neg
;
4081 isl_seq_neg(ineq
->el
, ineq
->el
, ineq
->size
);
4082 isl_int_sub_ui(ineq
->el
[0], ineq
->el
[0], 1);
4084 context
->op
->add_ineq(context
, ineq
->el
, 0, 1);
4092 row
= first_non_integer_row(tab
, &flags
);
4095 if (ISL_FL_ISSET(flags
, I_PAR
)) {
4096 if (ISL_FL_ISSET(flags
, I_VAR
)) {
4097 if (isl_tab_mark_empty(tab
) < 0)
4101 row
= add_cut(tab
, row
);
4102 } else if (ISL_FL_ISSET(flags
, I_VAR
)) {
4103 struct isl_vec
*div
;
4104 struct isl_vec
*ineq
;
4106 div
= get_row_split_div(tab
, row
);
4109 d
= context
->op
->get_div(context
, tab
, div
);
4113 ineq
= ineq_for_div(context
->op
->peek_basic_set(context
), d
);
4117 no_sol_in_strict(sol
, tab
, ineq
);
4118 isl_seq_neg(ineq
->el
, ineq
->el
, ineq
->size
);
4119 context
->op
->add_ineq(context
, ineq
->el
, 1, 1);
4121 if (sol
->error
|| !context
->op
->is_ok(context
))
4123 tab
= set_row_cst_to_div(tab
, row
, d
);
4124 if (context
->op
->is_empty(context
))
4127 row
= add_parametric_cut(tab
, row
, context
);
4142 /* Does "sol" contain a pair of partial solutions that could potentially
4145 * We currently only check that "sol" is not in an error state
4146 * and that there are at least two partial solutions of which the final two
4147 * are defined at the same level.
4149 static int sol_has_mergeable_solutions(struct isl_sol
*sol
)
4155 if (!sol
->partial
->next
)
4157 return sol
->partial
->level
== sol
->partial
->next
->level
;
4160 /* Compute the lexicographic minimum of the set represented by the main
4161 * tableau "tab" within the context "sol->context_tab".
4163 * As a preprocessing step, we first transfer all the purely parametric
4164 * equalities from the main tableau to the context tableau, i.e.,
4165 * parameters that have been pivoted to a row.
4166 * These equalities are ignored by the main algorithm, because the
4167 * corresponding rows may not be marked as being non-negative.
4168 * In parts of the context where the added equality does not hold,
4169 * the main tableau is marked as being empty.
4171 * Before we embark on the actual computation, we save a copy
4172 * of the context. When we return, we check if there are any
4173 * partial solutions that can potentially be merged. If so,
4174 * we perform a rollback to the initial state of the context.
4175 * The merging of partial solutions happens inside calls to
4176 * sol_dec_level that are pushed onto the undo stack of the context.
4177 * If there are no partial solutions that can potentially be merged
4178 * then the rollback is skipped as it would just be wasted effort.
4180 static void find_solutions_main(struct isl_sol
*sol
, struct isl_tab
*tab
)
4190 for (row
= tab
->n_redundant
; row
< tab
->n_row
; ++row
) {
4194 if (!row_is_parameter_var(tab
, row
))
4196 if (tab
->row_var
[row
] < tab
->n_param
)
4197 p
= tab
->row_var
[row
];
4199 p
= tab
->row_var
[row
]
4200 + tab
->n_param
- (tab
->n_var
- tab
->n_div
);
4202 eq
= isl_vec_alloc(tab
->mat
->ctx
, 1+tab
->n_param
+tab
->n_div
);
4205 get_row_parameter_line(tab
, row
, eq
->el
);
4206 isl_int_neg(eq
->el
[1 + p
], tab
->mat
->row
[row
][0]);
4207 eq
= isl_vec_normalize(eq
);
4210 no_sol_in_strict(sol
, tab
, eq
);
4212 isl_seq_neg(eq
->el
, eq
->el
, eq
->size
);
4214 no_sol_in_strict(sol
, tab
, eq
);
4215 isl_seq_neg(eq
->el
, eq
->el
, eq
->size
);
4217 sol
->context
->op
->add_eq(sol
->context
, eq
->el
, 1, 1);
4221 if (isl_tab_mark_redundant(tab
, row
) < 0)
4224 if (sol
->context
->op
->is_empty(sol
->context
))
4227 row
= tab
->n_redundant
- 1;
4230 saved
= sol
->context
->op
->save(sol
->context
);
4232 find_solutions(sol
, tab
);
4234 if (sol_has_mergeable_solutions(sol
))
4235 sol
->context
->op
->restore(sol
->context
, saved
);
4237 sol
->context
->op
->discard(saved
);
4248 /* Check if integer division "div" of "dom" also occurs in "bmap".
4249 * If so, return its position within the divs.
4250 * If not, return -1.
4252 static int find_context_div(struct isl_basic_map
*bmap
,
4253 struct isl_basic_set
*dom
, unsigned div
)
4256 unsigned b_dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
4257 unsigned d_dim
= isl_space_dim(dom
->dim
, isl_dim_all
);
4259 if (isl_int_is_zero(dom
->div
[div
][0]))
4261 if (isl_seq_first_non_zero(dom
->div
[div
] + 2 + d_dim
, dom
->n_div
) != -1)
4264 for (i
= 0; i
< bmap
->n_div
; ++i
) {
4265 if (isl_int_is_zero(bmap
->div
[i
][0]))
4267 if (isl_seq_first_non_zero(bmap
->div
[i
] + 2 + d_dim
,
4268 (b_dim
- d_dim
) + bmap
->n_div
) != -1)
4270 if (isl_seq_eq(bmap
->div
[i
], dom
->div
[div
], 2 + d_dim
))
4276 /* The correspondence between the variables in the main tableau,
4277 * the context tableau, and the input map and domain is as follows.
4278 * The first n_param and the last n_div variables of the main tableau
4279 * form the variables of the context tableau.
4280 * In the basic map, these n_param variables correspond to the
4281 * parameters and the input dimensions. In the domain, they correspond
4282 * to the parameters and the set dimensions.
4283 * The n_div variables correspond to the integer divisions in the domain.
4284 * To ensure that everything lines up, we may need to copy some of the
4285 * integer divisions of the domain to the map. These have to be placed
4286 * in the same order as those in the context and they have to be placed
4287 * after any other integer divisions that the map may have.
4288 * This function performs the required reordering.
4290 static __isl_give isl_basic_map
*align_context_divs(
4291 __isl_take isl_basic_map
*bmap
, __isl_keep isl_basic_set
*dom
)
4297 for (i
= 0; i
< dom
->n_div
; ++i
)
4298 if (find_context_div(bmap
, dom
, i
) != -1)
4300 other
= bmap
->n_div
- common
;
4301 if (dom
->n_div
- common
> 0) {
4302 bmap
= isl_basic_map_extend_space(bmap
, isl_space_copy(bmap
->dim
),
4303 dom
->n_div
- common
, 0, 0);
4307 for (i
= 0; i
< dom
->n_div
; ++i
) {
4308 int pos
= find_context_div(bmap
, dom
, i
);
4310 pos
= isl_basic_map_alloc_div(bmap
);
4313 isl_int_set_si(bmap
->div
[pos
][0], 0);
4315 if (pos
!= other
+ i
)
4316 isl_basic_map_swap_div(bmap
, pos
, other
+ i
);
4320 isl_basic_map_free(bmap
);
4324 /* Base case of isl_tab_basic_map_partial_lexopt, after removing
4325 * some obvious symmetries.
4327 * We make sure the divs in the domain are properly ordered,
4328 * because they will be added one by one in the given order
4329 * during the construction of the solution map.
4330 * Furthermore, make sure that the known integer divisions
4331 * appear before any unknown integer division because the solution
4332 * may depend on the known integer divisions, while anything that
4333 * depends on any variable starting from the first unknown integer
4334 * division is ignored in sol_pma_add.
4336 static struct isl_sol
*basic_map_partial_lexopt_base_sol(
4337 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_set
*dom
,
4338 __isl_give isl_set
**empty
, int max
,
4339 struct isl_sol
*(*init
)(__isl_keep isl_basic_map
*bmap
,
4340 __isl_take isl_basic_set
*dom
, int track_empty
, int max
))
4342 struct isl_tab
*tab
;
4343 struct isl_sol
*sol
= NULL
;
4344 struct isl_context
*context
;
4347 dom
= isl_basic_set_sort_divs(dom
);
4348 bmap
= align_context_divs(bmap
, dom
);
4350 sol
= init(bmap
, dom
, !!empty
, max
);
4354 context
= sol
->context
;
4355 if (isl_basic_set_plain_is_empty(context
->op
->peek_basic_set(context
)))
4357 else if (isl_basic_map_plain_is_empty(bmap
)) {
4360 isl_basic_set_copy(context
->op
->peek_basic_set(context
)));
4362 tab
= tab_for_lexmin(bmap
,
4363 context
->op
->peek_basic_set(context
), 1, max
);
4364 tab
= context
->op
->detect_nonnegative_parameters(context
, tab
);
4365 find_solutions_main(sol
, tab
);
4370 isl_basic_map_free(bmap
);
4374 isl_basic_map_free(bmap
);
4378 /* Base case of isl_tab_basic_map_partial_lexopt, after removing
4379 * some obvious symmetries.
4381 * We call basic_map_partial_lexopt_base_sol and extract the results.
4383 static __isl_give isl_map
*basic_map_partial_lexopt_base(
4384 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_set
*dom
,
4385 __isl_give isl_set
**empty
, int max
)
4387 isl_map
*result
= NULL
;
4388 struct isl_sol
*sol
;
4389 struct isl_sol_map
*sol_map
;
4391 sol
= basic_map_partial_lexopt_base_sol(bmap
, dom
, empty
, max
,
4395 sol_map
= (struct isl_sol_map
*) sol
;
4397 result
= isl_map_copy(sol_map
->map
);
4399 *empty
= isl_set_copy(sol_map
->empty
);
4400 sol_free(&sol_map
->sol
);
4404 /* Return a count of the number of occurrences of the "n" first
4405 * variables in the inequality constraints of "bmap".
4407 static __isl_give
int *count_occurrences(__isl_keep isl_basic_map
*bmap
,
4416 ctx
= isl_basic_map_get_ctx(bmap
);
4417 occurrences
= isl_calloc_array(ctx
, int, n
);
4421 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
4422 for (j
= 0; j
< n
; ++j
) {
4423 if (!isl_int_is_zero(bmap
->ineq
[i
][1 + j
]))
4431 /* Do all of the "n" variables with non-zero coefficients in "c"
4432 * occur in exactly a single constraint.
4433 * "occurrences" is an array of length "n" containing the number
4434 * of occurrences of each of the variables in the inequality constraints.
4436 static int single_occurrence(int n
, isl_int
*c
, int *occurrences
)
4440 for (i
= 0; i
< n
; ++i
) {
4441 if (isl_int_is_zero(c
[i
]))
4443 if (occurrences
[i
] != 1)
4450 /* Do all of the "n" initial variables that occur in inequality constraint
4451 * "ineq" of "bmap" only occur in that constraint?
4453 static int all_single_occurrence(__isl_keep isl_basic_map
*bmap
, int ineq
,
4458 for (i
= 0; i
< n
; ++i
) {
4459 if (isl_int_is_zero(bmap
->ineq
[ineq
][1 + i
]))
4461 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
4464 if (!isl_int_is_zero(bmap
->ineq
[j
][1 + i
]))
4472 /* Structure used during detection of parallel constraints.
4473 * n_in: number of "input" variables: isl_dim_param + isl_dim_in
4474 * n_out: number of "output" variables: isl_dim_out + isl_dim_div
4475 * val: the coefficients of the output variables
4477 struct isl_constraint_equal_info
{
4483 /* Check whether the coefficients of the output variables
4484 * of the constraint in "entry" are equal to info->val.
4486 static int constraint_equal(const void *entry
, const void *val
)
4488 isl_int
**row
= (isl_int
**)entry
;
4489 const struct isl_constraint_equal_info
*info
= val
;
4491 return isl_seq_eq((*row
) + 1 + info
->n_in
, info
->val
, info
->n_out
);
4494 /* Check whether "bmap" has a pair of constraints that have
4495 * the same coefficients for the output variables.
4496 * Note that the coefficients of the existentially quantified
4497 * variables need to be zero since the existentially quantified
4498 * of the result are usually not the same as those of the input.
4499 * Furthermore, check that each of the input variables that occur
4500 * in those constraints does not occur in any other constraint.
4501 * If so, return true and return the row indices of the two constraints
4502 * in *first and *second.
4504 static isl_bool
parallel_constraints(__isl_keep isl_basic_map
*bmap
,
4505 int *first
, int *second
)
4509 int *occurrences
= NULL
;
4510 struct isl_hash_table
*table
= NULL
;
4511 struct isl_hash_table_entry
*entry
;
4512 struct isl_constraint_equal_info info
;
4516 ctx
= isl_basic_map_get_ctx(bmap
);
4517 table
= isl_hash_table_alloc(ctx
, bmap
->n_ineq
);
4521 info
.n_in
= isl_basic_map_dim(bmap
, isl_dim_param
) +
4522 isl_basic_map_dim(bmap
, isl_dim_in
);
4523 occurrences
= count_occurrences(bmap
, info
.n_in
);
4524 if (info
.n_in
&& !occurrences
)
4526 n_out
= isl_basic_map_dim(bmap
, isl_dim_out
);
4527 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
4528 info
.n_out
= n_out
+ n_div
;
4529 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
4532 info
.val
= bmap
->ineq
[i
] + 1 + info
.n_in
;
4533 if (isl_seq_first_non_zero(info
.val
, n_out
) < 0)
4535 if (isl_seq_first_non_zero(info
.val
+ n_out
, n_div
) >= 0)
4537 if (!single_occurrence(info
.n_in
, bmap
->ineq
[i
] + 1,
4540 hash
= isl_seq_get_hash(info
.val
, info
.n_out
);
4541 entry
= isl_hash_table_find(ctx
, table
, hash
,
4542 constraint_equal
, &info
, 1);
4547 entry
->data
= &bmap
->ineq
[i
];
4550 if (i
< bmap
->n_ineq
) {
4551 *first
= ((isl_int
**)entry
->data
) - bmap
->ineq
;
4555 isl_hash_table_free(ctx
, table
);
4558 return i
< bmap
->n_ineq
;
4560 isl_hash_table_free(ctx
, table
);
4562 return isl_bool_error
;
4565 /* Given a set of upper bounds in "var", add constraints to "bset"
4566 * that make the i-th bound smallest.
4568 * In particular, if there are n bounds b_i, then add the constraints
4570 * b_i <= b_j for j > i
4571 * b_i < b_j for j < i
4573 static __isl_give isl_basic_set
*select_minimum(__isl_take isl_basic_set
*bset
,
4574 __isl_keep isl_mat
*var
, int i
)
4579 ctx
= isl_mat_get_ctx(var
);
4581 for (j
= 0; j
< var
->n_row
; ++j
) {
4584 k
= isl_basic_set_alloc_inequality(bset
);
4587 isl_seq_combine(bset
->ineq
[k
], ctx
->one
, var
->row
[j
],
4588 ctx
->negone
, var
->row
[i
], var
->n_col
);
4589 isl_int_set_si(bset
->ineq
[k
][var
->n_col
], 0);
4591 isl_int_sub_ui(bset
->ineq
[k
][0], bset
->ineq
[k
][0], 1);
4594 bset
= isl_basic_set_finalize(bset
);
4598 isl_basic_set_free(bset
);
4602 /* Given a set of upper bounds on the last "input" variable m,
4603 * construct a set that assigns the minimal upper bound to m, i.e.,
4604 * construct a set that divides the space into cells where one
4605 * of the upper bounds is smaller than all the others and assign
4606 * this upper bound to m.
4608 * In particular, if there are n bounds b_i, then the result
4609 * consists of n basic sets, each one of the form
4612 * b_i <= b_j for j > i
4613 * b_i < b_j for j < i
4615 static __isl_give isl_set
*set_minimum(__isl_take isl_space
*dim
,
4616 __isl_take isl_mat
*var
)
4619 isl_basic_set
*bset
= NULL
;
4620 isl_set
*set
= NULL
;
4625 set
= isl_set_alloc_space(isl_space_copy(dim
),
4626 var
->n_row
, ISL_SET_DISJOINT
);
4628 for (i
= 0; i
< var
->n_row
; ++i
) {
4629 bset
= isl_basic_set_alloc_space(isl_space_copy(dim
), 0,
4631 k
= isl_basic_set_alloc_equality(bset
);
4634 isl_seq_cpy(bset
->eq
[k
], var
->row
[i
], var
->n_col
);
4635 isl_int_set_si(bset
->eq
[k
][var
->n_col
], -1);
4636 bset
= select_minimum(bset
, var
, i
);
4637 set
= isl_set_add_basic_set(set
, bset
);
4640 isl_space_free(dim
);
4644 isl_basic_set_free(bset
);
4646 isl_space_free(dim
);
4651 /* Given that the last input variable of "bmap" represents the minimum
4652 * of the bounds in "cst", check whether we need to split the domain
4653 * based on which bound attains the minimum.
4655 * A split is needed when the minimum appears in an integer division
4656 * or in an equality. Otherwise, it is only needed if it appears in
4657 * an upper bound that is different from the upper bounds on which it
4660 static isl_bool
need_split_basic_map(__isl_keep isl_basic_map
*bmap
,
4661 __isl_keep isl_mat
*cst
)
4667 pos
= cst
->n_col
- 1;
4668 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
4670 for (i
= 0; i
< bmap
->n_div
; ++i
)
4671 if (!isl_int_is_zero(bmap
->div
[i
][2 + pos
]))
4672 return isl_bool_true
;
4674 for (i
= 0; i
< bmap
->n_eq
; ++i
)
4675 if (!isl_int_is_zero(bmap
->eq
[i
][1 + pos
]))
4676 return isl_bool_true
;
4678 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
4679 if (isl_int_is_nonneg(bmap
->ineq
[i
][1 + pos
]))
4681 if (!isl_int_is_negone(bmap
->ineq
[i
][1 + pos
]))
4682 return isl_bool_true
;
4683 if (isl_seq_first_non_zero(bmap
->ineq
[i
] + 1 + pos
+ 1,
4684 total
- pos
- 1) >= 0)
4685 return isl_bool_true
;
4687 for (j
= 0; j
< cst
->n_row
; ++j
)
4688 if (isl_seq_eq(bmap
->ineq
[i
], cst
->row
[j
], cst
->n_col
))
4690 if (j
>= cst
->n_row
)
4691 return isl_bool_true
;
4694 return isl_bool_false
;
4697 /* Given that the last set variable of "bset" represents the minimum
4698 * of the bounds in "cst", check whether we need to split the domain
4699 * based on which bound attains the minimum.
4701 * We simply call need_split_basic_map here. This is safe because
4702 * the position of the minimum is computed from "cst" and not
4705 static isl_bool
need_split_basic_set(__isl_keep isl_basic_set
*bset
,
4706 __isl_keep isl_mat
*cst
)
4708 return need_split_basic_map(bset_to_bmap(bset
), cst
);
4711 /* Given that the last set variable of "set" represents the minimum
4712 * of the bounds in "cst", check whether we need to split the domain
4713 * based on which bound attains the minimum.
4715 static isl_bool
need_split_set(__isl_keep isl_set
*set
, __isl_keep isl_mat
*cst
)
4719 for (i
= 0; i
< set
->n
; ++i
) {
4722 split
= need_split_basic_set(set
->p
[i
], cst
);
4723 if (split
< 0 || split
)
4727 return isl_bool_false
;
4730 /* Given a set of which the last set variable is the minimum
4731 * of the bounds in "cst", split each basic set in the set
4732 * in pieces where one of the bounds is (strictly) smaller than the others.
4733 * This subdivision is given in "min_expr".
4734 * The variable is subsequently projected out.
4736 * We only do the split when it is needed.
4737 * For example if the last input variable m = min(a,b) and the only
4738 * constraints in the given basic set are lower bounds on m,
4739 * i.e., l <= m = min(a,b), then we can simply project out m
4740 * to obtain l <= a and l <= b, without having to split on whether
4741 * m is equal to a or b.
4743 static __isl_give isl_set
*split(__isl_take isl_set
*empty
,
4744 __isl_take isl_set
*min_expr
, __isl_take isl_mat
*cst
)
4751 if (!empty
|| !min_expr
|| !cst
)
4754 n_in
= isl_set_dim(empty
, isl_dim_set
);
4755 dim
= isl_set_get_space(empty
);
4756 dim
= isl_space_drop_dims(dim
, isl_dim_set
, n_in
- 1, 1);
4757 res
= isl_set_empty(dim
);
4759 for (i
= 0; i
< empty
->n
; ++i
) {
4763 set
= isl_set_from_basic_set(isl_basic_set_copy(empty
->p
[i
]));
4764 split
= need_split_basic_set(empty
->p
[i
], cst
);
4766 set
= isl_set_free(set
);
4768 set
= isl_set_intersect(set
, isl_set_copy(min_expr
));
4769 set
= isl_set_remove_dims(set
, isl_dim_set
, n_in
- 1, 1);
4771 res
= isl_set_union_disjoint(res
, set
);
4774 isl_set_free(empty
);
4775 isl_set_free(min_expr
);
4779 isl_set_free(empty
);
4780 isl_set_free(min_expr
);
4785 /* Given a map of which the last input variable is the minimum
4786 * of the bounds in "cst", split each basic set in the set
4787 * in pieces where one of the bounds is (strictly) smaller than the others.
4788 * This subdivision is given in "min_expr".
4789 * The variable is subsequently projected out.
4791 * The implementation is essentially the same as that of "split".
4793 static __isl_give isl_map
*split_domain(__isl_take isl_map
*opt
,
4794 __isl_take isl_set
*min_expr
, __isl_take isl_mat
*cst
)
4801 if (!opt
|| !min_expr
|| !cst
)
4804 n_in
= isl_map_dim(opt
, isl_dim_in
);
4805 dim
= isl_map_get_space(opt
);
4806 dim
= isl_space_drop_dims(dim
, isl_dim_in
, n_in
- 1, 1);
4807 res
= isl_map_empty(dim
);
4809 for (i
= 0; i
< opt
->n
; ++i
) {
4813 map
= isl_map_from_basic_map(isl_basic_map_copy(opt
->p
[i
]));
4814 split
= need_split_basic_map(opt
->p
[i
], cst
);
4816 map
= isl_map_free(map
);
4818 map
= isl_map_intersect_domain(map
,
4819 isl_set_copy(min_expr
));
4820 map
= isl_map_remove_dims(map
, isl_dim_in
, n_in
- 1, 1);
4822 res
= isl_map_union_disjoint(res
, map
);
4826 isl_set_free(min_expr
);
4831 isl_set_free(min_expr
);
4836 static __isl_give isl_map
*basic_map_partial_lexopt(
4837 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_set
*dom
,
4838 __isl_give isl_set
**empty
, int max
);
4840 /* This function is called from basic_map_partial_lexopt_symm.
4841 * The last variable of "bmap" and "dom" corresponds to the minimum
4842 * of the bounds in "cst". "map_space" is the space of the original
4843 * input relation (of basic_map_partial_lexopt_symm) and "set_space"
4844 * is the space of the original domain.
4846 * We recursively call basic_map_partial_lexopt and then plug in
4847 * the definition of the minimum in the result.
4849 static __isl_give isl_map
*basic_map_partial_lexopt_symm_core(
4850 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_set
*dom
,
4851 __isl_give isl_set
**empty
, int max
, __isl_take isl_mat
*cst
,
4852 __isl_take isl_space
*map_space
, __isl_take isl_space
*set_space
)
4857 min_expr
= set_minimum(isl_basic_set_get_space(dom
), isl_mat_copy(cst
));
4859 opt
= basic_map_partial_lexopt(bmap
, dom
, empty
, max
);
4862 *empty
= split(*empty
,
4863 isl_set_copy(min_expr
), isl_mat_copy(cst
));
4864 *empty
= isl_set_reset_space(*empty
, set_space
);
4867 opt
= split_domain(opt
, min_expr
, cst
);
4868 opt
= isl_map_reset_space(opt
, map_space
);
4873 /* Extract a domain from "bmap" for the purpose of computing
4874 * a lexicographic optimum.
4876 * This function is only called when the caller wants to compute a full
4877 * lexicographic optimum, i.e., without specifying a domain. In this case,
4878 * the caller is not interested in the part of the domain space where
4879 * there is no solution and the domain can be initialized to those constraints
4880 * of "bmap" that only involve the parameters and the input dimensions.
4881 * This relieves the parametric programming engine from detecting those
4882 * inequalities and transferring them to the context. More importantly,
4883 * it ensures that those inequalities are transferred first and not
4884 * intermixed with inequalities that actually split the domain.
4886 * If the caller does not require the absence of existentially quantified
4887 * variables in the result (i.e., if ISL_OPT_QE is not set in "flags"),
4888 * then the actual domain of "bmap" can be used. This ensures that
4889 * the domain does not need to be split at all just to separate out
4890 * pieces of the domain that do not have a solution from piece that do.
4891 * This domain cannot be used in general because it may involve
4892 * (unknown) existentially quantified variables which will then also
4893 * appear in the solution.
4895 static __isl_give isl_basic_set
*extract_domain(__isl_keep isl_basic_map
*bmap
,
4901 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
4902 n_out
= isl_basic_map_dim(bmap
, isl_dim_out
);
4903 bmap
= isl_basic_map_copy(bmap
);
4904 if (ISL_FL_ISSET(flags
, ISL_OPT_QE
)) {
4905 bmap
= isl_basic_map_drop_constraints_involving_dims(bmap
,
4906 isl_dim_div
, 0, n_div
);
4907 bmap
= isl_basic_map_drop_constraints_involving_dims(bmap
,
4908 isl_dim_out
, 0, n_out
);
4910 return isl_basic_map_domain(bmap
);
4914 #define TYPE isl_map
4917 #include "isl_tab_lexopt_templ.c"
4919 struct isl_sol_for
{
4921 isl_stat (*fn
)(__isl_take isl_basic_set
*dom
,
4922 __isl_take isl_aff_list
*list
, void *user
);
4926 static void sol_for_free(struct isl_sol
*sol
)
4930 /* Add the solution identified by the tableau and the context tableau.
4931 * In particular, "dom" represents the context and "ma" expresses
4932 * the solution on that context.
4934 * See documentation of sol_add for more details.
4936 * Instead of constructing a basic map, this function calls a user
4937 * defined function with the current context as a basic set and
4938 * a list of affine expressions representing the relation between
4939 * the input and output. The space over which the affine expressions
4940 * are defined is the same as that of the domain. The number of
4941 * affine expressions in the list is equal to the number of output variables.
4943 static void sol_for_add(struct isl_sol_for
*sol
,
4944 __isl_take isl_basic_set
*dom
, __isl_take isl_multi_aff
*ma
)
4951 if (sol
->sol
.error
|| !dom
|| !ma
)
4954 ctx
= isl_basic_set_get_ctx(dom
);
4955 n
= isl_multi_aff_dim(ma
, isl_dim_out
);
4956 list
= isl_aff_list_alloc(ctx
, n
);
4957 for (i
= 0; i
< n
; ++i
) {
4958 aff
= isl_multi_aff_get_aff(ma
, i
);
4959 list
= isl_aff_list_add(list
, aff
);
4962 dom
= isl_basic_set_finalize(dom
);
4964 if (sol
->fn(isl_basic_set_copy(dom
), list
, sol
->user
) < 0)
4967 isl_basic_set_free(dom
);
4968 isl_multi_aff_free(ma
);
4971 isl_basic_set_free(dom
);
4972 isl_multi_aff_free(ma
);
4976 static void sol_for_add_wrap(struct isl_sol
*sol
,
4977 __isl_take isl_basic_set
*dom
, __isl_take isl_multi_aff
*ma
)
4979 sol_for_add((struct isl_sol_for
*)sol
, dom
, ma
);
4982 static struct isl_sol_for
*sol_for_init(__isl_keep isl_basic_map
*bmap
, int max
,
4983 isl_stat (*fn
)(__isl_take isl_basic_set
*dom
,
4984 __isl_take isl_aff_list
*list
, void *user
),
4987 struct isl_sol_for
*sol_for
= NULL
;
4989 struct isl_basic_set
*dom
= NULL
;
4991 sol_for
= isl_calloc_type(bmap
->ctx
, struct isl_sol_for
);
4995 dom_dim
= isl_space_domain(isl_space_copy(bmap
->dim
));
4996 dom
= isl_basic_set_universe(dom_dim
);
4998 sol_for
->sol
.free
= &sol_for_free
;
4999 if (sol_init(&sol_for
->sol
, bmap
, dom
, max
) < 0)
5002 sol_for
->user
= user
;
5003 sol_for
->sol
.add
= &sol_for_add_wrap
;
5004 sol_for
->sol
.add_empty
= NULL
;
5006 isl_basic_set_free(dom
);
5009 isl_basic_set_free(dom
);
5010 sol_free(&sol_for
->sol
);
5014 static void sol_for_find_solutions(struct isl_sol_for
*sol_for
,
5015 struct isl_tab
*tab
)
5017 find_solutions_main(&sol_for
->sol
, tab
);
5020 isl_stat
isl_basic_map_foreach_lexopt(__isl_keep isl_basic_map
*bmap
, int max
,
5021 isl_stat (*fn
)(__isl_take isl_basic_set
*dom
,
5022 __isl_take isl_aff_list
*list
, void *user
),
5025 struct isl_sol_for
*sol_for
= NULL
;
5027 bmap
= isl_basic_map_copy(bmap
);
5028 bmap
= isl_basic_map_detect_equalities(bmap
);
5030 return isl_stat_error
;
5032 sol_for
= sol_for_init(bmap
, max
, fn
, user
);
5036 if (isl_basic_map_plain_is_empty(bmap
))
5039 struct isl_tab
*tab
;
5040 struct isl_context
*context
= sol_for
->sol
.context
;
5041 tab
= tab_for_lexmin(bmap
,
5042 context
->op
->peek_basic_set(context
), 1, max
);
5043 tab
= context
->op
->detect_nonnegative_parameters(context
, tab
);
5044 sol_for_find_solutions(sol_for
, tab
);
5045 if (sol_for
->sol
.error
)
5049 sol_free(&sol_for
->sol
);
5050 isl_basic_map_free(bmap
);
5053 sol_free(&sol_for
->sol
);
5054 isl_basic_map_free(bmap
);
5055 return isl_stat_error
;
5058 /* Extract the subsequence of the sample value of "tab"
5059 * starting at "pos" and of length "len".
5061 static __isl_give isl_vec
*extract_sample_sequence(struct isl_tab
*tab
,
5068 ctx
= isl_tab_get_ctx(tab
);
5069 v
= isl_vec_alloc(ctx
, len
);
5072 for (i
= 0; i
< len
; ++i
) {
5073 if (!tab
->var
[pos
+ i
].is_row
) {
5074 isl_int_set_si(v
->el
[i
], 0);
5078 row
= tab
->var
[pos
+ i
].index
;
5079 isl_int_divexact(v
->el
[i
], tab
->mat
->row
[row
][1],
5080 tab
->mat
->row
[row
][0]);
5087 /* Check if the sequence of variables starting at "pos"
5088 * represents a trivial solution according to "trivial".
5089 * That is, is the result of applying "trivial" to this sequence
5090 * equal to the zero vector?
5092 static isl_bool
region_is_trivial(struct isl_tab
*tab
, int pos
,
5093 __isl_keep isl_mat
*trivial
)
5097 isl_bool is_trivial
;
5100 return isl_bool_error
;
5102 n
= isl_mat_rows(trivial
);
5104 return isl_bool_false
;
5106 len
= isl_mat_cols(trivial
);
5107 v
= extract_sample_sequence(tab
, pos
, len
);
5108 v
= isl_mat_vec_product(isl_mat_copy(trivial
), v
);
5109 is_trivial
= isl_vec_is_zero(v
);
5115 /* Global internal data for isl_tab_basic_set_non_trivial_lexmin.
5117 * "n_op" is the number of initial coordinates to optimize,
5118 * as passed to isl_tab_basic_set_non_trivial_lexmin.
5119 * "region" is the "n_region"-sized array of regions passed
5120 * to isl_tab_basic_set_non_trivial_lexmin.
5122 * "tab" is the tableau that corresponds to the ILP problem.
5123 * "local" is an array of local data structure, one for each
5124 * (potential) level of the backtracking procedure of
5125 * isl_tab_basic_set_non_trivial_lexmin.
5126 * "v" is a pre-allocated vector that can be used for adding
5127 * constraints to the tableau.
5129 * "sol" contains the best solution found so far.
5130 * It is initialized to a vector of size zero.
5132 struct isl_lexmin_data
{
5135 struct isl_trivial_region
*region
;
5137 struct isl_tab
*tab
;
5138 struct isl_local_region
*local
;
5144 /* Return the index of the first trivial region, "n_region" if all regions
5145 * are non-trivial or -1 in case of error.
5147 static int first_trivial_region(struct isl_lexmin_data
*data
)
5151 for (i
= 0; i
< data
->n_region
; ++i
) {
5153 trivial
= region_is_trivial(data
->tab
, data
->region
[i
].pos
,
5154 data
->region
[i
].trivial
);
5161 return data
->n_region
;
5164 /* Check if the solution is optimal, i.e., whether the first
5165 * n_op entries are zero.
5167 static int is_optimal(__isl_keep isl_vec
*sol
, int n_op
)
5171 for (i
= 0; i
< n_op
; ++i
)
5172 if (!isl_int_is_zero(sol
->el
[1 + i
]))
5177 /* Add constraints to "tab" that ensure that any solution is significantly
5178 * better than that represented by "sol". That is, find the first
5179 * relevant (within first n_op) non-zero coefficient and force it (along
5180 * with all previous coefficients) to be zero.
5181 * If the solution is already optimal (all relevant coefficients are zero),
5182 * then just mark the table as empty.
5183 * "n_zero" is the number of coefficients that have been forced zero
5184 * by previous calls to this function at the same level.
5185 * Return the updated number of forced zero coefficients or -1 on error.
5187 * This function assumes that at least 2 * (n_op - n_zero) more rows and
5188 * at least 2 * (n_op - n_zero) more elements in the constraint array
5189 * are available in the tableau.
5191 static int force_better_solution(struct isl_tab
*tab
,
5192 __isl_keep isl_vec
*sol
, int n_op
, int n_zero
)
5201 for (i
= n_zero
; i
< n_op
; ++i
)
5202 if (!isl_int_is_zero(sol
->el
[1 + i
]))
5206 if (isl_tab_mark_empty(tab
) < 0)
5211 ctx
= isl_vec_get_ctx(sol
);
5212 v
= isl_vec_alloc(ctx
, 1 + tab
->n_var
);
5217 for (; i
>= n_zero
; --i
) {
5219 isl_int_set_si(v
->el
[1 + i
], -1);
5220 if (add_lexmin_eq(tab
, v
->el
) < 0)
5231 /* Fix triviality direction "dir" of the given region to zero.
5233 * This function assumes that at least two more rows and at least
5234 * two more elements in the constraint array are available in the tableau.
5236 static isl_stat
fix_zero(struct isl_tab
*tab
, struct isl_trivial_region
*region
,
5237 int dir
, struct isl_lexmin_data
*data
)
5241 data
->v
= isl_vec_clr(data
->v
);
5243 return isl_stat_error
;
5244 len
= isl_mat_cols(region
->trivial
);
5245 isl_seq_cpy(data
->v
->el
+ 1 + region
->pos
, region
->trivial
->row
[dir
],
5247 if (add_lexmin_eq(tab
, data
->v
->el
) < 0)
5248 return isl_stat_error
;
5253 /* This function selects case "side" for non-triviality region "region",
5254 * assuming all the equality constraints have been imposed already.
5255 * In particular, the triviality direction side/2 is made positive
5256 * if side is even and made negative if side is odd.
5258 * This function assumes that at least one more row and at least
5259 * one more element in the constraint array are available in the tableau.
5261 static struct isl_tab
*pos_neg(struct isl_tab
*tab
,
5262 struct isl_trivial_region
*region
,
5263 int side
, struct isl_lexmin_data
*data
)
5267 data
->v
= isl_vec_clr(data
->v
);
5270 isl_int_set_si(data
->v
->el
[0], -1);
5271 len
= isl_mat_cols(region
->trivial
);
5273 isl_seq_cpy(data
->v
->el
+ 1 + region
->pos
,
5274 region
->trivial
->row
[side
/ 2], len
);
5276 isl_seq_neg(data
->v
->el
+ 1 + region
->pos
,
5277 region
->trivial
->row
[side
/ 2], len
);
5278 return add_lexmin_ineq(tab
, data
->v
->el
);
5284 /* Local data at each level of the backtracking procedure of
5285 * isl_tab_basic_set_non_trivial_lexmin.
5287 * "update" is set if a solution has been found in the current case
5288 * of this level, such that a better solution needs to be enforced
5290 * "n_zero" is the number of initial coordinates that have already
5291 * been forced to be zero at this level.
5292 * "region" is the non-triviality region considered at this level.
5293 * "side" is the index of the current case at this level.
5294 * "n" is the number of triviality directions.
5295 * "snap" is a snapshot of the tableau holding a state that needs
5296 * to be satisfied by all subsequent cases.
5298 struct isl_local_region
{
5304 struct isl_tab_undo
*snap
;
5307 /* Initialize the global data structure "data" used while solving
5308 * the ILP problem "bset".
5310 static isl_stat
init_lexmin_data(struct isl_lexmin_data
*data
,
5311 __isl_keep isl_basic_set
*bset
)
5315 ctx
= isl_basic_set_get_ctx(bset
);
5317 data
->tab
= tab_for_lexmin(bset
, NULL
, 0, 0);
5319 return isl_stat_error
;
5321 data
->v
= isl_vec_alloc(ctx
, 1 + data
->tab
->n_var
);
5323 return isl_stat_error
;
5324 data
->local
= isl_calloc_array(ctx
, struct isl_local_region
,
5326 if (data
->n_region
&& !data
->local
)
5327 return isl_stat_error
;
5329 data
->sol
= isl_vec_alloc(ctx
, 0);
5334 /* Mark all outer levels as requiring a better solution
5335 * in the next cases.
5337 static void update_outer_levels(struct isl_lexmin_data
*data
, int level
)
5341 for (i
= 0; i
< level
; ++i
)
5342 data
->local
[i
].update
= 1;
5345 /* Initialize "local" to refer to region "region" and
5346 * to initiate processing at this level.
5348 static void init_local_region(struct isl_local_region
*local
, int region
,
5349 struct isl_lexmin_data
*data
)
5351 local
->n
= isl_mat_rows(data
->region
[region
].trivial
);
5352 local
->region
= region
;
5358 /* What to do next after entering a level of the backtracking procedure.
5360 * error: some error has occurred; abort
5361 * done: an optimal solution has been found; stop search
5362 * backtrack: backtrack to the previous level
5363 * handle: add the constraints for the current level and
5364 * move to the next level
5367 isl_next_error
= -1,
5373 /* Have all cases of the current region been considered?
5374 * If there are n directions, then there are 2n cases.
5376 * The constraints in the current tableau are imposed
5377 * in all subsequent cases. This means that if the current
5378 * tableau is empty, then none of those cases should be considered
5379 * anymore and all cases have effectively been considered.
5381 static int finished_all_cases(struct isl_local_region
*local
,
5382 struct isl_lexmin_data
*data
)
5384 if (data
->tab
->empty
)
5386 return local
->side
>= 2 * local
->n
;
5389 /* Enter level "level" of the backtracking search and figure out
5390 * what to do next. "init" is set if the level was entered
5391 * from a higher level and needs to be initialized.
5392 * Otherwise, the level is entered as a result of backtracking and
5393 * the tableau needs to be restored to a position that can
5394 * be used for the next case at this level.
5395 * The snapshot is assumed to have been saved in the previous case,
5396 * before the constraints specific to that case were added.
5398 * In the initialization case, the local region is initialized
5399 * to point to the first violated region.
5400 * If the constraints of all regions are satisfied by the current
5401 * sample of the tableau, then tell the caller to continue looking
5402 * for a better solution or to stop searching if an optimal solution
5405 * If the tableau is empty or if all cases at the current level
5406 * have been considered, then the caller needs to backtrack as well.
5408 static enum isl_next
enter_level(int level
, int init
,
5409 struct isl_lexmin_data
*data
)
5411 struct isl_local_region
*local
= &data
->local
[level
];
5416 data
->tab
= cut_to_integer_lexmin(data
->tab
, CUT_ONE
);
5418 return isl_next_error
;
5419 if (data
->tab
->empty
)
5420 return isl_next_backtrack
;
5421 r
= first_trivial_region(data
);
5423 return isl_next_error
;
5424 if (r
== data
->n_region
) {
5425 update_outer_levels(data
, level
);
5426 isl_vec_free(data
->sol
);
5427 data
->sol
= isl_tab_get_sample_value(data
->tab
);
5429 return isl_next_error
;
5430 if (is_optimal(data
->sol
, data
->n_op
))
5431 return isl_next_done
;
5432 return isl_next_backtrack
;
5434 if (level
>= data
->n_region
)
5435 isl_die(isl_vec_get_ctx(data
->v
), isl_error_internal
,
5436 "nesting level too deep",
5437 return isl_next_error
);
5438 init_local_region(local
, r
, data
);
5439 if (isl_tab_extend_cons(data
->tab
,
5440 2 * local
->n
+ 2 * data
->n_op
) < 0)
5441 return isl_next_error
;
5443 if (isl_tab_rollback(data
->tab
, local
->snap
) < 0)
5444 return isl_next_error
;
5447 if (finished_all_cases(local
, data
))
5448 return isl_next_backtrack
;
5449 return isl_next_handle
;
5452 /* If a solution has been found in the previous case at this level
5453 * (marked by local->update being set), then add constraints
5454 * that enforce a better solution in the present and all following cases.
5455 * The constraints only need to be imposed once because they are
5456 * included in the snapshot (taken in pick_side) that will be used in
5459 static isl_stat
better_next_side(struct isl_local_region
*local
,
5460 struct isl_lexmin_data
*data
)
5465 local
->n_zero
= force_better_solution(data
->tab
,
5466 data
->sol
, data
->n_op
, local
->n_zero
);
5467 if (local
->n_zero
< 0)
5468 return isl_stat_error
;
5475 /* Add constraints to data->tab that select the current case (local->side)
5476 * at the current level.
5478 * If the linear combinations v should not be zero, then the cases are
5481 * v_0 = 0 and v_1 >= 1
5482 * v_0 = 0 and v_1 <= -1
5483 * v_0 = 0 and v_1 = 0 and v_2 >= 1
5484 * v_0 = 0 and v_1 = 0 and v_2 <= -1
5488 * A snapshot is taken after the equality constraint (if any) has been added
5489 * such that the next case can start off from this position.
5490 * The rollback to this position is performed in enter_level.
5492 static isl_stat
pick_side(struct isl_local_region
*local
,
5493 struct isl_lexmin_data
*data
)
5495 struct isl_trivial_region
*region
;
5498 region
= &data
->region
[local
->region
];
5500 base
= 2 * (side
/2);
5502 if (side
== base
&& base
>= 2 &&
5503 fix_zero(data
->tab
, region
, base
/ 2 - 1, data
) < 0)
5504 return isl_stat_error
;
5506 local
->snap
= isl_tab_snap(data
->tab
);
5507 if (isl_tab_push_basis(data
->tab
) < 0)
5508 return isl_stat_error
;
5510 data
->tab
= pos_neg(data
->tab
, region
, side
, data
);
5512 return isl_stat_error
;
5516 /* Free the memory associated to "data".
5518 static void clear_lexmin_data(struct isl_lexmin_data
*data
)
5521 isl_vec_free(data
->v
);
5522 isl_tab_free(data
->tab
);
5525 /* Return the lexicographically smallest non-trivial solution of the
5526 * given ILP problem.
5528 * All variables are assumed to be non-negative.
5530 * n_op is the number of initial coordinates to optimize.
5531 * That is, once a solution has been found, we will only continue looking
5532 * for solutions that result in significantly better values for those
5533 * initial coordinates. That is, we only continue looking for solutions
5534 * that increase the number of initial zeros in this sequence.
5536 * A solution is non-trivial, if it is non-trivial on each of the
5537 * specified regions. Each region represents a sequence of
5538 * triviality directions on a sequence of variables that starts
5539 * at a given position. A solution is non-trivial on such a region if
5540 * at least one of the triviality directions is non-zero
5541 * on that sequence of variables.
5543 * Whenever a conflict is encountered, all constraints involved are
5544 * reported to the caller through a call to "conflict".
5546 * We perform a simple branch-and-bound backtracking search.
5547 * Each level in the search represents an initially trivial region
5548 * that is forced to be non-trivial.
5549 * At each level we consider 2 * n cases, where n
5550 * is the number of triviality directions.
5551 * In terms of those n directions v_i, we consider the cases
5554 * v_0 = 0 and v_1 >= 1
5555 * v_0 = 0 and v_1 <= -1
5556 * v_0 = 0 and v_1 = 0 and v_2 >= 1
5557 * v_0 = 0 and v_1 = 0 and v_2 <= -1
5561 __isl_give isl_vec
*isl_tab_basic_set_non_trivial_lexmin(
5562 __isl_take isl_basic_set
*bset
, int n_op
, int n_region
,
5563 struct isl_trivial_region
*region
,
5564 int (*conflict
)(int con
, void *user
), void *user
)
5566 struct isl_lexmin_data data
= { n_op
, n_region
, region
};
5572 if (init_lexmin_data(&data
, bset
) < 0)
5574 data
.tab
->conflict
= conflict
;
5575 data
.tab
->conflict_user
= user
;
5580 while (level
>= 0) {
5582 struct isl_local_region
*local
= &data
.local
[level
];
5584 next
= enter_level(level
, init
, &data
);
5587 if (next
== isl_next_done
)
5589 if (next
== isl_next_backtrack
) {
5595 if (better_next_side(local
, &data
) < 0)
5597 if (pick_side(local
, &data
) < 0)
5605 clear_lexmin_data(&data
);
5606 isl_basic_set_free(bset
);
5610 clear_lexmin_data(&data
);
5611 isl_basic_set_free(bset
);
5612 isl_vec_free(data
.sol
);
5616 /* Wrapper for a tableau that is used for computing
5617 * the lexicographically smallest rational point of a non-negative set.
5618 * This point is represented by the sample value of "tab",
5619 * unless "tab" is empty.
5621 struct isl_tab_lexmin
{
5623 struct isl_tab
*tab
;
5626 /* Free "tl" and return NULL.
5628 __isl_null isl_tab_lexmin
*isl_tab_lexmin_free(__isl_take isl_tab_lexmin
*tl
)
5632 isl_ctx_deref(tl
->ctx
);
5633 isl_tab_free(tl
->tab
);
5639 /* Construct an isl_tab_lexmin for computing
5640 * the lexicographically smallest rational point in "bset",
5641 * assuming that all variables are non-negative.
5643 __isl_give isl_tab_lexmin
*isl_tab_lexmin_from_basic_set(
5644 __isl_take isl_basic_set
*bset
)
5652 ctx
= isl_basic_set_get_ctx(bset
);
5653 tl
= isl_calloc_type(ctx
, struct isl_tab_lexmin
);
5658 tl
->tab
= tab_for_lexmin(bset
, NULL
, 0, 0);
5659 isl_basic_set_free(bset
);
5661 return isl_tab_lexmin_free(tl
);
5664 isl_basic_set_free(bset
);
5665 isl_tab_lexmin_free(tl
);
5669 /* Return the dimension of the set represented by "tl".
5671 int isl_tab_lexmin_dim(__isl_keep isl_tab_lexmin
*tl
)
5673 return tl
? tl
->tab
->n_var
: -1;
5676 /* Add the equality with coefficients "eq" to "tl", updating the optimal
5677 * solution if needed.
5678 * The equality is added as two opposite inequality constraints.
5680 __isl_give isl_tab_lexmin
*isl_tab_lexmin_add_eq(__isl_take isl_tab_lexmin
*tl
,
5686 return isl_tab_lexmin_free(tl
);
5688 if (isl_tab_extend_cons(tl
->tab
, 2) < 0)
5689 return isl_tab_lexmin_free(tl
);
5690 n_var
= tl
->tab
->n_var
;
5691 isl_seq_neg(eq
, eq
, 1 + n_var
);
5692 tl
->tab
= add_lexmin_ineq(tl
->tab
, eq
);
5693 isl_seq_neg(eq
, eq
, 1 + n_var
);
5694 tl
->tab
= add_lexmin_ineq(tl
->tab
, eq
);
5697 return isl_tab_lexmin_free(tl
);
5702 /* Add cuts to "tl" until the sample value reaches an integer value or
5703 * until the result becomes empty.
5705 __isl_give isl_tab_lexmin
*isl_tab_lexmin_cut_to_integer(
5706 __isl_take isl_tab_lexmin
*tl
)
5710 tl
->tab
= cut_to_integer_lexmin(tl
->tab
, CUT_ONE
);
5712 return isl_tab_lexmin_free(tl
);
5716 /* Return the lexicographically smallest rational point in the basic set
5717 * from which "tl" was constructed.
5718 * If the original input was empty, then return a zero-length vector.
5720 __isl_give isl_vec
*isl_tab_lexmin_get_solution(__isl_keep isl_tab_lexmin
*tl
)
5725 return isl_vec_alloc(tl
->ctx
, 0);
5727 return isl_tab_get_sample_value(tl
->tab
);
5730 struct isl_sol_pma
{
5732 isl_pw_multi_aff
*pma
;
5736 static void sol_pma_free(struct isl_sol
*sol
)
5738 struct isl_sol_pma
*sol_pma
= (struct isl_sol_pma
*) sol
;
5739 isl_pw_multi_aff_free(sol_pma
->pma
);
5740 isl_set_free(sol_pma
->empty
);
5743 /* This function is called for parts of the context where there is
5744 * no solution, with "bset" corresponding to the context tableau.
5745 * Simply add the basic set to the set "empty".
5747 static void sol_pma_add_empty(struct isl_sol_pma
*sol
,
5748 __isl_take isl_basic_set
*bset
)
5750 if (!bset
|| !sol
->empty
)
5753 sol
->empty
= isl_set_grow(sol
->empty
, 1);
5754 bset
= isl_basic_set_simplify(bset
);
5755 bset
= isl_basic_set_finalize(bset
);
5756 sol
->empty
= isl_set_add_basic_set(sol
->empty
, bset
);
5761 isl_basic_set_free(bset
);
5765 /* Given a basic set "dom" that represents the context and a tuple of
5766 * affine expressions "maff" defined over this domain, construct
5767 * an isl_pw_multi_aff with a single cell corresponding to "dom" and
5768 * the affine expressions in "maff".
5770 static void sol_pma_add(struct isl_sol_pma
*sol
,
5771 __isl_take isl_basic_set
*dom
, __isl_take isl_multi_aff
*maff
)
5773 isl_pw_multi_aff
*pma
;
5775 dom
= isl_basic_set_simplify(dom
);
5776 dom
= isl_basic_set_finalize(dom
);
5777 pma
= isl_pw_multi_aff_alloc(isl_set_from_basic_set(dom
), maff
);
5778 sol
->pma
= isl_pw_multi_aff_add_disjoint(sol
->pma
, pma
);
5783 static void sol_pma_add_empty_wrap(struct isl_sol
*sol
,
5784 __isl_take isl_basic_set
*bset
)
5786 sol_pma_add_empty((struct isl_sol_pma
*)sol
, bset
);
5789 static void sol_pma_add_wrap(struct isl_sol
*sol
,
5790 __isl_take isl_basic_set
*dom
, __isl_take isl_multi_aff
*ma
)
5792 sol_pma_add((struct isl_sol_pma
*)sol
, dom
, ma
);
5795 /* Construct an isl_sol_pma structure for accumulating the solution.
5796 * If track_empty is set, then we also keep track of the parts
5797 * of the context where there is no solution.
5798 * If max is set, then we are solving a maximization, rather than
5799 * a minimization problem, which means that the variables in the
5800 * tableau have value "M - x" rather than "M + x".
5802 static struct isl_sol
*sol_pma_init(__isl_keep isl_basic_map
*bmap
,
5803 __isl_take isl_basic_set
*dom
, int track_empty
, int max
)
5805 struct isl_sol_pma
*sol_pma
= NULL
;
5811 sol_pma
= isl_calloc_type(bmap
->ctx
, struct isl_sol_pma
);
5815 sol_pma
->sol
.free
= &sol_pma_free
;
5816 if (sol_init(&sol_pma
->sol
, bmap
, dom
, max
) < 0)
5818 sol_pma
->sol
.add
= &sol_pma_add_wrap
;
5819 sol_pma
->sol
.add_empty
= track_empty
? &sol_pma_add_empty_wrap
: NULL
;
5820 space
= isl_space_copy(sol_pma
->sol
.space
);
5821 sol_pma
->pma
= isl_pw_multi_aff_empty(space
);
5826 sol_pma
->empty
= isl_set_alloc_space(isl_basic_set_get_space(dom
),
5827 1, ISL_SET_DISJOINT
);
5828 if (!sol_pma
->empty
)
5832 isl_basic_set_free(dom
);
5833 return &sol_pma
->sol
;
5835 isl_basic_set_free(dom
);
5836 sol_free(&sol_pma
->sol
);
5840 /* Base case of isl_tab_basic_map_partial_lexopt, after removing
5841 * some obvious symmetries.
5843 * We call basic_map_partial_lexopt_base_sol and extract the results.
5845 static __isl_give isl_pw_multi_aff
*basic_map_partial_lexopt_base_pw_multi_aff(
5846 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_set
*dom
,
5847 __isl_give isl_set
**empty
, int max
)
5849 isl_pw_multi_aff
*result
= NULL
;
5850 struct isl_sol
*sol
;
5851 struct isl_sol_pma
*sol_pma
;
5853 sol
= basic_map_partial_lexopt_base_sol(bmap
, dom
, empty
, max
,
5857 sol_pma
= (struct isl_sol_pma
*) sol
;
5859 result
= isl_pw_multi_aff_copy(sol_pma
->pma
);
5861 *empty
= isl_set_copy(sol_pma
->empty
);
5862 sol_free(&sol_pma
->sol
);
5866 /* Given that the last input variable of "maff" represents the minimum
5867 * of some bounds, check whether we need to plug in the expression
5870 * In particular, check if the last input variable appears in any
5871 * of the expressions in "maff".
5873 static int need_substitution(__isl_keep isl_multi_aff
*maff
)
5878 pos
= isl_multi_aff_dim(maff
, isl_dim_in
) - 1;
5880 for (i
= 0; i
< maff
->n
; ++i
)
5881 if (isl_aff_involves_dims(maff
->p
[i
], isl_dim_in
, pos
, 1))
5887 /* Given a set of upper bounds on the last "input" variable m,
5888 * construct a piecewise affine expression that selects
5889 * the minimal upper bound to m, i.e.,
5890 * divide the space into cells where one
5891 * of the upper bounds is smaller than all the others and select
5892 * this upper bound on that cell.
5894 * In particular, if there are n bounds b_i, then the result
5895 * consists of n cell, each one of the form
5897 * b_i <= b_j for j > i
5898 * b_i < b_j for j < i
5900 * The affine expression on this cell is
5904 static __isl_give isl_pw_aff
*set_minimum_pa(__isl_take isl_space
*space
,
5905 __isl_take isl_mat
*var
)
5908 isl_aff
*aff
= NULL
;
5909 isl_basic_set
*bset
= NULL
;
5910 isl_pw_aff
*paff
= NULL
;
5911 isl_space
*pw_space
;
5912 isl_local_space
*ls
= NULL
;
5917 ls
= isl_local_space_from_space(isl_space_copy(space
));
5918 pw_space
= isl_space_copy(space
);
5919 pw_space
= isl_space_from_domain(pw_space
);
5920 pw_space
= isl_space_add_dims(pw_space
, isl_dim_out
, 1);
5921 paff
= isl_pw_aff_alloc_size(pw_space
, var
->n_row
);
5923 for (i
= 0; i
< var
->n_row
; ++i
) {
5926 aff
= isl_aff_alloc(isl_local_space_copy(ls
));
5927 bset
= isl_basic_set_alloc_space(isl_space_copy(space
), 0,
5931 isl_int_set_si(aff
->v
->el
[0], 1);
5932 isl_seq_cpy(aff
->v
->el
+ 1, var
->row
[i
], var
->n_col
);
5933 isl_int_set_si(aff
->v
->el
[1 + var
->n_col
], 0);
5934 bset
= select_minimum(bset
, var
, i
);
5935 paff_i
= isl_pw_aff_alloc(isl_set_from_basic_set(bset
), aff
);
5936 paff
= isl_pw_aff_add_disjoint(paff
, paff_i
);
5939 isl_local_space_free(ls
);
5940 isl_space_free(space
);
5945 isl_basic_set_free(bset
);
5946 isl_pw_aff_free(paff
);
5947 isl_local_space_free(ls
);
5948 isl_space_free(space
);
5953 /* Given a piecewise multi-affine expression of which the last input variable
5954 * is the minimum of the bounds in "cst", plug in the value of the minimum.
5955 * This minimum expression is given in "min_expr_pa".
5956 * The set "min_expr" contains the same information, but in the form of a set.
5957 * The variable is subsequently projected out.
5959 * The implementation is similar to those of "split" and "split_domain".
5960 * If the variable appears in a given expression, then minimum expression
5961 * is plugged in. Otherwise, if the variable appears in the constraints
5962 * and a split is required, then the domain is split. Otherwise, no split
5965 static __isl_give isl_pw_multi_aff
*split_domain_pma(
5966 __isl_take isl_pw_multi_aff
*opt
, __isl_take isl_pw_aff
*min_expr_pa
,
5967 __isl_take isl_set
*min_expr
, __isl_take isl_mat
*cst
)
5972 isl_pw_multi_aff
*res
;
5974 if (!opt
|| !min_expr
|| !cst
)
5977 n_in
= isl_pw_multi_aff_dim(opt
, isl_dim_in
);
5978 space
= isl_pw_multi_aff_get_space(opt
);
5979 space
= isl_space_drop_dims(space
, isl_dim_in
, n_in
- 1, 1);
5980 res
= isl_pw_multi_aff_empty(space
);
5982 for (i
= 0; i
< opt
->n
; ++i
) {
5983 isl_pw_multi_aff
*pma
;
5985 pma
= isl_pw_multi_aff_alloc(isl_set_copy(opt
->p
[i
].set
),
5986 isl_multi_aff_copy(opt
->p
[i
].maff
));
5987 if (need_substitution(opt
->p
[i
].maff
))
5988 pma
= isl_pw_multi_aff_substitute(pma
,
5989 isl_dim_in
, n_in
- 1, min_expr_pa
);
5992 split
= need_split_set(opt
->p
[i
].set
, cst
);
5994 pma
= isl_pw_multi_aff_free(pma
);
5996 pma
= isl_pw_multi_aff_intersect_domain(pma
,
5997 isl_set_copy(min_expr
));
5999 pma
= isl_pw_multi_aff_project_out(pma
,
6000 isl_dim_in
, n_in
- 1, 1);
6002 res
= isl_pw_multi_aff_add_disjoint(res
, pma
);
6005 isl_pw_multi_aff_free(opt
);
6006 isl_pw_aff_free(min_expr_pa
);
6007 isl_set_free(min_expr
);
6011 isl_pw_multi_aff_free(opt
);
6012 isl_pw_aff_free(min_expr_pa
);
6013 isl_set_free(min_expr
);
6018 static __isl_give isl_pw_multi_aff
*basic_map_partial_lexopt_pw_multi_aff(
6019 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_set
*dom
,
6020 __isl_give isl_set
**empty
, int max
);
6022 /* This function is called from basic_map_partial_lexopt_symm.
6023 * The last variable of "bmap" and "dom" corresponds to the minimum
6024 * of the bounds in "cst". "map_space" is the space of the original
6025 * input relation (of basic_map_partial_lexopt_symm) and "set_space"
6026 * is the space of the original domain.
6028 * We recursively call basic_map_partial_lexopt and then plug in
6029 * the definition of the minimum in the result.
6031 static __isl_give isl_pw_multi_aff
*
6032 basic_map_partial_lexopt_symm_core_pw_multi_aff(
6033 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_set
*dom
,
6034 __isl_give isl_set
**empty
, int max
, __isl_take isl_mat
*cst
,
6035 __isl_take isl_space
*map_space
, __isl_take isl_space
*set_space
)
6037 isl_pw_multi_aff
*opt
;
6038 isl_pw_aff
*min_expr_pa
;
6041 min_expr
= set_minimum(isl_basic_set_get_space(dom
), isl_mat_copy(cst
));
6042 min_expr_pa
= set_minimum_pa(isl_basic_set_get_space(dom
),
6045 opt
= basic_map_partial_lexopt_pw_multi_aff(bmap
, dom
, empty
, max
);
6048 *empty
= split(*empty
,
6049 isl_set_copy(min_expr
), isl_mat_copy(cst
));
6050 *empty
= isl_set_reset_space(*empty
, set_space
);
6053 opt
= split_domain_pma(opt
, min_expr_pa
, min_expr
, cst
);
6054 opt
= isl_pw_multi_aff_reset_space(opt
, map_space
);
6060 #define TYPE isl_pw_multi_aff
6062 #define SUFFIX _pw_multi_aff
6063 #include "isl_tab_lexopt_templ.c"