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 two 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.
189 struct isl_context
*context
;
190 struct isl_partial_sol
*partial
;
191 void (*add
)(struct isl_sol
*sol
,
192 __isl_take isl_basic_set
*dom
, __isl_take isl_multi_aff
*ma
);
193 void (*add_empty
)(struct isl_sol
*sol
, struct isl_basic_set
*bset
);
194 void (*free
)(struct isl_sol
*sol
);
195 struct isl_sol_callback dec_level
;
198 static void sol_free(struct isl_sol
*sol
)
200 struct isl_partial_sol
*partial
, *next
;
203 for (partial
= sol
->partial
; partial
; partial
= next
) {
204 next
= partial
->next
;
205 isl_basic_set_free(partial
->dom
);
206 isl_multi_aff_free(partial
->ma
);
209 isl_space_free(sol
->space
);
211 sol
->context
->op
->free(sol
->context
);
216 /* Push a partial solution represented by a domain and function "ma"
217 * onto the stack of partial solutions.
218 * If "ma" is NULL, then "dom" represents a part of the domain
221 static void sol_push_sol(struct isl_sol
*sol
,
222 __isl_take isl_basic_set
*dom
, __isl_take isl_multi_aff
*ma
)
224 struct isl_partial_sol
*partial
;
226 if (sol
->error
|| !dom
)
229 partial
= isl_alloc_type(dom
->ctx
, struct isl_partial_sol
);
233 partial
->level
= sol
->level
;
236 partial
->next
= sol
->partial
;
238 sol
->partial
= partial
;
242 isl_basic_set_free(dom
);
243 isl_multi_aff_free(ma
);
247 /* Check that the final columns of "M", starting at "first", are zero.
249 static isl_stat
check_final_columns_are_zero(__isl_keep isl_mat
*M
,
253 unsigned rows
, cols
, n
;
256 return isl_stat_error
;
257 rows
= isl_mat_rows(M
);
258 cols
= isl_mat_cols(M
);
260 for (i
= 0; i
< rows
; ++i
)
261 if (isl_seq_first_non_zero(M
->row
[i
] + first
, n
) != -1)
262 isl_die(isl_mat_get_ctx(M
), isl_error_internal
,
263 "final columns should be zero",
264 return isl_stat_error
);
268 /* Set the affine expressions in "ma" according to the rows in "M", which
269 * are defined over the local space "ls".
270 * The matrix "M" may have extra (zero) columns beyond the number
271 * of variables in "ls".
273 static __isl_give isl_multi_aff
*set_from_affine_matrix(
274 __isl_take isl_multi_aff
*ma
, __isl_take isl_local_space
*ls
,
275 __isl_take isl_mat
*M
)
280 if (!ma
|| !ls
|| !M
)
283 dim
= isl_local_space_dim(ls
, isl_dim_all
);
284 if (check_final_columns_are_zero(M
, 1 + dim
) < 0)
286 for (i
= 1; i
< M
->n_row
; ++i
) {
287 aff
= isl_aff_alloc(isl_local_space_copy(ls
));
289 isl_int_set(aff
->v
->el
[0], M
->row
[0][0]);
290 isl_seq_cpy(aff
->v
->el
+ 1, M
->row
[i
], 1 + dim
);
292 aff
= isl_aff_normalize(aff
);
293 ma
= isl_multi_aff_set_aff(ma
, i
- 1, aff
);
295 isl_local_space_free(ls
);
300 isl_local_space_free(ls
);
302 isl_multi_aff_free(ma
);
306 /* Push a partial solution represented by a domain and mapping M
307 * onto the stack of partial solutions.
309 * The affine matrix "M" maps the dimensions of the context
310 * to the output variables. Convert it into an isl_multi_aff and
311 * then call sol_push_sol.
313 * Note that the description of the initial context may have involved
314 * existentially quantified variables, in which case they also appear
315 * in "dom". These need to be removed before creating the affine
316 * expression because an affine expression cannot be defined in terms
317 * of existentially quantified variables without a known representation.
318 * Since newly added integer divisions are inserted before these
319 * existentially quantified variables, they are still in the final
320 * positions and the corresponding final columns of "M" are zero
321 * because align_context_divs adds the existentially quantified
322 * variables of the context to the main tableau without any constraints and
323 * any equality constraints that are added later on can only serve
324 * to eliminate these existentially quantified variables.
326 static void sol_push_sol_mat(struct isl_sol
*sol
,
327 __isl_take isl_basic_set
*dom
, __isl_take isl_mat
*M
)
333 n_div
= isl_basic_set_dim(dom
, isl_dim_div
);
334 n_known
= n_div
- sol
->context
->n_unknown
;
336 ma
= isl_multi_aff_alloc(isl_space_copy(sol
->space
));
337 ls
= isl_basic_set_get_local_space(dom
);
338 ls
= isl_local_space_drop_dims(ls
, isl_dim_div
,
339 n_known
, n_div
- n_known
);
340 ma
= set_from_affine_matrix(ma
, ls
, M
);
343 dom
= isl_basic_set_free(dom
);
344 sol_push_sol(sol
, dom
, ma
);
347 /* Pop one partial solution from the partial solution stack and
348 * pass it on to sol->add or sol->add_empty.
350 static void sol_pop_one(struct isl_sol
*sol
)
352 struct isl_partial_sol
*partial
;
354 partial
= sol
->partial
;
355 sol
->partial
= partial
->next
;
358 sol
->add(sol
, partial
->dom
, partial
->ma
);
360 sol
->add_empty(sol
, partial
->dom
);
364 /* Return a fresh copy of the domain represented by the context tableau.
366 static struct isl_basic_set
*sol_domain(struct isl_sol
*sol
)
368 struct isl_basic_set
*bset
;
373 bset
= isl_basic_set_dup(sol
->context
->op
->peek_basic_set(sol
->context
));
374 bset
= isl_basic_set_update_from_tab(bset
,
375 sol
->context
->op
->peek_tab(sol
->context
));
380 /* Check whether two partial solutions have the same affine expressions.
382 static isl_bool
same_solution(struct isl_partial_sol
*s1
,
383 struct isl_partial_sol
*s2
)
385 if (!s1
->ma
!= !s2
->ma
)
386 return isl_bool_false
;
388 return isl_bool_true
;
390 return isl_multi_aff_plain_is_equal(s1
->ma
, s2
->ma
);
393 /* Swap the initial two partial solutions in "sol".
397 * sol->partial = p1; p1->next = p2; p2->next = p3
401 * sol->partial = p2; p2->next = p1; p1->next = p3
403 static void swap_initial(struct isl_sol
*sol
)
405 struct isl_partial_sol
*partial
;
407 partial
= sol
->partial
;
408 sol
->partial
= partial
->next
;
409 partial
->next
= partial
->next
->next
;
410 sol
->partial
->next
= partial
;
413 /* Combine the initial two partial solution of "sol" into
414 * a partial solution with the current context domain of "sol" and
415 * the function description of the second partial solution in the list.
416 * The level of the new partial solution is set to the current level.
418 * That is, the first two partial solutions (D1,M1) and (D2,M2) are
419 * replaced by (D,M2), where D is the domain of "sol", which is assumed
420 * to be the union of D1 and D2, while M1 is assumed to be equal to M2
423 static isl_stat
combine_initial_into_second(struct isl_sol
*sol
)
425 struct isl_partial_sol
*partial
;
428 partial
= sol
->partial
;
430 bset
= sol_domain(sol
);
431 isl_basic_set_free(partial
->next
->dom
);
432 partial
->next
->dom
= bset
;
433 partial
->next
->level
= sol
->level
;
436 return isl_stat_error
;
438 sol
->partial
= partial
->next
;
439 isl_basic_set_free(partial
->dom
);
440 isl_multi_aff_free(partial
->ma
);
446 /* Are "ma1" and "ma2" equal to each other on "dom"?
448 * Combine "ma1" and "ma2" with "dom" and check if the results are the same.
449 * "dom" may have existentially quantified variables. Eliminate them first
450 * as otherwise they would have to be eliminated twice, in a more complicated
453 static isl_bool
equal_on_domain(__isl_keep isl_multi_aff
*ma1
,
454 __isl_keep isl_multi_aff
*ma2
, __isl_keep isl_basic_set
*dom
)
457 isl_pw_multi_aff
*pma1
, *pma2
;
460 set
= isl_basic_set_compute_divs(isl_basic_set_copy(dom
));
461 pma1
= isl_pw_multi_aff_alloc(isl_set_copy(set
),
462 isl_multi_aff_copy(ma1
));
463 pma2
= isl_pw_multi_aff_alloc(set
, isl_multi_aff_copy(ma2
));
464 equal
= isl_pw_multi_aff_is_equal(pma1
, pma2
);
465 isl_pw_multi_aff_free(pma1
);
466 isl_pw_multi_aff_free(pma2
);
471 /* The initial two partial solutions of "sol" are known to be at
473 * If they represent the same solution (on different parts of the domain),
474 * then combine them into a single solution at the current level.
475 * Otherwise, pop them both.
477 * Even if the two partial solution are not obviously the same,
478 * one may still be a simplification of the other over its own domain.
479 * Also check if the two sets of affine functions are equal when
480 * restricted to one of the domains. If so, combine the two
481 * using the set of affine functions on the other domain.
482 * That is, for two partial solutions (D1,M1) and (D2,M2),
483 * if M1 = M2 on D1, then the pair of partial solutions can
484 * be replaced by (D1+D2,M2) and similarly when M1 = M2 on D2.
486 static isl_stat
combine_initial_if_equal(struct isl_sol
*sol
)
488 struct isl_partial_sol
*partial
;
491 partial
= sol
->partial
;
493 same
= same_solution(partial
, partial
->next
);
495 return isl_stat_error
;
497 return combine_initial_into_second(sol
);
498 if (partial
->ma
&& partial
->next
->ma
) {
499 same
= equal_on_domain(partial
->ma
, partial
->next
->ma
,
502 return isl_stat_error
;
504 return combine_initial_into_second(sol
);
505 same
= equal_on_domain(partial
->ma
, partial
->next
->ma
,
509 return combine_initial_into_second(sol
);
519 /* Pop all solutions from the partial solution stack that were pushed onto
520 * the stack at levels that are deeper than the current level.
521 * If the two topmost elements on the stack have the same level
522 * and represent the same solution, then their domains are combined.
523 * This combined domain is the same as the current context domain
524 * as sol_pop is called each time we move back to a higher level.
525 * If the outer level (0) has been reached, then all partial solutions
526 * at the current level are also popped off.
528 static void sol_pop(struct isl_sol
*sol
)
530 struct isl_partial_sol
*partial
;
535 partial
= sol
->partial
;
539 if (partial
->level
== 0 && sol
->level
== 0) {
540 for (partial
= sol
->partial
; partial
; partial
= sol
->partial
)
545 if (partial
->level
<= sol
->level
)
548 if (partial
->next
&& partial
->next
->level
== partial
->level
) {
549 if (combine_initial_if_equal(sol
) < 0)
554 if (sol
->level
== 0) {
555 for (partial
= sol
->partial
; partial
; partial
= sol
->partial
)
561 error
: sol
->error
= 1;
564 static void sol_dec_level(struct isl_sol
*sol
)
574 static isl_stat
sol_dec_level_wrap(struct isl_tab_callback
*cb
)
576 struct isl_sol_callback
*callback
= (struct isl_sol_callback
*)cb
;
578 sol_dec_level(callback
->sol
);
580 return callback
->sol
->error
? isl_stat_error
: isl_stat_ok
;
583 /* Move down to next level and push callback onto context tableau
584 * to decrease the level again when it gets rolled back across
585 * the current state. That is, dec_level will be called with
586 * the context tableau in the same state as it is when inc_level
589 static void sol_inc_level(struct isl_sol
*sol
)
597 tab
= sol
->context
->op
->peek_tab(sol
->context
);
598 if (isl_tab_push_callback(tab
, &sol
->dec_level
.callback
) < 0)
602 static void scale_rows(struct isl_mat
*mat
, isl_int m
, int n_row
)
606 if (isl_int_is_one(m
))
609 for (i
= 0; i
< n_row
; ++i
)
610 isl_seq_scale(mat
->row
[i
], mat
->row
[i
], m
, mat
->n_col
);
613 /* Add the solution identified by the tableau and the context tableau.
615 * The layout of the variables is as follows.
616 * tab->n_var is equal to the total number of variables in the input
617 * map (including divs that were copied from the context)
618 * + the number of extra divs constructed
619 * Of these, the first tab->n_param and the last tab->n_div variables
620 * correspond to the variables in the context, i.e.,
621 * tab->n_param + tab->n_div = context_tab->n_var
622 * tab->n_param is equal to the number of parameters and input
623 * dimensions in the input map
624 * tab->n_div is equal to the number of divs in the context
626 * If there is no solution, then call add_empty with a basic set
627 * that corresponds to the context tableau. (If add_empty is NULL,
630 * If there is a solution, then first construct a matrix that maps
631 * all dimensions of the context to the output variables, i.e.,
632 * the output dimensions in the input map.
633 * The divs in the input map (if any) that do not correspond to any
634 * div in the context do not appear in the solution.
635 * The algorithm will make sure that they have an integer value,
636 * but these values themselves are of no interest.
637 * We have to be careful not to drop or rearrange any divs in the
638 * context because that would change the meaning of the matrix.
640 * To extract the value of the output variables, it should be noted
641 * that we always use a big parameter M in the main tableau and so
642 * the variable stored in this tableau is not an output variable x itself, but
643 * x' = M + x (in case of minimization)
645 * x' = M - x (in case of maximization)
646 * If x' appears in a column, then its optimal value is zero,
647 * which means that the optimal value of x is an unbounded number
648 * (-M for minimization and M for maximization).
649 * We currently assume that the output dimensions in the original map
650 * are bounded, so this cannot occur.
651 * Similarly, when x' appears in a row, then the coefficient of M in that
652 * row is necessarily 1.
653 * If the row in the tableau represents
654 * d x' = c + d M + e(y)
655 * then, in case of minimization, the corresponding row in the matrix
658 * with a d = m, the (updated) common denominator of the matrix.
659 * In case of maximization, the row will be
662 static void sol_add(struct isl_sol
*sol
, struct isl_tab
*tab
)
664 struct isl_basic_set
*bset
= NULL
;
665 struct isl_mat
*mat
= NULL
;
670 if (sol
->error
|| !tab
)
673 if (tab
->empty
&& !sol
->add_empty
)
675 if (sol
->context
->op
->is_empty(sol
->context
))
678 bset
= sol_domain(sol
);
681 sol_push_sol(sol
, bset
, NULL
);
687 mat
= isl_mat_alloc(tab
->mat
->ctx
, 1 + sol
->n_out
,
688 1 + tab
->n_param
+ tab
->n_div
);
694 isl_seq_clr(mat
->row
[0] + 1, mat
->n_col
- 1);
695 isl_int_set_si(mat
->row
[0][0], 1);
696 for (row
= 0; row
< sol
->n_out
; ++row
) {
697 int i
= tab
->n_param
+ row
;
700 isl_seq_clr(mat
->row
[1 + row
], mat
->n_col
);
701 if (!tab
->var
[i
].is_row
) {
703 isl_die(mat
->ctx
, isl_error_invalid
,
704 "unbounded optimum", goto error2
);
708 r
= tab
->var
[i
].index
;
710 isl_int_ne(tab
->mat
->row
[r
][2], tab
->mat
->row
[r
][0]))
711 isl_die(mat
->ctx
, isl_error_invalid
,
712 "unbounded optimum", goto error2
);
713 isl_int_gcd(m
, mat
->row
[0][0], tab
->mat
->row
[r
][0]);
714 isl_int_divexact(m
, tab
->mat
->row
[r
][0], m
);
715 scale_rows(mat
, m
, 1 + row
);
716 isl_int_divexact(m
, mat
->row
[0][0], tab
->mat
->row
[r
][0]);
717 isl_int_mul(mat
->row
[1 + row
][0], m
, tab
->mat
->row
[r
][1]);
718 for (j
= 0; j
< tab
->n_param
; ++j
) {
720 if (tab
->var
[j
].is_row
)
722 col
= tab
->var
[j
].index
;
723 isl_int_mul(mat
->row
[1 + row
][1 + j
], m
,
724 tab
->mat
->row
[r
][off
+ col
]);
726 for (j
= 0; j
< tab
->n_div
; ++j
) {
728 if (tab
->var
[tab
->n_var
- tab
->n_div
+j
].is_row
)
730 col
= tab
->var
[tab
->n_var
- tab
->n_div
+j
].index
;
731 isl_int_mul(mat
->row
[1 + row
][1 + tab
->n_param
+ j
], m
,
732 tab
->mat
->row
[r
][off
+ col
]);
735 isl_seq_neg(mat
->row
[1 + row
], mat
->row
[1 + row
],
741 sol_push_sol_mat(sol
, bset
, mat
);
746 isl_basic_set_free(bset
);
754 struct isl_set
*empty
;
757 static void sol_map_free(struct isl_sol
*sol
)
759 struct isl_sol_map
*sol_map
= (struct isl_sol_map
*) sol
;
760 isl_map_free(sol_map
->map
);
761 isl_set_free(sol_map
->empty
);
764 /* This function is called for parts of the context where there is
765 * no solution, with "bset" corresponding to the context tableau.
766 * Simply add the basic set to the set "empty".
768 static void sol_map_add_empty(struct isl_sol_map
*sol
,
769 struct isl_basic_set
*bset
)
771 if (!bset
|| !sol
->empty
)
774 sol
->empty
= isl_set_grow(sol
->empty
, 1);
775 bset
= isl_basic_set_simplify(bset
);
776 bset
= isl_basic_set_finalize(bset
);
777 sol
->empty
= isl_set_add_basic_set(sol
->empty
, isl_basic_set_copy(bset
));
780 isl_basic_set_free(bset
);
783 isl_basic_set_free(bset
);
787 static void sol_map_add_empty_wrap(struct isl_sol
*sol
,
788 struct isl_basic_set
*bset
)
790 sol_map_add_empty((struct isl_sol_map
*)sol
, bset
);
793 /* Given a basic set "dom" that represents the context and a tuple of
794 * affine expressions "ma" defined over this domain, construct a basic map
795 * that expresses this function on the domain.
797 static void sol_map_add(struct isl_sol_map
*sol
,
798 __isl_take isl_basic_set
*dom
, __isl_take isl_multi_aff
*ma
)
802 if (sol
->sol
.error
|| !dom
|| !ma
)
805 bmap
= isl_basic_map_from_multi_aff2(ma
, sol
->sol
.rational
);
806 bmap
= isl_basic_map_intersect_domain(bmap
, dom
);
807 sol
->map
= isl_map_grow(sol
->map
, 1);
808 sol
->map
= isl_map_add_basic_map(sol
->map
, bmap
);
813 isl_basic_set_free(dom
);
814 isl_multi_aff_free(ma
);
818 static void sol_map_add_wrap(struct isl_sol
*sol
,
819 __isl_take isl_basic_set
*dom
, __isl_take isl_multi_aff
*ma
)
821 sol_map_add((struct isl_sol_map
*)sol
, dom
, ma
);
825 /* Store the "parametric constant" of row "row" of tableau "tab" in "line",
826 * i.e., the constant term and the coefficients of all variables that
827 * appear in the context tableau.
828 * Note that the coefficient of the big parameter M is NOT copied.
829 * The context tableau may not have a big parameter and even when it
830 * does, it is a different big parameter.
832 static void get_row_parameter_line(struct isl_tab
*tab
, int row
, isl_int
*line
)
835 unsigned off
= 2 + tab
->M
;
837 isl_int_set(line
[0], tab
->mat
->row
[row
][1]);
838 for (i
= 0; i
< tab
->n_param
; ++i
) {
839 if (tab
->var
[i
].is_row
)
840 isl_int_set_si(line
[1 + i
], 0);
842 int col
= tab
->var
[i
].index
;
843 isl_int_set(line
[1 + i
], tab
->mat
->row
[row
][off
+ col
]);
846 for (i
= 0; i
< tab
->n_div
; ++i
) {
847 if (tab
->var
[tab
->n_var
- tab
->n_div
+ i
].is_row
)
848 isl_int_set_si(line
[1 + tab
->n_param
+ i
], 0);
850 int col
= tab
->var
[tab
->n_var
- tab
->n_div
+ i
].index
;
851 isl_int_set(line
[1 + tab
->n_param
+ i
],
852 tab
->mat
->row
[row
][off
+ col
]);
857 /* Check if rows "row1" and "row2" have identical "parametric constants",
858 * as explained above.
859 * In this case, we also insist that the coefficients of the big parameter
860 * be the same as the values of the constants will only be the same
861 * if these coefficients are also the same.
863 static int identical_parameter_line(struct isl_tab
*tab
, int row1
, int row2
)
866 unsigned off
= 2 + tab
->M
;
868 if (isl_int_ne(tab
->mat
->row
[row1
][1], tab
->mat
->row
[row2
][1]))
871 if (tab
->M
&& isl_int_ne(tab
->mat
->row
[row1
][2],
872 tab
->mat
->row
[row2
][2]))
875 for (i
= 0; i
< tab
->n_param
+ tab
->n_div
; ++i
) {
876 int pos
= i
< tab
->n_param
? i
:
877 tab
->n_var
- tab
->n_div
+ i
- tab
->n_param
;
880 if (tab
->var
[pos
].is_row
)
882 col
= tab
->var
[pos
].index
;
883 if (isl_int_ne(tab
->mat
->row
[row1
][off
+ col
],
884 tab
->mat
->row
[row2
][off
+ col
]))
890 /* Return an inequality that expresses that the "parametric constant"
891 * should be non-negative.
892 * This function is only called when the coefficient of the big parameter
895 static struct isl_vec
*get_row_parameter_ineq(struct isl_tab
*tab
, int row
)
897 struct isl_vec
*ineq
;
899 ineq
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_param
+ tab
->n_div
);
903 get_row_parameter_line(tab
, row
, ineq
->el
);
905 ineq
= isl_vec_normalize(ineq
);
910 /* Normalize a div expression of the form
912 * [(g*f(x) + c)/(g * m)]
914 * with c the constant term and f(x) the remaining coefficients, to
918 static void normalize_div(__isl_keep isl_vec
*div
)
920 isl_ctx
*ctx
= isl_vec_get_ctx(div
);
921 int len
= div
->size
- 2;
923 isl_seq_gcd(div
->el
+ 2, len
, &ctx
->normalize_gcd
);
924 isl_int_gcd(ctx
->normalize_gcd
, ctx
->normalize_gcd
, div
->el
[0]);
926 if (isl_int_is_one(ctx
->normalize_gcd
))
929 isl_int_divexact(div
->el
[0], div
->el
[0], ctx
->normalize_gcd
);
930 isl_int_fdiv_q(div
->el
[1], div
->el
[1], ctx
->normalize_gcd
);
931 isl_seq_scale_down(div
->el
+ 2, div
->el
+ 2, ctx
->normalize_gcd
, len
);
934 /* Return an integer division for use in a parametric cut based
936 * In particular, let the parametric constant of the row be
940 * where y_0 = 1, but none of the y_i corresponds to the big parameter M.
941 * The div returned is equal to
943 * floor(\sum_i {-a_i} y_i) = floor((\sum_i (-a_i mod d) y_i)/d)
945 static struct isl_vec
*get_row_parameter_div(struct isl_tab
*tab
, int row
)
949 div
= isl_vec_alloc(tab
->mat
->ctx
, 1 + 1 + tab
->n_param
+ tab
->n_div
);
953 isl_int_set(div
->el
[0], tab
->mat
->row
[row
][0]);
954 get_row_parameter_line(tab
, row
, div
->el
+ 1);
955 isl_seq_neg(div
->el
+ 1, div
->el
+ 1, div
->size
- 1);
957 isl_seq_fdiv_r(div
->el
+ 1, div
->el
+ 1, div
->el
[0], div
->size
- 1);
962 /* Return an integer division for use in transferring an integrality constraint
964 * In particular, let the parametric constant of the row be
968 * where y_0 = 1, but none of the y_i corresponds to the big parameter M.
969 * The the returned div is equal to
971 * floor(\sum_i {a_i} y_i) = floor((\sum_i (a_i mod d) y_i)/d)
973 static struct isl_vec
*get_row_split_div(struct isl_tab
*tab
, int row
)
977 div
= isl_vec_alloc(tab
->mat
->ctx
, 1 + 1 + tab
->n_param
+ tab
->n_div
);
981 isl_int_set(div
->el
[0], tab
->mat
->row
[row
][0]);
982 get_row_parameter_line(tab
, row
, div
->el
+ 1);
984 isl_seq_fdiv_r(div
->el
+ 1, div
->el
+ 1, div
->el
[0], div
->size
- 1);
989 /* Construct and return an inequality that expresses an upper bound
991 * In particular, if the div is given by
995 * then the inequality expresses
999 static __isl_give isl_vec
*ineq_for_div(__isl_keep isl_basic_set
*bset
,
1004 struct isl_vec
*ineq
;
1009 total
= isl_basic_set_total_dim(bset
);
1010 div_pos
= 1 + total
- bset
->n_div
+ div
;
1012 ineq
= isl_vec_alloc(bset
->ctx
, 1 + total
);
1016 isl_seq_cpy(ineq
->el
, bset
->div
[div
] + 1, 1 + total
);
1017 isl_int_neg(ineq
->el
[div_pos
], bset
->div
[div
][0]);
1021 /* Given a row in the tableau and a div that was created
1022 * using get_row_split_div and that has been constrained to equality, i.e.,
1024 * d = floor(\sum_i {a_i} y_i) = \sum_i {a_i} y_i
1026 * replace the expression "\sum_i {a_i} y_i" in the row by d,
1027 * i.e., we subtract "\sum_i {a_i} y_i" and add 1 d.
1028 * The coefficients of the non-parameters in the tableau have been
1029 * verified to be integral. We can therefore simply replace coefficient b
1030 * by floor(b). For the coefficients of the parameters we have
1031 * floor(a_i) = a_i - {a_i}, while for the other coefficients, we have
1034 static struct isl_tab
*set_row_cst_to_div(struct isl_tab
*tab
, int row
, int div
)
1036 isl_seq_fdiv_q(tab
->mat
->row
[row
] + 1, tab
->mat
->row
[row
] + 1,
1037 tab
->mat
->row
[row
][0], 1 + tab
->M
+ tab
->n_col
);
1039 isl_int_set_si(tab
->mat
->row
[row
][0], 1);
1041 if (tab
->var
[tab
->n_var
- tab
->n_div
+ div
].is_row
) {
1042 int drow
= tab
->var
[tab
->n_var
- tab
->n_div
+ div
].index
;
1044 isl_assert(tab
->mat
->ctx
,
1045 isl_int_is_one(tab
->mat
->row
[drow
][0]), goto error
);
1046 isl_seq_combine(tab
->mat
->row
[row
] + 1,
1047 tab
->mat
->ctx
->one
, tab
->mat
->row
[row
] + 1,
1048 tab
->mat
->ctx
->one
, tab
->mat
->row
[drow
] + 1,
1049 1 + tab
->M
+ tab
->n_col
);
1051 int dcol
= tab
->var
[tab
->n_var
- tab
->n_div
+ div
].index
;
1053 isl_int_add_ui(tab
->mat
->row
[row
][2 + tab
->M
+ dcol
],
1054 tab
->mat
->row
[row
][2 + tab
->M
+ dcol
], 1);
1063 /* Check if the (parametric) constant of the given row is obviously
1064 * negative, meaning that we don't need to consult the context tableau.
1065 * If there is a big parameter and its coefficient is non-zero,
1066 * then this coefficient determines the outcome.
1067 * Otherwise, we check whether the constant is negative and
1068 * all non-zero coefficients of parameters are negative and
1069 * belong to non-negative parameters.
1071 static int is_obviously_neg(struct isl_tab
*tab
, int row
)
1075 unsigned off
= 2 + tab
->M
;
1078 if (isl_int_is_pos(tab
->mat
->row
[row
][2]))
1080 if (isl_int_is_neg(tab
->mat
->row
[row
][2]))
1084 if (isl_int_is_nonneg(tab
->mat
->row
[row
][1]))
1086 for (i
= 0; i
< tab
->n_param
; ++i
) {
1087 /* Eliminated parameter */
1088 if (tab
->var
[i
].is_row
)
1090 col
= tab
->var
[i
].index
;
1091 if (isl_int_is_zero(tab
->mat
->row
[row
][off
+ col
]))
1093 if (!tab
->var
[i
].is_nonneg
)
1095 if (isl_int_is_pos(tab
->mat
->row
[row
][off
+ col
]))
1098 for (i
= 0; i
< tab
->n_div
; ++i
) {
1099 if (tab
->var
[tab
->n_var
- tab
->n_div
+ i
].is_row
)
1101 col
= tab
->var
[tab
->n_var
- tab
->n_div
+ i
].index
;
1102 if (isl_int_is_zero(tab
->mat
->row
[row
][off
+ col
]))
1104 if (!tab
->var
[tab
->n_var
- tab
->n_div
+ i
].is_nonneg
)
1106 if (isl_int_is_pos(tab
->mat
->row
[row
][off
+ col
]))
1112 /* Check if the (parametric) constant of the given row is obviously
1113 * non-negative, meaning that we don't need to consult the context tableau.
1114 * If there is a big parameter and its coefficient is non-zero,
1115 * then this coefficient determines the outcome.
1116 * Otherwise, we check whether the constant is non-negative and
1117 * all non-zero coefficients of parameters are positive and
1118 * belong to non-negative parameters.
1120 static int is_obviously_nonneg(struct isl_tab
*tab
, int row
)
1124 unsigned off
= 2 + tab
->M
;
1127 if (isl_int_is_pos(tab
->mat
->row
[row
][2]))
1129 if (isl_int_is_neg(tab
->mat
->row
[row
][2]))
1133 if (isl_int_is_neg(tab
->mat
->row
[row
][1]))
1135 for (i
= 0; i
< tab
->n_param
; ++i
) {
1136 /* Eliminated parameter */
1137 if (tab
->var
[i
].is_row
)
1139 col
= tab
->var
[i
].index
;
1140 if (isl_int_is_zero(tab
->mat
->row
[row
][off
+ col
]))
1142 if (!tab
->var
[i
].is_nonneg
)
1144 if (isl_int_is_neg(tab
->mat
->row
[row
][off
+ col
]))
1147 for (i
= 0; i
< tab
->n_div
; ++i
) {
1148 if (tab
->var
[tab
->n_var
- tab
->n_div
+ i
].is_row
)
1150 col
= tab
->var
[tab
->n_var
- tab
->n_div
+ i
].index
;
1151 if (isl_int_is_zero(tab
->mat
->row
[row
][off
+ col
]))
1153 if (!tab
->var
[tab
->n_var
- tab
->n_div
+ i
].is_nonneg
)
1155 if (isl_int_is_neg(tab
->mat
->row
[row
][off
+ col
]))
1161 /* Given a row r and two columns, return the column that would
1162 * lead to the lexicographically smallest increment in the sample
1163 * solution when leaving the basis in favor of the row.
1164 * Pivoting with column c will increment the sample value by a non-negative
1165 * constant times a_{V,c}/a_{r,c}, with a_{V,c} the elements of column c
1166 * corresponding to the non-parametric variables.
1167 * If variable v appears in a column c_v, the a_{v,c} = 1 iff c = c_v,
1168 * with all other entries in this virtual row equal to zero.
1169 * If variable v appears in a row, then a_{v,c} is the element in column c
1172 * Let v be the first variable with a_{v,c1}/a_{r,c1} != a_{v,c2}/a_{r,c2}.
1173 * Then if a_{v,c1}/a_{r,c1} < a_{v,c2}/a_{r,c2}, i.e.,
1174 * a_{v,c2} a_{r,c1} - a_{v,c1} a_{r,c2} > 0, c1 results in the minimal
1175 * increment. Otherwise, it's c2.
1177 static int lexmin_col_pair(struct isl_tab
*tab
,
1178 int row
, int col1
, int col2
, isl_int tmp
)
1183 tr
= tab
->mat
->row
[row
] + 2 + tab
->M
;
1185 for (i
= tab
->n_param
; i
< tab
->n_var
- tab
->n_div
; ++i
) {
1189 if (!tab
->var
[i
].is_row
) {
1190 if (tab
->var
[i
].index
== col1
)
1192 if (tab
->var
[i
].index
== col2
)
1197 if (tab
->var
[i
].index
== row
)
1200 r
= tab
->mat
->row
[tab
->var
[i
].index
] + 2 + tab
->M
;
1201 s1
= isl_int_sgn(r
[col1
]);
1202 s2
= isl_int_sgn(r
[col2
]);
1203 if (s1
== 0 && s2
== 0)
1210 isl_int_mul(tmp
, r
[col2
], tr
[col1
]);
1211 isl_int_submul(tmp
, r
[col1
], tr
[col2
]);
1212 if (isl_int_is_pos(tmp
))
1214 if (isl_int_is_neg(tmp
))
1220 /* Does the index into the tab->var or tab->con array "index"
1221 * correspond to a variable in the context tableau?
1222 * In particular, it needs to be an index into the tab->var array and
1223 * it needs to refer to either one of the first tab->n_param variables or
1224 * one of the last tab->n_div variables.
1226 static int is_parameter_var(struct isl_tab
*tab
, int index
)
1230 if (index
< tab
->n_param
)
1232 if (index
>= tab
->n_var
- tab
->n_div
)
1237 /* Does column "col" of "tab" refer to a variable in the context tableau?
1239 static int col_is_parameter_var(struct isl_tab
*tab
, int col
)
1241 return is_parameter_var(tab
, tab
->col_var
[col
]);
1244 /* Does row "row" of "tab" refer to a variable in the context tableau?
1246 static int row_is_parameter_var(struct isl_tab
*tab
, int row
)
1248 return is_parameter_var(tab
, tab
->row_var
[row
]);
1251 /* Given a row in the tableau, find and return the column that would
1252 * result in the lexicographically smallest, but positive, increment
1253 * in the sample point.
1254 * If there is no such column, then return tab->n_col.
1255 * If anything goes wrong, return -1.
1257 static int lexmin_pivot_col(struct isl_tab
*tab
, int row
)
1260 int col
= tab
->n_col
;
1264 tr
= tab
->mat
->row
[row
] + 2 + tab
->M
;
1268 for (j
= tab
->n_dead
; j
< tab
->n_col
; ++j
) {
1269 if (col_is_parameter_var(tab
, j
))
1272 if (!isl_int_is_pos(tr
[j
]))
1275 if (col
== tab
->n_col
)
1278 col
= lexmin_col_pair(tab
, row
, col
, j
, tmp
);
1279 isl_assert(tab
->mat
->ctx
, col
>= 0, goto error
);
1289 /* Return the first known violated constraint, i.e., a non-negative
1290 * constraint that currently has an either obviously negative value
1291 * or a previously determined to be negative value.
1293 * If any constraint has a negative coefficient for the big parameter,
1294 * if any, then we return one of these first.
1296 static int first_neg(struct isl_tab
*tab
)
1301 for (row
= tab
->n_redundant
; row
< tab
->n_row
; ++row
) {
1302 if (!isl_tab_var_from_row(tab
, row
)->is_nonneg
)
1304 if (!isl_int_is_neg(tab
->mat
->row
[row
][2]))
1307 tab
->row_sign
[row
] = isl_tab_row_neg
;
1310 for (row
= tab
->n_redundant
; row
< tab
->n_row
; ++row
) {
1311 if (!isl_tab_var_from_row(tab
, row
)->is_nonneg
)
1313 if (tab
->row_sign
) {
1314 if (tab
->row_sign
[row
] == 0 &&
1315 is_obviously_neg(tab
, row
))
1316 tab
->row_sign
[row
] = isl_tab_row_neg
;
1317 if (tab
->row_sign
[row
] != isl_tab_row_neg
)
1319 } else if (!is_obviously_neg(tab
, row
))
1326 /* Check whether the invariant that all columns are lexico-positive
1327 * is satisfied. This function is not called from the current code
1328 * but is useful during debugging.
1330 static void check_lexpos(struct isl_tab
*tab
) __attribute__ ((unused
));
1331 static void check_lexpos(struct isl_tab
*tab
)
1333 unsigned off
= 2 + tab
->M
;
1338 for (col
= tab
->n_dead
; col
< tab
->n_col
; ++col
) {
1339 if (col_is_parameter_var(tab
, col
))
1341 for (var
= tab
->n_param
; var
< tab
->n_var
- tab
->n_div
; ++var
) {
1342 if (!tab
->var
[var
].is_row
) {
1343 if (tab
->var
[var
].index
== col
)
1348 row
= tab
->var
[var
].index
;
1349 if (isl_int_is_zero(tab
->mat
->row
[row
][off
+ col
]))
1351 if (isl_int_is_pos(tab
->mat
->row
[row
][off
+ col
]))
1353 fprintf(stderr
, "lexneg column %d (row %d)\n",
1356 if (var
>= tab
->n_var
- tab
->n_div
)
1357 fprintf(stderr
, "zero column %d\n", col
);
1361 /* Report to the caller that the given constraint is part of an encountered
1364 static int report_conflicting_constraint(struct isl_tab
*tab
, int con
)
1366 return tab
->conflict(con
, tab
->conflict_user
);
1369 /* Given a conflicting row in the tableau, report all constraints
1370 * involved in the row to the caller. That is, the row itself
1371 * (if it represents a constraint) and all constraint columns with
1372 * non-zero (and therefore negative) coefficients.
1374 static int report_conflict(struct isl_tab
*tab
, int row
)
1382 if (tab
->row_var
[row
] < 0 &&
1383 report_conflicting_constraint(tab
, ~tab
->row_var
[row
]) < 0)
1386 tr
= tab
->mat
->row
[row
] + 2 + tab
->M
;
1388 for (j
= tab
->n_dead
; j
< tab
->n_col
; ++j
) {
1389 if (col_is_parameter_var(tab
, j
))
1392 if (!isl_int_is_neg(tr
[j
]))
1395 if (tab
->col_var
[j
] < 0 &&
1396 report_conflicting_constraint(tab
, ~tab
->col_var
[j
]) < 0)
1403 /* Resolve all known or obviously violated constraints through pivoting.
1404 * In particular, as long as we can find any violated constraint, we
1405 * look for a pivoting column that would result in the lexicographically
1406 * smallest increment in the sample point. If there is no such column
1407 * then the tableau is infeasible.
1409 static int restore_lexmin(struct isl_tab
*tab
) WARN_UNUSED
;
1410 static int restore_lexmin(struct isl_tab
*tab
)
1418 while ((row
= first_neg(tab
)) != -1) {
1419 col
= lexmin_pivot_col(tab
, row
);
1420 if (col
>= tab
->n_col
) {
1421 if (report_conflict(tab
, row
) < 0)
1423 if (isl_tab_mark_empty(tab
) < 0)
1429 if (isl_tab_pivot(tab
, row
, col
) < 0)
1435 /* Given a row that represents an equality, look for an appropriate
1437 * In particular, if there are any non-zero coefficients among
1438 * the non-parameter variables, then we take the last of these
1439 * variables. Eliminating this variable in terms of the other
1440 * variables and/or parameters does not influence the property
1441 * that all column in the initial tableau are lexicographically
1442 * positive. The row corresponding to the eliminated variable
1443 * will only have non-zero entries below the diagonal of the
1444 * initial tableau. That is, we transform
1450 * If there is no such non-parameter variable, then we are dealing with
1451 * pure parameter equality and we pick any parameter with coefficient 1 or -1
1452 * for elimination. This will ensure that the eliminated parameter
1453 * always has an integer value whenever all the other parameters are integral.
1454 * If there is no such parameter then we return -1.
1456 static int last_var_col_or_int_par_col(struct isl_tab
*tab
, int row
)
1458 unsigned off
= 2 + tab
->M
;
1461 for (i
= tab
->n_var
- tab
->n_div
- 1; i
>= 0 && i
>= tab
->n_param
; --i
) {
1463 if (tab
->var
[i
].is_row
)
1465 col
= tab
->var
[i
].index
;
1466 if (col
<= tab
->n_dead
)
1468 if (!isl_int_is_zero(tab
->mat
->row
[row
][off
+ col
]))
1471 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
1472 if (isl_int_is_one(tab
->mat
->row
[row
][off
+ i
]))
1474 if (isl_int_is_negone(tab
->mat
->row
[row
][off
+ i
]))
1480 /* Add an equality that is known to be valid to the tableau.
1481 * We first check if we can eliminate a variable or a parameter.
1482 * If not, we add the equality as two inequalities.
1483 * In this case, the equality was a pure parameter equality and there
1484 * is no need to resolve any constraint violations.
1486 * This function assumes that at least two more rows and at least
1487 * two more elements in the constraint array are available in the tableau.
1489 static struct isl_tab
*add_lexmin_valid_eq(struct isl_tab
*tab
, isl_int
*eq
)
1496 r
= isl_tab_add_row(tab
, eq
);
1500 r
= tab
->con
[r
].index
;
1501 i
= last_var_col_or_int_par_col(tab
, r
);
1503 tab
->con
[r
].is_nonneg
= 1;
1504 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]) < 0)
1506 isl_seq_neg(eq
, eq
, 1 + tab
->n_var
);
1507 r
= isl_tab_add_row(tab
, eq
);
1510 tab
->con
[r
].is_nonneg
= 1;
1511 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]) < 0)
1514 if (isl_tab_pivot(tab
, r
, i
) < 0)
1516 if (isl_tab_kill_col(tab
, i
) < 0)
1527 /* Check if the given row is a pure constant.
1529 static int is_constant(struct isl_tab
*tab
, int row
)
1531 unsigned off
= 2 + tab
->M
;
1533 return isl_seq_first_non_zero(tab
->mat
->row
[row
] + off
+ tab
->n_dead
,
1534 tab
->n_col
- tab
->n_dead
) == -1;
1537 /* Is the given row a parametric constant?
1538 * That is, does it only involve variables that also appear in the context?
1540 static int is_parametric_constant(struct isl_tab
*tab
, int row
)
1542 unsigned off
= 2 + tab
->M
;
1545 for (col
= tab
->n_dead
; col
< tab
->n_col
; ++col
) {
1546 if (col_is_parameter_var(tab
, col
))
1548 if (isl_int_is_zero(tab
->mat
->row
[row
][off
+ col
]))
1556 /* Add an equality that may or may not be valid to the tableau.
1557 * If the resulting row is a pure constant, then it must be zero.
1558 * Otherwise, the resulting tableau is empty.
1560 * If the row is not a pure constant, then we add two inequalities,
1561 * each time checking that they can be satisfied.
1562 * In the end we try to use one of the two constraints to eliminate
1565 * This function assumes that at least two more rows and at least
1566 * two more elements in the constraint array are available in the tableau.
1568 static int add_lexmin_eq(struct isl_tab
*tab
, isl_int
*eq
) WARN_UNUSED
;
1569 static int add_lexmin_eq(struct isl_tab
*tab
, isl_int
*eq
)
1573 struct isl_tab_undo
*snap
;
1577 snap
= isl_tab_snap(tab
);
1578 r1
= isl_tab_add_row(tab
, eq
);
1581 tab
->con
[r1
].is_nonneg
= 1;
1582 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r1
]) < 0)
1585 row
= tab
->con
[r1
].index
;
1586 if (is_constant(tab
, row
)) {
1587 if (!isl_int_is_zero(tab
->mat
->row
[row
][1]) ||
1588 (tab
->M
&& !isl_int_is_zero(tab
->mat
->row
[row
][2]))) {
1589 if (isl_tab_mark_empty(tab
) < 0)
1593 if (isl_tab_rollback(tab
, snap
) < 0)
1598 if (restore_lexmin(tab
) < 0)
1603 isl_seq_neg(eq
, eq
, 1 + tab
->n_var
);
1605 r2
= isl_tab_add_row(tab
, eq
);
1608 tab
->con
[r2
].is_nonneg
= 1;
1609 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r2
]) < 0)
1612 if (restore_lexmin(tab
) < 0)
1617 if (!tab
->con
[r1
].is_row
) {
1618 if (isl_tab_kill_col(tab
, tab
->con
[r1
].index
) < 0)
1620 } else if (!tab
->con
[r2
].is_row
) {
1621 if (isl_tab_kill_col(tab
, tab
->con
[r2
].index
) < 0)
1626 tab
->bmap
= isl_basic_map_add_ineq(tab
->bmap
, eq
);
1627 if (isl_tab_push(tab
, isl_tab_undo_bmap_ineq
) < 0)
1629 isl_seq_neg(eq
, eq
, 1 + tab
->n_var
);
1630 tab
->bmap
= isl_basic_map_add_ineq(tab
->bmap
, eq
);
1631 isl_seq_neg(eq
, eq
, 1 + tab
->n_var
);
1632 if (isl_tab_push(tab
, isl_tab_undo_bmap_ineq
) < 0)
1641 /* Add an inequality to the tableau, resolving violations using
1644 * This function assumes that at least one more row and at least
1645 * one more element in the constraint array are available in the tableau.
1647 static struct isl_tab
*add_lexmin_ineq(struct isl_tab
*tab
, isl_int
*ineq
)
1654 tab
->bmap
= isl_basic_map_add_ineq(tab
->bmap
, ineq
);
1655 if (isl_tab_push(tab
, isl_tab_undo_bmap_ineq
) < 0)
1660 r
= isl_tab_add_row(tab
, ineq
);
1663 tab
->con
[r
].is_nonneg
= 1;
1664 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]) < 0)
1666 if (isl_tab_row_is_redundant(tab
, tab
->con
[r
].index
)) {
1667 if (isl_tab_mark_redundant(tab
, tab
->con
[r
].index
) < 0)
1672 if (restore_lexmin(tab
) < 0)
1674 if (!tab
->empty
&& tab
->con
[r
].is_row
&&
1675 isl_tab_row_is_redundant(tab
, tab
->con
[r
].index
))
1676 if (isl_tab_mark_redundant(tab
, tab
->con
[r
].index
) < 0)
1684 /* Check if the coefficients of the parameters are all integral.
1686 static int integer_parameter(struct isl_tab
*tab
, int row
)
1690 unsigned off
= 2 + tab
->M
;
1692 for (i
= 0; i
< tab
->n_param
; ++i
) {
1693 /* Eliminated parameter */
1694 if (tab
->var
[i
].is_row
)
1696 col
= tab
->var
[i
].index
;
1697 if (!isl_int_is_divisible_by(tab
->mat
->row
[row
][off
+ col
],
1698 tab
->mat
->row
[row
][0]))
1701 for (i
= 0; i
< tab
->n_div
; ++i
) {
1702 if (tab
->var
[tab
->n_var
- tab
->n_div
+ i
].is_row
)
1704 col
= tab
->var
[tab
->n_var
- tab
->n_div
+ i
].index
;
1705 if (!isl_int_is_divisible_by(tab
->mat
->row
[row
][off
+ col
],
1706 tab
->mat
->row
[row
][0]))
1712 /* Check if the coefficients of the non-parameter variables are all integral.
1714 static int integer_variable(struct isl_tab
*tab
, int row
)
1717 unsigned off
= 2 + tab
->M
;
1719 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
1720 if (col_is_parameter_var(tab
, i
))
1722 if (!isl_int_is_divisible_by(tab
->mat
->row
[row
][off
+ i
],
1723 tab
->mat
->row
[row
][0]))
1729 /* Check if the constant term is integral.
1731 static int integer_constant(struct isl_tab
*tab
, int row
)
1733 return isl_int_is_divisible_by(tab
->mat
->row
[row
][1],
1734 tab
->mat
->row
[row
][0]);
1737 #define I_CST 1 << 0
1738 #define I_PAR 1 << 1
1739 #define I_VAR 1 << 2
1741 /* Check for next (non-parameter) variable after "var" (first if var == -1)
1742 * that is non-integer and therefore requires a cut and return
1743 * the index of the variable.
1744 * For parametric tableaus, there are three parts in a row,
1745 * the constant, the coefficients of the parameters and the rest.
1746 * For each part, we check whether the coefficients in that part
1747 * are all integral and if so, set the corresponding flag in *f.
1748 * If the constant and the parameter part are integral, then the
1749 * current sample value is integral and no cut is required
1750 * (irrespective of whether the variable part is integral).
1752 static int next_non_integer_var(struct isl_tab
*tab
, int var
, int *f
)
1754 var
= var
< 0 ? tab
->n_param
: var
+ 1;
1756 for (; var
< tab
->n_var
- tab
->n_div
; ++var
) {
1759 if (!tab
->var
[var
].is_row
)
1761 row
= tab
->var
[var
].index
;
1762 if (integer_constant(tab
, row
))
1763 ISL_FL_SET(flags
, I_CST
);
1764 if (integer_parameter(tab
, row
))
1765 ISL_FL_SET(flags
, I_PAR
);
1766 if (ISL_FL_ISSET(flags
, I_CST
) && ISL_FL_ISSET(flags
, I_PAR
))
1768 if (integer_variable(tab
, row
))
1769 ISL_FL_SET(flags
, I_VAR
);
1776 /* Check for first (non-parameter) variable that is non-integer and
1777 * therefore requires a cut and return the corresponding row.
1778 * For parametric tableaus, there are three parts in a row,
1779 * the constant, the coefficients of the parameters and the rest.
1780 * For each part, we check whether the coefficients in that part
1781 * are all integral and if so, set the corresponding flag in *f.
1782 * If the constant and the parameter part are integral, then the
1783 * current sample value is integral and no cut is required
1784 * (irrespective of whether the variable part is integral).
1786 static int first_non_integer_row(struct isl_tab
*tab
, int *f
)
1788 int var
= next_non_integer_var(tab
, -1, f
);
1790 return var
< 0 ? -1 : tab
->var
[var
].index
;
1793 /* Add a (non-parametric) cut to cut away the non-integral sample
1794 * value of the given row.
1796 * If the row is given by
1798 * m r = f + \sum_i a_i y_i
1802 * c = - {-f/m} + \sum_i {a_i/m} y_i >= 0
1804 * The big parameter, if any, is ignored, since it is assumed to be big
1805 * enough to be divisible by any integer.
1806 * If the tableau is actually a parametric tableau, then this function
1807 * is only called when all coefficients of the parameters are integral.
1808 * The cut therefore has zero coefficients for the parameters.
1810 * The current value is known to be negative, so row_sign, if it
1811 * exists, is set accordingly.
1813 * Return the row of the cut or -1.
1815 static int add_cut(struct isl_tab
*tab
, int row
)
1820 unsigned off
= 2 + tab
->M
;
1822 if (isl_tab_extend_cons(tab
, 1) < 0)
1824 r
= isl_tab_allocate_con(tab
);
1828 r_row
= tab
->mat
->row
[tab
->con
[r
].index
];
1829 isl_int_set(r_row
[0], tab
->mat
->row
[row
][0]);
1830 isl_int_neg(r_row
[1], tab
->mat
->row
[row
][1]);
1831 isl_int_fdiv_r(r_row
[1], r_row
[1], tab
->mat
->row
[row
][0]);
1832 isl_int_neg(r_row
[1], r_row
[1]);
1834 isl_int_set_si(r_row
[2], 0);
1835 for (i
= 0; i
< tab
->n_col
; ++i
)
1836 isl_int_fdiv_r(r_row
[off
+ i
],
1837 tab
->mat
->row
[row
][off
+ i
], tab
->mat
->row
[row
][0]);
1839 tab
->con
[r
].is_nonneg
= 1;
1840 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]) < 0)
1843 tab
->row_sign
[tab
->con
[r
].index
] = isl_tab_row_neg
;
1845 return tab
->con
[r
].index
;
1851 /* Given a non-parametric tableau, add cuts until an integer
1852 * sample point is obtained or until the tableau is determined
1853 * to be integer infeasible.
1854 * As long as there is any non-integer value in the sample point,
1855 * we add appropriate cuts, if possible, for each of these
1856 * non-integer values and then resolve the violated
1857 * cut constraints using restore_lexmin.
1858 * If one of the corresponding rows is equal to an integral
1859 * combination of variables/constraints plus a non-integral constant,
1860 * then there is no way to obtain an integer point and we return
1861 * a tableau that is marked empty.
1862 * The parameter cutting_strategy controls the strategy used when adding cuts
1863 * to remove non-integer points. CUT_ALL adds all possible cuts
1864 * before continuing the search. CUT_ONE adds only one cut at a time.
1866 static struct isl_tab
*cut_to_integer_lexmin(struct isl_tab
*tab
,
1867 int cutting_strategy
)
1878 while ((var
= next_non_integer_var(tab
, -1, &flags
)) != -1) {
1880 if (ISL_FL_ISSET(flags
, I_VAR
)) {
1881 if (isl_tab_mark_empty(tab
) < 0)
1885 row
= tab
->var
[var
].index
;
1886 row
= add_cut(tab
, row
);
1889 if (cutting_strategy
== CUT_ONE
)
1891 } while ((var
= next_non_integer_var(tab
, var
, &flags
)) != -1);
1892 if (restore_lexmin(tab
) < 0)
1903 /* Check whether all the currently active samples also satisfy the inequality
1904 * "ineq" (treated as an equality if eq is set).
1905 * Remove those samples that do not.
1907 static struct isl_tab
*check_samples(struct isl_tab
*tab
, isl_int
*ineq
, int eq
)
1915 isl_assert(tab
->mat
->ctx
, tab
->bmap
, goto error
);
1916 isl_assert(tab
->mat
->ctx
, tab
->samples
, goto error
);
1917 isl_assert(tab
->mat
->ctx
, tab
->samples
->n_col
== 1 + tab
->n_var
, goto error
);
1920 for (i
= tab
->n_outside
; i
< tab
->n_sample
; ++i
) {
1922 isl_seq_inner_product(ineq
, tab
->samples
->row
[i
],
1923 1 + tab
->n_var
, &v
);
1924 sgn
= isl_int_sgn(v
);
1925 if (eq
? (sgn
== 0) : (sgn
>= 0))
1927 tab
= isl_tab_drop_sample(tab
, i
);
1939 /* Check whether the sample value of the tableau is finite,
1940 * i.e., either the tableau does not use a big parameter, or
1941 * all values of the variables are equal to the big parameter plus
1942 * some constant. This constant is the actual sample value.
1944 static int sample_is_finite(struct isl_tab
*tab
)
1951 for (i
= 0; i
< tab
->n_var
; ++i
) {
1953 if (!tab
->var
[i
].is_row
)
1955 row
= tab
->var
[i
].index
;
1956 if (isl_int_ne(tab
->mat
->row
[row
][0], tab
->mat
->row
[row
][2]))
1962 /* Check if the context tableau of sol has any integer points.
1963 * Leave tab in empty state if no integer point can be found.
1964 * If an integer point can be found and if moreover it is finite,
1965 * then it is added to the list of sample values.
1967 * This function is only called when none of the currently active sample
1968 * values satisfies the most recently added constraint.
1970 static struct isl_tab
*check_integer_feasible(struct isl_tab
*tab
)
1972 struct isl_tab_undo
*snap
;
1977 snap
= isl_tab_snap(tab
);
1978 if (isl_tab_push_basis(tab
) < 0)
1981 tab
= cut_to_integer_lexmin(tab
, CUT_ALL
);
1985 if (!tab
->empty
&& sample_is_finite(tab
)) {
1986 struct isl_vec
*sample
;
1988 sample
= isl_tab_get_sample_value(tab
);
1990 if (isl_tab_add_sample(tab
, sample
) < 0)
1994 if (!tab
->empty
&& isl_tab_rollback(tab
, snap
) < 0)
2003 /* Check if any of the currently active sample values satisfies
2004 * the inequality "ineq" (an equality if eq is set).
2006 static int tab_has_valid_sample(struct isl_tab
*tab
, isl_int
*ineq
, int eq
)
2014 isl_assert(tab
->mat
->ctx
, tab
->bmap
, return -1);
2015 isl_assert(tab
->mat
->ctx
, tab
->samples
, return -1);
2016 isl_assert(tab
->mat
->ctx
, tab
->samples
->n_col
== 1 + tab
->n_var
, return -1);
2019 for (i
= tab
->n_outside
; i
< tab
->n_sample
; ++i
) {
2021 isl_seq_inner_product(ineq
, tab
->samples
->row
[i
],
2022 1 + tab
->n_var
, &v
);
2023 sgn
= isl_int_sgn(v
);
2024 if (eq
? (sgn
== 0) : (sgn
>= 0))
2029 return i
< tab
->n_sample
;
2032 /* Insert a div specified by "div" to the tableau "tab" at position "pos" and
2033 * return isl_bool_true if the div is obviously non-negative.
2035 static isl_bool
context_tab_insert_div(struct isl_tab
*tab
, int pos
,
2036 __isl_keep isl_vec
*div
,
2037 isl_stat (*add_ineq
)(void *user
, isl_int
*), void *user
)
2041 struct isl_mat
*samples
;
2044 r
= isl_tab_insert_div(tab
, pos
, div
, add_ineq
, user
);
2046 return isl_bool_error
;
2047 nonneg
= tab
->var
[r
].is_nonneg
;
2048 tab
->var
[r
].frozen
= 1;
2050 samples
= isl_mat_extend(tab
->samples
,
2051 tab
->n_sample
, 1 + tab
->n_var
);
2052 tab
->samples
= samples
;
2054 return isl_bool_error
;
2055 for (i
= tab
->n_outside
; i
< samples
->n_row
; ++i
) {
2056 isl_seq_inner_product(div
->el
+ 1, samples
->row
[i
],
2057 div
->size
- 1, &samples
->row
[i
][samples
->n_col
- 1]);
2058 isl_int_fdiv_q(samples
->row
[i
][samples
->n_col
- 1],
2059 samples
->row
[i
][samples
->n_col
- 1], div
->el
[0]);
2061 tab
->samples
= isl_mat_move_cols(tab
->samples
, 1 + pos
,
2062 1 + tab
->n_var
- 1, 1);
2064 return isl_bool_error
;
2069 /* Add a div specified by "div" to both the main tableau and
2070 * the context tableau. In case of the main tableau, we only
2071 * need to add an extra div. In the context tableau, we also
2072 * need to express the meaning of the div.
2073 * Return the index of the div or -1 if anything went wrong.
2075 * The new integer division is added before any unknown integer
2076 * divisions in the context to ensure that it does not get
2077 * equated to some linear combination involving unknown integer
2080 static int add_div(struct isl_tab
*tab
, struct isl_context
*context
,
2081 __isl_keep isl_vec
*div
)
2086 struct isl_tab
*context_tab
= context
->op
->peek_tab(context
);
2088 if (!tab
|| !context_tab
)
2091 pos
= context_tab
->n_var
- context
->n_unknown
;
2092 if ((nonneg
= context
->op
->insert_div(context
, pos
, div
)) < 0)
2095 if (!context
->op
->is_ok(context
))
2098 pos
= tab
->n_var
- context
->n_unknown
;
2099 if (isl_tab_extend_vars(tab
, 1) < 0)
2101 r
= isl_tab_insert_var(tab
, pos
);
2105 tab
->var
[r
].is_nonneg
= 1;
2106 tab
->var
[r
].frozen
= 1;
2109 return tab
->n_div
- 1 - context
->n_unknown
;
2111 context
->op
->invalidate(context
);
2115 static int find_div(struct isl_tab
*tab
, isl_int
*div
, isl_int denom
)
2118 unsigned total
= isl_basic_map_total_dim(tab
->bmap
);
2120 for (i
= 0; i
< tab
->bmap
->n_div
; ++i
) {
2121 if (isl_int_ne(tab
->bmap
->div
[i
][0], denom
))
2123 if (!isl_seq_eq(tab
->bmap
->div
[i
] + 1, div
, 1 + total
))
2130 /* Return the index of a div that corresponds to "div".
2131 * We first check if we already have such a div and if not, we create one.
2133 static int get_div(struct isl_tab
*tab
, struct isl_context
*context
,
2134 struct isl_vec
*div
)
2137 struct isl_tab
*context_tab
= context
->op
->peek_tab(context
);
2142 d
= find_div(context_tab
, div
->el
+ 1, div
->el
[0]);
2146 return add_div(tab
, context
, div
);
2149 /* Add a parametric cut to cut away the non-integral sample value
2151 * Let a_i be the coefficients of the constant term and the parameters
2152 * and let b_i be the coefficients of the variables or constraints
2153 * in basis of the tableau.
2154 * Let q be the div q = floor(\sum_i {-a_i} y_i).
2156 * The cut is expressed as
2158 * c = \sum_i -{-a_i} y_i + \sum_i {b_i} x_i + q >= 0
2160 * If q did not already exist in the context tableau, then it is added first.
2161 * If q is in a column of the main tableau then the "+ q" can be accomplished
2162 * by setting the corresponding entry to the denominator of the constraint.
2163 * If q happens to be in a row of the main tableau, then the corresponding
2164 * row needs to be added instead (taking care of the denominators).
2165 * Note that this is very unlikely, but perhaps not entirely impossible.
2167 * The current value of the cut is known to be negative (or at least
2168 * non-positive), so row_sign is set accordingly.
2170 * Return the row of the cut or -1.
2172 static int add_parametric_cut(struct isl_tab
*tab
, int row
,
2173 struct isl_context
*context
)
2175 struct isl_vec
*div
;
2182 unsigned off
= 2 + tab
->M
;
2187 div
= get_row_parameter_div(tab
, row
);
2191 n
= tab
->n_div
- context
->n_unknown
;
2192 d
= context
->op
->get_div(context
, tab
, div
);
2197 if (isl_tab_extend_cons(tab
, 1) < 0)
2199 r
= isl_tab_allocate_con(tab
);
2203 r_row
= tab
->mat
->row
[tab
->con
[r
].index
];
2204 isl_int_set(r_row
[0], tab
->mat
->row
[row
][0]);
2205 isl_int_neg(r_row
[1], tab
->mat
->row
[row
][1]);
2206 isl_int_fdiv_r(r_row
[1], r_row
[1], tab
->mat
->row
[row
][0]);
2207 isl_int_neg(r_row
[1], r_row
[1]);
2209 isl_int_set_si(r_row
[2], 0);
2210 for (i
= 0; i
< tab
->n_param
; ++i
) {
2211 if (tab
->var
[i
].is_row
)
2213 col
= tab
->var
[i
].index
;
2214 isl_int_neg(r_row
[off
+ col
], tab
->mat
->row
[row
][off
+ col
]);
2215 isl_int_fdiv_r(r_row
[off
+ col
], r_row
[off
+ col
],
2216 tab
->mat
->row
[row
][0]);
2217 isl_int_neg(r_row
[off
+ col
], r_row
[off
+ col
]);
2219 for (i
= 0; i
< tab
->n_div
; ++i
) {
2220 if (tab
->var
[tab
->n_var
- tab
->n_div
+ i
].is_row
)
2222 col
= tab
->var
[tab
->n_var
- tab
->n_div
+ i
].index
;
2223 isl_int_neg(r_row
[off
+ col
], tab
->mat
->row
[row
][off
+ col
]);
2224 isl_int_fdiv_r(r_row
[off
+ col
], r_row
[off
+ col
],
2225 tab
->mat
->row
[row
][0]);
2226 isl_int_neg(r_row
[off
+ col
], r_row
[off
+ col
]);
2228 for (i
= 0; i
< tab
->n_col
; ++i
) {
2229 if (tab
->col_var
[i
] >= 0 &&
2230 (tab
->col_var
[i
] < tab
->n_param
||
2231 tab
->col_var
[i
] >= tab
->n_var
- tab
->n_div
))
2233 isl_int_fdiv_r(r_row
[off
+ i
],
2234 tab
->mat
->row
[row
][off
+ i
], tab
->mat
->row
[row
][0]);
2236 if (tab
->var
[tab
->n_var
- tab
->n_div
+ d
].is_row
) {
2238 int d_row
= tab
->var
[tab
->n_var
- tab
->n_div
+ d
].index
;
2240 isl_int_gcd(gcd
, tab
->mat
->row
[d_row
][0], r_row
[0]);
2241 isl_int_divexact(r_row
[0], r_row
[0], gcd
);
2242 isl_int_divexact(gcd
, tab
->mat
->row
[d_row
][0], gcd
);
2243 isl_seq_combine(r_row
+ 1, gcd
, r_row
+ 1,
2244 r_row
[0], tab
->mat
->row
[d_row
] + 1,
2245 off
- 1 + tab
->n_col
);
2246 isl_int_mul(r_row
[0], r_row
[0], tab
->mat
->row
[d_row
][0]);
2249 col
= tab
->var
[tab
->n_var
- tab
->n_div
+ d
].index
;
2250 isl_int_set(r_row
[off
+ col
], tab
->mat
->row
[row
][0]);
2253 tab
->con
[r
].is_nonneg
= 1;
2254 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]) < 0)
2257 tab
->row_sign
[tab
->con
[r
].index
] = isl_tab_row_neg
;
2259 row
= tab
->con
[r
].index
;
2261 if (d
>= n
&& context
->op
->detect_equalities(context
, tab
) < 0)
2267 /* Construct a tableau for bmap that can be used for computing
2268 * the lexicographic minimum (or maximum) of bmap.
2269 * If not NULL, then dom is the domain where the minimum
2270 * should be computed. In this case, we set up a parametric
2271 * tableau with row signs (initialized to "unknown").
2272 * If M is set, then the tableau will use a big parameter.
2273 * If max is set, then a maximum should be computed instead of a minimum.
2274 * This means that for each variable x, the tableau will contain the variable
2275 * x' = M - x, rather than x' = M + x. This in turn means that the coefficient
2276 * of the variables in all constraints are negated prior to adding them
2279 static __isl_give
struct isl_tab
*tab_for_lexmin(__isl_keep isl_basic_map
*bmap
,
2280 __isl_keep isl_basic_set
*dom
, unsigned M
, int max
)
2283 struct isl_tab
*tab
;
2287 tab
= isl_tab_alloc(bmap
->ctx
, 2 * bmap
->n_eq
+ bmap
->n_ineq
+ 1,
2288 isl_basic_map_total_dim(bmap
), M
);
2292 tab
->rational
= ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
);
2294 tab
->n_param
= isl_basic_set_total_dim(dom
) - dom
->n_div
;
2295 tab
->n_div
= dom
->n_div
;
2296 tab
->row_sign
= isl_calloc_array(bmap
->ctx
,
2297 enum isl_tab_row_sign
, tab
->mat
->n_row
);
2298 if (tab
->mat
->n_row
&& !tab
->row_sign
)
2301 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
)) {
2302 if (isl_tab_mark_empty(tab
) < 0)
2307 for (i
= tab
->n_param
; i
< tab
->n_var
- tab
->n_div
; ++i
) {
2308 tab
->var
[i
].is_nonneg
= 1;
2309 tab
->var
[i
].frozen
= 1;
2311 o_var
= 1 + tab
->n_param
;
2312 n_var
= tab
->n_var
- tab
->n_param
- tab
->n_div
;
2313 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
2315 isl_seq_neg(bmap
->eq
[i
] + o_var
,
2316 bmap
->eq
[i
] + o_var
, n_var
);
2317 tab
= add_lexmin_valid_eq(tab
, bmap
->eq
[i
]);
2319 isl_seq_neg(bmap
->eq
[i
] + o_var
,
2320 bmap
->eq
[i
] + o_var
, n_var
);
2321 if (!tab
|| tab
->empty
)
2324 if (bmap
->n_eq
&& restore_lexmin(tab
) < 0)
2326 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
2328 isl_seq_neg(bmap
->ineq
[i
] + o_var
,
2329 bmap
->ineq
[i
] + o_var
, n_var
);
2330 tab
= add_lexmin_ineq(tab
, bmap
->ineq
[i
]);
2332 isl_seq_neg(bmap
->ineq
[i
] + o_var
,
2333 bmap
->ineq
[i
] + o_var
, n_var
);
2334 if (!tab
|| tab
->empty
)
2343 /* Given a main tableau where more than one row requires a split,
2344 * determine and return the "best" row to split on.
2346 * If any of the rows requiring a split only involves
2347 * variables that also appear in the context tableau,
2348 * then the negative part is guaranteed not to have a solution.
2349 * It is therefore best to split on any of these rows first.
2352 * given two rows in the main tableau, if the inequality corresponding
2353 * to the first row is redundant with respect to that of the second row
2354 * in the current tableau, then it is better to split on the second row,
2355 * since in the positive part, both rows will be positive.
2356 * (In the negative part a pivot will have to be performed and just about
2357 * anything can happen to the sign of the other row.)
2359 * As a simple heuristic, we therefore select the row that makes the most
2360 * of the other rows redundant.
2362 * Perhaps it would also be useful to look at the number of constraints
2363 * that conflict with any given constraint.
2365 * best is the best row so far (-1 when we have not found any row yet).
2366 * best_r is the number of other rows made redundant by row best.
2367 * When best is still -1, bset_r is meaningless, but it is initialized
2368 * to some arbitrary value (0) anyway. Without this redundant initialization
2369 * valgrind may warn about uninitialized memory accesses when isl
2370 * is compiled with some versions of gcc.
2372 static int best_split(struct isl_tab
*tab
, struct isl_tab
*context_tab
)
2374 struct isl_tab_undo
*snap
;
2380 if (isl_tab_extend_cons(context_tab
, 2) < 0)
2383 snap
= isl_tab_snap(context_tab
);
2385 for (split
= tab
->n_redundant
; split
< tab
->n_row
; ++split
) {
2386 struct isl_tab_undo
*snap2
;
2387 struct isl_vec
*ineq
= NULL
;
2391 if (!isl_tab_var_from_row(tab
, split
)->is_nonneg
)
2393 if (tab
->row_sign
[split
] != isl_tab_row_any
)
2396 if (is_parametric_constant(tab
, split
))
2399 ineq
= get_row_parameter_ineq(tab
, split
);
2402 ok
= isl_tab_add_ineq(context_tab
, ineq
->el
) >= 0;
2407 snap2
= isl_tab_snap(context_tab
);
2409 for (row
= tab
->n_redundant
; row
< tab
->n_row
; ++row
) {
2410 struct isl_tab_var
*var
;
2414 if (!isl_tab_var_from_row(tab
, row
)->is_nonneg
)
2416 if (tab
->row_sign
[row
] != isl_tab_row_any
)
2419 ineq
= get_row_parameter_ineq(tab
, row
);
2422 ok
= isl_tab_add_ineq(context_tab
, ineq
->el
) >= 0;
2426 var
= &context_tab
->con
[context_tab
->n_con
- 1];
2427 if (!context_tab
->empty
&&
2428 !isl_tab_min_at_most_neg_one(context_tab
, var
))
2430 if (isl_tab_rollback(context_tab
, snap2
) < 0)
2433 if (best
== -1 || r
> best_r
) {
2437 if (isl_tab_rollback(context_tab
, snap
) < 0)
2444 static struct isl_basic_set
*context_lex_peek_basic_set(
2445 struct isl_context
*context
)
2447 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2450 return isl_tab_peek_bset(clex
->tab
);
2453 static struct isl_tab
*context_lex_peek_tab(struct isl_context
*context
)
2455 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2459 static void context_lex_add_eq(struct isl_context
*context
, isl_int
*eq
,
2460 int check
, int update
)
2462 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2463 if (isl_tab_extend_cons(clex
->tab
, 2) < 0)
2465 if (add_lexmin_eq(clex
->tab
, eq
) < 0)
2468 int v
= tab_has_valid_sample(clex
->tab
, eq
, 1);
2472 clex
->tab
= check_integer_feasible(clex
->tab
);
2475 clex
->tab
= check_samples(clex
->tab
, eq
, 1);
2478 isl_tab_free(clex
->tab
);
2482 static void context_lex_add_ineq(struct isl_context
*context
, isl_int
*ineq
,
2483 int check
, int update
)
2485 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2486 if (isl_tab_extend_cons(clex
->tab
, 1) < 0)
2488 clex
->tab
= add_lexmin_ineq(clex
->tab
, ineq
);
2490 int v
= tab_has_valid_sample(clex
->tab
, ineq
, 0);
2494 clex
->tab
= check_integer_feasible(clex
->tab
);
2497 clex
->tab
= check_samples(clex
->tab
, ineq
, 0);
2500 isl_tab_free(clex
->tab
);
2504 static isl_stat
context_lex_add_ineq_wrap(void *user
, isl_int
*ineq
)
2506 struct isl_context
*context
= (struct isl_context
*)user
;
2507 context_lex_add_ineq(context
, ineq
, 0, 0);
2508 return context
->op
->is_ok(context
) ? isl_stat_ok
: isl_stat_error
;
2511 /* Check which signs can be obtained by "ineq" on all the currently
2512 * active sample values. See row_sign for more information.
2514 static enum isl_tab_row_sign
tab_ineq_sign(struct isl_tab
*tab
, isl_int
*ineq
,
2520 enum isl_tab_row_sign res
= isl_tab_row_unknown
;
2522 isl_assert(tab
->mat
->ctx
, tab
->samples
, return isl_tab_row_unknown
);
2523 isl_assert(tab
->mat
->ctx
, tab
->samples
->n_col
== 1 + tab
->n_var
,
2524 return isl_tab_row_unknown
);
2527 for (i
= tab
->n_outside
; i
< tab
->n_sample
; ++i
) {
2528 isl_seq_inner_product(tab
->samples
->row
[i
], ineq
,
2529 1 + tab
->n_var
, &tmp
);
2530 sgn
= isl_int_sgn(tmp
);
2531 if (sgn
> 0 || (sgn
== 0 && strict
)) {
2532 if (res
== isl_tab_row_unknown
)
2533 res
= isl_tab_row_pos
;
2534 if (res
== isl_tab_row_neg
)
2535 res
= isl_tab_row_any
;
2538 if (res
== isl_tab_row_unknown
)
2539 res
= isl_tab_row_neg
;
2540 if (res
== isl_tab_row_pos
)
2541 res
= isl_tab_row_any
;
2543 if (res
== isl_tab_row_any
)
2551 static enum isl_tab_row_sign
context_lex_ineq_sign(struct isl_context
*context
,
2552 isl_int
*ineq
, int strict
)
2554 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2555 return tab_ineq_sign(clex
->tab
, ineq
, strict
);
2558 /* Check whether "ineq" can be added to the tableau without rendering
2561 static int context_lex_test_ineq(struct isl_context
*context
, isl_int
*ineq
)
2563 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2564 struct isl_tab_undo
*snap
;
2570 if (isl_tab_extend_cons(clex
->tab
, 1) < 0)
2573 snap
= isl_tab_snap(clex
->tab
);
2574 if (isl_tab_push_basis(clex
->tab
) < 0)
2576 clex
->tab
= add_lexmin_ineq(clex
->tab
, ineq
);
2577 clex
->tab
= check_integer_feasible(clex
->tab
);
2580 feasible
= !clex
->tab
->empty
;
2581 if (isl_tab_rollback(clex
->tab
, snap
) < 0)
2587 static int context_lex_get_div(struct isl_context
*context
, struct isl_tab
*tab
,
2588 struct isl_vec
*div
)
2590 return get_div(tab
, context
, div
);
2593 /* Insert a div specified by "div" to the context tableau at position "pos" and
2594 * return isl_bool_true if the div is obviously non-negative.
2595 * context_tab_add_div will always return isl_bool_true, because all variables
2596 * in a isl_context_lex tableau are non-negative.
2597 * However, if we are using a big parameter in the context, then this only
2598 * reflects the non-negativity of the variable used to _encode_ the
2599 * div, i.e., div' = M + div, so we can't draw any conclusions.
2601 static isl_bool
context_lex_insert_div(struct isl_context
*context
, int pos
,
2602 __isl_keep isl_vec
*div
)
2604 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2606 nonneg
= context_tab_insert_div(clex
->tab
, pos
, div
,
2607 context_lex_add_ineq_wrap
, context
);
2609 return isl_bool_error
;
2611 return isl_bool_false
;
2615 static int context_lex_detect_equalities(struct isl_context
*context
,
2616 struct isl_tab
*tab
)
2621 static int context_lex_best_split(struct isl_context
*context
,
2622 struct isl_tab
*tab
)
2624 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2625 struct isl_tab_undo
*snap
;
2628 snap
= isl_tab_snap(clex
->tab
);
2629 if (isl_tab_push_basis(clex
->tab
) < 0)
2631 r
= best_split(tab
, clex
->tab
);
2633 if (r
>= 0 && isl_tab_rollback(clex
->tab
, snap
) < 0)
2639 static int context_lex_is_empty(struct isl_context
*context
)
2641 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2644 return clex
->tab
->empty
;
2647 static void *context_lex_save(struct isl_context
*context
)
2649 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2650 struct isl_tab_undo
*snap
;
2652 snap
= isl_tab_snap(clex
->tab
);
2653 if (isl_tab_push_basis(clex
->tab
) < 0)
2655 if (isl_tab_save_samples(clex
->tab
) < 0)
2661 static void context_lex_restore(struct isl_context
*context
, void *save
)
2663 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2664 if (isl_tab_rollback(clex
->tab
, (struct isl_tab_undo
*)save
) < 0) {
2665 isl_tab_free(clex
->tab
);
2670 static void context_lex_discard(void *save
)
2674 static int context_lex_is_ok(struct isl_context
*context
)
2676 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2680 /* For each variable in the context tableau, check if the variable can
2681 * only attain non-negative values. If so, mark the parameter as non-negative
2682 * in the main tableau. This allows for a more direct identification of some
2683 * cases of violated constraints.
2685 static struct isl_tab
*tab_detect_nonnegative_parameters(struct isl_tab
*tab
,
2686 struct isl_tab
*context_tab
)
2689 struct isl_tab_undo
*snap
;
2690 struct isl_vec
*ineq
= NULL
;
2691 struct isl_tab_var
*var
;
2694 if (context_tab
->n_var
== 0)
2697 ineq
= isl_vec_alloc(tab
->mat
->ctx
, 1 + context_tab
->n_var
);
2701 if (isl_tab_extend_cons(context_tab
, 1) < 0)
2704 snap
= isl_tab_snap(context_tab
);
2707 isl_seq_clr(ineq
->el
, ineq
->size
);
2708 for (i
= 0; i
< context_tab
->n_var
; ++i
) {
2709 isl_int_set_si(ineq
->el
[1 + i
], 1);
2710 if (isl_tab_add_ineq(context_tab
, ineq
->el
) < 0)
2712 var
= &context_tab
->con
[context_tab
->n_con
- 1];
2713 if (!context_tab
->empty
&&
2714 !isl_tab_min_at_most_neg_one(context_tab
, var
)) {
2716 if (i
>= tab
->n_param
)
2717 j
= i
- tab
->n_param
+ tab
->n_var
- tab
->n_div
;
2718 tab
->var
[j
].is_nonneg
= 1;
2721 isl_int_set_si(ineq
->el
[1 + i
], 0);
2722 if (isl_tab_rollback(context_tab
, snap
) < 0)
2726 if (context_tab
->M
&& n
== context_tab
->n_var
) {
2727 context_tab
->mat
= isl_mat_drop_cols(context_tab
->mat
, 2, 1);
2739 static struct isl_tab
*context_lex_detect_nonnegative_parameters(
2740 struct isl_context
*context
, struct isl_tab
*tab
)
2742 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2743 struct isl_tab_undo
*snap
;
2748 snap
= isl_tab_snap(clex
->tab
);
2749 if (isl_tab_push_basis(clex
->tab
) < 0)
2752 tab
= tab_detect_nonnegative_parameters(tab
, clex
->tab
);
2754 if (isl_tab_rollback(clex
->tab
, snap
) < 0)
2763 static void context_lex_invalidate(struct isl_context
*context
)
2765 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2766 isl_tab_free(clex
->tab
);
2770 static __isl_null
struct isl_context
*context_lex_free(
2771 struct isl_context
*context
)
2773 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2774 isl_tab_free(clex
->tab
);
2780 struct isl_context_op isl_context_lex_op
= {
2781 context_lex_detect_nonnegative_parameters
,
2782 context_lex_peek_basic_set
,
2783 context_lex_peek_tab
,
2785 context_lex_add_ineq
,
2786 context_lex_ineq_sign
,
2787 context_lex_test_ineq
,
2788 context_lex_get_div
,
2789 context_lex_insert_div
,
2790 context_lex_detect_equalities
,
2791 context_lex_best_split
,
2792 context_lex_is_empty
,
2795 context_lex_restore
,
2796 context_lex_discard
,
2797 context_lex_invalidate
,
2801 static struct isl_tab
*context_tab_for_lexmin(__isl_take isl_basic_set
*bset
)
2803 struct isl_tab
*tab
;
2807 tab
= tab_for_lexmin(bset_to_bmap(bset
), NULL
, 1, 0);
2808 if (isl_tab_track_bset(tab
, bset
) < 0)
2810 tab
= isl_tab_init_samples(tab
);
2817 static struct isl_context
*isl_context_lex_alloc(struct isl_basic_set
*dom
)
2819 struct isl_context_lex
*clex
;
2824 clex
= isl_alloc_type(dom
->ctx
, struct isl_context_lex
);
2828 clex
->context
.op
= &isl_context_lex_op
;
2830 clex
->tab
= context_tab_for_lexmin(isl_basic_set_copy(dom
));
2831 if (restore_lexmin(clex
->tab
) < 0)
2833 clex
->tab
= check_integer_feasible(clex
->tab
);
2837 return &clex
->context
;
2839 clex
->context
.op
->free(&clex
->context
);
2843 /* Representation of the context when using generalized basis reduction.
2845 * "shifted" contains the offsets of the unit hypercubes that lie inside the
2846 * context. Any rational point in "shifted" can therefore be rounded
2847 * up to an integer point in the context.
2848 * If the context is constrained by any equality, then "shifted" is not used
2849 * as it would be empty.
2851 struct isl_context_gbr
{
2852 struct isl_context context
;
2853 struct isl_tab
*tab
;
2854 struct isl_tab
*shifted
;
2855 struct isl_tab
*cone
;
2858 static struct isl_tab
*context_gbr_detect_nonnegative_parameters(
2859 struct isl_context
*context
, struct isl_tab
*tab
)
2861 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
2864 return tab_detect_nonnegative_parameters(tab
, cgbr
->tab
);
2867 static struct isl_basic_set
*context_gbr_peek_basic_set(
2868 struct isl_context
*context
)
2870 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
2873 return isl_tab_peek_bset(cgbr
->tab
);
2876 static struct isl_tab
*context_gbr_peek_tab(struct isl_context
*context
)
2878 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
2882 /* Initialize the "shifted" tableau of the context, which
2883 * contains the constraints of the original tableau shifted
2884 * by the sum of all negative coefficients. This ensures
2885 * that any rational point in the shifted tableau can
2886 * be rounded up to yield an integer point in the original tableau.
2888 static void gbr_init_shifted(struct isl_context_gbr
*cgbr
)
2891 struct isl_vec
*cst
;
2892 struct isl_basic_set
*bset
= isl_tab_peek_bset(cgbr
->tab
);
2893 unsigned dim
= isl_basic_set_total_dim(bset
);
2895 cst
= isl_vec_alloc(cgbr
->tab
->mat
->ctx
, bset
->n_ineq
);
2899 for (i
= 0; i
< bset
->n_ineq
; ++i
) {
2900 isl_int_set(cst
->el
[i
], bset
->ineq
[i
][0]);
2901 for (j
= 0; j
< dim
; ++j
) {
2902 if (!isl_int_is_neg(bset
->ineq
[i
][1 + j
]))
2904 isl_int_add(bset
->ineq
[i
][0], bset
->ineq
[i
][0],
2905 bset
->ineq
[i
][1 + j
]);
2909 cgbr
->shifted
= isl_tab_from_basic_set(bset
, 0);
2911 for (i
= 0; i
< bset
->n_ineq
; ++i
)
2912 isl_int_set(bset
->ineq
[i
][0], cst
->el
[i
]);
2917 /* Check if the shifted tableau is non-empty, and if so
2918 * use the sample point to construct an integer point
2919 * of the context tableau.
2921 static struct isl_vec
*gbr_get_shifted_sample(struct isl_context_gbr
*cgbr
)
2923 struct isl_vec
*sample
;
2926 gbr_init_shifted(cgbr
);
2929 if (cgbr
->shifted
->empty
)
2930 return isl_vec_alloc(cgbr
->tab
->mat
->ctx
, 0);
2932 sample
= isl_tab_get_sample_value(cgbr
->shifted
);
2933 sample
= isl_vec_ceil(sample
);
2938 static __isl_give isl_basic_set
*drop_constant_terms(
2939 __isl_take isl_basic_set
*bset
)
2946 for (i
= 0; i
< bset
->n_eq
; ++i
)
2947 isl_int_set_si(bset
->eq
[i
][0], 0);
2949 for (i
= 0; i
< bset
->n_ineq
; ++i
)
2950 isl_int_set_si(bset
->ineq
[i
][0], 0);
2955 static int use_shifted(struct isl_context_gbr
*cgbr
)
2959 return cgbr
->tab
->bmap
->n_eq
== 0 && cgbr
->tab
->bmap
->n_div
== 0;
2962 static struct isl_vec
*gbr_get_sample(struct isl_context_gbr
*cgbr
)
2964 struct isl_basic_set
*bset
;
2965 struct isl_basic_set
*cone
;
2967 if (isl_tab_sample_is_integer(cgbr
->tab
))
2968 return isl_tab_get_sample_value(cgbr
->tab
);
2970 if (use_shifted(cgbr
)) {
2971 struct isl_vec
*sample
;
2973 sample
= gbr_get_shifted_sample(cgbr
);
2974 if (!sample
|| sample
->size
> 0)
2977 isl_vec_free(sample
);
2981 bset
= isl_tab_peek_bset(cgbr
->tab
);
2982 cgbr
->cone
= isl_tab_from_recession_cone(bset
, 0);
2985 if (isl_tab_track_bset(cgbr
->cone
,
2986 isl_basic_set_copy(bset
)) < 0)
2989 if (isl_tab_detect_implicit_equalities(cgbr
->cone
) < 0)
2992 if (cgbr
->cone
->n_dead
== cgbr
->cone
->n_col
) {
2993 struct isl_vec
*sample
;
2994 struct isl_tab_undo
*snap
;
2996 if (cgbr
->tab
->basis
) {
2997 if (cgbr
->tab
->basis
->n_col
!= 1 + cgbr
->tab
->n_var
) {
2998 isl_mat_free(cgbr
->tab
->basis
);
2999 cgbr
->tab
->basis
= NULL
;
3001 cgbr
->tab
->n_zero
= 0;
3002 cgbr
->tab
->n_unbounded
= 0;
3005 snap
= isl_tab_snap(cgbr
->tab
);
3007 sample
= isl_tab_sample(cgbr
->tab
);
3009 if (!sample
|| isl_tab_rollback(cgbr
->tab
, snap
) < 0) {
3010 isl_vec_free(sample
);
3017 cone
= isl_basic_set_dup(isl_tab_peek_bset(cgbr
->cone
));
3018 cone
= drop_constant_terms(cone
);
3019 cone
= isl_basic_set_update_from_tab(cone
, cgbr
->cone
);
3020 cone
= isl_basic_set_underlying_set(cone
);
3021 cone
= isl_basic_set_gauss(cone
, NULL
);
3023 bset
= isl_basic_set_dup(isl_tab_peek_bset(cgbr
->tab
));
3024 bset
= isl_basic_set_update_from_tab(bset
, cgbr
->tab
);
3025 bset
= isl_basic_set_underlying_set(bset
);
3026 bset
= isl_basic_set_gauss(bset
, NULL
);
3028 return isl_basic_set_sample_with_cone(bset
, cone
);
3031 static void check_gbr_integer_feasible(struct isl_context_gbr
*cgbr
)
3033 struct isl_vec
*sample
;
3038 if (cgbr
->tab
->empty
)
3041 sample
= gbr_get_sample(cgbr
);
3045 if (sample
->size
== 0) {
3046 isl_vec_free(sample
);
3047 if (isl_tab_mark_empty(cgbr
->tab
) < 0)
3052 if (isl_tab_add_sample(cgbr
->tab
, sample
) < 0)
3057 isl_tab_free(cgbr
->tab
);
3061 static struct isl_tab
*add_gbr_eq(struct isl_tab
*tab
, isl_int
*eq
)
3066 if (isl_tab_extend_cons(tab
, 2) < 0)
3069 if (isl_tab_add_eq(tab
, eq
) < 0)
3078 /* Add the equality described by "eq" to the context.
3079 * If "check" is set, then we check if the context is empty after
3080 * adding the equality.
3081 * If "update" is set, then we check if the samples are still valid.
3083 * We do not explicitly add shifted copies of the equality to
3084 * cgbr->shifted since they would conflict with each other.
3085 * Instead, we directly mark cgbr->shifted empty.
3087 static void context_gbr_add_eq(struct isl_context
*context
, isl_int
*eq
,
3088 int check
, int update
)
3090 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3092 cgbr
->tab
= add_gbr_eq(cgbr
->tab
, eq
);
3094 if (cgbr
->shifted
&& !cgbr
->shifted
->empty
&& use_shifted(cgbr
)) {
3095 if (isl_tab_mark_empty(cgbr
->shifted
) < 0)
3099 if (cgbr
->cone
&& cgbr
->cone
->n_col
!= cgbr
->cone
->n_dead
) {
3100 if (isl_tab_extend_cons(cgbr
->cone
, 2) < 0)
3102 if (isl_tab_add_eq(cgbr
->cone
, eq
) < 0)
3107 int v
= tab_has_valid_sample(cgbr
->tab
, eq
, 1);
3111 check_gbr_integer_feasible(cgbr
);
3114 cgbr
->tab
= check_samples(cgbr
->tab
, eq
, 1);
3117 isl_tab_free(cgbr
->tab
);
3121 static void add_gbr_ineq(struct isl_context_gbr
*cgbr
, isl_int
*ineq
)
3126 if (isl_tab_extend_cons(cgbr
->tab
, 1) < 0)
3129 if (isl_tab_add_ineq(cgbr
->tab
, ineq
) < 0)
3132 if (cgbr
->shifted
&& !cgbr
->shifted
->empty
&& use_shifted(cgbr
)) {
3135 dim
= isl_basic_map_total_dim(cgbr
->tab
->bmap
);
3137 if (isl_tab_extend_cons(cgbr
->shifted
, 1) < 0)
3140 for (i
= 0; i
< dim
; ++i
) {
3141 if (!isl_int_is_neg(ineq
[1 + i
]))
3143 isl_int_add(ineq
[0], ineq
[0], ineq
[1 + i
]);
3146 if (isl_tab_add_ineq(cgbr
->shifted
, ineq
) < 0)
3149 for (i
= 0; i
< dim
; ++i
) {
3150 if (!isl_int_is_neg(ineq
[1 + i
]))
3152 isl_int_sub(ineq
[0], ineq
[0], ineq
[1 + i
]);
3156 if (cgbr
->cone
&& cgbr
->cone
->n_col
!= cgbr
->cone
->n_dead
) {
3157 if (isl_tab_extend_cons(cgbr
->cone
, 1) < 0)
3159 if (isl_tab_add_ineq(cgbr
->cone
, ineq
) < 0)
3165 isl_tab_free(cgbr
->tab
);
3169 static void context_gbr_add_ineq(struct isl_context
*context
, isl_int
*ineq
,
3170 int check
, int update
)
3172 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3174 add_gbr_ineq(cgbr
, ineq
);
3179 int v
= tab_has_valid_sample(cgbr
->tab
, ineq
, 0);
3183 check_gbr_integer_feasible(cgbr
);
3186 cgbr
->tab
= check_samples(cgbr
->tab
, ineq
, 0);
3189 isl_tab_free(cgbr
->tab
);
3193 static isl_stat
context_gbr_add_ineq_wrap(void *user
, isl_int
*ineq
)
3195 struct isl_context
*context
= (struct isl_context
*)user
;
3196 context_gbr_add_ineq(context
, ineq
, 0, 0);
3197 return context
->op
->is_ok(context
) ? isl_stat_ok
: isl_stat_error
;
3200 static enum isl_tab_row_sign
context_gbr_ineq_sign(struct isl_context
*context
,
3201 isl_int
*ineq
, int strict
)
3203 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3204 return tab_ineq_sign(cgbr
->tab
, ineq
, strict
);
3207 /* Check whether "ineq" can be added to the tableau without rendering
3210 static int context_gbr_test_ineq(struct isl_context
*context
, isl_int
*ineq
)
3212 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3213 struct isl_tab_undo
*snap
;
3214 struct isl_tab_undo
*shifted_snap
= NULL
;
3215 struct isl_tab_undo
*cone_snap
= NULL
;
3221 if (isl_tab_extend_cons(cgbr
->tab
, 1) < 0)
3224 snap
= isl_tab_snap(cgbr
->tab
);
3226 shifted_snap
= isl_tab_snap(cgbr
->shifted
);
3228 cone_snap
= isl_tab_snap(cgbr
->cone
);
3229 add_gbr_ineq(cgbr
, ineq
);
3230 check_gbr_integer_feasible(cgbr
);
3233 feasible
= !cgbr
->tab
->empty
;
3234 if (isl_tab_rollback(cgbr
->tab
, snap
) < 0)
3237 if (isl_tab_rollback(cgbr
->shifted
, shifted_snap
))
3239 } else if (cgbr
->shifted
) {
3240 isl_tab_free(cgbr
->shifted
);
3241 cgbr
->shifted
= NULL
;
3244 if (isl_tab_rollback(cgbr
->cone
, cone_snap
))
3246 } else if (cgbr
->cone
) {
3247 isl_tab_free(cgbr
->cone
);
3254 /* Return the column of the last of the variables associated to
3255 * a column that has a non-zero coefficient.
3256 * This function is called in a context where only coefficients
3257 * of parameters or divs can be non-zero.
3259 static int last_non_zero_var_col(struct isl_tab
*tab
, isl_int
*p
)
3264 if (tab
->n_var
== 0)
3267 for (i
= tab
->n_var
- 1; i
>= 0; --i
) {
3268 if (i
>= tab
->n_param
&& i
< tab
->n_var
- tab
->n_div
)
3270 if (tab
->var
[i
].is_row
)
3272 col
= tab
->var
[i
].index
;
3273 if (!isl_int_is_zero(p
[col
]))
3280 /* Look through all the recently added equalities in the context
3281 * to see if we can propagate any of them to the main tableau.
3283 * The newly added equalities in the context are encoded as pairs
3284 * of inequalities starting at inequality "first".
3286 * We tentatively add each of these equalities to the main tableau
3287 * and if this happens to result in a row with a final coefficient
3288 * that is one or negative one, we use it to kill a column
3289 * in the main tableau. Otherwise, we discard the tentatively
3291 * This tentative addition of equality constraints turns
3292 * on the undo facility of the tableau. Turn it off again
3293 * at the end, assuming it was turned off to begin with.
3295 * Return 0 on success and -1 on failure.
3297 static int propagate_equalities(struct isl_context_gbr
*cgbr
,
3298 struct isl_tab
*tab
, unsigned first
)
3301 struct isl_vec
*eq
= NULL
;
3302 isl_bool needs_undo
;
3304 needs_undo
= isl_tab_need_undo(tab
);
3307 eq
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_var
);
3311 if (isl_tab_extend_cons(tab
, (cgbr
->tab
->bmap
->n_ineq
- first
)/2) < 0)
3314 isl_seq_clr(eq
->el
+ 1 + tab
->n_param
,
3315 tab
->n_var
- tab
->n_param
- tab
->n_div
);
3316 for (i
= first
; i
< cgbr
->tab
->bmap
->n_ineq
; i
+= 2) {
3319 struct isl_tab_undo
*snap
;
3320 snap
= isl_tab_snap(tab
);
3322 isl_seq_cpy(eq
->el
, cgbr
->tab
->bmap
->ineq
[i
], 1 + tab
->n_param
);
3323 isl_seq_cpy(eq
->el
+ 1 + tab
->n_var
- tab
->n_div
,
3324 cgbr
->tab
->bmap
->ineq
[i
] + 1 + tab
->n_param
,
3327 r
= isl_tab_add_row(tab
, eq
->el
);
3330 r
= tab
->con
[r
].index
;
3331 j
= last_non_zero_var_col(tab
, tab
->mat
->row
[r
] + 2 + tab
->M
);
3332 if (j
< 0 || j
< tab
->n_dead
||
3333 !isl_int_is_one(tab
->mat
->row
[r
][0]) ||
3334 (!isl_int_is_one(tab
->mat
->row
[r
][2 + tab
->M
+ j
]) &&
3335 !isl_int_is_negone(tab
->mat
->row
[r
][2 + tab
->M
+ j
]))) {
3336 if (isl_tab_rollback(tab
, snap
) < 0)
3340 if (isl_tab_pivot(tab
, r
, j
) < 0)
3342 if (isl_tab_kill_col(tab
, j
) < 0)
3345 if (restore_lexmin(tab
) < 0)
3350 isl_tab_clear_undo(tab
);
3356 isl_tab_free(cgbr
->tab
);
3361 static int context_gbr_detect_equalities(struct isl_context
*context
,
3362 struct isl_tab
*tab
)
3364 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3368 struct isl_basic_set
*bset
= isl_tab_peek_bset(cgbr
->tab
);
3369 cgbr
->cone
= isl_tab_from_recession_cone(bset
, 0);
3372 if (isl_tab_track_bset(cgbr
->cone
,
3373 isl_basic_set_copy(bset
)) < 0)
3376 if (isl_tab_detect_implicit_equalities(cgbr
->cone
) < 0)
3379 n_ineq
= cgbr
->tab
->bmap
->n_ineq
;
3380 cgbr
->tab
= isl_tab_detect_equalities(cgbr
->tab
, cgbr
->cone
);
3383 if (cgbr
->tab
->bmap
->n_ineq
> n_ineq
&&
3384 propagate_equalities(cgbr
, tab
, n_ineq
) < 0)
3389 isl_tab_free(cgbr
->tab
);
3394 static int context_gbr_get_div(struct isl_context
*context
, struct isl_tab
*tab
,
3395 struct isl_vec
*div
)
3397 return get_div(tab
, context
, div
);
3400 static isl_bool
context_gbr_insert_div(struct isl_context
*context
, int pos
,
3401 __isl_keep isl_vec
*div
)
3403 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3405 int r
, n_div
, o_div
;
3407 n_div
= isl_basic_map_dim(cgbr
->cone
->bmap
, isl_dim_div
);
3408 o_div
= cgbr
->cone
->n_var
- n_div
;
3410 if (isl_tab_extend_cons(cgbr
->cone
, 3) < 0)
3411 return isl_bool_error
;
3412 if (isl_tab_extend_vars(cgbr
->cone
, 1) < 0)
3413 return isl_bool_error
;
3414 if ((r
= isl_tab_insert_var(cgbr
->cone
, pos
)) <0)
3415 return isl_bool_error
;
3417 cgbr
->cone
->bmap
= isl_basic_map_insert_div(cgbr
->cone
->bmap
,
3419 if (!cgbr
->cone
->bmap
)
3420 return isl_bool_error
;
3421 if (isl_tab_push_var(cgbr
->cone
, isl_tab_undo_bmap_div
,
3422 &cgbr
->cone
->var
[r
]) < 0)
3423 return isl_bool_error
;
3425 return context_tab_insert_div(cgbr
->tab
, pos
, div
,
3426 context_gbr_add_ineq_wrap
, context
);
3429 static int context_gbr_best_split(struct isl_context
*context
,
3430 struct isl_tab
*tab
)
3432 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3433 struct isl_tab_undo
*snap
;
3436 snap
= isl_tab_snap(cgbr
->tab
);
3437 r
= best_split(tab
, cgbr
->tab
);
3439 if (r
>= 0 && isl_tab_rollback(cgbr
->tab
, snap
) < 0)
3445 static int context_gbr_is_empty(struct isl_context
*context
)
3447 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3450 return cgbr
->tab
->empty
;
3453 struct isl_gbr_tab_undo
{
3454 struct isl_tab_undo
*tab_snap
;
3455 struct isl_tab_undo
*shifted_snap
;
3456 struct isl_tab_undo
*cone_snap
;
3459 static void *context_gbr_save(struct isl_context
*context
)
3461 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3462 struct isl_gbr_tab_undo
*snap
;
3467 snap
= isl_alloc_type(cgbr
->tab
->mat
->ctx
, struct isl_gbr_tab_undo
);
3471 snap
->tab_snap
= isl_tab_snap(cgbr
->tab
);
3472 if (isl_tab_save_samples(cgbr
->tab
) < 0)
3476 snap
->shifted_snap
= isl_tab_snap(cgbr
->shifted
);
3478 snap
->shifted_snap
= NULL
;
3481 snap
->cone_snap
= isl_tab_snap(cgbr
->cone
);
3483 snap
->cone_snap
= NULL
;
3491 static void context_gbr_restore(struct isl_context
*context
, void *save
)
3493 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3494 struct isl_gbr_tab_undo
*snap
= (struct isl_gbr_tab_undo
*)save
;
3497 if (isl_tab_rollback(cgbr
->tab
, snap
->tab_snap
) < 0)
3500 if (snap
->shifted_snap
) {
3501 if (isl_tab_rollback(cgbr
->shifted
, snap
->shifted_snap
) < 0)
3503 } else if (cgbr
->shifted
) {
3504 isl_tab_free(cgbr
->shifted
);
3505 cgbr
->shifted
= NULL
;
3508 if (snap
->cone_snap
) {
3509 if (isl_tab_rollback(cgbr
->cone
, snap
->cone_snap
) < 0)
3511 } else if (cgbr
->cone
) {
3512 isl_tab_free(cgbr
->cone
);
3521 isl_tab_free(cgbr
->tab
);
3525 static void context_gbr_discard(void *save
)
3527 struct isl_gbr_tab_undo
*snap
= (struct isl_gbr_tab_undo
*)save
;
3531 static int context_gbr_is_ok(struct isl_context
*context
)
3533 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3537 static void context_gbr_invalidate(struct isl_context
*context
)
3539 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3540 isl_tab_free(cgbr
->tab
);
3544 static __isl_null
struct isl_context
*context_gbr_free(
3545 struct isl_context
*context
)
3547 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3548 isl_tab_free(cgbr
->tab
);
3549 isl_tab_free(cgbr
->shifted
);
3550 isl_tab_free(cgbr
->cone
);
3556 struct isl_context_op isl_context_gbr_op
= {
3557 context_gbr_detect_nonnegative_parameters
,
3558 context_gbr_peek_basic_set
,
3559 context_gbr_peek_tab
,
3561 context_gbr_add_ineq
,
3562 context_gbr_ineq_sign
,
3563 context_gbr_test_ineq
,
3564 context_gbr_get_div
,
3565 context_gbr_insert_div
,
3566 context_gbr_detect_equalities
,
3567 context_gbr_best_split
,
3568 context_gbr_is_empty
,
3571 context_gbr_restore
,
3572 context_gbr_discard
,
3573 context_gbr_invalidate
,
3577 static struct isl_context
*isl_context_gbr_alloc(__isl_keep isl_basic_set
*dom
)
3579 struct isl_context_gbr
*cgbr
;
3584 cgbr
= isl_calloc_type(dom
->ctx
, struct isl_context_gbr
);
3588 cgbr
->context
.op
= &isl_context_gbr_op
;
3590 cgbr
->shifted
= NULL
;
3592 cgbr
->tab
= isl_tab_from_basic_set(dom
, 1);
3593 cgbr
->tab
= isl_tab_init_samples(cgbr
->tab
);
3596 check_gbr_integer_feasible(cgbr
);
3598 return &cgbr
->context
;
3600 cgbr
->context
.op
->free(&cgbr
->context
);
3604 /* Allocate a context corresponding to "dom".
3605 * The representation specific fields are initialized by
3606 * isl_context_lex_alloc or isl_context_gbr_alloc.
3607 * The shared "n_unknown" field is initialized to the number
3608 * of final unknown integer divisions in "dom".
3610 static struct isl_context
*isl_context_alloc(__isl_keep isl_basic_set
*dom
)
3612 struct isl_context
*context
;
3618 if (dom
->ctx
->opt
->context
== ISL_CONTEXT_LEXMIN
)
3619 context
= isl_context_lex_alloc(dom
);
3621 context
= isl_context_gbr_alloc(dom
);
3626 first
= isl_basic_set_first_unknown_div(dom
);
3628 return context
->op
->free(context
);
3629 context
->n_unknown
= isl_basic_set_dim(dom
, isl_dim_div
) - first
;
3634 /* Initialize some common fields of "sol", which keeps track
3635 * of the solution of an optimization problem on "bmap" over
3637 * If "max" is set, then a maximization problem is being solved, rather than
3638 * a minimization problem, which means that the variables in the
3639 * tableau have value "M - x" rather than "M + x".
3641 static isl_stat
sol_init(struct isl_sol
*sol
, __isl_keep isl_basic_map
*bmap
,
3642 __isl_keep isl_basic_set
*dom
, int max
)
3644 sol
->rational
= ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
);
3645 sol
->dec_level
.callback
.run
= &sol_dec_level_wrap
;
3646 sol
->dec_level
.sol
= sol
;
3648 sol
->n_out
= isl_basic_map_dim(bmap
, isl_dim_out
);
3649 sol
->space
= isl_basic_map_get_space(bmap
);
3651 sol
->context
= isl_context_alloc(dom
);
3652 if (!sol
->space
|| !sol
->context
)
3653 return isl_stat_error
;
3658 /* Construct an isl_sol_map structure for accumulating the solution.
3659 * If track_empty is set, then we also keep track of the parts
3660 * of the context where there is no solution.
3661 * If max is set, then we are solving a maximization, rather than
3662 * a minimization problem, which means that the variables in the
3663 * tableau have value "M - x" rather than "M + x".
3665 static struct isl_sol
*sol_map_init(__isl_keep isl_basic_map
*bmap
,
3666 __isl_take isl_basic_set
*dom
, int track_empty
, int max
)
3668 struct isl_sol_map
*sol_map
= NULL
;
3674 sol_map
= isl_calloc_type(bmap
->ctx
, struct isl_sol_map
);
3678 sol_map
->sol
.free
= &sol_map_free
;
3679 if (sol_init(&sol_map
->sol
, bmap
, dom
, max
) < 0)
3681 sol_map
->sol
.add
= &sol_map_add_wrap
;
3682 sol_map
->sol
.add_empty
= track_empty
? &sol_map_add_empty_wrap
: NULL
;
3683 space
= isl_space_copy(sol_map
->sol
.space
);
3684 sol_map
->map
= isl_map_alloc_space(space
, 1, ISL_MAP_DISJOINT
);
3689 sol_map
->empty
= isl_set_alloc_space(isl_basic_set_get_space(dom
),
3690 1, ISL_SET_DISJOINT
);
3691 if (!sol_map
->empty
)
3695 isl_basic_set_free(dom
);
3696 return &sol_map
->sol
;
3698 isl_basic_set_free(dom
);
3699 sol_free(&sol_map
->sol
);
3703 /* Check whether all coefficients of (non-parameter) variables
3704 * are non-positive, meaning that no pivots can be performed on the row.
3706 static int is_critical(struct isl_tab
*tab
, int row
)
3709 unsigned off
= 2 + tab
->M
;
3711 for (j
= tab
->n_dead
; j
< tab
->n_col
; ++j
) {
3712 if (col_is_parameter_var(tab
, j
))
3715 if (isl_int_is_pos(tab
->mat
->row
[row
][off
+ j
]))
3722 /* Check whether the inequality represented by vec is strict over the integers,
3723 * i.e., there are no integer values satisfying the constraint with
3724 * equality. This happens if the gcd of the coefficients is not a divisor
3725 * of the constant term. If so, scale the constraint down by the gcd
3726 * of the coefficients.
3728 static int is_strict(struct isl_vec
*vec
)
3734 isl_seq_gcd(vec
->el
+ 1, vec
->size
- 1, &gcd
);
3735 if (!isl_int_is_one(gcd
)) {
3736 strict
= !isl_int_is_divisible_by(vec
->el
[0], gcd
);
3737 isl_int_fdiv_q(vec
->el
[0], vec
->el
[0], gcd
);
3738 isl_seq_scale_down(vec
->el
+ 1, vec
->el
+ 1, gcd
, vec
->size
-1);
3745 /* Determine the sign of the given row of the main tableau.
3746 * The result is one of
3747 * isl_tab_row_pos: always non-negative; no pivot needed
3748 * isl_tab_row_neg: always non-positive; pivot
3749 * isl_tab_row_any: can be both positive and negative; split
3751 * We first handle some simple cases
3752 * - the row sign may be known already
3753 * - the row may be obviously non-negative
3754 * - the parametric constant may be equal to that of another row
3755 * for which we know the sign. This sign will be either "pos" or
3756 * "any". If it had been "neg" then we would have pivoted before.
3758 * If none of these cases hold, we check the value of the row for each
3759 * of the currently active samples. Based on the signs of these values
3760 * we make an initial determination of the sign of the row.
3762 * all zero -> unk(nown)
3763 * all non-negative -> pos
3764 * all non-positive -> neg
3765 * both negative and positive -> all
3767 * If we end up with "all", we are done.
3768 * Otherwise, we perform a check for positive and/or negative
3769 * values as follows.
3771 * samples neg unk pos
3777 * There is no special sign for "zero", because we can usually treat zero
3778 * as either non-negative or non-positive, whatever works out best.
3779 * However, if the row is "critical", meaning that pivoting is impossible
3780 * then we don't want to limp zero with the non-positive case, because
3781 * then we we would lose the solution for those values of the parameters
3782 * where the value of the row is zero. Instead, we treat 0 as non-negative
3783 * ensuring a split if the row can attain both zero and negative values.
3784 * The same happens when the original constraint was one that could not
3785 * be satisfied with equality by any integer values of the parameters.
3786 * In this case, we normalize the constraint, but then a value of zero
3787 * for the normalized constraint is actually a positive value for the
3788 * original constraint, so again we need to treat zero as non-negative.
3789 * In both these cases, we have the following decision tree instead:
3791 * all non-negative -> pos
3792 * all negative -> neg
3793 * both negative and non-negative -> all
3801 static enum isl_tab_row_sign
row_sign(struct isl_tab
*tab
,
3802 struct isl_sol
*sol
, int row
)
3804 struct isl_vec
*ineq
= NULL
;
3805 enum isl_tab_row_sign res
= isl_tab_row_unknown
;
3810 if (tab
->row_sign
[row
] != isl_tab_row_unknown
)
3811 return tab
->row_sign
[row
];
3812 if (is_obviously_nonneg(tab
, row
))
3813 return isl_tab_row_pos
;
3814 for (row2
= tab
->n_redundant
; row2
< tab
->n_row
; ++row2
) {
3815 if (tab
->row_sign
[row2
] == isl_tab_row_unknown
)
3817 if (identical_parameter_line(tab
, row
, row2
))
3818 return tab
->row_sign
[row2
];
3821 critical
= is_critical(tab
, row
);
3823 ineq
= get_row_parameter_ineq(tab
, row
);
3827 strict
= is_strict(ineq
);
3829 res
= sol
->context
->op
->ineq_sign(sol
->context
, ineq
->el
,
3830 critical
|| strict
);
3832 if (res
== isl_tab_row_unknown
|| res
== isl_tab_row_pos
) {
3833 /* test for negative values */
3835 isl_seq_neg(ineq
->el
, ineq
->el
, ineq
->size
);
3836 isl_int_sub_ui(ineq
->el
[0], ineq
->el
[0], 1);
3838 feasible
= sol
->context
->op
->test_ineq(sol
->context
, ineq
->el
);
3842 res
= isl_tab_row_pos
;
3844 res
= (res
== isl_tab_row_unknown
) ? isl_tab_row_neg
3846 if (res
== isl_tab_row_neg
) {
3847 isl_seq_neg(ineq
->el
, ineq
->el
, ineq
->size
);
3848 isl_int_sub_ui(ineq
->el
[0], ineq
->el
[0], 1);
3852 if (res
== isl_tab_row_neg
) {
3853 /* test for positive values */
3855 if (!critical
&& !strict
)
3856 isl_int_sub_ui(ineq
->el
[0], ineq
->el
[0], 1);
3858 feasible
= sol
->context
->op
->test_ineq(sol
->context
, ineq
->el
);
3862 res
= isl_tab_row_any
;
3869 return isl_tab_row_unknown
;
3872 static void find_solutions(struct isl_sol
*sol
, struct isl_tab
*tab
);
3874 /* Find solutions for values of the parameters that satisfy the given
3877 * We currently take a snapshot of the context tableau that is reset
3878 * when we return from this function, while we make a copy of the main
3879 * tableau, leaving the original main tableau untouched.
3880 * These are fairly arbitrary choices. Making a copy also of the context
3881 * tableau would obviate the need to undo any changes made to it later,
3882 * while taking a snapshot of the main tableau could reduce memory usage.
3883 * If we were to switch to taking a snapshot of the main tableau,
3884 * we would have to keep in mind that we need to save the row signs
3885 * and that we need to do this before saving the current basis
3886 * such that the basis has been restore before we restore the row signs.
3888 static void find_in_pos(struct isl_sol
*sol
, struct isl_tab
*tab
, isl_int
*ineq
)
3894 saved
= sol
->context
->op
->save(sol
->context
);
3896 tab
= isl_tab_dup(tab
);
3900 sol
->context
->op
->add_ineq(sol
->context
, ineq
, 0, 1);
3902 find_solutions(sol
, tab
);
3905 sol
->context
->op
->restore(sol
->context
, saved
);
3907 sol
->context
->op
->discard(saved
);
3913 /* Record the absence of solutions for those values of the parameters
3914 * that do not satisfy the given inequality with equality.
3916 static void no_sol_in_strict(struct isl_sol
*sol
,
3917 struct isl_tab
*tab
, struct isl_vec
*ineq
)
3922 if (!sol
->context
|| sol
->error
)
3924 saved
= sol
->context
->op
->save(sol
->context
);
3926 isl_int_sub_ui(ineq
->el
[0], ineq
->el
[0], 1);
3928 sol
->context
->op
->add_ineq(sol
->context
, ineq
->el
, 1, 0);
3937 isl_int_add_ui(ineq
->el
[0], ineq
->el
[0], 1);
3939 sol
->context
->op
->restore(sol
->context
, saved
);
3945 /* Reset all row variables that are marked to have a sign that may
3946 * be both positive and negative to have an unknown sign.
3948 static void reset_any_to_unknown(struct isl_tab
*tab
)
3952 for (row
= tab
->n_redundant
; row
< tab
->n_row
; ++row
) {
3953 if (!isl_tab_var_from_row(tab
, row
)->is_nonneg
)
3955 if (tab
->row_sign
[row
] == isl_tab_row_any
)
3956 tab
->row_sign
[row
] = isl_tab_row_unknown
;
3960 /* Compute the lexicographic minimum of the set represented by the main
3961 * tableau "tab" within the context "sol->context_tab".
3962 * On entry the sample value of the main tableau is lexicographically
3963 * less than or equal to this lexicographic minimum.
3964 * Pivots are performed until a feasible point is found, which is then
3965 * necessarily equal to the minimum, or until the tableau is found to
3966 * be infeasible. Some pivots may need to be performed for only some
3967 * feasible values of the context tableau. If so, the context tableau
3968 * is split into a part where the pivot is needed and a part where it is not.
3970 * Whenever we enter the main loop, the main tableau is such that no
3971 * "obvious" pivots need to be performed on it, where "obvious" means
3972 * that the given row can be seen to be negative without looking at
3973 * the context tableau. In particular, for non-parametric problems,
3974 * no pivots need to be performed on the main tableau.
3975 * The caller of find_solutions is responsible for making this property
3976 * hold prior to the first iteration of the loop, while restore_lexmin
3977 * is called before every other iteration.
3979 * Inside the main loop, we first examine the signs of the rows of
3980 * the main tableau within the context of the context tableau.
3981 * If we find a row that is always non-positive for all values of
3982 * the parameters satisfying the context tableau and negative for at
3983 * least one value of the parameters, we perform the appropriate pivot
3984 * and start over. An exception is the case where no pivot can be
3985 * performed on the row. In this case, we require that the sign of
3986 * the row is negative for all values of the parameters (rather than just
3987 * non-positive). This special case is handled inside row_sign, which
3988 * will say that the row can have any sign if it determines that it can
3989 * attain both negative and zero values.
3991 * If we can't find a row that always requires a pivot, but we can find
3992 * one or more rows that require a pivot for some values of the parameters
3993 * (i.e., the row can attain both positive and negative signs), then we split
3994 * the context tableau into two parts, one where we force the sign to be
3995 * non-negative and one where we force is to be negative.
3996 * The non-negative part is handled by a recursive call (through find_in_pos).
3997 * Upon returning from this call, we continue with the negative part and
3998 * perform the required pivot.
4000 * If no such rows can be found, all rows are non-negative and we have
4001 * found a (rational) feasible point. If we only wanted a rational point
4003 * Otherwise, we check if all values of the sample point of the tableau
4004 * are integral for the variables. If so, we have found the minimal
4005 * integral point and we are done.
4006 * If the sample point is not integral, then we need to make a distinction
4007 * based on whether the constant term is non-integral or the coefficients
4008 * of the parameters. Furthermore, in order to decide how to handle
4009 * the non-integrality, we also need to know whether the coefficients
4010 * of the other columns in the tableau are integral. This leads
4011 * to the following table. The first two rows do not correspond
4012 * to a non-integral sample point and are only mentioned for completeness.
4014 * constant parameters other
4017 * int int rat | -> no problem
4019 * rat int int -> fail
4021 * rat int rat -> cut
4024 * rat rat rat | -> parametric cut
4027 * rat rat int | -> split context
4029 * If the parametric constant is completely integral, then there is nothing
4030 * to be done. If the constant term is non-integral, but all the other
4031 * coefficient are integral, then there is nothing that can be done
4032 * and the tableau has no integral solution.
4033 * If, on the other hand, one or more of the other columns have rational
4034 * coefficients, but the parameter coefficients are all integral, then
4035 * we can perform a regular (non-parametric) cut.
4036 * Finally, if there is any parameter coefficient that is non-integral,
4037 * then we need to involve the context tableau. There are two cases here.
4038 * If at least one other column has a rational coefficient, then we
4039 * can perform a parametric cut in the main tableau by adding a new
4040 * integer division in the context tableau.
4041 * If all other columns have integral coefficients, then we need to
4042 * enforce that the rational combination of parameters (c + \sum a_i y_i)/m
4043 * is always integral. We do this by introducing an integer division
4044 * q = floor((c + \sum a_i y_i)/m) and stipulating that its argument should
4045 * always be integral in the context tableau, i.e., m q = c + \sum a_i y_i.
4046 * Since q is expressed in the tableau as
4047 * c + \sum a_i y_i - m q >= 0
4048 * -c - \sum a_i y_i + m q + m - 1 >= 0
4049 * it is sufficient to add the inequality
4050 * -c - \sum a_i y_i + m q >= 0
4051 * In the part of the context where this inequality does not hold, the
4052 * main tableau is marked as being empty.
4054 static void find_solutions(struct isl_sol
*sol
, struct isl_tab
*tab
)
4056 struct isl_context
*context
;
4059 if (!tab
|| sol
->error
)
4062 context
= sol
->context
;
4066 if (context
->op
->is_empty(context
))
4069 for (r
= 0; r
>= 0 && tab
&& !tab
->empty
; r
= restore_lexmin(tab
)) {
4072 enum isl_tab_row_sign sgn
;
4076 for (row
= tab
->n_redundant
; row
< tab
->n_row
; ++row
) {
4077 if (!isl_tab_var_from_row(tab
, row
)->is_nonneg
)
4079 sgn
= row_sign(tab
, sol
, row
);
4082 tab
->row_sign
[row
] = sgn
;
4083 if (sgn
== isl_tab_row_any
)
4085 if (sgn
== isl_tab_row_any
&& split
== -1)
4087 if (sgn
== isl_tab_row_neg
)
4090 if (row
< tab
->n_row
)
4093 struct isl_vec
*ineq
;
4095 split
= context
->op
->best_split(context
, tab
);
4098 ineq
= get_row_parameter_ineq(tab
, split
);
4102 reset_any_to_unknown(tab
);
4103 tab
->row_sign
[split
] = isl_tab_row_pos
;
4105 find_in_pos(sol
, tab
, ineq
->el
);
4106 tab
->row_sign
[split
] = isl_tab_row_neg
;
4107 isl_seq_neg(ineq
->el
, ineq
->el
, ineq
->size
);
4108 isl_int_sub_ui(ineq
->el
[0], ineq
->el
[0], 1);
4110 context
->op
->add_ineq(context
, ineq
->el
, 0, 1);
4118 row
= first_non_integer_row(tab
, &flags
);
4121 if (ISL_FL_ISSET(flags
, I_PAR
)) {
4122 if (ISL_FL_ISSET(flags
, I_VAR
)) {
4123 if (isl_tab_mark_empty(tab
) < 0)
4127 row
= add_cut(tab
, row
);
4128 } else if (ISL_FL_ISSET(flags
, I_VAR
)) {
4129 struct isl_vec
*div
;
4130 struct isl_vec
*ineq
;
4132 div
= get_row_split_div(tab
, row
);
4135 d
= context
->op
->get_div(context
, tab
, div
);
4139 ineq
= ineq_for_div(context
->op
->peek_basic_set(context
), d
);
4143 no_sol_in_strict(sol
, tab
, ineq
);
4144 isl_seq_neg(ineq
->el
, ineq
->el
, ineq
->size
);
4145 context
->op
->add_ineq(context
, ineq
->el
, 1, 1);
4147 if (sol
->error
|| !context
->op
->is_ok(context
))
4149 tab
= set_row_cst_to_div(tab
, row
, d
);
4150 if (context
->op
->is_empty(context
))
4153 row
= add_parametric_cut(tab
, row
, context
);
4168 /* Does "sol" contain a pair of partial solutions that could potentially
4171 * We currently only check that "sol" is not in an error state
4172 * and that there are at least two partial solutions of which the final two
4173 * are defined at the same level.
4175 static int sol_has_mergeable_solutions(struct isl_sol
*sol
)
4181 if (!sol
->partial
->next
)
4183 return sol
->partial
->level
== sol
->partial
->next
->level
;
4186 /* Compute the lexicographic minimum of the set represented by the main
4187 * tableau "tab" within the context "sol->context_tab".
4189 * As a preprocessing step, we first transfer all the purely parametric
4190 * equalities from the main tableau to the context tableau, i.e.,
4191 * parameters that have been pivoted to a row.
4192 * These equalities are ignored by the main algorithm, because the
4193 * corresponding rows may not be marked as being non-negative.
4194 * In parts of the context where the added equality does not hold,
4195 * the main tableau is marked as being empty.
4197 * Before we embark on the actual computation, we save a copy
4198 * of the context. When we return, we check if there are any
4199 * partial solutions that can potentially be merged. If so,
4200 * we perform a rollback to the initial state of the context.
4201 * The merging of partial solutions happens inside calls to
4202 * sol_dec_level that are pushed onto the undo stack of the context.
4203 * If there are no partial solutions that can potentially be merged
4204 * then the rollback is skipped as it would just be wasted effort.
4206 static void find_solutions_main(struct isl_sol
*sol
, struct isl_tab
*tab
)
4216 for (row
= tab
->n_redundant
; row
< tab
->n_row
; ++row
) {
4220 if (!row_is_parameter_var(tab
, row
))
4222 if (tab
->row_var
[row
] < tab
->n_param
)
4223 p
= tab
->row_var
[row
];
4225 p
= tab
->row_var
[row
]
4226 + tab
->n_param
- (tab
->n_var
- tab
->n_div
);
4228 eq
= isl_vec_alloc(tab
->mat
->ctx
, 1+tab
->n_param
+tab
->n_div
);
4231 get_row_parameter_line(tab
, row
, eq
->el
);
4232 isl_int_neg(eq
->el
[1 + p
], tab
->mat
->row
[row
][0]);
4233 eq
= isl_vec_normalize(eq
);
4236 no_sol_in_strict(sol
, tab
, eq
);
4238 isl_seq_neg(eq
->el
, eq
->el
, eq
->size
);
4240 no_sol_in_strict(sol
, tab
, eq
);
4241 isl_seq_neg(eq
->el
, eq
->el
, eq
->size
);
4243 sol
->context
->op
->add_eq(sol
->context
, eq
->el
, 1, 1);
4247 if (isl_tab_mark_redundant(tab
, row
) < 0)
4250 if (sol
->context
->op
->is_empty(sol
->context
))
4253 row
= tab
->n_redundant
- 1;
4256 saved
= sol
->context
->op
->save(sol
->context
);
4258 find_solutions(sol
, tab
);
4260 if (sol_has_mergeable_solutions(sol
))
4261 sol
->context
->op
->restore(sol
->context
, saved
);
4263 sol
->context
->op
->discard(saved
);
4274 /* Check if integer division "div" of "dom" also occurs in "bmap".
4275 * If so, return its position within the divs.
4276 * If not, return -1.
4278 static int find_context_div(struct isl_basic_map
*bmap
,
4279 struct isl_basic_set
*dom
, unsigned div
)
4282 unsigned b_dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
4283 unsigned d_dim
= isl_space_dim(dom
->dim
, isl_dim_all
);
4285 if (isl_int_is_zero(dom
->div
[div
][0]))
4287 if (isl_seq_first_non_zero(dom
->div
[div
] + 2 + d_dim
, dom
->n_div
) != -1)
4290 for (i
= 0; i
< bmap
->n_div
; ++i
) {
4291 if (isl_int_is_zero(bmap
->div
[i
][0]))
4293 if (isl_seq_first_non_zero(bmap
->div
[i
] + 2 + d_dim
,
4294 (b_dim
- d_dim
) + bmap
->n_div
) != -1)
4296 if (isl_seq_eq(bmap
->div
[i
], dom
->div
[div
], 2 + d_dim
))
4302 /* The correspondence between the variables in the main tableau,
4303 * the context tableau, and the input map and domain is as follows.
4304 * The first n_param and the last n_div variables of the main tableau
4305 * form the variables of the context tableau.
4306 * In the basic map, these n_param variables correspond to the
4307 * parameters and the input dimensions. In the domain, they correspond
4308 * to the parameters and the set dimensions.
4309 * The n_div variables correspond to the integer divisions in the domain.
4310 * To ensure that everything lines up, we may need to copy some of the
4311 * integer divisions of the domain to the map. These have to be placed
4312 * in the same order as those in the context and they have to be placed
4313 * after any other integer divisions that the map may have.
4314 * This function performs the required reordering.
4316 static __isl_give isl_basic_map
*align_context_divs(
4317 __isl_take isl_basic_map
*bmap
, __isl_keep isl_basic_set
*dom
)
4323 for (i
= 0; i
< dom
->n_div
; ++i
)
4324 if (find_context_div(bmap
, dom
, i
) != -1)
4326 other
= bmap
->n_div
- common
;
4327 if (dom
->n_div
- common
> 0) {
4328 bmap
= isl_basic_map_extend_space(bmap
, isl_space_copy(bmap
->dim
),
4329 dom
->n_div
- common
, 0, 0);
4333 for (i
= 0; i
< dom
->n_div
; ++i
) {
4334 int pos
= find_context_div(bmap
, dom
, i
);
4336 pos
= isl_basic_map_alloc_div(bmap
);
4339 isl_int_set_si(bmap
->div
[pos
][0], 0);
4341 if (pos
!= other
+ i
)
4342 isl_basic_map_swap_div(bmap
, pos
, other
+ i
);
4346 isl_basic_map_free(bmap
);
4350 /* Base case of isl_tab_basic_map_partial_lexopt, after removing
4351 * some obvious symmetries.
4353 * We make sure the divs in the domain are properly ordered,
4354 * because they will be added one by one in the given order
4355 * during the construction of the solution map.
4356 * Furthermore, make sure that the known integer divisions
4357 * appear before any unknown integer division because the solution
4358 * may depend on the known integer divisions, while anything that
4359 * depends on any variable starting from the first unknown integer
4360 * division is ignored in sol_pma_add.
4362 static struct isl_sol
*basic_map_partial_lexopt_base_sol(
4363 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_set
*dom
,
4364 __isl_give isl_set
**empty
, int max
,
4365 struct isl_sol
*(*init
)(__isl_keep isl_basic_map
*bmap
,
4366 __isl_take isl_basic_set
*dom
, int track_empty
, int max
))
4368 struct isl_tab
*tab
;
4369 struct isl_sol
*sol
= NULL
;
4370 struct isl_context
*context
;
4373 dom
= isl_basic_set_sort_divs(dom
);
4374 bmap
= align_context_divs(bmap
, dom
);
4376 sol
= init(bmap
, dom
, !!empty
, max
);
4380 context
= sol
->context
;
4381 if (isl_basic_set_plain_is_empty(context
->op
->peek_basic_set(context
)))
4383 else if (isl_basic_map_plain_is_empty(bmap
)) {
4386 isl_basic_set_copy(context
->op
->peek_basic_set(context
)));
4388 tab
= tab_for_lexmin(bmap
,
4389 context
->op
->peek_basic_set(context
), 1, max
);
4390 tab
= context
->op
->detect_nonnegative_parameters(context
, tab
);
4391 find_solutions_main(sol
, tab
);
4396 isl_basic_map_free(bmap
);
4400 isl_basic_map_free(bmap
);
4404 /* Base case of isl_tab_basic_map_partial_lexopt, after removing
4405 * some obvious symmetries.
4407 * We call basic_map_partial_lexopt_base_sol and extract the results.
4409 static __isl_give isl_map
*basic_map_partial_lexopt_base(
4410 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_set
*dom
,
4411 __isl_give isl_set
**empty
, int max
)
4413 isl_map
*result
= NULL
;
4414 struct isl_sol
*sol
;
4415 struct isl_sol_map
*sol_map
;
4417 sol
= basic_map_partial_lexopt_base_sol(bmap
, dom
, empty
, max
,
4421 sol_map
= (struct isl_sol_map
*) sol
;
4423 result
= isl_map_copy(sol_map
->map
);
4425 *empty
= isl_set_copy(sol_map
->empty
);
4426 sol_free(&sol_map
->sol
);
4430 /* Return a count of the number of occurrences of the "n" first
4431 * variables in the inequality constraints of "bmap".
4433 static __isl_give
int *count_occurrences(__isl_keep isl_basic_map
*bmap
,
4442 ctx
= isl_basic_map_get_ctx(bmap
);
4443 occurrences
= isl_calloc_array(ctx
, int, n
);
4447 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
4448 for (j
= 0; j
< n
; ++j
) {
4449 if (!isl_int_is_zero(bmap
->ineq
[i
][1 + j
]))
4457 /* Do all of the "n" variables with non-zero coefficients in "c"
4458 * occur in exactly a single constraint.
4459 * "occurrences" is an array of length "n" containing the number
4460 * of occurrences of each of the variables in the inequality constraints.
4462 static int single_occurrence(int n
, isl_int
*c
, int *occurrences
)
4466 for (i
= 0; i
< n
; ++i
) {
4467 if (isl_int_is_zero(c
[i
]))
4469 if (occurrences
[i
] != 1)
4476 /* Do all of the "n" initial variables that occur in inequality constraint
4477 * "ineq" of "bmap" only occur in that constraint?
4479 static int all_single_occurrence(__isl_keep isl_basic_map
*bmap
, int ineq
,
4484 for (i
= 0; i
< n
; ++i
) {
4485 if (isl_int_is_zero(bmap
->ineq
[ineq
][1 + i
]))
4487 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
4490 if (!isl_int_is_zero(bmap
->ineq
[j
][1 + i
]))
4498 /* Structure used during detection of parallel constraints.
4499 * n_in: number of "input" variables: isl_dim_param + isl_dim_in
4500 * n_out: number of "output" variables: isl_dim_out + isl_dim_div
4501 * val: the coefficients of the output variables
4503 struct isl_constraint_equal_info
{
4509 /* Check whether the coefficients of the output variables
4510 * of the constraint in "entry" are equal to info->val.
4512 static int constraint_equal(const void *entry
, const void *val
)
4514 isl_int
**row
= (isl_int
**)entry
;
4515 const struct isl_constraint_equal_info
*info
= val
;
4517 return isl_seq_eq((*row
) + 1 + info
->n_in
, info
->val
, info
->n_out
);
4520 /* Check whether "bmap" has a pair of constraints that have
4521 * the same coefficients for the output variables.
4522 * Note that the coefficients of the existentially quantified
4523 * variables need to be zero since the existentially quantified
4524 * of the result are usually not the same as those of the input.
4525 * Furthermore, check that each of the input variables that occur
4526 * in those constraints does not occur in any other constraint.
4527 * If so, return true and return the row indices of the two constraints
4528 * in *first and *second.
4530 static isl_bool
parallel_constraints(__isl_keep isl_basic_map
*bmap
,
4531 int *first
, int *second
)
4535 int *occurrences
= NULL
;
4536 struct isl_hash_table
*table
= NULL
;
4537 struct isl_hash_table_entry
*entry
;
4538 struct isl_constraint_equal_info info
;
4542 ctx
= isl_basic_map_get_ctx(bmap
);
4543 table
= isl_hash_table_alloc(ctx
, bmap
->n_ineq
);
4547 info
.n_in
= isl_basic_map_dim(bmap
, isl_dim_param
) +
4548 isl_basic_map_dim(bmap
, isl_dim_in
);
4549 occurrences
= count_occurrences(bmap
, info
.n_in
);
4550 if (info
.n_in
&& !occurrences
)
4552 n_out
= isl_basic_map_dim(bmap
, isl_dim_out
);
4553 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
4554 info
.n_out
= n_out
+ n_div
;
4555 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
4558 info
.val
= bmap
->ineq
[i
] + 1 + info
.n_in
;
4559 if (isl_seq_first_non_zero(info
.val
, n_out
) < 0)
4561 if (isl_seq_first_non_zero(info
.val
+ n_out
, n_div
) >= 0)
4563 if (!single_occurrence(info
.n_in
, bmap
->ineq
[i
] + 1,
4566 hash
= isl_seq_get_hash(info
.val
, info
.n_out
);
4567 entry
= isl_hash_table_find(ctx
, table
, hash
,
4568 constraint_equal
, &info
, 1);
4573 entry
->data
= &bmap
->ineq
[i
];
4576 if (i
< bmap
->n_ineq
) {
4577 *first
= ((isl_int
**)entry
->data
) - bmap
->ineq
;
4581 isl_hash_table_free(ctx
, table
);
4584 return i
< bmap
->n_ineq
;
4586 isl_hash_table_free(ctx
, table
);
4588 return isl_bool_error
;
4591 /* Given a set of upper bounds in "var", add constraints to "bset"
4592 * that make the i-th bound smallest.
4594 * In particular, if there are n bounds b_i, then add the constraints
4596 * b_i <= b_j for j > i
4597 * b_i < b_j for j < i
4599 static __isl_give isl_basic_set
*select_minimum(__isl_take isl_basic_set
*bset
,
4600 __isl_keep isl_mat
*var
, int i
)
4605 ctx
= isl_mat_get_ctx(var
);
4607 for (j
= 0; j
< var
->n_row
; ++j
) {
4610 k
= isl_basic_set_alloc_inequality(bset
);
4613 isl_seq_combine(bset
->ineq
[k
], ctx
->one
, var
->row
[j
],
4614 ctx
->negone
, var
->row
[i
], var
->n_col
);
4615 isl_int_set_si(bset
->ineq
[k
][var
->n_col
], 0);
4617 isl_int_sub_ui(bset
->ineq
[k
][0], bset
->ineq
[k
][0], 1);
4620 bset
= isl_basic_set_finalize(bset
);
4624 isl_basic_set_free(bset
);
4628 /* Given a set of upper bounds on the last "input" variable m,
4629 * construct a set that assigns the minimal upper bound to m, i.e.,
4630 * construct a set that divides the space into cells where one
4631 * of the upper bounds is smaller than all the others and assign
4632 * this upper bound to m.
4634 * In particular, if there are n bounds b_i, then the result
4635 * consists of n basic sets, each one of the form
4638 * b_i <= b_j for j > i
4639 * b_i < b_j for j < i
4641 static __isl_give isl_set
*set_minimum(__isl_take isl_space
*dim
,
4642 __isl_take isl_mat
*var
)
4645 isl_basic_set
*bset
= NULL
;
4646 isl_set
*set
= NULL
;
4651 set
= isl_set_alloc_space(isl_space_copy(dim
),
4652 var
->n_row
, ISL_SET_DISJOINT
);
4654 for (i
= 0; i
< var
->n_row
; ++i
) {
4655 bset
= isl_basic_set_alloc_space(isl_space_copy(dim
), 0,
4657 k
= isl_basic_set_alloc_equality(bset
);
4660 isl_seq_cpy(bset
->eq
[k
], var
->row
[i
], var
->n_col
);
4661 isl_int_set_si(bset
->eq
[k
][var
->n_col
], -1);
4662 bset
= select_minimum(bset
, var
, i
);
4663 set
= isl_set_add_basic_set(set
, bset
);
4666 isl_space_free(dim
);
4670 isl_basic_set_free(bset
);
4672 isl_space_free(dim
);
4677 /* Given that the last input variable of "bmap" represents the minimum
4678 * of the bounds in "cst", check whether we need to split the domain
4679 * based on which bound attains the minimum.
4681 * A split is needed when the minimum appears in an integer division
4682 * or in an equality. Otherwise, it is only needed if it appears in
4683 * an upper bound that is different from the upper bounds on which it
4686 static isl_bool
need_split_basic_map(__isl_keep isl_basic_map
*bmap
,
4687 __isl_keep isl_mat
*cst
)
4693 pos
= cst
->n_col
- 1;
4694 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
4696 for (i
= 0; i
< bmap
->n_div
; ++i
)
4697 if (!isl_int_is_zero(bmap
->div
[i
][2 + pos
]))
4698 return isl_bool_true
;
4700 for (i
= 0; i
< bmap
->n_eq
; ++i
)
4701 if (!isl_int_is_zero(bmap
->eq
[i
][1 + pos
]))
4702 return isl_bool_true
;
4704 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
4705 if (isl_int_is_nonneg(bmap
->ineq
[i
][1 + pos
]))
4707 if (!isl_int_is_negone(bmap
->ineq
[i
][1 + pos
]))
4708 return isl_bool_true
;
4709 if (isl_seq_first_non_zero(bmap
->ineq
[i
] + 1 + pos
+ 1,
4710 total
- pos
- 1) >= 0)
4711 return isl_bool_true
;
4713 for (j
= 0; j
< cst
->n_row
; ++j
)
4714 if (isl_seq_eq(bmap
->ineq
[i
], cst
->row
[j
], cst
->n_col
))
4716 if (j
>= cst
->n_row
)
4717 return isl_bool_true
;
4720 return isl_bool_false
;
4723 /* Given that the last set variable of "bset" represents the minimum
4724 * of the bounds in "cst", check whether we need to split the domain
4725 * based on which bound attains the minimum.
4727 * We simply call need_split_basic_map here. This is safe because
4728 * the position of the minimum is computed from "cst" and not
4731 static isl_bool
need_split_basic_set(__isl_keep isl_basic_set
*bset
,
4732 __isl_keep isl_mat
*cst
)
4734 return need_split_basic_map(bset_to_bmap(bset
), cst
);
4737 /* Given that the last set variable of "set" represents the minimum
4738 * of the bounds in "cst", check whether we need to split the domain
4739 * based on which bound attains the minimum.
4741 static isl_bool
need_split_set(__isl_keep isl_set
*set
, __isl_keep isl_mat
*cst
)
4745 for (i
= 0; i
< set
->n
; ++i
) {
4748 split
= need_split_basic_set(set
->p
[i
], cst
);
4749 if (split
< 0 || split
)
4753 return isl_bool_false
;
4756 /* Given a set of which the last set variable is the minimum
4757 * of the bounds in "cst", split each basic set in the set
4758 * in pieces where one of the bounds is (strictly) smaller than the others.
4759 * This subdivision is given in "min_expr".
4760 * The variable is subsequently projected out.
4762 * We only do the split when it is needed.
4763 * For example if the last input variable m = min(a,b) and the only
4764 * constraints in the given basic set are lower bounds on m,
4765 * i.e., l <= m = min(a,b), then we can simply project out m
4766 * to obtain l <= a and l <= b, without having to split on whether
4767 * m is equal to a or b.
4769 static __isl_give isl_set
*split(__isl_take isl_set
*empty
,
4770 __isl_take isl_set
*min_expr
, __isl_take isl_mat
*cst
)
4777 if (!empty
|| !min_expr
|| !cst
)
4780 n_in
= isl_set_dim(empty
, isl_dim_set
);
4781 dim
= isl_set_get_space(empty
);
4782 dim
= isl_space_drop_dims(dim
, isl_dim_set
, n_in
- 1, 1);
4783 res
= isl_set_empty(dim
);
4785 for (i
= 0; i
< empty
->n
; ++i
) {
4789 set
= isl_set_from_basic_set(isl_basic_set_copy(empty
->p
[i
]));
4790 split
= need_split_basic_set(empty
->p
[i
], cst
);
4792 set
= isl_set_free(set
);
4794 set
= isl_set_intersect(set
, isl_set_copy(min_expr
));
4795 set
= isl_set_remove_dims(set
, isl_dim_set
, n_in
- 1, 1);
4797 res
= isl_set_union_disjoint(res
, set
);
4800 isl_set_free(empty
);
4801 isl_set_free(min_expr
);
4805 isl_set_free(empty
);
4806 isl_set_free(min_expr
);
4811 /* Given a map of which the last input variable is the minimum
4812 * of the bounds in "cst", split each basic set in the set
4813 * in pieces where one of the bounds is (strictly) smaller than the others.
4814 * This subdivision is given in "min_expr".
4815 * The variable is subsequently projected out.
4817 * The implementation is essentially the same as that of "split".
4819 static __isl_give isl_map
*split_domain(__isl_take isl_map
*opt
,
4820 __isl_take isl_set
*min_expr
, __isl_take isl_mat
*cst
)
4827 if (!opt
|| !min_expr
|| !cst
)
4830 n_in
= isl_map_dim(opt
, isl_dim_in
);
4831 dim
= isl_map_get_space(opt
);
4832 dim
= isl_space_drop_dims(dim
, isl_dim_in
, n_in
- 1, 1);
4833 res
= isl_map_empty(dim
);
4835 for (i
= 0; i
< opt
->n
; ++i
) {
4839 map
= isl_map_from_basic_map(isl_basic_map_copy(opt
->p
[i
]));
4840 split
= need_split_basic_map(opt
->p
[i
], cst
);
4842 map
= isl_map_free(map
);
4844 map
= isl_map_intersect_domain(map
,
4845 isl_set_copy(min_expr
));
4846 map
= isl_map_remove_dims(map
, isl_dim_in
, n_in
- 1, 1);
4848 res
= isl_map_union_disjoint(res
, map
);
4852 isl_set_free(min_expr
);
4857 isl_set_free(min_expr
);
4862 static __isl_give isl_map
*basic_map_partial_lexopt(
4863 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_set
*dom
,
4864 __isl_give isl_set
**empty
, int max
);
4866 /* This function is called from basic_map_partial_lexopt_symm.
4867 * The last variable of "bmap" and "dom" corresponds to the minimum
4868 * of the bounds in "cst". "map_space" is the space of the original
4869 * input relation (of basic_map_partial_lexopt_symm) and "set_space"
4870 * is the space of the original domain.
4872 * We recursively call basic_map_partial_lexopt and then plug in
4873 * the definition of the minimum in the result.
4875 static __isl_give isl_map
*basic_map_partial_lexopt_symm_core(
4876 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_set
*dom
,
4877 __isl_give isl_set
**empty
, int max
, __isl_take isl_mat
*cst
,
4878 __isl_take isl_space
*map_space
, __isl_take isl_space
*set_space
)
4883 min_expr
= set_minimum(isl_basic_set_get_space(dom
), isl_mat_copy(cst
));
4885 opt
= basic_map_partial_lexopt(bmap
, dom
, empty
, max
);
4888 *empty
= split(*empty
,
4889 isl_set_copy(min_expr
), isl_mat_copy(cst
));
4890 *empty
= isl_set_reset_space(*empty
, set_space
);
4893 opt
= split_domain(opt
, min_expr
, cst
);
4894 opt
= isl_map_reset_space(opt
, map_space
);
4899 /* Extract a domain from "bmap" for the purpose of computing
4900 * a lexicographic optimum.
4902 * This function is only called when the caller wants to compute a full
4903 * lexicographic optimum, i.e., without specifying a domain. In this case,
4904 * the caller is not interested in the part of the domain space where
4905 * there is no solution and the domain can be initialized to those constraints
4906 * of "bmap" that only involve the parameters and the input dimensions.
4907 * This relieves the parametric programming engine from detecting those
4908 * inequalities and transferring them to the context. More importantly,
4909 * it ensures that those inequalities are transferred first and not
4910 * intermixed with inequalities that actually split the domain.
4912 * If the caller does not require the absence of existentially quantified
4913 * variables in the result (i.e., if ISL_OPT_QE is not set in "flags"),
4914 * then the actual domain of "bmap" can be used. This ensures that
4915 * the domain does not need to be split at all just to separate out
4916 * pieces of the domain that do not have a solution from piece that do.
4917 * This domain cannot be used in general because it may involve
4918 * (unknown) existentially quantified variables which will then also
4919 * appear in the solution.
4921 static __isl_give isl_basic_set
*extract_domain(__isl_keep isl_basic_map
*bmap
,
4927 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
4928 n_out
= isl_basic_map_dim(bmap
, isl_dim_out
);
4929 bmap
= isl_basic_map_copy(bmap
);
4930 if (ISL_FL_ISSET(flags
, ISL_OPT_QE
)) {
4931 bmap
= isl_basic_map_drop_constraints_involving_dims(bmap
,
4932 isl_dim_div
, 0, n_div
);
4933 bmap
= isl_basic_map_drop_constraints_involving_dims(bmap
,
4934 isl_dim_out
, 0, n_out
);
4936 return isl_basic_map_domain(bmap
);
4940 #define TYPE isl_map
4943 #include "isl_tab_lexopt_templ.c"
4945 /* Extract the subsequence of the sample value of "tab"
4946 * starting at "pos" and of length "len".
4948 static __isl_give isl_vec
*extract_sample_sequence(struct isl_tab
*tab
,
4955 ctx
= isl_tab_get_ctx(tab
);
4956 v
= isl_vec_alloc(ctx
, len
);
4959 for (i
= 0; i
< len
; ++i
) {
4960 if (!tab
->var
[pos
+ i
].is_row
) {
4961 isl_int_set_si(v
->el
[i
], 0);
4965 row
= tab
->var
[pos
+ i
].index
;
4966 isl_int_divexact(v
->el
[i
], tab
->mat
->row
[row
][1],
4967 tab
->mat
->row
[row
][0]);
4974 /* Check whether the constraint specified by "region" is violated on its own.
4975 * In particular, if region->has_non_zero is set,
4976 * then check if the linear combinations of
4977 * the specified sequence of variables that are required to be non-zero
4979 * If region->has_fixed is set, then check if the linear combinations
4980 * result in the expected values.
4982 static isl_bool
single_region_is_violated(struct isl_tab
*tab
,
4983 struct isl_ilp_region
*region
)
4989 if (region
->has_non_zero
) {
4990 if (!region
->non_zero
)
4991 return isl_bool_error
;
4993 n
= isl_mat_rows(region
->non_zero
);
4995 return isl_bool_true
;
4997 len
= isl_mat_cols(region
->non_zero
);
4998 v
= extract_sample_sequence(tab
, region
->pos
, len
);
4999 v
= isl_mat_vec_product(isl_mat_copy(region
->non_zero
), v
);
5000 violated
= isl_vec_is_zero(v
);
5002 if (violated
< 0 || violated
)
5006 if (region
->has_fixed
) {
5007 if (!region
->fixed
|| !region
->fixed_val
)
5008 return isl_bool_error
;
5010 len
= isl_mat_cols(region
->fixed
);
5011 v
= extract_sample_sequence(tab
, region
->pos
, len
);
5012 v
= isl_mat_vec_product(isl_mat_copy(region
->fixed
), v
);
5013 violated
= isl_bool_not(isl_vec_is_equal(v
, region
->fixed_val
));
5015 if (violated
< 0 || violated
)
5019 return isl_bool_false
;
5022 /* Check whether the (possibly disjunctive) constraint starting at region[pos]
5024 * A disjunctive constraint is only violated if all
5025 * of the disjuncts are violated.
5027 * If the constraint is marked conditional and the previous constraint
5028 * is not currently disabled, then ignore the constraint.
5030 static isl_bool
region_is_violated(struct isl_tab
*tab
,
5031 struct isl_ilp_region
*region
, int pos
)
5035 if (pos
> 0 && region
[pos
].conditional
&& !region
[pos
- 1].disabled
)
5036 return isl_bool_false
;
5039 violated
= single_region_is_violated(tab
, ®ion
[pos
]);
5040 if (violated
< 0 || !violated
)
5042 } while (region
[pos
++].disjunctive
);
5047 /* Global internal data for isl_tab_basic_set_constrained_lexmin.
5049 * "n_op" is the number of initial coordinates to optimize,
5050 * as passed to isl_tab_basic_set_constrained_lexmin.
5051 * "region" is the "n_region"-sized array of regions passed
5052 * to isl_tab_basic_set_constrained_lexmin.
5054 * "tab" is the tableau that corresponds to the ILP problem.
5055 * "local" is an array of local data structure, one for each
5056 * (potential) level of the backtracking procedure of
5057 * isl_tab_basic_set_constrained_lexmin.
5058 * "v" is a pre-allocated vector that can be used for adding
5059 * constraints to the tableau.
5061 * "sol" contains the best solution found so far.
5062 * It is initialized to a vector of size zero.
5064 struct isl_lexmin_data
{
5067 struct isl_ilp_region
*region
;
5069 struct isl_tab
*tab
;
5070 struct isl_local_region
*local
;
5076 /* Return the index of the first violated region, "n_region" if no regions
5077 * are violated or -1 in case of error.
5079 * Disabled optional constraints are skipped.
5081 * If a disjunctive constraint was found not be violated, then skip
5082 * over the other disjuncts.
5084 static int first_violated_region(struct isl_lexmin_data
*data
)
5088 for (i
= 0; i
< data
->n_region
; ++i
) {
5091 if (data
->region
[i
].optional
&& data
->region
[i
].disabled
)
5093 violated
= region_is_violated(data
->tab
, data
->region
, i
);
5098 while (data
->region
[i
].disjunctive
)
5102 return data
->n_region
;
5105 /* Check if the solution is optimal, i.e., whether the first
5106 * n_op entries are zero.
5108 static int is_optimal(__isl_keep isl_vec
*sol
, int n_op
)
5112 for (i
= 0; i
< n_op
; ++i
)
5113 if (!isl_int_is_zero(sol
->el
[1 + i
]))
5118 /* Add constraints to "tab" that ensure that any solution is significantly
5119 * better than that represented by "sol". That is, find the first
5120 * relevant (within first n_op) non-zero coefficient and force it (along
5121 * with all previous coefficients) to be zero.
5122 * If the solution is already optimal (all relevant coefficients are zero),
5123 * then just mark the table as empty.
5124 * "n_zero" is the number of coefficients that have been forced zero
5125 * by previous calls to this function at the same level.
5126 * Return the updated number of forced zero coefficients or -1 on error.
5128 * This function assumes that at least 2 * (n_op - n_zero) more rows and
5129 * at least 2 * (n_op - n_zero) more elements in the constraint array
5130 * are available in the tableau.
5132 static int force_better_solution(struct isl_tab
*tab
,
5133 __isl_keep isl_vec
*sol
, int n_op
, int n_zero
)
5142 for (i
= n_zero
; i
< n_op
; ++i
)
5143 if (!isl_int_is_zero(sol
->el
[1 + i
]))
5147 if (isl_tab_mark_empty(tab
) < 0)
5152 ctx
= isl_vec_get_ctx(sol
);
5153 v
= isl_vec_alloc(ctx
, 1 + tab
->n_var
);
5158 for (; i
>= n_zero
; --i
) {
5160 isl_int_set_si(v
->el
[1 + i
], -1);
5161 if (add_lexmin_eq(tab
, v
->el
) < 0)
5172 /* Fix non-zero direction "dir" of the given region to zero.
5174 * This function assumes that at least two more rows and at least
5175 * two more elements in the constraint array are available in the tableau.
5177 static isl_stat
fix_zero(struct isl_tab
*tab
, struct isl_ilp_region
*region
,
5178 int dir
, struct isl_lexmin_data
*data
)
5182 data
->v
= isl_vec_clr(data
->v
);
5184 return isl_stat_error
;
5185 len
= isl_mat_cols(region
->non_zero
);
5186 isl_seq_cpy(data
->v
->el
+ 1 + region
->pos
, region
->non_zero
->row
[dir
],
5188 if (add_lexmin_eq(tab
, data
->v
->el
) < 0)
5189 return isl_stat_error
;
5194 /* This function selects case "side" for the non-zero constraint
5195 * of region "region",
5196 * assuming all the equality constraints have been imposed already.
5197 * In particular, the non-zero direction side/2 is made positive
5198 * if side is even and made negative if side is odd.
5200 * This function assumes that at least one more row and at least
5201 * one more element in the constraint array are available in the tableau.
5203 static struct isl_tab
*pos_neg(struct isl_tab
*tab
,
5204 struct isl_ilp_region
*region
,
5205 int side
, struct isl_lexmin_data
*data
)
5209 data
->v
= isl_vec_clr(data
->v
);
5212 isl_int_set_si(data
->v
->el
[0], -1);
5213 len
= isl_mat_cols(region
->non_zero
);
5215 isl_seq_cpy(data
->v
->el
+ 1 + region
->pos
,
5216 region
->non_zero
->row
[side
/ 2], len
);
5218 isl_seq_neg(data
->v
->el
+ 1 + region
->pos
,
5219 region
->non_zero
->row
[side
/ 2], len
);
5220 return add_lexmin_ineq(tab
, data
->v
->el
);
5226 /* Local data at each level of the backtracking procedure of
5227 * isl_tab_basic_set_constrained_lexmin.
5229 * "update_init" is set if a solution has been found in any previously
5230 * considered case at this level. If the constraint ends up getting
5231 * ignored, then a better solution needs to be enforced in the next level.
5232 * "update" is set if a solution has been found in the current case
5233 * of this level, such that a better solution needs to be enforced
5235 * "n_zero" is the number of initial coordinates that have already
5236 * been forced to be zero at this level.
5237 * "region" is the region considered at this level.
5238 * "side" is the index of the current case at this level.
5239 * "n" is the number of non-zero directions, provided "region"
5240 * has a non-zero constraint.
5241 * "snap_init" is a snapshot of the tableau when this level was
5242 * initialized. It is only set if the corresponding region constraint
5243 * is optional and is used when the optional constraint is disabled.
5244 * "snap" is a snapshot of the tableau holding a state that needs
5245 * to be satisfied by all subsequent cases.
5247 struct isl_local_region
{
5254 struct isl_tab_undo
*snap_init
;
5255 struct isl_tab_undo
*snap
;
5258 /* Initialize the global data structure "data" used while solving
5259 * the ILP problem "bset".
5261 static isl_stat
init_lexmin_data(struct isl_lexmin_data
*data
,
5262 __isl_keep isl_basic_set
*bset
)
5266 ctx
= isl_basic_set_get_ctx(bset
);
5268 data
->tab
= tab_for_lexmin(bset
, NULL
, 0, 0);
5270 return isl_stat_error
;
5272 data
->v
= isl_vec_alloc(ctx
, 1 + data
->tab
->n_var
);
5274 return isl_stat_error
;
5275 data
->local
= isl_calloc_array(ctx
, struct isl_local_region
,
5277 if (data
->n_region
&& !data
->local
)
5278 return isl_stat_error
;
5280 data
->sol
= isl_vec_alloc(ctx
, 0);
5285 /* Clear the disabled field of all regions.
5287 static void clear_disabled( int n_region
, struct isl_ilp_region
*region
)
5291 for (i
= 0; i
< n_region
; ++i
)
5292 region
[i
].disabled
= 0;
5295 /* Remove the optional character of all currently optional constraints
5296 * that have not been disabled.
5297 * In case of a disjunctive constraint, only the last disjunct is made
5298 * required. The other disjuncts need to remain optional such that
5299 * a failing disjunct still allows the next disjunct to be considered.
5301 * Note that this also affects conditional constraints
5302 * that have not been activated yet. Even if they are no longer "optional",
5303 * they will remain "conditional" and since the constraints on which
5304 * they depend were not disabled, they will no longer be optional,
5305 * meaning that they can no longer get disabled and the conditional
5306 * constraints will never be activated.
5308 static void force_enabled_optional_constraints(int n_region
,
5309 struct isl_ilp_region
*region
)
5313 for (i
= 0; i
< n_region
; ++i
) {
5314 if (region
[i
].optional
&&
5315 !region
[i
].disjunctive
&& !region
[i
].disabled
)
5316 region
[i
].optional
= 0;
5320 /* Mark all outer levels as requiring a better solution
5321 * in the next cases.
5322 * For optional constraints, this means that all those that
5323 * are satisfied in the current solution, need to remain
5324 * satisfied in any subsequent solution.
5326 static void update_regions_and_outer_levels(struct isl_lexmin_data
*data
,
5331 for (i
= 0; i
< level
; ++i
) {
5332 data
->local
[i
].update_init
= 1;
5333 data
->local
[i
].update
= 1;
5335 force_enabled_optional_constraints(data
->n_region
, data
->region
);
5338 /* Initialize "local" to refer to region "region" and
5339 * to initiate processing at this level.
5341 static void init_local_region(struct isl_local_region
*local
, int region
,
5342 struct isl_lexmin_data
*data
)
5344 local
->n
= isl_mat_rows(data
->region
[region
].non_zero
);
5345 local
->region
= region
;
5347 local
->update_init
= 0;
5352 /* What to do next after entering a level of the backtracking procedure.
5354 * error: some error has occurred; abort
5355 * done: an optimal solution has been found; stop search
5356 * backtrack: backtrack to the previous level
5357 * handle: add the constraints for the current level and
5358 * move to the next level
5361 isl_next_error
= -1,
5367 /* If the region referenced by "local" has any associated
5368 * linear combinations that need to be equal to fixed values,
5369 * then impose those constraints on data->tab.
5371 static isl_stat
set_fixed(struct isl_local_region
*local
,
5372 struct isl_lexmin_data
*data
)
5374 struct isl_ilp_region
*region
;
5377 region
= &data
->region
[local
->region
];
5378 if (!region
->has_fixed
)
5381 data
->v
= isl_vec_clr(data
->v
);
5383 return isl_stat_error
;
5385 n
= isl_mat_rows(region
->fixed
);
5386 len
= isl_mat_cols(region
->fixed
);
5387 for (i
= 0; i
< n
; ++i
) {
5388 isl_seq_cpy(data
->v
->el
+ 1 + region
->pos
,
5389 region
->fixed
->row
[i
], len
);
5390 isl_int_neg(data
->v
->el
[0], region
->fixed_val
->el
[i
]);
5391 if (add_lexmin_eq(data
->tab
, data
->v
->el
) < 0)
5392 return isl_stat_error
;
5398 /* Have all cases of the current region been considered?
5399 * If there is a non-zero constraint with n directions, then there are 2n cases.
5400 * Otherwise, if there is fixed-value constraint, then there is one case
5401 * (in which the fixed-value constraint is imposed).
5403 * The constraints in the current tableau are imposed
5404 * in all subsequent cases. This means that if the current
5405 * tableau is empty, then none of those cases should be considered
5406 * anymore and all cases have effectively been considered.
5408 static int finished_all_cases(struct isl_local_region
*local
,
5409 struct isl_lexmin_data
*data
)
5411 struct isl_ilp_region
*region
;
5413 if (data
->tab
->empty
)
5415 region
= &data
->region
[local
->region
];
5416 if (region
->has_non_zero
)
5417 return local
->side
>= 2 * local
->n
;
5418 if (region
->has_fixed
)
5419 return local
->side
>= 1;
5423 /* Figure out what to do next when level "level" has been entered and
5424 * it turns out that there are no more cases left at this level.
5426 * If the constraint is not optional, then the caller needs to backtrack.
5427 * Otherwise, rollback to the state of the tableau when the level
5428 * was first entered, disable the constraint and tell the caller
5429 * to move on to the next level. A better solution should be enforced
5430 * on this next level if a solution has been found in any
5431 * of the previous cases at this level (marked by local->update_init being set).
5432 * However, any previously added such constraints at this level
5433 * have been removed in the rollback, so reset local->n_zero to zero.
5435 * If the constraint was already disabled, then enable it again
5438 static enum isl_next
enter_level_finished(int level
,
5439 struct isl_lexmin_data
*data
)
5441 struct isl_local_region
*local
= &data
->local
[level
];
5442 struct isl_ilp_region
*region
= &data
->region
[local
->region
];
5444 if (!region
->optional
)
5445 return isl_next_backtrack
;
5446 if (region
->disabled
) {
5447 region
->disabled
= 0;
5448 return isl_next_backtrack
;
5451 if (isl_tab_rollback(data
->tab
, local
->snap_init
) < 0)
5452 return isl_next_error
;
5453 region
->disabled
= 1;
5454 local
->update
= local
->update_init
;
5456 return isl_next_handle
;
5459 /* Enter level "level" of the backtracking search and figure out
5460 * what to do next. "init" is set if the level was entered
5461 * from a higher level and needs to be initialized.
5462 * Otherwise, the level is entered as a result of backtracking and
5463 * the tableau needs to be restored to a position that can
5464 * be used for the next case at this level.
5465 * The snapshot is assumed to have been saved in the previous case,
5466 * before the constraints specific to that case were added.
5467 * If the region constraint has been disabled, then the snapshot
5468 * is not available and it is not needed either because
5469 * the caller simply needs to backtrack.
5471 * In the initialization case, the local region is initialized
5472 * to point to the first violated region.
5473 * If this violated region has any fixed-value constraints,
5474 * then impose them on the tableau.
5475 * If the violated region has an optional constraint, then take
5476 * a snapshot first to be able to revert to the original state
5477 * when the constraint gets disabled.
5478 * If the constraints of all regions are satisfied by the current
5479 * sample of the tableau, then tell the caller to continue looking
5480 * for a better solution or to stop searching if an optimal solution
5483 * If the tableau is empty or if all cases at the current level
5484 * have been considered, then the caller needs to backtrack as well.
5486 static enum isl_next
enter_level(int level
, int init
,
5487 struct isl_lexmin_data
*data
)
5489 struct isl_local_region
*local
= &data
->local
[level
];
5494 data
->tab
= cut_to_integer_lexmin(data
->tab
, CUT_ONE
);
5496 return isl_next_error
;
5497 if (data
->tab
->empty
)
5498 return isl_next_backtrack
;
5499 r
= first_violated_region(data
);
5501 return isl_next_error
;
5502 if (r
== data
->n_region
) {
5503 update_regions_and_outer_levels(data
, level
);
5504 isl_vec_free(data
->sol
);
5505 data
->sol
= isl_tab_get_sample_value(data
->tab
);
5507 return isl_next_error
;
5508 if (is_optimal(data
->sol
, data
->n_op
))
5509 return isl_next_done
;
5510 return isl_next_backtrack
;
5512 if (level
>= data
->n_region
)
5513 isl_die(isl_vec_get_ctx(data
->v
), isl_error_internal
,
5514 "nesting level too deep",
5515 return isl_next_error
);
5516 init_local_region(local
, r
, data
);
5518 if (data
->region
[r
].has_non_zero
)
5520 if (data
->region
[r
].has_fixed
)
5521 n
+= 2 * isl_mat_rows(data
->region
[r
].fixed
);
5522 if (isl_tab_extend_cons(data
->tab
, n
+ 2 * data
->n_op
) < 0)
5523 return isl_next_error
;
5524 if (data
->region
[r
].optional
) {
5525 local
->snap_init
= isl_tab_snap(data
->tab
);
5526 if (isl_tab_push_basis(data
->tab
) < 0)
5527 return isl_next_error
;
5529 if (set_fixed(local
, data
) < 0)
5530 return isl_next_error
;
5532 if (!data
->region
[local
->region
].disabled
&&
5533 isl_tab_rollback(data
->tab
, local
->snap
) < 0)
5534 return isl_next_error
;
5537 if (finished_all_cases(local
, data
))
5538 return enter_level_finished(level
, data
);
5539 return isl_next_handle
;
5542 /* If a solution has been found in the previous case at this level
5543 * (marked by local->update being set), then add constraints
5544 * that enforce a better solution in the present and all following cases.
5545 * The constraints only need to be imposed once because they are
5546 * included in the snapshot (taken in pick_side) that will be used in
5549 static isl_stat
better_next_side(struct isl_local_region
*local
,
5550 struct isl_lexmin_data
*data
)
5555 local
->n_zero
= force_better_solution(data
->tab
,
5556 data
->sol
, data
->n_op
, local
->n_zero
);
5557 if (local
->n_zero
< 0)
5558 return isl_stat_error
;
5565 /* Add constraints to data->tab that select the current case (local->side)
5566 * at the current level.
5568 * If the linear combinations v should not be zero, then the cases are
5571 * v_0 = 0 and v_1 >= 1
5572 * v_0 = 0 and v_1 <= -1
5573 * v_0 = 0 and v_1 = 0 and v_2 >= 1
5574 * v_0 = 0 and v_1 = 0 and v_2 <= -1
5578 * A snapshot is taken after the equality constraint (if any) has been added
5579 * such that the next case can start off from this position.
5580 * The rollback to this position is performed in enter_level.
5582 * If there are no non-zero constraints, then no constraints need
5583 * to be added to data->tab. A snapshot is still taken even though
5584 * there is no subsequent case because enter_level performs a rollback
5585 * before deciding whether there are any subsequent cases.
5586 * The only exception is when the constraint has been disabled.
5587 * In this case, no snapshot is taken and enter_level will
5588 * not try to use any snapshot.
5590 static isl_stat
pick_side(struct isl_local_region
*local
,
5591 struct isl_lexmin_data
*data
)
5593 struct isl_ilp_region
*region
;
5596 region
= &data
->region
[local
->region
];
5597 if (region
->disabled
)
5601 base
= 2 * (side
/2);
5603 if (region
->has_non_zero
&& side
== base
&& base
>= 2 &&
5604 fix_zero(data
->tab
, region
, base
/ 2 - 1, data
) < 0)
5605 return isl_stat_error
;
5607 local
->snap
= isl_tab_snap(data
->tab
);
5608 if (isl_tab_push_basis(data
->tab
) < 0)
5609 return isl_stat_error
;
5611 if (!region
->has_non_zero
)
5614 data
->tab
= pos_neg(data
->tab
, region
, side
, data
);
5616 return isl_stat_error
;
5620 /* Mark all constraints that are still optional as failed.
5622 * This function is only called when a solution has been found.
5623 * At that point, force_enabled_optional_constraints was called
5624 * to remove the optional character of optional constraints
5625 * that had not been disabled.
5626 * The remaining optional constraints are therefore those
5627 * that were disabled in the last solution, meaning that
5628 * they could not be imposed.
5629 * In case of disjunctive constraints, only the last disjunct
5630 * may get its optional character removed, so only this last disjunct
5631 * may be marked as failed.
5633 * Conditional constraints that have not been activated are
5634 * also marked non-optional by force_enabled_optional_constraints and
5635 * will therefore not get marked failed.
5637 static void mark_failed(int n_region
, struct isl_ilp_region
*region
)
5641 for (i
= 0; i
< n_region
; ++i
)
5642 region
[i
].failed
= region
[i
].optional
&& !region
[i
].disjunctive
;
5645 /* Free the memory associated to "data".
5647 static void clear_lexmin_data(struct isl_lexmin_data
*data
)
5650 isl_vec_free(data
->v
);
5651 isl_tab_free(data
->tab
);
5654 static void dump_regions(int n_region
, struct isl_ilp_region
*region
)
5655 __attribute__ ((unused
));
5657 /* Dump information about the "n_region" regions starting at "region".
5659 static void dump_regions(int n_region
, struct isl_ilp_region
*region
)
5663 for (i
= 0; i
< n_region
; ++i
) {
5664 fprintf(stderr
, "%d (%d)%s%s:\n", i
, region
[i
].pos
,
5665 region
[i
].optional
? " optional" : "",
5666 region
[i
].conditional
? " conditional" : "");
5667 if (region
[i
].has_non_zero
) {
5668 fprintf(stderr
, "non_zero\n");
5669 isl_mat_dump(region
[i
].non_zero
);
5671 if (region
[i
].has_fixed
) {
5672 fprintf(stderr
, "fixed\n");
5673 isl_mat_dump(region
[i
].fixed
);
5674 isl_vec_dump(region
[i
].fixed_val
);
5676 if (region
[i
].disjunctive
)
5677 fprintf(stderr
, "or\n");
5681 /* Return the lexicographically smallest solution of the given ILP problem
5682 * that satisfies a sequence of constraints.
5684 * All variables are assumed to be non-negative.
5686 * n_op is the number of initial coordinates to optimize.
5687 * That is, once a solution has been found, we will only continue looking
5688 * for solutions that result in significantly better values for those
5689 * initial coordinates. That is, we only continue looking for solutions
5690 * that increase the number of initial zeros in this sequence.
5692 * Each region represents a constraint that needs to be satisfied.
5693 * In particular, it represents a sequence of
5694 * non-zero directions on a sequence of variables that starts
5695 * at a given position. A solution satisfies the non-zero
5696 * constraint of such a region if
5697 * at least one of the non-zero directions is non-zero
5698 * on that sequence of variables.
5700 * Whenever a conflict is encountered, all constraints involved are
5701 * reported to the caller through a call to "conflict".
5703 * We perform a simple branch-and-bound backtracking search.
5704 * Each level in the search represents an initially violated region
5705 * the constraint of which is forced to hold.
5706 * For a region with a non-zero constraint, 2 * n cases are considered,
5707 * where n is the number of non-zero directions.
5708 * In terms of those n directions v_i, we consider the cases
5711 * v_0 = 0 and v_1 >= 1
5712 * v_0 = 0 and v_1 <= -1
5713 * v_0 = 0 and v_1 = 0 and v_2 >= 1
5714 * v_0 = 0 and v_1 = 0 and v_2 <= -1
5717 * If there is no non-zero constraint, then the violation must be due
5718 * to a fixed-value constraint and a single case is considered
5719 * in which this fixed-value constraint is imposed.
5721 __isl_give isl_vec
*isl_tab_basic_set_constrained_lexmin(
5722 __isl_take isl_basic_set
*bset
, int n_op
, int n_region
,
5723 struct isl_ilp_region
*region
,
5724 int (*conflict
)(int con
, void *user
), void *user
)
5726 struct isl_lexmin_data data
= { n_op
, n_region
, region
};
5732 clear_disabled(n_region
, region
);
5733 if (init_lexmin_data(&data
, bset
) < 0)
5735 data
.tab
->conflict
= conflict
;
5736 data
.tab
->conflict_user
= user
;
5741 while (level
>= 0) {
5743 struct isl_local_region
*local
= &data
.local
[level
];
5745 next
= enter_level(level
, init
, &data
);
5748 if (next
== isl_next_done
)
5750 if (next
== isl_next_backtrack
) {
5756 if (better_next_side(local
, &data
) < 0)
5758 if (pick_side(local
, &data
) < 0)
5766 if (isl_vec_size(data
.sol
) != 0)
5767 mark_failed(n_region
, region
);
5769 clear_lexmin_data(&data
);
5770 isl_basic_set_free(bset
);
5774 clear_lexmin_data(&data
);
5775 isl_basic_set_free(bset
);
5776 isl_vec_free(data
.sol
);
5780 /* Wrapper for a tableau that is used for computing
5781 * the lexicographically smallest rational point of a non-negative set.
5782 * This point is represented by the sample value of "tab",
5783 * unless "tab" is empty.
5785 struct isl_tab_lexmin
{
5787 struct isl_tab
*tab
;
5790 /* Free "tl" and return NULL.
5792 __isl_null isl_tab_lexmin
*isl_tab_lexmin_free(__isl_take isl_tab_lexmin
*tl
)
5796 isl_ctx_deref(tl
->ctx
);
5797 isl_tab_free(tl
->tab
);
5803 /* Construct an isl_tab_lexmin for computing
5804 * the lexicographically smallest rational point in "bset",
5805 * assuming that all variables are non-negative.
5807 __isl_give isl_tab_lexmin
*isl_tab_lexmin_from_basic_set(
5808 __isl_take isl_basic_set
*bset
)
5816 ctx
= isl_basic_set_get_ctx(bset
);
5817 tl
= isl_calloc_type(ctx
, struct isl_tab_lexmin
);
5822 tl
->tab
= tab_for_lexmin(bset
, NULL
, 0, 0);
5823 isl_basic_set_free(bset
);
5825 return isl_tab_lexmin_free(tl
);
5828 isl_basic_set_free(bset
);
5829 isl_tab_lexmin_free(tl
);
5833 /* Return the dimension of the set represented by "tl".
5835 int isl_tab_lexmin_dim(__isl_keep isl_tab_lexmin
*tl
)
5837 return tl
? tl
->tab
->n_var
: -1;
5840 /* Add the equality with coefficients "eq" to "tl", updating the optimal
5841 * solution if needed.
5842 * The equality is added as two opposite inequality constraints.
5844 __isl_give isl_tab_lexmin
*isl_tab_lexmin_add_eq(__isl_take isl_tab_lexmin
*tl
,
5850 return isl_tab_lexmin_free(tl
);
5852 if (isl_tab_extend_cons(tl
->tab
, 2) < 0)
5853 return isl_tab_lexmin_free(tl
);
5854 n_var
= tl
->tab
->n_var
;
5855 isl_seq_neg(eq
, eq
, 1 + n_var
);
5856 tl
->tab
= add_lexmin_ineq(tl
->tab
, eq
);
5857 isl_seq_neg(eq
, eq
, 1 + n_var
);
5858 tl
->tab
= add_lexmin_ineq(tl
->tab
, eq
);
5861 return isl_tab_lexmin_free(tl
);
5866 /* Add cuts to "tl" until the sample value reaches an integer value or
5867 * until the result becomes empty.
5869 __isl_give isl_tab_lexmin
*isl_tab_lexmin_cut_to_integer(
5870 __isl_take isl_tab_lexmin
*tl
)
5874 tl
->tab
= cut_to_integer_lexmin(tl
->tab
, CUT_ONE
);
5876 return isl_tab_lexmin_free(tl
);
5880 /* Return the lexicographically smallest rational point in the basic set
5881 * from which "tl" was constructed.
5882 * If the original input was empty, then return a zero-length vector.
5884 __isl_give isl_vec
*isl_tab_lexmin_get_solution(__isl_keep isl_tab_lexmin
*tl
)
5889 return isl_vec_alloc(tl
->ctx
, 0);
5891 return isl_tab_get_sample_value(tl
->tab
);
5894 struct isl_sol_pma
{
5896 isl_pw_multi_aff
*pma
;
5900 static void sol_pma_free(struct isl_sol
*sol
)
5902 struct isl_sol_pma
*sol_pma
= (struct isl_sol_pma
*) sol
;
5903 isl_pw_multi_aff_free(sol_pma
->pma
);
5904 isl_set_free(sol_pma
->empty
);
5907 /* This function is called for parts of the context where there is
5908 * no solution, with "bset" corresponding to the context tableau.
5909 * Simply add the basic set to the set "empty".
5911 static void sol_pma_add_empty(struct isl_sol_pma
*sol
,
5912 __isl_take isl_basic_set
*bset
)
5914 if (!bset
|| !sol
->empty
)
5917 sol
->empty
= isl_set_grow(sol
->empty
, 1);
5918 bset
= isl_basic_set_simplify(bset
);
5919 bset
= isl_basic_set_finalize(bset
);
5920 sol
->empty
= isl_set_add_basic_set(sol
->empty
, bset
);
5925 isl_basic_set_free(bset
);
5929 /* Given a basic set "dom" that represents the context and a tuple of
5930 * affine expressions "maff" defined over this domain, construct
5931 * an isl_pw_multi_aff with a single cell corresponding to "dom" and
5932 * the affine expressions in "maff".
5934 static void sol_pma_add(struct isl_sol_pma
*sol
,
5935 __isl_take isl_basic_set
*dom
, __isl_take isl_multi_aff
*maff
)
5937 isl_pw_multi_aff
*pma
;
5939 dom
= isl_basic_set_simplify(dom
);
5940 dom
= isl_basic_set_finalize(dom
);
5941 pma
= isl_pw_multi_aff_alloc(isl_set_from_basic_set(dom
), maff
);
5942 sol
->pma
= isl_pw_multi_aff_add_disjoint(sol
->pma
, pma
);
5947 static void sol_pma_add_empty_wrap(struct isl_sol
*sol
,
5948 __isl_take isl_basic_set
*bset
)
5950 sol_pma_add_empty((struct isl_sol_pma
*)sol
, bset
);
5953 static void sol_pma_add_wrap(struct isl_sol
*sol
,
5954 __isl_take isl_basic_set
*dom
, __isl_take isl_multi_aff
*ma
)
5956 sol_pma_add((struct isl_sol_pma
*)sol
, dom
, ma
);
5959 /* Construct an isl_sol_pma structure for accumulating the solution.
5960 * If track_empty is set, then we also keep track of the parts
5961 * of the context where there is no solution.
5962 * If max is set, then we are solving a maximization, rather than
5963 * a minimization problem, which means that the variables in the
5964 * tableau have value "M - x" rather than "M + x".
5966 static struct isl_sol
*sol_pma_init(__isl_keep isl_basic_map
*bmap
,
5967 __isl_take isl_basic_set
*dom
, int track_empty
, int max
)
5969 struct isl_sol_pma
*sol_pma
= NULL
;
5975 sol_pma
= isl_calloc_type(bmap
->ctx
, struct isl_sol_pma
);
5979 sol_pma
->sol
.free
= &sol_pma_free
;
5980 if (sol_init(&sol_pma
->sol
, bmap
, dom
, max
) < 0)
5982 sol_pma
->sol
.add
= &sol_pma_add_wrap
;
5983 sol_pma
->sol
.add_empty
= track_empty
? &sol_pma_add_empty_wrap
: NULL
;
5984 space
= isl_space_copy(sol_pma
->sol
.space
);
5985 sol_pma
->pma
= isl_pw_multi_aff_empty(space
);
5990 sol_pma
->empty
= isl_set_alloc_space(isl_basic_set_get_space(dom
),
5991 1, ISL_SET_DISJOINT
);
5992 if (!sol_pma
->empty
)
5996 isl_basic_set_free(dom
);
5997 return &sol_pma
->sol
;
5999 isl_basic_set_free(dom
);
6000 sol_free(&sol_pma
->sol
);
6004 /* Base case of isl_tab_basic_map_partial_lexopt, after removing
6005 * some obvious symmetries.
6007 * We call basic_map_partial_lexopt_base_sol and extract the results.
6009 static __isl_give isl_pw_multi_aff
*basic_map_partial_lexopt_base_pw_multi_aff(
6010 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_set
*dom
,
6011 __isl_give isl_set
**empty
, int max
)
6013 isl_pw_multi_aff
*result
= NULL
;
6014 struct isl_sol
*sol
;
6015 struct isl_sol_pma
*sol_pma
;
6017 sol
= basic_map_partial_lexopt_base_sol(bmap
, dom
, empty
, max
,
6021 sol_pma
= (struct isl_sol_pma
*) sol
;
6023 result
= isl_pw_multi_aff_copy(sol_pma
->pma
);
6025 *empty
= isl_set_copy(sol_pma
->empty
);
6026 sol_free(&sol_pma
->sol
);
6030 /* Given that the last input variable of "maff" represents the minimum
6031 * of some bounds, check whether we need to plug in the expression
6034 * In particular, check if the last input variable appears in any
6035 * of the expressions in "maff".
6037 static int need_substitution(__isl_keep isl_multi_aff
*maff
)
6042 pos
= isl_multi_aff_dim(maff
, isl_dim_in
) - 1;
6044 for (i
= 0; i
< maff
->n
; ++i
)
6045 if (isl_aff_involves_dims(maff
->p
[i
], isl_dim_in
, pos
, 1))
6051 /* Given a set of upper bounds on the last "input" variable m,
6052 * construct a piecewise affine expression that selects
6053 * the minimal upper bound to m, i.e.,
6054 * divide the space into cells where one
6055 * of the upper bounds is smaller than all the others and select
6056 * this upper bound on that cell.
6058 * In particular, if there are n bounds b_i, then the result
6059 * consists of n cell, each one of the form
6061 * b_i <= b_j for j > i
6062 * b_i < b_j for j < i
6064 * The affine expression on this cell is
6068 static __isl_give isl_pw_aff
*set_minimum_pa(__isl_take isl_space
*space
,
6069 __isl_take isl_mat
*var
)
6072 isl_aff
*aff
= NULL
;
6073 isl_basic_set
*bset
= NULL
;
6074 isl_pw_aff
*paff
= NULL
;
6075 isl_space
*pw_space
;
6076 isl_local_space
*ls
= NULL
;
6081 ls
= isl_local_space_from_space(isl_space_copy(space
));
6082 pw_space
= isl_space_copy(space
);
6083 pw_space
= isl_space_from_domain(pw_space
);
6084 pw_space
= isl_space_add_dims(pw_space
, isl_dim_out
, 1);
6085 paff
= isl_pw_aff_alloc_size(pw_space
, var
->n_row
);
6087 for (i
= 0; i
< var
->n_row
; ++i
) {
6090 aff
= isl_aff_alloc(isl_local_space_copy(ls
));
6091 bset
= isl_basic_set_alloc_space(isl_space_copy(space
), 0,
6095 isl_int_set_si(aff
->v
->el
[0], 1);
6096 isl_seq_cpy(aff
->v
->el
+ 1, var
->row
[i
], var
->n_col
);
6097 isl_int_set_si(aff
->v
->el
[1 + var
->n_col
], 0);
6098 bset
= select_minimum(bset
, var
, i
);
6099 paff_i
= isl_pw_aff_alloc(isl_set_from_basic_set(bset
), aff
);
6100 paff
= isl_pw_aff_add_disjoint(paff
, paff_i
);
6103 isl_local_space_free(ls
);
6104 isl_space_free(space
);
6109 isl_basic_set_free(bset
);
6110 isl_pw_aff_free(paff
);
6111 isl_local_space_free(ls
);
6112 isl_space_free(space
);
6117 /* Given a piecewise multi-affine expression of which the last input variable
6118 * is the minimum of the bounds in "cst", plug in the value of the minimum.
6119 * This minimum expression is given in "min_expr_pa".
6120 * The set "min_expr" contains the same information, but in the form of a set.
6121 * The variable is subsequently projected out.
6123 * The implementation is similar to those of "split" and "split_domain".
6124 * If the variable appears in a given expression, then minimum expression
6125 * is plugged in. Otherwise, if the variable appears in the constraints
6126 * and a split is required, then the domain is split. Otherwise, no split
6129 static __isl_give isl_pw_multi_aff
*split_domain_pma(
6130 __isl_take isl_pw_multi_aff
*opt
, __isl_take isl_pw_aff
*min_expr_pa
,
6131 __isl_take isl_set
*min_expr
, __isl_take isl_mat
*cst
)
6136 isl_pw_multi_aff
*res
;
6138 if (!opt
|| !min_expr
|| !cst
)
6141 n_in
= isl_pw_multi_aff_dim(opt
, isl_dim_in
);
6142 space
= isl_pw_multi_aff_get_space(opt
);
6143 space
= isl_space_drop_dims(space
, isl_dim_in
, n_in
- 1, 1);
6144 res
= isl_pw_multi_aff_empty(space
);
6146 for (i
= 0; i
< opt
->n
; ++i
) {
6147 isl_pw_multi_aff
*pma
;
6149 pma
= isl_pw_multi_aff_alloc(isl_set_copy(opt
->p
[i
].set
),
6150 isl_multi_aff_copy(opt
->p
[i
].maff
));
6151 if (need_substitution(opt
->p
[i
].maff
))
6152 pma
= isl_pw_multi_aff_substitute(pma
,
6153 isl_dim_in
, n_in
- 1, min_expr_pa
);
6156 split
= need_split_set(opt
->p
[i
].set
, cst
);
6158 pma
= isl_pw_multi_aff_free(pma
);
6160 pma
= isl_pw_multi_aff_intersect_domain(pma
,
6161 isl_set_copy(min_expr
));
6163 pma
= isl_pw_multi_aff_project_out(pma
,
6164 isl_dim_in
, n_in
- 1, 1);
6166 res
= isl_pw_multi_aff_add_disjoint(res
, pma
);
6169 isl_pw_multi_aff_free(opt
);
6170 isl_pw_aff_free(min_expr_pa
);
6171 isl_set_free(min_expr
);
6175 isl_pw_multi_aff_free(opt
);
6176 isl_pw_aff_free(min_expr_pa
);
6177 isl_set_free(min_expr
);
6182 static __isl_give isl_pw_multi_aff
*basic_map_partial_lexopt_pw_multi_aff(
6183 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_set
*dom
,
6184 __isl_give isl_set
**empty
, int max
);
6186 /* This function is called from basic_map_partial_lexopt_symm.
6187 * The last variable of "bmap" and "dom" corresponds to the minimum
6188 * of the bounds in "cst". "map_space" is the space of the original
6189 * input relation (of basic_map_partial_lexopt_symm) and "set_space"
6190 * is the space of the original domain.
6192 * We recursively call basic_map_partial_lexopt and then plug in
6193 * the definition of the minimum in the result.
6195 static __isl_give isl_pw_multi_aff
*
6196 basic_map_partial_lexopt_symm_core_pw_multi_aff(
6197 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_set
*dom
,
6198 __isl_give isl_set
**empty
, int max
, __isl_take isl_mat
*cst
,
6199 __isl_take isl_space
*map_space
, __isl_take isl_space
*set_space
)
6201 isl_pw_multi_aff
*opt
;
6202 isl_pw_aff
*min_expr_pa
;
6205 min_expr
= set_minimum(isl_basic_set_get_space(dom
), isl_mat_copy(cst
));
6206 min_expr_pa
= set_minimum_pa(isl_basic_set_get_space(dom
),
6209 opt
= basic_map_partial_lexopt_pw_multi_aff(bmap
, dom
, empty
, max
);
6212 *empty
= split(*empty
,
6213 isl_set_copy(min_expr
), isl_mat_copy(cst
));
6214 *empty
= isl_set_reset_space(*empty
, set_space
);
6217 opt
= split_domain_pma(opt
, min_expr_pa
, min_expr
, cst
);
6218 opt
= isl_pw_multi_aff_reset_space(opt
, map_space
);
6224 #define TYPE isl_pw_multi_aff
6226 #define SUFFIX _pw_multi_aff
6227 #include "isl_tab_lexopt_templ.c"