2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2010 INRIA Saclay
5 * Use of this software is governed by the MIT license
7 * Written by Sven Verdoolaege, K.U.Leuven, Departement
8 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
9 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
10 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
13 #include <isl_ctx_private.h>
14 #include "isl_map_private.h"
17 #include "isl_sample.h"
18 #include <isl_mat_private.h>
19 #include <isl_aff_private.h>
20 #include <isl_options_private.h>
21 #include <isl_config.h>
24 * The implementation of parametric integer linear programming in this file
25 * was inspired by the paper "Parametric Integer Programming" and the
26 * report "Solving systems of affine (in)equalities" by Paul Feautrier
29 * The strategy used for obtaining a feasible solution is different
30 * from the one used in isl_tab.c. In particular, in isl_tab.c,
31 * upon finding a constraint that is not yet satisfied, we pivot
32 * in a row that increases the constant term of the row holding the
33 * constraint, making sure the sample solution remains feasible
34 * for all the constraints it already satisfied.
35 * Here, we always pivot in the row holding the constraint,
36 * choosing a column that induces the lexicographically smallest
37 * increment to the sample solution.
39 * By starting out from a sample value that is lexicographically
40 * smaller than any integer point in the problem space, the first
41 * feasible integer sample point we find will also be the lexicographically
42 * smallest. If all variables can be assumed to be non-negative,
43 * then the initial sample value may be chosen equal to zero.
44 * However, we will not make this assumption. Instead, we apply
45 * the "big parameter" trick. Any variable x is then not directly
46 * used in the tableau, but instead it is represented by another
47 * variable x' = M + x, where M is an arbitrarily large (positive)
48 * value. x' is therefore always non-negative, whatever the value of x.
49 * Taking as initial sample value x' = 0 corresponds to x = -M,
50 * which is always smaller than any possible value of x.
52 * The big parameter trick is used in the main tableau and
53 * also in the context tableau if isl_context_lex is used.
54 * In this case, each tableaus has its own big parameter.
55 * Before doing any real work, we check if all the parameters
56 * happen to be non-negative. If so, we drop the column corresponding
57 * to M from the initial context tableau.
58 * If isl_context_gbr is used, then the big parameter trick is only
59 * used in the main tableau.
63 struct isl_context_op
{
64 /* detect nonnegative parameters in context and mark them in tab */
65 struct isl_tab
*(*detect_nonnegative_parameters
)(
66 struct isl_context
*context
, struct isl_tab
*tab
);
67 /* return temporary reference to basic set representation of context */
68 struct isl_basic_set
*(*peek_basic_set
)(struct isl_context
*context
);
69 /* return temporary reference to tableau representation of context */
70 struct isl_tab
*(*peek_tab
)(struct isl_context
*context
);
71 /* add equality; check is 1 if eq may not be valid;
72 * update is 1 if we may want to call ineq_sign on context later.
74 void (*add_eq
)(struct isl_context
*context
, isl_int
*eq
,
75 int check
, int update
);
76 /* add inequality; check is 1 if ineq may not be valid;
77 * update is 1 if we may want to call ineq_sign on context later.
79 void (*add_ineq
)(struct isl_context
*context
, isl_int
*ineq
,
80 int check
, int update
);
81 /* check sign of ineq based on previous information.
82 * strict is 1 if saturation should be treated as a positive sign.
84 enum isl_tab_row_sign (*ineq_sign
)(struct isl_context
*context
,
85 isl_int
*ineq
, int strict
);
86 /* check if inequality maintains feasibility */
87 int (*test_ineq
)(struct isl_context
*context
, isl_int
*ineq
);
88 /* return index of a div that corresponds to "div" */
89 int (*get_div
)(struct isl_context
*context
, struct isl_tab
*tab
,
91 /* add div "div" to context and return non-negativity */
92 int (*add_div
)(struct isl_context
*context
, struct isl_vec
*div
);
93 int (*detect_equalities
)(struct isl_context
*context
,
95 /* return row index of "best" split */
96 int (*best_split
)(struct isl_context
*context
, struct isl_tab
*tab
);
97 /* check if context has already been determined to be empty */
98 int (*is_empty
)(struct isl_context
*context
);
99 /* check if context is still usable */
100 int (*is_ok
)(struct isl_context
*context
);
101 /* save a copy/snapshot of context */
102 void *(*save
)(struct isl_context
*context
);
103 /* restore saved context */
104 void (*restore
)(struct isl_context
*context
, void *);
105 /* discard saved context */
106 void (*discard
)(void *);
107 /* invalidate context */
108 void (*invalidate
)(struct isl_context
*context
);
110 void (*free
)(struct isl_context
*context
);
114 struct isl_context_op
*op
;
117 struct isl_context_lex
{
118 struct isl_context context
;
122 struct isl_partial_sol
{
124 struct isl_basic_set
*dom
;
127 struct isl_partial_sol
*next
;
131 struct isl_sol_callback
{
132 struct isl_tab_callback callback
;
136 /* isl_sol is an interface for constructing a solution to
137 * a parametric integer linear programming problem.
138 * Every time the algorithm reaches a state where a solution
139 * can be read off from the tableau (including cases where the tableau
140 * is empty), the function "add" is called on the isl_sol passed
141 * to find_solutions_main.
143 * The context tableau is owned by isl_sol and is updated incrementally.
145 * There are currently two implementations of this interface,
146 * isl_sol_map, which simply collects the solutions in an isl_map
147 * and (optionally) the parts of the context where there is no solution
149 * isl_sol_for, which calls a user-defined function for each part of
158 struct isl_context
*context
;
159 struct isl_partial_sol
*partial
;
160 void (*add
)(struct isl_sol
*sol
,
161 struct isl_basic_set
*dom
, struct isl_mat
*M
);
162 void (*add_empty
)(struct isl_sol
*sol
, struct isl_basic_set
*bset
);
163 void (*free
)(struct isl_sol
*sol
);
164 struct isl_sol_callback dec_level
;
167 static void sol_free(struct isl_sol
*sol
)
169 struct isl_partial_sol
*partial
, *next
;
172 for (partial
= sol
->partial
; partial
; partial
= next
) {
173 next
= partial
->next
;
174 isl_basic_set_free(partial
->dom
);
175 isl_mat_free(partial
->M
);
181 /* Push a partial solution represented by a domain and mapping M
182 * onto the stack of partial solutions.
184 static void sol_push_sol(struct isl_sol
*sol
,
185 struct isl_basic_set
*dom
, struct isl_mat
*M
)
187 struct isl_partial_sol
*partial
;
189 if (sol
->error
|| !dom
)
192 partial
= isl_alloc_type(dom
->ctx
, struct isl_partial_sol
);
196 partial
->level
= sol
->level
;
199 partial
->next
= sol
->partial
;
201 sol
->partial
= partial
;
205 isl_basic_set_free(dom
);
210 /* Pop one partial solution from the partial solution stack and
211 * pass it on to sol->add or sol->add_empty.
213 static void sol_pop_one(struct isl_sol
*sol
)
215 struct isl_partial_sol
*partial
;
217 partial
= sol
->partial
;
218 sol
->partial
= partial
->next
;
221 sol
->add(sol
, partial
->dom
, partial
->M
);
223 sol
->add_empty(sol
, partial
->dom
);
227 /* Return a fresh copy of the domain represented by the context tableau.
229 static struct isl_basic_set
*sol_domain(struct isl_sol
*sol
)
231 struct isl_basic_set
*bset
;
236 bset
= isl_basic_set_dup(sol
->context
->op
->peek_basic_set(sol
->context
));
237 bset
= isl_basic_set_update_from_tab(bset
,
238 sol
->context
->op
->peek_tab(sol
->context
));
243 /* Check whether two partial solutions have the same mapping, where n_div
244 * is the number of divs that the two partial solutions have in common.
246 static int same_solution(struct isl_partial_sol
*s1
, struct isl_partial_sol
*s2
,
252 if (!s1
->M
!= !s2
->M
)
257 dim
= isl_basic_set_total_dim(s1
->dom
) - s1
->dom
->n_div
;
259 for (i
= 0; i
< s1
->M
->n_row
; ++i
) {
260 if (isl_seq_first_non_zero(s1
->M
->row
[i
]+1+dim
+n_div
,
261 s1
->M
->n_col
-1-dim
-n_div
) != -1)
263 if (isl_seq_first_non_zero(s2
->M
->row
[i
]+1+dim
+n_div
,
264 s2
->M
->n_col
-1-dim
-n_div
) != -1)
266 if (!isl_seq_eq(s1
->M
->row
[i
], s2
->M
->row
[i
], 1+dim
+n_div
))
272 /* Pop all solutions from the partial solution stack that were pushed onto
273 * the stack at levels that are deeper than the current level.
274 * If the two topmost elements on the stack have the same level
275 * and represent the same solution, then their domains are combined.
276 * This combined domain is the same as the current context domain
277 * as sol_pop is called each time we move back to a higher level.
279 static void sol_pop(struct isl_sol
*sol
)
281 struct isl_partial_sol
*partial
;
287 if (sol
->level
== 0) {
288 for (partial
= sol
->partial
; partial
; partial
= sol
->partial
)
293 partial
= sol
->partial
;
297 if (partial
->level
<= sol
->level
)
300 if (partial
->next
&& partial
->next
->level
== partial
->level
) {
301 n_div
= isl_basic_set_dim(
302 sol
->context
->op
->peek_basic_set(sol
->context
),
305 if (!same_solution(partial
, partial
->next
, n_div
)) {
309 struct isl_basic_set
*bset
;
311 bset
= sol_domain(sol
);
313 isl_basic_set_free(partial
->next
->dom
);
314 partial
->next
->dom
= bset
;
315 partial
->next
->level
= sol
->level
;
317 sol
->partial
= partial
->next
;
318 isl_basic_set_free(partial
->dom
);
319 isl_mat_free(partial
->M
);
326 static void sol_dec_level(struct isl_sol
*sol
)
336 static int sol_dec_level_wrap(struct isl_tab_callback
*cb
)
338 struct isl_sol_callback
*callback
= (struct isl_sol_callback
*)cb
;
340 sol_dec_level(callback
->sol
);
342 return callback
->sol
->error
? -1 : 0;
345 /* Move down to next level and push callback onto context tableau
346 * to decrease the level again when it gets rolled back across
347 * the current state. That is, dec_level will be called with
348 * the context tableau in the same state as it is when inc_level
351 static void sol_inc_level(struct isl_sol
*sol
)
359 tab
= sol
->context
->op
->peek_tab(sol
->context
);
360 if (isl_tab_push_callback(tab
, &sol
->dec_level
.callback
) < 0)
364 static void scale_rows(struct isl_mat
*mat
, isl_int m
, int n_row
)
368 if (isl_int_is_one(m
))
371 for (i
= 0; i
< n_row
; ++i
)
372 isl_seq_scale(mat
->row
[i
], mat
->row
[i
], m
, mat
->n_col
);
375 /* Add the solution identified by the tableau and the context tableau.
377 * The layout of the variables is as follows.
378 * tab->n_var is equal to the total number of variables in the input
379 * map (including divs that were copied from the context)
380 * + the number of extra divs constructed
381 * Of these, the first tab->n_param and the last tab->n_div variables
382 * correspond to the variables in the context, i.e.,
383 * tab->n_param + tab->n_div = context_tab->n_var
384 * tab->n_param is equal to the number of parameters and input
385 * dimensions in the input map
386 * tab->n_div is equal to the number of divs in the context
388 * If there is no solution, then call add_empty with a basic set
389 * that corresponds to the context tableau. (If add_empty is NULL,
392 * If there is a solution, then first construct a matrix that maps
393 * all dimensions of the context to the output variables, i.e.,
394 * the output dimensions in the input map.
395 * The divs in the input map (if any) that do not correspond to any
396 * div in the context do not appear in the solution.
397 * The algorithm will make sure that they have an integer value,
398 * but these values themselves are of no interest.
399 * We have to be careful not to drop or rearrange any divs in the
400 * context because that would change the meaning of the matrix.
402 * To extract the value of the output variables, it should be noted
403 * that we always use a big parameter M in the main tableau and so
404 * the variable stored in this tableau is not an output variable x itself, but
405 * x' = M + x (in case of minimization)
407 * x' = M - x (in case of maximization)
408 * If x' appears in a column, then its optimal value is zero,
409 * which means that the optimal value of x is an unbounded number
410 * (-M for minimization and M for maximization).
411 * We currently assume that the output dimensions in the original map
412 * are bounded, so this cannot occur.
413 * Similarly, when x' appears in a row, then the coefficient of M in that
414 * row is necessarily 1.
415 * If the row in the tableau represents
416 * d x' = c + d M + e(y)
417 * then, in case of minimization, the corresponding row in the matrix
420 * with a d = m, the (updated) common denominator of the matrix.
421 * In case of maximization, the row will be
424 static void sol_add(struct isl_sol
*sol
, struct isl_tab
*tab
)
426 struct isl_basic_set
*bset
= NULL
;
427 struct isl_mat
*mat
= NULL
;
432 if (sol
->error
|| !tab
)
435 if (tab
->empty
&& !sol
->add_empty
)
437 if (sol
->context
->op
->is_empty(sol
->context
))
440 bset
= sol_domain(sol
);
443 sol_push_sol(sol
, bset
, NULL
);
449 mat
= isl_mat_alloc(tab
->mat
->ctx
, 1 + sol
->n_out
,
450 1 + tab
->n_param
+ tab
->n_div
);
456 isl_seq_clr(mat
->row
[0] + 1, mat
->n_col
- 1);
457 isl_int_set_si(mat
->row
[0][0], 1);
458 for (row
= 0; row
< sol
->n_out
; ++row
) {
459 int i
= tab
->n_param
+ row
;
462 isl_seq_clr(mat
->row
[1 + row
], mat
->n_col
);
463 if (!tab
->var
[i
].is_row
) {
465 isl_die(mat
->ctx
, isl_error_invalid
,
466 "unbounded optimum", goto error2
);
470 r
= tab
->var
[i
].index
;
472 isl_int_ne(tab
->mat
->row
[r
][2], tab
->mat
->row
[r
][0]))
473 isl_die(mat
->ctx
, isl_error_invalid
,
474 "unbounded optimum", goto error2
);
475 isl_int_gcd(m
, mat
->row
[0][0], tab
->mat
->row
[r
][0]);
476 isl_int_divexact(m
, tab
->mat
->row
[r
][0], m
);
477 scale_rows(mat
, m
, 1 + row
);
478 isl_int_divexact(m
, mat
->row
[0][0], tab
->mat
->row
[r
][0]);
479 isl_int_mul(mat
->row
[1 + row
][0], m
, tab
->mat
->row
[r
][1]);
480 for (j
= 0; j
< tab
->n_param
; ++j
) {
482 if (tab
->var
[j
].is_row
)
484 col
= tab
->var
[j
].index
;
485 isl_int_mul(mat
->row
[1 + row
][1 + j
], m
,
486 tab
->mat
->row
[r
][off
+ col
]);
488 for (j
= 0; j
< tab
->n_div
; ++j
) {
490 if (tab
->var
[tab
->n_var
- tab
->n_div
+j
].is_row
)
492 col
= tab
->var
[tab
->n_var
- tab
->n_div
+j
].index
;
493 isl_int_mul(mat
->row
[1 + row
][1 + tab
->n_param
+ j
], m
,
494 tab
->mat
->row
[r
][off
+ col
]);
497 isl_seq_neg(mat
->row
[1 + row
], mat
->row
[1 + row
],
503 sol_push_sol(sol
, bset
, mat
);
508 isl_basic_set_free(bset
);
516 struct isl_set
*empty
;
519 static void sol_map_free(struct isl_sol_map
*sol_map
)
523 if (sol_map
->sol
.context
)
524 sol_map
->sol
.context
->op
->free(sol_map
->sol
.context
);
525 isl_map_free(sol_map
->map
);
526 isl_set_free(sol_map
->empty
);
530 static void sol_map_free_wrap(struct isl_sol
*sol
)
532 sol_map_free((struct isl_sol_map
*)sol
);
535 /* This function is called for parts of the context where there is
536 * no solution, with "bset" corresponding to the context tableau.
537 * Simply add the basic set to the set "empty".
539 static void sol_map_add_empty(struct isl_sol_map
*sol
,
540 struct isl_basic_set
*bset
)
544 isl_assert(bset
->ctx
, sol
->empty
, goto error
);
546 sol
->empty
= isl_set_grow(sol
->empty
, 1);
547 bset
= isl_basic_set_simplify(bset
);
548 bset
= isl_basic_set_finalize(bset
);
549 sol
->empty
= isl_set_add_basic_set(sol
->empty
, isl_basic_set_copy(bset
));
552 isl_basic_set_free(bset
);
555 isl_basic_set_free(bset
);
559 static void sol_map_add_empty_wrap(struct isl_sol
*sol
,
560 struct isl_basic_set
*bset
)
562 sol_map_add_empty((struct isl_sol_map
*)sol
, bset
);
565 /* Given a basic map "dom" that represents the context and an affine
566 * matrix "M" that maps the dimensions of the context to the
567 * output variables, construct a basic map with the same parameters
568 * and divs as the context, the dimensions of the context as input
569 * dimensions and a number of output dimensions that is equal to
570 * the number of output dimensions in the input map.
572 * The constraints and divs of the context are simply copied
573 * from "dom". For each row
577 * is added, with d the common denominator of M.
579 static void sol_map_add(struct isl_sol_map
*sol
,
580 struct isl_basic_set
*dom
, struct isl_mat
*M
)
583 struct isl_basic_map
*bmap
= NULL
;
591 if (sol
->sol
.error
|| !dom
|| !M
)
594 n_out
= sol
->sol
.n_out
;
595 n_eq
= dom
->n_eq
+ n_out
;
596 n_ineq
= dom
->n_ineq
;
598 nparam
= isl_basic_set_total_dim(dom
) - n_div
;
599 total
= isl_map_dim(sol
->map
, isl_dim_all
);
600 bmap
= isl_basic_map_alloc_space(isl_map_get_space(sol
->map
),
601 n_div
, n_eq
, 2 * n_div
+ n_ineq
);
604 if (sol
->sol
.rational
)
605 ISL_F_SET(bmap
, ISL_BASIC_MAP_RATIONAL
);
606 for (i
= 0; i
< dom
->n_div
; ++i
) {
607 int k
= isl_basic_map_alloc_div(bmap
);
610 isl_seq_cpy(bmap
->div
[k
], dom
->div
[i
], 1 + 1 + nparam
);
611 isl_seq_clr(bmap
->div
[k
] + 1 + 1 + nparam
, total
- nparam
);
612 isl_seq_cpy(bmap
->div
[k
] + 1 + 1 + total
,
613 dom
->div
[i
] + 1 + 1 + nparam
, i
);
615 for (i
= 0; i
< dom
->n_eq
; ++i
) {
616 int k
= isl_basic_map_alloc_equality(bmap
);
619 isl_seq_cpy(bmap
->eq
[k
], dom
->eq
[i
], 1 + nparam
);
620 isl_seq_clr(bmap
->eq
[k
] + 1 + nparam
, total
- nparam
);
621 isl_seq_cpy(bmap
->eq
[k
] + 1 + total
,
622 dom
->eq
[i
] + 1 + nparam
, n_div
);
624 for (i
= 0; i
< dom
->n_ineq
; ++i
) {
625 int k
= isl_basic_map_alloc_inequality(bmap
);
628 isl_seq_cpy(bmap
->ineq
[k
], dom
->ineq
[i
], 1 + nparam
);
629 isl_seq_clr(bmap
->ineq
[k
] + 1 + nparam
, total
- nparam
);
630 isl_seq_cpy(bmap
->ineq
[k
] + 1 + total
,
631 dom
->ineq
[i
] + 1 + nparam
, n_div
);
633 for (i
= 0; i
< M
->n_row
- 1; ++i
) {
634 int k
= isl_basic_map_alloc_equality(bmap
);
637 isl_seq_cpy(bmap
->eq
[k
], M
->row
[1 + i
], 1 + nparam
);
638 isl_seq_clr(bmap
->eq
[k
] + 1 + nparam
, n_out
);
639 isl_int_neg(bmap
->eq
[k
][1 + nparam
+ i
], M
->row
[0][0]);
640 isl_seq_cpy(bmap
->eq
[k
] + 1 + nparam
+ n_out
,
641 M
->row
[1 + i
] + 1 + nparam
, n_div
);
643 bmap
= isl_basic_map_simplify(bmap
);
644 bmap
= isl_basic_map_finalize(bmap
);
645 sol
->map
= isl_map_grow(sol
->map
, 1);
646 sol
->map
= isl_map_add_basic_map(sol
->map
, bmap
);
647 isl_basic_set_free(dom
);
653 isl_basic_set_free(dom
);
655 isl_basic_map_free(bmap
);
659 static void sol_map_add_wrap(struct isl_sol
*sol
,
660 struct isl_basic_set
*dom
, struct isl_mat
*M
)
662 sol_map_add((struct isl_sol_map
*)sol
, dom
, M
);
666 /* Store the "parametric constant" of row "row" of tableau "tab" in "line",
667 * i.e., the constant term and the coefficients of all variables that
668 * appear in the context tableau.
669 * Note that the coefficient of the big parameter M is NOT copied.
670 * The context tableau may not have a big parameter and even when it
671 * does, it is a different big parameter.
673 static void get_row_parameter_line(struct isl_tab
*tab
, int row
, isl_int
*line
)
676 unsigned off
= 2 + tab
->M
;
678 isl_int_set(line
[0], tab
->mat
->row
[row
][1]);
679 for (i
= 0; i
< tab
->n_param
; ++i
) {
680 if (tab
->var
[i
].is_row
)
681 isl_int_set_si(line
[1 + i
], 0);
683 int col
= tab
->var
[i
].index
;
684 isl_int_set(line
[1 + i
], tab
->mat
->row
[row
][off
+ col
]);
687 for (i
= 0; i
< tab
->n_div
; ++i
) {
688 if (tab
->var
[tab
->n_var
- tab
->n_div
+ i
].is_row
)
689 isl_int_set_si(line
[1 + tab
->n_param
+ i
], 0);
691 int col
= tab
->var
[tab
->n_var
- tab
->n_div
+ i
].index
;
692 isl_int_set(line
[1 + tab
->n_param
+ i
],
693 tab
->mat
->row
[row
][off
+ col
]);
698 /* Check if rows "row1" and "row2" have identical "parametric constants",
699 * as explained above.
700 * In this case, we also insist that the coefficients of the big parameter
701 * be the same as the values of the constants will only be the same
702 * if these coefficients are also the same.
704 static int identical_parameter_line(struct isl_tab
*tab
, int row1
, int row2
)
707 unsigned off
= 2 + tab
->M
;
709 if (isl_int_ne(tab
->mat
->row
[row1
][1], tab
->mat
->row
[row2
][1]))
712 if (tab
->M
&& isl_int_ne(tab
->mat
->row
[row1
][2],
713 tab
->mat
->row
[row2
][2]))
716 for (i
= 0; i
< tab
->n_param
+ tab
->n_div
; ++i
) {
717 int pos
= i
< tab
->n_param
? i
:
718 tab
->n_var
- tab
->n_div
+ i
- tab
->n_param
;
721 if (tab
->var
[pos
].is_row
)
723 col
= tab
->var
[pos
].index
;
724 if (isl_int_ne(tab
->mat
->row
[row1
][off
+ col
],
725 tab
->mat
->row
[row2
][off
+ col
]))
731 /* Return an inequality that expresses that the "parametric constant"
732 * should be non-negative.
733 * This function is only called when the coefficient of the big parameter
736 static struct isl_vec
*get_row_parameter_ineq(struct isl_tab
*tab
, int row
)
738 struct isl_vec
*ineq
;
740 ineq
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_param
+ tab
->n_div
);
744 get_row_parameter_line(tab
, row
, ineq
->el
);
746 ineq
= isl_vec_normalize(ineq
);
751 /* Normalize a div expression of the form
753 * [(g*f(x) + c)/(g * m)]
755 * with c the constant term and f(x) the remaining coefficients, to
759 static void normalize_div(__isl_keep isl_vec
*div
)
761 isl_ctx
*ctx
= isl_vec_get_ctx(div
);
762 int len
= div
->size
- 2;
764 isl_seq_gcd(div
->el
+ 2, len
, &ctx
->normalize_gcd
);
765 isl_int_gcd(ctx
->normalize_gcd
, ctx
->normalize_gcd
, div
->el
[0]);
767 if (isl_int_is_one(ctx
->normalize_gcd
))
770 isl_int_divexact(div
->el
[0], div
->el
[0], ctx
->normalize_gcd
);
771 isl_int_fdiv_q(div
->el
[1], div
->el
[1], ctx
->normalize_gcd
);
772 isl_seq_scale_down(div
->el
+ 2, div
->el
+ 2, ctx
->normalize_gcd
, len
);
775 /* Return a integer division for use in a parametric cut based on the given row.
776 * In particular, let the parametric constant of the row be
780 * where y_0 = 1, but none of the y_i corresponds to the big parameter M.
781 * The div returned is equal to
783 * floor(\sum_i {-a_i} y_i) = floor((\sum_i (-a_i mod d) y_i)/d)
785 static struct isl_vec
*get_row_parameter_div(struct isl_tab
*tab
, int row
)
789 div
= isl_vec_alloc(tab
->mat
->ctx
, 1 + 1 + tab
->n_param
+ tab
->n_div
);
793 isl_int_set(div
->el
[0], tab
->mat
->row
[row
][0]);
794 get_row_parameter_line(tab
, row
, div
->el
+ 1);
795 isl_seq_neg(div
->el
+ 1, div
->el
+ 1, div
->size
- 1);
797 isl_seq_fdiv_r(div
->el
+ 1, div
->el
+ 1, div
->el
[0], div
->size
- 1);
802 /* Return a integer division for use in transferring an integrality constraint
804 * In particular, let the parametric constant of the row be
808 * where y_0 = 1, but none of the y_i corresponds to the big parameter M.
809 * The the returned div is equal to
811 * floor(\sum_i {a_i} y_i) = floor((\sum_i (a_i mod d) y_i)/d)
813 static struct isl_vec
*get_row_split_div(struct isl_tab
*tab
, int row
)
817 div
= isl_vec_alloc(tab
->mat
->ctx
, 1 + 1 + tab
->n_param
+ tab
->n_div
);
821 isl_int_set(div
->el
[0], tab
->mat
->row
[row
][0]);
822 get_row_parameter_line(tab
, row
, div
->el
+ 1);
824 isl_seq_fdiv_r(div
->el
+ 1, div
->el
+ 1, div
->el
[0], div
->size
- 1);
829 /* Construct and return an inequality that expresses an upper bound
831 * In particular, if the div is given by
835 * then the inequality expresses
839 static struct isl_vec
*ineq_for_div(struct isl_basic_set
*bset
, unsigned div
)
843 struct isl_vec
*ineq
;
848 total
= isl_basic_set_total_dim(bset
);
849 div_pos
= 1 + total
- bset
->n_div
+ div
;
851 ineq
= isl_vec_alloc(bset
->ctx
, 1 + total
);
855 isl_seq_cpy(ineq
->el
, bset
->div
[div
] + 1, 1 + total
);
856 isl_int_neg(ineq
->el
[div_pos
], bset
->div
[div
][0]);
860 /* Given a row in the tableau and a div that was created
861 * using get_row_split_div and that has been constrained to equality, i.e.,
863 * d = floor(\sum_i {a_i} y_i) = \sum_i {a_i} y_i
865 * replace the expression "\sum_i {a_i} y_i" in the row by d,
866 * i.e., we subtract "\sum_i {a_i} y_i" and add 1 d.
867 * The coefficients of the non-parameters in the tableau have been
868 * verified to be integral. We can therefore simply replace coefficient b
869 * by floor(b). For the coefficients of the parameters we have
870 * floor(a_i) = a_i - {a_i}, while for the other coefficients, we have
873 static struct isl_tab
*set_row_cst_to_div(struct isl_tab
*tab
, int row
, int div
)
875 isl_seq_fdiv_q(tab
->mat
->row
[row
] + 1, tab
->mat
->row
[row
] + 1,
876 tab
->mat
->row
[row
][0], 1 + tab
->M
+ tab
->n_col
);
878 isl_int_set_si(tab
->mat
->row
[row
][0], 1);
880 if (tab
->var
[tab
->n_var
- tab
->n_div
+ div
].is_row
) {
881 int drow
= tab
->var
[tab
->n_var
- tab
->n_div
+ div
].index
;
883 isl_assert(tab
->mat
->ctx
,
884 isl_int_is_one(tab
->mat
->row
[drow
][0]), goto error
);
885 isl_seq_combine(tab
->mat
->row
[row
] + 1,
886 tab
->mat
->ctx
->one
, tab
->mat
->row
[row
] + 1,
887 tab
->mat
->ctx
->one
, tab
->mat
->row
[drow
] + 1,
888 1 + tab
->M
+ tab
->n_col
);
890 int dcol
= tab
->var
[tab
->n_var
- tab
->n_div
+ div
].index
;
892 isl_int_add_ui(tab
->mat
->row
[row
][2 + tab
->M
+ dcol
],
893 tab
->mat
->row
[row
][2 + tab
->M
+ dcol
], 1);
902 /* Check if the (parametric) constant of the given row is obviously
903 * negative, meaning that we don't need to consult the context tableau.
904 * If there is a big parameter and its coefficient is non-zero,
905 * then this coefficient determines the outcome.
906 * Otherwise, we check whether the constant is negative and
907 * all non-zero coefficients of parameters are negative and
908 * belong to non-negative parameters.
910 static int is_obviously_neg(struct isl_tab
*tab
, int row
)
914 unsigned off
= 2 + tab
->M
;
917 if (isl_int_is_pos(tab
->mat
->row
[row
][2]))
919 if (isl_int_is_neg(tab
->mat
->row
[row
][2]))
923 if (isl_int_is_nonneg(tab
->mat
->row
[row
][1]))
925 for (i
= 0; i
< tab
->n_param
; ++i
) {
926 /* Eliminated parameter */
927 if (tab
->var
[i
].is_row
)
929 col
= tab
->var
[i
].index
;
930 if (isl_int_is_zero(tab
->mat
->row
[row
][off
+ col
]))
932 if (!tab
->var
[i
].is_nonneg
)
934 if (isl_int_is_pos(tab
->mat
->row
[row
][off
+ col
]))
937 for (i
= 0; i
< tab
->n_div
; ++i
) {
938 if (tab
->var
[tab
->n_var
- tab
->n_div
+ i
].is_row
)
940 col
= tab
->var
[tab
->n_var
- tab
->n_div
+ i
].index
;
941 if (isl_int_is_zero(tab
->mat
->row
[row
][off
+ col
]))
943 if (!tab
->var
[tab
->n_var
- tab
->n_div
+ i
].is_nonneg
)
945 if (isl_int_is_pos(tab
->mat
->row
[row
][off
+ col
]))
951 /* Check if the (parametric) constant of the given row is obviously
952 * non-negative, meaning that we don't need to consult the context tableau.
953 * If there is a big parameter and its coefficient is non-zero,
954 * then this coefficient determines the outcome.
955 * Otherwise, we check whether the constant is non-negative and
956 * all non-zero coefficients of parameters are positive and
957 * belong to non-negative parameters.
959 static int is_obviously_nonneg(struct isl_tab
*tab
, int row
)
963 unsigned off
= 2 + tab
->M
;
966 if (isl_int_is_pos(tab
->mat
->row
[row
][2]))
968 if (isl_int_is_neg(tab
->mat
->row
[row
][2]))
972 if (isl_int_is_neg(tab
->mat
->row
[row
][1]))
974 for (i
= 0; i
< tab
->n_param
; ++i
) {
975 /* Eliminated parameter */
976 if (tab
->var
[i
].is_row
)
978 col
= tab
->var
[i
].index
;
979 if (isl_int_is_zero(tab
->mat
->row
[row
][off
+ col
]))
981 if (!tab
->var
[i
].is_nonneg
)
983 if (isl_int_is_neg(tab
->mat
->row
[row
][off
+ col
]))
986 for (i
= 0; i
< tab
->n_div
; ++i
) {
987 if (tab
->var
[tab
->n_var
- tab
->n_div
+ i
].is_row
)
989 col
= tab
->var
[tab
->n_var
- tab
->n_div
+ i
].index
;
990 if (isl_int_is_zero(tab
->mat
->row
[row
][off
+ col
]))
992 if (!tab
->var
[tab
->n_var
- tab
->n_div
+ i
].is_nonneg
)
994 if (isl_int_is_neg(tab
->mat
->row
[row
][off
+ col
]))
1000 /* Given a row r and two columns, return the column that would
1001 * lead to the lexicographically smallest increment in the sample
1002 * solution when leaving the basis in favor of the row.
1003 * Pivoting with column c will increment the sample value by a non-negative
1004 * constant times a_{V,c}/a_{r,c}, with a_{V,c} the elements of column c
1005 * corresponding to the non-parametric variables.
1006 * If variable v appears in a column c_v, the a_{v,c} = 1 iff c = c_v,
1007 * with all other entries in this virtual row equal to zero.
1008 * If variable v appears in a row, then a_{v,c} is the element in column c
1011 * Let v be the first variable with a_{v,c1}/a_{r,c1} != a_{v,c2}/a_{r,c2}.
1012 * Then if a_{v,c1}/a_{r,c1} < a_{v,c2}/a_{r,c2}, i.e.,
1013 * a_{v,c2} a_{r,c1} - a_{v,c1} a_{r,c2} > 0, c1 results in the minimal
1014 * increment. Otherwise, it's c2.
1016 static int lexmin_col_pair(struct isl_tab
*tab
,
1017 int row
, int col1
, int col2
, isl_int tmp
)
1022 tr
= tab
->mat
->row
[row
] + 2 + tab
->M
;
1024 for (i
= tab
->n_param
; i
< tab
->n_var
- tab
->n_div
; ++i
) {
1028 if (!tab
->var
[i
].is_row
) {
1029 if (tab
->var
[i
].index
== col1
)
1031 if (tab
->var
[i
].index
== col2
)
1036 if (tab
->var
[i
].index
== row
)
1039 r
= tab
->mat
->row
[tab
->var
[i
].index
] + 2 + tab
->M
;
1040 s1
= isl_int_sgn(r
[col1
]);
1041 s2
= isl_int_sgn(r
[col2
]);
1042 if (s1
== 0 && s2
== 0)
1049 isl_int_mul(tmp
, r
[col2
], tr
[col1
]);
1050 isl_int_submul(tmp
, r
[col1
], tr
[col2
]);
1051 if (isl_int_is_pos(tmp
))
1053 if (isl_int_is_neg(tmp
))
1059 /* Given a row in the tableau, find and return the column that would
1060 * result in the lexicographically smallest, but positive, increment
1061 * in the sample point.
1062 * If there is no such column, then return tab->n_col.
1063 * If anything goes wrong, return -1.
1065 static int lexmin_pivot_col(struct isl_tab
*tab
, int row
)
1068 int col
= tab
->n_col
;
1072 tr
= tab
->mat
->row
[row
] + 2 + tab
->M
;
1076 for (j
= tab
->n_dead
; j
< tab
->n_col
; ++j
) {
1077 if (tab
->col_var
[j
] >= 0 &&
1078 (tab
->col_var
[j
] < tab
->n_param
||
1079 tab
->col_var
[j
] >= tab
->n_var
- tab
->n_div
))
1082 if (!isl_int_is_pos(tr
[j
]))
1085 if (col
== tab
->n_col
)
1088 col
= lexmin_col_pair(tab
, row
, col
, j
, tmp
);
1089 isl_assert(tab
->mat
->ctx
, col
>= 0, goto error
);
1099 /* Return the first known violated constraint, i.e., a non-negative
1100 * constraint that currently has an either obviously negative value
1101 * or a previously determined to be negative value.
1103 * If any constraint has a negative coefficient for the big parameter,
1104 * if any, then we return one of these first.
1106 static int first_neg(struct isl_tab
*tab
)
1111 for (row
= tab
->n_redundant
; row
< tab
->n_row
; ++row
) {
1112 if (!isl_tab_var_from_row(tab
, row
)->is_nonneg
)
1114 if (!isl_int_is_neg(tab
->mat
->row
[row
][2]))
1117 tab
->row_sign
[row
] = isl_tab_row_neg
;
1120 for (row
= tab
->n_redundant
; row
< tab
->n_row
; ++row
) {
1121 if (!isl_tab_var_from_row(tab
, row
)->is_nonneg
)
1123 if (tab
->row_sign
) {
1124 if (tab
->row_sign
[row
] == 0 &&
1125 is_obviously_neg(tab
, row
))
1126 tab
->row_sign
[row
] = isl_tab_row_neg
;
1127 if (tab
->row_sign
[row
] != isl_tab_row_neg
)
1129 } else if (!is_obviously_neg(tab
, row
))
1136 /* Check whether the invariant that all columns are lexico-positive
1137 * is satisfied. This function is not called from the current code
1138 * but is useful during debugging.
1140 static void check_lexpos(struct isl_tab
*tab
) __attribute__ ((unused
));
1141 static void check_lexpos(struct isl_tab
*tab
)
1143 unsigned off
= 2 + tab
->M
;
1148 for (col
= tab
->n_dead
; col
< tab
->n_col
; ++col
) {
1149 if (tab
->col_var
[col
] >= 0 &&
1150 (tab
->col_var
[col
] < tab
->n_param
||
1151 tab
->col_var
[col
] >= tab
->n_var
- tab
->n_div
))
1153 for (var
= tab
->n_param
; var
< tab
->n_var
- tab
->n_div
; ++var
) {
1154 if (!tab
->var
[var
].is_row
) {
1155 if (tab
->var
[var
].index
== col
)
1160 row
= tab
->var
[var
].index
;
1161 if (isl_int_is_zero(tab
->mat
->row
[row
][off
+ col
]))
1163 if (isl_int_is_pos(tab
->mat
->row
[row
][off
+ col
]))
1165 fprintf(stderr
, "lexneg column %d (row %d)\n",
1168 if (var
>= tab
->n_var
- tab
->n_div
)
1169 fprintf(stderr
, "zero column %d\n", col
);
1173 /* Report to the caller that the given constraint is part of an encountered
1176 static int report_conflicting_constraint(struct isl_tab
*tab
, int con
)
1178 return tab
->conflict(con
, tab
->conflict_user
);
1181 /* Given a conflicting row in the tableau, report all constraints
1182 * involved in the row to the caller. That is, the row itself
1183 * (if it represents a constraint) and all constraint columns with
1184 * non-zero (and therefore negative) coefficients.
1186 static int report_conflict(struct isl_tab
*tab
, int row
)
1194 if (tab
->row_var
[row
] < 0 &&
1195 report_conflicting_constraint(tab
, ~tab
->row_var
[row
]) < 0)
1198 tr
= tab
->mat
->row
[row
] + 2 + tab
->M
;
1200 for (j
= tab
->n_dead
; j
< tab
->n_col
; ++j
) {
1201 if (tab
->col_var
[j
] >= 0 &&
1202 (tab
->col_var
[j
] < tab
->n_param
||
1203 tab
->col_var
[j
] >= tab
->n_var
- tab
->n_div
))
1206 if (!isl_int_is_neg(tr
[j
]))
1209 if (tab
->col_var
[j
] < 0 &&
1210 report_conflicting_constraint(tab
, ~tab
->col_var
[j
]) < 0)
1217 /* Resolve all known or obviously violated constraints through pivoting.
1218 * In particular, as long as we can find any violated constraint, we
1219 * look for a pivoting column that would result in the lexicographically
1220 * smallest increment in the sample point. If there is no such column
1221 * then the tableau is infeasible.
1223 static int restore_lexmin(struct isl_tab
*tab
) WARN_UNUSED
;
1224 static int restore_lexmin(struct isl_tab
*tab
)
1232 while ((row
= first_neg(tab
)) != -1) {
1233 col
= lexmin_pivot_col(tab
, row
);
1234 if (col
>= tab
->n_col
) {
1235 if (report_conflict(tab
, row
) < 0)
1237 if (isl_tab_mark_empty(tab
) < 0)
1243 if (isl_tab_pivot(tab
, row
, col
) < 0)
1249 /* Given a row that represents an equality, look for an appropriate
1251 * In particular, if there are any non-zero coefficients among
1252 * the non-parameter variables, then we take the last of these
1253 * variables. Eliminating this variable in terms of the other
1254 * variables and/or parameters does not influence the property
1255 * that all column in the initial tableau are lexicographically
1256 * positive. The row corresponding to the eliminated variable
1257 * will only have non-zero entries below the diagonal of the
1258 * initial tableau. That is, we transform
1264 * If there is no such non-parameter variable, then we are dealing with
1265 * pure parameter equality and we pick any parameter with coefficient 1 or -1
1266 * for elimination. This will ensure that the eliminated parameter
1267 * always has an integer value whenever all the other parameters are integral.
1268 * If there is no such parameter then we return -1.
1270 static int last_var_col_or_int_par_col(struct isl_tab
*tab
, int row
)
1272 unsigned off
= 2 + tab
->M
;
1275 for (i
= tab
->n_var
- tab
->n_div
- 1; i
>= 0 && i
>= tab
->n_param
; --i
) {
1277 if (tab
->var
[i
].is_row
)
1279 col
= tab
->var
[i
].index
;
1280 if (col
<= tab
->n_dead
)
1282 if (!isl_int_is_zero(tab
->mat
->row
[row
][off
+ col
]))
1285 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
1286 if (isl_int_is_one(tab
->mat
->row
[row
][off
+ i
]))
1288 if (isl_int_is_negone(tab
->mat
->row
[row
][off
+ i
]))
1294 /* Add an equality that is known to be valid to the tableau.
1295 * We first check if we can eliminate a variable or a parameter.
1296 * If not, we add the equality as two inequalities.
1297 * In this case, the equality was a pure parameter equality and there
1298 * is no need to resolve any constraint violations.
1300 static struct isl_tab
*add_lexmin_valid_eq(struct isl_tab
*tab
, isl_int
*eq
)
1307 r
= isl_tab_add_row(tab
, eq
);
1311 r
= tab
->con
[r
].index
;
1312 i
= last_var_col_or_int_par_col(tab
, r
);
1314 tab
->con
[r
].is_nonneg
= 1;
1315 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]) < 0)
1317 isl_seq_neg(eq
, eq
, 1 + tab
->n_var
);
1318 r
= isl_tab_add_row(tab
, eq
);
1321 tab
->con
[r
].is_nonneg
= 1;
1322 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]) < 0)
1325 if (isl_tab_pivot(tab
, r
, i
) < 0)
1327 if (isl_tab_kill_col(tab
, i
) < 0)
1338 /* Check if the given row is a pure constant.
1340 static int is_constant(struct isl_tab
*tab
, int row
)
1342 unsigned off
= 2 + tab
->M
;
1344 return isl_seq_first_non_zero(tab
->mat
->row
[row
] + off
+ tab
->n_dead
,
1345 tab
->n_col
- tab
->n_dead
) == -1;
1348 /* Add an equality that may or may not be valid to the tableau.
1349 * If the resulting row is a pure constant, then it must be zero.
1350 * Otherwise, the resulting tableau is empty.
1352 * If the row is not a pure constant, then we add two inequalities,
1353 * each time checking that they can be satisfied.
1354 * In the end we try to use one of the two constraints to eliminate
1357 static int add_lexmin_eq(struct isl_tab
*tab
, isl_int
*eq
) WARN_UNUSED
;
1358 static int add_lexmin_eq(struct isl_tab
*tab
, isl_int
*eq
)
1362 struct isl_tab_undo
*snap
;
1366 snap
= isl_tab_snap(tab
);
1367 r1
= isl_tab_add_row(tab
, eq
);
1370 tab
->con
[r1
].is_nonneg
= 1;
1371 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r1
]) < 0)
1374 row
= tab
->con
[r1
].index
;
1375 if (is_constant(tab
, row
)) {
1376 if (!isl_int_is_zero(tab
->mat
->row
[row
][1]) ||
1377 (tab
->M
&& !isl_int_is_zero(tab
->mat
->row
[row
][2]))) {
1378 if (isl_tab_mark_empty(tab
) < 0)
1382 if (isl_tab_rollback(tab
, snap
) < 0)
1387 if (restore_lexmin(tab
) < 0)
1392 isl_seq_neg(eq
, eq
, 1 + tab
->n_var
);
1394 r2
= isl_tab_add_row(tab
, eq
);
1397 tab
->con
[r2
].is_nonneg
= 1;
1398 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r2
]) < 0)
1401 if (restore_lexmin(tab
) < 0)
1406 if (!tab
->con
[r1
].is_row
) {
1407 if (isl_tab_kill_col(tab
, tab
->con
[r1
].index
) < 0)
1409 } else if (!tab
->con
[r2
].is_row
) {
1410 if (isl_tab_kill_col(tab
, tab
->con
[r2
].index
) < 0)
1415 tab
->bmap
= isl_basic_map_add_ineq(tab
->bmap
, eq
);
1416 if (isl_tab_push(tab
, isl_tab_undo_bmap_ineq
) < 0)
1418 isl_seq_neg(eq
, eq
, 1 + tab
->n_var
);
1419 tab
->bmap
= isl_basic_map_add_ineq(tab
->bmap
, eq
);
1420 isl_seq_neg(eq
, eq
, 1 + tab
->n_var
);
1421 if (isl_tab_push(tab
, isl_tab_undo_bmap_ineq
) < 0)
1430 /* Add an inequality to the tableau, resolving violations using
1433 static struct isl_tab
*add_lexmin_ineq(struct isl_tab
*tab
, isl_int
*ineq
)
1440 tab
->bmap
= isl_basic_map_add_ineq(tab
->bmap
, ineq
);
1441 if (isl_tab_push(tab
, isl_tab_undo_bmap_ineq
) < 0)
1446 r
= isl_tab_add_row(tab
, ineq
);
1449 tab
->con
[r
].is_nonneg
= 1;
1450 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]) < 0)
1452 if (isl_tab_row_is_redundant(tab
, tab
->con
[r
].index
)) {
1453 if (isl_tab_mark_redundant(tab
, tab
->con
[r
].index
) < 0)
1458 if (restore_lexmin(tab
) < 0)
1460 if (!tab
->empty
&& tab
->con
[r
].is_row
&&
1461 isl_tab_row_is_redundant(tab
, tab
->con
[r
].index
))
1462 if (isl_tab_mark_redundant(tab
, tab
->con
[r
].index
) < 0)
1470 /* Check if the coefficients of the parameters are all integral.
1472 static int integer_parameter(struct isl_tab
*tab
, int row
)
1476 unsigned off
= 2 + tab
->M
;
1478 for (i
= 0; i
< tab
->n_param
; ++i
) {
1479 /* Eliminated parameter */
1480 if (tab
->var
[i
].is_row
)
1482 col
= tab
->var
[i
].index
;
1483 if (!isl_int_is_divisible_by(tab
->mat
->row
[row
][off
+ col
],
1484 tab
->mat
->row
[row
][0]))
1487 for (i
= 0; i
< tab
->n_div
; ++i
) {
1488 if (tab
->var
[tab
->n_var
- tab
->n_div
+ i
].is_row
)
1490 col
= tab
->var
[tab
->n_var
- tab
->n_div
+ i
].index
;
1491 if (!isl_int_is_divisible_by(tab
->mat
->row
[row
][off
+ col
],
1492 tab
->mat
->row
[row
][0]))
1498 /* Check if the coefficients of the non-parameter variables are all integral.
1500 static int integer_variable(struct isl_tab
*tab
, int row
)
1503 unsigned off
= 2 + tab
->M
;
1505 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
1506 if (tab
->col_var
[i
] >= 0 &&
1507 (tab
->col_var
[i
] < tab
->n_param
||
1508 tab
->col_var
[i
] >= tab
->n_var
- tab
->n_div
))
1510 if (!isl_int_is_divisible_by(tab
->mat
->row
[row
][off
+ i
],
1511 tab
->mat
->row
[row
][0]))
1517 /* Check if the constant term is integral.
1519 static int integer_constant(struct isl_tab
*tab
, int row
)
1521 return isl_int_is_divisible_by(tab
->mat
->row
[row
][1],
1522 tab
->mat
->row
[row
][0]);
1525 #define I_CST 1 << 0
1526 #define I_PAR 1 << 1
1527 #define I_VAR 1 << 2
1529 /* Check for next (non-parameter) variable after "var" (first if var == -1)
1530 * that is non-integer and therefore requires a cut and return
1531 * the index of the variable.
1532 * For parametric tableaus, there are three parts in a row,
1533 * the constant, the coefficients of the parameters and the rest.
1534 * For each part, we check whether the coefficients in that part
1535 * are all integral and if so, set the corresponding flag in *f.
1536 * If the constant and the parameter part are integral, then the
1537 * current sample value is integral and no cut is required
1538 * (irrespective of whether the variable part is integral).
1540 static int next_non_integer_var(struct isl_tab
*tab
, int var
, int *f
)
1542 var
= var
< 0 ? tab
->n_param
: var
+ 1;
1544 for (; var
< tab
->n_var
- tab
->n_div
; ++var
) {
1547 if (!tab
->var
[var
].is_row
)
1549 row
= tab
->var
[var
].index
;
1550 if (integer_constant(tab
, row
))
1551 ISL_FL_SET(flags
, I_CST
);
1552 if (integer_parameter(tab
, row
))
1553 ISL_FL_SET(flags
, I_PAR
);
1554 if (ISL_FL_ISSET(flags
, I_CST
) && ISL_FL_ISSET(flags
, I_PAR
))
1556 if (integer_variable(tab
, row
))
1557 ISL_FL_SET(flags
, I_VAR
);
1564 /* Check for first (non-parameter) variable that is non-integer and
1565 * therefore requires a cut and return the corresponding row.
1566 * For parametric tableaus, there are three parts in a row,
1567 * the constant, the coefficients of the parameters and the rest.
1568 * For each part, we check whether the coefficients in that part
1569 * are all integral and if so, set the corresponding flag in *f.
1570 * If the constant and the parameter part are integral, then the
1571 * current sample value is integral and no cut is required
1572 * (irrespective of whether the variable part is integral).
1574 static int first_non_integer_row(struct isl_tab
*tab
, int *f
)
1576 int var
= next_non_integer_var(tab
, -1, f
);
1578 return var
< 0 ? -1 : tab
->var
[var
].index
;
1581 /* Add a (non-parametric) cut to cut away the non-integral sample
1582 * value of the given row.
1584 * If the row is given by
1586 * m r = f + \sum_i a_i y_i
1590 * c = - {-f/m} + \sum_i {a_i/m} y_i >= 0
1592 * The big parameter, if any, is ignored, since it is assumed to be big
1593 * enough to be divisible by any integer.
1594 * If the tableau is actually a parametric tableau, then this function
1595 * is only called when all coefficients of the parameters are integral.
1596 * The cut therefore has zero coefficients for the parameters.
1598 * The current value is known to be negative, so row_sign, if it
1599 * exists, is set accordingly.
1601 * Return the row of the cut or -1.
1603 static int add_cut(struct isl_tab
*tab
, int row
)
1608 unsigned off
= 2 + tab
->M
;
1610 if (isl_tab_extend_cons(tab
, 1) < 0)
1612 r
= isl_tab_allocate_con(tab
);
1616 r_row
= tab
->mat
->row
[tab
->con
[r
].index
];
1617 isl_int_set(r_row
[0], tab
->mat
->row
[row
][0]);
1618 isl_int_neg(r_row
[1], tab
->mat
->row
[row
][1]);
1619 isl_int_fdiv_r(r_row
[1], r_row
[1], tab
->mat
->row
[row
][0]);
1620 isl_int_neg(r_row
[1], r_row
[1]);
1622 isl_int_set_si(r_row
[2], 0);
1623 for (i
= 0; i
< tab
->n_col
; ++i
)
1624 isl_int_fdiv_r(r_row
[off
+ i
],
1625 tab
->mat
->row
[row
][off
+ i
], tab
->mat
->row
[row
][0]);
1627 tab
->con
[r
].is_nonneg
= 1;
1628 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]) < 0)
1631 tab
->row_sign
[tab
->con
[r
].index
] = isl_tab_row_neg
;
1633 return tab
->con
[r
].index
;
1639 /* Given a non-parametric tableau, add cuts until an integer
1640 * sample point is obtained or until the tableau is determined
1641 * to be integer infeasible.
1642 * As long as there is any non-integer value in the sample point,
1643 * we add appropriate cuts, if possible, for each of these
1644 * non-integer values and then resolve the violated
1645 * cut constraints using restore_lexmin.
1646 * If one of the corresponding rows is equal to an integral
1647 * combination of variables/constraints plus a non-integral constant,
1648 * then there is no way to obtain an integer point and we return
1649 * a tableau that is marked empty.
1650 * The parameter cutting_strategy controls the strategy used when adding cuts
1651 * to remove non-integer points. CUT_ALL adds all possible cuts
1652 * before continuing the search. CUT_ONE adds only one cut at a time.
1654 static struct isl_tab
*cut_to_integer_lexmin(struct isl_tab
*tab
,
1655 int cutting_strategy
)
1666 while ((var
= next_non_integer_var(tab
, -1, &flags
)) != -1) {
1668 if (ISL_FL_ISSET(flags
, I_VAR
)) {
1669 if (isl_tab_mark_empty(tab
) < 0)
1673 row
= tab
->var
[var
].index
;
1674 row
= add_cut(tab
, row
);
1677 if (cutting_strategy
== CUT_ONE
)
1679 } while ((var
= next_non_integer_var(tab
, var
, &flags
)) != -1);
1680 if (restore_lexmin(tab
) < 0)
1691 /* Check whether all the currently active samples also satisfy the inequality
1692 * "ineq" (treated as an equality if eq is set).
1693 * Remove those samples that do not.
1695 static struct isl_tab
*check_samples(struct isl_tab
*tab
, isl_int
*ineq
, int eq
)
1703 isl_assert(tab
->mat
->ctx
, tab
->bmap
, goto error
);
1704 isl_assert(tab
->mat
->ctx
, tab
->samples
, goto error
);
1705 isl_assert(tab
->mat
->ctx
, tab
->samples
->n_col
== 1 + tab
->n_var
, goto error
);
1708 for (i
= tab
->n_outside
; i
< tab
->n_sample
; ++i
) {
1710 isl_seq_inner_product(ineq
, tab
->samples
->row
[i
],
1711 1 + tab
->n_var
, &v
);
1712 sgn
= isl_int_sgn(v
);
1713 if (eq
? (sgn
== 0) : (sgn
>= 0))
1715 tab
= isl_tab_drop_sample(tab
, i
);
1727 /* Check whether the sample value of the tableau is finite,
1728 * i.e., either the tableau does not use a big parameter, or
1729 * all values of the variables are equal to the big parameter plus
1730 * some constant. This constant is the actual sample value.
1732 static int sample_is_finite(struct isl_tab
*tab
)
1739 for (i
= 0; i
< tab
->n_var
; ++i
) {
1741 if (!tab
->var
[i
].is_row
)
1743 row
= tab
->var
[i
].index
;
1744 if (isl_int_ne(tab
->mat
->row
[row
][0], tab
->mat
->row
[row
][2]))
1750 /* Check if the context tableau of sol has any integer points.
1751 * Leave tab in empty state if no integer point can be found.
1752 * If an integer point can be found and if moreover it is finite,
1753 * then it is added to the list of sample values.
1755 * This function is only called when none of the currently active sample
1756 * values satisfies the most recently added constraint.
1758 static struct isl_tab
*check_integer_feasible(struct isl_tab
*tab
)
1760 struct isl_tab_undo
*snap
;
1765 snap
= isl_tab_snap(tab
);
1766 if (isl_tab_push_basis(tab
) < 0)
1769 tab
= cut_to_integer_lexmin(tab
, CUT_ALL
);
1773 if (!tab
->empty
&& sample_is_finite(tab
)) {
1774 struct isl_vec
*sample
;
1776 sample
= isl_tab_get_sample_value(tab
);
1778 tab
= isl_tab_add_sample(tab
, sample
);
1781 if (!tab
->empty
&& isl_tab_rollback(tab
, snap
) < 0)
1790 /* Check if any of the currently active sample values satisfies
1791 * the inequality "ineq" (an equality if eq is set).
1793 static int tab_has_valid_sample(struct isl_tab
*tab
, isl_int
*ineq
, int eq
)
1801 isl_assert(tab
->mat
->ctx
, tab
->bmap
, return -1);
1802 isl_assert(tab
->mat
->ctx
, tab
->samples
, return -1);
1803 isl_assert(tab
->mat
->ctx
, tab
->samples
->n_col
== 1 + tab
->n_var
, return -1);
1806 for (i
= tab
->n_outside
; i
< tab
->n_sample
; ++i
) {
1808 isl_seq_inner_product(ineq
, tab
->samples
->row
[i
],
1809 1 + tab
->n_var
, &v
);
1810 sgn
= isl_int_sgn(v
);
1811 if (eq
? (sgn
== 0) : (sgn
>= 0))
1816 return i
< tab
->n_sample
;
1819 /* Add a div specified by "div" to the tableau "tab" and return
1820 * 1 if the div is obviously non-negative.
1822 static int context_tab_add_div(struct isl_tab
*tab
, struct isl_vec
*div
,
1823 int (*add_ineq
)(void *user
, isl_int
*), void *user
)
1827 struct isl_mat
*samples
;
1830 r
= isl_tab_add_div(tab
, div
, add_ineq
, user
);
1833 nonneg
= tab
->var
[r
].is_nonneg
;
1834 tab
->var
[r
].frozen
= 1;
1836 samples
= isl_mat_extend(tab
->samples
,
1837 tab
->n_sample
, 1 + tab
->n_var
);
1838 tab
->samples
= samples
;
1841 for (i
= tab
->n_outside
; i
< samples
->n_row
; ++i
) {
1842 isl_seq_inner_product(div
->el
+ 1, samples
->row
[i
],
1843 div
->size
- 1, &samples
->row
[i
][samples
->n_col
- 1]);
1844 isl_int_fdiv_q(samples
->row
[i
][samples
->n_col
- 1],
1845 samples
->row
[i
][samples
->n_col
- 1], div
->el
[0]);
1851 /* Add a div specified by "div" to both the main tableau and
1852 * the context tableau. In case of the main tableau, we only
1853 * need to add an extra div. In the context tableau, we also
1854 * need to express the meaning of the div.
1855 * Return the index of the div or -1 if anything went wrong.
1857 static int add_div(struct isl_tab
*tab
, struct isl_context
*context
,
1858 struct isl_vec
*div
)
1863 if ((nonneg
= context
->op
->add_div(context
, div
)) < 0)
1866 if (!context
->op
->is_ok(context
))
1869 if (isl_tab_extend_vars(tab
, 1) < 0)
1871 r
= isl_tab_allocate_var(tab
);
1875 tab
->var
[r
].is_nonneg
= 1;
1876 tab
->var
[r
].frozen
= 1;
1879 return tab
->n_div
- 1;
1881 context
->op
->invalidate(context
);
1885 static int find_div(struct isl_tab
*tab
, isl_int
*div
, isl_int denom
)
1888 unsigned total
= isl_basic_map_total_dim(tab
->bmap
);
1890 for (i
= 0; i
< tab
->bmap
->n_div
; ++i
) {
1891 if (isl_int_ne(tab
->bmap
->div
[i
][0], denom
))
1893 if (!isl_seq_eq(tab
->bmap
->div
[i
] + 1, div
, 1 + total
))
1900 /* Return the index of a div that corresponds to "div".
1901 * We first check if we already have such a div and if not, we create one.
1903 static int get_div(struct isl_tab
*tab
, struct isl_context
*context
,
1904 struct isl_vec
*div
)
1907 struct isl_tab
*context_tab
= context
->op
->peek_tab(context
);
1912 d
= find_div(context_tab
, div
->el
+ 1, div
->el
[0]);
1916 return add_div(tab
, context
, div
);
1919 /* Add a parametric cut to cut away the non-integral sample value
1921 * Let a_i be the coefficients of the constant term and the parameters
1922 * and let b_i be the coefficients of the variables or constraints
1923 * in basis of the tableau.
1924 * Let q be the div q = floor(\sum_i {-a_i} y_i).
1926 * The cut is expressed as
1928 * c = \sum_i -{-a_i} y_i + \sum_i {b_i} x_i + q >= 0
1930 * If q did not already exist in the context tableau, then it is added first.
1931 * If q is in a column of the main tableau then the "+ q" can be accomplished
1932 * by setting the corresponding entry to the denominator of the constraint.
1933 * If q happens to be in a row of the main tableau, then the corresponding
1934 * row needs to be added instead (taking care of the denominators).
1935 * Note that this is very unlikely, but perhaps not entirely impossible.
1937 * The current value of the cut is known to be negative (or at least
1938 * non-positive), so row_sign is set accordingly.
1940 * Return the row of the cut or -1.
1942 static int add_parametric_cut(struct isl_tab
*tab
, int row
,
1943 struct isl_context
*context
)
1945 struct isl_vec
*div
;
1952 unsigned off
= 2 + tab
->M
;
1957 div
= get_row_parameter_div(tab
, row
);
1962 d
= context
->op
->get_div(context
, tab
, div
);
1967 if (isl_tab_extend_cons(tab
, 1) < 0)
1969 r
= isl_tab_allocate_con(tab
);
1973 r_row
= tab
->mat
->row
[tab
->con
[r
].index
];
1974 isl_int_set(r_row
[0], tab
->mat
->row
[row
][0]);
1975 isl_int_neg(r_row
[1], tab
->mat
->row
[row
][1]);
1976 isl_int_fdiv_r(r_row
[1], r_row
[1], tab
->mat
->row
[row
][0]);
1977 isl_int_neg(r_row
[1], r_row
[1]);
1979 isl_int_set_si(r_row
[2], 0);
1980 for (i
= 0; i
< tab
->n_param
; ++i
) {
1981 if (tab
->var
[i
].is_row
)
1983 col
= tab
->var
[i
].index
;
1984 isl_int_neg(r_row
[off
+ col
], tab
->mat
->row
[row
][off
+ col
]);
1985 isl_int_fdiv_r(r_row
[off
+ col
], r_row
[off
+ col
],
1986 tab
->mat
->row
[row
][0]);
1987 isl_int_neg(r_row
[off
+ col
], r_row
[off
+ col
]);
1989 for (i
= 0; i
< tab
->n_div
; ++i
) {
1990 if (tab
->var
[tab
->n_var
- tab
->n_div
+ i
].is_row
)
1992 col
= tab
->var
[tab
->n_var
- tab
->n_div
+ i
].index
;
1993 isl_int_neg(r_row
[off
+ col
], tab
->mat
->row
[row
][off
+ col
]);
1994 isl_int_fdiv_r(r_row
[off
+ col
], r_row
[off
+ col
],
1995 tab
->mat
->row
[row
][0]);
1996 isl_int_neg(r_row
[off
+ col
], r_row
[off
+ col
]);
1998 for (i
= 0; i
< tab
->n_col
; ++i
) {
1999 if (tab
->col_var
[i
] >= 0 &&
2000 (tab
->col_var
[i
] < tab
->n_param
||
2001 tab
->col_var
[i
] >= tab
->n_var
- tab
->n_div
))
2003 isl_int_fdiv_r(r_row
[off
+ i
],
2004 tab
->mat
->row
[row
][off
+ i
], tab
->mat
->row
[row
][0]);
2006 if (tab
->var
[tab
->n_var
- tab
->n_div
+ d
].is_row
) {
2008 int d_row
= tab
->var
[tab
->n_var
- tab
->n_div
+ d
].index
;
2010 isl_int_gcd(gcd
, tab
->mat
->row
[d_row
][0], r_row
[0]);
2011 isl_int_divexact(r_row
[0], r_row
[0], gcd
);
2012 isl_int_divexact(gcd
, tab
->mat
->row
[d_row
][0], gcd
);
2013 isl_seq_combine(r_row
+ 1, gcd
, r_row
+ 1,
2014 r_row
[0], tab
->mat
->row
[d_row
] + 1,
2015 off
- 1 + tab
->n_col
);
2016 isl_int_mul(r_row
[0], r_row
[0], tab
->mat
->row
[d_row
][0]);
2019 col
= tab
->var
[tab
->n_var
- tab
->n_div
+ d
].index
;
2020 isl_int_set(r_row
[off
+ col
], tab
->mat
->row
[row
][0]);
2023 tab
->con
[r
].is_nonneg
= 1;
2024 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]) < 0)
2027 tab
->row_sign
[tab
->con
[r
].index
] = isl_tab_row_neg
;
2029 row
= tab
->con
[r
].index
;
2031 if (d
>= n
&& context
->op
->detect_equalities(context
, tab
) < 0)
2037 /* Construct a tableau for bmap that can be used for computing
2038 * the lexicographic minimum (or maximum) of bmap.
2039 * If not NULL, then dom is the domain where the minimum
2040 * should be computed. In this case, we set up a parametric
2041 * tableau with row signs (initialized to "unknown").
2042 * If M is set, then the tableau will use a big parameter.
2043 * If max is set, then a maximum should be computed instead of a minimum.
2044 * This means that for each variable x, the tableau will contain the variable
2045 * x' = M - x, rather than x' = M + x. This in turn means that the coefficient
2046 * of the variables in all constraints are negated prior to adding them
2049 static struct isl_tab
*tab_for_lexmin(struct isl_basic_map
*bmap
,
2050 struct isl_basic_set
*dom
, unsigned M
, int max
)
2053 struct isl_tab
*tab
;
2055 tab
= isl_tab_alloc(bmap
->ctx
, 2 * bmap
->n_eq
+ bmap
->n_ineq
+ 1,
2056 isl_basic_map_total_dim(bmap
), M
);
2060 tab
->rational
= ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
);
2062 tab
->n_param
= isl_basic_set_total_dim(dom
) - dom
->n_div
;
2063 tab
->n_div
= dom
->n_div
;
2064 tab
->row_sign
= isl_calloc_array(bmap
->ctx
,
2065 enum isl_tab_row_sign
, tab
->mat
->n_row
);
2069 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
)) {
2070 if (isl_tab_mark_empty(tab
) < 0)
2075 for (i
= tab
->n_param
; i
< tab
->n_var
- tab
->n_div
; ++i
) {
2076 tab
->var
[i
].is_nonneg
= 1;
2077 tab
->var
[i
].frozen
= 1;
2079 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
2081 isl_seq_neg(bmap
->eq
[i
] + 1 + tab
->n_param
,
2082 bmap
->eq
[i
] + 1 + tab
->n_param
,
2083 tab
->n_var
- tab
->n_param
- tab
->n_div
);
2084 tab
= add_lexmin_valid_eq(tab
, bmap
->eq
[i
]);
2086 isl_seq_neg(bmap
->eq
[i
] + 1 + tab
->n_param
,
2087 bmap
->eq
[i
] + 1 + tab
->n_param
,
2088 tab
->n_var
- tab
->n_param
- tab
->n_div
);
2089 if (!tab
|| tab
->empty
)
2092 if (bmap
->n_eq
&& restore_lexmin(tab
) < 0)
2094 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
2096 isl_seq_neg(bmap
->ineq
[i
] + 1 + tab
->n_param
,
2097 bmap
->ineq
[i
] + 1 + tab
->n_param
,
2098 tab
->n_var
- tab
->n_param
- tab
->n_div
);
2099 tab
= add_lexmin_ineq(tab
, bmap
->ineq
[i
]);
2101 isl_seq_neg(bmap
->ineq
[i
] + 1 + tab
->n_param
,
2102 bmap
->ineq
[i
] + 1 + tab
->n_param
,
2103 tab
->n_var
- tab
->n_param
- tab
->n_div
);
2104 if (!tab
|| tab
->empty
)
2113 /* Given a main tableau where more than one row requires a split,
2114 * determine and return the "best" row to split on.
2116 * Given two rows in the main tableau, if the inequality corresponding
2117 * to the first row is redundant with respect to that of the second row
2118 * in the current tableau, then it is better to split on the second row,
2119 * since in the positive part, both row will be positive.
2120 * (In the negative part a pivot will have to be performed and just about
2121 * anything can happen to the sign of the other row.)
2123 * As a simple heuristic, we therefore select the row that makes the most
2124 * of the other rows redundant.
2126 * Perhaps it would also be useful to look at the number of constraints
2127 * that conflict with any given constraint.
2129 static int best_split(struct isl_tab
*tab
, struct isl_tab
*context_tab
)
2131 struct isl_tab_undo
*snap
;
2137 if (isl_tab_extend_cons(context_tab
, 2) < 0)
2140 snap
= isl_tab_snap(context_tab
);
2142 for (split
= tab
->n_redundant
; split
< tab
->n_row
; ++split
) {
2143 struct isl_tab_undo
*snap2
;
2144 struct isl_vec
*ineq
= NULL
;
2148 if (!isl_tab_var_from_row(tab
, split
)->is_nonneg
)
2150 if (tab
->row_sign
[split
] != isl_tab_row_any
)
2153 ineq
= get_row_parameter_ineq(tab
, split
);
2156 ok
= isl_tab_add_ineq(context_tab
, ineq
->el
) >= 0;
2161 snap2
= isl_tab_snap(context_tab
);
2163 for (row
= tab
->n_redundant
; row
< tab
->n_row
; ++row
) {
2164 struct isl_tab_var
*var
;
2168 if (!isl_tab_var_from_row(tab
, row
)->is_nonneg
)
2170 if (tab
->row_sign
[row
] != isl_tab_row_any
)
2173 ineq
= get_row_parameter_ineq(tab
, row
);
2176 ok
= isl_tab_add_ineq(context_tab
, ineq
->el
) >= 0;
2180 var
= &context_tab
->con
[context_tab
->n_con
- 1];
2181 if (!context_tab
->empty
&&
2182 !isl_tab_min_at_most_neg_one(context_tab
, var
))
2184 if (isl_tab_rollback(context_tab
, snap2
) < 0)
2187 if (best
== -1 || r
> best_r
) {
2191 if (isl_tab_rollback(context_tab
, snap
) < 0)
2198 static struct isl_basic_set
*context_lex_peek_basic_set(
2199 struct isl_context
*context
)
2201 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2204 return isl_tab_peek_bset(clex
->tab
);
2207 static struct isl_tab
*context_lex_peek_tab(struct isl_context
*context
)
2209 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2213 static void context_lex_add_eq(struct isl_context
*context
, isl_int
*eq
,
2214 int check
, int update
)
2216 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2217 if (isl_tab_extend_cons(clex
->tab
, 2) < 0)
2219 if (add_lexmin_eq(clex
->tab
, eq
) < 0)
2222 int v
= tab_has_valid_sample(clex
->tab
, eq
, 1);
2226 clex
->tab
= check_integer_feasible(clex
->tab
);
2229 clex
->tab
= check_samples(clex
->tab
, eq
, 1);
2232 isl_tab_free(clex
->tab
);
2236 static void context_lex_add_ineq(struct isl_context
*context
, isl_int
*ineq
,
2237 int check
, int update
)
2239 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2240 if (isl_tab_extend_cons(clex
->tab
, 1) < 0)
2242 clex
->tab
= add_lexmin_ineq(clex
->tab
, ineq
);
2244 int v
= tab_has_valid_sample(clex
->tab
, ineq
, 0);
2248 clex
->tab
= check_integer_feasible(clex
->tab
);
2251 clex
->tab
= check_samples(clex
->tab
, ineq
, 0);
2254 isl_tab_free(clex
->tab
);
2258 static int context_lex_add_ineq_wrap(void *user
, isl_int
*ineq
)
2260 struct isl_context
*context
= (struct isl_context
*)user
;
2261 context_lex_add_ineq(context
, ineq
, 0, 0);
2262 return context
->op
->is_ok(context
) ? 0 : -1;
2265 /* Check which signs can be obtained by "ineq" on all the currently
2266 * active sample values. See row_sign for more information.
2268 static enum isl_tab_row_sign
tab_ineq_sign(struct isl_tab
*tab
, isl_int
*ineq
,
2274 enum isl_tab_row_sign res
= isl_tab_row_unknown
;
2276 isl_assert(tab
->mat
->ctx
, tab
->samples
, return isl_tab_row_unknown
);
2277 isl_assert(tab
->mat
->ctx
, tab
->samples
->n_col
== 1 + tab
->n_var
,
2278 return isl_tab_row_unknown
);
2281 for (i
= tab
->n_outside
; i
< tab
->n_sample
; ++i
) {
2282 isl_seq_inner_product(tab
->samples
->row
[i
], ineq
,
2283 1 + tab
->n_var
, &tmp
);
2284 sgn
= isl_int_sgn(tmp
);
2285 if (sgn
> 0 || (sgn
== 0 && strict
)) {
2286 if (res
== isl_tab_row_unknown
)
2287 res
= isl_tab_row_pos
;
2288 if (res
== isl_tab_row_neg
)
2289 res
= isl_tab_row_any
;
2292 if (res
== isl_tab_row_unknown
)
2293 res
= isl_tab_row_neg
;
2294 if (res
== isl_tab_row_pos
)
2295 res
= isl_tab_row_any
;
2297 if (res
== isl_tab_row_any
)
2305 static enum isl_tab_row_sign
context_lex_ineq_sign(struct isl_context
*context
,
2306 isl_int
*ineq
, int strict
)
2308 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2309 return tab_ineq_sign(clex
->tab
, ineq
, strict
);
2312 /* Check whether "ineq" can be added to the tableau without rendering
2315 static int context_lex_test_ineq(struct isl_context
*context
, isl_int
*ineq
)
2317 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2318 struct isl_tab_undo
*snap
;
2324 if (isl_tab_extend_cons(clex
->tab
, 1) < 0)
2327 snap
= isl_tab_snap(clex
->tab
);
2328 if (isl_tab_push_basis(clex
->tab
) < 0)
2330 clex
->tab
= add_lexmin_ineq(clex
->tab
, ineq
);
2331 clex
->tab
= check_integer_feasible(clex
->tab
);
2334 feasible
= !clex
->tab
->empty
;
2335 if (isl_tab_rollback(clex
->tab
, snap
) < 0)
2341 static int context_lex_get_div(struct isl_context
*context
, struct isl_tab
*tab
,
2342 struct isl_vec
*div
)
2344 return get_div(tab
, context
, div
);
2347 /* Add a div specified by "div" to the context tableau and return
2348 * 1 if the div is obviously non-negative.
2349 * context_tab_add_div will always return 1, because all variables
2350 * in a isl_context_lex tableau are non-negative.
2351 * However, if we are using a big parameter in the context, then this only
2352 * reflects the non-negativity of the variable used to _encode_ the
2353 * div, i.e., div' = M + div, so we can't draw any conclusions.
2355 static int context_lex_add_div(struct isl_context
*context
, struct isl_vec
*div
)
2357 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2359 nonneg
= context_tab_add_div(clex
->tab
, div
,
2360 context_lex_add_ineq_wrap
, context
);
2368 static int context_lex_detect_equalities(struct isl_context
*context
,
2369 struct isl_tab
*tab
)
2374 static int context_lex_best_split(struct isl_context
*context
,
2375 struct isl_tab
*tab
)
2377 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2378 struct isl_tab_undo
*snap
;
2381 snap
= isl_tab_snap(clex
->tab
);
2382 if (isl_tab_push_basis(clex
->tab
) < 0)
2384 r
= best_split(tab
, clex
->tab
);
2386 if (r
>= 0 && isl_tab_rollback(clex
->tab
, snap
) < 0)
2392 static int context_lex_is_empty(struct isl_context
*context
)
2394 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2397 return clex
->tab
->empty
;
2400 static void *context_lex_save(struct isl_context
*context
)
2402 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2403 struct isl_tab_undo
*snap
;
2405 snap
= isl_tab_snap(clex
->tab
);
2406 if (isl_tab_push_basis(clex
->tab
) < 0)
2408 if (isl_tab_save_samples(clex
->tab
) < 0)
2414 static void context_lex_restore(struct isl_context
*context
, void *save
)
2416 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2417 if (isl_tab_rollback(clex
->tab
, (struct isl_tab_undo
*)save
) < 0) {
2418 isl_tab_free(clex
->tab
);
2423 static void context_lex_discard(void *save
)
2427 static int context_lex_is_ok(struct isl_context
*context
)
2429 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2433 /* For each variable in the context tableau, check if the variable can
2434 * only attain non-negative values. If so, mark the parameter as non-negative
2435 * in the main tableau. This allows for a more direct identification of some
2436 * cases of violated constraints.
2438 static struct isl_tab
*tab_detect_nonnegative_parameters(struct isl_tab
*tab
,
2439 struct isl_tab
*context_tab
)
2442 struct isl_tab_undo
*snap
;
2443 struct isl_vec
*ineq
= NULL
;
2444 struct isl_tab_var
*var
;
2447 if (context_tab
->n_var
== 0)
2450 ineq
= isl_vec_alloc(tab
->mat
->ctx
, 1 + context_tab
->n_var
);
2454 if (isl_tab_extend_cons(context_tab
, 1) < 0)
2457 snap
= isl_tab_snap(context_tab
);
2460 isl_seq_clr(ineq
->el
, ineq
->size
);
2461 for (i
= 0; i
< context_tab
->n_var
; ++i
) {
2462 isl_int_set_si(ineq
->el
[1 + i
], 1);
2463 if (isl_tab_add_ineq(context_tab
, ineq
->el
) < 0)
2465 var
= &context_tab
->con
[context_tab
->n_con
- 1];
2466 if (!context_tab
->empty
&&
2467 !isl_tab_min_at_most_neg_one(context_tab
, var
)) {
2469 if (i
>= tab
->n_param
)
2470 j
= i
- tab
->n_param
+ tab
->n_var
- tab
->n_div
;
2471 tab
->var
[j
].is_nonneg
= 1;
2474 isl_int_set_si(ineq
->el
[1 + i
], 0);
2475 if (isl_tab_rollback(context_tab
, snap
) < 0)
2479 if (context_tab
->M
&& n
== context_tab
->n_var
) {
2480 context_tab
->mat
= isl_mat_drop_cols(context_tab
->mat
, 2, 1);
2492 static struct isl_tab
*context_lex_detect_nonnegative_parameters(
2493 struct isl_context
*context
, struct isl_tab
*tab
)
2495 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2496 struct isl_tab_undo
*snap
;
2501 snap
= isl_tab_snap(clex
->tab
);
2502 if (isl_tab_push_basis(clex
->tab
) < 0)
2505 tab
= tab_detect_nonnegative_parameters(tab
, clex
->tab
);
2507 if (isl_tab_rollback(clex
->tab
, snap
) < 0)
2516 static void context_lex_invalidate(struct isl_context
*context
)
2518 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2519 isl_tab_free(clex
->tab
);
2523 static void context_lex_free(struct isl_context
*context
)
2525 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2526 isl_tab_free(clex
->tab
);
2530 struct isl_context_op isl_context_lex_op
= {
2531 context_lex_detect_nonnegative_parameters
,
2532 context_lex_peek_basic_set
,
2533 context_lex_peek_tab
,
2535 context_lex_add_ineq
,
2536 context_lex_ineq_sign
,
2537 context_lex_test_ineq
,
2538 context_lex_get_div
,
2539 context_lex_add_div
,
2540 context_lex_detect_equalities
,
2541 context_lex_best_split
,
2542 context_lex_is_empty
,
2545 context_lex_restore
,
2546 context_lex_discard
,
2547 context_lex_invalidate
,
2551 static struct isl_tab
*context_tab_for_lexmin(struct isl_basic_set
*bset
)
2553 struct isl_tab
*tab
;
2557 tab
= tab_for_lexmin((struct isl_basic_map
*)bset
, NULL
, 1, 0);
2560 if (isl_tab_track_bset(tab
, bset
) < 0)
2562 tab
= isl_tab_init_samples(tab
);
2565 isl_basic_set_free(bset
);
2569 static struct isl_context
*isl_context_lex_alloc(struct isl_basic_set
*dom
)
2571 struct isl_context_lex
*clex
;
2576 clex
= isl_alloc_type(dom
->ctx
, struct isl_context_lex
);
2580 clex
->context
.op
= &isl_context_lex_op
;
2582 clex
->tab
= context_tab_for_lexmin(isl_basic_set_copy(dom
));
2583 if (restore_lexmin(clex
->tab
) < 0)
2585 clex
->tab
= check_integer_feasible(clex
->tab
);
2589 return &clex
->context
;
2591 clex
->context
.op
->free(&clex
->context
);
2595 struct isl_context_gbr
{
2596 struct isl_context context
;
2597 struct isl_tab
*tab
;
2598 struct isl_tab
*shifted
;
2599 struct isl_tab
*cone
;
2602 static struct isl_tab
*context_gbr_detect_nonnegative_parameters(
2603 struct isl_context
*context
, struct isl_tab
*tab
)
2605 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
2608 return tab_detect_nonnegative_parameters(tab
, cgbr
->tab
);
2611 static struct isl_basic_set
*context_gbr_peek_basic_set(
2612 struct isl_context
*context
)
2614 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
2617 return isl_tab_peek_bset(cgbr
->tab
);
2620 static struct isl_tab
*context_gbr_peek_tab(struct isl_context
*context
)
2622 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
2626 /* Initialize the "shifted" tableau of the context, which
2627 * contains the constraints of the original tableau shifted
2628 * by the sum of all negative coefficients. This ensures
2629 * that any rational point in the shifted tableau can
2630 * be rounded up to yield an integer point in the original tableau.
2632 static void gbr_init_shifted(struct isl_context_gbr
*cgbr
)
2635 struct isl_vec
*cst
;
2636 struct isl_basic_set
*bset
= isl_tab_peek_bset(cgbr
->tab
);
2637 unsigned dim
= isl_basic_set_total_dim(bset
);
2639 cst
= isl_vec_alloc(cgbr
->tab
->mat
->ctx
, bset
->n_ineq
);
2643 for (i
= 0; i
< bset
->n_ineq
; ++i
) {
2644 isl_int_set(cst
->el
[i
], bset
->ineq
[i
][0]);
2645 for (j
= 0; j
< dim
; ++j
) {
2646 if (!isl_int_is_neg(bset
->ineq
[i
][1 + j
]))
2648 isl_int_add(bset
->ineq
[i
][0], bset
->ineq
[i
][0],
2649 bset
->ineq
[i
][1 + j
]);
2653 cgbr
->shifted
= isl_tab_from_basic_set(bset
, 0);
2655 for (i
= 0; i
< bset
->n_ineq
; ++i
)
2656 isl_int_set(bset
->ineq
[i
][0], cst
->el
[i
]);
2661 /* Check if the shifted tableau is non-empty, and if so
2662 * use the sample point to construct an integer point
2663 * of the context tableau.
2665 static struct isl_vec
*gbr_get_shifted_sample(struct isl_context_gbr
*cgbr
)
2667 struct isl_vec
*sample
;
2670 gbr_init_shifted(cgbr
);
2673 if (cgbr
->shifted
->empty
)
2674 return isl_vec_alloc(cgbr
->tab
->mat
->ctx
, 0);
2676 sample
= isl_tab_get_sample_value(cgbr
->shifted
);
2677 sample
= isl_vec_ceil(sample
);
2682 static struct isl_basic_set
*drop_constant_terms(struct isl_basic_set
*bset
)
2689 for (i
= 0; i
< bset
->n_eq
; ++i
)
2690 isl_int_set_si(bset
->eq
[i
][0], 0);
2692 for (i
= 0; i
< bset
->n_ineq
; ++i
)
2693 isl_int_set_si(bset
->ineq
[i
][0], 0);
2698 static int use_shifted(struct isl_context_gbr
*cgbr
)
2700 return cgbr
->tab
->bmap
->n_eq
== 0 && cgbr
->tab
->bmap
->n_div
== 0;
2703 static struct isl_vec
*gbr_get_sample(struct isl_context_gbr
*cgbr
)
2705 struct isl_basic_set
*bset
;
2706 struct isl_basic_set
*cone
;
2708 if (isl_tab_sample_is_integer(cgbr
->tab
))
2709 return isl_tab_get_sample_value(cgbr
->tab
);
2711 if (use_shifted(cgbr
)) {
2712 struct isl_vec
*sample
;
2714 sample
= gbr_get_shifted_sample(cgbr
);
2715 if (!sample
|| sample
->size
> 0)
2718 isl_vec_free(sample
);
2722 bset
= isl_tab_peek_bset(cgbr
->tab
);
2723 cgbr
->cone
= isl_tab_from_recession_cone(bset
, 0);
2726 if (isl_tab_track_bset(cgbr
->cone
,
2727 isl_basic_set_copy(bset
)) < 0)
2730 if (isl_tab_detect_implicit_equalities(cgbr
->cone
) < 0)
2733 if (cgbr
->cone
->n_dead
== cgbr
->cone
->n_col
) {
2734 struct isl_vec
*sample
;
2735 struct isl_tab_undo
*snap
;
2737 if (cgbr
->tab
->basis
) {
2738 if (cgbr
->tab
->basis
->n_col
!= 1 + cgbr
->tab
->n_var
) {
2739 isl_mat_free(cgbr
->tab
->basis
);
2740 cgbr
->tab
->basis
= NULL
;
2742 cgbr
->tab
->n_zero
= 0;
2743 cgbr
->tab
->n_unbounded
= 0;
2746 snap
= isl_tab_snap(cgbr
->tab
);
2748 sample
= isl_tab_sample(cgbr
->tab
);
2750 if (isl_tab_rollback(cgbr
->tab
, snap
) < 0) {
2751 isl_vec_free(sample
);
2758 cone
= isl_basic_set_dup(isl_tab_peek_bset(cgbr
->cone
));
2759 cone
= drop_constant_terms(cone
);
2760 cone
= isl_basic_set_update_from_tab(cone
, cgbr
->cone
);
2761 cone
= isl_basic_set_underlying_set(cone
);
2762 cone
= isl_basic_set_gauss(cone
, NULL
);
2764 bset
= isl_basic_set_dup(isl_tab_peek_bset(cgbr
->tab
));
2765 bset
= isl_basic_set_update_from_tab(bset
, cgbr
->tab
);
2766 bset
= isl_basic_set_underlying_set(bset
);
2767 bset
= isl_basic_set_gauss(bset
, NULL
);
2769 return isl_basic_set_sample_with_cone(bset
, cone
);
2772 static void check_gbr_integer_feasible(struct isl_context_gbr
*cgbr
)
2774 struct isl_vec
*sample
;
2779 if (cgbr
->tab
->empty
)
2782 sample
= gbr_get_sample(cgbr
);
2786 if (sample
->size
== 0) {
2787 isl_vec_free(sample
);
2788 if (isl_tab_mark_empty(cgbr
->tab
) < 0)
2793 cgbr
->tab
= isl_tab_add_sample(cgbr
->tab
, sample
);
2797 isl_tab_free(cgbr
->tab
);
2801 static struct isl_tab
*add_gbr_eq(struct isl_tab
*tab
, isl_int
*eq
)
2806 if (isl_tab_extend_cons(tab
, 2) < 0)
2809 if (isl_tab_add_eq(tab
, eq
) < 0)
2818 static void context_gbr_add_eq(struct isl_context
*context
, isl_int
*eq
,
2819 int check
, int update
)
2821 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
2823 cgbr
->tab
= add_gbr_eq(cgbr
->tab
, eq
);
2825 if (cgbr
->cone
&& cgbr
->cone
->n_col
!= cgbr
->cone
->n_dead
) {
2826 if (isl_tab_extend_cons(cgbr
->cone
, 2) < 0)
2828 if (isl_tab_add_eq(cgbr
->cone
, eq
) < 0)
2833 int v
= tab_has_valid_sample(cgbr
->tab
, eq
, 1);
2837 check_gbr_integer_feasible(cgbr
);
2840 cgbr
->tab
= check_samples(cgbr
->tab
, eq
, 1);
2843 isl_tab_free(cgbr
->tab
);
2847 static void add_gbr_ineq(struct isl_context_gbr
*cgbr
, isl_int
*ineq
)
2852 if (isl_tab_extend_cons(cgbr
->tab
, 1) < 0)
2855 if (isl_tab_add_ineq(cgbr
->tab
, ineq
) < 0)
2858 if (cgbr
->shifted
&& !cgbr
->shifted
->empty
&& use_shifted(cgbr
)) {
2861 dim
= isl_basic_map_total_dim(cgbr
->tab
->bmap
);
2863 if (isl_tab_extend_cons(cgbr
->shifted
, 1) < 0)
2866 for (i
= 0; i
< dim
; ++i
) {
2867 if (!isl_int_is_neg(ineq
[1 + i
]))
2869 isl_int_add(ineq
[0], ineq
[0], ineq
[1 + i
]);
2872 if (isl_tab_add_ineq(cgbr
->shifted
, ineq
) < 0)
2875 for (i
= 0; i
< dim
; ++i
) {
2876 if (!isl_int_is_neg(ineq
[1 + i
]))
2878 isl_int_sub(ineq
[0], ineq
[0], ineq
[1 + i
]);
2882 if (cgbr
->cone
&& cgbr
->cone
->n_col
!= cgbr
->cone
->n_dead
) {
2883 if (isl_tab_extend_cons(cgbr
->cone
, 1) < 0)
2885 if (isl_tab_add_ineq(cgbr
->cone
, ineq
) < 0)
2891 isl_tab_free(cgbr
->tab
);
2895 static void context_gbr_add_ineq(struct isl_context
*context
, isl_int
*ineq
,
2896 int check
, int update
)
2898 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
2900 add_gbr_ineq(cgbr
, ineq
);
2905 int v
= tab_has_valid_sample(cgbr
->tab
, ineq
, 0);
2909 check_gbr_integer_feasible(cgbr
);
2912 cgbr
->tab
= check_samples(cgbr
->tab
, ineq
, 0);
2915 isl_tab_free(cgbr
->tab
);
2919 static int context_gbr_add_ineq_wrap(void *user
, isl_int
*ineq
)
2921 struct isl_context
*context
= (struct isl_context
*)user
;
2922 context_gbr_add_ineq(context
, ineq
, 0, 0);
2923 return context
->op
->is_ok(context
) ? 0 : -1;
2926 static enum isl_tab_row_sign
context_gbr_ineq_sign(struct isl_context
*context
,
2927 isl_int
*ineq
, int strict
)
2929 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
2930 return tab_ineq_sign(cgbr
->tab
, ineq
, strict
);
2933 /* Check whether "ineq" can be added to the tableau without rendering
2936 static int context_gbr_test_ineq(struct isl_context
*context
, isl_int
*ineq
)
2938 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
2939 struct isl_tab_undo
*snap
;
2940 struct isl_tab_undo
*shifted_snap
= NULL
;
2941 struct isl_tab_undo
*cone_snap
= NULL
;
2947 if (isl_tab_extend_cons(cgbr
->tab
, 1) < 0)
2950 snap
= isl_tab_snap(cgbr
->tab
);
2952 shifted_snap
= isl_tab_snap(cgbr
->shifted
);
2954 cone_snap
= isl_tab_snap(cgbr
->cone
);
2955 add_gbr_ineq(cgbr
, ineq
);
2956 check_gbr_integer_feasible(cgbr
);
2959 feasible
= !cgbr
->tab
->empty
;
2960 if (isl_tab_rollback(cgbr
->tab
, snap
) < 0)
2963 if (isl_tab_rollback(cgbr
->shifted
, shifted_snap
))
2965 } else if (cgbr
->shifted
) {
2966 isl_tab_free(cgbr
->shifted
);
2967 cgbr
->shifted
= NULL
;
2970 if (isl_tab_rollback(cgbr
->cone
, cone_snap
))
2972 } else if (cgbr
->cone
) {
2973 isl_tab_free(cgbr
->cone
);
2980 /* Return the column of the last of the variables associated to
2981 * a column that has a non-zero coefficient.
2982 * This function is called in a context where only coefficients
2983 * of parameters or divs can be non-zero.
2985 static int last_non_zero_var_col(struct isl_tab
*tab
, isl_int
*p
)
2990 if (tab
->n_var
== 0)
2993 for (i
= tab
->n_var
- 1; i
>= 0; --i
) {
2994 if (i
>= tab
->n_param
&& i
< tab
->n_var
- tab
->n_div
)
2996 if (tab
->var
[i
].is_row
)
2998 col
= tab
->var
[i
].index
;
2999 if (!isl_int_is_zero(p
[col
]))
3006 /* Look through all the recently added equalities in the context
3007 * to see if we can propagate any of them to the main tableau.
3009 * The newly added equalities in the context are encoded as pairs
3010 * of inequalities starting at inequality "first".
3012 * We tentatively add each of these equalities to the main tableau
3013 * and if this happens to result in a row with a final coefficient
3014 * that is one or negative one, we use it to kill a column
3015 * in the main tableau. Otherwise, we discard the tentatively
3018 static void propagate_equalities(struct isl_context_gbr
*cgbr
,
3019 struct isl_tab
*tab
, unsigned first
)
3022 struct isl_vec
*eq
= NULL
;
3024 eq
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_var
);
3028 if (isl_tab_extend_cons(tab
, (cgbr
->tab
->bmap
->n_ineq
- first
)/2) < 0)
3031 isl_seq_clr(eq
->el
+ 1 + tab
->n_param
,
3032 tab
->n_var
- tab
->n_param
- tab
->n_div
);
3033 for (i
= first
; i
< cgbr
->tab
->bmap
->n_ineq
; i
+= 2) {
3036 struct isl_tab_undo
*snap
;
3037 snap
= isl_tab_snap(tab
);
3039 isl_seq_cpy(eq
->el
, cgbr
->tab
->bmap
->ineq
[i
], 1 + tab
->n_param
);
3040 isl_seq_cpy(eq
->el
+ 1 + tab
->n_var
- tab
->n_div
,
3041 cgbr
->tab
->bmap
->ineq
[i
] + 1 + tab
->n_param
,
3044 r
= isl_tab_add_row(tab
, eq
->el
);
3047 r
= tab
->con
[r
].index
;
3048 j
= last_non_zero_var_col(tab
, tab
->mat
->row
[r
] + 2 + tab
->M
);
3049 if (j
< 0 || j
< tab
->n_dead
||
3050 !isl_int_is_one(tab
->mat
->row
[r
][0]) ||
3051 (!isl_int_is_one(tab
->mat
->row
[r
][2 + tab
->M
+ j
]) &&
3052 !isl_int_is_negone(tab
->mat
->row
[r
][2 + tab
->M
+ j
]))) {
3053 if (isl_tab_rollback(tab
, snap
) < 0)
3057 if (isl_tab_pivot(tab
, r
, j
) < 0)
3059 if (isl_tab_kill_col(tab
, j
) < 0)
3062 if (restore_lexmin(tab
) < 0)
3071 isl_tab_free(cgbr
->tab
);
3075 static int context_gbr_detect_equalities(struct isl_context
*context
,
3076 struct isl_tab
*tab
)
3078 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3079 struct isl_ctx
*ctx
;
3082 ctx
= cgbr
->tab
->mat
->ctx
;
3085 struct isl_basic_set
*bset
= isl_tab_peek_bset(cgbr
->tab
);
3086 cgbr
->cone
= isl_tab_from_recession_cone(bset
, 0);
3089 if (isl_tab_track_bset(cgbr
->cone
,
3090 isl_basic_set_copy(bset
)) < 0)
3093 if (isl_tab_detect_implicit_equalities(cgbr
->cone
) < 0)
3096 n_ineq
= cgbr
->tab
->bmap
->n_ineq
;
3097 cgbr
->tab
= isl_tab_detect_equalities(cgbr
->tab
, cgbr
->cone
);
3098 if (cgbr
->tab
&& cgbr
->tab
->bmap
->n_ineq
> n_ineq
)
3099 propagate_equalities(cgbr
, tab
, n_ineq
);
3103 isl_tab_free(cgbr
->tab
);
3108 static int context_gbr_get_div(struct isl_context
*context
, struct isl_tab
*tab
,
3109 struct isl_vec
*div
)
3111 return get_div(tab
, context
, div
);
3114 static int context_gbr_add_div(struct isl_context
*context
, struct isl_vec
*div
)
3116 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3120 if (isl_tab_extend_cons(cgbr
->cone
, 3) < 0)
3122 if (isl_tab_extend_vars(cgbr
->cone
, 1) < 0)
3124 if (isl_tab_allocate_var(cgbr
->cone
) <0)
3127 cgbr
->cone
->bmap
= isl_basic_map_extend_space(cgbr
->cone
->bmap
,
3128 isl_basic_map_get_space(cgbr
->cone
->bmap
), 1, 0, 2);
3129 k
= isl_basic_map_alloc_div(cgbr
->cone
->bmap
);
3132 isl_seq_cpy(cgbr
->cone
->bmap
->div
[k
], div
->el
, div
->size
);
3133 if (isl_tab_push(cgbr
->cone
, isl_tab_undo_bmap_div
) < 0)
3136 return context_tab_add_div(cgbr
->tab
, div
,
3137 context_gbr_add_ineq_wrap
, context
);
3140 static int context_gbr_best_split(struct isl_context
*context
,
3141 struct isl_tab
*tab
)
3143 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3144 struct isl_tab_undo
*snap
;
3147 snap
= isl_tab_snap(cgbr
->tab
);
3148 r
= best_split(tab
, cgbr
->tab
);
3150 if (r
>= 0 && isl_tab_rollback(cgbr
->tab
, snap
) < 0)
3156 static int context_gbr_is_empty(struct isl_context
*context
)
3158 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3161 return cgbr
->tab
->empty
;
3164 struct isl_gbr_tab_undo
{
3165 struct isl_tab_undo
*tab_snap
;
3166 struct isl_tab_undo
*shifted_snap
;
3167 struct isl_tab_undo
*cone_snap
;
3170 static void *context_gbr_save(struct isl_context
*context
)
3172 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3173 struct isl_gbr_tab_undo
*snap
;
3175 snap
= isl_alloc_type(cgbr
->tab
->mat
->ctx
, struct isl_gbr_tab_undo
);
3179 snap
->tab_snap
= isl_tab_snap(cgbr
->tab
);
3180 if (isl_tab_save_samples(cgbr
->tab
) < 0)
3184 snap
->shifted_snap
= isl_tab_snap(cgbr
->shifted
);
3186 snap
->shifted_snap
= NULL
;
3189 snap
->cone_snap
= isl_tab_snap(cgbr
->cone
);
3191 snap
->cone_snap
= NULL
;
3199 static void context_gbr_restore(struct isl_context
*context
, void *save
)
3201 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3202 struct isl_gbr_tab_undo
*snap
= (struct isl_gbr_tab_undo
*)save
;
3205 if (isl_tab_rollback(cgbr
->tab
, snap
->tab_snap
) < 0) {
3206 isl_tab_free(cgbr
->tab
);
3210 if (snap
->shifted_snap
) {
3211 if (isl_tab_rollback(cgbr
->shifted
, snap
->shifted_snap
) < 0)
3213 } else if (cgbr
->shifted
) {
3214 isl_tab_free(cgbr
->shifted
);
3215 cgbr
->shifted
= NULL
;
3218 if (snap
->cone_snap
) {
3219 if (isl_tab_rollback(cgbr
->cone
, snap
->cone_snap
) < 0)
3221 } else if (cgbr
->cone
) {
3222 isl_tab_free(cgbr
->cone
);
3231 isl_tab_free(cgbr
->tab
);
3235 static void context_gbr_discard(void *save
)
3237 struct isl_gbr_tab_undo
*snap
= (struct isl_gbr_tab_undo
*)save
;
3241 static int context_gbr_is_ok(struct isl_context
*context
)
3243 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3247 static void context_gbr_invalidate(struct isl_context
*context
)
3249 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3250 isl_tab_free(cgbr
->tab
);
3254 static void context_gbr_free(struct isl_context
*context
)
3256 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3257 isl_tab_free(cgbr
->tab
);
3258 isl_tab_free(cgbr
->shifted
);
3259 isl_tab_free(cgbr
->cone
);
3263 struct isl_context_op isl_context_gbr_op
= {
3264 context_gbr_detect_nonnegative_parameters
,
3265 context_gbr_peek_basic_set
,
3266 context_gbr_peek_tab
,
3268 context_gbr_add_ineq
,
3269 context_gbr_ineq_sign
,
3270 context_gbr_test_ineq
,
3271 context_gbr_get_div
,
3272 context_gbr_add_div
,
3273 context_gbr_detect_equalities
,
3274 context_gbr_best_split
,
3275 context_gbr_is_empty
,
3278 context_gbr_restore
,
3279 context_gbr_discard
,
3280 context_gbr_invalidate
,
3284 static struct isl_context
*isl_context_gbr_alloc(struct isl_basic_set
*dom
)
3286 struct isl_context_gbr
*cgbr
;
3291 cgbr
= isl_calloc_type(dom
->ctx
, struct isl_context_gbr
);
3295 cgbr
->context
.op
= &isl_context_gbr_op
;
3297 cgbr
->shifted
= NULL
;
3299 cgbr
->tab
= isl_tab_from_basic_set(dom
, 1);
3300 cgbr
->tab
= isl_tab_init_samples(cgbr
->tab
);
3303 check_gbr_integer_feasible(cgbr
);
3305 return &cgbr
->context
;
3307 cgbr
->context
.op
->free(&cgbr
->context
);
3311 static struct isl_context
*isl_context_alloc(struct isl_basic_set
*dom
)
3316 if (dom
->ctx
->opt
->context
== ISL_CONTEXT_LEXMIN
)
3317 return isl_context_lex_alloc(dom
);
3319 return isl_context_gbr_alloc(dom
);
3322 /* Construct an isl_sol_map structure for accumulating the solution.
3323 * If track_empty is set, then we also keep track of the parts
3324 * of the context where there is no solution.
3325 * If max is set, then we are solving a maximization, rather than
3326 * a minimization problem, which means that the variables in the
3327 * tableau have value "M - x" rather than "M + x".
3329 static struct isl_sol
*sol_map_init(struct isl_basic_map
*bmap
,
3330 struct isl_basic_set
*dom
, int track_empty
, int max
)
3332 struct isl_sol_map
*sol_map
= NULL
;
3337 sol_map
= isl_calloc_type(bmap
->ctx
, struct isl_sol_map
);
3341 sol_map
->sol
.rational
= ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
);
3342 sol_map
->sol
.dec_level
.callback
.run
= &sol_dec_level_wrap
;
3343 sol_map
->sol
.dec_level
.sol
= &sol_map
->sol
;
3344 sol_map
->sol
.max
= max
;
3345 sol_map
->sol
.n_out
= isl_basic_map_dim(bmap
, isl_dim_out
);
3346 sol_map
->sol
.add
= &sol_map_add_wrap
;
3347 sol_map
->sol
.add_empty
= track_empty
? &sol_map_add_empty_wrap
: NULL
;
3348 sol_map
->sol
.free
= &sol_map_free_wrap
;
3349 sol_map
->map
= isl_map_alloc_space(isl_basic_map_get_space(bmap
), 1,
3354 sol_map
->sol
.context
= isl_context_alloc(dom
);
3355 if (!sol_map
->sol
.context
)
3359 sol_map
->empty
= isl_set_alloc_space(isl_basic_set_get_space(dom
),
3360 1, ISL_SET_DISJOINT
);
3361 if (!sol_map
->empty
)
3365 isl_basic_set_free(dom
);
3366 return &sol_map
->sol
;
3368 isl_basic_set_free(dom
);
3369 sol_map_free(sol_map
);
3373 /* Check whether all coefficients of (non-parameter) variables
3374 * are non-positive, meaning that no pivots can be performed on the row.
3376 static int is_critical(struct isl_tab
*tab
, int row
)
3379 unsigned off
= 2 + tab
->M
;
3381 for (j
= tab
->n_dead
; j
< tab
->n_col
; ++j
) {
3382 if (tab
->col_var
[j
] >= 0 &&
3383 (tab
->col_var
[j
] < tab
->n_param
||
3384 tab
->col_var
[j
] >= tab
->n_var
- tab
->n_div
))
3387 if (isl_int_is_pos(tab
->mat
->row
[row
][off
+ j
]))
3394 /* Check whether the inequality represented by vec is strict over the integers,
3395 * i.e., there are no integer values satisfying the constraint with
3396 * equality. This happens if the gcd of the coefficients is not a divisor
3397 * of the constant term. If so, scale the constraint down by the gcd
3398 * of the coefficients.
3400 static int is_strict(struct isl_vec
*vec
)
3406 isl_seq_gcd(vec
->el
+ 1, vec
->size
- 1, &gcd
);
3407 if (!isl_int_is_one(gcd
)) {
3408 strict
= !isl_int_is_divisible_by(vec
->el
[0], gcd
);
3409 isl_int_fdiv_q(vec
->el
[0], vec
->el
[0], gcd
);
3410 isl_seq_scale_down(vec
->el
+ 1, vec
->el
+ 1, gcd
, vec
->size
-1);
3417 /* Determine the sign of the given row of the main tableau.
3418 * The result is one of
3419 * isl_tab_row_pos: always non-negative; no pivot needed
3420 * isl_tab_row_neg: always non-positive; pivot
3421 * isl_tab_row_any: can be both positive and negative; split
3423 * We first handle some simple cases
3424 * - the row sign may be known already
3425 * - the row may be obviously non-negative
3426 * - the parametric constant may be equal to that of another row
3427 * for which we know the sign. This sign will be either "pos" or
3428 * "any". If it had been "neg" then we would have pivoted before.
3430 * If none of these cases hold, we check the value of the row for each
3431 * of the currently active samples. Based on the signs of these values
3432 * we make an initial determination of the sign of the row.
3434 * all zero -> unk(nown)
3435 * all non-negative -> pos
3436 * all non-positive -> neg
3437 * both negative and positive -> all
3439 * If we end up with "all", we are done.
3440 * Otherwise, we perform a check for positive and/or negative
3441 * values as follows.
3443 * samples neg unk pos
3449 * There is no special sign for "zero", because we can usually treat zero
3450 * as either non-negative or non-positive, whatever works out best.
3451 * However, if the row is "critical", meaning that pivoting is impossible
3452 * then we don't want to limp zero with the non-positive case, because
3453 * then we we would lose the solution for those values of the parameters
3454 * where the value of the row is zero. Instead, we treat 0 as non-negative
3455 * ensuring a split if the row can attain both zero and negative values.
3456 * The same happens when the original constraint was one that could not
3457 * be satisfied with equality by any integer values of the parameters.
3458 * In this case, we normalize the constraint, but then a value of zero
3459 * for the normalized constraint is actually a positive value for the
3460 * original constraint, so again we need to treat zero as non-negative.
3461 * In both these cases, we have the following decision tree instead:
3463 * all non-negative -> pos
3464 * all negative -> neg
3465 * both negative and non-negative -> all
3473 static enum isl_tab_row_sign
row_sign(struct isl_tab
*tab
,
3474 struct isl_sol
*sol
, int row
)
3476 struct isl_vec
*ineq
= NULL
;
3477 enum isl_tab_row_sign res
= isl_tab_row_unknown
;
3482 if (tab
->row_sign
[row
] != isl_tab_row_unknown
)
3483 return tab
->row_sign
[row
];
3484 if (is_obviously_nonneg(tab
, row
))
3485 return isl_tab_row_pos
;
3486 for (row2
= tab
->n_redundant
; row2
< tab
->n_row
; ++row2
) {
3487 if (tab
->row_sign
[row2
] == isl_tab_row_unknown
)
3489 if (identical_parameter_line(tab
, row
, row2
))
3490 return tab
->row_sign
[row2
];
3493 critical
= is_critical(tab
, row
);
3495 ineq
= get_row_parameter_ineq(tab
, row
);
3499 strict
= is_strict(ineq
);
3501 res
= sol
->context
->op
->ineq_sign(sol
->context
, ineq
->el
,
3502 critical
|| strict
);
3504 if (res
== isl_tab_row_unknown
|| res
== isl_tab_row_pos
) {
3505 /* test for negative values */
3507 isl_seq_neg(ineq
->el
, ineq
->el
, ineq
->size
);
3508 isl_int_sub_ui(ineq
->el
[0], ineq
->el
[0], 1);
3510 feasible
= sol
->context
->op
->test_ineq(sol
->context
, ineq
->el
);
3514 res
= isl_tab_row_pos
;
3516 res
= (res
== isl_tab_row_unknown
) ? isl_tab_row_neg
3518 if (res
== isl_tab_row_neg
) {
3519 isl_seq_neg(ineq
->el
, ineq
->el
, ineq
->size
);
3520 isl_int_sub_ui(ineq
->el
[0], ineq
->el
[0], 1);
3524 if (res
== isl_tab_row_neg
) {
3525 /* test for positive values */
3527 if (!critical
&& !strict
)
3528 isl_int_sub_ui(ineq
->el
[0], ineq
->el
[0], 1);
3530 feasible
= sol
->context
->op
->test_ineq(sol
->context
, ineq
->el
);
3534 res
= isl_tab_row_any
;
3541 return isl_tab_row_unknown
;
3544 static void find_solutions(struct isl_sol
*sol
, struct isl_tab
*tab
);
3546 /* Find solutions for values of the parameters that satisfy the given
3549 * We currently take a snapshot of the context tableau that is reset
3550 * when we return from this function, while we make a copy of the main
3551 * tableau, leaving the original main tableau untouched.
3552 * These are fairly arbitrary choices. Making a copy also of the context
3553 * tableau would obviate the need to undo any changes made to it later,
3554 * while taking a snapshot of the main tableau could reduce memory usage.
3555 * If we were to switch to taking a snapshot of the main tableau,
3556 * we would have to keep in mind that we need to save the row signs
3557 * and that we need to do this before saving the current basis
3558 * such that the basis has been restore before we restore the row signs.
3560 static void find_in_pos(struct isl_sol
*sol
, struct isl_tab
*tab
, isl_int
*ineq
)
3566 saved
= sol
->context
->op
->save(sol
->context
);
3568 tab
= isl_tab_dup(tab
);
3572 sol
->context
->op
->add_ineq(sol
->context
, ineq
, 0, 1);
3574 find_solutions(sol
, tab
);
3577 sol
->context
->op
->restore(sol
->context
, saved
);
3579 sol
->context
->op
->discard(saved
);
3585 /* Record the absence of solutions for those values of the parameters
3586 * that do not satisfy the given inequality with equality.
3588 static void no_sol_in_strict(struct isl_sol
*sol
,
3589 struct isl_tab
*tab
, struct isl_vec
*ineq
)
3594 if (!sol
->context
|| sol
->error
)
3596 saved
= sol
->context
->op
->save(sol
->context
);
3598 isl_int_sub_ui(ineq
->el
[0], ineq
->el
[0], 1);
3600 sol
->context
->op
->add_ineq(sol
->context
, ineq
->el
, 1, 0);
3609 isl_int_add_ui(ineq
->el
[0], ineq
->el
[0], 1);
3611 sol
->context
->op
->restore(sol
->context
, saved
);
3617 /* Compute the lexicographic minimum of the set represented by the main
3618 * tableau "tab" within the context "sol->context_tab".
3619 * On entry the sample value of the main tableau is lexicographically
3620 * less than or equal to this lexicographic minimum.
3621 * Pivots are performed until a feasible point is found, which is then
3622 * necessarily equal to the minimum, or until the tableau is found to
3623 * be infeasible. Some pivots may need to be performed for only some
3624 * feasible values of the context tableau. If so, the context tableau
3625 * is split into a part where the pivot is needed and a part where it is not.
3627 * Whenever we enter the main loop, the main tableau is such that no
3628 * "obvious" pivots need to be performed on it, where "obvious" means
3629 * that the given row can be seen to be negative without looking at
3630 * the context tableau. In particular, for non-parametric problems,
3631 * no pivots need to be performed on the main tableau.
3632 * The caller of find_solutions is responsible for making this property
3633 * hold prior to the first iteration of the loop, while restore_lexmin
3634 * is called before every other iteration.
3636 * Inside the main loop, we first examine the signs of the rows of
3637 * the main tableau within the context of the context tableau.
3638 * If we find a row that is always non-positive for all values of
3639 * the parameters satisfying the context tableau and negative for at
3640 * least one value of the parameters, we perform the appropriate pivot
3641 * and start over. An exception is the case where no pivot can be
3642 * performed on the row. In this case, we require that the sign of
3643 * the row is negative for all values of the parameters (rather than just
3644 * non-positive). This special case is handled inside row_sign, which
3645 * will say that the row can have any sign if it determines that it can
3646 * attain both negative and zero values.
3648 * If we can't find a row that always requires a pivot, but we can find
3649 * one or more rows that require a pivot for some values of the parameters
3650 * (i.e., the row can attain both positive and negative signs), then we split
3651 * the context tableau into two parts, one where we force the sign to be
3652 * non-negative and one where we force is to be negative.
3653 * The non-negative part is handled by a recursive call (through find_in_pos).
3654 * Upon returning from this call, we continue with the negative part and
3655 * perform the required pivot.
3657 * If no such rows can be found, all rows are non-negative and we have
3658 * found a (rational) feasible point. If we only wanted a rational point
3660 * Otherwise, we check if all values of the sample point of the tableau
3661 * are integral for the variables. If so, we have found the minimal
3662 * integral point and we are done.
3663 * If the sample point is not integral, then we need to make a distinction
3664 * based on whether the constant term is non-integral or the coefficients
3665 * of the parameters. Furthermore, in order to decide how to handle
3666 * the non-integrality, we also need to know whether the coefficients
3667 * of the other columns in the tableau are integral. This leads
3668 * to the following table. The first two rows do not correspond
3669 * to a non-integral sample point and are only mentioned for completeness.
3671 * constant parameters other
3674 * int int rat | -> no problem
3676 * rat int int -> fail
3678 * rat int rat -> cut
3681 * rat rat rat | -> parametric cut
3684 * rat rat int | -> split context
3686 * If the parametric constant is completely integral, then there is nothing
3687 * to be done. If the constant term is non-integral, but all the other
3688 * coefficient are integral, then there is nothing that can be done
3689 * and the tableau has no integral solution.
3690 * If, on the other hand, one or more of the other columns have rational
3691 * coefficients, but the parameter coefficients are all integral, then
3692 * we can perform a regular (non-parametric) cut.
3693 * Finally, if there is any parameter coefficient that is non-integral,
3694 * then we need to involve the context tableau. There are two cases here.
3695 * If at least one other column has a rational coefficient, then we
3696 * can perform a parametric cut in the main tableau by adding a new
3697 * integer division in the context tableau.
3698 * If all other columns have integral coefficients, then we need to
3699 * enforce that the rational combination of parameters (c + \sum a_i y_i)/m
3700 * is always integral. We do this by introducing an integer division
3701 * q = floor((c + \sum a_i y_i)/m) and stipulating that its argument should
3702 * always be integral in the context tableau, i.e., m q = c + \sum a_i y_i.
3703 * Since q is expressed in the tableau as
3704 * c + \sum a_i y_i - m q >= 0
3705 * -c - \sum a_i y_i + m q + m - 1 >= 0
3706 * it is sufficient to add the inequality
3707 * -c - \sum a_i y_i + m q >= 0
3708 * In the part of the context where this inequality does not hold, the
3709 * main tableau is marked as being empty.
3711 static void find_solutions(struct isl_sol
*sol
, struct isl_tab
*tab
)
3713 struct isl_context
*context
;
3716 if (!tab
|| sol
->error
)
3719 context
= sol
->context
;
3723 if (context
->op
->is_empty(context
))
3726 for (r
= 0; r
>= 0 && tab
&& !tab
->empty
; r
= restore_lexmin(tab
)) {
3729 enum isl_tab_row_sign sgn
;
3733 for (row
= tab
->n_redundant
; row
< tab
->n_row
; ++row
) {
3734 if (!isl_tab_var_from_row(tab
, row
)->is_nonneg
)
3736 sgn
= row_sign(tab
, sol
, row
);
3739 tab
->row_sign
[row
] = sgn
;
3740 if (sgn
== isl_tab_row_any
)
3742 if (sgn
== isl_tab_row_any
&& split
== -1)
3744 if (sgn
== isl_tab_row_neg
)
3747 if (row
< tab
->n_row
)
3750 struct isl_vec
*ineq
;
3752 split
= context
->op
->best_split(context
, tab
);
3755 ineq
= get_row_parameter_ineq(tab
, split
);
3759 for (row
= tab
->n_redundant
; row
< tab
->n_row
; ++row
) {
3760 if (!isl_tab_var_from_row(tab
, row
)->is_nonneg
)
3762 if (tab
->row_sign
[row
] == isl_tab_row_any
)
3763 tab
->row_sign
[row
] = isl_tab_row_unknown
;
3765 tab
->row_sign
[split
] = isl_tab_row_pos
;
3767 find_in_pos(sol
, tab
, ineq
->el
);
3768 tab
->row_sign
[split
] = isl_tab_row_neg
;
3770 isl_seq_neg(ineq
->el
, ineq
->el
, ineq
->size
);
3771 isl_int_sub_ui(ineq
->el
[0], ineq
->el
[0], 1);
3773 context
->op
->add_ineq(context
, ineq
->el
, 0, 1);
3781 row
= first_non_integer_row(tab
, &flags
);
3784 if (ISL_FL_ISSET(flags
, I_PAR
)) {
3785 if (ISL_FL_ISSET(flags
, I_VAR
)) {
3786 if (isl_tab_mark_empty(tab
) < 0)
3790 row
= add_cut(tab
, row
);
3791 } else if (ISL_FL_ISSET(flags
, I_VAR
)) {
3792 struct isl_vec
*div
;
3793 struct isl_vec
*ineq
;
3795 div
= get_row_split_div(tab
, row
);
3798 d
= context
->op
->get_div(context
, tab
, div
);
3802 ineq
= ineq_for_div(context
->op
->peek_basic_set(context
), d
);
3806 no_sol_in_strict(sol
, tab
, ineq
);
3807 isl_seq_neg(ineq
->el
, ineq
->el
, ineq
->size
);
3808 context
->op
->add_ineq(context
, ineq
->el
, 1, 1);
3810 if (sol
->error
|| !context
->op
->is_ok(context
))
3812 tab
= set_row_cst_to_div(tab
, row
, d
);
3813 if (context
->op
->is_empty(context
))
3816 row
= add_parametric_cut(tab
, row
, context
);
3831 /* Compute the lexicographic minimum of the set represented by the main
3832 * tableau "tab" within the context "sol->context_tab".
3834 * As a preprocessing step, we first transfer all the purely parametric
3835 * equalities from the main tableau to the context tableau, i.e.,
3836 * parameters that have been pivoted to a row.
3837 * These equalities are ignored by the main algorithm, because the
3838 * corresponding rows may not be marked as being non-negative.
3839 * In parts of the context where the added equality does not hold,
3840 * the main tableau is marked as being empty.
3842 static void find_solutions_main(struct isl_sol
*sol
, struct isl_tab
*tab
)
3851 for (row
= tab
->n_redundant
; row
< tab
->n_row
; ++row
) {
3855 if (tab
->row_var
[row
] < 0)
3857 if (tab
->row_var
[row
] >= tab
->n_param
&&
3858 tab
->row_var
[row
] < tab
->n_var
- tab
->n_div
)
3860 if (tab
->row_var
[row
] < tab
->n_param
)
3861 p
= tab
->row_var
[row
];
3863 p
= tab
->row_var
[row
]
3864 + tab
->n_param
- (tab
->n_var
- tab
->n_div
);
3866 eq
= isl_vec_alloc(tab
->mat
->ctx
, 1+tab
->n_param
+tab
->n_div
);
3869 get_row_parameter_line(tab
, row
, eq
->el
);
3870 isl_int_neg(eq
->el
[1 + p
], tab
->mat
->row
[row
][0]);
3871 eq
= isl_vec_normalize(eq
);
3874 no_sol_in_strict(sol
, tab
, eq
);
3876 isl_seq_neg(eq
->el
, eq
->el
, eq
->size
);
3878 no_sol_in_strict(sol
, tab
, eq
);
3879 isl_seq_neg(eq
->el
, eq
->el
, eq
->size
);
3881 sol
->context
->op
->add_eq(sol
->context
, eq
->el
, 1, 1);
3885 if (isl_tab_mark_redundant(tab
, row
) < 0)
3888 if (sol
->context
->op
->is_empty(sol
->context
))
3891 row
= tab
->n_redundant
- 1;
3894 find_solutions(sol
, tab
);
3905 /* Check if integer division "div" of "dom" also occurs in "bmap".
3906 * If so, return its position within the divs.
3907 * If not, return -1.
3909 static int find_context_div(struct isl_basic_map
*bmap
,
3910 struct isl_basic_set
*dom
, unsigned div
)
3913 unsigned b_dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
3914 unsigned d_dim
= isl_space_dim(dom
->dim
, isl_dim_all
);
3916 if (isl_int_is_zero(dom
->div
[div
][0]))
3918 if (isl_seq_first_non_zero(dom
->div
[div
] + 2 + d_dim
, dom
->n_div
) != -1)
3921 for (i
= 0; i
< bmap
->n_div
; ++i
) {
3922 if (isl_int_is_zero(bmap
->div
[i
][0]))
3924 if (isl_seq_first_non_zero(bmap
->div
[i
] + 2 + d_dim
,
3925 (b_dim
- d_dim
) + bmap
->n_div
) != -1)
3927 if (isl_seq_eq(bmap
->div
[i
], dom
->div
[div
], 2 + d_dim
))
3933 /* The correspondence between the variables in the main tableau,
3934 * the context tableau, and the input map and domain is as follows.
3935 * The first n_param and the last n_div variables of the main tableau
3936 * form the variables of the context tableau.
3937 * In the basic map, these n_param variables correspond to the
3938 * parameters and the input dimensions. In the domain, they correspond
3939 * to the parameters and the set dimensions.
3940 * The n_div variables correspond to the integer divisions in the domain.
3941 * To ensure that everything lines up, we may need to copy some of the
3942 * integer divisions of the domain to the map. These have to be placed
3943 * in the same order as those in the context and they have to be placed
3944 * after any other integer divisions that the map may have.
3945 * This function performs the required reordering.
3947 static struct isl_basic_map
*align_context_divs(struct isl_basic_map
*bmap
,
3948 struct isl_basic_set
*dom
)
3954 for (i
= 0; i
< dom
->n_div
; ++i
)
3955 if (find_context_div(bmap
, dom
, i
) != -1)
3957 other
= bmap
->n_div
- common
;
3958 if (dom
->n_div
- common
> 0) {
3959 bmap
= isl_basic_map_extend_space(bmap
, isl_space_copy(bmap
->dim
),
3960 dom
->n_div
- common
, 0, 0);
3964 for (i
= 0; i
< dom
->n_div
; ++i
) {
3965 int pos
= find_context_div(bmap
, dom
, i
);
3967 pos
= isl_basic_map_alloc_div(bmap
);
3970 isl_int_set_si(bmap
->div
[pos
][0], 0);
3972 if (pos
!= other
+ i
)
3973 isl_basic_map_swap_div(bmap
, pos
, other
+ i
);
3977 isl_basic_map_free(bmap
);
3981 /* Base case of isl_tab_basic_map_partial_lexopt, after removing
3982 * some obvious symmetries.
3984 * We make sure the divs in the domain are properly ordered,
3985 * because they will be added one by one in the given order
3986 * during the construction of the solution map.
3988 static struct isl_sol
*basic_map_partial_lexopt_base(
3989 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_set
*dom
,
3990 __isl_give isl_set
**empty
, int max
,
3991 struct isl_sol
*(*init
)(__isl_keep isl_basic_map
*bmap
,
3992 __isl_take isl_basic_set
*dom
, int track_empty
, int max
))
3994 struct isl_tab
*tab
;
3995 struct isl_sol
*sol
= NULL
;
3996 struct isl_context
*context
;
3999 dom
= isl_basic_set_order_divs(dom
);
4000 bmap
= align_context_divs(bmap
, dom
);
4002 sol
= init(bmap
, dom
, !!empty
, max
);
4006 context
= sol
->context
;
4007 if (isl_basic_set_plain_is_empty(context
->op
->peek_basic_set(context
)))
4009 else if (isl_basic_map_plain_is_empty(bmap
)) {
4012 isl_basic_set_copy(context
->op
->peek_basic_set(context
)));
4014 tab
= tab_for_lexmin(bmap
,
4015 context
->op
->peek_basic_set(context
), 1, max
);
4016 tab
= context
->op
->detect_nonnegative_parameters(context
, tab
);
4017 find_solutions_main(sol
, tab
);
4022 isl_basic_map_free(bmap
);
4026 isl_basic_map_free(bmap
);
4030 /* Base case of isl_tab_basic_map_partial_lexopt, after removing
4031 * some obvious symmetries.
4033 * We call basic_map_partial_lexopt_base and extract the results.
4035 static __isl_give isl_map
*basic_map_partial_lexopt_base_map(
4036 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_set
*dom
,
4037 __isl_give isl_set
**empty
, int max
)
4039 isl_map
*result
= NULL
;
4040 struct isl_sol
*sol
;
4041 struct isl_sol_map
*sol_map
;
4043 sol
= basic_map_partial_lexopt_base(bmap
, dom
, empty
, max
,
4047 sol_map
= (struct isl_sol_map
*) sol
;
4049 result
= isl_map_copy(sol_map
->map
);
4051 *empty
= isl_set_copy(sol_map
->empty
);
4052 sol_free(&sol_map
->sol
);
4056 /* Structure used during detection of parallel constraints.
4057 * n_in: number of "input" variables: isl_dim_param + isl_dim_in
4058 * n_out: number of "output" variables: isl_dim_out + isl_dim_div
4059 * val: the coefficients of the output variables
4061 struct isl_constraint_equal_info
{
4062 isl_basic_map
*bmap
;
4068 /* Check whether the coefficients of the output variables
4069 * of the constraint in "entry" are equal to info->val.
4071 static int constraint_equal(const void *entry
, const void *val
)
4073 isl_int
**row
= (isl_int
**)entry
;
4074 const struct isl_constraint_equal_info
*info
= val
;
4076 return isl_seq_eq((*row
) + 1 + info
->n_in
, info
->val
, info
->n_out
);
4079 /* Check whether "bmap" has a pair of constraints that have
4080 * the same coefficients for the output variables.
4081 * Note that the coefficients of the existentially quantified
4082 * variables need to be zero since the existentially quantified
4083 * of the result are usually not the same as those of the input.
4084 * the isl_dim_out and isl_dim_div dimensions.
4085 * If so, return 1 and return the row indices of the two constraints
4086 * in *first and *second.
4088 static int parallel_constraints(__isl_keep isl_basic_map
*bmap
,
4089 int *first
, int *second
)
4092 isl_ctx
*ctx
= isl_basic_map_get_ctx(bmap
);
4093 struct isl_hash_table
*table
= NULL
;
4094 struct isl_hash_table_entry
*entry
;
4095 struct isl_constraint_equal_info info
;
4099 ctx
= isl_basic_map_get_ctx(bmap
);
4100 table
= isl_hash_table_alloc(ctx
, bmap
->n_ineq
);
4104 info
.n_in
= isl_basic_map_dim(bmap
, isl_dim_param
) +
4105 isl_basic_map_dim(bmap
, isl_dim_in
);
4107 n_out
= isl_basic_map_dim(bmap
, isl_dim_out
);
4108 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
4109 info
.n_out
= n_out
+ n_div
;
4110 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
4113 info
.val
= bmap
->ineq
[i
] + 1 + info
.n_in
;
4114 if (isl_seq_first_non_zero(info
.val
, n_out
) < 0)
4116 if (isl_seq_first_non_zero(info
.val
+ n_out
, n_div
) >= 0)
4118 hash
= isl_seq_get_hash(info
.val
, info
.n_out
);
4119 entry
= isl_hash_table_find(ctx
, table
, hash
,
4120 constraint_equal
, &info
, 1);
4125 entry
->data
= &bmap
->ineq
[i
];
4128 if (i
< bmap
->n_ineq
) {
4129 *first
= ((isl_int
**)entry
->data
) - bmap
->ineq
;
4133 isl_hash_table_free(ctx
, table
);
4135 return i
< bmap
->n_ineq
;
4137 isl_hash_table_free(ctx
, table
);
4141 /* Given a set of upper bounds in "var", add constraints to "bset"
4142 * that make the i-th bound smallest.
4144 * In particular, if there are n bounds b_i, then add the constraints
4146 * b_i <= b_j for j > i
4147 * b_i < b_j for j < i
4149 static __isl_give isl_basic_set
*select_minimum(__isl_take isl_basic_set
*bset
,
4150 __isl_keep isl_mat
*var
, int i
)
4155 ctx
= isl_mat_get_ctx(var
);
4157 for (j
= 0; j
< var
->n_row
; ++j
) {
4160 k
= isl_basic_set_alloc_inequality(bset
);
4163 isl_seq_combine(bset
->ineq
[k
], ctx
->one
, var
->row
[j
],
4164 ctx
->negone
, var
->row
[i
], var
->n_col
);
4165 isl_int_set_si(bset
->ineq
[k
][var
->n_col
], 0);
4167 isl_int_sub_ui(bset
->ineq
[k
][0], bset
->ineq
[k
][0], 1);
4170 bset
= isl_basic_set_finalize(bset
);
4174 isl_basic_set_free(bset
);
4178 /* Given a set of upper bounds on the last "input" variable m,
4179 * construct a set that assigns the minimal upper bound to m, i.e.,
4180 * construct a set that divides the space into cells where one
4181 * of the upper bounds is smaller than all the others and assign
4182 * this upper bound to m.
4184 * In particular, if there are n bounds b_i, then the result
4185 * consists of n basic sets, each one of the form
4188 * b_i <= b_j for j > i
4189 * b_i < b_j for j < i
4191 static __isl_give isl_set
*set_minimum(__isl_take isl_space
*dim
,
4192 __isl_take isl_mat
*var
)
4195 isl_basic_set
*bset
= NULL
;
4197 isl_set
*set
= NULL
;
4202 ctx
= isl_space_get_ctx(dim
);
4203 set
= isl_set_alloc_space(isl_space_copy(dim
),
4204 var
->n_row
, ISL_SET_DISJOINT
);
4206 for (i
= 0; i
< var
->n_row
; ++i
) {
4207 bset
= isl_basic_set_alloc_space(isl_space_copy(dim
), 0,
4209 k
= isl_basic_set_alloc_equality(bset
);
4212 isl_seq_cpy(bset
->eq
[k
], var
->row
[i
], var
->n_col
);
4213 isl_int_set_si(bset
->eq
[k
][var
->n_col
], -1);
4214 bset
= select_minimum(bset
, var
, i
);
4215 set
= isl_set_add_basic_set(set
, bset
);
4218 isl_space_free(dim
);
4222 isl_basic_set_free(bset
);
4224 isl_space_free(dim
);
4229 /* Given that the last input variable of "bmap" represents the minimum
4230 * of the bounds in "cst", check whether we need to split the domain
4231 * based on which bound attains the minimum.
4233 * A split is needed when the minimum appears in an integer division
4234 * or in an equality. Otherwise, it is only needed if it appears in
4235 * an upper bound that is different from the upper bounds on which it
4238 static int need_split_basic_map(__isl_keep isl_basic_map
*bmap
,
4239 __isl_keep isl_mat
*cst
)
4245 pos
= cst
->n_col
- 1;
4246 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
4248 for (i
= 0; i
< bmap
->n_div
; ++i
)
4249 if (!isl_int_is_zero(bmap
->div
[i
][2 + pos
]))
4252 for (i
= 0; i
< bmap
->n_eq
; ++i
)
4253 if (!isl_int_is_zero(bmap
->eq
[i
][1 + pos
]))
4256 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
4257 if (isl_int_is_nonneg(bmap
->ineq
[i
][1 + pos
]))
4259 if (!isl_int_is_negone(bmap
->ineq
[i
][1 + pos
]))
4261 if (isl_seq_first_non_zero(bmap
->ineq
[i
] + 1 + pos
+ 1,
4262 total
- pos
- 1) >= 0)
4265 for (j
= 0; j
< cst
->n_row
; ++j
)
4266 if (isl_seq_eq(bmap
->ineq
[i
], cst
->row
[j
], cst
->n_col
))
4268 if (j
>= cst
->n_row
)
4275 /* Given that the last set variable of "bset" represents the minimum
4276 * of the bounds in "cst", check whether we need to split the domain
4277 * based on which bound attains the minimum.
4279 * We simply call need_split_basic_map here. This is safe because
4280 * the position of the minimum is computed from "cst" and not
4283 static int need_split_basic_set(__isl_keep isl_basic_set
*bset
,
4284 __isl_keep isl_mat
*cst
)
4286 return need_split_basic_map((isl_basic_map
*)bset
, cst
);
4289 /* Given that the last set variable of "set" represents the minimum
4290 * of the bounds in "cst", check whether we need to split the domain
4291 * based on which bound attains the minimum.
4293 static int need_split_set(__isl_keep isl_set
*set
, __isl_keep isl_mat
*cst
)
4297 for (i
= 0; i
< set
->n
; ++i
)
4298 if (need_split_basic_set(set
->p
[i
], cst
))
4304 /* Given a set of which the last set variable is the minimum
4305 * of the bounds in "cst", split each basic set in the set
4306 * in pieces where one of the bounds is (strictly) smaller than the others.
4307 * This subdivision is given in "min_expr".
4308 * The variable is subsequently projected out.
4310 * We only do the split when it is needed.
4311 * For example if the last input variable m = min(a,b) and the only
4312 * constraints in the given basic set are lower bounds on m,
4313 * i.e., l <= m = min(a,b), then we can simply project out m
4314 * to obtain l <= a and l <= b, without having to split on whether
4315 * m is equal to a or b.
4317 static __isl_give isl_set
*split(__isl_take isl_set
*empty
,
4318 __isl_take isl_set
*min_expr
, __isl_take isl_mat
*cst
)
4325 if (!empty
|| !min_expr
|| !cst
)
4328 n_in
= isl_set_dim(empty
, isl_dim_set
);
4329 dim
= isl_set_get_space(empty
);
4330 dim
= isl_space_drop_dims(dim
, isl_dim_set
, n_in
- 1, 1);
4331 res
= isl_set_empty(dim
);
4333 for (i
= 0; i
< empty
->n
; ++i
) {
4336 set
= isl_set_from_basic_set(isl_basic_set_copy(empty
->p
[i
]));
4337 if (need_split_basic_set(empty
->p
[i
], cst
))
4338 set
= isl_set_intersect(set
, isl_set_copy(min_expr
));
4339 set
= isl_set_remove_dims(set
, isl_dim_set
, n_in
- 1, 1);
4341 res
= isl_set_union_disjoint(res
, set
);
4344 isl_set_free(empty
);
4345 isl_set_free(min_expr
);
4349 isl_set_free(empty
);
4350 isl_set_free(min_expr
);
4355 /* Given a map of which the last input variable is the minimum
4356 * of the bounds in "cst", split each basic set in the set
4357 * in pieces where one of the bounds is (strictly) smaller than the others.
4358 * This subdivision is given in "min_expr".
4359 * The variable is subsequently projected out.
4361 * The implementation is essentially the same as that of "split".
4363 static __isl_give isl_map
*split_domain(__isl_take isl_map
*opt
,
4364 __isl_take isl_set
*min_expr
, __isl_take isl_mat
*cst
)
4371 if (!opt
|| !min_expr
|| !cst
)
4374 n_in
= isl_map_dim(opt
, isl_dim_in
);
4375 dim
= isl_map_get_space(opt
);
4376 dim
= isl_space_drop_dims(dim
, isl_dim_in
, n_in
- 1, 1);
4377 res
= isl_map_empty(dim
);
4379 for (i
= 0; i
< opt
->n
; ++i
) {
4382 map
= isl_map_from_basic_map(isl_basic_map_copy(opt
->p
[i
]));
4383 if (need_split_basic_map(opt
->p
[i
], cst
))
4384 map
= isl_map_intersect_domain(map
,
4385 isl_set_copy(min_expr
));
4386 map
= isl_map_remove_dims(map
, isl_dim_in
, n_in
- 1, 1);
4388 res
= isl_map_union_disjoint(res
, map
);
4392 isl_set_free(min_expr
);
4397 isl_set_free(min_expr
);
4402 static __isl_give isl_map
*basic_map_partial_lexopt(
4403 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_set
*dom
,
4404 __isl_give isl_set
**empty
, int max
);
4409 isl_pw_multi_aff
*pma
;
4412 /* This function is called from basic_map_partial_lexopt_symm.
4413 * The last variable of "bmap" and "dom" corresponds to the minimum
4414 * of the bounds in "cst". "map_space" is the space of the original
4415 * input relation (of basic_map_partial_lexopt_symm) and "set_space"
4416 * is the space of the original domain.
4418 * We recursively call basic_map_partial_lexopt and then plug in
4419 * the definition of the minimum in the result.
4421 static __isl_give
union isl_lex_res
basic_map_partial_lexopt_symm_map_core(
4422 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_set
*dom
,
4423 __isl_give isl_set
**empty
, int max
, __isl_take isl_mat
*cst
,
4424 __isl_take isl_space
*map_space
, __isl_take isl_space
*set_space
)
4428 union isl_lex_res res
;
4430 min_expr
= set_minimum(isl_basic_set_get_space(dom
), isl_mat_copy(cst
));
4432 opt
= basic_map_partial_lexopt(bmap
, dom
, empty
, max
);
4435 *empty
= split(*empty
,
4436 isl_set_copy(min_expr
), isl_mat_copy(cst
));
4437 *empty
= isl_set_reset_space(*empty
, set_space
);
4440 opt
= split_domain(opt
, min_expr
, cst
);
4441 opt
= isl_map_reset_space(opt
, map_space
);
4447 /* Given a basic map with at least two parallel constraints (as found
4448 * by the function parallel_constraints), first look for more constraints
4449 * parallel to the two constraint and replace the found list of parallel
4450 * constraints by a single constraint with as "input" part the minimum
4451 * of the input parts of the list of constraints. Then, recursively call
4452 * basic_map_partial_lexopt (possibly finding more parallel constraints)
4453 * and plug in the definition of the minimum in the result.
4455 * More specifically, given a set of constraints
4459 * Replace this set by a single constraint
4463 * with u a new parameter with constraints
4467 * Any solution to the new system is also a solution for the original system
4470 * a x >= -u >= -b_i(p)
4472 * Moreover, m = min_i(b_i(p)) satisfies the constraints on u and can
4473 * therefore be plugged into the solution.
4475 static union isl_lex_res
basic_map_partial_lexopt_symm(
4476 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_set
*dom
,
4477 __isl_give isl_set
**empty
, int max
, int first
, int second
,
4478 __isl_give
union isl_lex_res (*core
)(__isl_take isl_basic_map
*bmap
,
4479 __isl_take isl_basic_set
*dom
,
4480 __isl_give isl_set
**empty
,
4481 int max
, __isl_take isl_mat
*cst
,
4482 __isl_take isl_space
*map_space
,
4483 __isl_take isl_space
*set_space
))
4487 unsigned n_in
, n_out
, n_div
;
4489 isl_vec
*var
= NULL
;
4490 isl_mat
*cst
= NULL
;
4491 isl_space
*map_space
, *set_space
;
4492 union isl_lex_res res
;
4494 map_space
= isl_basic_map_get_space(bmap
);
4495 set_space
= empty
? isl_basic_set_get_space(dom
) : NULL
;
4497 n_in
= isl_basic_map_dim(bmap
, isl_dim_param
) +
4498 isl_basic_map_dim(bmap
, isl_dim_in
);
4499 n_out
= isl_basic_map_dim(bmap
, isl_dim_all
) - n_in
;
4501 ctx
= isl_basic_map_get_ctx(bmap
);
4502 list
= isl_alloc_array(ctx
, int, bmap
->n_ineq
);
4503 var
= isl_vec_alloc(ctx
, n_out
);
4509 isl_seq_cpy(var
->el
, bmap
->ineq
[first
] + 1 + n_in
, n_out
);
4510 for (i
= second
+ 1, n
= 2; i
< bmap
->n_ineq
; ++i
) {
4511 if (isl_seq_eq(var
->el
, bmap
->ineq
[i
] + 1 + n_in
, n_out
))
4515 cst
= isl_mat_alloc(ctx
, n
, 1 + n_in
);
4519 for (i
= 0; i
< n
; ++i
)
4520 isl_seq_cpy(cst
->row
[i
], bmap
->ineq
[list
[i
]], 1 + n_in
);
4522 bmap
= isl_basic_map_cow(bmap
);
4525 for (i
= n
- 1; i
>= 0; --i
)
4526 if (isl_basic_map_drop_inequality(bmap
, list
[i
]) < 0)
4529 bmap
= isl_basic_map_add(bmap
, isl_dim_in
, 1);
4530 bmap
= isl_basic_map_extend_constraints(bmap
, 0, 1);
4531 k
= isl_basic_map_alloc_inequality(bmap
);
4534 isl_seq_clr(bmap
->ineq
[k
], 1 + n_in
);
4535 isl_int_set_si(bmap
->ineq
[k
][1 + n_in
], 1);
4536 isl_seq_cpy(bmap
->ineq
[k
] + 1 + n_in
+ 1, var
->el
, n_out
);
4537 bmap
= isl_basic_map_finalize(bmap
);
4539 n_div
= isl_basic_set_dim(dom
, isl_dim_div
);
4540 dom
= isl_basic_set_add_dims(dom
, isl_dim_set
, 1);
4541 dom
= isl_basic_set_extend_constraints(dom
, 0, n
);
4542 for (i
= 0; i
< n
; ++i
) {
4543 k
= isl_basic_set_alloc_inequality(dom
);
4546 isl_seq_cpy(dom
->ineq
[k
], cst
->row
[i
], 1 + n_in
);
4547 isl_int_set_si(dom
->ineq
[k
][1 + n_in
], -1);
4548 isl_seq_clr(dom
->ineq
[k
] + 1 + n_in
+ 1, n_div
);
4554 return core(bmap
, dom
, empty
, max
, cst
, map_space
, set_space
);
4556 isl_space_free(map_space
);
4557 isl_space_free(set_space
);
4561 isl_basic_set_free(dom
);
4562 isl_basic_map_free(bmap
);
4567 static __isl_give isl_map
*basic_map_partial_lexopt_symm_map(
4568 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_set
*dom
,
4569 __isl_give isl_set
**empty
, int max
, int first
, int second
)
4571 return basic_map_partial_lexopt_symm(bmap
, dom
, empty
, max
,
4572 first
, second
, &basic_map_partial_lexopt_symm_map_core
).map
;
4575 /* Recursive part of isl_tab_basic_map_partial_lexopt, after detecting
4576 * equalities and removing redundant constraints.
4578 * We first check if there are any parallel constraints (left).
4579 * If not, we are in the base case.
4580 * If there are parallel constraints, we replace them by a single
4581 * constraint in basic_map_partial_lexopt_symm and then call
4582 * this function recursively to look for more parallel constraints.
4584 static __isl_give isl_map
*basic_map_partial_lexopt(
4585 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_set
*dom
,
4586 __isl_give isl_set
**empty
, int max
)
4594 if (bmap
->ctx
->opt
->pip_symmetry
)
4595 par
= parallel_constraints(bmap
, &first
, &second
);
4599 return basic_map_partial_lexopt_base_map(bmap
, dom
, empty
, max
);
4601 return basic_map_partial_lexopt_symm_map(bmap
, dom
, empty
, max
,
4604 isl_basic_set_free(dom
);
4605 isl_basic_map_free(bmap
);
4609 /* Compute the lexicographic minimum (or maximum if "max" is set)
4610 * of "bmap" over the domain "dom" and return the result as a map.
4611 * If "empty" is not NULL, then *empty is assigned a set that
4612 * contains those parts of the domain where there is no solution.
4613 * If "bmap" is marked as rational (ISL_BASIC_MAP_RATIONAL),
4614 * then we compute the rational optimum. Otherwise, we compute
4615 * the integral optimum.
4617 * We perform some preprocessing. As the PILP solver does not
4618 * handle implicit equalities very well, we first make sure all
4619 * the equalities are explicitly available.
4621 * We also add context constraints to the basic map and remove
4622 * redundant constraints. This is only needed because of the
4623 * way we handle simple symmetries. In particular, we currently look
4624 * for symmetries on the constraints, before we set up the main tableau.
4625 * It is then no good to look for symmetries on possibly redundant constraints.
4627 struct isl_map
*isl_tab_basic_map_partial_lexopt(
4628 struct isl_basic_map
*bmap
, struct isl_basic_set
*dom
,
4629 struct isl_set
**empty
, int max
)
4636 isl_assert(bmap
->ctx
,
4637 isl_basic_map_compatible_domain(bmap
, dom
), goto error
);
4639 if (isl_basic_set_dim(dom
, isl_dim_all
) == 0)
4640 return basic_map_partial_lexopt(bmap
, dom
, empty
, max
);
4642 bmap
= isl_basic_map_intersect_domain(bmap
, isl_basic_set_copy(dom
));
4643 bmap
= isl_basic_map_detect_equalities(bmap
);
4644 bmap
= isl_basic_map_remove_redundancies(bmap
);
4646 return basic_map_partial_lexopt(bmap
, dom
, empty
, max
);
4648 isl_basic_set_free(dom
);
4649 isl_basic_map_free(bmap
);
4653 struct isl_sol_for
{
4655 int (*fn
)(__isl_take isl_basic_set
*dom
,
4656 __isl_take isl_aff_list
*list
, void *user
);
4660 static void sol_for_free(struct isl_sol_for
*sol_for
)
4662 if (sol_for
->sol
.context
)
4663 sol_for
->sol
.context
->op
->free(sol_for
->sol
.context
);
4667 static void sol_for_free_wrap(struct isl_sol
*sol
)
4669 sol_for_free((struct isl_sol_for
*)sol
);
4672 /* Add the solution identified by the tableau and the context tableau.
4674 * See documentation of sol_add for more details.
4676 * Instead of constructing a basic map, this function calls a user
4677 * defined function with the current context as a basic set and
4678 * a list of affine expressions representing the relation between
4679 * the input and output. The space over which the affine expressions
4680 * are defined is the same as that of the domain. The number of
4681 * affine expressions in the list is equal to the number of output variables.
4683 static void sol_for_add(struct isl_sol_for
*sol
,
4684 struct isl_basic_set
*dom
, struct isl_mat
*M
)
4688 isl_local_space
*ls
;
4692 if (sol
->sol
.error
|| !dom
|| !M
)
4695 ctx
= isl_basic_set_get_ctx(dom
);
4696 ls
= isl_basic_set_get_local_space(dom
);
4697 list
= isl_aff_list_alloc(ctx
, M
->n_row
- 1);
4698 for (i
= 1; i
< M
->n_row
; ++i
) {
4699 aff
= isl_aff_alloc(isl_local_space_copy(ls
));
4701 isl_int_set(aff
->v
->el
[0], M
->row
[0][0]);
4702 isl_seq_cpy(aff
->v
->el
+ 1, M
->row
[i
], M
->n_col
);
4704 aff
= isl_aff_normalize(aff
);
4705 list
= isl_aff_list_add(list
, aff
);
4707 isl_local_space_free(ls
);
4709 dom
= isl_basic_set_finalize(dom
);
4711 if (sol
->fn(isl_basic_set_copy(dom
), list
, sol
->user
) < 0)
4714 isl_basic_set_free(dom
);
4718 isl_basic_set_free(dom
);
4723 static void sol_for_add_wrap(struct isl_sol
*sol
,
4724 struct isl_basic_set
*dom
, struct isl_mat
*M
)
4726 sol_for_add((struct isl_sol_for
*)sol
, dom
, M
);
4729 static struct isl_sol_for
*sol_for_init(struct isl_basic_map
*bmap
, int max
,
4730 int (*fn
)(__isl_take isl_basic_set
*dom
, __isl_take isl_aff_list
*list
,
4734 struct isl_sol_for
*sol_for
= NULL
;
4736 struct isl_basic_set
*dom
= NULL
;
4738 sol_for
= isl_calloc_type(bmap
->ctx
, struct isl_sol_for
);
4742 dom_dim
= isl_space_domain(isl_space_copy(bmap
->dim
));
4743 dom
= isl_basic_set_universe(dom_dim
);
4745 sol_for
->sol
.rational
= ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
);
4746 sol_for
->sol
.dec_level
.callback
.run
= &sol_dec_level_wrap
;
4747 sol_for
->sol
.dec_level
.sol
= &sol_for
->sol
;
4749 sol_for
->user
= user
;
4750 sol_for
->sol
.max
= max
;
4751 sol_for
->sol
.n_out
= isl_basic_map_dim(bmap
, isl_dim_out
);
4752 sol_for
->sol
.add
= &sol_for_add_wrap
;
4753 sol_for
->sol
.add_empty
= NULL
;
4754 sol_for
->sol
.free
= &sol_for_free_wrap
;
4756 sol_for
->sol
.context
= isl_context_alloc(dom
);
4757 if (!sol_for
->sol
.context
)
4760 isl_basic_set_free(dom
);
4763 isl_basic_set_free(dom
);
4764 sol_for_free(sol_for
);
4768 static void sol_for_find_solutions(struct isl_sol_for
*sol_for
,
4769 struct isl_tab
*tab
)
4771 find_solutions_main(&sol_for
->sol
, tab
);
4774 int isl_basic_map_foreach_lexopt(__isl_keep isl_basic_map
*bmap
, int max
,
4775 int (*fn
)(__isl_take isl_basic_set
*dom
, __isl_take isl_aff_list
*list
,
4779 struct isl_sol_for
*sol_for
= NULL
;
4781 bmap
= isl_basic_map_copy(bmap
);
4785 bmap
= isl_basic_map_detect_equalities(bmap
);
4786 sol_for
= sol_for_init(bmap
, max
, fn
, user
);
4788 if (isl_basic_map_plain_is_empty(bmap
))
4791 struct isl_tab
*tab
;
4792 struct isl_context
*context
= sol_for
->sol
.context
;
4793 tab
= tab_for_lexmin(bmap
,
4794 context
->op
->peek_basic_set(context
), 1, max
);
4795 tab
= context
->op
->detect_nonnegative_parameters(context
, tab
);
4796 sol_for_find_solutions(sol_for
, tab
);
4797 if (sol_for
->sol
.error
)
4801 sol_free(&sol_for
->sol
);
4802 isl_basic_map_free(bmap
);
4805 sol_free(&sol_for
->sol
);
4806 isl_basic_map_free(bmap
);
4810 int isl_basic_set_foreach_lexopt(__isl_keep isl_basic_set
*bset
, int max
,
4811 int (*fn
)(__isl_take isl_basic_set
*dom
, __isl_take isl_aff_list
*list
,
4815 return isl_basic_map_foreach_lexopt(bset
, max
, fn
, user
);
4818 /* Check if the given sequence of len variables starting at pos
4819 * represents a trivial (i.e., zero) solution.
4820 * The variables are assumed to be non-negative and to come in pairs,
4821 * with each pair representing a variable of unrestricted sign.
4822 * The solution is trivial if each such pair in the sequence consists
4823 * of two identical values, meaning that the variable being represented
4826 static int region_is_trivial(struct isl_tab
*tab
, int pos
, int len
)
4833 for (i
= 0; i
< len
; i
+= 2) {
4837 neg_row
= tab
->var
[pos
+ i
].is_row
?
4838 tab
->var
[pos
+ i
].index
: -1;
4839 pos_row
= tab
->var
[pos
+ i
+ 1].is_row
?
4840 tab
->var
[pos
+ i
+ 1].index
: -1;
4843 isl_int_is_zero(tab
->mat
->row
[neg_row
][1])) &&
4845 isl_int_is_zero(tab
->mat
->row
[pos_row
][1])))
4848 if (neg_row
< 0 || pos_row
< 0)
4850 if (isl_int_ne(tab
->mat
->row
[neg_row
][1],
4851 tab
->mat
->row
[pos_row
][1]))
4858 /* Return the index of the first trivial region or -1 if all regions
4861 static int first_trivial_region(struct isl_tab
*tab
,
4862 int n_region
, struct isl_region
*region
)
4866 for (i
= 0; i
< n_region
; ++i
) {
4867 if (region_is_trivial(tab
, region
[i
].pos
, region
[i
].len
))
4874 /* Check if the solution is optimal, i.e., whether the first
4875 * n_op entries are zero.
4877 static int is_optimal(__isl_keep isl_vec
*sol
, int n_op
)
4881 for (i
= 0; i
< n_op
; ++i
)
4882 if (!isl_int_is_zero(sol
->el
[1 + i
]))
4887 /* Add constraints to "tab" that ensure that any solution is significantly
4888 * better that that represented by "sol". That is, find the first
4889 * relevant (within first n_op) non-zero coefficient and force it (along
4890 * with all previous coefficients) to be zero.
4891 * If the solution is already optimal (all relevant coefficients are zero),
4892 * then just mark the table as empty.
4894 static int force_better_solution(struct isl_tab
*tab
,
4895 __isl_keep isl_vec
*sol
, int n_op
)
4904 for (i
= 0; i
< n_op
; ++i
)
4905 if (!isl_int_is_zero(sol
->el
[1 + i
]))
4909 if (isl_tab_mark_empty(tab
) < 0)
4914 ctx
= isl_vec_get_ctx(sol
);
4915 v
= isl_vec_alloc(ctx
, 1 + tab
->n_var
);
4919 for (; i
>= 0; --i
) {
4921 isl_int_set_si(v
->el
[1 + i
], -1);
4922 if (add_lexmin_eq(tab
, v
->el
) < 0)
4933 struct isl_trivial
{
4937 struct isl_tab_undo
*snap
;
4940 /* Return the lexicographically smallest non-trivial solution of the
4941 * given ILP problem.
4943 * All variables are assumed to be non-negative.
4945 * n_op is the number of initial coordinates to optimize.
4946 * That is, once a solution has been found, we will only continue looking
4947 * for solution that result in significantly better values for those
4948 * initial coordinates. That is, we only continue looking for solutions
4949 * that increase the number of initial zeros in this sequence.
4951 * A solution is non-trivial, if it is non-trivial on each of the
4952 * specified regions. Each region represents a sequence of pairs
4953 * of variables. A solution is non-trivial on such a region if
4954 * at least one of these pairs consists of different values, i.e.,
4955 * such that the non-negative variable represented by the pair is non-zero.
4957 * Whenever a conflict is encountered, all constraints involved are
4958 * reported to the caller through a call to "conflict".
4960 * We perform a simple branch-and-bound backtracking search.
4961 * Each level in the search represents initially trivial region that is forced
4962 * to be non-trivial.
4963 * At each level we consider n cases, where n is the length of the region.
4964 * In terms of the n/2 variables of unrestricted signs being encoded by
4965 * the region, we consider the cases
4968 * x_0 = 0 and x_1 >= 1
4969 * x_0 = 0 and x_1 <= -1
4970 * x_0 = 0 and x_1 = 0 and x_2 >= 1
4971 * x_0 = 0 and x_1 = 0 and x_2 <= -1
4973 * The cases are considered in this order, assuming that each pair
4974 * x_i_a x_i_b represents the value x_i_b - x_i_a.
4975 * That is, x_0 >= 1 is enforced by adding the constraint
4976 * x_0_b - x_0_a >= 1
4978 __isl_give isl_vec
*isl_tab_basic_set_non_trivial_lexmin(
4979 __isl_take isl_basic_set
*bset
, int n_op
, int n_region
,
4980 struct isl_region
*region
,
4981 int (*conflict
)(int con
, void *user
), void *user
)
4985 isl_ctx
*ctx
= isl_basic_set_get_ctx(bset
);
4987 isl_vec
*sol
= isl_vec_alloc(ctx
, 0);
4988 struct isl_tab
*tab
;
4989 struct isl_trivial
*triv
= NULL
;
4992 tab
= tab_for_lexmin(bset
, NULL
, 0, 0);
4995 tab
->conflict
= conflict
;
4996 tab
->conflict_user
= user
;
4998 v
= isl_vec_alloc(ctx
, 1 + tab
->n_var
);
4999 triv
= isl_calloc_array(ctx
, struct isl_trivial
, n_region
);
5006 while (level
>= 0) {
5010 tab
= cut_to_integer_lexmin(tab
, CUT_ONE
);
5015 r
= first_trivial_region(tab
, n_region
, region
);
5017 for (i
= 0; i
< level
; ++i
)
5020 sol
= isl_tab_get_sample_value(tab
);
5023 if (is_optimal(sol
, n_op
))
5027 if (level
>= n_region
)
5028 isl_die(ctx
, isl_error_internal
,
5029 "nesting level too deep", goto error
);
5030 if (isl_tab_extend_cons(tab
,
5031 2 * region
[r
].len
+ 2 * n_op
) < 0)
5033 triv
[level
].region
= r
;
5034 triv
[level
].side
= 0;
5037 r
= triv
[level
].region
;
5038 side
= triv
[level
].side
;
5039 base
= 2 * (side
/2);
5041 if (side
>= region
[r
].len
) {
5046 if (isl_tab_rollback(tab
, triv
[level
].snap
) < 0)
5051 if (triv
[level
].update
) {
5052 if (force_better_solution(tab
, sol
, n_op
) < 0)
5054 triv
[level
].update
= 0;
5057 if (side
== base
&& base
>= 2) {
5058 for (j
= base
- 2; j
< base
; ++j
) {
5060 isl_int_set_si(v
->el
[1 + region
[r
].pos
+ j
], 1);
5061 if (add_lexmin_eq(tab
, v
->el
) < 0)
5066 triv
[level
].snap
= isl_tab_snap(tab
);
5067 if (isl_tab_push_basis(tab
) < 0)
5071 isl_int_set_si(v
->el
[0], -1);
5072 isl_int_set_si(v
->el
[1 + region
[r
].pos
+ side
], -1);
5073 isl_int_set_si(v
->el
[1 + region
[r
].pos
+ (side
^ 1)], 1);
5074 tab
= add_lexmin_ineq(tab
, v
->el
);
5084 isl_basic_set_free(bset
);
5091 isl_basic_set_free(bset
);
5096 /* Return the lexicographically smallest rational point in "bset",
5097 * assuming that all variables are non-negative.
5098 * If "bset" is empty, then return a zero-length vector.
5100 __isl_give isl_vec
*isl_tab_basic_set_non_neg_lexmin(
5101 __isl_take isl_basic_set
*bset
)
5103 struct isl_tab
*tab
;
5104 isl_ctx
*ctx
= isl_basic_set_get_ctx(bset
);
5107 tab
= tab_for_lexmin(bset
, NULL
, 0, 0);
5111 sol
= isl_vec_alloc(ctx
, 0);
5113 sol
= isl_tab_get_sample_value(tab
);
5115 isl_basic_set_free(bset
);
5119 isl_basic_set_free(bset
);
5123 struct isl_sol_pma
{
5125 isl_pw_multi_aff
*pma
;
5129 static void sol_pma_free(struct isl_sol_pma
*sol_pma
)
5133 if (sol_pma
->sol
.context
)
5134 sol_pma
->sol
.context
->op
->free(sol_pma
->sol
.context
);
5135 isl_pw_multi_aff_free(sol_pma
->pma
);
5136 isl_set_free(sol_pma
->empty
);
5140 /* This function is called for parts of the context where there is
5141 * no solution, with "bset" corresponding to the context tableau.
5142 * Simply add the basic set to the set "empty".
5144 static void sol_pma_add_empty(struct isl_sol_pma
*sol
,
5145 __isl_take isl_basic_set
*bset
)
5149 isl_assert(bset
->ctx
, sol
->empty
, goto error
);
5151 sol
->empty
= isl_set_grow(sol
->empty
, 1);
5152 bset
= isl_basic_set_simplify(bset
);
5153 bset
= isl_basic_set_finalize(bset
);
5154 sol
->empty
= isl_set_add_basic_set(sol
->empty
, bset
);
5159 isl_basic_set_free(bset
);
5163 /* Given a basic map "dom" that represents the context and an affine
5164 * matrix "M" that maps the dimensions of the context to the
5165 * output variables, construct an isl_pw_multi_aff with a single
5166 * cell corresponding to "dom" and affine expressions copied from "M".
5168 static void sol_pma_add(struct isl_sol_pma
*sol
,
5169 __isl_take isl_basic_set
*dom
, __isl_take isl_mat
*M
)
5172 isl_local_space
*ls
;
5174 isl_multi_aff
*maff
;
5175 isl_pw_multi_aff
*pma
;
5177 maff
= isl_multi_aff_alloc(isl_pw_multi_aff_get_space(sol
->pma
));
5178 ls
= isl_basic_set_get_local_space(dom
);
5179 for (i
= 1; i
< M
->n_row
; ++i
) {
5180 aff
= isl_aff_alloc(isl_local_space_copy(ls
));
5182 isl_int_set(aff
->v
->el
[0], M
->row
[0][0]);
5183 isl_seq_cpy(aff
->v
->el
+ 1, M
->row
[i
], M
->n_col
);
5185 aff
= isl_aff_normalize(aff
);
5186 maff
= isl_multi_aff_set_aff(maff
, i
- 1, aff
);
5188 isl_local_space_free(ls
);
5190 dom
= isl_basic_set_simplify(dom
);
5191 dom
= isl_basic_set_finalize(dom
);
5192 pma
= isl_pw_multi_aff_alloc(isl_set_from_basic_set(dom
), maff
);
5193 sol
->pma
= isl_pw_multi_aff_add_disjoint(sol
->pma
, pma
);
5198 static void sol_pma_free_wrap(struct isl_sol
*sol
)
5200 sol_pma_free((struct isl_sol_pma
*)sol
);
5203 static void sol_pma_add_empty_wrap(struct isl_sol
*sol
,
5204 __isl_take isl_basic_set
*bset
)
5206 sol_pma_add_empty((struct isl_sol_pma
*)sol
, bset
);
5209 static void sol_pma_add_wrap(struct isl_sol
*sol
,
5210 __isl_take isl_basic_set
*dom
, __isl_take isl_mat
*M
)
5212 sol_pma_add((struct isl_sol_pma
*)sol
, dom
, M
);
5215 /* Construct an isl_sol_pma structure for accumulating the solution.
5216 * If track_empty is set, then we also keep track of the parts
5217 * of the context where there is no solution.
5218 * If max is set, then we are solving a maximization, rather than
5219 * a minimization problem, which means that the variables in the
5220 * tableau have value "M - x" rather than "M + x".
5222 static struct isl_sol
*sol_pma_init(__isl_keep isl_basic_map
*bmap
,
5223 __isl_take isl_basic_set
*dom
, int track_empty
, int max
)
5225 struct isl_sol_pma
*sol_pma
= NULL
;
5230 sol_pma
= isl_calloc_type(bmap
->ctx
, struct isl_sol_pma
);
5234 sol_pma
->sol
.rational
= ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
);
5235 sol_pma
->sol
.dec_level
.callback
.run
= &sol_dec_level_wrap
;
5236 sol_pma
->sol
.dec_level
.sol
= &sol_pma
->sol
;
5237 sol_pma
->sol
.max
= max
;
5238 sol_pma
->sol
.n_out
= isl_basic_map_dim(bmap
, isl_dim_out
);
5239 sol_pma
->sol
.add
= &sol_pma_add_wrap
;
5240 sol_pma
->sol
.add_empty
= track_empty
? &sol_pma_add_empty_wrap
: NULL
;
5241 sol_pma
->sol
.free
= &sol_pma_free_wrap
;
5242 sol_pma
->pma
= isl_pw_multi_aff_empty(isl_basic_map_get_space(bmap
));
5246 sol_pma
->sol
.context
= isl_context_alloc(dom
);
5247 if (!sol_pma
->sol
.context
)
5251 sol_pma
->empty
= isl_set_alloc_space(isl_basic_set_get_space(dom
),
5252 1, ISL_SET_DISJOINT
);
5253 if (!sol_pma
->empty
)
5257 isl_basic_set_free(dom
);
5258 return &sol_pma
->sol
;
5260 isl_basic_set_free(dom
);
5261 sol_pma_free(sol_pma
);
5265 /* Base case of isl_tab_basic_map_partial_lexopt, after removing
5266 * some obvious symmetries.
5268 * We call basic_map_partial_lexopt_base and extract the results.
5270 static __isl_give isl_pw_multi_aff
*basic_map_partial_lexopt_base_pma(
5271 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_set
*dom
,
5272 __isl_give isl_set
**empty
, int max
)
5274 isl_pw_multi_aff
*result
= NULL
;
5275 struct isl_sol
*sol
;
5276 struct isl_sol_pma
*sol_pma
;
5278 sol
= basic_map_partial_lexopt_base(bmap
, dom
, empty
, max
,
5282 sol_pma
= (struct isl_sol_pma
*) sol
;
5284 result
= isl_pw_multi_aff_copy(sol_pma
->pma
);
5286 *empty
= isl_set_copy(sol_pma
->empty
);
5287 sol_free(&sol_pma
->sol
);
5291 /* Given that the last input variable of "maff" represents the minimum
5292 * of some bounds, check whether we need to plug in the expression
5295 * In particular, check if the last input variable appears in any
5296 * of the expressions in "maff".
5298 static int need_substitution(__isl_keep isl_multi_aff
*maff
)
5303 pos
= isl_multi_aff_dim(maff
, isl_dim_in
) - 1;
5305 for (i
= 0; i
< maff
->n
; ++i
)
5306 if (isl_aff_involves_dims(maff
->p
[i
], isl_dim_in
, pos
, 1))
5312 /* Given a set of upper bounds on the last "input" variable m,
5313 * construct a piecewise affine expression that selects
5314 * the minimal upper bound to m, i.e.,
5315 * divide the space into cells where one
5316 * of the upper bounds is smaller than all the others and select
5317 * this upper bound on that cell.
5319 * In particular, if there are n bounds b_i, then the result
5320 * consists of n cell, each one of the form
5322 * b_i <= b_j for j > i
5323 * b_i < b_j for j < i
5325 * The affine expression on this cell is
5329 static __isl_give isl_pw_aff
*set_minimum_pa(__isl_take isl_space
*space
,
5330 __isl_take isl_mat
*var
)
5333 isl_aff
*aff
= NULL
;
5334 isl_basic_set
*bset
= NULL
;
5336 isl_pw_aff
*paff
= NULL
;
5337 isl_space
*pw_space
;
5338 isl_local_space
*ls
= NULL
;
5343 ctx
= isl_space_get_ctx(space
);
5344 ls
= isl_local_space_from_space(isl_space_copy(space
));
5345 pw_space
= isl_space_copy(space
);
5346 pw_space
= isl_space_from_domain(pw_space
);
5347 pw_space
= isl_space_add_dims(pw_space
, isl_dim_out
, 1);
5348 paff
= isl_pw_aff_alloc_size(pw_space
, var
->n_row
);
5350 for (i
= 0; i
< var
->n_row
; ++i
) {
5353 aff
= isl_aff_alloc(isl_local_space_copy(ls
));
5354 bset
= isl_basic_set_alloc_space(isl_space_copy(space
), 0,
5358 isl_int_set_si(aff
->v
->el
[0], 1);
5359 isl_seq_cpy(aff
->v
->el
+ 1, var
->row
[i
], var
->n_col
);
5360 isl_int_set_si(aff
->v
->el
[1 + var
->n_col
], 0);
5361 bset
= select_minimum(bset
, var
, i
);
5362 paff_i
= isl_pw_aff_alloc(isl_set_from_basic_set(bset
), aff
);
5363 paff
= isl_pw_aff_add_disjoint(paff
, paff_i
);
5366 isl_local_space_free(ls
);
5367 isl_space_free(space
);
5372 isl_basic_set_free(bset
);
5373 isl_pw_aff_free(paff
);
5374 isl_local_space_free(ls
);
5375 isl_space_free(space
);
5380 /* Given a piecewise multi-affine expression of which the last input variable
5381 * is the minimum of the bounds in "cst", plug in the value of the minimum.
5382 * This minimum expression is given in "min_expr_pa".
5383 * The set "min_expr" contains the same information, but in the form of a set.
5384 * The variable is subsequently projected out.
5386 * The implementation is similar to those of "split" and "split_domain".
5387 * If the variable appears in a given expression, then minimum expression
5388 * is plugged in. Otherwise, if the variable appears in the constraints
5389 * and a split is required, then the domain is split. Otherwise, no split
5392 static __isl_give isl_pw_multi_aff
*split_domain_pma(
5393 __isl_take isl_pw_multi_aff
*opt
, __isl_take isl_pw_aff
*min_expr_pa
,
5394 __isl_take isl_set
*min_expr
, __isl_take isl_mat
*cst
)
5399 isl_pw_multi_aff
*res
;
5401 if (!opt
|| !min_expr
|| !cst
)
5404 n_in
= isl_pw_multi_aff_dim(opt
, isl_dim_in
);
5405 space
= isl_pw_multi_aff_get_space(opt
);
5406 space
= isl_space_drop_dims(space
, isl_dim_in
, n_in
- 1, 1);
5407 res
= isl_pw_multi_aff_empty(space
);
5409 for (i
= 0; i
< opt
->n
; ++i
) {
5410 isl_pw_multi_aff
*pma
;
5412 pma
= isl_pw_multi_aff_alloc(isl_set_copy(opt
->p
[i
].set
),
5413 isl_multi_aff_copy(opt
->p
[i
].maff
));
5414 if (need_substitution(opt
->p
[i
].maff
))
5415 pma
= isl_pw_multi_aff_substitute(pma
,
5416 isl_dim_in
, n_in
- 1, min_expr_pa
);
5417 else if (need_split_set(opt
->p
[i
].set
, cst
))
5418 pma
= isl_pw_multi_aff_intersect_domain(pma
,
5419 isl_set_copy(min_expr
));
5420 pma
= isl_pw_multi_aff_project_out(pma
,
5421 isl_dim_in
, n_in
- 1, 1);
5423 res
= isl_pw_multi_aff_add_disjoint(res
, pma
);
5426 isl_pw_multi_aff_free(opt
);
5427 isl_pw_aff_free(min_expr_pa
);
5428 isl_set_free(min_expr
);
5432 isl_pw_multi_aff_free(opt
);
5433 isl_pw_aff_free(min_expr_pa
);
5434 isl_set_free(min_expr
);
5439 static __isl_give isl_pw_multi_aff
*basic_map_partial_lexopt_pma(
5440 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_set
*dom
,
5441 __isl_give isl_set
**empty
, int max
);
5443 /* This function is called from basic_map_partial_lexopt_symm.
5444 * The last variable of "bmap" and "dom" corresponds to the minimum
5445 * of the bounds in "cst". "map_space" is the space of the original
5446 * input relation (of basic_map_partial_lexopt_symm) and "set_space"
5447 * is the space of the original domain.
5449 * We recursively call basic_map_partial_lexopt and then plug in
5450 * the definition of the minimum in the result.
5452 static __isl_give
union isl_lex_res
basic_map_partial_lexopt_symm_pma_core(
5453 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_set
*dom
,
5454 __isl_give isl_set
**empty
, int max
, __isl_take isl_mat
*cst
,
5455 __isl_take isl_space
*map_space
, __isl_take isl_space
*set_space
)
5457 isl_pw_multi_aff
*opt
;
5458 isl_pw_aff
*min_expr_pa
;
5460 union isl_lex_res res
;
5462 min_expr
= set_minimum(isl_basic_set_get_space(dom
), isl_mat_copy(cst
));
5463 min_expr_pa
= set_minimum_pa(isl_basic_set_get_space(dom
),
5466 opt
= basic_map_partial_lexopt_pma(bmap
, dom
, empty
, max
);
5469 *empty
= split(*empty
,
5470 isl_set_copy(min_expr
), isl_mat_copy(cst
));
5471 *empty
= isl_set_reset_space(*empty
, set_space
);
5474 opt
= split_domain_pma(opt
, min_expr_pa
, min_expr
, cst
);
5475 opt
= isl_pw_multi_aff_reset_space(opt
, map_space
);
5481 static __isl_give isl_pw_multi_aff
*basic_map_partial_lexopt_symm_pma(
5482 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_set
*dom
,
5483 __isl_give isl_set
**empty
, int max
, int first
, int second
)
5485 return basic_map_partial_lexopt_symm(bmap
, dom
, empty
, max
,
5486 first
, second
, &basic_map_partial_lexopt_symm_pma_core
).pma
;
5489 /* Recursive part of isl_basic_map_partial_lexopt_pw_multi_aff, after detecting
5490 * equalities and removing redundant constraints.
5492 * We first check if there are any parallel constraints (left).
5493 * If not, we are in the base case.
5494 * If there are parallel constraints, we replace them by a single
5495 * constraint in basic_map_partial_lexopt_symm_pma and then call
5496 * this function recursively to look for more parallel constraints.
5498 static __isl_give isl_pw_multi_aff
*basic_map_partial_lexopt_pma(
5499 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_set
*dom
,
5500 __isl_give isl_set
**empty
, int max
)
5508 if (bmap
->ctx
->opt
->pip_symmetry
)
5509 par
= parallel_constraints(bmap
, &first
, &second
);
5513 return basic_map_partial_lexopt_base_pma(bmap
, dom
, empty
, max
);
5515 return basic_map_partial_lexopt_symm_pma(bmap
, dom
, empty
, max
,
5518 isl_basic_set_free(dom
);
5519 isl_basic_map_free(bmap
);
5523 /* Compute the lexicographic minimum (or maximum if "max" is set)
5524 * of "bmap" over the domain "dom" and return the result as a piecewise
5525 * multi-affine expression.
5526 * If "empty" is not NULL, then *empty is assigned a set that
5527 * contains those parts of the domain where there is no solution.
5528 * If "bmap" is marked as rational (ISL_BASIC_MAP_RATIONAL),
5529 * then we compute the rational optimum. Otherwise, we compute
5530 * the integral optimum.
5532 * We perform some preprocessing. As the PILP solver does not
5533 * handle implicit equalities very well, we first make sure all
5534 * the equalities are explicitly available.
5536 * We also add context constraints to the basic map and remove
5537 * redundant constraints. This is only needed because of the
5538 * way we handle simple symmetries. In particular, we currently look
5539 * for symmetries on the constraints, before we set up the main tableau.
5540 * It is then no good to look for symmetries on possibly redundant constraints.
5542 __isl_give isl_pw_multi_aff
*isl_basic_map_partial_lexopt_pw_multi_aff(
5543 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_set
*dom
,
5544 __isl_give isl_set
**empty
, int max
)
5551 isl_assert(bmap
->ctx
,
5552 isl_basic_map_compatible_domain(bmap
, dom
), goto error
);
5554 if (isl_basic_set_dim(dom
, isl_dim_all
) == 0)
5555 return basic_map_partial_lexopt_pma(bmap
, dom
, empty
, max
);
5557 bmap
= isl_basic_map_intersect_domain(bmap
, isl_basic_set_copy(dom
));
5558 bmap
= isl_basic_map_detect_equalities(bmap
);
5559 bmap
= isl_basic_map_remove_redundancies(bmap
);
5561 return basic_map_partial_lexopt_pma(bmap
, dom
, empty
, max
);
5563 isl_basic_set_free(dom
);
5564 isl_basic_map_free(bmap
);