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_vec_private.h>
20 #include <isl_aff_private.h>
21 #include <isl_options_private.h>
22 #include <isl_config.h>
25 * The implementation of parametric integer linear programming in this file
26 * was inspired by the paper "Parametric Integer Programming" and the
27 * report "Solving systems of affine (in)equalities" by Paul Feautrier
30 * The strategy used for obtaining a feasible solution is different
31 * from the one used in isl_tab.c. In particular, in isl_tab.c,
32 * upon finding a constraint that is not yet satisfied, we pivot
33 * in a row that increases the constant term of the row holding the
34 * constraint, making sure the sample solution remains feasible
35 * for all the constraints it already satisfied.
36 * Here, we always pivot in the row holding the constraint,
37 * choosing a column that induces the lexicographically smallest
38 * increment to the sample solution.
40 * By starting out from a sample value that is lexicographically
41 * smaller than any integer point in the problem space, the first
42 * feasible integer sample point we find will also be the lexicographically
43 * smallest. If all variables can be assumed to be non-negative,
44 * then the initial sample value may be chosen equal to zero.
45 * However, we will not make this assumption. Instead, we apply
46 * the "big parameter" trick. Any variable x is then not directly
47 * used in the tableau, but instead it is represented by another
48 * variable x' = M + x, where M is an arbitrarily large (positive)
49 * value. x' is therefore always non-negative, whatever the value of x.
50 * Taking as initial sample value x' = 0 corresponds to x = -M,
51 * which is always smaller than any possible value of x.
53 * The big parameter trick is used in the main tableau and
54 * also in the context tableau if isl_context_lex is used.
55 * In this case, each tableaus has its own big parameter.
56 * Before doing any real work, we check if all the parameters
57 * happen to be non-negative. If so, we drop the column corresponding
58 * to M from the initial context tableau.
59 * If isl_context_gbr is used, then the big parameter trick is only
60 * used in the main tableau.
64 struct isl_context_op
{
65 /* detect nonnegative parameters in context and mark them in tab */
66 struct isl_tab
*(*detect_nonnegative_parameters
)(
67 struct isl_context
*context
, struct isl_tab
*tab
);
68 /* return temporary reference to basic set representation of context */
69 struct isl_basic_set
*(*peek_basic_set
)(struct isl_context
*context
);
70 /* return temporary reference to tableau representation of context */
71 struct isl_tab
*(*peek_tab
)(struct isl_context
*context
);
72 /* add equality; check is 1 if eq may not be valid;
73 * update is 1 if we may want to call ineq_sign on context later.
75 void (*add_eq
)(struct isl_context
*context
, isl_int
*eq
,
76 int check
, int update
);
77 /* add inequality; check is 1 if ineq may not be valid;
78 * update is 1 if we may want to call ineq_sign on context later.
80 void (*add_ineq
)(struct isl_context
*context
, isl_int
*ineq
,
81 int check
, int update
);
82 /* check sign of ineq based on previous information.
83 * strict is 1 if saturation should be treated as a positive sign.
85 enum isl_tab_row_sign (*ineq_sign
)(struct isl_context
*context
,
86 isl_int
*ineq
, int strict
);
87 /* check if inequality maintains feasibility */
88 int (*test_ineq
)(struct isl_context
*context
, isl_int
*ineq
);
89 /* return index of a div that corresponds to "div" */
90 int (*get_div
)(struct isl_context
*context
, struct isl_tab
*tab
,
92 /* add div "div" to context and return non-negativity */
93 int (*add_div
)(struct isl_context
*context
, struct isl_vec
*div
);
94 int (*detect_equalities
)(struct isl_context
*context
,
96 /* return row index of "best" split */
97 int (*best_split
)(struct isl_context
*context
, struct isl_tab
*tab
);
98 /* check if context has already been determined to be empty */
99 int (*is_empty
)(struct isl_context
*context
);
100 /* check if context is still usable */
101 int (*is_ok
)(struct isl_context
*context
);
102 /* save a copy/snapshot of context */
103 void *(*save
)(struct isl_context
*context
);
104 /* restore saved context */
105 void (*restore
)(struct isl_context
*context
, void *);
106 /* discard saved context */
107 void (*discard
)(void *);
108 /* invalidate context */
109 void (*invalidate
)(struct isl_context
*context
);
111 void (*free
)(struct isl_context
*context
);
115 struct isl_context_op
*op
;
118 struct isl_context_lex
{
119 struct isl_context context
;
123 /* A stack (linked list) of solutions of subtrees of the search space.
125 * "M" describes the solution in terms of the dimensions of "dom".
126 * The number of columns of "M" is one more than the total number
127 * of dimensions of "dom".
129 * If "M" is NULL, then there is no solution on "dom".
131 struct isl_partial_sol
{
133 struct isl_basic_set
*dom
;
136 struct isl_partial_sol
*next
;
140 struct isl_sol_callback
{
141 struct isl_tab_callback callback
;
145 /* isl_sol is an interface for constructing a solution to
146 * a parametric integer linear programming problem.
147 * Every time the algorithm reaches a state where a solution
148 * can be read off from the tableau (including cases where the tableau
149 * is empty), the function "add" is called on the isl_sol passed
150 * to find_solutions_main.
152 * The context tableau is owned by isl_sol and is updated incrementally.
154 * There are currently two implementations of this interface,
155 * isl_sol_map, which simply collects the solutions in an isl_map
156 * and (optionally) the parts of the context where there is no solution
158 * isl_sol_for, which calls a user-defined function for each part of
167 struct isl_context
*context
;
168 struct isl_partial_sol
*partial
;
169 void (*add
)(struct isl_sol
*sol
,
170 struct isl_basic_set
*dom
, struct isl_mat
*M
);
171 void (*add_empty
)(struct isl_sol
*sol
, struct isl_basic_set
*bset
);
172 void (*free
)(struct isl_sol
*sol
);
173 struct isl_sol_callback dec_level
;
176 static void sol_free(struct isl_sol
*sol
)
178 struct isl_partial_sol
*partial
, *next
;
181 for (partial
= sol
->partial
; partial
; partial
= next
) {
182 next
= partial
->next
;
183 isl_basic_set_free(partial
->dom
);
184 isl_mat_free(partial
->M
);
190 /* Push a partial solution represented by a domain and mapping M
191 * onto the stack of partial solutions.
193 static void sol_push_sol(struct isl_sol
*sol
,
194 struct isl_basic_set
*dom
, struct isl_mat
*M
)
196 struct isl_partial_sol
*partial
;
198 if (sol
->error
|| !dom
)
201 partial
= isl_alloc_type(dom
->ctx
, struct isl_partial_sol
);
205 partial
->level
= sol
->level
;
208 partial
->next
= sol
->partial
;
210 sol
->partial
= partial
;
214 isl_basic_set_free(dom
);
219 /* Pop one partial solution from the partial solution stack and
220 * pass it on to sol->add or sol->add_empty.
222 static void sol_pop_one(struct isl_sol
*sol
)
224 struct isl_partial_sol
*partial
;
226 partial
= sol
->partial
;
227 sol
->partial
= partial
->next
;
230 sol
->add(sol
, partial
->dom
, partial
->M
);
232 sol
->add_empty(sol
, partial
->dom
);
236 /* Return a fresh copy of the domain represented by the context tableau.
238 static struct isl_basic_set
*sol_domain(struct isl_sol
*sol
)
240 struct isl_basic_set
*bset
;
245 bset
= isl_basic_set_dup(sol
->context
->op
->peek_basic_set(sol
->context
));
246 bset
= isl_basic_set_update_from_tab(bset
,
247 sol
->context
->op
->peek_tab(sol
->context
));
252 /* Check whether two partial solutions have the same mapping, where n_div
253 * is the number of divs that the two partial solutions have in common.
255 static int same_solution(struct isl_partial_sol
*s1
, struct isl_partial_sol
*s2
,
261 if (!s1
->M
!= !s2
->M
)
266 dim
= isl_basic_set_total_dim(s1
->dom
) - s1
->dom
->n_div
;
268 for (i
= 0; i
< s1
->M
->n_row
; ++i
) {
269 if (isl_seq_first_non_zero(s1
->M
->row
[i
]+1+dim
+n_div
,
270 s1
->M
->n_col
-1-dim
-n_div
) != -1)
272 if (isl_seq_first_non_zero(s2
->M
->row
[i
]+1+dim
+n_div
,
273 s2
->M
->n_col
-1-dim
-n_div
) != -1)
275 if (!isl_seq_eq(s1
->M
->row
[i
], s2
->M
->row
[i
], 1+dim
+n_div
))
281 /* Pop all solutions from the partial solution stack that were pushed onto
282 * the stack at levels that are deeper than the current level.
283 * If the two topmost elements on the stack have the same level
284 * and represent the same solution, then their domains are combined.
285 * This combined domain is the same as the current context domain
286 * as sol_pop is called each time we move back to a higher level.
287 * If the outer level (0) has been reached, then all partial solutions
288 * at the current level are also popped off.
290 static void sol_pop(struct isl_sol
*sol
)
292 struct isl_partial_sol
*partial
;
298 partial
= sol
->partial
;
302 if (partial
->level
== 0 && sol
->level
== 0) {
303 for (partial
= sol
->partial
; partial
; partial
= sol
->partial
)
308 if (partial
->level
<= sol
->level
)
311 if (partial
->next
&& partial
->next
->level
== partial
->level
) {
312 n_div
= isl_basic_set_dim(
313 sol
->context
->op
->peek_basic_set(sol
->context
),
316 if (!same_solution(partial
, partial
->next
, n_div
)) {
320 struct isl_basic_set
*bset
;
324 n
= isl_basic_set_dim(partial
->next
->dom
, isl_dim_div
);
326 bset
= sol_domain(sol
);
327 isl_basic_set_free(partial
->next
->dom
);
328 partial
->next
->dom
= bset
;
329 M
= partial
->next
->M
;
331 M
= isl_mat_drop_cols(M
, M
->n_col
- n
, n
);
332 partial
->next
->M
= M
;
336 partial
->next
->level
= sol
->level
;
341 sol
->partial
= partial
->next
;
342 isl_basic_set_free(partial
->dom
);
343 isl_mat_free(partial
->M
);
349 if (sol
->level
== 0) {
350 for (partial
= sol
->partial
; partial
; partial
= sol
->partial
)
356 error
: sol
->error
= 1;
359 static void sol_dec_level(struct isl_sol
*sol
)
369 static int sol_dec_level_wrap(struct isl_tab_callback
*cb
)
371 struct isl_sol_callback
*callback
= (struct isl_sol_callback
*)cb
;
373 sol_dec_level(callback
->sol
);
375 return callback
->sol
->error
? -1 : 0;
378 /* Move down to next level and push callback onto context tableau
379 * to decrease the level again when it gets rolled back across
380 * the current state. That is, dec_level will be called with
381 * the context tableau in the same state as it is when inc_level
384 static void sol_inc_level(struct isl_sol
*sol
)
392 tab
= sol
->context
->op
->peek_tab(sol
->context
);
393 if (isl_tab_push_callback(tab
, &sol
->dec_level
.callback
) < 0)
397 static void scale_rows(struct isl_mat
*mat
, isl_int m
, int n_row
)
401 if (isl_int_is_one(m
))
404 for (i
= 0; i
< n_row
; ++i
)
405 isl_seq_scale(mat
->row
[i
], mat
->row
[i
], m
, mat
->n_col
);
408 /* Add the solution identified by the tableau and the context tableau.
410 * The layout of the variables is as follows.
411 * tab->n_var is equal to the total number of variables in the input
412 * map (including divs that were copied from the context)
413 * + the number of extra divs constructed
414 * Of these, the first tab->n_param and the last tab->n_div variables
415 * correspond to the variables in the context, i.e.,
416 * tab->n_param + tab->n_div = context_tab->n_var
417 * tab->n_param is equal to the number of parameters and input
418 * dimensions in the input map
419 * tab->n_div is equal to the number of divs in the context
421 * If there is no solution, then call add_empty with a basic set
422 * that corresponds to the context tableau. (If add_empty is NULL,
425 * If there is a solution, then first construct a matrix that maps
426 * all dimensions of the context to the output variables, i.e.,
427 * the output dimensions in the input map.
428 * The divs in the input map (if any) that do not correspond to any
429 * div in the context do not appear in the solution.
430 * The algorithm will make sure that they have an integer value,
431 * but these values themselves are of no interest.
432 * We have to be careful not to drop or rearrange any divs in the
433 * context because that would change the meaning of the matrix.
435 * To extract the value of the output variables, it should be noted
436 * that we always use a big parameter M in the main tableau and so
437 * the variable stored in this tableau is not an output variable x itself, but
438 * x' = M + x (in case of minimization)
440 * x' = M - x (in case of maximization)
441 * If x' appears in a column, then its optimal value is zero,
442 * which means that the optimal value of x is an unbounded number
443 * (-M for minimization and M for maximization).
444 * We currently assume that the output dimensions in the original map
445 * are bounded, so this cannot occur.
446 * Similarly, when x' appears in a row, then the coefficient of M in that
447 * row is necessarily 1.
448 * If the row in the tableau represents
449 * d x' = c + d M + e(y)
450 * then, in case of minimization, the corresponding row in the matrix
453 * with a d = m, the (updated) common denominator of the matrix.
454 * In case of maximization, the row will be
457 static void sol_add(struct isl_sol
*sol
, struct isl_tab
*tab
)
459 struct isl_basic_set
*bset
= NULL
;
460 struct isl_mat
*mat
= NULL
;
465 if (sol
->error
|| !tab
)
468 if (tab
->empty
&& !sol
->add_empty
)
470 if (sol
->context
->op
->is_empty(sol
->context
))
473 bset
= sol_domain(sol
);
476 sol_push_sol(sol
, bset
, NULL
);
482 mat
= isl_mat_alloc(tab
->mat
->ctx
, 1 + sol
->n_out
,
483 1 + tab
->n_param
+ tab
->n_div
);
489 isl_seq_clr(mat
->row
[0] + 1, mat
->n_col
- 1);
490 isl_int_set_si(mat
->row
[0][0], 1);
491 for (row
= 0; row
< sol
->n_out
; ++row
) {
492 int i
= tab
->n_param
+ row
;
495 isl_seq_clr(mat
->row
[1 + row
], mat
->n_col
);
496 if (!tab
->var
[i
].is_row
) {
498 isl_die(mat
->ctx
, isl_error_invalid
,
499 "unbounded optimum", goto error2
);
503 r
= tab
->var
[i
].index
;
505 isl_int_ne(tab
->mat
->row
[r
][2], tab
->mat
->row
[r
][0]))
506 isl_die(mat
->ctx
, isl_error_invalid
,
507 "unbounded optimum", goto error2
);
508 isl_int_gcd(m
, mat
->row
[0][0], tab
->mat
->row
[r
][0]);
509 isl_int_divexact(m
, tab
->mat
->row
[r
][0], m
);
510 scale_rows(mat
, m
, 1 + row
);
511 isl_int_divexact(m
, mat
->row
[0][0], tab
->mat
->row
[r
][0]);
512 isl_int_mul(mat
->row
[1 + row
][0], m
, tab
->mat
->row
[r
][1]);
513 for (j
= 0; j
< tab
->n_param
; ++j
) {
515 if (tab
->var
[j
].is_row
)
517 col
= tab
->var
[j
].index
;
518 isl_int_mul(mat
->row
[1 + row
][1 + j
], m
,
519 tab
->mat
->row
[r
][off
+ col
]);
521 for (j
= 0; j
< tab
->n_div
; ++j
) {
523 if (tab
->var
[tab
->n_var
- tab
->n_div
+j
].is_row
)
525 col
= tab
->var
[tab
->n_var
- tab
->n_div
+j
].index
;
526 isl_int_mul(mat
->row
[1 + row
][1 + tab
->n_param
+ j
], m
,
527 tab
->mat
->row
[r
][off
+ col
]);
530 isl_seq_neg(mat
->row
[1 + row
], mat
->row
[1 + row
],
536 sol_push_sol(sol
, bset
, mat
);
541 isl_basic_set_free(bset
);
549 struct isl_set
*empty
;
552 static void sol_map_free(struct isl_sol_map
*sol_map
)
556 if (sol_map
->sol
.context
)
557 sol_map
->sol
.context
->op
->free(sol_map
->sol
.context
);
558 isl_map_free(sol_map
->map
);
559 isl_set_free(sol_map
->empty
);
563 static void sol_map_free_wrap(struct isl_sol
*sol
)
565 sol_map_free((struct isl_sol_map
*)sol
);
568 /* This function is called for parts of the context where there is
569 * no solution, with "bset" corresponding to the context tableau.
570 * Simply add the basic set to the set "empty".
572 static void sol_map_add_empty(struct isl_sol_map
*sol
,
573 struct isl_basic_set
*bset
)
575 if (!bset
|| !sol
->empty
)
578 sol
->empty
= isl_set_grow(sol
->empty
, 1);
579 bset
= isl_basic_set_simplify(bset
);
580 bset
= isl_basic_set_finalize(bset
);
581 sol
->empty
= isl_set_add_basic_set(sol
->empty
, isl_basic_set_copy(bset
));
584 isl_basic_set_free(bset
);
587 isl_basic_set_free(bset
);
591 static void sol_map_add_empty_wrap(struct isl_sol
*sol
,
592 struct isl_basic_set
*bset
)
594 sol_map_add_empty((struct isl_sol_map
*)sol
, bset
);
597 /* Given a basic map "dom" that represents the context and an affine
598 * matrix "M" that maps the dimensions of the context to the
599 * output variables, construct a basic map with the same parameters
600 * and divs as the context, the dimensions of the context as input
601 * dimensions and a number of output dimensions that is equal to
602 * the number of output dimensions in the input map.
604 * The constraints and divs of the context are simply copied
605 * from "dom". For each row
609 * is added, with d the common denominator of M.
611 static void sol_map_add(struct isl_sol_map
*sol
,
612 struct isl_basic_set
*dom
, struct isl_mat
*M
)
615 struct isl_basic_map
*bmap
= NULL
;
623 if (sol
->sol
.error
|| !dom
|| !M
)
626 n_out
= sol
->sol
.n_out
;
627 n_eq
= dom
->n_eq
+ n_out
;
628 n_ineq
= dom
->n_ineq
;
630 nparam
= isl_basic_set_total_dim(dom
) - n_div
;
631 total
= isl_map_dim(sol
->map
, isl_dim_all
);
632 bmap
= isl_basic_map_alloc_space(isl_map_get_space(sol
->map
),
633 n_div
, n_eq
, 2 * n_div
+ n_ineq
);
636 if (sol
->sol
.rational
)
637 ISL_F_SET(bmap
, ISL_BASIC_MAP_RATIONAL
);
638 for (i
= 0; i
< dom
->n_div
; ++i
) {
639 int k
= isl_basic_map_alloc_div(bmap
);
642 isl_seq_cpy(bmap
->div
[k
], dom
->div
[i
], 1 + 1 + nparam
);
643 isl_seq_clr(bmap
->div
[k
] + 1 + 1 + nparam
, total
- nparam
);
644 isl_seq_cpy(bmap
->div
[k
] + 1 + 1 + total
,
645 dom
->div
[i
] + 1 + 1 + nparam
, i
);
647 for (i
= 0; i
< dom
->n_eq
; ++i
) {
648 int k
= isl_basic_map_alloc_equality(bmap
);
651 isl_seq_cpy(bmap
->eq
[k
], dom
->eq
[i
], 1 + nparam
);
652 isl_seq_clr(bmap
->eq
[k
] + 1 + nparam
, total
- nparam
);
653 isl_seq_cpy(bmap
->eq
[k
] + 1 + total
,
654 dom
->eq
[i
] + 1 + nparam
, n_div
);
656 for (i
= 0; i
< dom
->n_ineq
; ++i
) {
657 int k
= isl_basic_map_alloc_inequality(bmap
);
660 isl_seq_cpy(bmap
->ineq
[k
], dom
->ineq
[i
], 1 + nparam
);
661 isl_seq_clr(bmap
->ineq
[k
] + 1 + nparam
, total
- nparam
);
662 isl_seq_cpy(bmap
->ineq
[k
] + 1 + total
,
663 dom
->ineq
[i
] + 1 + nparam
, n_div
);
665 for (i
= 0; i
< M
->n_row
- 1; ++i
) {
666 int k
= isl_basic_map_alloc_equality(bmap
);
669 isl_seq_cpy(bmap
->eq
[k
], M
->row
[1 + i
], 1 + nparam
);
670 isl_seq_clr(bmap
->eq
[k
] + 1 + nparam
, n_out
);
671 isl_int_neg(bmap
->eq
[k
][1 + nparam
+ i
], M
->row
[0][0]);
672 isl_seq_cpy(bmap
->eq
[k
] + 1 + nparam
+ n_out
,
673 M
->row
[1 + i
] + 1 + nparam
, n_div
);
675 bmap
= isl_basic_map_simplify(bmap
);
676 bmap
= isl_basic_map_finalize(bmap
);
677 sol
->map
= isl_map_grow(sol
->map
, 1);
678 sol
->map
= isl_map_add_basic_map(sol
->map
, bmap
);
679 isl_basic_set_free(dom
);
685 isl_basic_set_free(dom
);
687 isl_basic_map_free(bmap
);
691 static void sol_map_add_wrap(struct isl_sol
*sol
,
692 struct isl_basic_set
*dom
, struct isl_mat
*M
)
694 sol_map_add((struct isl_sol_map
*)sol
, dom
, M
);
698 /* Store the "parametric constant" of row "row" of tableau "tab" in "line",
699 * i.e., the constant term and the coefficients of all variables that
700 * appear in the context tableau.
701 * Note that the coefficient of the big parameter M is NOT copied.
702 * The context tableau may not have a big parameter and even when it
703 * does, it is a different big parameter.
705 static void get_row_parameter_line(struct isl_tab
*tab
, int row
, isl_int
*line
)
708 unsigned off
= 2 + tab
->M
;
710 isl_int_set(line
[0], tab
->mat
->row
[row
][1]);
711 for (i
= 0; i
< tab
->n_param
; ++i
) {
712 if (tab
->var
[i
].is_row
)
713 isl_int_set_si(line
[1 + i
], 0);
715 int col
= tab
->var
[i
].index
;
716 isl_int_set(line
[1 + i
], tab
->mat
->row
[row
][off
+ col
]);
719 for (i
= 0; i
< tab
->n_div
; ++i
) {
720 if (tab
->var
[tab
->n_var
- tab
->n_div
+ i
].is_row
)
721 isl_int_set_si(line
[1 + tab
->n_param
+ i
], 0);
723 int col
= tab
->var
[tab
->n_var
- tab
->n_div
+ i
].index
;
724 isl_int_set(line
[1 + tab
->n_param
+ i
],
725 tab
->mat
->row
[row
][off
+ col
]);
730 /* Check if rows "row1" and "row2" have identical "parametric constants",
731 * as explained above.
732 * In this case, we also insist that the coefficients of the big parameter
733 * be the same as the values of the constants will only be the same
734 * if these coefficients are also the same.
736 static int identical_parameter_line(struct isl_tab
*tab
, int row1
, int row2
)
739 unsigned off
= 2 + tab
->M
;
741 if (isl_int_ne(tab
->mat
->row
[row1
][1], tab
->mat
->row
[row2
][1]))
744 if (tab
->M
&& isl_int_ne(tab
->mat
->row
[row1
][2],
745 tab
->mat
->row
[row2
][2]))
748 for (i
= 0; i
< tab
->n_param
+ tab
->n_div
; ++i
) {
749 int pos
= i
< tab
->n_param
? i
:
750 tab
->n_var
- tab
->n_div
+ i
- tab
->n_param
;
753 if (tab
->var
[pos
].is_row
)
755 col
= tab
->var
[pos
].index
;
756 if (isl_int_ne(tab
->mat
->row
[row1
][off
+ col
],
757 tab
->mat
->row
[row2
][off
+ col
]))
763 /* Return an inequality that expresses that the "parametric constant"
764 * should be non-negative.
765 * This function is only called when the coefficient of the big parameter
768 static struct isl_vec
*get_row_parameter_ineq(struct isl_tab
*tab
, int row
)
770 struct isl_vec
*ineq
;
772 ineq
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_param
+ tab
->n_div
);
776 get_row_parameter_line(tab
, row
, ineq
->el
);
778 ineq
= isl_vec_normalize(ineq
);
783 /* Normalize a div expression of the form
785 * [(g*f(x) + c)/(g * m)]
787 * with c the constant term and f(x) the remaining coefficients, to
791 static void normalize_div(__isl_keep isl_vec
*div
)
793 isl_ctx
*ctx
= isl_vec_get_ctx(div
);
794 int len
= div
->size
- 2;
796 isl_seq_gcd(div
->el
+ 2, len
, &ctx
->normalize_gcd
);
797 isl_int_gcd(ctx
->normalize_gcd
, ctx
->normalize_gcd
, div
->el
[0]);
799 if (isl_int_is_one(ctx
->normalize_gcd
))
802 isl_int_divexact(div
->el
[0], div
->el
[0], ctx
->normalize_gcd
);
803 isl_int_fdiv_q(div
->el
[1], div
->el
[1], ctx
->normalize_gcd
);
804 isl_seq_scale_down(div
->el
+ 2, div
->el
+ 2, ctx
->normalize_gcd
, len
);
807 /* Return a integer division for use in a parametric cut based on the given row.
808 * In particular, let the parametric constant of the row be
812 * where y_0 = 1, but none of the y_i corresponds to the big parameter M.
813 * The div returned is equal to
815 * floor(\sum_i {-a_i} y_i) = floor((\sum_i (-a_i mod d) y_i)/d)
817 static struct isl_vec
*get_row_parameter_div(struct isl_tab
*tab
, int row
)
821 div
= isl_vec_alloc(tab
->mat
->ctx
, 1 + 1 + tab
->n_param
+ tab
->n_div
);
825 isl_int_set(div
->el
[0], tab
->mat
->row
[row
][0]);
826 get_row_parameter_line(tab
, row
, div
->el
+ 1);
827 isl_seq_neg(div
->el
+ 1, div
->el
+ 1, div
->size
- 1);
829 isl_seq_fdiv_r(div
->el
+ 1, div
->el
+ 1, div
->el
[0], div
->size
- 1);
834 /* Return a integer division for use in transferring an integrality constraint
836 * In particular, let the parametric constant of the row be
840 * where y_0 = 1, but none of the y_i corresponds to the big parameter M.
841 * The the returned div is equal to
843 * floor(\sum_i {a_i} y_i) = floor((\sum_i (a_i mod d) y_i)/d)
845 static struct isl_vec
*get_row_split_div(struct isl_tab
*tab
, int row
)
849 div
= isl_vec_alloc(tab
->mat
->ctx
, 1 + 1 + tab
->n_param
+ tab
->n_div
);
853 isl_int_set(div
->el
[0], tab
->mat
->row
[row
][0]);
854 get_row_parameter_line(tab
, row
, div
->el
+ 1);
856 isl_seq_fdiv_r(div
->el
+ 1, div
->el
+ 1, div
->el
[0], div
->size
- 1);
861 /* Construct and return an inequality that expresses an upper bound
863 * In particular, if the div is given by
867 * then the inequality expresses
871 static struct isl_vec
*ineq_for_div(struct isl_basic_set
*bset
, unsigned div
)
875 struct isl_vec
*ineq
;
880 total
= isl_basic_set_total_dim(bset
);
881 div_pos
= 1 + total
- bset
->n_div
+ div
;
883 ineq
= isl_vec_alloc(bset
->ctx
, 1 + total
);
887 isl_seq_cpy(ineq
->el
, bset
->div
[div
] + 1, 1 + total
);
888 isl_int_neg(ineq
->el
[div_pos
], bset
->div
[div
][0]);
892 /* Given a row in the tableau and a div that was created
893 * using get_row_split_div and that has been constrained to equality, i.e.,
895 * d = floor(\sum_i {a_i} y_i) = \sum_i {a_i} y_i
897 * replace the expression "\sum_i {a_i} y_i" in the row by d,
898 * i.e., we subtract "\sum_i {a_i} y_i" and add 1 d.
899 * The coefficients of the non-parameters in the tableau have been
900 * verified to be integral. We can therefore simply replace coefficient b
901 * by floor(b). For the coefficients of the parameters we have
902 * floor(a_i) = a_i - {a_i}, while for the other coefficients, we have
905 static struct isl_tab
*set_row_cst_to_div(struct isl_tab
*tab
, int row
, int div
)
907 isl_seq_fdiv_q(tab
->mat
->row
[row
] + 1, tab
->mat
->row
[row
] + 1,
908 tab
->mat
->row
[row
][0], 1 + tab
->M
+ tab
->n_col
);
910 isl_int_set_si(tab
->mat
->row
[row
][0], 1);
912 if (tab
->var
[tab
->n_var
- tab
->n_div
+ div
].is_row
) {
913 int drow
= tab
->var
[tab
->n_var
- tab
->n_div
+ div
].index
;
915 isl_assert(tab
->mat
->ctx
,
916 isl_int_is_one(tab
->mat
->row
[drow
][0]), goto error
);
917 isl_seq_combine(tab
->mat
->row
[row
] + 1,
918 tab
->mat
->ctx
->one
, tab
->mat
->row
[row
] + 1,
919 tab
->mat
->ctx
->one
, tab
->mat
->row
[drow
] + 1,
920 1 + tab
->M
+ tab
->n_col
);
922 int dcol
= tab
->var
[tab
->n_var
- tab
->n_div
+ div
].index
;
924 isl_int_add_ui(tab
->mat
->row
[row
][2 + tab
->M
+ dcol
],
925 tab
->mat
->row
[row
][2 + tab
->M
+ dcol
], 1);
934 /* Check if the (parametric) constant of the given row is obviously
935 * negative, meaning that we don't need to consult the context tableau.
936 * If there is a big parameter and its coefficient is non-zero,
937 * then this coefficient determines the outcome.
938 * Otherwise, we check whether the constant is negative and
939 * all non-zero coefficients of parameters are negative and
940 * belong to non-negative parameters.
942 static int is_obviously_neg(struct isl_tab
*tab
, int row
)
946 unsigned off
= 2 + tab
->M
;
949 if (isl_int_is_pos(tab
->mat
->row
[row
][2]))
951 if (isl_int_is_neg(tab
->mat
->row
[row
][2]))
955 if (isl_int_is_nonneg(tab
->mat
->row
[row
][1]))
957 for (i
= 0; i
< tab
->n_param
; ++i
) {
958 /* Eliminated parameter */
959 if (tab
->var
[i
].is_row
)
961 col
= tab
->var
[i
].index
;
962 if (isl_int_is_zero(tab
->mat
->row
[row
][off
+ col
]))
964 if (!tab
->var
[i
].is_nonneg
)
966 if (isl_int_is_pos(tab
->mat
->row
[row
][off
+ col
]))
969 for (i
= 0; i
< tab
->n_div
; ++i
) {
970 if (tab
->var
[tab
->n_var
- tab
->n_div
+ i
].is_row
)
972 col
= tab
->var
[tab
->n_var
- tab
->n_div
+ i
].index
;
973 if (isl_int_is_zero(tab
->mat
->row
[row
][off
+ col
]))
975 if (!tab
->var
[tab
->n_var
- tab
->n_div
+ i
].is_nonneg
)
977 if (isl_int_is_pos(tab
->mat
->row
[row
][off
+ col
]))
983 /* Check if the (parametric) constant of the given row is obviously
984 * non-negative, meaning that we don't need to consult the context tableau.
985 * If there is a big parameter and its coefficient is non-zero,
986 * then this coefficient determines the outcome.
987 * Otherwise, we check whether the constant is non-negative and
988 * all non-zero coefficients of parameters are positive and
989 * belong to non-negative parameters.
991 static int is_obviously_nonneg(struct isl_tab
*tab
, int row
)
995 unsigned off
= 2 + tab
->M
;
998 if (isl_int_is_pos(tab
->mat
->row
[row
][2]))
1000 if (isl_int_is_neg(tab
->mat
->row
[row
][2]))
1004 if (isl_int_is_neg(tab
->mat
->row
[row
][1]))
1006 for (i
= 0; i
< tab
->n_param
; ++i
) {
1007 /* Eliminated parameter */
1008 if (tab
->var
[i
].is_row
)
1010 col
= tab
->var
[i
].index
;
1011 if (isl_int_is_zero(tab
->mat
->row
[row
][off
+ col
]))
1013 if (!tab
->var
[i
].is_nonneg
)
1015 if (isl_int_is_neg(tab
->mat
->row
[row
][off
+ col
]))
1018 for (i
= 0; i
< tab
->n_div
; ++i
) {
1019 if (tab
->var
[tab
->n_var
- tab
->n_div
+ i
].is_row
)
1021 col
= tab
->var
[tab
->n_var
- tab
->n_div
+ i
].index
;
1022 if (isl_int_is_zero(tab
->mat
->row
[row
][off
+ col
]))
1024 if (!tab
->var
[tab
->n_var
- tab
->n_div
+ i
].is_nonneg
)
1026 if (isl_int_is_neg(tab
->mat
->row
[row
][off
+ col
]))
1032 /* Given a row r and two columns, return the column that would
1033 * lead to the lexicographically smallest increment in the sample
1034 * solution when leaving the basis in favor of the row.
1035 * Pivoting with column c will increment the sample value by a non-negative
1036 * constant times a_{V,c}/a_{r,c}, with a_{V,c} the elements of column c
1037 * corresponding to the non-parametric variables.
1038 * If variable v appears in a column c_v, the a_{v,c} = 1 iff c = c_v,
1039 * with all other entries in this virtual row equal to zero.
1040 * If variable v appears in a row, then a_{v,c} is the element in column c
1043 * Let v be the first variable with a_{v,c1}/a_{r,c1} != a_{v,c2}/a_{r,c2}.
1044 * Then if a_{v,c1}/a_{r,c1} < a_{v,c2}/a_{r,c2}, i.e.,
1045 * a_{v,c2} a_{r,c1} - a_{v,c1} a_{r,c2} > 0, c1 results in the minimal
1046 * increment. Otherwise, it's c2.
1048 static int lexmin_col_pair(struct isl_tab
*tab
,
1049 int row
, int col1
, int col2
, isl_int tmp
)
1054 tr
= tab
->mat
->row
[row
] + 2 + tab
->M
;
1056 for (i
= tab
->n_param
; i
< tab
->n_var
- tab
->n_div
; ++i
) {
1060 if (!tab
->var
[i
].is_row
) {
1061 if (tab
->var
[i
].index
== col1
)
1063 if (tab
->var
[i
].index
== col2
)
1068 if (tab
->var
[i
].index
== row
)
1071 r
= tab
->mat
->row
[tab
->var
[i
].index
] + 2 + tab
->M
;
1072 s1
= isl_int_sgn(r
[col1
]);
1073 s2
= isl_int_sgn(r
[col2
]);
1074 if (s1
== 0 && s2
== 0)
1081 isl_int_mul(tmp
, r
[col2
], tr
[col1
]);
1082 isl_int_submul(tmp
, r
[col1
], tr
[col2
]);
1083 if (isl_int_is_pos(tmp
))
1085 if (isl_int_is_neg(tmp
))
1091 /* Given a row in the tableau, find and return the column that would
1092 * result in the lexicographically smallest, but positive, increment
1093 * in the sample point.
1094 * If there is no such column, then return tab->n_col.
1095 * If anything goes wrong, return -1.
1097 static int lexmin_pivot_col(struct isl_tab
*tab
, int row
)
1100 int col
= tab
->n_col
;
1104 tr
= tab
->mat
->row
[row
] + 2 + tab
->M
;
1108 for (j
= tab
->n_dead
; j
< tab
->n_col
; ++j
) {
1109 if (tab
->col_var
[j
] >= 0 &&
1110 (tab
->col_var
[j
] < tab
->n_param
||
1111 tab
->col_var
[j
] >= tab
->n_var
- tab
->n_div
))
1114 if (!isl_int_is_pos(tr
[j
]))
1117 if (col
== tab
->n_col
)
1120 col
= lexmin_col_pair(tab
, row
, col
, j
, tmp
);
1121 isl_assert(tab
->mat
->ctx
, col
>= 0, goto error
);
1131 /* Return the first known violated constraint, i.e., a non-negative
1132 * constraint that currently has an either obviously negative value
1133 * or a previously determined to be negative value.
1135 * If any constraint has a negative coefficient for the big parameter,
1136 * if any, then we return one of these first.
1138 static int first_neg(struct isl_tab
*tab
)
1143 for (row
= tab
->n_redundant
; row
< tab
->n_row
; ++row
) {
1144 if (!isl_tab_var_from_row(tab
, row
)->is_nonneg
)
1146 if (!isl_int_is_neg(tab
->mat
->row
[row
][2]))
1149 tab
->row_sign
[row
] = isl_tab_row_neg
;
1152 for (row
= tab
->n_redundant
; row
< tab
->n_row
; ++row
) {
1153 if (!isl_tab_var_from_row(tab
, row
)->is_nonneg
)
1155 if (tab
->row_sign
) {
1156 if (tab
->row_sign
[row
] == 0 &&
1157 is_obviously_neg(tab
, row
))
1158 tab
->row_sign
[row
] = isl_tab_row_neg
;
1159 if (tab
->row_sign
[row
] != isl_tab_row_neg
)
1161 } else if (!is_obviously_neg(tab
, row
))
1168 /* Check whether the invariant that all columns are lexico-positive
1169 * is satisfied. This function is not called from the current code
1170 * but is useful during debugging.
1172 static void check_lexpos(struct isl_tab
*tab
) __attribute__ ((unused
));
1173 static void check_lexpos(struct isl_tab
*tab
)
1175 unsigned off
= 2 + tab
->M
;
1180 for (col
= tab
->n_dead
; col
< tab
->n_col
; ++col
) {
1181 if (tab
->col_var
[col
] >= 0 &&
1182 (tab
->col_var
[col
] < tab
->n_param
||
1183 tab
->col_var
[col
] >= tab
->n_var
- tab
->n_div
))
1185 for (var
= tab
->n_param
; var
< tab
->n_var
- tab
->n_div
; ++var
) {
1186 if (!tab
->var
[var
].is_row
) {
1187 if (tab
->var
[var
].index
== col
)
1192 row
= tab
->var
[var
].index
;
1193 if (isl_int_is_zero(tab
->mat
->row
[row
][off
+ col
]))
1195 if (isl_int_is_pos(tab
->mat
->row
[row
][off
+ col
]))
1197 fprintf(stderr
, "lexneg column %d (row %d)\n",
1200 if (var
>= tab
->n_var
- tab
->n_div
)
1201 fprintf(stderr
, "zero column %d\n", col
);
1205 /* Report to the caller that the given constraint is part of an encountered
1208 static int report_conflicting_constraint(struct isl_tab
*tab
, int con
)
1210 return tab
->conflict(con
, tab
->conflict_user
);
1213 /* Given a conflicting row in the tableau, report all constraints
1214 * involved in the row to the caller. That is, the row itself
1215 * (if it represents a constraint) and all constraint columns with
1216 * non-zero (and therefore negative) coefficients.
1218 static int report_conflict(struct isl_tab
*tab
, int row
)
1226 if (tab
->row_var
[row
] < 0 &&
1227 report_conflicting_constraint(tab
, ~tab
->row_var
[row
]) < 0)
1230 tr
= tab
->mat
->row
[row
] + 2 + tab
->M
;
1232 for (j
= tab
->n_dead
; j
< tab
->n_col
; ++j
) {
1233 if (tab
->col_var
[j
] >= 0 &&
1234 (tab
->col_var
[j
] < tab
->n_param
||
1235 tab
->col_var
[j
] >= tab
->n_var
- tab
->n_div
))
1238 if (!isl_int_is_neg(tr
[j
]))
1241 if (tab
->col_var
[j
] < 0 &&
1242 report_conflicting_constraint(tab
, ~tab
->col_var
[j
]) < 0)
1249 /* Resolve all known or obviously violated constraints through pivoting.
1250 * In particular, as long as we can find any violated constraint, we
1251 * look for a pivoting column that would result in the lexicographically
1252 * smallest increment in the sample point. If there is no such column
1253 * then the tableau is infeasible.
1255 static int restore_lexmin(struct isl_tab
*tab
) WARN_UNUSED
;
1256 static int restore_lexmin(struct isl_tab
*tab
)
1264 while ((row
= first_neg(tab
)) != -1) {
1265 col
= lexmin_pivot_col(tab
, row
);
1266 if (col
>= tab
->n_col
) {
1267 if (report_conflict(tab
, row
) < 0)
1269 if (isl_tab_mark_empty(tab
) < 0)
1275 if (isl_tab_pivot(tab
, row
, col
) < 0)
1281 /* Given a row that represents an equality, look for an appropriate
1283 * In particular, if there are any non-zero coefficients among
1284 * the non-parameter variables, then we take the last of these
1285 * variables. Eliminating this variable in terms of the other
1286 * variables and/or parameters does not influence the property
1287 * that all column in the initial tableau are lexicographically
1288 * positive. The row corresponding to the eliminated variable
1289 * will only have non-zero entries below the diagonal of the
1290 * initial tableau. That is, we transform
1296 * If there is no such non-parameter variable, then we are dealing with
1297 * pure parameter equality and we pick any parameter with coefficient 1 or -1
1298 * for elimination. This will ensure that the eliminated parameter
1299 * always has an integer value whenever all the other parameters are integral.
1300 * If there is no such parameter then we return -1.
1302 static int last_var_col_or_int_par_col(struct isl_tab
*tab
, int row
)
1304 unsigned off
= 2 + tab
->M
;
1307 for (i
= tab
->n_var
- tab
->n_div
- 1; i
>= 0 && i
>= tab
->n_param
; --i
) {
1309 if (tab
->var
[i
].is_row
)
1311 col
= tab
->var
[i
].index
;
1312 if (col
<= tab
->n_dead
)
1314 if (!isl_int_is_zero(tab
->mat
->row
[row
][off
+ col
]))
1317 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
1318 if (isl_int_is_one(tab
->mat
->row
[row
][off
+ i
]))
1320 if (isl_int_is_negone(tab
->mat
->row
[row
][off
+ i
]))
1326 /* Add an equality that is known to be valid to the tableau.
1327 * We first check if we can eliminate a variable or a parameter.
1328 * If not, we add the equality as two inequalities.
1329 * In this case, the equality was a pure parameter equality and there
1330 * is no need to resolve any constraint violations.
1332 * This function assumes that at least two more rows and at least
1333 * two more elements in the constraint array are available in the tableau.
1335 static struct isl_tab
*add_lexmin_valid_eq(struct isl_tab
*tab
, isl_int
*eq
)
1342 r
= isl_tab_add_row(tab
, eq
);
1346 r
= tab
->con
[r
].index
;
1347 i
= last_var_col_or_int_par_col(tab
, r
);
1349 tab
->con
[r
].is_nonneg
= 1;
1350 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]) < 0)
1352 isl_seq_neg(eq
, eq
, 1 + tab
->n_var
);
1353 r
= isl_tab_add_row(tab
, eq
);
1356 tab
->con
[r
].is_nonneg
= 1;
1357 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]) < 0)
1360 if (isl_tab_pivot(tab
, r
, i
) < 0)
1362 if (isl_tab_kill_col(tab
, i
) < 0)
1373 /* Check if the given row is a pure constant.
1375 static int is_constant(struct isl_tab
*tab
, int row
)
1377 unsigned off
= 2 + tab
->M
;
1379 return isl_seq_first_non_zero(tab
->mat
->row
[row
] + off
+ tab
->n_dead
,
1380 tab
->n_col
- tab
->n_dead
) == -1;
1383 /* Add an equality that may or may not be valid to the tableau.
1384 * If the resulting row is a pure constant, then it must be zero.
1385 * Otherwise, the resulting tableau is empty.
1387 * If the row is not a pure constant, then we add two inequalities,
1388 * each time checking that they can be satisfied.
1389 * In the end we try to use one of the two constraints to eliminate
1392 * This function assumes that at least two more rows and at least
1393 * two more elements in the constraint array are available in the tableau.
1395 static int add_lexmin_eq(struct isl_tab
*tab
, isl_int
*eq
) WARN_UNUSED
;
1396 static int add_lexmin_eq(struct isl_tab
*tab
, isl_int
*eq
)
1400 struct isl_tab_undo
*snap
;
1404 snap
= isl_tab_snap(tab
);
1405 r1
= isl_tab_add_row(tab
, eq
);
1408 tab
->con
[r1
].is_nonneg
= 1;
1409 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r1
]) < 0)
1412 row
= tab
->con
[r1
].index
;
1413 if (is_constant(tab
, row
)) {
1414 if (!isl_int_is_zero(tab
->mat
->row
[row
][1]) ||
1415 (tab
->M
&& !isl_int_is_zero(tab
->mat
->row
[row
][2]))) {
1416 if (isl_tab_mark_empty(tab
) < 0)
1420 if (isl_tab_rollback(tab
, snap
) < 0)
1425 if (restore_lexmin(tab
) < 0)
1430 isl_seq_neg(eq
, eq
, 1 + tab
->n_var
);
1432 r2
= isl_tab_add_row(tab
, eq
);
1435 tab
->con
[r2
].is_nonneg
= 1;
1436 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r2
]) < 0)
1439 if (restore_lexmin(tab
) < 0)
1444 if (!tab
->con
[r1
].is_row
) {
1445 if (isl_tab_kill_col(tab
, tab
->con
[r1
].index
) < 0)
1447 } else if (!tab
->con
[r2
].is_row
) {
1448 if (isl_tab_kill_col(tab
, tab
->con
[r2
].index
) < 0)
1453 tab
->bmap
= isl_basic_map_add_ineq(tab
->bmap
, eq
);
1454 if (isl_tab_push(tab
, isl_tab_undo_bmap_ineq
) < 0)
1456 isl_seq_neg(eq
, eq
, 1 + tab
->n_var
);
1457 tab
->bmap
= isl_basic_map_add_ineq(tab
->bmap
, eq
);
1458 isl_seq_neg(eq
, eq
, 1 + tab
->n_var
);
1459 if (isl_tab_push(tab
, isl_tab_undo_bmap_ineq
) < 0)
1468 /* Add an inequality to the tableau, resolving violations using
1471 * This function assumes that at least one more row and at least
1472 * one more element in the constraint array are available in the tableau.
1474 static struct isl_tab
*add_lexmin_ineq(struct isl_tab
*tab
, isl_int
*ineq
)
1481 tab
->bmap
= isl_basic_map_add_ineq(tab
->bmap
, ineq
);
1482 if (isl_tab_push(tab
, isl_tab_undo_bmap_ineq
) < 0)
1487 r
= isl_tab_add_row(tab
, ineq
);
1490 tab
->con
[r
].is_nonneg
= 1;
1491 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]) < 0)
1493 if (isl_tab_row_is_redundant(tab
, tab
->con
[r
].index
)) {
1494 if (isl_tab_mark_redundant(tab
, tab
->con
[r
].index
) < 0)
1499 if (restore_lexmin(tab
) < 0)
1501 if (!tab
->empty
&& tab
->con
[r
].is_row
&&
1502 isl_tab_row_is_redundant(tab
, tab
->con
[r
].index
))
1503 if (isl_tab_mark_redundant(tab
, tab
->con
[r
].index
) < 0)
1511 /* Check if the coefficients of the parameters are all integral.
1513 static int integer_parameter(struct isl_tab
*tab
, int row
)
1517 unsigned off
= 2 + tab
->M
;
1519 for (i
= 0; i
< tab
->n_param
; ++i
) {
1520 /* Eliminated parameter */
1521 if (tab
->var
[i
].is_row
)
1523 col
= tab
->var
[i
].index
;
1524 if (!isl_int_is_divisible_by(tab
->mat
->row
[row
][off
+ col
],
1525 tab
->mat
->row
[row
][0]))
1528 for (i
= 0; i
< tab
->n_div
; ++i
) {
1529 if (tab
->var
[tab
->n_var
- tab
->n_div
+ i
].is_row
)
1531 col
= tab
->var
[tab
->n_var
- tab
->n_div
+ i
].index
;
1532 if (!isl_int_is_divisible_by(tab
->mat
->row
[row
][off
+ col
],
1533 tab
->mat
->row
[row
][0]))
1539 /* Check if the coefficients of the non-parameter variables are all integral.
1541 static int integer_variable(struct isl_tab
*tab
, int row
)
1544 unsigned off
= 2 + tab
->M
;
1546 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
1547 if (tab
->col_var
[i
] >= 0 &&
1548 (tab
->col_var
[i
] < tab
->n_param
||
1549 tab
->col_var
[i
] >= tab
->n_var
- tab
->n_div
))
1551 if (!isl_int_is_divisible_by(tab
->mat
->row
[row
][off
+ i
],
1552 tab
->mat
->row
[row
][0]))
1558 /* Check if the constant term is integral.
1560 static int integer_constant(struct isl_tab
*tab
, int row
)
1562 return isl_int_is_divisible_by(tab
->mat
->row
[row
][1],
1563 tab
->mat
->row
[row
][0]);
1566 #define I_CST 1 << 0
1567 #define I_PAR 1 << 1
1568 #define I_VAR 1 << 2
1570 /* Check for next (non-parameter) variable after "var" (first if var == -1)
1571 * that is non-integer and therefore requires a cut and return
1572 * the index of the variable.
1573 * For parametric tableaus, there are three parts in a row,
1574 * the constant, the coefficients of the parameters and the rest.
1575 * For each part, we check whether the coefficients in that part
1576 * are all integral and if so, set the corresponding flag in *f.
1577 * If the constant and the parameter part are integral, then the
1578 * current sample value is integral and no cut is required
1579 * (irrespective of whether the variable part is integral).
1581 static int next_non_integer_var(struct isl_tab
*tab
, int var
, int *f
)
1583 var
= var
< 0 ? tab
->n_param
: var
+ 1;
1585 for (; var
< tab
->n_var
- tab
->n_div
; ++var
) {
1588 if (!tab
->var
[var
].is_row
)
1590 row
= tab
->var
[var
].index
;
1591 if (integer_constant(tab
, row
))
1592 ISL_FL_SET(flags
, I_CST
);
1593 if (integer_parameter(tab
, row
))
1594 ISL_FL_SET(flags
, I_PAR
);
1595 if (ISL_FL_ISSET(flags
, I_CST
) && ISL_FL_ISSET(flags
, I_PAR
))
1597 if (integer_variable(tab
, row
))
1598 ISL_FL_SET(flags
, I_VAR
);
1605 /* Check for first (non-parameter) variable that is non-integer and
1606 * therefore requires a cut and return the corresponding row.
1607 * For parametric tableaus, there are three parts in a row,
1608 * the constant, the coefficients of the parameters and the rest.
1609 * For each part, we check whether the coefficients in that part
1610 * are all integral and if so, set the corresponding flag in *f.
1611 * If the constant and the parameter part are integral, then the
1612 * current sample value is integral and no cut is required
1613 * (irrespective of whether the variable part is integral).
1615 static int first_non_integer_row(struct isl_tab
*tab
, int *f
)
1617 int var
= next_non_integer_var(tab
, -1, f
);
1619 return var
< 0 ? -1 : tab
->var
[var
].index
;
1622 /* Add a (non-parametric) cut to cut away the non-integral sample
1623 * value of the given row.
1625 * If the row is given by
1627 * m r = f + \sum_i a_i y_i
1631 * c = - {-f/m} + \sum_i {a_i/m} y_i >= 0
1633 * The big parameter, if any, is ignored, since it is assumed to be big
1634 * enough to be divisible by any integer.
1635 * If the tableau is actually a parametric tableau, then this function
1636 * is only called when all coefficients of the parameters are integral.
1637 * The cut therefore has zero coefficients for the parameters.
1639 * The current value is known to be negative, so row_sign, if it
1640 * exists, is set accordingly.
1642 * Return the row of the cut or -1.
1644 static int add_cut(struct isl_tab
*tab
, int row
)
1649 unsigned off
= 2 + tab
->M
;
1651 if (isl_tab_extend_cons(tab
, 1) < 0)
1653 r
= isl_tab_allocate_con(tab
);
1657 r_row
= tab
->mat
->row
[tab
->con
[r
].index
];
1658 isl_int_set(r_row
[0], tab
->mat
->row
[row
][0]);
1659 isl_int_neg(r_row
[1], tab
->mat
->row
[row
][1]);
1660 isl_int_fdiv_r(r_row
[1], r_row
[1], tab
->mat
->row
[row
][0]);
1661 isl_int_neg(r_row
[1], r_row
[1]);
1663 isl_int_set_si(r_row
[2], 0);
1664 for (i
= 0; i
< tab
->n_col
; ++i
)
1665 isl_int_fdiv_r(r_row
[off
+ i
],
1666 tab
->mat
->row
[row
][off
+ i
], tab
->mat
->row
[row
][0]);
1668 tab
->con
[r
].is_nonneg
= 1;
1669 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]) < 0)
1672 tab
->row_sign
[tab
->con
[r
].index
] = isl_tab_row_neg
;
1674 return tab
->con
[r
].index
;
1680 /* Given a non-parametric tableau, add cuts until an integer
1681 * sample point is obtained or until the tableau is determined
1682 * to be integer infeasible.
1683 * As long as there is any non-integer value in the sample point,
1684 * we add appropriate cuts, if possible, for each of these
1685 * non-integer values and then resolve the violated
1686 * cut constraints using restore_lexmin.
1687 * If one of the corresponding rows is equal to an integral
1688 * combination of variables/constraints plus a non-integral constant,
1689 * then there is no way to obtain an integer point and we return
1690 * a tableau that is marked empty.
1691 * The parameter cutting_strategy controls the strategy used when adding cuts
1692 * to remove non-integer points. CUT_ALL adds all possible cuts
1693 * before continuing the search. CUT_ONE adds only one cut at a time.
1695 static struct isl_tab
*cut_to_integer_lexmin(struct isl_tab
*tab
,
1696 int cutting_strategy
)
1707 while ((var
= next_non_integer_var(tab
, -1, &flags
)) != -1) {
1709 if (ISL_FL_ISSET(flags
, I_VAR
)) {
1710 if (isl_tab_mark_empty(tab
) < 0)
1714 row
= tab
->var
[var
].index
;
1715 row
= add_cut(tab
, row
);
1718 if (cutting_strategy
== CUT_ONE
)
1720 } while ((var
= next_non_integer_var(tab
, var
, &flags
)) != -1);
1721 if (restore_lexmin(tab
) < 0)
1732 /* Check whether all the currently active samples also satisfy the inequality
1733 * "ineq" (treated as an equality if eq is set).
1734 * Remove those samples that do not.
1736 static struct isl_tab
*check_samples(struct isl_tab
*tab
, isl_int
*ineq
, int eq
)
1744 isl_assert(tab
->mat
->ctx
, tab
->bmap
, goto error
);
1745 isl_assert(tab
->mat
->ctx
, tab
->samples
, goto error
);
1746 isl_assert(tab
->mat
->ctx
, tab
->samples
->n_col
== 1 + tab
->n_var
, goto error
);
1749 for (i
= tab
->n_outside
; i
< tab
->n_sample
; ++i
) {
1751 isl_seq_inner_product(ineq
, tab
->samples
->row
[i
],
1752 1 + tab
->n_var
, &v
);
1753 sgn
= isl_int_sgn(v
);
1754 if (eq
? (sgn
== 0) : (sgn
>= 0))
1756 tab
= isl_tab_drop_sample(tab
, i
);
1768 /* Check whether the sample value of the tableau is finite,
1769 * i.e., either the tableau does not use a big parameter, or
1770 * all values of the variables are equal to the big parameter plus
1771 * some constant. This constant is the actual sample value.
1773 static int sample_is_finite(struct isl_tab
*tab
)
1780 for (i
= 0; i
< tab
->n_var
; ++i
) {
1782 if (!tab
->var
[i
].is_row
)
1784 row
= tab
->var
[i
].index
;
1785 if (isl_int_ne(tab
->mat
->row
[row
][0], tab
->mat
->row
[row
][2]))
1791 /* Check if the context tableau of sol has any integer points.
1792 * Leave tab in empty state if no integer point can be found.
1793 * If an integer point can be found and if moreover it is finite,
1794 * then it is added to the list of sample values.
1796 * This function is only called when none of the currently active sample
1797 * values satisfies the most recently added constraint.
1799 static struct isl_tab
*check_integer_feasible(struct isl_tab
*tab
)
1801 struct isl_tab_undo
*snap
;
1806 snap
= isl_tab_snap(tab
);
1807 if (isl_tab_push_basis(tab
) < 0)
1810 tab
= cut_to_integer_lexmin(tab
, CUT_ALL
);
1814 if (!tab
->empty
&& sample_is_finite(tab
)) {
1815 struct isl_vec
*sample
;
1817 sample
= isl_tab_get_sample_value(tab
);
1819 if (isl_tab_add_sample(tab
, sample
) < 0)
1823 if (!tab
->empty
&& isl_tab_rollback(tab
, snap
) < 0)
1832 /* Check if any of the currently active sample values satisfies
1833 * the inequality "ineq" (an equality if eq is set).
1835 static int tab_has_valid_sample(struct isl_tab
*tab
, isl_int
*ineq
, int eq
)
1843 isl_assert(tab
->mat
->ctx
, tab
->bmap
, return -1);
1844 isl_assert(tab
->mat
->ctx
, tab
->samples
, return -1);
1845 isl_assert(tab
->mat
->ctx
, tab
->samples
->n_col
== 1 + tab
->n_var
, return -1);
1848 for (i
= tab
->n_outside
; i
< tab
->n_sample
; ++i
) {
1850 isl_seq_inner_product(ineq
, tab
->samples
->row
[i
],
1851 1 + tab
->n_var
, &v
);
1852 sgn
= isl_int_sgn(v
);
1853 if (eq
? (sgn
== 0) : (sgn
>= 0))
1858 return i
< tab
->n_sample
;
1861 /* Add a div specified by "div" to the tableau "tab" and return
1862 * 1 if the div is obviously non-negative.
1864 static int context_tab_add_div(struct isl_tab
*tab
, struct isl_vec
*div
,
1865 int (*add_ineq
)(void *user
, isl_int
*), void *user
)
1869 struct isl_mat
*samples
;
1872 r
= isl_tab_add_div(tab
, div
, add_ineq
, user
);
1875 nonneg
= tab
->var
[r
].is_nonneg
;
1876 tab
->var
[r
].frozen
= 1;
1878 samples
= isl_mat_extend(tab
->samples
,
1879 tab
->n_sample
, 1 + tab
->n_var
);
1880 tab
->samples
= samples
;
1883 for (i
= tab
->n_outside
; i
< samples
->n_row
; ++i
) {
1884 isl_seq_inner_product(div
->el
+ 1, samples
->row
[i
],
1885 div
->size
- 1, &samples
->row
[i
][samples
->n_col
- 1]);
1886 isl_int_fdiv_q(samples
->row
[i
][samples
->n_col
- 1],
1887 samples
->row
[i
][samples
->n_col
- 1], div
->el
[0]);
1893 /* Add a div specified by "div" to both the main tableau and
1894 * the context tableau. In case of the main tableau, we only
1895 * need to add an extra div. In the context tableau, we also
1896 * need to express the meaning of the div.
1897 * Return the index of the div or -1 if anything went wrong.
1899 static int add_div(struct isl_tab
*tab
, struct isl_context
*context
,
1900 struct isl_vec
*div
)
1905 if ((nonneg
= context
->op
->add_div(context
, div
)) < 0)
1908 if (!context
->op
->is_ok(context
))
1911 if (isl_tab_extend_vars(tab
, 1) < 0)
1913 r
= isl_tab_allocate_var(tab
);
1917 tab
->var
[r
].is_nonneg
= 1;
1918 tab
->var
[r
].frozen
= 1;
1921 return tab
->n_div
- 1;
1923 context
->op
->invalidate(context
);
1927 static int find_div(struct isl_tab
*tab
, isl_int
*div
, isl_int denom
)
1930 unsigned total
= isl_basic_map_total_dim(tab
->bmap
);
1932 for (i
= 0; i
< tab
->bmap
->n_div
; ++i
) {
1933 if (isl_int_ne(tab
->bmap
->div
[i
][0], denom
))
1935 if (!isl_seq_eq(tab
->bmap
->div
[i
] + 1, div
, 1 + total
))
1942 /* Return the index of a div that corresponds to "div".
1943 * We first check if we already have such a div and if not, we create one.
1945 static int get_div(struct isl_tab
*tab
, struct isl_context
*context
,
1946 struct isl_vec
*div
)
1949 struct isl_tab
*context_tab
= context
->op
->peek_tab(context
);
1954 d
= find_div(context_tab
, div
->el
+ 1, div
->el
[0]);
1958 return add_div(tab
, context
, div
);
1961 /* Add a parametric cut to cut away the non-integral sample value
1963 * Let a_i be the coefficients of the constant term and the parameters
1964 * and let b_i be the coefficients of the variables or constraints
1965 * in basis of the tableau.
1966 * Let q be the div q = floor(\sum_i {-a_i} y_i).
1968 * The cut is expressed as
1970 * c = \sum_i -{-a_i} y_i + \sum_i {b_i} x_i + q >= 0
1972 * If q did not already exist in the context tableau, then it is added first.
1973 * If q is in a column of the main tableau then the "+ q" can be accomplished
1974 * by setting the corresponding entry to the denominator of the constraint.
1975 * If q happens to be in a row of the main tableau, then the corresponding
1976 * row needs to be added instead (taking care of the denominators).
1977 * Note that this is very unlikely, but perhaps not entirely impossible.
1979 * The current value of the cut is known to be negative (or at least
1980 * non-positive), so row_sign is set accordingly.
1982 * Return the row of the cut or -1.
1984 static int add_parametric_cut(struct isl_tab
*tab
, int row
,
1985 struct isl_context
*context
)
1987 struct isl_vec
*div
;
1994 unsigned off
= 2 + tab
->M
;
1999 div
= get_row_parameter_div(tab
, row
);
2004 d
= context
->op
->get_div(context
, tab
, div
);
2009 if (isl_tab_extend_cons(tab
, 1) < 0)
2011 r
= isl_tab_allocate_con(tab
);
2015 r_row
= tab
->mat
->row
[tab
->con
[r
].index
];
2016 isl_int_set(r_row
[0], tab
->mat
->row
[row
][0]);
2017 isl_int_neg(r_row
[1], tab
->mat
->row
[row
][1]);
2018 isl_int_fdiv_r(r_row
[1], r_row
[1], tab
->mat
->row
[row
][0]);
2019 isl_int_neg(r_row
[1], r_row
[1]);
2021 isl_int_set_si(r_row
[2], 0);
2022 for (i
= 0; i
< tab
->n_param
; ++i
) {
2023 if (tab
->var
[i
].is_row
)
2025 col
= tab
->var
[i
].index
;
2026 isl_int_neg(r_row
[off
+ col
], tab
->mat
->row
[row
][off
+ col
]);
2027 isl_int_fdiv_r(r_row
[off
+ col
], r_row
[off
+ col
],
2028 tab
->mat
->row
[row
][0]);
2029 isl_int_neg(r_row
[off
+ col
], r_row
[off
+ col
]);
2031 for (i
= 0; i
< tab
->n_div
; ++i
) {
2032 if (tab
->var
[tab
->n_var
- tab
->n_div
+ i
].is_row
)
2034 col
= tab
->var
[tab
->n_var
- tab
->n_div
+ i
].index
;
2035 isl_int_neg(r_row
[off
+ col
], tab
->mat
->row
[row
][off
+ col
]);
2036 isl_int_fdiv_r(r_row
[off
+ col
], r_row
[off
+ col
],
2037 tab
->mat
->row
[row
][0]);
2038 isl_int_neg(r_row
[off
+ col
], r_row
[off
+ col
]);
2040 for (i
= 0; i
< tab
->n_col
; ++i
) {
2041 if (tab
->col_var
[i
] >= 0 &&
2042 (tab
->col_var
[i
] < tab
->n_param
||
2043 tab
->col_var
[i
] >= tab
->n_var
- tab
->n_div
))
2045 isl_int_fdiv_r(r_row
[off
+ i
],
2046 tab
->mat
->row
[row
][off
+ i
], tab
->mat
->row
[row
][0]);
2048 if (tab
->var
[tab
->n_var
- tab
->n_div
+ d
].is_row
) {
2050 int d_row
= tab
->var
[tab
->n_var
- tab
->n_div
+ d
].index
;
2052 isl_int_gcd(gcd
, tab
->mat
->row
[d_row
][0], r_row
[0]);
2053 isl_int_divexact(r_row
[0], r_row
[0], gcd
);
2054 isl_int_divexact(gcd
, tab
->mat
->row
[d_row
][0], gcd
);
2055 isl_seq_combine(r_row
+ 1, gcd
, r_row
+ 1,
2056 r_row
[0], tab
->mat
->row
[d_row
] + 1,
2057 off
- 1 + tab
->n_col
);
2058 isl_int_mul(r_row
[0], r_row
[0], tab
->mat
->row
[d_row
][0]);
2061 col
= tab
->var
[tab
->n_var
- tab
->n_div
+ d
].index
;
2062 isl_int_set(r_row
[off
+ col
], tab
->mat
->row
[row
][0]);
2065 tab
->con
[r
].is_nonneg
= 1;
2066 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]) < 0)
2069 tab
->row_sign
[tab
->con
[r
].index
] = isl_tab_row_neg
;
2071 row
= tab
->con
[r
].index
;
2073 if (d
>= n
&& context
->op
->detect_equalities(context
, tab
) < 0)
2079 /* Construct a tableau for bmap that can be used for computing
2080 * the lexicographic minimum (or maximum) of bmap.
2081 * If not NULL, then dom is the domain where the minimum
2082 * should be computed. In this case, we set up a parametric
2083 * tableau with row signs (initialized to "unknown").
2084 * If M is set, then the tableau will use a big parameter.
2085 * If max is set, then a maximum should be computed instead of a minimum.
2086 * This means that for each variable x, the tableau will contain the variable
2087 * x' = M - x, rather than x' = M + x. This in turn means that the coefficient
2088 * of the variables in all constraints are negated prior to adding them
2091 static struct isl_tab
*tab_for_lexmin(struct isl_basic_map
*bmap
,
2092 struct isl_basic_set
*dom
, unsigned M
, int max
)
2095 struct isl_tab
*tab
;
2099 tab
= isl_tab_alloc(bmap
->ctx
, 2 * bmap
->n_eq
+ bmap
->n_ineq
+ 1,
2100 isl_basic_map_total_dim(bmap
), M
);
2104 tab
->rational
= ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
);
2106 tab
->n_param
= isl_basic_set_total_dim(dom
) - dom
->n_div
;
2107 tab
->n_div
= dom
->n_div
;
2108 tab
->row_sign
= isl_calloc_array(bmap
->ctx
,
2109 enum isl_tab_row_sign
, tab
->mat
->n_row
);
2110 if (tab
->mat
->n_row
&& !tab
->row_sign
)
2113 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
)) {
2114 if (isl_tab_mark_empty(tab
) < 0)
2119 for (i
= tab
->n_param
; i
< tab
->n_var
- tab
->n_div
; ++i
) {
2120 tab
->var
[i
].is_nonneg
= 1;
2121 tab
->var
[i
].frozen
= 1;
2123 o_var
= 1 + tab
->n_param
;
2124 n_var
= tab
->n_var
- tab
->n_param
- tab
->n_div
;
2125 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
2127 isl_seq_neg(bmap
->eq
[i
] + o_var
,
2128 bmap
->eq
[i
] + o_var
, n_var
);
2129 tab
= add_lexmin_valid_eq(tab
, bmap
->eq
[i
]);
2131 isl_seq_neg(bmap
->eq
[i
] + o_var
,
2132 bmap
->eq
[i
] + o_var
, n_var
);
2133 if (!tab
|| tab
->empty
)
2136 if (bmap
->n_eq
&& restore_lexmin(tab
) < 0)
2138 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
2140 isl_seq_neg(bmap
->ineq
[i
] + o_var
,
2141 bmap
->ineq
[i
] + o_var
, n_var
);
2142 tab
= add_lexmin_ineq(tab
, bmap
->ineq
[i
]);
2144 isl_seq_neg(bmap
->ineq
[i
] + o_var
,
2145 bmap
->ineq
[i
] + o_var
, n_var
);
2146 if (!tab
|| tab
->empty
)
2155 /* Given a main tableau where more than one row requires a split,
2156 * determine and return the "best" row to split on.
2158 * Given two rows in the main tableau, if the inequality corresponding
2159 * to the first row is redundant with respect to that of the second row
2160 * in the current tableau, then it is better to split on the second row,
2161 * since in the positive part, both rows will be positive.
2162 * (In the negative part a pivot will have to be performed and just about
2163 * anything can happen to the sign of the other row.)
2165 * As a simple heuristic, we therefore select the row that makes the most
2166 * of the other rows redundant.
2168 * Perhaps it would also be useful to look at the number of constraints
2169 * that conflict with any given constraint.
2171 * best is the best row so far (-1 when we have not found any row yet).
2172 * best_r is the number of other rows made redundant by row best.
2173 * When best is still -1, bset_r is meaningless, but it is initialized
2174 * to some arbitrary value (0) anyway. Without this redundant initialization
2175 * valgrind may warn about uninitialized memory accesses when isl
2176 * is compiled with some versions of gcc.
2178 static int best_split(struct isl_tab
*tab
, struct isl_tab
*context_tab
)
2180 struct isl_tab_undo
*snap
;
2186 if (isl_tab_extend_cons(context_tab
, 2) < 0)
2189 snap
= isl_tab_snap(context_tab
);
2191 for (split
= tab
->n_redundant
; split
< tab
->n_row
; ++split
) {
2192 struct isl_tab_undo
*snap2
;
2193 struct isl_vec
*ineq
= NULL
;
2197 if (!isl_tab_var_from_row(tab
, split
)->is_nonneg
)
2199 if (tab
->row_sign
[split
] != isl_tab_row_any
)
2202 ineq
= get_row_parameter_ineq(tab
, split
);
2205 ok
= isl_tab_add_ineq(context_tab
, ineq
->el
) >= 0;
2210 snap2
= isl_tab_snap(context_tab
);
2212 for (row
= tab
->n_redundant
; row
< tab
->n_row
; ++row
) {
2213 struct isl_tab_var
*var
;
2217 if (!isl_tab_var_from_row(tab
, row
)->is_nonneg
)
2219 if (tab
->row_sign
[row
] != isl_tab_row_any
)
2222 ineq
= get_row_parameter_ineq(tab
, row
);
2225 ok
= isl_tab_add_ineq(context_tab
, ineq
->el
) >= 0;
2229 var
= &context_tab
->con
[context_tab
->n_con
- 1];
2230 if (!context_tab
->empty
&&
2231 !isl_tab_min_at_most_neg_one(context_tab
, var
))
2233 if (isl_tab_rollback(context_tab
, snap2
) < 0)
2236 if (best
== -1 || r
> best_r
) {
2240 if (isl_tab_rollback(context_tab
, snap
) < 0)
2247 static struct isl_basic_set
*context_lex_peek_basic_set(
2248 struct isl_context
*context
)
2250 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2253 return isl_tab_peek_bset(clex
->tab
);
2256 static struct isl_tab
*context_lex_peek_tab(struct isl_context
*context
)
2258 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2262 static void context_lex_add_eq(struct isl_context
*context
, isl_int
*eq
,
2263 int check
, int update
)
2265 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2266 if (isl_tab_extend_cons(clex
->tab
, 2) < 0)
2268 if (add_lexmin_eq(clex
->tab
, eq
) < 0)
2271 int v
= tab_has_valid_sample(clex
->tab
, eq
, 1);
2275 clex
->tab
= check_integer_feasible(clex
->tab
);
2278 clex
->tab
= check_samples(clex
->tab
, eq
, 1);
2281 isl_tab_free(clex
->tab
);
2285 static void context_lex_add_ineq(struct isl_context
*context
, isl_int
*ineq
,
2286 int check
, int update
)
2288 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2289 if (isl_tab_extend_cons(clex
->tab
, 1) < 0)
2291 clex
->tab
= add_lexmin_ineq(clex
->tab
, ineq
);
2293 int v
= tab_has_valid_sample(clex
->tab
, ineq
, 0);
2297 clex
->tab
= check_integer_feasible(clex
->tab
);
2300 clex
->tab
= check_samples(clex
->tab
, ineq
, 0);
2303 isl_tab_free(clex
->tab
);
2307 static int context_lex_add_ineq_wrap(void *user
, isl_int
*ineq
)
2309 struct isl_context
*context
= (struct isl_context
*)user
;
2310 context_lex_add_ineq(context
, ineq
, 0, 0);
2311 return context
->op
->is_ok(context
) ? 0 : -1;
2314 /* Check which signs can be obtained by "ineq" on all the currently
2315 * active sample values. See row_sign for more information.
2317 static enum isl_tab_row_sign
tab_ineq_sign(struct isl_tab
*tab
, isl_int
*ineq
,
2323 enum isl_tab_row_sign res
= isl_tab_row_unknown
;
2325 isl_assert(tab
->mat
->ctx
, tab
->samples
, return isl_tab_row_unknown
);
2326 isl_assert(tab
->mat
->ctx
, tab
->samples
->n_col
== 1 + tab
->n_var
,
2327 return isl_tab_row_unknown
);
2330 for (i
= tab
->n_outside
; i
< tab
->n_sample
; ++i
) {
2331 isl_seq_inner_product(tab
->samples
->row
[i
], ineq
,
2332 1 + tab
->n_var
, &tmp
);
2333 sgn
= isl_int_sgn(tmp
);
2334 if (sgn
> 0 || (sgn
== 0 && strict
)) {
2335 if (res
== isl_tab_row_unknown
)
2336 res
= isl_tab_row_pos
;
2337 if (res
== isl_tab_row_neg
)
2338 res
= isl_tab_row_any
;
2341 if (res
== isl_tab_row_unknown
)
2342 res
= isl_tab_row_neg
;
2343 if (res
== isl_tab_row_pos
)
2344 res
= isl_tab_row_any
;
2346 if (res
== isl_tab_row_any
)
2354 static enum isl_tab_row_sign
context_lex_ineq_sign(struct isl_context
*context
,
2355 isl_int
*ineq
, int strict
)
2357 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2358 return tab_ineq_sign(clex
->tab
, ineq
, strict
);
2361 /* Check whether "ineq" can be added to the tableau without rendering
2364 static int context_lex_test_ineq(struct isl_context
*context
, isl_int
*ineq
)
2366 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2367 struct isl_tab_undo
*snap
;
2373 if (isl_tab_extend_cons(clex
->tab
, 1) < 0)
2376 snap
= isl_tab_snap(clex
->tab
);
2377 if (isl_tab_push_basis(clex
->tab
) < 0)
2379 clex
->tab
= add_lexmin_ineq(clex
->tab
, ineq
);
2380 clex
->tab
= check_integer_feasible(clex
->tab
);
2383 feasible
= !clex
->tab
->empty
;
2384 if (isl_tab_rollback(clex
->tab
, snap
) < 0)
2390 static int context_lex_get_div(struct isl_context
*context
, struct isl_tab
*tab
,
2391 struct isl_vec
*div
)
2393 return get_div(tab
, context
, div
);
2396 /* Add a div specified by "div" to the context tableau and return
2397 * 1 if the div is obviously non-negative.
2398 * context_tab_add_div will always return 1, because all variables
2399 * in a isl_context_lex tableau are non-negative.
2400 * However, if we are using a big parameter in the context, then this only
2401 * reflects the non-negativity of the variable used to _encode_ the
2402 * div, i.e., div' = M + div, so we can't draw any conclusions.
2404 static int context_lex_add_div(struct isl_context
*context
, struct isl_vec
*div
)
2406 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2408 nonneg
= context_tab_add_div(clex
->tab
, div
,
2409 context_lex_add_ineq_wrap
, context
);
2417 static int context_lex_detect_equalities(struct isl_context
*context
,
2418 struct isl_tab
*tab
)
2423 static int context_lex_best_split(struct isl_context
*context
,
2424 struct isl_tab
*tab
)
2426 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2427 struct isl_tab_undo
*snap
;
2430 snap
= isl_tab_snap(clex
->tab
);
2431 if (isl_tab_push_basis(clex
->tab
) < 0)
2433 r
= best_split(tab
, clex
->tab
);
2435 if (r
>= 0 && isl_tab_rollback(clex
->tab
, snap
) < 0)
2441 static int context_lex_is_empty(struct isl_context
*context
)
2443 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2446 return clex
->tab
->empty
;
2449 static void *context_lex_save(struct isl_context
*context
)
2451 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2452 struct isl_tab_undo
*snap
;
2454 snap
= isl_tab_snap(clex
->tab
);
2455 if (isl_tab_push_basis(clex
->tab
) < 0)
2457 if (isl_tab_save_samples(clex
->tab
) < 0)
2463 static void context_lex_restore(struct isl_context
*context
, void *save
)
2465 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2466 if (isl_tab_rollback(clex
->tab
, (struct isl_tab_undo
*)save
) < 0) {
2467 isl_tab_free(clex
->tab
);
2472 static void context_lex_discard(void *save
)
2476 static int context_lex_is_ok(struct isl_context
*context
)
2478 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2482 /* For each variable in the context tableau, check if the variable can
2483 * only attain non-negative values. If so, mark the parameter as non-negative
2484 * in the main tableau. This allows for a more direct identification of some
2485 * cases of violated constraints.
2487 static struct isl_tab
*tab_detect_nonnegative_parameters(struct isl_tab
*tab
,
2488 struct isl_tab
*context_tab
)
2491 struct isl_tab_undo
*snap
;
2492 struct isl_vec
*ineq
= NULL
;
2493 struct isl_tab_var
*var
;
2496 if (context_tab
->n_var
== 0)
2499 ineq
= isl_vec_alloc(tab
->mat
->ctx
, 1 + context_tab
->n_var
);
2503 if (isl_tab_extend_cons(context_tab
, 1) < 0)
2506 snap
= isl_tab_snap(context_tab
);
2509 isl_seq_clr(ineq
->el
, ineq
->size
);
2510 for (i
= 0; i
< context_tab
->n_var
; ++i
) {
2511 isl_int_set_si(ineq
->el
[1 + i
], 1);
2512 if (isl_tab_add_ineq(context_tab
, ineq
->el
) < 0)
2514 var
= &context_tab
->con
[context_tab
->n_con
- 1];
2515 if (!context_tab
->empty
&&
2516 !isl_tab_min_at_most_neg_one(context_tab
, var
)) {
2518 if (i
>= tab
->n_param
)
2519 j
= i
- tab
->n_param
+ tab
->n_var
- tab
->n_div
;
2520 tab
->var
[j
].is_nonneg
= 1;
2523 isl_int_set_si(ineq
->el
[1 + i
], 0);
2524 if (isl_tab_rollback(context_tab
, snap
) < 0)
2528 if (context_tab
->M
&& n
== context_tab
->n_var
) {
2529 context_tab
->mat
= isl_mat_drop_cols(context_tab
->mat
, 2, 1);
2541 static struct isl_tab
*context_lex_detect_nonnegative_parameters(
2542 struct isl_context
*context
, struct isl_tab
*tab
)
2544 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2545 struct isl_tab_undo
*snap
;
2550 snap
= isl_tab_snap(clex
->tab
);
2551 if (isl_tab_push_basis(clex
->tab
) < 0)
2554 tab
= tab_detect_nonnegative_parameters(tab
, clex
->tab
);
2556 if (isl_tab_rollback(clex
->tab
, snap
) < 0)
2565 static void context_lex_invalidate(struct isl_context
*context
)
2567 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2568 isl_tab_free(clex
->tab
);
2572 static void context_lex_free(struct isl_context
*context
)
2574 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2575 isl_tab_free(clex
->tab
);
2579 struct isl_context_op isl_context_lex_op
= {
2580 context_lex_detect_nonnegative_parameters
,
2581 context_lex_peek_basic_set
,
2582 context_lex_peek_tab
,
2584 context_lex_add_ineq
,
2585 context_lex_ineq_sign
,
2586 context_lex_test_ineq
,
2587 context_lex_get_div
,
2588 context_lex_add_div
,
2589 context_lex_detect_equalities
,
2590 context_lex_best_split
,
2591 context_lex_is_empty
,
2594 context_lex_restore
,
2595 context_lex_discard
,
2596 context_lex_invalidate
,
2600 static struct isl_tab
*context_tab_for_lexmin(struct isl_basic_set
*bset
)
2602 struct isl_tab
*tab
;
2606 tab
= tab_for_lexmin((struct isl_basic_map
*)bset
, NULL
, 1, 0);
2609 if (isl_tab_track_bset(tab
, bset
) < 0)
2611 tab
= isl_tab_init_samples(tab
);
2614 isl_basic_set_free(bset
);
2618 static struct isl_context
*isl_context_lex_alloc(struct isl_basic_set
*dom
)
2620 struct isl_context_lex
*clex
;
2625 clex
= isl_alloc_type(dom
->ctx
, struct isl_context_lex
);
2629 clex
->context
.op
= &isl_context_lex_op
;
2631 clex
->tab
= context_tab_for_lexmin(isl_basic_set_copy(dom
));
2632 if (restore_lexmin(clex
->tab
) < 0)
2634 clex
->tab
= check_integer_feasible(clex
->tab
);
2638 return &clex
->context
;
2640 clex
->context
.op
->free(&clex
->context
);
2644 /* Representation of the context when using generalized basis reduction.
2646 * "shifted" contains the offsets of the unit hypercubes that lie inside the
2647 * context. Any rational point in "shifted" can therefore be rounded
2648 * up to an integer point in the context.
2649 * If the context is constrained by any equality, then "shifted" is not used
2650 * as it would be empty.
2652 struct isl_context_gbr
{
2653 struct isl_context context
;
2654 struct isl_tab
*tab
;
2655 struct isl_tab
*shifted
;
2656 struct isl_tab
*cone
;
2659 static struct isl_tab
*context_gbr_detect_nonnegative_parameters(
2660 struct isl_context
*context
, struct isl_tab
*tab
)
2662 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
2665 return tab_detect_nonnegative_parameters(tab
, cgbr
->tab
);
2668 static struct isl_basic_set
*context_gbr_peek_basic_set(
2669 struct isl_context
*context
)
2671 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
2674 return isl_tab_peek_bset(cgbr
->tab
);
2677 static struct isl_tab
*context_gbr_peek_tab(struct isl_context
*context
)
2679 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
2683 /* Initialize the "shifted" tableau of the context, which
2684 * contains the constraints of the original tableau shifted
2685 * by the sum of all negative coefficients. This ensures
2686 * that any rational point in the shifted tableau can
2687 * be rounded up to yield an integer point in the original tableau.
2689 static void gbr_init_shifted(struct isl_context_gbr
*cgbr
)
2692 struct isl_vec
*cst
;
2693 struct isl_basic_set
*bset
= isl_tab_peek_bset(cgbr
->tab
);
2694 unsigned dim
= isl_basic_set_total_dim(bset
);
2696 cst
= isl_vec_alloc(cgbr
->tab
->mat
->ctx
, bset
->n_ineq
);
2700 for (i
= 0; i
< bset
->n_ineq
; ++i
) {
2701 isl_int_set(cst
->el
[i
], bset
->ineq
[i
][0]);
2702 for (j
= 0; j
< dim
; ++j
) {
2703 if (!isl_int_is_neg(bset
->ineq
[i
][1 + j
]))
2705 isl_int_add(bset
->ineq
[i
][0], bset
->ineq
[i
][0],
2706 bset
->ineq
[i
][1 + j
]);
2710 cgbr
->shifted
= isl_tab_from_basic_set(bset
, 0);
2712 for (i
= 0; i
< bset
->n_ineq
; ++i
)
2713 isl_int_set(bset
->ineq
[i
][0], cst
->el
[i
]);
2718 /* Check if the shifted tableau is non-empty, and if so
2719 * use the sample point to construct an integer point
2720 * of the context tableau.
2722 static struct isl_vec
*gbr_get_shifted_sample(struct isl_context_gbr
*cgbr
)
2724 struct isl_vec
*sample
;
2727 gbr_init_shifted(cgbr
);
2730 if (cgbr
->shifted
->empty
)
2731 return isl_vec_alloc(cgbr
->tab
->mat
->ctx
, 0);
2733 sample
= isl_tab_get_sample_value(cgbr
->shifted
);
2734 sample
= isl_vec_ceil(sample
);
2739 static struct isl_basic_set
*drop_constant_terms(struct isl_basic_set
*bset
)
2746 for (i
= 0; i
< bset
->n_eq
; ++i
)
2747 isl_int_set_si(bset
->eq
[i
][0], 0);
2749 for (i
= 0; i
< bset
->n_ineq
; ++i
)
2750 isl_int_set_si(bset
->ineq
[i
][0], 0);
2755 static int use_shifted(struct isl_context_gbr
*cgbr
)
2759 return cgbr
->tab
->bmap
->n_eq
== 0 && cgbr
->tab
->bmap
->n_div
== 0;
2762 static struct isl_vec
*gbr_get_sample(struct isl_context_gbr
*cgbr
)
2764 struct isl_basic_set
*bset
;
2765 struct isl_basic_set
*cone
;
2767 if (isl_tab_sample_is_integer(cgbr
->tab
))
2768 return isl_tab_get_sample_value(cgbr
->tab
);
2770 if (use_shifted(cgbr
)) {
2771 struct isl_vec
*sample
;
2773 sample
= gbr_get_shifted_sample(cgbr
);
2774 if (!sample
|| sample
->size
> 0)
2777 isl_vec_free(sample
);
2781 bset
= isl_tab_peek_bset(cgbr
->tab
);
2782 cgbr
->cone
= isl_tab_from_recession_cone(bset
, 0);
2785 if (isl_tab_track_bset(cgbr
->cone
,
2786 isl_basic_set_copy(bset
)) < 0)
2789 if (isl_tab_detect_implicit_equalities(cgbr
->cone
) < 0)
2792 if (cgbr
->cone
->n_dead
== cgbr
->cone
->n_col
) {
2793 struct isl_vec
*sample
;
2794 struct isl_tab_undo
*snap
;
2796 if (cgbr
->tab
->basis
) {
2797 if (cgbr
->tab
->basis
->n_col
!= 1 + cgbr
->tab
->n_var
) {
2798 isl_mat_free(cgbr
->tab
->basis
);
2799 cgbr
->tab
->basis
= NULL
;
2801 cgbr
->tab
->n_zero
= 0;
2802 cgbr
->tab
->n_unbounded
= 0;
2805 snap
= isl_tab_snap(cgbr
->tab
);
2807 sample
= isl_tab_sample(cgbr
->tab
);
2809 if (!sample
|| isl_tab_rollback(cgbr
->tab
, snap
) < 0) {
2810 isl_vec_free(sample
);
2817 cone
= isl_basic_set_dup(isl_tab_peek_bset(cgbr
->cone
));
2818 cone
= drop_constant_terms(cone
);
2819 cone
= isl_basic_set_update_from_tab(cone
, cgbr
->cone
);
2820 cone
= isl_basic_set_underlying_set(cone
);
2821 cone
= isl_basic_set_gauss(cone
, NULL
);
2823 bset
= isl_basic_set_dup(isl_tab_peek_bset(cgbr
->tab
));
2824 bset
= isl_basic_set_update_from_tab(bset
, cgbr
->tab
);
2825 bset
= isl_basic_set_underlying_set(bset
);
2826 bset
= isl_basic_set_gauss(bset
, NULL
);
2828 return isl_basic_set_sample_with_cone(bset
, cone
);
2831 static void check_gbr_integer_feasible(struct isl_context_gbr
*cgbr
)
2833 struct isl_vec
*sample
;
2838 if (cgbr
->tab
->empty
)
2841 sample
= gbr_get_sample(cgbr
);
2845 if (sample
->size
== 0) {
2846 isl_vec_free(sample
);
2847 if (isl_tab_mark_empty(cgbr
->tab
) < 0)
2852 if (isl_tab_add_sample(cgbr
->tab
, sample
) < 0)
2857 isl_tab_free(cgbr
->tab
);
2861 static struct isl_tab
*add_gbr_eq(struct isl_tab
*tab
, isl_int
*eq
)
2866 if (isl_tab_extend_cons(tab
, 2) < 0)
2869 if (isl_tab_add_eq(tab
, eq
) < 0)
2878 /* Add the equality described by "eq" to the context.
2879 * If "check" is set, then we check if the context is empty after
2880 * adding the equality.
2881 * If "update" is set, then we check if the samples are still valid.
2883 * We do not explicitly add shifted copies of the equality to
2884 * cgbr->shifted since they would conflict with each other.
2885 * Instead, we directly mark cgbr->shifted empty.
2887 static void context_gbr_add_eq(struct isl_context
*context
, isl_int
*eq
,
2888 int check
, int update
)
2890 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
2892 cgbr
->tab
= add_gbr_eq(cgbr
->tab
, eq
);
2894 if (cgbr
->shifted
&& !cgbr
->shifted
->empty
&& use_shifted(cgbr
)) {
2895 if (isl_tab_mark_empty(cgbr
->shifted
) < 0)
2899 if (cgbr
->cone
&& cgbr
->cone
->n_col
!= cgbr
->cone
->n_dead
) {
2900 if (isl_tab_extend_cons(cgbr
->cone
, 2) < 0)
2902 if (isl_tab_add_eq(cgbr
->cone
, eq
) < 0)
2907 int v
= tab_has_valid_sample(cgbr
->tab
, eq
, 1);
2911 check_gbr_integer_feasible(cgbr
);
2914 cgbr
->tab
= check_samples(cgbr
->tab
, eq
, 1);
2917 isl_tab_free(cgbr
->tab
);
2921 static void add_gbr_ineq(struct isl_context_gbr
*cgbr
, isl_int
*ineq
)
2926 if (isl_tab_extend_cons(cgbr
->tab
, 1) < 0)
2929 if (isl_tab_add_ineq(cgbr
->tab
, ineq
) < 0)
2932 if (cgbr
->shifted
&& !cgbr
->shifted
->empty
&& use_shifted(cgbr
)) {
2935 dim
= isl_basic_map_total_dim(cgbr
->tab
->bmap
);
2937 if (isl_tab_extend_cons(cgbr
->shifted
, 1) < 0)
2940 for (i
= 0; i
< dim
; ++i
) {
2941 if (!isl_int_is_neg(ineq
[1 + i
]))
2943 isl_int_add(ineq
[0], ineq
[0], ineq
[1 + i
]);
2946 if (isl_tab_add_ineq(cgbr
->shifted
, ineq
) < 0)
2949 for (i
= 0; i
< dim
; ++i
) {
2950 if (!isl_int_is_neg(ineq
[1 + i
]))
2952 isl_int_sub(ineq
[0], ineq
[0], ineq
[1 + i
]);
2956 if (cgbr
->cone
&& cgbr
->cone
->n_col
!= cgbr
->cone
->n_dead
) {
2957 if (isl_tab_extend_cons(cgbr
->cone
, 1) < 0)
2959 if (isl_tab_add_ineq(cgbr
->cone
, ineq
) < 0)
2965 isl_tab_free(cgbr
->tab
);
2969 static void context_gbr_add_ineq(struct isl_context
*context
, isl_int
*ineq
,
2970 int check
, int update
)
2972 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
2974 add_gbr_ineq(cgbr
, ineq
);
2979 int v
= tab_has_valid_sample(cgbr
->tab
, ineq
, 0);
2983 check_gbr_integer_feasible(cgbr
);
2986 cgbr
->tab
= check_samples(cgbr
->tab
, ineq
, 0);
2989 isl_tab_free(cgbr
->tab
);
2993 static int context_gbr_add_ineq_wrap(void *user
, isl_int
*ineq
)
2995 struct isl_context
*context
= (struct isl_context
*)user
;
2996 context_gbr_add_ineq(context
, ineq
, 0, 0);
2997 return context
->op
->is_ok(context
) ? 0 : -1;
3000 static enum isl_tab_row_sign
context_gbr_ineq_sign(struct isl_context
*context
,
3001 isl_int
*ineq
, int strict
)
3003 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3004 return tab_ineq_sign(cgbr
->tab
, ineq
, strict
);
3007 /* Check whether "ineq" can be added to the tableau without rendering
3010 static int context_gbr_test_ineq(struct isl_context
*context
, isl_int
*ineq
)
3012 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3013 struct isl_tab_undo
*snap
;
3014 struct isl_tab_undo
*shifted_snap
= NULL
;
3015 struct isl_tab_undo
*cone_snap
= NULL
;
3021 if (isl_tab_extend_cons(cgbr
->tab
, 1) < 0)
3024 snap
= isl_tab_snap(cgbr
->tab
);
3026 shifted_snap
= isl_tab_snap(cgbr
->shifted
);
3028 cone_snap
= isl_tab_snap(cgbr
->cone
);
3029 add_gbr_ineq(cgbr
, ineq
);
3030 check_gbr_integer_feasible(cgbr
);
3033 feasible
= !cgbr
->tab
->empty
;
3034 if (isl_tab_rollback(cgbr
->tab
, snap
) < 0)
3037 if (isl_tab_rollback(cgbr
->shifted
, shifted_snap
))
3039 } else if (cgbr
->shifted
) {
3040 isl_tab_free(cgbr
->shifted
);
3041 cgbr
->shifted
= NULL
;
3044 if (isl_tab_rollback(cgbr
->cone
, cone_snap
))
3046 } else if (cgbr
->cone
) {
3047 isl_tab_free(cgbr
->cone
);
3054 /* Return the column of the last of the variables associated to
3055 * a column that has a non-zero coefficient.
3056 * This function is called in a context where only coefficients
3057 * of parameters or divs can be non-zero.
3059 static int last_non_zero_var_col(struct isl_tab
*tab
, isl_int
*p
)
3064 if (tab
->n_var
== 0)
3067 for (i
= tab
->n_var
- 1; i
>= 0; --i
) {
3068 if (i
>= tab
->n_param
&& i
< tab
->n_var
- tab
->n_div
)
3070 if (tab
->var
[i
].is_row
)
3072 col
= tab
->var
[i
].index
;
3073 if (!isl_int_is_zero(p
[col
]))
3080 /* Look through all the recently added equalities in the context
3081 * to see if we can propagate any of them to the main tableau.
3083 * The newly added equalities in the context are encoded as pairs
3084 * of inequalities starting at inequality "first".
3086 * We tentatively add each of these equalities to the main tableau
3087 * and if this happens to result in a row with a final coefficient
3088 * that is one or negative one, we use it to kill a column
3089 * in the main tableau. Otherwise, we discard the tentatively
3092 * Return 0 on success and -1 on failure.
3094 static int propagate_equalities(struct isl_context_gbr
*cgbr
,
3095 struct isl_tab
*tab
, unsigned first
)
3098 struct isl_vec
*eq
= NULL
;
3100 eq
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_var
);
3104 if (isl_tab_extend_cons(tab
, (cgbr
->tab
->bmap
->n_ineq
- first
)/2) < 0)
3107 isl_seq_clr(eq
->el
+ 1 + tab
->n_param
,
3108 tab
->n_var
- tab
->n_param
- tab
->n_div
);
3109 for (i
= first
; i
< cgbr
->tab
->bmap
->n_ineq
; i
+= 2) {
3112 struct isl_tab_undo
*snap
;
3113 snap
= isl_tab_snap(tab
);
3115 isl_seq_cpy(eq
->el
, cgbr
->tab
->bmap
->ineq
[i
], 1 + tab
->n_param
);
3116 isl_seq_cpy(eq
->el
+ 1 + tab
->n_var
- tab
->n_div
,
3117 cgbr
->tab
->bmap
->ineq
[i
] + 1 + tab
->n_param
,
3120 r
= isl_tab_add_row(tab
, eq
->el
);
3123 r
= tab
->con
[r
].index
;
3124 j
= last_non_zero_var_col(tab
, tab
->mat
->row
[r
] + 2 + tab
->M
);
3125 if (j
< 0 || j
< tab
->n_dead
||
3126 !isl_int_is_one(tab
->mat
->row
[r
][0]) ||
3127 (!isl_int_is_one(tab
->mat
->row
[r
][2 + tab
->M
+ j
]) &&
3128 !isl_int_is_negone(tab
->mat
->row
[r
][2 + tab
->M
+ j
]))) {
3129 if (isl_tab_rollback(tab
, snap
) < 0)
3133 if (isl_tab_pivot(tab
, r
, j
) < 0)
3135 if (isl_tab_kill_col(tab
, j
) < 0)
3138 if (restore_lexmin(tab
) < 0)
3147 isl_tab_free(cgbr
->tab
);
3152 static int context_gbr_detect_equalities(struct isl_context
*context
,
3153 struct isl_tab
*tab
)
3155 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3159 struct isl_basic_set
*bset
= isl_tab_peek_bset(cgbr
->tab
);
3160 cgbr
->cone
= isl_tab_from_recession_cone(bset
, 0);
3163 if (isl_tab_track_bset(cgbr
->cone
,
3164 isl_basic_set_copy(bset
)) < 0)
3167 if (isl_tab_detect_implicit_equalities(cgbr
->cone
) < 0)
3170 n_ineq
= cgbr
->tab
->bmap
->n_ineq
;
3171 cgbr
->tab
= isl_tab_detect_equalities(cgbr
->tab
, cgbr
->cone
);
3174 if (cgbr
->tab
->bmap
->n_ineq
> n_ineq
&&
3175 propagate_equalities(cgbr
, tab
, n_ineq
) < 0)
3180 isl_tab_free(cgbr
->tab
);
3185 static int context_gbr_get_div(struct isl_context
*context
, struct isl_tab
*tab
,
3186 struct isl_vec
*div
)
3188 return get_div(tab
, context
, div
);
3191 static int context_gbr_add_div(struct isl_context
*context
, struct isl_vec
*div
)
3193 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3197 if (isl_tab_extend_cons(cgbr
->cone
, 3) < 0)
3199 if (isl_tab_extend_vars(cgbr
->cone
, 1) < 0)
3201 if (isl_tab_allocate_var(cgbr
->cone
) <0)
3204 cgbr
->cone
->bmap
= isl_basic_map_extend_space(cgbr
->cone
->bmap
,
3205 isl_basic_map_get_space(cgbr
->cone
->bmap
), 1, 0, 2);
3206 k
= isl_basic_map_alloc_div(cgbr
->cone
->bmap
);
3209 isl_seq_cpy(cgbr
->cone
->bmap
->div
[k
], div
->el
, div
->size
);
3210 if (isl_tab_push(cgbr
->cone
, isl_tab_undo_bmap_div
) < 0)
3213 return context_tab_add_div(cgbr
->tab
, div
,
3214 context_gbr_add_ineq_wrap
, context
);
3217 static int context_gbr_best_split(struct isl_context
*context
,
3218 struct isl_tab
*tab
)
3220 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3221 struct isl_tab_undo
*snap
;
3224 snap
= isl_tab_snap(cgbr
->tab
);
3225 r
= best_split(tab
, cgbr
->tab
);
3227 if (r
>= 0 && isl_tab_rollback(cgbr
->tab
, snap
) < 0)
3233 static int context_gbr_is_empty(struct isl_context
*context
)
3235 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3238 return cgbr
->tab
->empty
;
3241 struct isl_gbr_tab_undo
{
3242 struct isl_tab_undo
*tab_snap
;
3243 struct isl_tab_undo
*shifted_snap
;
3244 struct isl_tab_undo
*cone_snap
;
3247 static void *context_gbr_save(struct isl_context
*context
)
3249 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3250 struct isl_gbr_tab_undo
*snap
;
3255 snap
= isl_alloc_type(cgbr
->tab
->mat
->ctx
, struct isl_gbr_tab_undo
);
3259 snap
->tab_snap
= isl_tab_snap(cgbr
->tab
);
3260 if (isl_tab_save_samples(cgbr
->tab
) < 0)
3264 snap
->shifted_snap
= isl_tab_snap(cgbr
->shifted
);
3266 snap
->shifted_snap
= NULL
;
3269 snap
->cone_snap
= isl_tab_snap(cgbr
->cone
);
3271 snap
->cone_snap
= NULL
;
3279 static void context_gbr_restore(struct isl_context
*context
, void *save
)
3281 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3282 struct isl_gbr_tab_undo
*snap
= (struct isl_gbr_tab_undo
*)save
;
3285 if (isl_tab_rollback(cgbr
->tab
, snap
->tab_snap
) < 0)
3288 if (snap
->shifted_snap
) {
3289 if (isl_tab_rollback(cgbr
->shifted
, snap
->shifted_snap
) < 0)
3291 } else if (cgbr
->shifted
) {
3292 isl_tab_free(cgbr
->shifted
);
3293 cgbr
->shifted
= NULL
;
3296 if (snap
->cone_snap
) {
3297 if (isl_tab_rollback(cgbr
->cone
, snap
->cone_snap
) < 0)
3299 } else if (cgbr
->cone
) {
3300 isl_tab_free(cgbr
->cone
);
3309 isl_tab_free(cgbr
->tab
);
3313 static void context_gbr_discard(void *save
)
3315 struct isl_gbr_tab_undo
*snap
= (struct isl_gbr_tab_undo
*)save
;
3319 static int context_gbr_is_ok(struct isl_context
*context
)
3321 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3325 static void context_gbr_invalidate(struct isl_context
*context
)
3327 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3328 isl_tab_free(cgbr
->tab
);
3332 static void context_gbr_free(struct isl_context
*context
)
3334 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3335 isl_tab_free(cgbr
->tab
);
3336 isl_tab_free(cgbr
->shifted
);
3337 isl_tab_free(cgbr
->cone
);
3341 struct isl_context_op isl_context_gbr_op
= {
3342 context_gbr_detect_nonnegative_parameters
,
3343 context_gbr_peek_basic_set
,
3344 context_gbr_peek_tab
,
3346 context_gbr_add_ineq
,
3347 context_gbr_ineq_sign
,
3348 context_gbr_test_ineq
,
3349 context_gbr_get_div
,
3350 context_gbr_add_div
,
3351 context_gbr_detect_equalities
,
3352 context_gbr_best_split
,
3353 context_gbr_is_empty
,
3356 context_gbr_restore
,
3357 context_gbr_discard
,
3358 context_gbr_invalidate
,
3362 static struct isl_context
*isl_context_gbr_alloc(struct isl_basic_set
*dom
)
3364 struct isl_context_gbr
*cgbr
;
3369 cgbr
= isl_calloc_type(dom
->ctx
, struct isl_context_gbr
);
3373 cgbr
->context
.op
= &isl_context_gbr_op
;
3375 cgbr
->shifted
= NULL
;
3377 cgbr
->tab
= isl_tab_from_basic_set(dom
, 1);
3378 cgbr
->tab
= isl_tab_init_samples(cgbr
->tab
);
3381 check_gbr_integer_feasible(cgbr
);
3383 return &cgbr
->context
;
3385 cgbr
->context
.op
->free(&cgbr
->context
);
3389 static struct isl_context
*isl_context_alloc(struct isl_basic_set
*dom
)
3394 if (dom
->ctx
->opt
->context
== ISL_CONTEXT_LEXMIN
)
3395 return isl_context_lex_alloc(dom
);
3397 return isl_context_gbr_alloc(dom
);
3400 /* Construct an isl_sol_map structure for accumulating the solution.
3401 * If track_empty is set, then we also keep track of the parts
3402 * of the context where there is no solution.
3403 * If max is set, then we are solving a maximization, rather than
3404 * a minimization problem, which means that the variables in the
3405 * tableau have value "M - x" rather than "M + x".
3407 static struct isl_sol
*sol_map_init(struct isl_basic_map
*bmap
,
3408 struct isl_basic_set
*dom
, int track_empty
, int max
)
3410 struct isl_sol_map
*sol_map
= NULL
;
3415 sol_map
= isl_calloc_type(bmap
->ctx
, struct isl_sol_map
);
3419 sol_map
->sol
.rational
= ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
);
3420 sol_map
->sol
.dec_level
.callback
.run
= &sol_dec_level_wrap
;
3421 sol_map
->sol
.dec_level
.sol
= &sol_map
->sol
;
3422 sol_map
->sol
.max
= max
;
3423 sol_map
->sol
.n_out
= isl_basic_map_dim(bmap
, isl_dim_out
);
3424 sol_map
->sol
.add
= &sol_map_add_wrap
;
3425 sol_map
->sol
.add_empty
= track_empty
? &sol_map_add_empty_wrap
: NULL
;
3426 sol_map
->sol
.free
= &sol_map_free_wrap
;
3427 sol_map
->map
= isl_map_alloc_space(isl_basic_map_get_space(bmap
), 1,
3432 sol_map
->sol
.context
= isl_context_alloc(dom
);
3433 if (!sol_map
->sol
.context
)
3437 sol_map
->empty
= isl_set_alloc_space(isl_basic_set_get_space(dom
),
3438 1, ISL_SET_DISJOINT
);
3439 if (!sol_map
->empty
)
3443 isl_basic_set_free(dom
);
3444 return &sol_map
->sol
;
3446 isl_basic_set_free(dom
);
3447 sol_map_free(sol_map
);
3451 /* Check whether all coefficients of (non-parameter) variables
3452 * are non-positive, meaning that no pivots can be performed on the row.
3454 static int is_critical(struct isl_tab
*tab
, int row
)
3457 unsigned off
= 2 + tab
->M
;
3459 for (j
= tab
->n_dead
; j
< tab
->n_col
; ++j
) {
3460 if (tab
->col_var
[j
] >= 0 &&
3461 (tab
->col_var
[j
] < tab
->n_param
||
3462 tab
->col_var
[j
] >= tab
->n_var
- tab
->n_div
))
3465 if (isl_int_is_pos(tab
->mat
->row
[row
][off
+ j
]))
3472 /* Check whether the inequality represented by vec is strict over the integers,
3473 * i.e., there are no integer values satisfying the constraint with
3474 * equality. This happens if the gcd of the coefficients is not a divisor
3475 * of the constant term. If so, scale the constraint down by the gcd
3476 * of the coefficients.
3478 static int is_strict(struct isl_vec
*vec
)
3484 isl_seq_gcd(vec
->el
+ 1, vec
->size
- 1, &gcd
);
3485 if (!isl_int_is_one(gcd
)) {
3486 strict
= !isl_int_is_divisible_by(vec
->el
[0], gcd
);
3487 isl_int_fdiv_q(vec
->el
[0], vec
->el
[0], gcd
);
3488 isl_seq_scale_down(vec
->el
+ 1, vec
->el
+ 1, gcd
, vec
->size
-1);
3495 /* Determine the sign of the given row of the main tableau.
3496 * The result is one of
3497 * isl_tab_row_pos: always non-negative; no pivot needed
3498 * isl_tab_row_neg: always non-positive; pivot
3499 * isl_tab_row_any: can be both positive and negative; split
3501 * We first handle some simple cases
3502 * - the row sign may be known already
3503 * - the row may be obviously non-negative
3504 * - the parametric constant may be equal to that of another row
3505 * for which we know the sign. This sign will be either "pos" or
3506 * "any". If it had been "neg" then we would have pivoted before.
3508 * If none of these cases hold, we check the value of the row for each
3509 * of the currently active samples. Based on the signs of these values
3510 * we make an initial determination of the sign of the row.
3512 * all zero -> unk(nown)
3513 * all non-negative -> pos
3514 * all non-positive -> neg
3515 * both negative and positive -> all
3517 * If we end up with "all", we are done.
3518 * Otherwise, we perform a check for positive and/or negative
3519 * values as follows.
3521 * samples neg unk pos
3527 * There is no special sign for "zero", because we can usually treat zero
3528 * as either non-negative or non-positive, whatever works out best.
3529 * However, if the row is "critical", meaning that pivoting is impossible
3530 * then we don't want to limp zero with the non-positive case, because
3531 * then we we would lose the solution for those values of the parameters
3532 * where the value of the row is zero. Instead, we treat 0 as non-negative
3533 * ensuring a split if the row can attain both zero and negative values.
3534 * The same happens when the original constraint was one that could not
3535 * be satisfied with equality by any integer values of the parameters.
3536 * In this case, we normalize the constraint, but then a value of zero
3537 * for the normalized constraint is actually a positive value for the
3538 * original constraint, so again we need to treat zero as non-negative.
3539 * In both these cases, we have the following decision tree instead:
3541 * all non-negative -> pos
3542 * all negative -> neg
3543 * both negative and non-negative -> all
3551 static enum isl_tab_row_sign
row_sign(struct isl_tab
*tab
,
3552 struct isl_sol
*sol
, int row
)
3554 struct isl_vec
*ineq
= NULL
;
3555 enum isl_tab_row_sign res
= isl_tab_row_unknown
;
3560 if (tab
->row_sign
[row
] != isl_tab_row_unknown
)
3561 return tab
->row_sign
[row
];
3562 if (is_obviously_nonneg(tab
, row
))
3563 return isl_tab_row_pos
;
3564 for (row2
= tab
->n_redundant
; row2
< tab
->n_row
; ++row2
) {
3565 if (tab
->row_sign
[row2
] == isl_tab_row_unknown
)
3567 if (identical_parameter_line(tab
, row
, row2
))
3568 return tab
->row_sign
[row2
];
3571 critical
= is_critical(tab
, row
);
3573 ineq
= get_row_parameter_ineq(tab
, row
);
3577 strict
= is_strict(ineq
);
3579 res
= sol
->context
->op
->ineq_sign(sol
->context
, ineq
->el
,
3580 critical
|| strict
);
3582 if (res
== isl_tab_row_unknown
|| res
== isl_tab_row_pos
) {
3583 /* test for negative values */
3585 isl_seq_neg(ineq
->el
, ineq
->el
, ineq
->size
);
3586 isl_int_sub_ui(ineq
->el
[0], ineq
->el
[0], 1);
3588 feasible
= sol
->context
->op
->test_ineq(sol
->context
, ineq
->el
);
3592 res
= isl_tab_row_pos
;
3594 res
= (res
== isl_tab_row_unknown
) ? isl_tab_row_neg
3596 if (res
== isl_tab_row_neg
) {
3597 isl_seq_neg(ineq
->el
, ineq
->el
, ineq
->size
);
3598 isl_int_sub_ui(ineq
->el
[0], ineq
->el
[0], 1);
3602 if (res
== isl_tab_row_neg
) {
3603 /* test for positive values */
3605 if (!critical
&& !strict
)
3606 isl_int_sub_ui(ineq
->el
[0], ineq
->el
[0], 1);
3608 feasible
= sol
->context
->op
->test_ineq(sol
->context
, ineq
->el
);
3612 res
= isl_tab_row_any
;
3619 return isl_tab_row_unknown
;
3622 static void find_solutions(struct isl_sol
*sol
, struct isl_tab
*tab
);
3624 /* Find solutions for values of the parameters that satisfy the given
3627 * We currently take a snapshot of the context tableau that is reset
3628 * when we return from this function, while we make a copy of the main
3629 * tableau, leaving the original main tableau untouched.
3630 * These are fairly arbitrary choices. Making a copy also of the context
3631 * tableau would obviate the need to undo any changes made to it later,
3632 * while taking a snapshot of the main tableau could reduce memory usage.
3633 * If we were to switch to taking a snapshot of the main tableau,
3634 * we would have to keep in mind that we need to save the row signs
3635 * and that we need to do this before saving the current basis
3636 * such that the basis has been restore before we restore the row signs.
3638 static void find_in_pos(struct isl_sol
*sol
, struct isl_tab
*tab
, isl_int
*ineq
)
3644 saved
= sol
->context
->op
->save(sol
->context
);
3646 tab
= isl_tab_dup(tab
);
3650 sol
->context
->op
->add_ineq(sol
->context
, ineq
, 0, 1);
3652 find_solutions(sol
, tab
);
3655 sol
->context
->op
->restore(sol
->context
, saved
);
3657 sol
->context
->op
->discard(saved
);
3663 /* Record the absence of solutions for those values of the parameters
3664 * that do not satisfy the given inequality with equality.
3666 static void no_sol_in_strict(struct isl_sol
*sol
,
3667 struct isl_tab
*tab
, struct isl_vec
*ineq
)
3672 if (!sol
->context
|| sol
->error
)
3674 saved
= sol
->context
->op
->save(sol
->context
);
3676 isl_int_sub_ui(ineq
->el
[0], ineq
->el
[0], 1);
3678 sol
->context
->op
->add_ineq(sol
->context
, ineq
->el
, 1, 0);
3687 isl_int_add_ui(ineq
->el
[0], ineq
->el
[0], 1);
3689 sol
->context
->op
->restore(sol
->context
, saved
);
3695 /* Compute the lexicographic minimum of the set represented by the main
3696 * tableau "tab" within the context "sol->context_tab".
3697 * On entry the sample value of the main tableau is lexicographically
3698 * less than or equal to this lexicographic minimum.
3699 * Pivots are performed until a feasible point is found, which is then
3700 * necessarily equal to the minimum, or until the tableau is found to
3701 * be infeasible. Some pivots may need to be performed for only some
3702 * feasible values of the context tableau. If so, the context tableau
3703 * is split into a part where the pivot is needed and a part where it is not.
3705 * Whenever we enter the main loop, the main tableau is such that no
3706 * "obvious" pivots need to be performed on it, where "obvious" means
3707 * that the given row can be seen to be negative without looking at
3708 * the context tableau. In particular, for non-parametric problems,
3709 * no pivots need to be performed on the main tableau.
3710 * The caller of find_solutions is responsible for making this property
3711 * hold prior to the first iteration of the loop, while restore_lexmin
3712 * is called before every other iteration.
3714 * Inside the main loop, we first examine the signs of the rows of
3715 * the main tableau within the context of the context tableau.
3716 * If we find a row that is always non-positive for all values of
3717 * the parameters satisfying the context tableau and negative for at
3718 * least one value of the parameters, we perform the appropriate pivot
3719 * and start over. An exception is the case where no pivot can be
3720 * performed on the row. In this case, we require that the sign of
3721 * the row is negative for all values of the parameters (rather than just
3722 * non-positive). This special case is handled inside row_sign, which
3723 * will say that the row can have any sign if it determines that it can
3724 * attain both negative and zero values.
3726 * If we can't find a row that always requires a pivot, but we can find
3727 * one or more rows that require a pivot for some values of the parameters
3728 * (i.e., the row can attain both positive and negative signs), then we split
3729 * the context tableau into two parts, one where we force the sign to be
3730 * non-negative and one where we force is to be negative.
3731 * The non-negative part is handled by a recursive call (through find_in_pos).
3732 * Upon returning from this call, we continue with the negative part and
3733 * perform the required pivot.
3735 * If no such rows can be found, all rows are non-negative and we have
3736 * found a (rational) feasible point. If we only wanted a rational point
3738 * Otherwise, we check if all values of the sample point of the tableau
3739 * are integral for the variables. If so, we have found the minimal
3740 * integral point and we are done.
3741 * If the sample point is not integral, then we need to make a distinction
3742 * based on whether the constant term is non-integral or the coefficients
3743 * of the parameters. Furthermore, in order to decide how to handle
3744 * the non-integrality, we also need to know whether the coefficients
3745 * of the other columns in the tableau are integral. This leads
3746 * to the following table. The first two rows do not correspond
3747 * to a non-integral sample point and are only mentioned for completeness.
3749 * constant parameters other
3752 * int int rat | -> no problem
3754 * rat int int -> fail
3756 * rat int rat -> cut
3759 * rat rat rat | -> parametric cut
3762 * rat rat int | -> split context
3764 * If the parametric constant is completely integral, then there is nothing
3765 * to be done. If the constant term is non-integral, but all the other
3766 * coefficient are integral, then there is nothing that can be done
3767 * and the tableau has no integral solution.
3768 * If, on the other hand, one or more of the other columns have rational
3769 * coefficients, but the parameter coefficients are all integral, then
3770 * we can perform a regular (non-parametric) cut.
3771 * Finally, if there is any parameter coefficient that is non-integral,
3772 * then we need to involve the context tableau. There are two cases here.
3773 * If at least one other column has a rational coefficient, then we
3774 * can perform a parametric cut in the main tableau by adding a new
3775 * integer division in the context tableau.
3776 * If all other columns have integral coefficients, then we need to
3777 * enforce that the rational combination of parameters (c + \sum a_i y_i)/m
3778 * is always integral. We do this by introducing an integer division
3779 * q = floor((c + \sum a_i y_i)/m) and stipulating that its argument should
3780 * always be integral in the context tableau, i.e., m q = c + \sum a_i y_i.
3781 * Since q is expressed in the tableau as
3782 * c + \sum a_i y_i - m q >= 0
3783 * -c - \sum a_i y_i + m q + m - 1 >= 0
3784 * it is sufficient to add the inequality
3785 * -c - \sum a_i y_i + m q >= 0
3786 * In the part of the context where this inequality does not hold, the
3787 * main tableau is marked as being empty.
3789 static void find_solutions(struct isl_sol
*sol
, struct isl_tab
*tab
)
3791 struct isl_context
*context
;
3794 if (!tab
|| sol
->error
)
3797 context
= sol
->context
;
3801 if (context
->op
->is_empty(context
))
3804 for (r
= 0; r
>= 0 && tab
&& !tab
->empty
; r
= restore_lexmin(tab
)) {
3807 enum isl_tab_row_sign sgn
;
3811 for (row
= tab
->n_redundant
; row
< tab
->n_row
; ++row
) {
3812 if (!isl_tab_var_from_row(tab
, row
)->is_nonneg
)
3814 sgn
= row_sign(tab
, sol
, row
);
3817 tab
->row_sign
[row
] = sgn
;
3818 if (sgn
== isl_tab_row_any
)
3820 if (sgn
== isl_tab_row_any
&& split
== -1)
3822 if (sgn
== isl_tab_row_neg
)
3825 if (row
< tab
->n_row
)
3828 struct isl_vec
*ineq
;
3830 split
= context
->op
->best_split(context
, tab
);
3833 ineq
= get_row_parameter_ineq(tab
, split
);
3837 for (row
= tab
->n_redundant
; row
< tab
->n_row
; ++row
) {
3838 if (!isl_tab_var_from_row(tab
, row
)->is_nonneg
)
3840 if (tab
->row_sign
[row
] == isl_tab_row_any
)
3841 tab
->row_sign
[row
] = isl_tab_row_unknown
;
3843 tab
->row_sign
[split
] = isl_tab_row_pos
;
3845 find_in_pos(sol
, tab
, ineq
->el
);
3846 tab
->row_sign
[split
] = isl_tab_row_neg
;
3847 isl_seq_neg(ineq
->el
, ineq
->el
, ineq
->size
);
3848 isl_int_sub_ui(ineq
->el
[0], ineq
->el
[0], 1);
3850 context
->op
->add_ineq(context
, ineq
->el
, 0, 1);
3858 row
= first_non_integer_row(tab
, &flags
);
3861 if (ISL_FL_ISSET(flags
, I_PAR
)) {
3862 if (ISL_FL_ISSET(flags
, I_VAR
)) {
3863 if (isl_tab_mark_empty(tab
) < 0)
3867 row
= add_cut(tab
, row
);
3868 } else if (ISL_FL_ISSET(flags
, I_VAR
)) {
3869 struct isl_vec
*div
;
3870 struct isl_vec
*ineq
;
3872 div
= get_row_split_div(tab
, row
);
3875 d
= context
->op
->get_div(context
, tab
, div
);
3879 ineq
= ineq_for_div(context
->op
->peek_basic_set(context
), d
);
3883 no_sol_in_strict(sol
, tab
, ineq
);
3884 isl_seq_neg(ineq
->el
, ineq
->el
, ineq
->size
);
3885 context
->op
->add_ineq(context
, ineq
->el
, 1, 1);
3887 if (sol
->error
|| !context
->op
->is_ok(context
))
3889 tab
= set_row_cst_to_div(tab
, row
, d
);
3890 if (context
->op
->is_empty(context
))
3893 row
= add_parametric_cut(tab
, row
, context
);
3908 /* Does "sol" contain a pair of partial solutions that could potentially
3911 * We currently only check that "sol" is not in an error state
3912 * and that there are at least two partial solutions of which the final two
3913 * are defined at the same level.
3915 static int sol_has_mergeable_solutions(struct isl_sol
*sol
)
3921 if (!sol
->partial
->next
)
3923 return sol
->partial
->level
== sol
->partial
->next
->level
;
3926 /* Compute the lexicographic minimum of the set represented by the main
3927 * tableau "tab" within the context "sol->context_tab".
3929 * As a preprocessing step, we first transfer all the purely parametric
3930 * equalities from the main tableau to the context tableau, i.e.,
3931 * parameters that have been pivoted to a row.
3932 * These equalities are ignored by the main algorithm, because the
3933 * corresponding rows may not be marked as being non-negative.
3934 * In parts of the context where the added equality does not hold,
3935 * the main tableau is marked as being empty.
3937 * Before we embark on the actual computation, we save a copy
3938 * of the context. When we return, we check if there are any
3939 * partial solutions that can potentially be merged. If so,
3940 * we perform a rollback to the initial state of the context.
3941 * The merging of partial solutions happens inside calls to
3942 * sol_dec_level that are pushed onto the undo stack of the context.
3943 * If there are no partial solutions that can potentially be merged
3944 * then the rollback is skipped as it would just be wasted effort.
3946 static void find_solutions_main(struct isl_sol
*sol
, struct isl_tab
*tab
)
3956 for (row
= tab
->n_redundant
; row
< tab
->n_row
; ++row
) {
3960 if (tab
->row_var
[row
] < 0)
3962 if (tab
->row_var
[row
] >= tab
->n_param
&&
3963 tab
->row_var
[row
] < tab
->n_var
- tab
->n_div
)
3965 if (tab
->row_var
[row
] < tab
->n_param
)
3966 p
= tab
->row_var
[row
];
3968 p
= tab
->row_var
[row
]
3969 + tab
->n_param
- (tab
->n_var
- tab
->n_div
);
3971 eq
= isl_vec_alloc(tab
->mat
->ctx
, 1+tab
->n_param
+tab
->n_div
);
3974 get_row_parameter_line(tab
, row
, eq
->el
);
3975 isl_int_neg(eq
->el
[1 + p
], tab
->mat
->row
[row
][0]);
3976 eq
= isl_vec_normalize(eq
);
3979 no_sol_in_strict(sol
, tab
, eq
);
3981 isl_seq_neg(eq
->el
, eq
->el
, eq
->size
);
3983 no_sol_in_strict(sol
, tab
, eq
);
3984 isl_seq_neg(eq
->el
, eq
->el
, eq
->size
);
3986 sol
->context
->op
->add_eq(sol
->context
, eq
->el
, 1, 1);
3990 if (isl_tab_mark_redundant(tab
, row
) < 0)
3993 if (sol
->context
->op
->is_empty(sol
->context
))
3996 row
= tab
->n_redundant
- 1;
3999 saved
= sol
->context
->op
->save(sol
->context
);
4001 find_solutions(sol
, tab
);
4003 if (sol_has_mergeable_solutions(sol
))
4004 sol
->context
->op
->restore(sol
->context
, saved
);
4006 sol
->context
->op
->discard(saved
);
4017 /* Check if integer division "div" of "dom" also occurs in "bmap".
4018 * If so, return its position within the divs.
4019 * If not, return -1.
4021 static int find_context_div(struct isl_basic_map
*bmap
,
4022 struct isl_basic_set
*dom
, unsigned div
)
4025 unsigned b_dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
4026 unsigned d_dim
= isl_space_dim(dom
->dim
, isl_dim_all
);
4028 if (isl_int_is_zero(dom
->div
[div
][0]))
4030 if (isl_seq_first_non_zero(dom
->div
[div
] + 2 + d_dim
, dom
->n_div
) != -1)
4033 for (i
= 0; i
< bmap
->n_div
; ++i
) {
4034 if (isl_int_is_zero(bmap
->div
[i
][0]))
4036 if (isl_seq_first_non_zero(bmap
->div
[i
] + 2 + d_dim
,
4037 (b_dim
- d_dim
) + bmap
->n_div
) != -1)
4039 if (isl_seq_eq(bmap
->div
[i
], dom
->div
[div
], 2 + d_dim
))
4045 /* The correspondence between the variables in the main tableau,
4046 * the context tableau, and the input map and domain is as follows.
4047 * The first n_param and the last n_div variables of the main tableau
4048 * form the variables of the context tableau.
4049 * In the basic map, these n_param variables correspond to the
4050 * parameters and the input dimensions. In the domain, they correspond
4051 * to the parameters and the set dimensions.
4052 * The n_div variables correspond to the integer divisions in the domain.
4053 * To ensure that everything lines up, we may need to copy some of the
4054 * integer divisions of the domain to the map. These have to be placed
4055 * in the same order as those in the context and they have to be placed
4056 * after any other integer divisions that the map may have.
4057 * This function performs the required reordering.
4059 static struct isl_basic_map
*align_context_divs(struct isl_basic_map
*bmap
,
4060 struct isl_basic_set
*dom
)
4066 for (i
= 0; i
< dom
->n_div
; ++i
)
4067 if (find_context_div(bmap
, dom
, i
) != -1)
4069 other
= bmap
->n_div
- common
;
4070 if (dom
->n_div
- common
> 0) {
4071 bmap
= isl_basic_map_extend_space(bmap
, isl_space_copy(bmap
->dim
),
4072 dom
->n_div
- common
, 0, 0);
4076 for (i
= 0; i
< dom
->n_div
; ++i
) {
4077 int pos
= find_context_div(bmap
, dom
, i
);
4079 pos
= isl_basic_map_alloc_div(bmap
);
4082 isl_int_set_si(bmap
->div
[pos
][0], 0);
4084 if (pos
!= other
+ i
)
4085 isl_basic_map_swap_div(bmap
, pos
, other
+ i
);
4089 isl_basic_map_free(bmap
);
4093 /* Base case of isl_tab_basic_map_partial_lexopt, after removing
4094 * some obvious symmetries.
4096 * We make sure the divs in the domain are properly ordered,
4097 * because they will be added one by one in the given order
4098 * during the construction of the solution map.
4100 static struct isl_sol
*basic_map_partial_lexopt_base(
4101 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_set
*dom
,
4102 __isl_give isl_set
**empty
, int max
,
4103 struct isl_sol
*(*init
)(__isl_keep isl_basic_map
*bmap
,
4104 __isl_take isl_basic_set
*dom
, int track_empty
, int max
))
4106 struct isl_tab
*tab
;
4107 struct isl_sol
*sol
= NULL
;
4108 struct isl_context
*context
;
4111 dom
= isl_basic_set_order_divs(dom
);
4112 bmap
= align_context_divs(bmap
, dom
);
4114 sol
= init(bmap
, dom
, !!empty
, max
);
4118 context
= sol
->context
;
4119 if (isl_basic_set_plain_is_empty(context
->op
->peek_basic_set(context
)))
4121 else if (isl_basic_map_plain_is_empty(bmap
)) {
4124 isl_basic_set_copy(context
->op
->peek_basic_set(context
)));
4126 tab
= tab_for_lexmin(bmap
,
4127 context
->op
->peek_basic_set(context
), 1, max
);
4128 tab
= context
->op
->detect_nonnegative_parameters(context
, tab
);
4129 find_solutions_main(sol
, tab
);
4134 isl_basic_map_free(bmap
);
4138 isl_basic_map_free(bmap
);
4142 /* Base case of isl_tab_basic_map_partial_lexopt, after removing
4143 * some obvious symmetries.
4145 * We call basic_map_partial_lexopt_base and extract the results.
4147 static __isl_give isl_map
*basic_map_partial_lexopt_base_map(
4148 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_set
*dom
,
4149 __isl_give isl_set
**empty
, int max
)
4151 isl_map
*result
= NULL
;
4152 struct isl_sol
*sol
;
4153 struct isl_sol_map
*sol_map
;
4155 sol
= basic_map_partial_lexopt_base(bmap
, dom
, empty
, max
,
4159 sol_map
= (struct isl_sol_map
*) sol
;
4161 result
= isl_map_copy(sol_map
->map
);
4163 *empty
= isl_set_copy(sol_map
->empty
);
4164 sol_free(&sol_map
->sol
);
4168 /* Structure used during detection of parallel constraints.
4169 * n_in: number of "input" variables: isl_dim_param + isl_dim_in
4170 * n_out: number of "output" variables: isl_dim_out + isl_dim_div
4171 * val: the coefficients of the output variables
4173 struct isl_constraint_equal_info
{
4174 isl_basic_map
*bmap
;
4180 /* Check whether the coefficients of the output variables
4181 * of the constraint in "entry" are equal to info->val.
4183 static int constraint_equal(const void *entry
, const void *val
)
4185 isl_int
**row
= (isl_int
**)entry
;
4186 const struct isl_constraint_equal_info
*info
= val
;
4188 return isl_seq_eq((*row
) + 1 + info
->n_in
, info
->val
, info
->n_out
);
4191 /* Check whether "bmap" has a pair of constraints that have
4192 * the same coefficients for the output variables.
4193 * Note that the coefficients of the existentially quantified
4194 * variables need to be zero since the existentially quantified
4195 * of the result are usually not the same as those of the input.
4196 * the isl_dim_out and isl_dim_div dimensions.
4197 * If so, return 1 and return the row indices of the two constraints
4198 * in *first and *second.
4200 static int parallel_constraints(__isl_keep isl_basic_map
*bmap
,
4201 int *first
, int *second
)
4205 struct isl_hash_table
*table
= NULL
;
4206 struct isl_hash_table_entry
*entry
;
4207 struct isl_constraint_equal_info info
;
4211 ctx
= isl_basic_map_get_ctx(bmap
);
4212 table
= isl_hash_table_alloc(ctx
, bmap
->n_ineq
);
4216 info
.n_in
= isl_basic_map_dim(bmap
, isl_dim_param
) +
4217 isl_basic_map_dim(bmap
, isl_dim_in
);
4219 n_out
= isl_basic_map_dim(bmap
, isl_dim_out
);
4220 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
4221 info
.n_out
= n_out
+ n_div
;
4222 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
4225 info
.val
= bmap
->ineq
[i
] + 1 + info
.n_in
;
4226 if (isl_seq_first_non_zero(info
.val
, n_out
) < 0)
4228 if (isl_seq_first_non_zero(info
.val
+ n_out
, n_div
) >= 0)
4230 hash
= isl_seq_get_hash(info
.val
, info
.n_out
);
4231 entry
= isl_hash_table_find(ctx
, table
, hash
,
4232 constraint_equal
, &info
, 1);
4237 entry
->data
= &bmap
->ineq
[i
];
4240 if (i
< bmap
->n_ineq
) {
4241 *first
= ((isl_int
**)entry
->data
) - bmap
->ineq
;
4245 isl_hash_table_free(ctx
, table
);
4247 return i
< bmap
->n_ineq
;
4249 isl_hash_table_free(ctx
, table
);
4253 /* Given a set of upper bounds in "var", add constraints to "bset"
4254 * that make the i-th bound smallest.
4256 * In particular, if there are n bounds b_i, then add the constraints
4258 * b_i <= b_j for j > i
4259 * b_i < b_j for j < i
4261 static __isl_give isl_basic_set
*select_minimum(__isl_take isl_basic_set
*bset
,
4262 __isl_keep isl_mat
*var
, int i
)
4267 ctx
= isl_mat_get_ctx(var
);
4269 for (j
= 0; j
< var
->n_row
; ++j
) {
4272 k
= isl_basic_set_alloc_inequality(bset
);
4275 isl_seq_combine(bset
->ineq
[k
], ctx
->one
, var
->row
[j
],
4276 ctx
->negone
, var
->row
[i
], var
->n_col
);
4277 isl_int_set_si(bset
->ineq
[k
][var
->n_col
], 0);
4279 isl_int_sub_ui(bset
->ineq
[k
][0], bset
->ineq
[k
][0], 1);
4282 bset
= isl_basic_set_finalize(bset
);
4286 isl_basic_set_free(bset
);
4290 /* Given a set of upper bounds on the last "input" variable m,
4291 * construct a set that assigns the minimal upper bound to m, i.e.,
4292 * construct a set that divides the space into cells where one
4293 * of the upper bounds is smaller than all the others and assign
4294 * this upper bound to m.
4296 * In particular, if there are n bounds b_i, then the result
4297 * consists of n basic sets, each one of the form
4300 * b_i <= b_j for j > i
4301 * b_i < b_j for j < i
4303 static __isl_give isl_set
*set_minimum(__isl_take isl_space
*dim
,
4304 __isl_take isl_mat
*var
)
4307 isl_basic_set
*bset
= NULL
;
4308 isl_set
*set
= NULL
;
4313 set
= isl_set_alloc_space(isl_space_copy(dim
),
4314 var
->n_row
, ISL_SET_DISJOINT
);
4316 for (i
= 0; i
< var
->n_row
; ++i
) {
4317 bset
= isl_basic_set_alloc_space(isl_space_copy(dim
), 0,
4319 k
= isl_basic_set_alloc_equality(bset
);
4322 isl_seq_cpy(bset
->eq
[k
], var
->row
[i
], var
->n_col
);
4323 isl_int_set_si(bset
->eq
[k
][var
->n_col
], -1);
4324 bset
= select_minimum(bset
, var
, i
);
4325 set
= isl_set_add_basic_set(set
, bset
);
4328 isl_space_free(dim
);
4332 isl_basic_set_free(bset
);
4334 isl_space_free(dim
);
4339 /* Given that the last input variable of "bmap" represents the minimum
4340 * of the bounds in "cst", check whether we need to split the domain
4341 * based on which bound attains the minimum.
4343 * A split is needed when the minimum appears in an integer division
4344 * or in an equality. Otherwise, it is only needed if it appears in
4345 * an upper bound that is different from the upper bounds on which it
4348 static int need_split_basic_map(__isl_keep isl_basic_map
*bmap
,
4349 __isl_keep isl_mat
*cst
)
4355 pos
= cst
->n_col
- 1;
4356 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
4358 for (i
= 0; i
< bmap
->n_div
; ++i
)
4359 if (!isl_int_is_zero(bmap
->div
[i
][2 + pos
]))
4362 for (i
= 0; i
< bmap
->n_eq
; ++i
)
4363 if (!isl_int_is_zero(bmap
->eq
[i
][1 + pos
]))
4366 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
4367 if (isl_int_is_nonneg(bmap
->ineq
[i
][1 + pos
]))
4369 if (!isl_int_is_negone(bmap
->ineq
[i
][1 + pos
]))
4371 if (isl_seq_first_non_zero(bmap
->ineq
[i
] + 1 + pos
+ 1,
4372 total
- pos
- 1) >= 0)
4375 for (j
= 0; j
< cst
->n_row
; ++j
)
4376 if (isl_seq_eq(bmap
->ineq
[i
], cst
->row
[j
], cst
->n_col
))
4378 if (j
>= cst
->n_row
)
4385 /* Given that the last set variable of "bset" represents the minimum
4386 * of the bounds in "cst", check whether we need to split the domain
4387 * based on which bound attains the minimum.
4389 * We simply call need_split_basic_map here. This is safe because
4390 * the position of the minimum is computed from "cst" and not
4393 static int need_split_basic_set(__isl_keep isl_basic_set
*bset
,
4394 __isl_keep isl_mat
*cst
)
4396 return need_split_basic_map((isl_basic_map
*)bset
, cst
);
4399 /* Given that the last set variable of "set" represents the minimum
4400 * of the bounds in "cst", check whether we need to split the domain
4401 * based on which bound attains the minimum.
4403 static int need_split_set(__isl_keep isl_set
*set
, __isl_keep isl_mat
*cst
)
4407 for (i
= 0; i
< set
->n
; ++i
)
4408 if (need_split_basic_set(set
->p
[i
], cst
))
4414 /* Given a set of which the last set variable is the minimum
4415 * of the bounds in "cst", split each basic set in the set
4416 * in pieces where one of the bounds is (strictly) smaller than the others.
4417 * This subdivision is given in "min_expr".
4418 * The variable is subsequently projected out.
4420 * We only do the split when it is needed.
4421 * For example if the last input variable m = min(a,b) and the only
4422 * constraints in the given basic set are lower bounds on m,
4423 * i.e., l <= m = min(a,b), then we can simply project out m
4424 * to obtain l <= a and l <= b, without having to split on whether
4425 * m is equal to a or b.
4427 static __isl_give isl_set
*split(__isl_take isl_set
*empty
,
4428 __isl_take isl_set
*min_expr
, __isl_take isl_mat
*cst
)
4435 if (!empty
|| !min_expr
|| !cst
)
4438 n_in
= isl_set_dim(empty
, isl_dim_set
);
4439 dim
= isl_set_get_space(empty
);
4440 dim
= isl_space_drop_dims(dim
, isl_dim_set
, n_in
- 1, 1);
4441 res
= isl_set_empty(dim
);
4443 for (i
= 0; i
< empty
->n
; ++i
) {
4446 set
= isl_set_from_basic_set(isl_basic_set_copy(empty
->p
[i
]));
4447 if (need_split_basic_set(empty
->p
[i
], cst
))
4448 set
= isl_set_intersect(set
, isl_set_copy(min_expr
));
4449 set
= isl_set_remove_dims(set
, isl_dim_set
, n_in
- 1, 1);
4451 res
= isl_set_union_disjoint(res
, set
);
4454 isl_set_free(empty
);
4455 isl_set_free(min_expr
);
4459 isl_set_free(empty
);
4460 isl_set_free(min_expr
);
4465 /* Given a map of which the last input variable is the minimum
4466 * of the bounds in "cst", split each basic set in the set
4467 * in pieces where one of the bounds is (strictly) smaller than the others.
4468 * This subdivision is given in "min_expr".
4469 * The variable is subsequently projected out.
4471 * The implementation is essentially the same as that of "split".
4473 static __isl_give isl_map
*split_domain(__isl_take isl_map
*opt
,
4474 __isl_take isl_set
*min_expr
, __isl_take isl_mat
*cst
)
4481 if (!opt
|| !min_expr
|| !cst
)
4484 n_in
= isl_map_dim(opt
, isl_dim_in
);
4485 dim
= isl_map_get_space(opt
);
4486 dim
= isl_space_drop_dims(dim
, isl_dim_in
, n_in
- 1, 1);
4487 res
= isl_map_empty(dim
);
4489 for (i
= 0; i
< opt
->n
; ++i
) {
4492 map
= isl_map_from_basic_map(isl_basic_map_copy(opt
->p
[i
]));
4493 if (need_split_basic_map(opt
->p
[i
], cst
))
4494 map
= isl_map_intersect_domain(map
,
4495 isl_set_copy(min_expr
));
4496 map
= isl_map_remove_dims(map
, isl_dim_in
, n_in
- 1, 1);
4498 res
= isl_map_union_disjoint(res
, map
);
4502 isl_set_free(min_expr
);
4507 isl_set_free(min_expr
);
4512 static __isl_give isl_map
*basic_map_partial_lexopt(
4513 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_set
*dom
,
4514 __isl_give isl_set
**empty
, int max
);
4519 isl_pw_multi_aff
*pma
;
4522 /* This function is called from basic_map_partial_lexopt_symm.
4523 * The last variable of "bmap" and "dom" corresponds to the minimum
4524 * of the bounds in "cst". "map_space" is the space of the original
4525 * input relation (of basic_map_partial_lexopt_symm) and "set_space"
4526 * is the space of the original domain.
4528 * We recursively call basic_map_partial_lexopt and then plug in
4529 * the definition of the minimum in the result.
4531 static __isl_give
union isl_lex_res
basic_map_partial_lexopt_symm_map_core(
4532 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_set
*dom
,
4533 __isl_give isl_set
**empty
, int max
, __isl_take isl_mat
*cst
,
4534 __isl_take isl_space
*map_space
, __isl_take isl_space
*set_space
)
4538 union isl_lex_res res
;
4540 min_expr
= set_minimum(isl_basic_set_get_space(dom
), isl_mat_copy(cst
));
4542 opt
= basic_map_partial_lexopt(bmap
, dom
, empty
, max
);
4545 *empty
= split(*empty
,
4546 isl_set_copy(min_expr
), isl_mat_copy(cst
));
4547 *empty
= isl_set_reset_space(*empty
, set_space
);
4550 opt
= split_domain(opt
, min_expr
, cst
);
4551 opt
= isl_map_reset_space(opt
, map_space
);
4557 /* Given a basic map with at least two parallel constraints (as found
4558 * by the function parallel_constraints), first look for more constraints
4559 * parallel to the two constraint and replace the found list of parallel
4560 * constraints by a single constraint with as "input" part the minimum
4561 * of the input parts of the list of constraints. Then, recursively call
4562 * basic_map_partial_lexopt (possibly finding more parallel constraints)
4563 * and plug in the definition of the minimum in the result.
4565 * More specifically, given a set of constraints
4569 * Replace this set by a single constraint
4573 * with u a new parameter with constraints
4577 * Any solution to the new system is also a solution for the original system
4580 * a x >= -u >= -b_i(p)
4582 * Moreover, m = min_i(b_i(p)) satisfies the constraints on u and can
4583 * therefore be plugged into the solution.
4585 static union isl_lex_res
basic_map_partial_lexopt_symm(
4586 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_set
*dom
,
4587 __isl_give isl_set
**empty
, int max
, int first
, int second
,
4588 __isl_give
union isl_lex_res (*core
)(__isl_take isl_basic_map
*bmap
,
4589 __isl_take isl_basic_set
*dom
,
4590 __isl_give isl_set
**empty
,
4591 int max
, __isl_take isl_mat
*cst
,
4592 __isl_take isl_space
*map_space
,
4593 __isl_take isl_space
*set_space
))
4597 unsigned n_in
, n_out
, n_div
;
4599 isl_vec
*var
= NULL
;
4600 isl_mat
*cst
= NULL
;
4601 isl_space
*map_space
, *set_space
;
4602 union isl_lex_res res
;
4604 map_space
= isl_basic_map_get_space(bmap
);
4605 set_space
= empty
? isl_basic_set_get_space(dom
) : NULL
;
4607 n_in
= isl_basic_map_dim(bmap
, isl_dim_param
) +
4608 isl_basic_map_dim(bmap
, isl_dim_in
);
4609 n_out
= isl_basic_map_dim(bmap
, isl_dim_all
) - n_in
;
4611 ctx
= isl_basic_map_get_ctx(bmap
);
4612 list
= isl_alloc_array(ctx
, int, bmap
->n_ineq
);
4613 var
= isl_vec_alloc(ctx
, n_out
);
4614 if ((bmap
->n_ineq
&& !list
) || (n_out
&& !var
))
4619 isl_seq_cpy(var
->el
, bmap
->ineq
[first
] + 1 + n_in
, n_out
);
4620 for (i
= second
+ 1, n
= 2; i
< bmap
->n_ineq
; ++i
) {
4621 if (isl_seq_eq(var
->el
, bmap
->ineq
[i
] + 1 + n_in
, n_out
))
4625 cst
= isl_mat_alloc(ctx
, n
, 1 + n_in
);
4629 for (i
= 0; i
< n
; ++i
)
4630 isl_seq_cpy(cst
->row
[i
], bmap
->ineq
[list
[i
]], 1 + n_in
);
4632 bmap
= isl_basic_map_cow(bmap
);
4635 for (i
= n
- 1; i
>= 0; --i
)
4636 if (isl_basic_map_drop_inequality(bmap
, list
[i
]) < 0)
4639 bmap
= isl_basic_map_add_dims(bmap
, isl_dim_in
, 1);
4640 bmap
= isl_basic_map_extend_constraints(bmap
, 0, 1);
4641 k
= isl_basic_map_alloc_inequality(bmap
);
4644 isl_seq_clr(bmap
->ineq
[k
], 1 + n_in
);
4645 isl_int_set_si(bmap
->ineq
[k
][1 + n_in
], 1);
4646 isl_seq_cpy(bmap
->ineq
[k
] + 1 + n_in
+ 1, var
->el
, n_out
);
4647 bmap
= isl_basic_map_finalize(bmap
);
4649 n_div
= isl_basic_set_dim(dom
, isl_dim_div
);
4650 dom
= isl_basic_set_add_dims(dom
, isl_dim_set
, 1);
4651 dom
= isl_basic_set_extend_constraints(dom
, 0, n
);
4652 for (i
= 0; i
< n
; ++i
) {
4653 k
= isl_basic_set_alloc_inequality(dom
);
4656 isl_seq_cpy(dom
->ineq
[k
], cst
->row
[i
], 1 + n_in
);
4657 isl_int_set_si(dom
->ineq
[k
][1 + n_in
], -1);
4658 isl_seq_clr(dom
->ineq
[k
] + 1 + n_in
+ 1, n_div
);
4664 return core(bmap
, dom
, empty
, max
, cst
, map_space
, set_space
);
4666 isl_space_free(map_space
);
4667 isl_space_free(set_space
);
4671 isl_basic_set_free(dom
);
4672 isl_basic_map_free(bmap
);
4677 static __isl_give isl_map
*basic_map_partial_lexopt_symm_map(
4678 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_set
*dom
,
4679 __isl_give isl_set
**empty
, int max
, int first
, int second
)
4681 return basic_map_partial_lexopt_symm(bmap
, dom
, empty
, max
,
4682 first
, second
, &basic_map_partial_lexopt_symm_map_core
).map
;
4685 /* Recursive part of isl_tab_basic_map_partial_lexopt, after detecting
4686 * equalities and removing redundant constraints.
4688 * We first check if there are any parallel constraints (left).
4689 * If not, we are in the base case.
4690 * If there are parallel constraints, we replace them by a single
4691 * constraint in basic_map_partial_lexopt_symm and then call
4692 * this function recursively to look for more parallel constraints.
4694 static __isl_give isl_map
*basic_map_partial_lexopt(
4695 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_set
*dom
,
4696 __isl_give isl_set
**empty
, int max
)
4704 if (bmap
->ctx
->opt
->pip_symmetry
)
4705 par
= parallel_constraints(bmap
, &first
, &second
);
4709 return basic_map_partial_lexopt_base_map(bmap
, dom
, empty
, max
);
4711 return basic_map_partial_lexopt_symm_map(bmap
, dom
, empty
, max
,
4714 isl_basic_set_free(dom
);
4715 isl_basic_map_free(bmap
);
4719 /* Compute the lexicographic minimum (or maximum if "max" is set)
4720 * of "bmap" over the domain "dom" and return the result as a map.
4721 * If "empty" is not NULL, then *empty is assigned a set that
4722 * contains those parts of the domain where there is no solution.
4723 * If "bmap" is marked as rational (ISL_BASIC_MAP_RATIONAL),
4724 * then we compute the rational optimum. Otherwise, we compute
4725 * the integral optimum.
4727 * We perform some preprocessing. As the PILP solver does not
4728 * handle implicit equalities very well, we first make sure all
4729 * the equalities are explicitly available.
4731 * We also add context constraints to the basic map and remove
4732 * redundant constraints. This is only needed because of the
4733 * way we handle simple symmetries. In particular, we currently look
4734 * for symmetries on the constraints, before we set up the main tableau.
4735 * It is then no good to look for symmetries on possibly redundant constraints.
4737 struct isl_map
*isl_tab_basic_map_partial_lexopt(
4738 struct isl_basic_map
*bmap
, struct isl_basic_set
*dom
,
4739 struct isl_set
**empty
, int max
)
4746 isl_assert(bmap
->ctx
,
4747 isl_basic_map_compatible_domain(bmap
, dom
), goto error
);
4749 if (isl_basic_set_dim(dom
, isl_dim_all
) == 0)
4750 return basic_map_partial_lexopt(bmap
, dom
, empty
, max
);
4752 bmap
= isl_basic_map_intersect_domain(bmap
, isl_basic_set_copy(dom
));
4753 bmap
= isl_basic_map_detect_equalities(bmap
);
4754 bmap
= isl_basic_map_remove_redundancies(bmap
);
4756 return basic_map_partial_lexopt(bmap
, dom
, empty
, max
);
4758 isl_basic_set_free(dom
);
4759 isl_basic_map_free(bmap
);
4763 struct isl_sol_for
{
4765 int (*fn
)(__isl_take isl_basic_set
*dom
,
4766 __isl_take isl_aff_list
*list
, void *user
);
4770 static void sol_for_free(struct isl_sol_for
*sol_for
)
4774 if (sol_for
->sol
.context
)
4775 sol_for
->sol
.context
->op
->free(sol_for
->sol
.context
);
4779 static void sol_for_free_wrap(struct isl_sol
*sol
)
4781 sol_for_free((struct isl_sol_for
*)sol
);
4784 /* Add the solution identified by the tableau and the context tableau.
4786 * See documentation of sol_add for more details.
4788 * Instead of constructing a basic map, this function calls a user
4789 * defined function with the current context as a basic set and
4790 * a list of affine expressions representing the relation between
4791 * the input and output. The space over which the affine expressions
4792 * are defined is the same as that of the domain. The number of
4793 * affine expressions in the list is equal to the number of output variables.
4795 static void sol_for_add(struct isl_sol_for
*sol
,
4796 struct isl_basic_set
*dom
, struct isl_mat
*M
)
4800 isl_local_space
*ls
;
4804 if (sol
->sol
.error
|| !dom
|| !M
)
4807 ctx
= isl_basic_set_get_ctx(dom
);
4808 ls
= isl_basic_set_get_local_space(dom
);
4809 list
= isl_aff_list_alloc(ctx
, M
->n_row
- 1);
4810 for (i
= 1; i
< M
->n_row
; ++i
) {
4811 aff
= isl_aff_alloc(isl_local_space_copy(ls
));
4813 isl_int_set(aff
->v
->el
[0], M
->row
[0][0]);
4814 isl_seq_cpy(aff
->v
->el
+ 1, M
->row
[i
], M
->n_col
);
4816 aff
= isl_aff_normalize(aff
);
4817 list
= isl_aff_list_add(list
, aff
);
4819 isl_local_space_free(ls
);
4821 dom
= isl_basic_set_finalize(dom
);
4823 if (sol
->fn(isl_basic_set_copy(dom
), list
, sol
->user
) < 0)
4826 isl_basic_set_free(dom
);
4830 isl_basic_set_free(dom
);
4835 static void sol_for_add_wrap(struct isl_sol
*sol
,
4836 struct isl_basic_set
*dom
, struct isl_mat
*M
)
4838 sol_for_add((struct isl_sol_for
*)sol
, dom
, M
);
4841 static struct isl_sol_for
*sol_for_init(struct isl_basic_map
*bmap
, int max
,
4842 int (*fn
)(__isl_take isl_basic_set
*dom
, __isl_take isl_aff_list
*list
,
4846 struct isl_sol_for
*sol_for
= NULL
;
4848 struct isl_basic_set
*dom
= NULL
;
4850 sol_for
= isl_calloc_type(bmap
->ctx
, struct isl_sol_for
);
4854 dom_dim
= isl_space_domain(isl_space_copy(bmap
->dim
));
4855 dom
= isl_basic_set_universe(dom_dim
);
4857 sol_for
->sol
.rational
= ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
);
4858 sol_for
->sol
.dec_level
.callback
.run
= &sol_dec_level_wrap
;
4859 sol_for
->sol
.dec_level
.sol
= &sol_for
->sol
;
4861 sol_for
->user
= user
;
4862 sol_for
->sol
.max
= max
;
4863 sol_for
->sol
.n_out
= isl_basic_map_dim(bmap
, isl_dim_out
);
4864 sol_for
->sol
.add
= &sol_for_add_wrap
;
4865 sol_for
->sol
.add_empty
= NULL
;
4866 sol_for
->sol
.free
= &sol_for_free_wrap
;
4868 sol_for
->sol
.context
= isl_context_alloc(dom
);
4869 if (!sol_for
->sol
.context
)
4872 isl_basic_set_free(dom
);
4875 isl_basic_set_free(dom
);
4876 sol_for_free(sol_for
);
4880 static void sol_for_find_solutions(struct isl_sol_for
*sol_for
,
4881 struct isl_tab
*tab
)
4883 find_solutions_main(&sol_for
->sol
, tab
);
4886 int isl_basic_map_foreach_lexopt(__isl_keep isl_basic_map
*bmap
, int max
,
4887 int (*fn
)(__isl_take isl_basic_set
*dom
, __isl_take isl_aff_list
*list
,
4891 struct isl_sol_for
*sol_for
= NULL
;
4893 bmap
= isl_basic_map_copy(bmap
);
4894 bmap
= isl_basic_map_detect_equalities(bmap
);
4898 sol_for
= sol_for_init(bmap
, max
, fn
, user
);
4902 if (isl_basic_map_plain_is_empty(bmap
))
4905 struct isl_tab
*tab
;
4906 struct isl_context
*context
= sol_for
->sol
.context
;
4907 tab
= tab_for_lexmin(bmap
,
4908 context
->op
->peek_basic_set(context
), 1, max
);
4909 tab
= context
->op
->detect_nonnegative_parameters(context
, tab
);
4910 sol_for_find_solutions(sol_for
, tab
);
4911 if (sol_for
->sol
.error
)
4915 sol_free(&sol_for
->sol
);
4916 isl_basic_map_free(bmap
);
4919 sol_free(&sol_for
->sol
);
4920 isl_basic_map_free(bmap
);
4924 int isl_basic_set_foreach_lexopt(__isl_keep isl_basic_set
*bset
, int max
,
4925 int (*fn
)(__isl_take isl_basic_set
*dom
, __isl_take isl_aff_list
*list
,
4929 return isl_basic_map_foreach_lexopt(bset
, max
, fn
, user
);
4932 /* Check if the given sequence of len variables starting at pos
4933 * represents a trivial (i.e., zero) solution.
4934 * The variables are assumed to be non-negative and to come in pairs,
4935 * with each pair representing a variable of unrestricted sign.
4936 * The solution is trivial if each such pair in the sequence consists
4937 * of two identical values, meaning that the variable being represented
4940 static int region_is_trivial(struct isl_tab
*tab
, int pos
, int len
)
4947 for (i
= 0; i
< len
; i
+= 2) {
4951 neg_row
= tab
->var
[pos
+ i
].is_row
?
4952 tab
->var
[pos
+ i
].index
: -1;
4953 pos_row
= tab
->var
[pos
+ i
+ 1].is_row
?
4954 tab
->var
[pos
+ i
+ 1].index
: -1;
4957 isl_int_is_zero(tab
->mat
->row
[neg_row
][1])) &&
4959 isl_int_is_zero(tab
->mat
->row
[pos_row
][1])))
4962 if (neg_row
< 0 || pos_row
< 0)
4964 if (isl_int_ne(tab
->mat
->row
[neg_row
][1],
4965 tab
->mat
->row
[pos_row
][1]))
4972 /* Return the index of the first trivial region or -1 if all regions
4975 static int first_trivial_region(struct isl_tab
*tab
,
4976 int n_region
, struct isl_region
*region
)
4980 for (i
= 0; i
< n_region
; ++i
) {
4981 if (region_is_trivial(tab
, region
[i
].pos
, region
[i
].len
))
4988 /* Check if the solution is optimal, i.e., whether the first
4989 * n_op entries are zero.
4991 static int is_optimal(__isl_keep isl_vec
*sol
, int n_op
)
4995 for (i
= 0; i
< n_op
; ++i
)
4996 if (!isl_int_is_zero(sol
->el
[1 + i
]))
5001 /* Add constraints to "tab" that ensure that any solution is significantly
5002 * better than that represented by "sol". That is, find the first
5003 * relevant (within first n_op) non-zero coefficient and force it (along
5004 * with all previous coefficients) to be zero.
5005 * If the solution is already optimal (all relevant coefficients are zero),
5006 * then just mark the table as empty.
5008 * This function assumes that at least 2 * n_op more rows and at least
5009 * 2 * n_op more elements in the constraint array are available in the tableau.
5011 static int force_better_solution(struct isl_tab
*tab
,
5012 __isl_keep isl_vec
*sol
, int n_op
)
5021 for (i
= 0; i
< n_op
; ++i
)
5022 if (!isl_int_is_zero(sol
->el
[1 + i
]))
5026 if (isl_tab_mark_empty(tab
) < 0)
5031 ctx
= isl_vec_get_ctx(sol
);
5032 v
= isl_vec_alloc(ctx
, 1 + tab
->n_var
);
5036 for (; i
>= 0; --i
) {
5038 isl_int_set_si(v
->el
[1 + i
], -1);
5039 if (add_lexmin_eq(tab
, v
->el
) < 0)
5050 struct isl_trivial
{
5054 struct isl_tab_undo
*snap
;
5057 /* Return the lexicographically smallest non-trivial solution of the
5058 * given ILP problem.
5060 * All variables are assumed to be non-negative.
5062 * n_op is the number of initial coordinates to optimize.
5063 * That is, once a solution has been found, we will only continue looking
5064 * for solution that result in significantly better values for those
5065 * initial coordinates. That is, we only continue looking for solutions
5066 * that increase the number of initial zeros in this sequence.
5068 * A solution is non-trivial, if it is non-trivial on each of the
5069 * specified regions. Each region represents a sequence of pairs
5070 * of variables. A solution is non-trivial on such a region if
5071 * at least one of these pairs consists of different values, i.e.,
5072 * such that the non-negative variable represented by the pair is non-zero.
5074 * Whenever a conflict is encountered, all constraints involved are
5075 * reported to the caller through a call to "conflict".
5077 * We perform a simple branch-and-bound backtracking search.
5078 * Each level in the search represents initially trivial region that is forced
5079 * to be non-trivial.
5080 * At each level we consider n cases, where n is the length of the region.
5081 * In terms of the n/2 variables of unrestricted signs being encoded by
5082 * the region, we consider the cases
5085 * x_0 = 0 and x_1 >= 1
5086 * x_0 = 0 and x_1 <= -1
5087 * x_0 = 0 and x_1 = 0 and x_2 >= 1
5088 * x_0 = 0 and x_1 = 0 and x_2 <= -1
5090 * The cases are considered in this order, assuming that each pair
5091 * x_i_a x_i_b represents the value x_i_b - x_i_a.
5092 * That is, x_0 >= 1 is enforced by adding the constraint
5093 * x_0_b - x_0_a >= 1
5095 __isl_give isl_vec
*isl_tab_basic_set_non_trivial_lexmin(
5096 __isl_take isl_basic_set
*bset
, int n_op
, int n_region
,
5097 struct isl_region
*region
,
5098 int (*conflict
)(int con
, void *user
), void *user
)
5104 isl_vec
*sol
= NULL
;
5105 struct isl_tab
*tab
;
5106 struct isl_trivial
*triv
= NULL
;
5112 ctx
= isl_basic_set_get_ctx(bset
);
5113 sol
= isl_vec_alloc(ctx
, 0);
5115 tab
= tab_for_lexmin(bset
, NULL
, 0, 0);
5118 tab
->conflict
= conflict
;
5119 tab
->conflict_user
= user
;
5121 v
= isl_vec_alloc(ctx
, 1 + tab
->n_var
);
5122 triv
= isl_calloc_array(ctx
, struct isl_trivial
, n_region
);
5123 if (!v
|| (n_region
&& !triv
))
5129 while (level
>= 0) {
5133 tab
= cut_to_integer_lexmin(tab
, CUT_ONE
);
5138 r
= first_trivial_region(tab
, n_region
, region
);
5140 for (i
= 0; i
< level
; ++i
)
5143 sol
= isl_tab_get_sample_value(tab
);
5146 if (is_optimal(sol
, n_op
))
5150 if (level
>= n_region
)
5151 isl_die(ctx
, isl_error_internal
,
5152 "nesting level too deep", goto error
);
5153 if (isl_tab_extend_cons(tab
,
5154 2 * region
[r
].len
+ 2 * n_op
) < 0)
5156 triv
[level
].region
= r
;
5157 triv
[level
].side
= 0;
5160 r
= triv
[level
].region
;
5161 side
= triv
[level
].side
;
5162 base
= 2 * (side
/2);
5164 if (side
>= region
[r
].len
) {
5169 if (isl_tab_rollback(tab
, triv
[level
].snap
) < 0)
5174 if (triv
[level
].update
) {
5175 if (force_better_solution(tab
, sol
, n_op
) < 0)
5177 triv
[level
].update
= 0;
5180 if (side
== base
&& base
>= 2) {
5181 for (j
= base
- 2; j
< base
; ++j
) {
5183 isl_int_set_si(v
->el
[1 + region
[r
].pos
+ j
], 1);
5184 if (add_lexmin_eq(tab
, v
->el
) < 0)
5189 triv
[level
].snap
= isl_tab_snap(tab
);
5190 if (isl_tab_push_basis(tab
) < 0)
5194 isl_int_set_si(v
->el
[0], -1);
5195 isl_int_set_si(v
->el
[1 + region
[r
].pos
+ side
], -1);
5196 isl_int_set_si(v
->el
[1 + region
[r
].pos
+ (side
^ 1)], 1);
5197 tab
= add_lexmin_ineq(tab
, v
->el
);
5207 isl_basic_set_free(bset
);
5214 isl_basic_set_free(bset
);
5219 /* Wrapper for a tableau that is used for computing
5220 * the lexicographically smallest rational point of a non-negative set.
5221 * This point is represented by the sample value of "tab",
5222 * unless "tab" is empty.
5224 struct isl_tab_lexmin
{
5226 struct isl_tab
*tab
;
5229 /* Free "tl" and return NULL.
5231 __isl_null isl_tab_lexmin
*isl_tab_lexmin_free(__isl_take isl_tab_lexmin
*tl
)
5235 isl_ctx_deref(tl
->ctx
);
5236 isl_tab_free(tl
->tab
);
5242 /* Construct an isl_tab_lexmin for computing
5243 * the lexicographically smallest rational point in "bset",
5244 * assuming that all variables are non-negative.
5246 __isl_give isl_tab_lexmin
*isl_tab_lexmin_from_basic_set(
5247 __isl_take isl_basic_set
*bset
)
5255 ctx
= isl_basic_set_get_ctx(bset
);
5256 tl
= isl_calloc_type(ctx
, struct isl_tab_lexmin
);
5261 tl
->tab
= tab_for_lexmin(bset
, NULL
, 0, 0);
5262 isl_basic_set_free(bset
);
5264 return isl_tab_lexmin_free(tl
);
5267 isl_basic_set_free(bset
);
5268 isl_tab_lexmin_free(tl
);
5272 /* Return the dimension of the set represented by "tl".
5274 int isl_tab_lexmin_dim(__isl_keep isl_tab_lexmin
*tl
)
5276 return tl
? tl
->tab
->n_var
: -1;
5279 /* Add the equality with coefficients "eq" to "tl", updating the optimal
5280 * solution if needed.
5281 * The equality is added as two opposite inequality constraints.
5283 __isl_give isl_tab_lexmin
*isl_tab_lexmin_add_eq(__isl_take isl_tab_lexmin
*tl
,
5289 return isl_tab_lexmin_free(tl
);
5291 if (isl_tab_extend_cons(tl
->tab
, 2) < 0)
5292 return isl_tab_lexmin_free(tl
);
5293 n_var
= tl
->tab
->n_var
;
5294 isl_seq_neg(eq
, eq
, 1 + n_var
);
5295 tl
->tab
= add_lexmin_ineq(tl
->tab
, eq
);
5296 isl_seq_neg(eq
, eq
, 1 + n_var
);
5297 tl
->tab
= add_lexmin_ineq(tl
->tab
, eq
);
5300 return isl_tab_lexmin_free(tl
);
5305 /* Return the lexicographically smallest rational point in the basic set
5306 * from which "tl" was constructed.
5307 * If the original input was empty, then return a zero-length vector.
5309 __isl_give isl_vec
*isl_tab_lexmin_get_solution(__isl_keep isl_tab_lexmin
*tl
)
5314 return isl_vec_alloc(tl
->ctx
, 0);
5316 return isl_tab_get_sample_value(tl
->tab
);
5319 /* Return the lexicographically smallest rational point in "bset",
5320 * assuming that all variables are non-negative.
5321 * If "bset" is empty, then return a zero-length vector.
5323 __isl_give isl_vec
*isl_tab_basic_set_non_neg_lexmin(
5324 __isl_take isl_basic_set
*bset
)
5329 tl
= isl_tab_lexmin_from_basic_set(bset
);
5330 sol
= isl_tab_lexmin_get_solution(tl
);
5331 isl_tab_lexmin_free(tl
);
5335 struct isl_sol_pma
{
5337 isl_pw_multi_aff
*pma
;
5341 static void sol_pma_free(struct isl_sol_pma
*sol_pma
)
5345 if (sol_pma
->sol
.context
)
5346 sol_pma
->sol
.context
->op
->free(sol_pma
->sol
.context
);
5347 isl_pw_multi_aff_free(sol_pma
->pma
);
5348 isl_set_free(sol_pma
->empty
);
5352 /* This function is called for parts of the context where there is
5353 * no solution, with "bset" corresponding to the context tableau.
5354 * Simply add the basic set to the set "empty".
5356 static void sol_pma_add_empty(struct isl_sol_pma
*sol
,
5357 __isl_take isl_basic_set
*bset
)
5359 if (!bset
|| !sol
->empty
)
5362 sol
->empty
= isl_set_grow(sol
->empty
, 1);
5363 bset
= isl_basic_set_simplify(bset
);
5364 bset
= isl_basic_set_finalize(bset
);
5365 sol
->empty
= isl_set_add_basic_set(sol
->empty
, bset
);
5370 isl_basic_set_free(bset
);
5374 /* Given a basic map "dom" that represents the context and an affine
5375 * matrix "M" that maps the dimensions of the context to the
5376 * output variables, construct an isl_pw_multi_aff with a single
5377 * cell corresponding to "dom" and affine expressions copied from "M".
5379 static void sol_pma_add(struct isl_sol_pma
*sol
,
5380 __isl_take isl_basic_set
*dom
, __isl_take isl_mat
*M
)
5383 isl_local_space
*ls
;
5385 isl_multi_aff
*maff
;
5386 isl_pw_multi_aff
*pma
;
5388 maff
= isl_multi_aff_alloc(isl_pw_multi_aff_get_space(sol
->pma
));
5389 ls
= isl_basic_set_get_local_space(dom
);
5390 for (i
= 1; i
< M
->n_row
; ++i
) {
5391 aff
= isl_aff_alloc(isl_local_space_copy(ls
));
5393 isl_int_set(aff
->v
->el
[0], M
->row
[0][0]);
5394 isl_seq_cpy(aff
->v
->el
+ 1, M
->row
[i
], M
->n_col
);
5396 aff
= isl_aff_normalize(aff
);
5397 maff
= isl_multi_aff_set_aff(maff
, i
- 1, aff
);
5399 isl_local_space_free(ls
);
5401 dom
= isl_basic_set_simplify(dom
);
5402 dom
= isl_basic_set_finalize(dom
);
5403 pma
= isl_pw_multi_aff_alloc(isl_set_from_basic_set(dom
), maff
);
5404 sol
->pma
= isl_pw_multi_aff_add_disjoint(sol
->pma
, pma
);
5409 static void sol_pma_free_wrap(struct isl_sol
*sol
)
5411 sol_pma_free((struct isl_sol_pma
*)sol
);
5414 static void sol_pma_add_empty_wrap(struct isl_sol
*sol
,
5415 __isl_take isl_basic_set
*bset
)
5417 sol_pma_add_empty((struct isl_sol_pma
*)sol
, bset
);
5420 static void sol_pma_add_wrap(struct isl_sol
*sol
,
5421 __isl_take isl_basic_set
*dom
, __isl_take isl_mat
*M
)
5423 sol_pma_add((struct isl_sol_pma
*)sol
, dom
, M
);
5426 /* Construct an isl_sol_pma structure for accumulating the solution.
5427 * If track_empty is set, then we also keep track of the parts
5428 * of the context where there is no solution.
5429 * If max is set, then we are solving a maximization, rather than
5430 * a minimization problem, which means that the variables in the
5431 * tableau have value "M - x" rather than "M + x".
5433 static struct isl_sol
*sol_pma_init(__isl_keep isl_basic_map
*bmap
,
5434 __isl_take isl_basic_set
*dom
, int track_empty
, int max
)
5436 struct isl_sol_pma
*sol_pma
= NULL
;
5441 sol_pma
= isl_calloc_type(bmap
->ctx
, struct isl_sol_pma
);
5445 sol_pma
->sol
.rational
= ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
);
5446 sol_pma
->sol
.dec_level
.callback
.run
= &sol_dec_level_wrap
;
5447 sol_pma
->sol
.dec_level
.sol
= &sol_pma
->sol
;
5448 sol_pma
->sol
.max
= max
;
5449 sol_pma
->sol
.n_out
= isl_basic_map_dim(bmap
, isl_dim_out
);
5450 sol_pma
->sol
.add
= &sol_pma_add_wrap
;
5451 sol_pma
->sol
.add_empty
= track_empty
? &sol_pma_add_empty_wrap
: NULL
;
5452 sol_pma
->sol
.free
= &sol_pma_free_wrap
;
5453 sol_pma
->pma
= isl_pw_multi_aff_empty(isl_basic_map_get_space(bmap
));
5457 sol_pma
->sol
.context
= isl_context_alloc(dom
);
5458 if (!sol_pma
->sol
.context
)
5462 sol_pma
->empty
= isl_set_alloc_space(isl_basic_set_get_space(dom
),
5463 1, ISL_SET_DISJOINT
);
5464 if (!sol_pma
->empty
)
5468 isl_basic_set_free(dom
);
5469 return &sol_pma
->sol
;
5471 isl_basic_set_free(dom
);
5472 sol_pma_free(sol_pma
);
5476 /* Base case of isl_tab_basic_map_partial_lexopt, after removing
5477 * some obvious symmetries.
5479 * We call basic_map_partial_lexopt_base and extract the results.
5481 static __isl_give isl_pw_multi_aff
*basic_map_partial_lexopt_base_pma(
5482 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_set
*dom
,
5483 __isl_give isl_set
**empty
, int max
)
5485 isl_pw_multi_aff
*result
= NULL
;
5486 struct isl_sol
*sol
;
5487 struct isl_sol_pma
*sol_pma
;
5489 sol
= basic_map_partial_lexopt_base(bmap
, dom
, empty
, max
,
5493 sol_pma
= (struct isl_sol_pma
*) sol
;
5495 result
= isl_pw_multi_aff_copy(sol_pma
->pma
);
5497 *empty
= isl_set_copy(sol_pma
->empty
);
5498 sol_free(&sol_pma
->sol
);
5502 /* Given that the last input variable of "maff" represents the minimum
5503 * of some bounds, check whether we need to plug in the expression
5506 * In particular, check if the last input variable appears in any
5507 * of the expressions in "maff".
5509 static int need_substitution(__isl_keep isl_multi_aff
*maff
)
5514 pos
= isl_multi_aff_dim(maff
, isl_dim_in
) - 1;
5516 for (i
= 0; i
< maff
->n
; ++i
)
5517 if (isl_aff_involves_dims(maff
->p
[i
], isl_dim_in
, pos
, 1))
5523 /* Given a set of upper bounds on the last "input" variable m,
5524 * construct a piecewise affine expression that selects
5525 * the minimal upper bound to m, i.e.,
5526 * divide the space into cells where one
5527 * of the upper bounds is smaller than all the others and select
5528 * this upper bound on that cell.
5530 * In particular, if there are n bounds b_i, then the result
5531 * consists of n cell, each one of the form
5533 * b_i <= b_j for j > i
5534 * b_i < b_j for j < i
5536 * The affine expression on this cell is
5540 static __isl_give isl_pw_aff
*set_minimum_pa(__isl_take isl_space
*space
,
5541 __isl_take isl_mat
*var
)
5544 isl_aff
*aff
= NULL
;
5545 isl_basic_set
*bset
= NULL
;
5546 isl_pw_aff
*paff
= NULL
;
5547 isl_space
*pw_space
;
5548 isl_local_space
*ls
= NULL
;
5553 ls
= isl_local_space_from_space(isl_space_copy(space
));
5554 pw_space
= isl_space_copy(space
);
5555 pw_space
= isl_space_from_domain(pw_space
);
5556 pw_space
= isl_space_add_dims(pw_space
, isl_dim_out
, 1);
5557 paff
= isl_pw_aff_alloc_size(pw_space
, var
->n_row
);
5559 for (i
= 0; i
< var
->n_row
; ++i
) {
5562 aff
= isl_aff_alloc(isl_local_space_copy(ls
));
5563 bset
= isl_basic_set_alloc_space(isl_space_copy(space
), 0,
5567 isl_int_set_si(aff
->v
->el
[0], 1);
5568 isl_seq_cpy(aff
->v
->el
+ 1, var
->row
[i
], var
->n_col
);
5569 isl_int_set_si(aff
->v
->el
[1 + var
->n_col
], 0);
5570 bset
= select_minimum(bset
, var
, i
);
5571 paff_i
= isl_pw_aff_alloc(isl_set_from_basic_set(bset
), aff
);
5572 paff
= isl_pw_aff_add_disjoint(paff
, paff_i
);
5575 isl_local_space_free(ls
);
5576 isl_space_free(space
);
5581 isl_basic_set_free(bset
);
5582 isl_pw_aff_free(paff
);
5583 isl_local_space_free(ls
);
5584 isl_space_free(space
);
5589 /* Given a piecewise multi-affine expression of which the last input variable
5590 * is the minimum of the bounds in "cst", plug in the value of the minimum.
5591 * This minimum expression is given in "min_expr_pa".
5592 * The set "min_expr" contains the same information, but in the form of a set.
5593 * The variable is subsequently projected out.
5595 * The implementation is similar to those of "split" and "split_domain".
5596 * If the variable appears in a given expression, then minimum expression
5597 * is plugged in. Otherwise, if the variable appears in the constraints
5598 * and a split is required, then the domain is split. Otherwise, no split
5601 static __isl_give isl_pw_multi_aff
*split_domain_pma(
5602 __isl_take isl_pw_multi_aff
*opt
, __isl_take isl_pw_aff
*min_expr_pa
,
5603 __isl_take isl_set
*min_expr
, __isl_take isl_mat
*cst
)
5608 isl_pw_multi_aff
*res
;
5610 if (!opt
|| !min_expr
|| !cst
)
5613 n_in
= isl_pw_multi_aff_dim(opt
, isl_dim_in
);
5614 space
= isl_pw_multi_aff_get_space(opt
);
5615 space
= isl_space_drop_dims(space
, isl_dim_in
, n_in
- 1, 1);
5616 res
= isl_pw_multi_aff_empty(space
);
5618 for (i
= 0; i
< opt
->n
; ++i
) {
5619 isl_pw_multi_aff
*pma
;
5621 pma
= isl_pw_multi_aff_alloc(isl_set_copy(opt
->p
[i
].set
),
5622 isl_multi_aff_copy(opt
->p
[i
].maff
));
5623 if (need_substitution(opt
->p
[i
].maff
))
5624 pma
= isl_pw_multi_aff_substitute(pma
,
5625 isl_dim_in
, n_in
- 1, min_expr_pa
);
5626 else if (need_split_set(opt
->p
[i
].set
, cst
))
5627 pma
= isl_pw_multi_aff_intersect_domain(pma
,
5628 isl_set_copy(min_expr
));
5629 pma
= isl_pw_multi_aff_project_out(pma
,
5630 isl_dim_in
, n_in
- 1, 1);
5632 res
= isl_pw_multi_aff_add_disjoint(res
, pma
);
5635 isl_pw_multi_aff_free(opt
);
5636 isl_pw_aff_free(min_expr_pa
);
5637 isl_set_free(min_expr
);
5641 isl_pw_multi_aff_free(opt
);
5642 isl_pw_aff_free(min_expr_pa
);
5643 isl_set_free(min_expr
);
5648 static __isl_give isl_pw_multi_aff
*basic_map_partial_lexopt_pma(
5649 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_set
*dom
,
5650 __isl_give isl_set
**empty
, int max
);
5652 /* This function is called from basic_map_partial_lexopt_symm.
5653 * The last variable of "bmap" and "dom" corresponds to the minimum
5654 * of the bounds in "cst". "map_space" is the space of the original
5655 * input relation (of basic_map_partial_lexopt_symm) and "set_space"
5656 * is the space of the original domain.
5658 * We recursively call basic_map_partial_lexopt and then plug in
5659 * the definition of the minimum in the result.
5661 static __isl_give
union isl_lex_res
basic_map_partial_lexopt_symm_pma_core(
5662 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_set
*dom
,
5663 __isl_give isl_set
**empty
, int max
, __isl_take isl_mat
*cst
,
5664 __isl_take isl_space
*map_space
, __isl_take isl_space
*set_space
)
5666 isl_pw_multi_aff
*opt
;
5667 isl_pw_aff
*min_expr_pa
;
5669 union isl_lex_res res
;
5671 min_expr
= set_minimum(isl_basic_set_get_space(dom
), isl_mat_copy(cst
));
5672 min_expr_pa
= set_minimum_pa(isl_basic_set_get_space(dom
),
5675 opt
= basic_map_partial_lexopt_pma(bmap
, dom
, empty
, max
);
5678 *empty
= split(*empty
,
5679 isl_set_copy(min_expr
), isl_mat_copy(cst
));
5680 *empty
= isl_set_reset_space(*empty
, set_space
);
5683 opt
= split_domain_pma(opt
, min_expr_pa
, min_expr
, cst
);
5684 opt
= isl_pw_multi_aff_reset_space(opt
, map_space
);
5690 static __isl_give isl_pw_multi_aff
*basic_map_partial_lexopt_symm_pma(
5691 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_set
*dom
,
5692 __isl_give isl_set
**empty
, int max
, int first
, int second
)
5694 return basic_map_partial_lexopt_symm(bmap
, dom
, empty
, max
,
5695 first
, second
, &basic_map_partial_lexopt_symm_pma_core
).pma
;
5698 /* Recursive part of isl_basic_map_partial_lexopt_pw_multi_aff, after detecting
5699 * equalities and removing redundant constraints.
5701 * We first check if there are any parallel constraints (left).
5702 * If not, we are in the base case.
5703 * If there are parallel constraints, we replace them by a single
5704 * constraint in basic_map_partial_lexopt_symm_pma and then call
5705 * this function recursively to look for more parallel constraints.
5707 static __isl_give isl_pw_multi_aff
*basic_map_partial_lexopt_pma(
5708 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_set
*dom
,
5709 __isl_give isl_set
**empty
, int max
)
5717 if (bmap
->ctx
->opt
->pip_symmetry
)
5718 par
= parallel_constraints(bmap
, &first
, &second
);
5722 return basic_map_partial_lexopt_base_pma(bmap
, dom
, empty
, max
);
5724 return basic_map_partial_lexopt_symm_pma(bmap
, dom
, empty
, max
,
5727 isl_basic_set_free(dom
);
5728 isl_basic_map_free(bmap
);
5732 /* Compute the lexicographic minimum (or maximum if "max" is set)
5733 * of "bmap" over the domain "dom" and return the result as a piecewise
5734 * multi-affine expression.
5735 * If "empty" is not NULL, then *empty is assigned a set that
5736 * contains those parts of the domain where there is no solution.
5737 * If "bmap" is marked as rational (ISL_BASIC_MAP_RATIONAL),
5738 * then we compute the rational optimum. Otherwise, we compute
5739 * the integral optimum.
5741 * We perform some preprocessing. As the PILP solver does not
5742 * handle implicit equalities very well, we first make sure all
5743 * the equalities are explicitly available.
5745 * We also add context constraints to the basic map and remove
5746 * redundant constraints. This is only needed because of the
5747 * way we handle simple symmetries. In particular, we currently look
5748 * for symmetries on the constraints, before we set up the main tableau.
5749 * It is then no good to look for symmetries on possibly redundant constraints.
5751 __isl_give isl_pw_multi_aff
*isl_basic_map_partial_lexopt_pw_multi_aff(
5752 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_set
*dom
,
5753 __isl_give isl_set
**empty
, int max
)
5760 isl_assert(bmap
->ctx
,
5761 isl_basic_map_compatible_domain(bmap
, dom
), goto error
);
5763 if (isl_basic_set_dim(dom
, isl_dim_all
) == 0)
5764 return basic_map_partial_lexopt_pma(bmap
, dom
, empty
, max
);
5766 bmap
= isl_basic_map_intersect_domain(bmap
, isl_basic_set_copy(dom
));
5767 bmap
= isl_basic_map_detect_equalities(bmap
);
5768 bmap
= isl_basic_map_remove_redundancies(bmap
);
5770 return basic_map_partial_lexopt_pma(bmap
, dom
, empty
, max
);
5772 isl_basic_set_free(dom
);
5773 isl_basic_map_free(bmap
);