2 * Copyright 2008-2009 Katholieke Universiteit Leuven
4 * Use of this software is governed by the GNU LGPLv2.1 license
6 * Written by Sven Verdoolaege, K.U.Leuven, Departement
7 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
10 #include "isl_map_private.h"
13 #include "isl_sample.h"
16 * The implementation of parametric integer linear programming in this file
17 * was inspired by the paper "Parametric Integer Programming" and the
18 * report "Solving systems of affine (in)equalities" by Paul Feautrier
21 * The strategy used for obtaining a feasible solution is different
22 * from the one used in isl_tab.c. In particular, in isl_tab.c,
23 * upon finding a constraint that is not yet satisfied, we pivot
24 * in a row that increases the constant term of row holding the
25 * constraint, making sure the sample solution remains feasible
26 * for all the constraints it already satisfied.
27 * Here, we always pivot in the row holding the constraint,
28 * choosing a column that induces the lexicographically smallest
29 * increment to the sample solution.
31 * By starting out from a sample value that is lexicographically
32 * smaller than any integer point in the problem space, the first
33 * feasible integer sample point we find will also be the lexicographically
34 * smallest. If all variables can be assumed to be non-negative,
35 * then the initial sample value may be chosen equal to zero.
36 * However, we will not make this assumption. Instead, we apply
37 * the "big parameter" trick. Any variable x is then not directly
38 * used in the tableau, but instead it its represented by another
39 * variable x' = M + x, where M is an arbitrarily large (positive)
40 * value. x' is therefore always non-negative, whatever the value of x.
41 * Taking as initial smaple value x' = 0 corresponds to x = -M,
42 * which is always smaller than any possible value of x.
44 * The big parameter trick is used in the main tableau and
45 * also in the context tableau if isl_context_lex is used.
46 * In this case, each tableaus has its own big parameter.
47 * Before doing any real work, we check if all the parameters
48 * happen to be non-negative. If so, we drop the column corresponding
49 * to M from the initial context tableau.
50 * If isl_context_gbr is used, then the big parameter trick is only
51 * used in the main tableau.
55 struct isl_context_op
{
56 /* detect nonnegative parameters in context and mark them in tab */
57 struct isl_tab
*(*detect_nonnegative_parameters
)(
58 struct isl_context
*context
, struct isl_tab
*tab
);
59 /* return temporary reference to basic set representation of context */
60 struct isl_basic_set
*(*peek_basic_set
)(struct isl_context
*context
);
61 /* return temporary reference to tableau representation of context */
62 struct isl_tab
*(*peek_tab
)(struct isl_context
*context
);
63 /* add equality; check is 1 if eq may not be valid;
64 * update is 1 if we may want to call ineq_sign on context later.
66 void (*add_eq
)(struct isl_context
*context
, isl_int
*eq
,
67 int check
, int update
);
68 /* add inequality; check is 1 if ineq may not be valid;
69 * update is 1 if we may want to call ineq_sign on context later.
71 void (*add_ineq
)(struct isl_context
*context
, isl_int
*ineq
,
72 int check
, int update
);
73 /* check sign of ineq based on previous information.
74 * strict is 1 if saturation should be treated as a positive sign.
76 enum isl_tab_row_sign (*ineq_sign
)(struct isl_context
*context
,
77 isl_int
*ineq
, int strict
);
78 /* check if inequality maintains feasibility */
79 int (*test_ineq
)(struct isl_context
*context
, isl_int
*ineq
);
80 /* return index of a div that corresponds to "div" */
81 int (*get_div
)(struct isl_context
*context
, struct isl_tab
*tab
,
83 /* add div "div" to context and return index and non-negativity */
84 int (*add_div
)(struct isl_context
*context
, struct isl_vec
*div
,
86 int (*detect_equalities
)(struct isl_context
*context
,
88 /* return row index of "best" split */
89 int (*best_split
)(struct isl_context
*context
, struct isl_tab
*tab
);
90 /* check if context has already been determined to be empty */
91 int (*is_empty
)(struct isl_context
*context
);
92 /* check if context is still usable */
93 int (*is_ok
)(struct isl_context
*context
);
94 /* save a copy/snapshot of context */
95 void *(*save
)(struct isl_context
*context
);
96 /* restore saved context */
97 void (*restore
)(struct isl_context
*context
, void *);
98 /* invalidate context */
99 void (*invalidate
)(struct isl_context
*context
);
101 void (*free
)(struct isl_context
*context
);
105 struct isl_context_op
*op
;
108 struct isl_context_lex
{
109 struct isl_context context
;
113 struct isl_partial_sol
{
115 struct isl_basic_set
*dom
;
118 struct isl_partial_sol
*next
;
122 struct isl_sol_callback
{
123 struct isl_tab_callback callback
;
127 /* isl_sol is an interface for constructing a solution to
128 * a parametric integer linear programming problem.
129 * Every time the algorithm reaches a state where a solution
130 * can be read off from the tableau (including cases where the tableau
131 * is empty), the function "add" is called on the isl_sol passed
132 * to find_solutions_main.
134 * The context tableau is owned by isl_sol and is updated incrementally.
136 * There are currently two implementations of this interface,
137 * isl_sol_map, which simply collects the solutions in an isl_map
138 * and (optionally) the parts of the context where there is no solution
140 * isl_sol_for, which calls a user-defined function for each part of
149 struct isl_context
*context
;
150 struct isl_partial_sol
*partial
;
151 void (*add
)(struct isl_sol
*sol
,
152 struct isl_basic_set
*dom
, struct isl_mat
*M
);
153 void (*add_empty
)(struct isl_sol
*sol
, struct isl_basic_set
*bset
);
154 void (*free
)(struct isl_sol
*sol
);
155 struct isl_sol_callback dec_level
;
158 static void sol_free(struct isl_sol
*sol
)
160 struct isl_partial_sol
*partial
, *next
;
163 for (partial
= sol
->partial
; partial
; partial
= next
) {
164 next
= partial
->next
;
165 isl_basic_set_free(partial
->dom
);
166 isl_mat_free(partial
->M
);
172 /* Push a partial solution represented by a domain and mapping M
173 * onto the stack of partial solutions.
175 static void sol_push_sol(struct isl_sol
*sol
,
176 struct isl_basic_set
*dom
, struct isl_mat
*M
)
178 struct isl_partial_sol
*partial
;
180 if (sol
->error
|| !dom
)
183 partial
= isl_alloc_type(dom
->ctx
, struct isl_partial_sol
);
187 partial
->level
= sol
->level
;
190 partial
->next
= sol
->partial
;
192 sol
->partial
= partial
;
196 isl_basic_set_free(dom
);
200 /* Pop one partial solution from the partial solution stack and
201 * pass it on to sol->add or sol->add_empty.
203 static void sol_pop_one(struct isl_sol
*sol
)
205 struct isl_partial_sol
*partial
;
207 partial
= sol
->partial
;
208 sol
->partial
= partial
->next
;
211 sol
->add(sol
, partial
->dom
, partial
->M
);
213 sol
->add_empty(sol
, partial
->dom
);
217 /* Return a fresh copy of the domain represented by the context tableau.
219 static struct isl_basic_set
*sol_domain(struct isl_sol
*sol
)
221 struct isl_basic_set
*bset
;
226 bset
= isl_basic_set_dup(sol
->context
->op
->peek_basic_set(sol
->context
));
227 bset
= isl_basic_set_update_from_tab(bset
,
228 sol
->context
->op
->peek_tab(sol
->context
));
233 /* Check whether two partial solutions have the same mapping, where n_div
234 * is the number of divs that the two partial solutions have in common.
236 static int same_solution(struct isl_partial_sol
*s1
, struct isl_partial_sol
*s2
,
242 if (!s1
->M
!= !s2
->M
)
247 dim
= isl_basic_set_total_dim(s1
->dom
) - s1
->dom
->n_div
;
249 for (i
= 0; i
< s1
->M
->n_row
; ++i
) {
250 if (isl_seq_first_non_zero(s1
->M
->row
[i
]+1+dim
+n_div
,
251 s1
->M
->n_col
-1-dim
-n_div
) != -1)
253 if (isl_seq_first_non_zero(s2
->M
->row
[i
]+1+dim
+n_div
,
254 s2
->M
->n_col
-1-dim
-n_div
) != -1)
256 if (!isl_seq_eq(s1
->M
->row
[i
], s2
->M
->row
[i
], 1+dim
+n_div
))
262 /* Pop all solutions from the partial solution stack that were pushed onto
263 * the stack at levels that are deeper than the current level.
264 * If the two topmost elements on the stack have the same level
265 * and represent the same solution, then their domains are combined.
266 * This combined domain is the same as the current context domain
267 * as sol_pop is called each time we move back to a higher level.
269 static void sol_pop(struct isl_sol
*sol
)
271 struct isl_partial_sol
*partial
;
277 if (sol
->level
== 0) {
278 for (partial
= sol
->partial
; partial
; partial
= sol
->partial
)
283 partial
= sol
->partial
;
287 if (partial
->level
<= sol
->level
)
290 if (partial
->next
&& partial
->next
->level
== partial
->level
) {
291 n_div
= isl_basic_set_dim(
292 sol
->context
->op
->peek_basic_set(sol
->context
),
295 if (!same_solution(partial
, partial
->next
, n_div
)) {
299 struct isl_basic_set
*bset
;
301 bset
= sol_domain(sol
);
303 isl_basic_set_free(partial
->next
->dom
);
304 partial
->next
->dom
= bset
;
305 partial
->next
->level
= sol
->level
;
307 sol
->partial
= partial
->next
;
308 isl_basic_set_free(partial
->dom
);
309 isl_mat_free(partial
->M
);
316 static void sol_dec_level(struct isl_sol
*sol
)
326 static int sol_dec_level_wrap(struct isl_tab_callback
*cb
)
328 struct isl_sol_callback
*callback
= (struct isl_sol_callback
*)cb
;
330 sol_dec_level(callback
->sol
);
332 return callback
->sol
->error
? -1 : 0;
335 /* Move down to next level and push callback onto context tableau
336 * to decrease the level again when it gets rolled back across
337 * the current state. That is, dec_level will be called with
338 * the context tableau in the same state as it is when inc_level
341 static void sol_inc_level(struct isl_sol
*sol
)
349 tab
= sol
->context
->op
->peek_tab(sol
->context
);
350 if (isl_tab_push_callback(tab
, &sol
->dec_level
.callback
) < 0)
354 static void scale_rows(struct isl_mat
*mat
, isl_int m
, int n_row
)
358 if (isl_int_is_one(m
))
361 for (i
= 0; i
< n_row
; ++i
)
362 isl_seq_scale(mat
->row
[i
], mat
->row
[i
], m
, mat
->n_col
);
365 /* Add the solution identified by the tableau and the context tableau.
367 * The layout of the variables is as follows.
368 * tab->n_var is equal to the total number of variables in the input
369 * map (including divs that were copied from the context)
370 * + the number of extra divs constructed
371 * Of these, the first tab->n_param and the last tab->n_div variables
372 * correspond to the variables in the context, i.e.,
373 * tab->n_param + tab->n_div = context_tab->n_var
374 * tab->n_param is equal to the number of parameters and input
375 * dimensions in the input map
376 * tab->n_div is equal to the number of divs in the context
378 * If there is no solution, then call add_empty with a basic set
379 * that corresponds to the context tableau. (If add_empty is NULL,
382 * If there is a solution, then first construct a matrix that maps
383 * all dimensions of the context to the output variables, i.e.,
384 * the output dimensions in the input map.
385 * The divs in the input map (if any) that do not correspond to any
386 * div in the context do not appear in the solution.
387 * The algorithm will make sure that they have an integer value,
388 * but these values themselves are of no interest.
389 * We have to be careful not to drop or rearrange any divs in the
390 * context because that would change the meaning of the matrix.
392 * To extract the value of the output variables, it should be noted
393 * that we always use a big parameter M in the main tableau and so
394 * the variable stored in this tableau is not an output variable x itself, but
395 * x' = M + x (in case of minimization)
397 * x' = M - x (in case of maximization)
398 * If x' appears in a column, then its optimal value is zero,
399 * which means that the optimal value of x is an unbounded number
400 * (-M for minimization and M for maximization).
401 * We currently assume that the output dimensions in the original map
402 * are bounded, so this cannot occur.
403 * Similarly, when x' appears in a row, then the coefficient of M in that
404 * row is necessarily 1.
405 * If the row in the tableau represents
406 * d x' = c + d M + e(y)
407 * then, in case of minimization, the corresponding row in the matrix
410 * with a d = m, the (updated) common denominator of the matrix.
411 * In case of maximization, the row will be
414 static void sol_add(struct isl_sol
*sol
, struct isl_tab
*tab
)
416 struct isl_basic_set
*bset
= NULL
;
417 struct isl_mat
*mat
= NULL
;
422 if (sol
->error
|| !tab
)
425 if (tab
->empty
&& !sol
->add_empty
)
428 bset
= sol_domain(sol
);
431 sol_push_sol(sol
, bset
, NULL
);
437 mat
= isl_mat_alloc(tab
->mat
->ctx
, 1 + sol
->n_out
,
438 1 + tab
->n_param
+ tab
->n_div
);
444 isl_seq_clr(mat
->row
[0] + 1, mat
->n_col
- 1);
445 isl_int_set_si(mat
->row
[0][0], 1);
446 for (row
= 0; row
< sol
->n_out
; ++row
) {
447 int i
= tab
->n_param
+ row
;
450 isl_seq_clr(mat
->row
[1 + row
], mat
->n_col
);
451 if (!tab
->var
[i
].is_row
) {
453 isl_assert(mat
->ctx
, !tab
->M
, goto error2
);
457 r
= tab
->var
[i
].index
;
460 isl_assert(mat
->ctx
, isl_int_eq(tab
->mat
->row
[r
][2],
461 tab
->mat
->row
[r
][0]),
463 isl_int_gcd(m
, mat
->row
[0][0], tab
->mat
->row
[r
][0]);
464 isl_int_divexact(m
, tab
->mat
->row
[r
][0], m
);
465 scale_rows(mat
, m
, 1 + row
);
466 isl_int_divexact(m
, mat
->row
[0][0], tab
->mat
->row
[r
][0]);
467 isl_int_mul(mat
->row
[1 + row
][0], m
, tab
->mat
->row
[r
][1]);
468 for (j
= 0; j
< tab
->n_param
; ++j
) {
470 if (tab
->var
[j
].is_row
)
472 col
= tab
->var
[j
].index
;
473 isl_int_mul(mat
->row
[1 + row
][1 + j
], m
,
474 tab
->mat
->row
[r
][off
+ col
]);
476 for (j
= 0; j
< tab
->n_div
; ++j
) {
478 if (tab
->var
[tab
->n_var
- tab
->n_div
+j
].is_row
)
480 col
= tab
->var
[tab
->n_var
- tab
->n_div
+j
].index
;
481 isl_int_mul(mat
->row
[1 + row
][1 + tab
->n_param
+ j
], m
,
482 tab
->mat
->row
[r
][off
+ col
]);
485 isl_seq_neg(mat
->row
[1 + row
], mat
->row
[1 + row
],
491 sol_push_sol(sol
, bset
, mat
);
496 isl_basic_set_free(bset
);
504 struct isl_set
*empty
;
507 static void sol_map_free(struct isl_sol_map
*sol_map
)
509 if (sol_map
->sol
.context
)
510 sol_map
->sol
.context
->op
->free(sol_map
->sol
.context
);
511 isl_map_free(sol_map
->map
);
512 isl_set_free(sol_map
->empty
);
516 static void sol_map_free_wrap(struct isl_sol
*sol
)
518 sol_map_free((struct isl_sol_map
*)sol
);
521 /* This function is called for parts of the context where there is
522 * no solution, with "bset" corresponding to the context tableau.
523 * Simply add the basic set to the set "empty".
525 static void sol_map_add_empty(struct isl_sol_map
*sol
,
526 struct isl_basic_set
*bset
)
530 isl_assert(bset
->ctx
, sol
->empty
, goto error
);
532 sol
->empty
= isl_set_grow(sol
->empty
, 1);
533 bset
= isl_basic_set_simplify(bset
);
534 bset
= isl_basic_set_finalize(bset
);
535 sol
->empty
= isl_set_add_basic_set(sol
->empty
, isl_basic_set_copy(bset
));
538 isl_basic_set_free(bset
);
541 isl_basic_set_free(bset
);
545 static void sol_map_add_empty_wrap(struct isl_sol
*sol
,
546 struct isl_basic_set
*bset
)
548 sol_map_add_empty((struct isl_sol_map
*)sol
, bset
);
551 /* Add bset to sol's empty, but only if we are actually collecting
554 static void sol_map_add_empty_if_needed(struct isl_sol_map
*sol
,
555 struct isl_basic_set
*bset
)
558 sol_map_add_empty(sol
, bset
);
560 isl_basic_set_free(bset
);
563 /* Given a basic map "dom" that represents the context and an affine
564 * matrix "M" that maps the dimensions of the context to the
565 * output variables, construct a basic map with the same parameters
566 * and divs as the context, the dimensions of the context as input
567 * dimensions and a number of output dimensions that is equal to
568 * the number of output dimensions in the input map.
570 * The constraints and divs of the context are simply copied
571 * from "dom". For each row
575 * is added, with d the common denominator of M.
577 static void sol_map_add(struct isl_sol_map
*sol
,
578 struct isl_basic_set
*dom
, struct isl_mat
*M
)
581 struct isl_basic_map
*bmap
= NULL
;
582 isl_basic_set
*context_bset
;
590 if (sol
->sol
.error
|| !dom
|| !M
)
593 n_out
= sol
->sol
.n_out
;
594 n_eq
= dom
->n_eq
+ n_out
;
595 n_ineq
= dom
->n_ineq
;
597 nparam
= isl_basic_set_total_dim(dom
) - n_div
;
598 total
= isl_map_dim(sol
->map
, isl_dim_all
);
599 bmap
= isl_basic_map_alloc_dim(isl_map_get_dim(sol
->map
),
600 n_div
, n_eq
, 2 * n_div
+ n_ineq
);
603 if (sol
->sol
.rational
)
604 ISL_F_SET(bmap
, ISL_BASIC_MAP_RATIONAL
);
605 for (i
= 0; i
< dom
->n_div
; ++i
) {
606 int k
= isl_basic_map_alloc_div(bmap
);
609 isl_seq_cpy(bmap
->div
[k
], dom
->div
[i
], 1 + 1 + nparam
);
610 isl_seq_clr(bmap
->div
[k
] + 1 + 1 + nparam
, total
- nparam
);
611 isl_seq_cpy(bmap
->div
[k
] + 1 + 1 + total
,
612 dom
->div
[i
] + 1 + 1 + nparam
, i
);
614 for (i
= 0; i
< dom
->n_eq
; ++i
) {
615 int k
= isl_basic_map_alloc_equality(bmap
);
618 isl_seq_cpy(bmap
->eq
[k
], dom
->eq
[i
], 1 + nparam
);
619 isl_seq_clr(bmap
->eq
[k
] + 1 + nparam
, total
- nparam
);
620 isl_seq_cpy(bmap
->eq
[k
] + 1 + total
,
621 dom
->eq
[i
] + 1 + nparam
, n_div
);
623 for (i
= 0; i
< dom
->n_ineq
; ++i
) {
624 int k
= isl_basic_map_alloc_inequality(bmap
);
627 isl_seq_cpy(bmap
->ineq
[k
], dom
->ineq
[i
], 1 + nparam
);
628 isl_seq_clr(bmap
->ineq
[k
] + 1 + nparam
, total
- nparam
);
629 isl_seq_cpy(bmap
->ineq
[k
] + 1 + total
,
630 dom
->ineq
[i
] + 1 + nparam
, n_div
);
632 for (i
= 0; i
< M
->n_row
- 1; ++i
) {
633 int k
= isl_basic_map_alloc_equality(bmap
);
636 isl_seq_cpy(bmap
->eq
[k
], M
->row
[1 + i
], 1 + nparam
);
637 isl_seq_clr(bmap
->eq
[k
] + 1 + nparam
, n_out
);
638 isl_int_neg(bmap
->eq
[k
][1 + nparam
+ i
], M
->row
[0][0]);
639 isl_seq_cpy(bmap
->eq
[k
] + 1 + nparam
+ n_out
,
640 M
->row
[1 + i
] + 1 + nparam
, n_div
);
642 bmap
= isl_basic_map_simplify(bmap
);
643 bmap
= isl_basic_map_finalize(bmap
);
644 sol
->map
= isl_map_grow(sol
->map
, 1);
645 sol
->map
= isl_map_add_basic_map(sol
->map
, bmap
);
648 isl_basic_set_free(dom
);
652 isl_basic_set_free(dom
);
654 isl_basic_map_free(bmap
);
658 static void sol_map_add_wrap(struct isl_sol
*sol
,
659 struct isl_basic_set
*dom
, struct isl_mat
*M
)
661 sol_map_add((struct isl_sol_map
*)sol
, dom
, M
);
665 /* Store the "parametric constant" of row "row" of tableau "tab" in "line",
666 * i.e., the constant term and the coefficients of all variables that
667 * appear in the context tableau.
668 * Note that the coefficient of the big parameter M is NOT copied.
669 * The context tableau may not have a big parameter and even when it
670 * does, it is a different big parameter.
672 static void get_row_parameter_line(struct isl_tab
*tab
, int row
, isl_int
*line
)
675 unsigned off
= 2 + tab
->M
;
677 isl_int_set(line
[0], tab
->mat
->row
[row
][1]);
678 for (i
= 0; i
< tab
->n_param
; ++i
) {
679 if (tab
->var
[i
].is_row
)
680 isl_int_set_si(line
[1 + i
], 0);
682 int col
= tab
->var
[i
].index
;
683 isl_int_set(line
[1 + i
], tab
->mat
->row
[row
][off
+ col
]);
686 for (i
= 0; i
< tab
->n_div
; ++i
) {
687 if (tab
->var
[tab
->n_var
- tab
->n_div
+ i
].is_row
)
688 isl_int_set_si(line
[1 + tab
->n_param
+ i
], 0);
690 int col
= tab
->var
[tab
->n_var
- tab
->n_div
+ i
].index
;
691 isl_int_set(line
[1 + tab
->n_param
+ i
],
692 tab
->mat
->row
[row
][off
+ col
]);
697 /* Check if rows "row1" and "row2" have identical "parametric constants",
698 * as explained above.
699 * In this case, we also insist that the coefficients of the big parameter
700 * be the same as the values of the constants will only be the same
701 * if these coefficients are also the same.
703 static int identical_parameter_line(struct isl_tab
*tab
, int row1
, int row2
)
706 unsigned off
= 2 + tab
->M
;
708 if (isl_int_ne(tab
->mat
->row
[row1
][1], tab
->mat
->row
[row2
][1]))
711 if (tab
->M
&& isl_int_ne(tab
->mat
->row
[row1
][2],
712 tab
->mat
->row
[row2
][2]))
715 for (i
= 0; i
< tab
->n_param
+ tab
->n_div
; ++i
) {
716 int pos
= i
< tab
->n_param
? i
:
717 tab
->n_var
- tab
->n_div
+ i
- tab
->n_param
;
720 if (tab
->var
[pos
].is_row
)
722 col
= tab
->var
[pos
].index
;
723 if (isl_int_ne(tab
->mat
->row
[row1
][off
+ col
],
724 tab
->mat
->row
[row2
][off
+ col
]))
730 /* Return an inequality that expresses that the "parametric constant"
731 * should be non-negative.
732 * This function is only called when the coefficient of the big parameter
735 static struct isl_vec
*get_row_parameter_ineq(struct isl_tab
*tab
, int row
)
737 struct isl_vec
*ineq
;
739 ineq
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_param
+ tab
->n_div
);
743 get_row_parameter_line(tab
, row
, ineq
->el
);
745 ineq
= isl_vec_normalize(ineq
);
750 /* Return a integer division for use in a parametric cut based on the given row.
751 * In particular, let the parametric constant of the row be
755 * where y_0 = 1, but none of the y_i corresponds to the big parameter M.
756 * The div returned is equal to
758 * floor(\sum_i {-a_i} y_i) = floor((\sum_i (-a_i mod d) y_i)/d)
760 static struct isl_vec
*get_row_parameter_div(struct isl_tab
*tab
, int row
)
764 div
= isl_vec_alloc(tab
->mat
->ctx
, 1 + 1 + tab
->n_param
+ tab
->n_div
);
768 isl_int_set(div
->el
[0], tab
->mat
->row
[row
][0]);
769 get_row_parameter_line(tab
, row
, div
->el
+ 1);
770 div
= isl_vec_normalize(div
);
771 isl_seq_neg(div
->el
+ 1, div
->el
+ 1, div
->size
- 1);
772 isl_seq_fdiv_r(div
->el
+ 1, div
->el
+ 1, div
->el
[0], div
->size
- 1);
777 /* Return a integer division for use in transferring an integrality constraint
779 * In particular, let the parametric constant of the row be
783 * where y_0 = 1, but none of the y_i corresponds to the big parameter M.
784 * The the returned div is equal to
786 * floor(\sum_i {a_i} y_i) = floor((\sum_i (a_i mod d) y_i)/d)
788 static struct isl_vec
*get_row_split_div(struct isl_tab
*tab
, int row
)
792 div
= isl_vec_alloc(tab
->mat
->ctx
, 1 + 1 + tab
->n_param
+ tab
->n_div
);
796 isl_int_set(div
->el
[0], tab
->mat
->row
[row
][0]);
797 get_row_parameter_line(tab
, row
, div
->el
+ 1);
798 div
= isl_vec_normalize(div
);
799 isl_seq_fdiv_r(div
->el
+ 1, div
->el
+ 1, div
->el
[0], div
->size
- 1);
804 /* Construct and return an inequality that expresses an upper bound
806 * In particular, if the div is given by
810 * then the inequality expresses
814 static struct isl_vec
*ineq_for_div(struct isl_basic_set
*bset
, unsigned div
)
818 struct isl_vec
*ineq
;
823 total
= isl_basic_set_total_dim(bset
);
824 div_pos
= 1 + total
- bset
->n_div
+ div
;
826 ineq
= isl_vec_alloc(bset
->ctx
, 1 + total
);
830 isl_seq_cpy(ineq
->el
, bset
->div
[div
] + 1, 1 + total
);
831 isl_int_neg(ineq
->el
[div_pos
], bset
->div
[div
][0]);
835 /* Given a row in the tableau and a div that was created
836 * using get_row_split_div and that been constrained to equality, i.e.,
838 * d = floor(\sum_i {a_i} y_i) = \sum_i {a_i} y_i
840 * replace the expression "\sum_i {a_i} y_i" in the row by d,
841 * i.e., we subtract "\sum_i {a_i} y_i" and add 1 d.
842 * The coefficients of the non-parameters in the tableau have been
843 * verified to be integral. We can therefore simply replace coefficient b
844 * by floor(b). For the coefficients of the parameters we have
845 * floor(a_i) = a_i - {a_i}, while for the other coefficients, we have
848 static struct isl_tab
*set_row_cst_to_div(struct isl_tab
*tab
, int row
, int div
)
850 isl_seq_fdiv_q(tab
->mat
->row
[row
] + 1, tab
->mat
->row
[row
] + 1,
851 tab
->mat
->row
[row
][0], 1 + tab
->M
+ tab
->n_col
);
853 isl_int_set_si(tab
->mat
->row
[row
][0], 1);
855 if (tab
->var
[tab
->n_var
- tab
->n_div
+ div
].is_row
) {
856 int drow
= tab
->var
[tab
->n_var
- tab
->n_div
+ div
].index
;
858 isl_assert(tab
->mat
->ctx
,
859 isl_int_is_one(tab
->mat
->row
[drow
][0]), goto error
);
860 isl_seq_combine(tab
->mat
->row
[row
] + 1,
861 tab
->mat
->ctx
->one
, tab
->mat
->row
[row
] + 1,
862 tab
->mat
->ctx
->one
, tab
->mat
->row
[drow
] + 1,
863 1 + tab
->M
+ tab
->n_col
);
865 int dcol
= tab
->var
[tab
->n_var
- tab
->n_div
+ div
].index
;
867 isl_int_set_si(tab
->mat
->row
[row
][2 + tab
->M
+ dcol
], 1);
876 /* Check if the (parametric) constant of the given row is obviously
877 * negative, meaning that we don't need to consult the context tableau.
878 * If there is a big parameter and its coefficient is non-zero,
879 * then this coefficient determines the outcome.
880 * Otherwise, we check whether the constant is negative and
881 * all non-zero coefficients of parameters are negative and
882 * belong to non-negative parameters.
884 static int is_obviously_neg(struct isl_tab
*tab
, int row
)
888 unsigned off
= 2 + tab
->M
;
891 if (isl_int_is_pos(tab
->mat
->row
[row
][2]))
893 if (isl_int_is_neg(tab
->mat
->row
[row
][2]))
897 if (isl_int_is_nonneg(tab
->mat
->row
[row
][1]))
899 for (i
= 0; i
< tab
->n_param
; ++i
) {
900 /* Eliminated parameter */
901 if (tab
->var
[i
].is_row
)
903 col
= tab
->var
[i
].index
;
904 if (isl_int_is_zero(tab
->mat
->row
[row
][off
+ col
]))
906 if (!tab
->var
[i
].is_nonneg
)
908 if (isl_int_is_pos(tab
->mat
->row
[row
][off
+ col
]))
911 for (i
= 0; i
< tab
->n_div
; ++i
) {
912 if (tab
->var
[tab
->n_var
- tab
->n_div
+ i
].is_row
)
914 col
= tab
->var
[tab
->n_var
- tab
->n_div
+ i
].index
;
915 if (isl_int_is_zero(tab
->mat
->row
[row
][off
+ col
]))
917 if (!tab
->var
[tab
->n_var
- tab
->n_div
+ i
].is_nonneg
)
919 if (isl_int_is_pos(tab
->mat
->row
[row
][off
+ col
]))
925 /* Check if the (parametric) constant of the given row is obviously
926 * non-negative, meaning that we don't need to consult the context tableau.
927 * If there is a big parameter and its coefficient is non-zero,
928 * then this coefficient determines the outcome.
929 * Otherwise, we check whether the constant is non-negative and
930 * all non-zero coefficients of parameters are positive and
931 * belong to non-negative parameters.
933 static int is_obviously_nonneg(struct isl_tab
*tab
, int row
)
937 unsigned off
= 2 + tab
->M
;
940 if (isl_int_is_pos(tab
->mat
->row
[row
][2]))
942 if (isl_int_is_neg(tab
->mat
->row
[row
][2]))
946 if (isl_int_is_neg(tab
->mat
->row
[row
][1]))
948 for (i
= 0; i
< tab
->n_param
; ++i
) {
949 /* Eliminated parameter */
950 if (tab
->var
[i
].is_row
)
952 col
= tab
->var
[i
].index
;
953 if (isl_int_is_zero(tab
->mat
->row
[row
][off
+ col
]))
955 if (!tab
->var
[i
].is_nonneg
)
957 if (isl_int_is_neg(tab
->mat
->row
[row
][off
+ col
]))
960 for (i
= 0; i
< tab
->n_div
; ++i
) {
961 if (tab
->var
[tab
->n_var
- tab
->n_div
+ i
].is_row
)
963 col
= tab
->var
[tab
->n_var
- tab
->n_div
+ i
].index
;
964 if (isl_int_is_zero(tab
->mat
->row
[row
][off
+ col
]))
966 if (!tab
->var
[tab
->n_var
- tab
->n_div
+ i
].is_nonneg
)
968 if (isl_int_is_neg(tab
->mat
->row
[row
][off
+ col
]))
974 /* Given a row r and two columns, return the column that would
975 * lead to the lexicographically smallest increment in the sample
976 * solution when leaving the basis in favor of the row.
977 * Pivoting with column c will increment the sample value by a non-negative
978 * constant times a_{V,c}/a_{r,c}, with a_{V,c} the elements of column c
979 * corresponding to the non-parametric variables.
980 * If variable v appears in a column c_v, the a_{v,c} = 1 iff c = c_v,
981 * with all other entries in this virtual row equal to zero.
982 * If variable v appears in a row, then a_{v,c} is the element in column c
985 * Let v be the first variable with a_{v,c1}/a_{r,c1} != a_{v,c2}/a_{r,c2}.
986 * Then if a_{v,c1}/a_{r,c1} < a_{v,c2}/a_{r,c2}, i.e.,
987 * a_{v,c2} a_{r,c1} - a_{v,c1} a_{r,c2} > 0, c1 results in the minimal
988 * increment. Otherwise, it's c2.
990 static int lexmin_col_pair(struct isl_tab
*tab
,
991 int row
, int col1
, int col2
, isl_int tmp
)
996 tr
= tab
->mat
->row
[row
] + 2 + tab
->M
;
998 for (i
= tab
->n_param
; i
< tab
->n_var
- tab
->n_div
; ++i
) {
1002 if (!tab
->var
[i
].is_row
) {
1003 if (tab
->var
[i
].index
== col1
)
1005 if (tab
->var
[i
].index
== col2
)
1010 if (tab
->var
[i
].index
== row
)
1013 r
= tab
->mat
->row
[tab
->var
[i
].index
] + 2 + tab
->M
;
1014 s1
= isl_int_sgn(r
[col1
]);
1015 s2
= isl_int_sgn(r
[col2
]);
1016 if (s1
== 0 && s2
== 0)
1023 isl_int_mul(tmp
, r
[col2
], tr
[col1
]);
1024 isl_int_submul(tmp
, r
[col1
], tr
[col2
]);
1025 if (isl_int_is_pos(tmp
))
1027 if (isl_int_is_neg(tmp
))
1033 /* Given a row in the tableau, find and return the column that would
1034 * result in the lexicographically smallest, but positive, increment
1035 * in the sample point.
1036 * If there is no such column, then return tab->n_col.
1037 * If anything goes wrong, return -1.
1039 static int lexmin_pivot_col(struct isl_tab
*tab
, int row
)
1042 int col
= tab
->n_col
;
1046 tr
= tab
->mat
->row
[row
] + 2 + tab
->M
;
1050 for (j
= tab
->n_dead
; j
< tab
->n_col
; ++j
) {
1051 if (tab
->col_var
[j
] >= 0 &&
1052 (tab
->col_var
[j
] < tab
->n_param
||
1053 tab
->col_var
[j
] >= tab
->n_var
- tab
->n_div
))
1056 if (!isl_int_is_pos(tr
[j
]))
1059 if (col
== tab
->n_col
)
1062 col
= lexmin_col_pair(tab
, row
, col
, j
, tmp
);
1063 isl_assert(tab
->mat
->ctx
, col
>= 0, goto error
);
1073 /* Return the first known violated constraint, i.e., a non-negative
1074 * contraint that currently has an either obviously negative value
1075 * or a previously determined to be negative value.
1077 * If any constraint has a negative coefficient for the big parameter,
1078 * if any, then we return one of these first.
1080 static int first_neg(struct isl_tab
*tab
)
1085 for (row
= tab
->n_redundant
; row
< tab
->n_row
; ++row
) {
1086 if (!isl_tab_var_from_row(tab
, row
)->is_nonneg
)
1088 if (isl_int_is_neg(tab
->mat
->row
[row
][2]))
1091 for (row
= tab
->n_redundant
; row
< tab
->n_row
; ++row
) {
1092 if (!isl_tab_var_from_row(tab
, row
)->is_nonneg
)
1094 if (tab
->row_sign
) {
1095 if (tab
->row_sign
[row
] == 0 &&
1096 is_obviously_neg(tab
, row
))
1097 tab
->row_sign
[row
] = isl_tab_row_neg
;
1098 if (tab
->row_sign
[row
] != isl_tab_row_neg
)
1100 } else if (!is_obviously_neg(tab
, row
))
1107 /* Resolve all known or obviously violated constraints through pivoting.
1108 * In particular, as long as we can find any violated constraint, we
1109 * look for a pivoting column that would result in the lexicographicallly
1110 * smallest increment in the sample point. If there is no such column
1111 * then the tableau is infeasible.
1113 static struct isl_tab
*restore_lexmin(struct isl_tab
*tab
) WARN_UNUSED
;
1114 static struct isl_tab
*restore_lexmin(struct isl_tab
*tab
)
1122 while ((row
= first_neg(tab
)) != -1) {
1123 col
= lexmin_pivot_col(tab
, row
);
1124 if (col
>= tab
->n_col
) {
1125 if (isl_tab_mark_empty(tab
) < 0)
1131 if (isl_tab_pivot(tab
, row
, col
) < 0)
1140 /* Given a row that represents an equality, look for an appropriate
1142 * In particular, if there are any non-zero coefficients among
1143 * the non-parameter variables, then we take the last of these
1144 * variables. Eliminating this variable in terms of the other
1145 * variables and/or parameters does not influence the property
1146 * that all column in the initial tableau are lexicographically
1147 * positive. The row corresponding to the eliminated variable
1148 * will only have non-zero entries below the diagonal of the
1149 * initial tableau. That is, we transform
1155 * If there is no such non-parameter variable, then we are dealing with
1156 * pure parameter equality and we pick any parameter with coefficient 1 or -1
1157 * for elimination. This will ensure that the eliminated parameter
1158 * always has an integer value whenever all the other parameters are integral.
1159 * If there is no such parameter then we return -1.
1161 static int last_var_col_or_int_par_col(struct isl_tab
*tab
, int row
)
1163 unsigned off
= 2 + tab
->M
;
1166 for (i
= tab
->n_var
- tab
->n_div
- 1; i
>= 0 && i
>= tab
->n_param
; --i
) {
1168 if (tab
->var
[i
].is_row
)
1170 col
= tab
->var
[i
].index
;
1171 if (col
<= tab
->n_dead
)
1173 if (!isl_int_is_zero(tab
->mat
->row
[row
][off
+ col
]))
1176 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
1177 if (isl_int_is_one(tab
->mat
->row
[row
][off
+ i
]))
1179 if (isl_int_is_negone(tab
->mat
->row
[row
][off
+ i
]))
1185 /* Add an equality that is known to be valid to the tableau.
1186 * We first check if we can eliminate a variable or a parameter.
1187 * If not, we add the equality as two inequalities.
1188 * In this case, the equality was a pure parameter equality and there
1189 * is no need to resolve any constraint violations.
1191 static struct isl_tab
*add_lexmin_valid_eq(struct isl_tab
*tab
, isl_int
*eq
)
1198 r
= isl_tab_add_row(tab
, eq
);
1202 r
= tab
->con
[r
].index
;
1203 i
= last_var_col_or_int_par_col(tab
, r
);
1205 tab
->con
[r
].is_nonneg
= 1;
1206 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]) < 0)
1208 isl_seq_neg(eq
, eq
, 1 + tab
->n_var
);
1209 r
= isl_tab_add_row(tab
, eq
);
1212 tab
->con
[r
].is_nonneg
= 1;
1213 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]) < 0)
1216 if (isl_tab_pivot(tab
, r
, i
) < 0)
1218 if (isl_tab_kill_col(tab
, i
) < 0)
1222 tab
= restore_lexmin(tab
);
1231 /* Check if the given row is a pure constant.
1233 static int is_constant(struct isl_tab
*tab
, int row
)
1235 unsigned off
= 2 + tab
->M
;
1237 return isl_seq_first_non_zero(tab
->mat
->row
[row
] + off
+ tab
->n_dead
,
1238 tab
->n_col
- tab
->n_dead
) == -1;
1241 /* Add an equality that may or may not be valid to the tableau.
1242 * If the resulting row is a pure constant, then it must be zero.
1243 * Otherwise, the resulting tableau is empty.
1245 * If the row is not a pure constant, then we add two inequalities,
1246 * each time checking that they can be satisfied.
1247 * In the end we try to use one of the two constraints to eliminate
1250 static struct isl_tab
*add_lexmin_eq(struct isl_tab
*tab
, isl_int
*eq
) WARN_UNUSED
;
1251 static struct isl_tab
*add_lexmin_eq(struct isl_tab
*tab
, isl_int
*eq
)
1255 struct isl_tab_undo
*snap
;
1259 snap
= isl_tab_snap(tab
);
1260 r1
= isl_tab_add_row(tab
, eq
);
1263 tab
->con
[r1
].is_nonneg
= 1;
1264 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r1
]) < 0)
1267 row
= tab
->con
[r1
].index
;
1268 if (is_constant(tab
, row
)) {
1269 if (!isl_int_is_zero(tab
->mat
->row
[row
][1]) ||
1270 (tab
->M
&& !isl_int_is_zero(tab
->mat
->row
[row
][2]))) {
1271 if (isl_tab_mark_empty(tab
) < 0)
1275 if (isl_tab_rollback(tab
, snap
) < 0)
1280 tab
= restore_lexmin(tab
);
1281 if (!tab
|| tab
->empty
)
1284 isl_seq_neg(eq
, eq
, 1 + tab
->n_var
);
1286 r2
= isl_tab_add_row(tab
, eq
);
1289 tab
->con
[r2
].is_nonneg
= 1;
1290 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r2
]) < 0)
1293 tab
= restore_lexmin(tab
);
1294 if (!tab
|| tab
->empty
)
1297 if (!tab
->con
[r1
].is_row
) {
1298 if (isl_tab_kill_col(tab
, tab
->con
[r1
].index
) < 0)
1300 } else if (!tab
->con
[r2
].is_row
) {
1301 if (isl_tab_kill_col(tab
, tab
->con
[r2
].index
) < 0)
1303 } else if (isl_int_is_zero(tab
->mat
->row
[tab
->con
[r1
].index
][1])) {
1304 unsigned off
= 2 + tab
->M
;
1306 int row
= tab
->con
[r1
].index
;
1307 i
= isl_seq_first_non_zero(tab
->mat
->row
[row
]+off
+tab
->n_dead
,
1308 tab
->n_col
- tab
->n_dead
);
1310 if (isl_tab_pivot(tab
, row
, tab
->n_dead
+ i
) < 0)
1312 if (isl_tab_kill_col(tab
, tab
->n_dead
+ i
) < 0)
1318 tab
->bmap
= isl_basic_map_add_ineq(tab
->bmap
, eq
);
1319 if (isl_tab_push(tab
, isl_tab_undo_bmap_ineq
) < 0)
1321 isl_seq_neg(eq
, eq
, 1 + tab
->n_var
);
1322 tab
->bmap
= isl_basic_map_add_ineq(tab
->bmap
, eq
);
1323 isl_seq_neg(eq
, eq
, 1 + tab
->n_var
);
1324 if (isl_tab_push(tab
, isl_tab_undo_bmap_ineq
) < 0)
1336 /* Add an inequality to the tableau, resolving violations using
1339 static struct isl_tab
*add_lexmin_ineq(struct isl_tab
*tab
, isl_int
*ineq
)
1346 tab
->bmap
= isl_basic_map_add_ineq(tab
->bmap
, ineq
);
1347 if (isl_tab_push(tab
, isl_tab_undo_bmap_ineq
) < 0)
1352 r
= isl_tab_add_row(tab
, ineq
);
1355 tab
->con
[r
].is_nonneg
= 1;
1356 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]) < 0)
1358 if (isl_tab_row_is_redundant(tab
, tab
->con
[r
].index
)) {
1359 if (isl_tab_mark_redundant(tab
, tab
->con
[r
].index
) < 0)
1364 tab
= restore_lexmin(tab
);
1365 if (tab
&& !tab
->empty
&& tab
->con
[r
].is_row
&&
1366 isl_tab_row_is_redundant(tab
, tab
->con
[r
].index
))
1367 if (isl_tab_mark_redundant(tab
, tab
->con
[r
].index
) < 0)
1375 /* Check if the coefficients of the parameters are all integral.
1377 static int integer_parameter(struct isl_tab
*tab
, int row
)
1381 unsigned off
= 2 + tab
->M
;
1383 for (i
= 0; i
< tab
->n_param
; ++i
) {
1384 /* Eliminated parameter */
1385 if (tab
->var
[i
].is_row
)
1387 col
= tab
->var
[i
].index
;
1388 if (!isl_int_is_divisible_by(tab
->mat
->row
[row
][off
+ col
],
1389 tab
->mat
->row
[row
][0]))
1392 for (i
= 0; i
< tab
->n_div
; ++i
) {
1393 if (tab
->var
[tab
->n_var
- tab
->n_div
+ i
].is_row
)
1395 col
= tab
->var
[tab
->n_var
- tab
->n_div
+ i
].index
;
1396 if (!isl_int_is_divisible_by(tab
->mat
->row
[row
][off
+ col
],
1397 tab
->mat
->row
[row
][0]))
1403 /* Check if the coefficients of the non-parameter variables are all integral.
1405 static int integer_variable(struct isl_tab
*tab
, int row
)
1408 unsigned off
= 2 + tab
->M
;
1410 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
1411 if (tab
->col_var
[i
] >= 0 &&
1412 (tab
->col_var
[i
] < tab
->n_param
||
1413 tab
->col_var
[i
] >= tab
->n_var
- tab
->n_div
))
1415 if (!isl_int_is_divisible_by(tab
->mat
->row
[row
][off
+ i
],
1416 tab
->mat
->row
[row
][0]))
1422 /* Check if the constant term is integral.
1424 static int integer_constant(struct isl_tab
*tab
, int row
)
1426 return isl_int_is_divisible_by(tab
->mat
->row
[row
][1],
1427 tab
->mat
->row
[row
][0]);
1430 #define I_CST 1 << 0
1431 #define I_PAR 1 << 1
1432 #define I_VAR 1 << 2
1434 /* Check for next (non-parameter) variable after "var" (first if var == -1)
1435 * that is non-integer and therefore requires a cut and return
1436 * the index of the variable.
1437 * For parametric tableaus, there are three parts in a row,
1438 * the constant, the coefficients of the parameters and the rest.
1439 * For each part, we check whether the coefficients in that part
1440 * are all integral and if so, set the corresponding flag in *f.
1441 * If the constant and the parameter part are integral, then the
1442 * current sample value is integral and no cut is required
1443 * (irrespective of whether the variable part is integral).
1445 static int next_non_integer_var(struct isl_tab
*tab
, int var
, int *f
)
1447 var
= var
< 0 ? tab
->n_param
: var
+ 1;
1449 for (; var
< tab
->n_var
- tab
->n_div
; ++var
) {
1452 if (!tab
->var
[var
].is_row
)
1454 row
= tab
->var
[var
].index
;
1455 if (integer_constant(tab
, row
))
1456 ISL_FL_SET(flags
, I_CST
);
1457 if (integer_parameter(tab
, row
))
1458 ISL_FL_SET(flags
, I_PAR
);
1459 if (ISL_FL_ISSET(flags
, I_CST
) && ISL_FL_ISSET(flags
, I_PAR
))
1461 if (integer_variable(tab
, row
))
1462 ISL_FL_SET(flags
, I_VAR
);
1469 /* Check for first (non-parameter) variable that is non-integer and
1470 * therefore requires a cut and return the corresponding row.
1471 * For parametric tableaus, there are three parts in a row,
1472 * the constant, the coefficients of the parameters and the rest.
1473 * For each part, we check whether the coefficients in that part
1474 * are all integral and if so, set the corresponding flag in *f.
1475 * If the constant and the parameter part are integral, then the
1476 * current sample value is integral and no cut is required
1477 * (irrespective of whether the variable part is integral).
1479 static int first_non_integer_row(struct isl_tab
*tab
, int *f
)
1481 int var
= next_non_integer_var(tab
, -1, f
);
1483 return var
< 0 ? -1 : tab
->var
[var
].index
;
1486 /* Add a (non-parametric) cut to cut away the non-integral sample
1487 * value of the given row.
1489 * If the row is given by
1491 * m r = f + \sum_i a_i y_i
1495 * c = - {-f/m} + \sum_i {a_i/m} y_i >= 0
1497 * The big parameter, if any, is ignored, since it is assumed to be big
1498 * enough to be divisible by any integer.
1499 * If the tableau is actually a parametric tableau, then this function
1500 * is only called when all coefficients of the parameters are integral.
1501 * The cut therefore has zero coefficients for the parameters.
1503 * The current value is known to be negative, so row_sign, if it
1504 * exists, is set accordingly.
1506 * Return the row of the cut or -1.
1508 static int add_cut(struct isl_tab
*tab
, int row
)
1513 unsigned off
= 2 + tab
->M
;
1515 if (isl_tab_extend_cons(tab
, 1) < 0)
1517 r
= isl_tab_allocate_con(tab
);
1521 r_row
= tab
->mat
->row
[tab
->con
[r
].index
];
1522 isl_int_set(r_row
[0], tab
->mat
->row
[row
][0]);
1523 isl_int_neg(r_row
[1], tab
->mat
->row
[row
][1]);
1524 isl_int_fdiv_r(r_row
[1], r_row
[1], tab
->mat
->row
[row
][0]);
1525 isl_int_neg(r_row
[1], r_row
[1]);
1527 isl_int_set_si(r_row
[2], 0);
1528 for (i
= 0; i
< tab
->n_col
; ++i
)
1529 isl_int_fdiv_r(r_row
[off
+ i
],
1530 tab
->mat
->row
[row
][off
+ i
], tab
->mat
->row
[row
][0]);
1532 tab
->con
[r
].is_nonneg
= 1;
1533 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]) < 0)
1536 tab
->row_sign
[tab
->con
[r
].index
] = isl_tab_row_neg
;
1538 return tab
->con
[r
].index
;
1541 /* Given a non-parametric tableau, add cuts until an integer
1542 * sample point is obtained or until the tableau is determined
1543 * to be integer infeasible.
1544 * As long as there is any non-integer value in the sample point,
1545 * we add appropriate cuts, if possible, for each of these
1546 * non-integer values and then resolve the violated
1547 * cut constraints using restore_lexmin.
1548 * If one of the corresponding rows is equal to an integral
1549 * combination of variables/constraints plus a non-integral constant,
1550 * then there is no way to obtain an integer point and we return
1551 * a tableau that is marked empty.
1553 static struct isl_tab
*cut_to_integer_lexmin(struct isl_tab
*tab
)
1564 while ((var
= next_non_integer_var(tab
, -1, &flags
)) != -1) {
1566 if (ISL_FL_ISSET(flags
, I_VAR
)) {
1567 if (isl_tab_mark_empty(tab
) < 0)
1571 row
= tab
->var
[var
].index
;
1572 row
= add_cut(tab
, row
);
1575 } while ((var
= next_non_integer_var(tab
, var
, &flags
)) != -1);
1576 tab
= restore_lexmin(tab
);
1577 if (!tab
|| tab
->empty
)
1586 /* Check whether all the currently active samples also satisfy the inequality
1587 * "ineq" (treated as an equality if eq is set).
1588 * Remove those samples that do not.
1590 static struct isl_tab
*check_samples(struct isl_tab
*tab
, isl_int
*ineq
, int eq
)
1598 isl_assert(tab
->mat
->ctx
, tab
->bmap
, goto error
);
1599 isl_assert(tab
->mat
->ctx
, tab
->samples
, goto error
);
1600 isl_assert(tab
->mat
->ctx
, tab
->samples
->n_col
== 1 + tab
->n_var
, goto error
);
1603 for (i
= tab
->n_outside
; i
< tab
->n_sample
; ++i
) {
1605 isl_seq_inner_product(ineq
, tab
->samples
->row
[i
],
1606 1 + tab
->n_var
, &v
);
1607 sgn
= isl_int_sgn(v
);
1608 if (eq
? (sgn
== 0) : (sgn
>= 0))
1610 tab
= isl_tab_drop_sample(tab
, i
);
1622 /* Check whether the sample value of the tableau is finite,
1623 * i.e., either the tableau does not use a big parameter, or
1624 * all values of the variables are equal to the big parameter plus
1625 * some constant. This constant is the actual sample value.
1627 static int sample_is_finite(struct isl_tab
*tab
)
1634 for (i
= 0; i
< tab
->n_var
; ++i
) {
1636 if (!tab
->var
[i
].is_row
)
1638 row
= tab
->var
[i
].index
;
1639 if (isl_int_ne(tab
->mat
->row
[row
][0], tab
->mat
->row
[row
][2]))
1645 /* Check if the context tableau of sol has any integer points.
1646 * Leave tab in empty state if no integer point can be found.
1647 * If an integer point can be found and if moreover it is finite,
1648 * then it is added to the list of sample values.
1650 * This function is only called when none of the currently active sample
1651 * values satisfies the most recently added constraint.
1653 static struct isl_tab
*check_integer_feasible(struct isl_tab
*tab
)
1655 struct isl_tab_undo
*snap
;
1661 snap
= isl_tab_snap(tab
);
1662 if (isl_tab_push_basis(tab
) < 0)
1665 tab
= cut_to_integer_lexmin(tab
);
1669 if (!tab
->empty
&& sample_is_finite(tab
)) {
1670 struct isl_vec
*sample
;
1672 sample
= isl_tab_get_sample_value(tab
);
1674 tab
= isl_tab_add_sample(tab
, sample
);
1677 if (!tab
->empty
&& isl_tab_rollback(tab
, snap
) < 0)
1686 /* Check if any of the currently active sample values satisfies
1687 * the inequality "ineq" (an equality if eq is set).
1689 static int tab_has_valid_sample(struct isl_tab
*tab
, isl_int
*ineq
, int eq
)
1697 isl_assert(tab
->mat
->ctx
, tab
->bmap
, return -1);
1698 isl_assert(tab
->mat
->ctx
, tab
->samples
, return -1);
1699 isl_assert(tab
->mat
->ctx
, tab
->samples
->n_col
== 1 + tab
->n_var
, return -1);
1702 for (i
= tab
->n_outside
; i
< tab
->n_sample
; ++i
) {
1704 isl_seq_inner_product(ineq
, tab
->samples
->row
[i
],
1705 1 + tab
->n_var
, &v
);
1706 sgn
= isl_int_sgn(v
);
1707 if (eq
? (sgn
== 0) : (sgn
>= 0))
1712 return i
< tab
->n_sample
;
1715 /* For a div d = floor(f/m), add the constraints
1718 * -(f-(m-1)) + m d >= 0
1720 * Note that the second constraint is the negation of
1724 static void add_div_constraints(struct isl_context
*context
, unsigned div
)
1728 struct isl_vec
*ineq
;
1729 struct isl_basic_set
*bset
;
1731 bset
= context
->op
->peek_basic_set(context
);
1735 total
= isl_basic_set_total_dim(bset
);
1736 div_pos
= 1 + total
- bset
->n_div
+ div
;
1738 ineq
= ineq_for_div(bset
, div
);
1742 context
->op
->add_ineq(context
, ineq
->el
, 0, 0);
1744 isl_seq_neg(ineq
->el
, bset
->div
[div
] + 1, 1 + total
);
1745 isl_int_set(ineq
->el
[div_pos
], bset
->div
[div
][0]);
1746 isl_int_add(ineq
->el
[0], ineq
->el
[0], ineq
->el
[div_pos
]);
1747 isl_int_sub_ui(ineq
->el
[0], ineq
->el
[0], 1);
1749 context
->op
->add_ineq(context
, ineq
->el
, 0, 0);
1755 context
->op
->invalidate(context
);
1758 /* Add a div specifed by "div" to the tableau "tab" and return
1759 * the index of the new div. *nonneg is set to 1 if the div
1760 * is obviously non-negative.
1762 static int context_tab_add_div(struct isl_tab
*tab
, struct isl_vec
*div
,
1768 struct isl_mat
*samples
;
1770 for (i
= 0; i
< tab
->n_var
; ++i
) {
1771 if (isl_int_is_zero(div
->el
[2 + i
]))
1773 if (!tab
->var
[i
].is_nonneg
)
1776 *nonneg
= i
== tab
->n_var
;
1778 if (isl_tab_extend_cons(tab
, 3) < 0)
1780 if (isl_tab_extend_vars(tab
, 1) < 0)
1782 r
= isl_tab_allocate_var(tab
);
1786 tab
->var
[r
].is_nonneg
= 1;
1787 tab
->var
[r
].frozen
= 1;
1789 samples
= isl_mat_extend(tab
->samples
,
1790 tab
->n_sample
, 1 + tab
->n_var
);
1791 tab
->samples
= samples
;
1794 for (i
= tab
->n_outside
; i
< samples
->n_row
; ++i
) {
1795 isl_seq_inner_product(div
->el
+ 1, samples
->row
[i
],
1796 div
->size
- 1, &samples
->row
[i
][samples
->n_col
- 1]);
1797 isl_int_fdiv_q(samples
->row
[i
][samples
->n_col
- 1],
1798 samples
->row
[i
][samples
->n_col
- 1], div
->el
[0]);
1801 tab
->bmap
= isl_basic_map_extend_dim(tab
->bmap
,
1802 isl_basic_map_get_dim(tab
->bmap
), 1, 0, 2);
1803 k
= isl_basic_map_alloc_div(tab
->bmap
);
1806 isl_seq_cpy(tab
->bmap
->div
[k
], div
->el
, div
->size
);
1807 if (isl_tab_push(tab
, isl_tab_undo_bmap_div
) < 0)
1813 /* Add a div specified by "div" to both the main tableau and
1814 * the context tableau. In case of the main tableau, we only
1815 * need to add an extra div. In the context tableau, we also
1816 * need to express the meaning of the div.
1817 * Return the index of the div or -1 if anything went wrong.
1819 static int add_div(struct isl_tab
*tab
, struct isl_context
*context
,
1820 struct isl_vec
*div
)
1826 k
= context
->op
->add_div(context
, div
, &nonneg
);
1830 add_div_constraints(context
, k
);
1831 if (!context
->op
->is_ok(context
))
1834 if (isl_tab_extend_vars(tab
, 1) < 0)
1836 r
= isl_tab_allocate_var(tab
);
1840 tab
->var
[r
].is_nonneg
= 1;
1841 tab
->var
[r
].frozen
= 1;
1844 return tab
->n_div
- 1;
1846 context
->op
->invalidate(context
);
1850 static int find_div(struct isl_tab
*tab
, isl_int
*div
, isl_int denom
)
1853 unsigned total
= isl_basic_map_total_dim(tab
->bmap
);
1855 for (i
= 0; i
< tab
->bmap
->n_div
; ++i
) {
1856 if (isl_int_ne(tab
->bmap
->div
[i
][0], denom
))
1858 if (!isl_seq_eq(tab
->bmap
->div
[i
] + 1, div
, total
))
1865 /* Return the index of a div that corresponds to "div".
1866 * We first check if we already have such a div and if not, we create one.
1868 static int get_div(struct isl_tab
*tab
, struct isl_context
*context
,
1869 struct isl_vec
*div
)
1872 struct isl_tab
*context_tab
= context
->op
->peek_tab(context
);
1877 d
= find_div(context_tab
, div
->el
+ 1, div
->el
[0]);
1881 return add_div(tab
, context
, div
);
1884 /* Add a parametric cut to cut away the non-integral sample value
1886 * Let a_i be the coefficients of the constant term and the parameters
1887 * and let b_i be the coefficients of the variables or constraints
1888 * in basis of the tableau.
1889 * Let q be the div q = floor(\sum_i {-a_i} y_i).
1891 * The cut is expressed as
1893 * c = \sum_i -{-a_i} y_i + \sum_i {b_i} x_i + q >= 0
1895 * If q did not already exist in the context tableau, then it is added first.
1896 * If q is in a column of the main tableau then the "+ q" can be accomplished
1897 * by setting the corresponding entry to the denominator of the constraint.
1898 * If q happens to be in a row of the main tableau, then the corresponding
1899 * row needs to be added instead (taking care of the denominators).
1900 * Note that this is very unlikely, but perhaps not entirely impossible.
1902 * The current value of the cut is known to be negative (or at least
1903 * non-positive), so row_sign is set accordingly.
1905 * Return the row of the cut or -1.
1907 static int add_parametric_cut(struct isl_tab
*tab
, int row
,
1908 struct isl_context
*context
)
1910 struct isl_vec
*div
;
1917 unsigned off
= 2 + tab
->M
;
1922 div
= get_row_parameter_div(tab
, row
);
1927 d
= context
->op
->get_div(context
, tab
, div
);
1931 if (isl_tab_extend_cons(tab
, 1) < 0)
1933 r
= isl_tab_allocate_con(tab
);
1937 r_row
= tab
->mat
->row
[tab
->con
[r
].index
];
1938 isl_int_set(r_row
[0], tab
->mat
->row
[row
][0]);
1939 isl_int_neg(r_row
[1], tab
->mat
->row
[row
][1]);
1940 isl_int_fdiv_r(r_row
[1], r_row
[1], tab
->mat
->row
[row
][0]);
1941 isl_int_neg(r_row
[1], r_row
[1]);
1943 isl_int_set_si(r_row
[2], 0);
1944 for (i
= 0; i
< tab
->n_param
; ++i
) {
1945 if (tab
->var
[i
].is_row
)
1947 col
= tab
->var
[i
].index
;
1948 isl_int_neg(r_row
[off
+ col
], tab
->mat
->row
[row
][off
+ col
]);
1949 isl_int_fdiv_r(r_row
[off
+ col
], r_row
[off
+ col
],
1950 tab
->mat
->row
[row
][0]);
1951 isl_int_neg(r_row
[off
+ col
], r_row
[off
+ col
]);
1953 for (i
= 0; i
< tab
->n_div
; ++i
) {
1954 if (tab
->var
[tab
->n_var
- tab
->n_div
+ i
].is_row
)
1956 col
= tab
->var
[tab
->n_var
- tab
->n_div
+ i
].index
;
1957 isl_int_neg(r_row
[off
+ col
], tab
->mat
->row
[row
][off
+ col
]);
1958 isl_int_fdiv_r(r_row
[off
+ col
], r_row
[off
+ col
],
1959 tab
->mat
->row
[row
][0]);
1960 isl_int_neg(r_row
[off
+ col
], r_row
[off
+ col
]);
1962 for (i
= 0; i
< tab
->n_col
; ++i
) {
1963 if (tab
->col_var
[i
] >= 0 &&
1964 (tab
->col_var
[i
] < tab
->n_param
||
1965 tab
->col_var
[i
] >= tab
->n_var
- tab
->n_div
))
1967 isl_int_fdiv_r(r_row
[off
+ i
],
1968 tab
->mat
->row
[row
][off
+ i
], tab
->mat
->row
[row
][0]);
1970 if (tab
->var
[tab
->n_var
- tab
->n_div
+ d
].is_row
) {
1972 int d_row
= tab
->var
[tab
->n_var
- tab
->n_div
+ d
].index
;
1974 isl_int_gcd(gcd
, tab
->mat
->row
[d_row
][0], r_row
[0]);
1975 isl_int_divexact(r_row
[0], r_row
[0], gcd
);
1976 isl_int_divexact(gcd
, tab
->mat
->row
[d_row
][0], gcd
);
1977 isl_seq_combine(r_row
+ 1, gcd
, r_row
+ 1,
1978 r_row
[0], tab
->mat
->row
[d_row
] + 1,
1979 off
- 1 + tab
->n_col
);
1980 isl_int_mul(r_row
[0], r_row
[0], tab
->mat
->row
[d_row
][0]);
1983 col
= tab
->var
[tab
->n_var
- tab
->n_div
+ d
].index
;
1984 isl_int_set(r_row
[off
+ col
], tab
->mat
->row
[row
][0]);
1987 tab
->con
[r
].is_nonneg
= 1;
1988 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]) < 0)
1991 tab
->row_sign
[tab
->con
[r
].index
] = isl_tab_row_neg
;
1995 row
= tab
->con
[r
].index
;
1997 if (d
>= n
&& context
->op
->detect_equalities(context
, tab
) < 0)
2003 /* Construct a tableau for bmap that can be used for computing
2004 * the lexicographic minimum (or maximum) of bmap.
2005 * If not NULL, then dom is the domain where the minimum
2006 * should be computed. In this case, we set up a parametric
2007 * tableau with row signs (initialized to "unknown").
2008 * If M is set, then the tableau will use a big parameter.
2009 * If max is set, then a maximum should be computed instead of a minimum.
2010 * This means that for each variable x, the tableau will contain the variable
2011 * x' = M - x, rather than x' = M + x. This in turn means that the coefficient
2012 * of the variables in all constraints are negated prior to adding them
2015 static struct isl_tab
*tab_for_lexmin(struct isl_basic_map
*bmap
,
2016 struct isl_basic_set
*dom
, unsigned M
, int max
)
2019 struct isl_tab
*tab
;
2021 tab
= isl_tab_alloc(bmap
->ctx
, 2 * bmap
->n_eq
+ bmap
->n_ineq
+ 1,
2022 isl_basic_map_total_dim(bmap
), M
);
2026 tab
->rational
= ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
);
2028 tab
->n_param
= isl_basic_set_total_dim(dom
) - dom
->n_div
;
2029 tab
->n_div
= dom
->n_div
;
2030 tab
->row_sign
= isl_calloc_array(bmap
->ctx
,
2031 enum isl_tab_row_sign
, tab
->mat
->n_row
);
2035 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
)) {
2036 if (isl_tab_mark_empty(tab
) < 0)
2041 for (i
= tab
->n_param
; i
< tab
->n_var
- tab
->n_div
; ++i
) {
2042 tab
->var
[i
].is_nonneg
= 1;
2043 tab
->var
[i
].frozen
= 1;
2045 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
2047 isl_seq_neg(bmap
->eq
[i
] + 1 + tab
->n_param
,
2048 bmap
->eq
[i
] + 1 + tab
->n_param
,
2049 tab
->n_var
- tab
->n_param
- tab
->n_div
);
2050 tab
= add_lexmin_valid_eq(tab
, bmap
->eq
[i
]);
2052 isl_seq_neg(bmap
->eq
[i
] + 1 + tab
->n_param
,
2053 bmap
->eq
[i
] + 1 + tab
->n_param
,
2054 tab
->n_var
- tab
->n_param
- tab
->n_div
);
2055 if (!tab
|| tab
->empty
)
2058 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
2060 isl_seq_neg(bmap
->ineq
[i
] + 1 + tab
->n_param
,
2061 bmap
->ineq
[i
] + 1 + tab
->n_param
,
2062 tab
->n_var
- tab
->n_param
- tab
->n_div
);
2063 tab
= add_lexmin_ineq(tab
, bmap
->ineq
[i
]);
2065 isl_seq_neg(bmap
->ineq
[i
] + 1 + tab
->n_param
,
2066 bmap
->ineq
[i
] + 1 + tab
->n_param
,
2067 tab
->n_var
- tab
->n_param
- tab
->n_div
);
2068 if (!tab
|| tab
->empty
)
2077 /* Given a main tableau where more than one row requires a split,
2078 * determine and return the "best" row to split on.
2080 * Given two rows in the main tableau, if the inequality corresponding
2081 * to the first row is redundant with respect to that of the second row
2082 * in the current tableau, then it is better to split on the second row,
2083 * since in the positive part, both row will be positive.
2084 * (In the negative part a pivot will have to be performed and just about
2085 * anything can happen to the sign of the other row.)
2087 * As a simple heuristic, we therefore select the row that makes the most
2088 * of the other rows redundant.
2090 * Perhaps it would also be useful to look at the number of constraints
2091 * that conflict with any given constraint.
2093 static int best_split(struct isl_tab
*tab
, struct isl_tab
*context_tab
)
2095 struct isl_tab_undo
*snap
;
2101 if (isl_tab_extend_cons(context_tab
, 2) < 0)
2104 snap
= isl_tab_snap(context_tab
);
2106 for (split
= tab
->n_redundant
; split
< tab
->n_row
; ++split
) {
2107 struct isl_tab_undo
*snap2
;
2108 struct isl_vec
*ineq
= NULL
;
2112 if (!isl_tab_var_from_row(tab
, split
)->is_nonneg
)
2114 if (tab
->row_sign
[split
] != isl_tab_row_any
)
2117 ineq
= get_row_parameter_ineq(tab
, split
);
2120 ok
= isl_tab_add_ineq(context_tab
, ineq
->el
) >= 0;
2125 snap2
= isl_tab_snap(context_tab
);
2127 for (row
= tab
->n_redundant
; row
< tab
->n_row
; ++row
) {
2128 struct isl_tab_var
*var
;
2132 if (!isl_tab_var_from_row(tab
, row
)->is_nonneg
)
2134 if (tab
->row_sign
[row
] != isl_tab_row_any
)
2137 ineq
= get_row_parameter_ineq(tab
, row
);
2140 ok
= isl_tab_add_ineq(context_tab
, ineq
->el
) >= 0;
2144 var
= &context_tab
->con
[context_tab
->n_con
- 1];
2145 if (!context_tab
->empty
&&
2146 !isl_tab_min_at_most_neg_one(context_tab
, var
))
2148 if (isl_tab_rollback(context_tab
, snap2
) < 0)
2151 if (best
== -1 || r
> best_r
) {
2155 if (isl_tab_rollback(context_tab
, snap
) < 0)
2162 static struct isl_basic_set
*context_lex_peek_basic_set(
2163 struct isl_context
*context
)
2165 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2168 return isl_tab_peek_bset(clex
->tab
);
2171 static struct isl_tab
*context_lex_peek_tab(struct isl_context
*context
)
2173 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2177 static void context_lex_extend(struct isl_context
*context
, int n
)
2179 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2182 if (isl_tab_extend_cons(clex
->tab
, n
) >= 0)
2184 isl_tab_free(clex
->tab
);
2188 static void context_lex_add_eq(struct isl_context
*context
, isl_int
*eq
,
2189 int check
, int update
)
2191 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2192 if (isl_tab_extend_cons(clex
->tab
, 2) < 0)
2194 clex
->tab
= add_lexmin_eq(clex
->tab
, eq
);
2196 int v
= tab_has_valid_sample(clex
->tab
, eq
, 1);
2200 clex
->tab
= check_integer_feasible(clex
->tab
);
2203 clex
->tab
= check_samples(clex
->tab
, eq
, 1);
2206 isl_tab_free(clex
->tab
);
2210 static void context_lex_add_ineq(struct isl_context
*context
, isl_int
*ineq
,
2211 int check
, int update
)
2213 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2214 if (isl_tab_extend_cons(clex
->tab
, 1) < 0)
2216 clex
->tab
= add_lexmin_ineq(clex
->tab
, ineq
);
2218 int v
= tab_has_valid_sample(clex
->tab
, ineq
, 0);
2222 clex
->tab
= check_integer_feasible(clex
->tab
);
2225 clex
->tab
= check_samples(clex
->tab
, ineq
, 0);
2228 isl_tab_free(clex
->tab
);
2232 /* Check which signs can be obtained by "ineq" on all the currently
2233 * active sample values. See row_sign for more information.
2235 static enum isl_tab_row_sign
tab_ineq_sign(struct isl_tab
*tab
, isl_int
*ineq
,
2241 int res
= isl_tab_row_unknown
;
2243 isl_assert(tab
->mat
->ctx
, tab
->samples
, return 0);
2244 isl_assert(tab
->mat
->ctx
, tab
->samples
->n_col
== 1 + tab
->n_var
, return 0);
2247 for (i
= tab
->n_outside
; i
< tab
->n_sample
; ++i
) {
2248 isl_seq_inner_product(tab
->samples
->row
[i
], ineq
,
2249 1 + tab
->n_var
, &tmp
);
2250 sgn
= isl_int_sgn(tmp
);
2251 if (sgn
> 0 || (sgn
== 0 && strict
)) {
2252 if (res
== isl_tab_row_unknown
)
2253 res
= isl_tab_row_pos
;
2254 if (res
== isl_tab_row_neg
)
2255 res
= isl_tab_row_any
;
2258 if (res
== isl_tab_row_unknown
)
2259 res
= isl_tab_row_neg
;
2260 if (res
== isl_tab_row_pos
)
2261 res
= isl_tab_row_any
;
2263 if (res
== isl_tab_row_any
)
2271 static enum isl_tab_row_sign
context_lex_ineq_sign(struct isl_context
*context
,
2272 isl_int
*ineq
, int strict
)
2274 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2275 return tab_ineq_sign(clex
->tab
, ineq
, strict
);
2278 /* Check whether "ineq" can be added to the tableau without rendering
2281 static int context_lex_test_ineq(struct isl_context
*context
, isl_int
*ineq
)
2283 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2284 struct isl_tab_undo
*snap
;
2290 if (isl_tab_extend_cons(clex
->tab
, 1) < 0)
2293 snap
= isl_tab_snap(clex
->tab
);
2294 if (isl_tab_push_basis(clex
->tab
) < 0)
2296 clex
->tab
= add_lexmin_ineq(clex
->tab
, ineq
);
2297 clex
->tab
= check_integer_feasible(clex
->tab
);
2300 feasible
= !clex
->tab
->empty
;
2301 if (isl_tab_rollback(clex
->tab
, snap
) < 0)
2307 static int context_lex_get_div(struct isl_context
*context
, struct isl_tab
*tab
,
2308 struct isl_vec
*div
)
2310 return get_div(tab
, context
, div
);
2313 static int context_lex_add_div(struct isl_context
*context
, struct isl_vec
*div
,
2316 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2317 return context_tab_add_div(clex
->tab
, div
, nonneg
);
2320 static int context_lex_detect_equalities(struct isl_context
*context
,
2321 struct isl_tab
*tab
)
2326 static int context_lex_best_split(struct isl_context
*context
,
2327 struct isl_tab
*tab
)
2329 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2330 struct isl_tab_undo
*snap
;
2333 snap
= isl_tab_snap(clex
->tab
);
2334 if (isl_tab_push_basis(clex
->tab
) < 0)
2336 r
= best_split(tab
, clex
->tab
);
2338 if (isl_tab_rollback(clex
->tab
, snap
) < 0)
2344 static int context_lex_is_empty(struct isl_context
*context
)
2346 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2349 return clex
->tab
->empty
;
2352 static void *context_lex_save(struct isl_context
*context
)
2354 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2355 struct isl_tab_undo
*snap
;
2357 snap
= isl_tab_snap(clex
->tab
);
2358 if (isl_tab_push_basis(clex
->tab
) < 0)
2360 if (isl_tab_save_samples(clex
->tab
) < 0)
2366 static void context_lex_restore(struct isl_context
*context
, void *save
)
2368 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2369 if (isl_tab_rollback(clex
->tab
, (struct isl_tab_undo
*)save
) < 0) {
2370 isl_tab_free(clex
->tab
);
2375 static int context_lex_is_ok(struct isl_context
*context
)
2377 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2381 /* For each variable in the context tableau, check if the variable can
2382 * only attain non-negative values. If so, mark the parameter as non-negative
2383 * in the main tableau. This allows for a more direct identification of some
2384 * cases of violated constraints.
2386 static struct isl_tab
*tab_detect_nonnegative_parameters(struct isl_tab
*tab
,
2387 struct isl_tab
*context_tab
)
2390 struct isl_tab_undo
*snap
;
2391 struct isl_vec
*ineq
= NULL
;
2392 struct isl_tab_var
*var
;
2395 if (context_tab
->n_var
== 0)
2398 ineq
= isl_vec_alloc(tab
->mat
->ctx
, 1 + context_tab
->n_var
);
2402 if (isl_tab_extend_cons(context_tab
, 1) < 0)
2405 snap
= isl_tab_snap(context_tab
);
2408 isl_seq_clr(ineq
->el
, ineq
->size
);
2409 for (i
= 0; i
< context_tab
->n_var
; ++i
) {
2410 isl_int_set_si(ineq
->el
[1 + i
], 1);
2411 if (isl_tab_add_ineq(context_tab
, ineq
->el
) < 0)
2413 var
= &context_tab
->con
[context_tab
->n_con
- 1];
2414 if (!context_tab
->empty
&&
2415 !isl_tab_min_at_most_neg_one(context_tab
, var
)) {
2417 if (i
>= tab
->n_param
)
2418 j
= i
- tab
->n_param
+ tab
->n_var
- tab
->n_div
;
2419 tab
->var
[j
].is_nonneg
= 1;
2422 isl_int_set_si(ineq
->el
[1 + i
], 0);
2423 if (isl_tab_rollback(context_tab
, snap
) < 0)
2427 if (context_tab
->M
&& n
== context_tab
->n_var
) {
2428 context_tab
->mat
= isl_mat_drop_cols(context_tab
->mat
, 2, 1);
2440 static struct isl_tab
*context_lex_detect_nonnegative_parameters(
2441 struct isl_context
*context
, struct isl_tab
*tab
)
2443 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2444 struct isl_tab_undo
*snap
;
2446 snap
= isl_tab_snap(clex
->tab
);
2447 if (isl_tab_push_basis(clex
->tab
) < 0)
2450 tab
= tab_detect_nonnegative_parameters(tab
, clex
->tab
);
2452 if (isl_tab_rollback(clex
->tab
, snap
) < 0)
2461 static void context_lex_invalidate(struct isl_context
*context
)
2463 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2464 isl_tab_free(clex
->tab
);
2468 static void context_lex_free(struct isl_context
*context
)
2470 struct isl_context_lex
*clex
= (struct isl_context_lex
*)context
;
2471 isl_tab_free(clex
->tab
);
2475 struct isl_context_op isl_context_lex_op
= {
2476 context_lex_detect_nonnegative_parameters
,
2477 context_lex_peek_basic_set
,
2478 context_lex_peek_tab
,
2480 context_lex_add_ineq
,
2481 context_lex_ineq_sign
,
2482 context_lex_test_ineq
,
2483 context_lex_get_div
,
2484 context_lex_add_div
,
2485 context_lex_detect_equalities
,
2486 context_lex_best_split
,
2487 context_lex_is_empty
,
2490 context_lex_restore
,
2491 context_lex_invalidate
,
2495 static struct isl_tab
*context_tab_for_lexmin(struct isl_basic_set
*bset
)
2497 struct isl_tab
*tab
;
2499 bset
= isl_basic_set_cow(bset
);
2502 tab
= tab_for_lexmin((struct isl_basic_map
*)bset
, NULL
, 1, 0);
2505 if (isl_tab_track_bset(tab
, bset
) < 0)
2507 tab
= isl_tab_init_samples(tab
);
2510 isl_basic_set_free(bset
);
2514 static struct isl_context
*isl_context_lex_alloc(struct isl_basic_set
*dom
)
2516 struct isl_context_lex
*clex
;
2521 clex
= isl_alloc_type(dom
->ctx
, struct isl_context_lex
);
2525 clex
->context
.op
= &isl_context_lex_op
;
2527 clex
->tab
= context_tab_for_lexmin(isl_basic_set_copy(dom
));
2528 clex
->tab
= restore_lexmin(clex
->tab
);
2529 clex
->tab
= check_integer_feasible(clex
->tab
);
2533 return &clex
->context
;
2535 clex
->context
.op
->free(&clex
->context
);
2539 struct isl_context_gbr
{
2540 struct isl_context context
;
2541 struct isl_tab
*tab
;
2542 struct isl_tab
*shifted
;
2543 struct isl_tab
*cone
;
2546 static struct isl_tab
*context_gbr_detect_nonnegative_parameters(
2547 struct isl_context
*context
, struct isl_tab
*tab
)
2549 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
2550 return tab_detect_nonnegative_parameters(tab
, cgbr
->tab
);
2553 static struct isl_basic_set
*context_gbr_peek_basic_set(
2554 struct isl_context
*context
)
2556 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
2559 return isl_tab_peek_bset(cgbr
->tab
);
2562 static struct isl_tab
*context_gbr_peek_tab(struct isl_context
*context
)
2564 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
2568 /* Initialize the "shifted" tableau of the context, which
2569 * contains the constraints of the original tableau shifted
2570 * by the sum of all negative coefficients. This ensures
2571 * that any rational point in the shifted tableau can
2572 * be rounded up to yield an integer point in the original tableau.
2574 static void gbr_init_shifted(struct isl_context_gbr
*cgbr
)
2577 struct isl_vec
*cst
;
2578 struct isl_basic_set
*bset
= isl_tab_peek_bset(cgbr
->tab
);
2579 unsigned dim
= isl_basic_set_total_dim(bset
);
2581 cst
= isl_vec_alloc(cgbr
->tab
->mat
->ctx
, bset
->n_ineq
);
2585 for (i
= 0; i
< bset
->n_ineq
; ++i
) {
2586 isl_int_set(cst
->el
[i
], bset
->ineq
[i
][0]);
2587 for (j
= 0; j
< dim
; ++j
) {
2588 if (!isl_int_is_neg(bset
->ineq
[i
][1 + j
]))
2590 isl_int_add(bset
->ineq
[i
][0], bset
->ineq
[i
][0],
2591 bset
->ineq
[i
][1 + j
]);
2595 cgbr
->shifted
= isl_tab_from_basic_set(bset
);
2597 for (i
= 0; i
< bset
->n_ineq
; ++i
)
2598 isl_int_set(bset
->ineq
[i
][0], cst
->el
[i
]);
2603 /* Check if the shifted tableau is non-empty, and if so
2604 * use the sample point to construct an integer point
2605 * of the context tableau.
2607 static struct isl_vec
*gbr_get_shifted_sample(struct isl_context_gbr
*cgbr
)
2609 struct isl_vec
*sample
;
2612 gbr_init_shifted(cgbr
);
2615 if (cgbr
->shifted
->empty
)
2616 return isl_vec_alloc(cgbr
->tab
->mat
->ctx
, 0);
2618 sample
= isl_tab_get_sample_value(cgbr
->shifted
);
2619 sample
= isl_vec_ceil(sample
);
2624 static struct isl_basic_set
*drop_constant_terms(struct isl_basic_set
*bset
)
2631 for (i
= 0; i
< bset
->n_eq
; ++i
)
2632 isl_int_set_si(bset
->eq
[i
][0], 0);
2634 for (i
= 0; i
< bset
->n_ineq
; ++i
)
2635 isl_int_set_si(bset
->ineq
[i
][0], 0);
2640 static int use_shifted(struct isl_context_gbr
*cgbr
)
2642 return cgbr
->tab
->bmap
->n_eq
== 0 && cgbr
->tab
->bmap
->n_div
== 0;
2645 static struct isl_vec
*gbr_get_sample(struct isl_context_gbr
*cgbr
)
2647 struct isl_basic_set
*bset
;
2648 struct isl_basic_set
*cone
;
2650 if (isl_tab_sample_is_integer(cgbr
->tab
))
2651 return isl_tab_get_sample_value(cgbr
->tab
);
2653 if (use_shifted(cgbr
)) {
2654 struct isl_vec
*sample
;
2656 sample
= gbr_get_shifted_sample(cgbr
);
2657 if (!sample
|| sample
->size
> 0)
2660 isl_vec_free(sample
);
2664 bset
= isl_tab_peek_bset(cgbr
->tab
);
2665 cgbr
->cone
= isl_tab_from_recession_cone(bset
);
2668 if (isl_tab_track_bset(cgbr
->cone
, isl_basic_set_dup(bset
)) < 0)
2671 cgbr
->cone
= isl_tab_detect_implicit_equalities(cgbr
->cone
);
2675 if (cgbr
->cone
->n_dead
== cgbr
->cone
->n_col
) {
2676 struct isl_vec
*sample
;
2677 struct isl_tab_undo
*snap
;
2679 if (cgbr
->tab
->basis
) {
2680 if (cgbr
->tab
->basis
->n_col
!= 1 + cgbr
->tab
->n_var
) {
2681 isl_mat_free(cgbr
->tab
->basis
);
2682 cgbr
->tab
->basis
= NULL
;
2684 cgbr
->tab
->n_zero
= 0;
2685 cgbr
->tab
->n_unbounded
= 0;
2689 snap
= isl_tab_snap(cgbr
->tab
);
2691 sample
= isl_tab_sample(cgbr
->tab
);
2693 if (isl_tab_rollback(cgbr
->tab
, snap
) < 0) {
2694 isl_vec_free(sample
);
2701 cone
= isl_basic_set_dup(isl_tab_peek_bset(cgbr
->cone
));
2702 cone
= drop_constant_terms(cone
);
2703 cone
= isl_basic_set_update_from_tab(cone
, cgbr
->cone
);
2704 cone
= isl_basic_set_underlying_set(cone
);
2705 cone
= isl_basic_set_gauss(cone
, NULL
);
2707 bset
= isl_basic_set_dup(isl_tab_peek_bset(cgbr
->tab
));
2708 bset
= isl_basic_set_update_from_tab(bset
, cgbr
->tab
);
2709 bset
= isl_basic_set_underlying_set(bset
);
2710 bset
= isl_basic_set_gauss(bset
, NULL
);
2712 return isl_basic_set_sample_with_cone(bset
, cone
);
2715 static void check_gbr_integer_feasible(struct isl_context_gbr
*cgbr
)
2717 struct isl_vec
*sample
;
2722 if (cgbr
->tab
->empty
)
2725 sample
= gbr_get_sample(cgbr
);
2729 if (sample
->size
== 0) {
2730 isl_vec_free(sample
);
2731 if (isl_tab_mark_empty(cgbr
->tab
) < 0)
2736 cgbr
->tab
= isl_tab_add_sample(cgbr
->tab
, sample
);
2740 isl_tab_free(cgbr
->tab
);
2744 static struct isl_tab
*add_gbr_eq(struct isl_tab
*tab
, isl_int
*eq
)
2751 if (isl_tab_extend_cons(tab
, 2) < 0)
2754 tab
= isl_tab_add_eq(tab
, eq
);
2762 static void context_gbr_add_eq(struct isl_context
*context
, isl_int
*eq
,
2763 int check
, int update
)
2765 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
2767 cgbr
->tab
= add_gbr_eq(cgbr
->tab
, eq
);
2769 if (cgbr
->cone
&& cgbr
->cone
->n_col
!= cgbr
->cone
->n_dead
) {
2770 if (isl_tab_extend_cons(cgbr
->cone
, 2) < 0)
2772 cgbr
->cone
= isl_tab_add_eq(cgbr
->cone
, eq
);
2776 int v
= tab_has_valid_sample(cgbr
->tab
, eq
, 1);
2780 check_gbr_integer_feasible(cgbr
);
2783 cgbr
->tab
= check_samples(cgbr
->tab
, eq
, 1);
2786 isl_tab_free(cgbr
->tab
);
2790 static void add_gbr_ineq(struct isl_context_gbr
*cgbr
, isl_int
*ineq
)
2795 if (isl_tab_extend_cons(cgbr
->tab
, 1) < 0)
2798 if (isl_tab_add_ineq(cgbr
->tab
, ineq
) < 0)
2801 if (cgbr
->shifted
&& !cgbr
->shifted
->empty
&& use_shifted(cgbr
)) {
2804 dim
= isl_basic_map_total_dim(cgbr
->tab
->bmap
);
2806 if (isl_tab_extend_cons(cgbr
->shifted
, 1) < 0)
2809 for (i
= 0; i
< dim
; ++i
) {
2810 if (!isl_int_is_neg(ineq
[1 + i
]))
2812 isl_int_add(ineq
[0], ineq
[0], ineq
[1 + i
]);
2815 if (isl_tab_add_ineq(cgbr
->shifted
, ineq
) < 0)
2818 for (i
= 0; i
< dim
; ++i
) {
2819 if (!isl_int_is_neg(ineq
[1 + i
]))
2821 isl_int_sub(ineq
[0], ineq
[0], ineq
[1 + i
]);
2825 if (cgbr
->cone
&& cgbr
->cone
->n_col
!= cgbr
->cone
->n_dead
) {
2826 if (isl_tab_extend_cons(cgbr
->cone
, 1) < 0)
2828 if (isl_tab_add_ineq(cgbr
->cone
, ineq
) < 0)
2834 isl_tab_free(cgbr
->tab
);
2838 static void context_gbr_add_ineq(struct isl_context
*context
, isl_int
*ineq
,
2839 int check
, int update
)
2841 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
2843 add_gbr_ineq(cgbr
, ineq
);
2848 int v
= tab_has_valid_sample(cgbr
->tab
, ineq
, 0);
2852 check_gbr_integer_feasible(cgbr
);
2855 cgbr
->tab
= check_samples(cgbr
->tab
, ineq
, 0);
2858 isl_tab_free(cgbr
->tab
);
2862 static enum isl_tab_row_sign
context_gbr_ineq_sign(struct isl_context
*context
,
2863 isl_int
*ineq
, int strict
)
2865 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
2866 return tab_ineq_sign(cgbr
->tab
, ineq
, strict
);
2869 /* Check whether "ineq" can be added to the tableau without rendering
2872 static int context_gbr_test_ineq(struct isl_context
*context
, isl_int
*ineq
)
2874 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
2875 struct isl_tab_undo
*snap
;
2876 struct isl_tab_undo
*shifted_snap
= NULL
;
2877 struct isl_tab_undo
*cone_snap
= NULL
;
2883 if (isl_tab_extend_cons(cgbr
->tab
, 1) < 0)
2886 snap
= isl_tab_snap(cgbr
->tab
);
2888 shifted_snap
= isl_tab_snap(cgbr
->shifted
);
2890 cone_snap
= isl_tab_snap(cgbr
->cone
);
2891 add_gbr_ineq(cgbr
, ineq
);
2892 check_gbr_integer_feasible(cgbr
);
2895 feasible
= !cgbr
->tab
->empty
;
2896 if (isl_tab_rollback(cgbr
->tab
, snap
) < 0)
2899 if (isl_tab_rollback(cgbr
->shifted
, shifted_snap
))
2901 } else if (cgbr
->shifted
) {
2902 isl_tab_free(cgbr
->shifted
);
2903 cgbr
->shifted
= NULL
;
2906 if (isl_tab_rollback(cgbr
->cone
, cone_snap
))
2908 } else if (cgbr
->cone
) {
2909 isl_tab_free(cgbr
->cone
);
2916 /* Return the column of the last of the variables associated to
2917 * a column that has a non-zero coefficient.
2918 * This function is called in a context where only coefficients
2919 * of parameters or divs can be non-zero.
2921 static int last_non_zero_var_col(struct isl_tab
*tab
, isl_int
*p
)
2925 unsigned dim
= tab
->n_var
- tab
->n_param
- tab
->n_div
;
2927 if (tab
->n_var
== 0)
2930 for (i
= tab
->n_var
- 1; i
>= 0; --i
) {
2931 if (i
>= tab
->n_param
&& i
< tab
->n_var
- tab
->n_div
)
2933 if (tab
->var
[i
].is_row
)
2935 col
= tab
->var
[i
].index
;
2936 if (!isl_int_is_zero(p
[col
]))
2943 /* Look through all the recently added equalities in the context
2944 * to see if we can propagate any of them to the main tableau.
2946 * The newly added equalities in the context are encoded as pairs
2947 * of inequalities starting at inequality "first".
2949 * We tentatively add each of these equalities to the main tableau
2950 * and if this happens to result in a row with a final coefficient
2951 * that is one or negative one, we use it to kill a column
2952 * in the main tableau. Otherwise, we discard the tentatively
2955 static void propagate_equalities(struct isl_context_gbr
*cgbr
,
2956 struct isl_tab
*tab
, unsigned first
)
2959 struct isl_vec
*eq
= NULL
;
2961 eq
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_var
);
2965 if (isl_tab_extend_cons(tab
, (cgbr
->tab
->bmap
->n_ineq
- first
)/2) < 0)
2968 isl_seq_clr(eq
->el
+ 1 + tab
->n_param
,
2969 tab
->n_var
- tab
->n_param
- tab
->n_div
);
2970 for (i
= first
; i
< cgbr
->tab
->bmap
->n_ineq
; i
+= 2) {
2973 struct isl_tab_undo
*snap
;
2974 snap
= isl_tab_snap(tab
);
2976 isl_seq_cpy(eq
->el
, cgbr
->tab
->bmap
->ineq
[i
], 1 + tab
->n_param
);
2977 isl_seq_cpy(eq
->el
+ 1 + tab
->n_var
- tab
->n_div
,
2978 cgbr
->tab
->bmap
->ineq
[i
] + 1 + tab
->n_param
,
2981 r
= isl_tab_add_row(tab
, eq
->el
);
2984 r
= tab
->con
[r
].index
;
2985 j
= last_non_zero_var_col(tab
, tab
->mat
->row
[r
] + 2 + tab
->M
);
2986 if (j
< 0 || j
< tab
->n_dead
||
2987 !isl_int_is_one(tab
->mat
->row
[r
][0]) ||
2988 (!isl_int_is_one(tab
->mat
->row
[r
][2 + tab
->M
+ j
]) &&
2989 !isl_int_is_negone(tab
->mat
->row
[r
][2 + tab
->M
+ j
]))) {
2990 if (isl_tab_rollback(tab
, snap
) < 0)
2994 if (isl_tab_pivot(tab
, r
, j
) < 0)
2996 if (isl_tab_kill_col(tab
, j
) < 0)
2999 tab
= restore_lexmin(tab
);
3007 isl_tab_free(cgbr
->tab
);
3011 static int context_gbr_detect_equalities(struct isl_context
*context
,
3012 struct isl_tab
*tab
)
3014 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3015 struct isl_ctx
*ctx
;
3017 enum isl_lp_result res
;
3020 ctx
= cgbr
->tab
->mat
->ctx
;
3023 struct isl_basic_set
*bset
= isl_tab_peek_bset(cgbr
->tab
);
3024 cgbr
->cone
= isl_tab_from_recession_cone(bset
);
3027 if (isl_tab_track_bset(cgbr
->cone
, isl_basic_set_dup(bset
)) < 0)
3030 cgbr
->cone
= isl_tab_detect_implicit_equalities(cgbr
->cone
);
3032 n_ineq
= cgbr
->tab
->bmap
->n_ineq
;
3033 cgbr
->tab
= isl_tab_detect_equalities(cgbr
->tab
, cgbr
->cone
);
3034 if (cgbr
->tab
&& cgbr
->tab
->bmap
->n_ineq
> n_ineq
)
3035 propagate_equalities(cgbr
, tab
, n_ineq
);
3039 isl_tab_free(cgbr
->tab
);
3044 static int context_gbr_get_div(struct isl_context
*context
, struct isl_tab
*tab
,
3045 struct isl_vec
*div
)
3047 return get_div(tab
, context
, div
);
3050 static int context_gbr_add_div(struct isl_context
*context
, struct isl_vec
*div
,
3053 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3057 if (isl_tab_extend_cons(cgbr
->cone
, 3) < 0)
3059 if (isl_tab_extend_vars(cgbr
->cone
, 1) < 0)
3061 if (isl_tab_allocate_var(cgbr
->cone
) <0)
3064 cgbr
->cone
->bmap
= isl_basic_map_extend_dim(cgbr
->cone
->bmap
,
3065 isl_basic_map_get_dim(cgbr
->cone
->bmap
), 1, 0, 2);
3066 k
= isl_basic_map_alloc_div(cgbr
->cone
->bmap
);
3069 isl_seq_cpy(cgbr
->cone
->bmap
->div
[k
], div
->el
, div
->size
);
3070 if (isl_tab_push(cgbr
->cone
, isl_tab_undo_bmap_div
) < 0)
3073 return context_tab_add_div(cgbr
->tab
, div
, nonneg
);
3076 static int context_gbr_best_split(struct isl_context
*context
,
3077 struct isl_tab
*tab
)
3079 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3080 struct isl_tab_undo
*snap
;
3083 snap
= isl_tab_snap(cgbr
->tab
);
3084 r
= best_split(tab
, cgbr
->tab
);
3086 if (isl_tab_rollback(cgbr
->tab
, snap
) < 0)
3092 static int context_gbr_is_empty(struct isl_context
*context
)
3094 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3097 return cgbr
->tab
->empty
;
3100 struct isl_gbr_tab_undo
{
3101 struct isl_tab_undo
*tab_snap
;
3102 struct isl_tab_undo
*shifted_snap
;
3103 struct isl_tab_undo
*cone_snap
;
3106 static void *context_gbr_save(struct isl_context
*context
)
3108 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3109 struct isl_gbr_tab_undo
*snap
;
3111 snap
= isl_alloc_type(cgbr
->tab
->mat
->ctx
, struct isl_gbr_tab_undo
);
3115 snap
->tab_snap
= isl_tab_snap(cgbr
->tab
);
3116 if (isl_tab_save_samples(cgbr
->tab
) < 0)
3120 snap
->shifted_snap
= isl_tab_snap(cgbr
->shifted
);
3122 snap
->shifted_snap
= NULL
;
3125 snap
->cone_snap
= isl_tab_snap(cgbr
->cone
);
3127 snap
->cone_snap
= NULL
;
3135 static void context_gbr_restore(struct isl_context
*context
, void *save
)
3137 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3138 struct isl_gbr_tab_undo
*snap
= (struct isl_gbr_tab_undo
*)save
;
3141 if (isl_tab_rollback(cgbr
->tab
, snap
->tab_snap
) < 0) {
3142 isl_tab_free(cgbr
->tab
);
3146 if (snap
->shifted_snap
) {
3147 if (isl_tab_rollback(cgbr
->shifted
, snap
->shifted_snap
) < 0)
3149 } else if (cgbr
->shifted
) {
3150 isl_tab_free(cgbr
->shifted
);
3151 cgbr
->shifted
= NULL
;
3154 if (snap
->cone_snap
) {
3155 if (isl_tab_rollback(cgbr
->cone
, snap
->cone_snap
) < 0)
3157 } else if (cgbr
->cone
) {
3158 isl_tab_free(cgbr
->cone
);
3167 isl_tab_free(cgbr
->tab
);
3171 static int context_gbr_is_ok(struct isl_context
*context
)
3173 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3177 static void context_gbr_invalidate(struct isl_context
*context
)
3179 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3180 isl_tab_free(cgbr
->tab
);
3184 static void context_gbr_free(struct isl_context
*context
)
3186 struct isl_context_gbr
*cgbr
= (struct isl_context_gbr
*)context
;
3187 isl_tab_free(cgbr
->tab
);
3188 isl_tab_free(cgbr
->shifted
);
3189 isl_tab_free(cgbr
->cone
);
3193 struct isl_context_op isl_context_gbr_op
= {
3194 context_gbr_detect_nonnegative_parameters
,
3195 context_gbr_peek_basic_set
,
3196 context_gbr_peek_tab
,
3198 context_gbr_add_ineq
,
3199 context_gbr_ineq_sign
,
3200 context_gbr_test_ineq
,
3201 context_gbr_get_div
,
3202 context_gbr_add_div
,
3203 context_gbr_detect_equalities
,
3204 context_gbr_best_split
,
3205 context_gbr_is_empty
,
3208 context_gbr_restore
,
3209 context_gbr_invalidate
,
3213 static struct isl_context
*isl_context_gbr_alloc(struct isl_basic_set
*dom
)
3215 struct isl_context_gbr
*cgbr
;
3220 cgbr
= isl_calloc_type(dom
->ctx
, struct isl_context_gbr
);
3224 cgbr
->context
.op
= &isl_context_gbr_op
;
3226 cgbr
->shifted
= NULL
;
3228 cgbr
->tab
= isl_tab_from_basic_set(dom
);
3229 cgbr
->tab
= isl_tab_init_samples(cgbr
->tab
);
3232 if (isl_tab_track_bset(cgbr
->tab
,
3233 isl_basic_set_cow(isl_basic_set_copy(dom
))) < 0)
3235 check_gbr_integer_feasible(cgbr
);
3237 return &cgbr
->context
;
3239 cgbr
->context
.op
->free(&cgbr
->context
);
3243 static struct isl_context
*isl_context_alloc(struct isl_basic_set
*dom
)
3248 if (dom
->ctx
->opt
->context
== ISL_CONTEXT_LEXMIN
)
3249 return isl_context_lex_alloc(dom
);
3251 return isl_context_gbr_alloc(dom
);
3254 /* Construct an isl_sol_map structure for accumulating the solution.
3255 * If track_empty is set, then we also keep track of the parts
3256 * of the context where there is no solution.
3257 * If max is set, then we are solving a maximization, rather than
3258 * a minimization problem, which means that the variables in the
3259 * tableau have value "M - x" rather than "M + x".
3261 static struct isl_sol_map
*sol_map_init(struct isl_basic_map
*bmap
,
3262 struct isl_basic_set
*dom
, int track_empty
, int max
)
3264 struct isl_sol_map
*sol_map
;
3266 sol_map
= isl_calloc_type(bset
->ctx
, struct isl_sol_map
);
3270 sol_map
->sol
.rational
= ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
);
3271 sol_map
->sol
.dec_level
.callback
.run
= &sol_dec_level_wrap
;
3272 sol_map
->sol
.dec_level
.sol
= &sol_map
->sol
;
3273 sol_map
->sol
.max
= max
;
3274 sol_map
->sol
.n_out
= isl_basic_map_dim(bmap
, isl_dim_out
);
3275 sol_map
->sol
.add
= &sol_map_add_wrap
;
3276 sol_map
->sol
.add_empty
= track_empty
? &sol_map_add_empty_wrap
: NULL
;
3277 sol_map
->sol
.free
= &sol_map_free_wrap
;
3278 sol_map
->map
= isl_map_alloc_dim(isl_basic_map_get_dim(bmap
), 1,
3283 sol_map
->sol
.context
= isl_context_alloc(dom
);
3284 if (!sol_map
->sol
.context
)
3288 sol_map
->empty
= isl_set_alloc_dim(isl_basic_set_get_dim(dom
),
3289 1, ISL_SET_DISJOINT
);
3290 if (!sol_map
->empty
)
3294 isl_basic_set_free(dom
);
3297 isl_basic_set_free(dom
);
3298 sol_map_free(sol_map
);
3302 /* Check whether all coefficients of (non-parameter) variables
3303 * are non-positive, meaning that no pivots can be performed on the row.
3305 static int is_critical(struct isl_tab
*tab
, int row
)
3308 unsigned off
= 2 + tab
->M
;
3310 for (j
= tab
->n_dead
; j
< tab
->n_col
; ++j
) {
3311 if (tab
->col_var
[j
] >= 0 &&
3312 (tab
->col_var
[j
] < tab
->n_param
||
3313 tab
->col_var
[j
] >= tab
->n_var
- tab
->n_div
))
3316 if (isl_int_is_pos(tab
->mat
->row
[row
][off
+ j
]))
3323 /* Check whether the inequality represented by vec is strict over the integers,
3324 * i.e., there are no integer values satisfying the constraint with
3325 * equality. This happens if the gcd of the coefficients is not a divisor
3326 * of the constant term. If so, scale the constraint down by the gcd
3327 * of the coefficients.
3329 static int is_strict(struct isl_vec
*vec
)
3335 isl_seq_gcd(vec
->el
+ 1, vec
->size
- 1, &gcd
);
3336 if (!isl_int_is_one(gcd
)) {
3337 strict
= !isl_int_is_divisible_by(vec
->el
[0], gcd
);
3338 isl_int_fdiv_q(vec
->el
[0], vec
->el
[0], gcd
);
3339 isl_seq_scale_down(vec
->el
+ 1, vec
->el
+ 1, gcd
, vec
->size
-1);
3346 /* Determine the sign of the given row of the main tableau.
3347 * The result is one of
3348 * isl_tab_row_pos: always non-negative; no pivot needed
3349 * isl_tab_row_neg: always non-positive; pivot
3350 * isl_tab_row_any: can be both positive and negative; split
3352 * We first handle some simple cases
3353 * - the row sign may be known already
3354 * - the row may be obviously non-negative
3355 * - the parametric constant may be equal to that of another row
3356 * for which we know the sign. This sign will be either "pos" or
3357 * "any". If it had been "neg" then we would have pivoted before.
3359 * If none of these cases hold, we check the value of the row for each
3360 * of the currently active samples. Based on the signs of these values
3361 * we make an initial determination of the sign of the row.
3363 * all zero -> unk(nown)
3364 * all non-negative -> pos
3365 * all non-positive -> neg
3366 * both negative and positive -> all
3368 * If we end up with "all", we are done.
3369 * Otherwise, we perform a check for positive and/or negative
3370 * values as follows.
3372 * samples neg unk pos
3378 * There is no special sign for "zero", because we can usually treat zero
3379 * as either non-negative or non-positive, whatever works out best.
3380 * However, if the row is "critical", meaning that pivoting is impossible
3381 * then we don't want to limp zero with the non-positive case, because
3382 * then we we would lose the solution for those values of the parameters
3383 * where the value of the row is zero. Instead, we treat 0 as non-negative
3384 * ensuring a split if the row can attain both zero and negative values.
3385 * The same happens when the original constraint was one that could not
3386 * be satisfied with equality by any integer values of the parameters.
3387 * In this case, we normalize the constraint, but then a value of zero
3388 * for the normalized constraint is actually a positive value for the
3389 * original constraint, so again we need to treat zero as non-negative.
3390 * In both these cases, we have the following decision tree instead:
3392 * all non-negative -> pos
3393 * all negative -> neg
3394 * both negative and non-negative -> all
3402 static enum isl_tab_row_sign
row_sign(struct isl_tab
*tab
,
3403 struct isl_sol
*sol
, int row
)
3405 struct isl_vec
*ineq
= NULL
;
3406 int res
= isl_tab_row_unknown
;
3411 if (tab
->row_sign
[row
] != isl_tab_row_unknown
)
3412 return tab
->row_sign
[row
];
3413 if (is_obviously_nonneg(tab
, row
))
3414 return isl_tab_row_pos
;
3415 for (row2
= tab
->n_redundant
; row2
< tab
->n_row
; ++row2
) {
3416 if (tab
->row_sign
[row2
] == isl_tab_row_unknown
)
3418 if (identical_parameter_line(tab
, row
, row2
))
3419 return tab
->row_sign
[row2
];
3422 critical
= is_critical(tab
, row
);
3424 ineq
= get_row_parameter_ineq(tab
, row
);
3428 strict
= is_strict(ineq
);
3430 res
= sol
->context
->op
->ineq_sign(sol
->context
, ineq
->el
,
3431 critical
|| strict
);
3433 if (res
== isl_tab_row_unknown
|| res
== isl_tab_row_pos
) {
3434 /* test for negative values */
3436 isl_seq_neg(ineq
->el
, ineq
->el
, ineq
->size
);
3437 isl_int_sub_ui(ineq
->el
[0], ineq
->el
[0], 1);
3439 feasible
= sol
->context
->op
->test_ineq(sol
->context
, ineq
->el
);
3443 res
= isl_tab_row_pos
;
3445 res
= (res
== isl_tab_row_unknown
) ? isl_tab_row_neg
3447 if (res
== isl_tab_row_neg
) {
3448 isl_seq_neg(ineq
->el
, ineq
->el
, ineq
->size
);
3449 isl_int_sub_ui(ineq
->el
[0], ineq
->el
[0], 1);
3453 if (res
== isl_tab_row_neg
) {
3454 /* test for positive values */
3456 if (!critical
&& !strict
)
3457 isl_int_sub_ui(ineq
->el
[0], ineq
->el
[0], 1);
3459 feasible
= sol
->context
->op
->test_ineq(sol
->context
, ineq
->el
);
3463 res
= isl_tab_row_any
;
3473 static void find_solutions(struct isl_sol
*sol
, struct isl_tab
*tab
);
3475 /* Find solutions for values of the parameters that satisfy the given
3478 * We currently take a snapshot of the context tableau that is reset
3479 * when we return from this function, while we make a copy of the main
3480 * tableau, leaving the original main tableau untouched.
3481 * These are fairly arbitrary choices. Making a copy also of the context
3482 * tableau would obviate the need to undo any changes made to it later,
3483 * while taking a snapshot of the main tableau could reduce memory usage.
3484 * If we were to switch to taking a snapshot of the main tableau,
3485 * we would have to keep in mind that we need to save the row signs
3486 * and that we need to do this before saving the current basis
3487 * such that the basis has been restore before we restore the row signs.
3489 static void find_in_pos(struct isl_sol
*sol
, struct isl_tab
*tab
, isl_int
*ineq
)
3495 saved
= sol
->context
->op
->save(sol
->context
);
3497 tab
= isl_tab_dup(tab
);
3501 sol
->context
->op
->add_ineq(sol
->context
, ineq
, 0, 1);
3503 find_solutions(sol
, tab
);
3505 sol
->context
->op
->restore(sol
->context
, saved
);
3511 /* Record the absence of solutions for those values of the parameters
3512 * that do not satisfy the given inequality with equality.
3514 static void no_sol_in_strict(struct isl_sol
*sol
,
3515 struct isl_tab
*tab
, struct isl_vec
*ineq
)
3522 saved
= sol
->context
->op
->save(sol
->context
);
3524 isl_int_sub_ui(ineq
->el
[0], ineq
->el
[0], 1);
3526 sol
->context
->op
->add_ineq(sol
->context
, ineq
->el
, 1, 0);
3535 isl_int_add_ui(ineq
->el
[0], ineq
->el
[0], 1);
3537 sol
->context
->op
->restore(sol
->context
, saved
);
3543 /* Compute the lexicographic minimum of the set represented by the main
3544 * tableau "tab" within the context "sol->context_tab".
3545 * On entry the sample value of the main tableau is lexicographically
3546 * less than or equal to this lexicographic minimum.
3547 * Pivots are performed until a feasible point is found, which is then
3548 * necessarily equal to the minimum, or until the tableau is found to
3549 * be infeasible. Some pivots may need to be performed for only some
3550 * feasible values of the context tableau. If so, the context tableau
3551 * is split into a part where the pivot is needed and a part where it is not.
3553 * Whenever we enter the main loop, the main tableau is such that no
3554 * "obvious" pivots need to be performed on it, where "obvious" means
3555 * that the given row can be seen to be negative without looking at
3556 * the context tableau. In particular, for non-parametric problems,
3557 * no pivots need to be performed on the main tableau.
3558 * The caller of find_solutions is responsible for making this property
3559 * hold prior to the first iteration of the loop, while restore_lexmin
3560 * is called before every other iteration.
3562 * Inside the main loop, we first examine the signs of the rows of
3563 * the main tableau within the context of the context tableau.
3564 * If we find a row that is always non-positive for all values of
3565 * the parameters satisfying the context tableau and negative for at
3566 * least one value of the parameters, we perform the appropriate pivot
3567 * and start over. An exception is the case where no pivot can be
3568 * performed on the row. In this case, we require that the sign of
3569 * the row is negative for all values of the parameters (rather than just
3570 * non-positive). This special case is handled inside row_sign, which
3571 * will say that the row can have any sign if it determines that it can
3572 * attain both negative and zero values.
3574 * If we can't find a row that always requires a pivot, but we can find
3575 * one or more rows that require a pivot for some values of the parameters
3576 * (i.e., the row can attain both positive and negative signs), then we split
3577 * the context tableau into two parts, one where we force the sign to be
3578 * non-negative and one where we force is to be negative.
3579 * The non-negative part is handled by a recursive call (through find_in_pos).
3580 * Upon returning from this call, we continue with the negative part and
3581 * perform the required pivot.
3583 * If no such rows can be found, all rows are non-negative and we have
3584 * found a (rational) feasible point. If we only wanted a rational point
3586 * Otherwise, we check if all values of the sample point of the tableau
3587 * are integral for the variables. If so, we have found the minimal
3588 * integral point and we are done.
3589 * If the sample point is not integral, then we need to make a distinction
3590 * based on whether the constant term is non-integral or the coefficients
3591 * of the parameters. Furthermore, in order to decide how to handle
3592 * the non-integrality, we also need to know whether the coefficients
3593 * of the other columns in the tableau are integral. This leads
3594 * to the following table. The first two rows do not correspond
3595 * to a non-integral sample point and are only mentioned for completeness.
3597 * constant parameters other
3600 * int int rat | -> no problem
3602 * rat int int -> fail
3604 * rat int rat -> cut
3607 * rat rat rat | -> parametric cut
3610 * rat rat int | -> split context
3612 * If the parametric constant is completely integral, then there is nothing
3613 * to be done. If the constant term is non-integral, but all the other
3614 * coefficient are integral, then there is nothing that can be done
3615 * and the tableau has no integral solution.
3616 * If, on the other hand, one or more of the other columns have rational
3617 * coeffcients, but the parameter coefficients are all integral, then
3618 * we can perform a regular (non-parametric) cut.
3619 * Finally, if there is any parameter coefficient that is non-integral,
3620 * then we need to involve the context tableau. There are two cases here.
3621 * If at least one other column has a rational coefficient, then we
3622 * can perform a parametric cut in the main tableau by adding a new
3623 * integer division in the context tableau.
3624 * If all other columns have integral coefficients, then we need to
3625 * enforce that the rational combination of parameters (c + \sum a_i y_i)/m
3626 * is always integral. We do this by introducing an integer division
3627 * q = floor((c + \sum a_i y_i)/m) and stipulating that its argument should
3628 * always be integral in the context tableau, i.e., m q = c + \sum a_i y_i.
3629 * Since q is expressed in the tableau as
3630 * c + \sum a_i y_i - m q >= 0
3631 * -c - \sum a_i y_i + m q + m - 1 >= 0
3632 * it is sufficient to add the inequality
3633 * -c - \sum a_i y_i + m q >= 0
3634 * In the part of the context where this inequality does not hold, the
3635 * main tableau is marked as being empty.
3637 static void find_solutions(struct isl_sol
*sol
, struct isl_tab
*tab
)
3639 struct isl_context
*context
;
3641 if (!tab
|| sol
->error
)
3644 context
= sol
->context
;
3648 if (context
->op
->is_empty(context
))
3651 for (; tab
&& !tab
->empty
; tab
= restore_lexmin(tab
)) {
3658 for (row
= tab
->n_redundant
; row
< tab
->n_row
; ++row
) {
3659 if (!isl_tab_var_from_row(tab
, row
)->is_nonneg
)
3661 sgn
= row_sign(tab
, sol
, row
);
3664 tab
->row_sign
[row
] = sgn
;
3665 if (sgn
== isl_tab_row_any
)
3667 if (sgn
== isl_tab_row_any
&& split
== -1)
3669 if (sgn
== isl_tab_row_neg
)
3672 if (row
< tab
->n_row
)
3675 struct isl_vec
*ineq
;
3677 split
= context
->op
->best_split(context
, tab
);
3680 ineq
= get_row_parameter_ineq(tab
, split
);
3684 for (row
= tab
->n_redundant
; row
< tab
->n_row
; ++row
) {
3685 if (!isl_tab_var_from_row(tab
, row
)->is_nonneg
)
3687 if (tab
->row_sign
[row
] == isl_tab_row_any
)
3688 tab
->row_sign
[row
] = isl_tab_row_unknown
;
3690 tab
->row_sign
[split
] = isl_tab_row_pos
;
3692 find_in_pos(sol
, tab
, ineq
->el
);
3693 tab
->row_sign
[split
] = isl_tab_row_neg
;
3695 isl_seq_neg(ineq
->el
, ineq
->el
, ineq
->size
);
3696 isl_int_sub_ui(ineq
->el
[0], ineq
->el
[0], 1);
3697 context
->op
->add_ineq(context
, ineq
->el
, 0, 1);
3705 row
= first_non_integer_row(tab
, &flags
);
3708 if (ISL_FL_ISSET(flags
, I_PAR
)) {
3709 if (ISL_FL_ISSET(flags
, I_VAR
)) {
3710 if (isl_tab_mark_empty(tab
) < 0)
3714 row
= add_cut(tab
, row
);
3715 } else if (ISL_FL_ISSET(flags
, I_VAR
)) {
3716 struct isl_vec
*div
;
3717 struct isl_vec
*ineq
;
3719 div
= get_row_split_div(tab
, row
);
3722 d
= context
->op
->get_div(context
, tab
, div
);
3726 ineq
= ineq_for_div(context
->op
->peek_basic_set(context
), d
);
3728 no_sol_in_strict(sol
, tab
, ineq
);
3729 isl_seq_neg(ineq
->el
, ineq
->el
, ineq
->size
);
3730 context
->op
->add_ineq(context
, ineq
->el
, 1, 1);
3732 if (sol
->error
|| !context
->op
->is_ok(context
))
3734 tab
= set_row_cst_to_div(tab
, row
, d
);
3735 if (context
->op
->is_empty(context
))
3738 row
= add_parametric_cut(tab
, row
, context
);
3751 /* Compute the lexicographic minimum of the set represented by the main
3752 * tableau "tab" within the context "sol->context_tab".
3754 * As a preprocessing step, we first transfer all the purely parametric
3755 * equalities from the main tableau to the context tableau, i.e.,
3756 * parameters that have been pivoted to a row.
3757 * These equalities are ignored by the main algorithm, because the
3758 * corresponding rows may not be marked as being non-negative.
3759 * In parts of the context where the added equality does not hold,
3760 * the main tableau is marked as being empty.
3762 static void find_solutions_main(struct isl_sol
*sol
, struct isl_tab
*tab
)
3768 for (row
= tab
->n_redundant
; row
< tab
->n_row
; ++row
) {
3772 if (tab
->row_var
[row
] < 0)
3774 if (tab
->row_var
[row
] >= tab
->n_param
&&
3775 tab
->row_var
[row
] < tab
->n_var
- tab
->n_div
)
3777 if (tab
->row_var
[row
] < tab
->n_param
)
3778 p
= tab
->row_var
[row
];
3780 p
= tab
->row_var
[row
]
3781 + tab
->n_param
- (tab
->n_var
- tab
->n_div
);
3783 eq
= isl_vec_alloc(tab
->mat
->ctx
, 1+tab
->n_param
+tab
->n_div
);
3784 get_row_parameter_line(tab
, row
, eq
->el
);
3785 isl_int_neg(eq
->el
[1 + p
], tab
->mat
->row
[row
][0]);
3786 eq
= isl_vec_normalize(eq
);
3789 no_sol_in_strict(sol
, tab
, eq
);
3791 isl_seq_neg(eq
->el
, eq
->el
, eq
->size
);
3793 no_sol_in_strict(sol
, tab
, eq
);
3794 isl_seq_neg(eq
->el
, eq
->el
, eq
->size
);
3796 sol
->context
->op
->add_eq(sol
->context
, eq
->el
, 1, 1);
3800 if (isl_tab_mark_redundant(tab
, row
) < 0)
3803 if (sol
->context
->op
->is_empty(sol
->context
))
3806 row
= tab
->n_redundant
- 1;
3809 find_solutions(sol
, tab
);
3820 static void sol_map_find_solutions(struct isl_sol_map
*sol_map
,
3821 struct isl_tab
*tab
)
3823 find_solutions_main(&sol_map
->sol
, tab
);
3826 /* Check if integer division "div" of "dom" also occurs in "bmap".
3827 * If so, return its position within the divs.
3828 * If not, return -1.
3830 static int find_context_div(struct isl_basic_map
*bmap
,
3831 struct isl_basic_set
*dom
, unsigned div
)
3834 unsigned b_dim
= isl_dim_total(bmap
->dim
);
3835 unsigned d_dim
= isl_dim_total(dom
->dim
);
3837 if (isl_int_is_zero(dom
->div
[div
][0]))
3839 if (isl_seq_first_non_zero(dom
->div
[div
] + 2 + d_dim
, dom
->n_div
) != -1)
3842 for (i
= 0; i
< bmap
->n_div
; ++i
) {
3843 if (isl_int_is_zero(bmap
->div
[i
][0]))
3845 if (isl_seq_first_non_zero(bmap
->div
[i
] + 2 + d_dim
,
3846 (b_dim
- d_dim
) + bmap
->n_div
) != -1)
3848 if (isl_seq_eq(bmap
->div
[i
], dom
->div
[div
], 2 + d_dim
))
3854 /* The correspondence between the variables in the main tableau,
3855 * the context tableau, and the input map and domain is as follows.
3856 * The first n_param and the last n_div variables of the main tableau
3857 * form the variables of the context tableau.
3858 * In the basic map, these n_param variables correspond to the
3859 * parameters and the input dimensions. In the domain, they correspond
3860 * to the parameters and the set dimensions.
3861 * The n_div variables correspond to the integer divisions in the domain.
3862 * To ensure that everything lines up, we may need to copy some of the
3863 * integer divisions of the domain to the map. These have to be placed
3864 * in the same order as those in the context and they have to be placed
3865 * after any other integer divisions that the map may have.
3866 * This function performs the required reordering.
3868 static struct isl_basic_map
*align_context_divs(struct isl_basic_map
*bmap
,
3869 struct isl_basic_set
*dom
)
3875 for (i
= 0; i
< dom
->n_div
; ++i
)
3876 if (find_context_div(bmap
, dom
, i
) != -1)
3878 other
= bmap
->n_div
- common
;
3879 if (dom
->n_div
- common
> 0) {
3880 bmap
= isl_basic_map_extend_dim(bmap
, isl_dim_copy(bmap
->dim
),
3881 dom
->n_div
- common
, 0, 0);
3885 for (i
= 0; i
< dom
->n_div
; ++i
) {
3886 int pos
= find_context_div(bmap
, dom
, i
);
3888 pos
= isl_basic_map_alloc_div(bmap
);
3891 isl_int_set_si(bmap
->div
[pos
][0], 0);
3893 if (pos
!= other
+ i
)
3894 isl_basic_map_swap_div(bmap
, pos
, other
+ i
);
3898 isl_basic_map_free(bmap
);
3902 /* Compute the lexicographic minimum (or maximum if "max" is set)
3903 * of "bmap" over the domain "dom" and return the result as a map.
3904 * If "empty" is not NULL, then *empty is assigned a set that
3905 * contains those parts of the domain where there is no solution.
3906 * If "bmap" is marked as rational (ISL_BASIC_MAP_RATIONAL),
3907 * then we compute the rational optimum. Otherwise, we compute
3908 * the integral optimum.
3910 * We perform some preprocessing. As the PILP solver does not
3911 * handle implicit equalities very well, we first make sure all
3912 * the equalities are explicitly available.
3913 * We also make sure the divs in the domain are properly order,
3914 * because they will be added one by one in the given order
3915 * during the construction of the solution map.
3917 struct isl_map
*isl_tab_basic_map_partial_lexopt(
3918 struct isl_basic_map
*bmap
, struct isl_basic_set
*dom
,
3919 struct isl_set
**empty
, int max
)
3921 struct isl_tab
*tab
;
3922 struct isl_map
*result
= NULL
;
3923 struct isl_sol_map
*sol_map
= NULL
;
3924 struct isl_context
*context
;
3925 struct isl_basic_map
*eq
;
3932 isl_assert(bmap
->ctx
,
3933 isl_basic_map_compatible_domain(bmap
, dom
), goto error
);
3935 eq
= isl_basic_map_copy(bmap
);
3936 eq
= isl_basic_map_intersect_domain(eq
, isl_basic_set_copy(dom
));
3937 eq
= isl_basic_map_affine_hull(eq
);
3938 bmap
= isl_basic_map_intersect(bmap
, eq
);
3941 dom
= isl_basic_set_order_divs(dom
);
3942 bmap
= align_context_divs(bmap
, dom
);
3944 sol_map
= sol_map_init(bmap
, dom
, !!empty
, max
);
3948 context
= sol_map
->sol
.context
;
3949 if (isl_basic_set_fast_is_empty(context
->op
->peek_basic_set(context
)))
3951 else if (isl_basic_map_fast_is_empty(bmap
))
3952 sol_map_add_empty_if_needed(sol_map
,
3953 isl_basic_set_copy(context
->op
->peek_basic_set(context
)));
3955 tab
= tab_for_lexmin(bmap
,
3956 context
->op
->peek_basic_set(context
), 1, max
);
3957 tab
= context
->op
->detect_nonnegative_parameters(context
, tab
);
3958 sol_map_find_solutions(sol_map
, tab
);
3960 if (sol_map
->sol
.error
)
3963 result
= isl_map_copy(sol_map
->map
);
3965 *empty
= isl_set_copy(sol_map
->empty
);
3966 sol_free(&sol_map
->sol
);
3967 isl_basic_map_free(bmap
);
3970 sol_free(&sol_map
->sol
);
3971 isl_basic_map_free(bmap
);
3975 struct isl_sol_for
{
3977 int (*fn
)(__isl_take isl_basic_set
*dom
,
3978 __isl_take isl_mat
*map
, void *user
);
3982 static void sol_for_free(struct isl_sol_for
*sol_for
)
3984 if (sol_for
->sol
.context
)
3985 sol_for
->sol
.context
->op
->free(sol_for
->sol
.context
);
3989 static void sol_for_free_wrap(struct isl_sol
*sol
)
3991 sol_for_free((struct isl_sol_for
*)sol
);
3994 /* Add the solution identified by the tableau and the context tableau.
3996 * See documentation of sol_add for more details.
3998 * Instead of constructing a basic map, this function calls a user
3999 * defined function with the current context as a basic set and
4000 * an affine matrix reprenting the relation between the input and output.
4001 * The number of rows in this matrix is equal to one plus the number
4002 * of output variables. The number of columns is equal to one plus
4003 * the total dimension of the context, i.e., the number of parameters,
4004 * input variables and divs. Since some of the columns in the matrix
4005 * may refer to the divs, the basic set is not simplified.
4006 * (Simplification may reorder or remove divs.)
4008 static void sol_for_add(struct isl_sol_for
*sol
,
4009 struct isl_basic_set
*dom
, struct isl_mat
*M
)
4011 if (sol
->sol
.error
|| !dom
|| !M
)
4014 dom
= isl_basic_set_simplify(dom
);
4015 dom
= isl_basic_set_finalize(dom
);
4017 if (sol
->fn(isl_basic_set_copy(dom
), isl_mat_copy(M
), sol
->user
) < 0)
4020 isl_basic_set_free(dom
);
4024 isl_basic_set_free(dom
);
4029 static void sol_for_add_wrap(struct isl_sol
*sol
,
4030 struct isl_basic_set
*dom
, struct isl_mat
*M
)
4032 sol_for_add((struct isl_sol_for
*)sol
, dom
, M
);
4035 static struct isl_sol_for
*sol_for_init(struct isl_basic_map
*bmap
, int max
,
4036 int (*fn
)(__isl_take isl_basic_set
*dom
, __isl_take isl_mat
*map
,
4040 struct isl_sol_for
*sol_for
= NULL
;
4041 struct isl_dim
*dom_dim
;
4042 struct isl_basic_set
*dom
= NULL
;
4044 sol_for
= isl_calloc_type(bset
->ctx
, struct isl_sol_for
);
4048 dom_dim
= isl_dim_domain(isl_dim_copy(bmap
->dim
));
4049 dom
= isl_basic_set_universe(dom_dim
);
4051 sol_for
->sol
.rational
= ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
);
4052 sol_for
->sol
.dec_level
.callback
.run
= &sol_dec_level_wrap
;
4053 sol_for
->sol
.dec_level
.sol
= &sol_for
->sol
;
4055 sol_for
->user
= user
;
4056 sol_for
->sol
.max
= max
;
4057 sol_for
->sol
.n_out
= isl_basic_map_dim(bmap
, isl_dim_out
);
4058 sol_for
->sol
.add
= &sol_for_add_wrap
;
4059 sol_for
->sol
.add_empty
= NULL
;
4060 sol_for
->sol
.free
= &sol_for_free_wrap
;
4062 sol_for
->sol
.context
= isl_context_alloc(dom
);
4063 if (!sol_for
->sol
.context
)
4066 isl_basic_set_free(dom
);
4069 isl_basic_set_free(dom
);
4070 sol_for_free(sol_for
);
4074 static void sol_for_find_solutions(struct isl_sol_for
*sol_for
,
4075 struct isl_tab
*tab
)
4077 find_solutions_main(&sol_for
->sol
, tab
);
4080 int isl_basic_map_foreach_lexopt(__isl_keep isl_basic_map
*bmap
, int max
,
4081 int (*fn
)(__isl_take isl_basic_set
*dom
, __isl_take isl_mat
*map
,
4085 struct isl_sol_for
*sol_for
= NULL
;
4087 bmap
= isl_basic_map_copy(bmap
);
4091 bmap
= isl_basic_map_detect_equalities(bmap
);
4092 sol_for
= sol_for_init(bmap
, max
, fn
, user
);
4094 if (isl_basic_map_fast_is_empty(bmap
))
4097 struct isl_tab
*tab
;
4098 struct isl_context
*context
= sol_for
->sol
.context
;
4099 tab
= tab_for_lexmin(bmap
,
4100 context
->op
->peek_basic_set(context
), 1, max
);
4101 tab
= context
->op
->detect_nonnegative_parameters(context
, tab
);
4102 sol_for_find_solutions(sol_for
, tab
);
4103 if (sol_for
->sol
.error
)
4107 sol_free(&sol_for
->sol
);
4108 isl_basic_map_free(bmap
);
4111 sol_free(&sol_for
->sol
);
4112 isl_basic_map_free(bmap
);
4116 int isl_basic_map_foreach_lexmin(__isl_keep isl_basic_map
*bmap
,
4117 int (*fn
)(__isl_take isl_basic_set
*dom
, __isl_take isl_mat
*map
,
4121 return isl_basic_map_foreach_lexopt(bmap
, 0, fn
, user
);
4124 int isl_basic_map_foreach_lexmax(__isl_keep isl_basic_map
*bmap
,
4125 int (*fn
)(__isl_take isl_basic_set
*dom
, __isl_take isl_mat
*map
,
4129 return isl_basic_map_foreach_lexopt(bmap
, 1, fn
, user
);