2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2010 INRIA Saclay
4 * Copyright 2012-2013 Ecole Normale Superieure
5 * Copyright 2014 INRIA Rocquencourt
6 * Copyright 2016 INRIA Paris
8 * Use of this software is governed by the MIT license
10 * Written by Sven Verdoolaege, K.U.Leuven, Departement
11 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
12 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
13 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
14 * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
15 * and Inria Paris - Rocquencourt, Domaine de Voluceau - Rocquencourt,
16 * B.P. 105 - 78153 Le Chesnay, France
17 * and Centre de Recherche Inria de Paris, 2 rue Simone Iff - Voie DQ12,
18 * CS 42112, 75589 Paris Cedex 12, France
21 #include <isl_ctx_private.h>
22 #include "isl_map_private.h"
24 #include <isl/options.h>
26 #include <isl_mat_private.h>
27 #include <isl_local_space_private.h>
28 #include <isl_val_private.h>
29 #include <isl_vec_private.h>
30 #include <isl_aff_private.h>
31 #include <isl_equalities.h>
32 #include <isl_constraint_private.h>
34 #include <set_to_map.c>
35 #include <set_from_map.c>
37 #define STATUS_ERROR -1
38 #define STATUS_REDUNDANT 1
39 #define STATUS_VALID 2
40 #define STATUS_SEPARATE 3
42 #define STATUS_ADJ_EQ 5
43 #define STATUS_ADJ_INEQ 6
45 static int status_in(isl_int
*ineq
, struct isl_tab
*tab
)
47 enum isl_ineq_type type
= isl_tab_ineq_type(tab
, ineq
);
50 case isl_ineq_error
: return STATUS_ERROR
;
51 case isl_ineq_redundant
: return STATUS_VALID
;
52 case isl_ineq_separate
: return STATUS_SEPARATE
;
53 case isl_ineq_cut
: return STATUS_CUT
;
54 case isl_ineq_adj_eq
: return STATUS_ADJ_EQ
;
55 case isl_ineq_adj_ineq
: return STATUS_ADJ_INEQ
;
59 /* Compute the position of the equalities of basic map "bmap_i"
60 * with respect to the basic map represented by "tab_j".
61 * The resulting array has twice as many entries as the number
62 * of equalities corresponding to the two inequalities to which
63 * each equality corresponds.
65 static int *eq_status_in(__isl_keep isl_basic_map
*bmap_i
,
66 struct isl_tab
*tab_j
)
72 dim
= isl_basic_map_dim(bmap_i
, isl_dim_all
);
76 eq
= isl_calloc_array(bmap_i
->ctx
, int, 2 * bmap_i
->n_eq
);
80 for (k
= 0; k
< bmap_i
->n_eq
; ++k
) {
81 for (l
= 0; l
< 2; ++l
) {
82 isl_seq_neg(bmap_i
->eq
[k
], bmap_i
->eq
[k
], 1+dim
);
83 eq
[2 * k
+ l
] = status_in(bmap_i
->eq
[k
], tab_j
);
84 if (eq
[2 * k
+ l
] == STATUS_ERROR
)
95 /* Compute the position of the inequalities of basic map "bmap_i"
96 * (also represented by "tab_i", if not NULL) with respect to the basic map
97 * represented by "tab_j".
99 static int *ineq_status_in(__isl_keep isl_basic_map
*bmap_i
,
100 struct isl_tab
*tab_i
, struct isl_tab
*tab_j
)
103 unsigned n_eq
= bmap_i
->n_eq
;
104 int *ineq
= isl_calloc_array(bmap_i
->ctx
, int, bmap_i
->n_ineq
);
109 for (k
= 0; k
< bmap_i
->n_ineq
; ++k
) {
110 if (tab_i
&& isl_tab_is_redundant(tab_i
, n_eq
+ k
)) {
111 ineq
[k
] = STATUS_REDUNDANT
;
114 ineq
[k
] = status_in(bmap_i
->ineq
[k
], tab_j
);
115 if (ineq
[k
] == STATUS_ERROR
)
117 if (ineq
[k
] == STATUS_SEPARATE
)
127 static int any(int *con
, unsigned len
, int status
)
131 for (i
= 0; i
< len
; ++i
)
132 if (con
[i
] == status
)
137 /* Return the first position of "status" in the list "con" of length "len".
138 * Return -1 if there is no such entry.
140 static int find(int *con
, unsigned len
, int status
)
144 for (i
= 0; i
< len
; ++i
)
145 if (con
[i
] == status
)
150 static int count(int *con
, unsigned len
, int status
)
155 for (i
= 0; i
< len
; ++i
)
156 if (con
[i
] == status
)
161 static int all(int *con
, unsigned len
, int status
)
165 for (i
= 0; i
< len
; ++i
) {
166 if (con
[i
] == STATUS_REDUNDANT
)
168 if (con
[i
] != status
)
174 /* Internal information associated to a basic map in a map
175 * that is to be coalesced by isl_map_coalesce.
177 * "bmap" is the basic map itself (or NULL if "removed" is set)
178 * "tab" is the corresponding tableau (or NULL if "removed" is set)
179 * "hull_hash" identifies the affine space in which "bmap" lives.
180 * "modified" is set if this basic map may not be identical
181 * to any of the basic maps in the input.
182 * "removed" is set if this basic map has been removed from the map
183 * "simplify" is set if this basic map may have some unknown integer
184 * divisions that were not present in the input basic maps. The basic
185 * map should then be simplified such that we may be able to find
186 * a definition among the constraints.
188 * "eq" and "ineq" are only set if we are currently trying to coalesce
189 * this basic map with another basic map, in which case they represent
190 * the position of the inequalities of this basic map with respect to
191 * the other basic map. The number of elements in the "eq" array
192 * is twice the number of equalities in the "bmap", corresponding
193 * to the two inequalities that make up each equality.
195 struct isl_coalesce_info
{
206 /* Is there any (half of an) equality constraint in the description
207 * of the basic map represented by "info" that
208 * has position "status" with respect to the other basic map?
210 static int any_eq(struct isl_coalesce_info
*info
, int status
)
214 n_eq
= isl_basic_map_n_equality(info
->bmap
);
215 return any(info
->eq
, 2 * n_eq
, status
);
218 /* Is there any inequality constraint in the description
219 * of the basic map represented by "info" that
220 * has position "status" with respect to the other basic map?
222 static int any_ineq(struct isl_coalesce_info
*info
, int status
)
226 n_ineq
= isl_basic_map_n_inequality(info
->bmap
);
227 return any(info
->ineq
, n_ineq
, status
);
230 /* Return the position of the first half on an equality constraint
231 * in the description of the basic map represented by "info" that
232 * has position "status" with respect to the other basic map.
233 * The returned value is twice the position of the equality constraint
234 * plus zero for the negative half and plus one for the positive half.
235 * Return -1 if there is no such entry.
237 static int find_eq(struct isl_coalesce_info
*info
, int status
)
241 n_eq
= isl_basic_map_n_equality(info
->bmap
);
242 return find(info
->eq
, 2 * n_eq
, status
);
245 /* Return the position of the first inequality constraint in the description
246 * of the basic map represented by "info" that
247 * has position "status" with respect to the other basic map.
248 * Return -1 if there is no such entry.
250 static int find_ineq(struct isl_coalesce_info
*info
, int status
)
254 n_ineq
= isl_basic_map_n_inequality(info
->bmap
);
255 return find(info
->ineq
, n_ineq
, status
);
258 /* Return the number of (halves of) equality constraints in the description
259 * of the basic map represented by "info" that
260 * have position "status" with respect to the other basic map.
262 static int count_eq(struct isl_coalesce_info
*info
, int status
)
266 n_eq
= isl_basic_map_n_equality(info
->bmap
);
267 return count(info
->eq
, 2 * n_eq
, status
);
270 /* Return the number of inequality constraints in the description
271 * of the basic map represented by "info" that
272 * have position "status" with respect to the other basic map.
274 static int count_ineq(struct isl_coalesce_info
*info
, int status
)
278 n_ineq
= isl_basic_map_n_inequality(info
->bmap
);
279 return count(info
->ineq
, n_ineq
, status
);
282 /* Are all non-redundant constraints of the basic map represented by "info"
283 * either valid or cut constraints with respect to the other basic map?
285 static int all_valid_or_cut(struct isl_coalesce_info
*info
)
289 for (i
= 0; i
< 2 * info
->bmap
->n_eq
; ++i
) {
290 if (info
->eq
[i
] == STATUS_REDUNDANT
)
292 if (info
->eq
[i
] == STATUS_VALID
)
294 if (info
->eq
[i
] == STATUS_CUT
)
299 for (i
= 0; i
< info
->bmap
->n_ineq
; ++i
) {
300 if (info
->ineq
[i
] == STATUS_REDUNDANT
)
302 if (info
->ineq
[i
] == STATUS_VALID
)
304 if (info
->ineq
[i
] == STATUS_CUT
)
312 /* Compute the hash of the (apparent) affine hull of info->bmap (with
313 * the existentially quantified variables removed) and store it
316 static int coalesce_info_set_hull_hash(struct isl_coalesce_info
*info
)
321 hull
= isl_basic_map_copy(info
->bmap
);
322 hull
= isl_basic_map_plain_affine_hull(hull
);
323 n_div
= isl_basic_map_dim(hull
, isl_dim_div
);
325 hull
= isl_basic_map_free(hull
);
326 hull
= isl_basic_map_drop_constraints_involving_dims(hull
,
327 isl_dim_div
, 0, n_div
);
328 info
->hull_hash
= isl_basic_map_get_hash(hull
);
329 isl_basic_map_free(hull
);
331 return hull
? 0 : -1;
334 /* Free all the allocated memory in an array
335 * of "n" isl_coalesce_info elements.
337 static void clear_coalesce_info(int n
, struct isl_coalesce_info
*info
)
344 for (i
= 0; i
< n
; ++i
) {
345 isl_basic_map_free(info
[i
].bmap
);
346 isl_tab_free(info
[i
].tab
);
352 /* Clear the memory associated to "info".
354 static void clear(struct isl_coalesce_info
*info
)
356 info
->bmap
= isl_basic_map_free(info
->bmap
);
357 isl_tab_free(info
->tab
);
361 /* Drop the basic map represented by "info".
362 * That is, clear the memory associated to the entry and
363 * mark it as having been removed.
365 static void drop(struct isl_coalesce_info
*info
)
371 /* Exchange the information in "info1" with that in "info2".
373 static void exchange(struct isl_coalesce_info
*info1
,
374 struct isl_coalesce_info
*info2
)
376 struct isl_coalesce_info info
;
383 /* This type represents the kind of change that has been performed
384 * while trying to coalesce two basic maps.
386 * isl_change_none: nothing was changed
387 * isl_change_drop_first: the first basic map was removed
388 * isl_change_drop_second: the second basic map was removed
389 * isl_change_fuse: the two basic maps were replaced by a new basic map.
392 isl_change_error
= -1,
394 isl_change_drop_first
,
395 isl_change_drop_second
,
399 /* Update "change" based on an interchange of the first and the second
400 * basic map. That is, interchange isl_change_drop_first and
401 * isl_change_drop_second.
403 static enum isl_change
invert_change(enum isl_change change
)
406 case isl_change_error
:
407 return isl_change_error
;
408 case isl_change_none
:
409 return isl_change_none
;
410 case isl_change_drop_first
:
411 return isl_change_drop_second
;
412 case isl_change_drop_second
:
413 return isl_change_drop_first
;
414 case isl_change_fuse
:
415 return isl_change_fuse
;
418 return isl_change_error
;
421 /* Add the valid constraints of the basic map represented by "info"
422 * to "bmap". "len" is the size of the constraints.
423 * If only one of the pair of inequalities that make up an equality
424 * is valid, then add that inequality.
426 static __isl_give isl_basic_map
*add_valid_constraints(
427 __isl_take isl_basic_map
*bmap
, struct isl_coalesce_info
*info
,
435 for (k
= 0; k
< info
->bmap
->n_eq
; ++k
) {
436 if (info
->eq
[2 * k
] == STATUS_VALID
&&
437 info
->eq
[2 * k
+ 1] == STATUS_VALID
) {
438 l
= isl_basic_map_alloc_equality(bmap
);
440 return isl_basic_map_free(bmap
);
441 isl_seq_cpy(bmap
->eq
[l
], info
->bmap
->eq
[k
], len
);
442 } else if (info
->eq
[2 * k
] == STATUS_VALID
) {
443 l
= isl_basic_map_alloc_inequality(bmap
);
445 return isl_basic_map_free(bmap
);
446 isl_seq_neg(bmap
->ineq
[l
], info
->bmap
->eq
[k
], len
);
447 } else if (info
->eq
[2 * k
+ 1] == STATUS_VALID
) {
448 l
= isl_basic_map_alloc_inequality(bmap
);
450 return isl_basic_map_free(bmap
);
451 isl_seq_cpy(bmap
->ineq
[l
], info
->bmap
->eq
[k
], len
);
455 for (k
= 0; k
< info
->bmap
->n_ineq
; ++k
) {
456 if (info
->ineq
[k
] != STATUS_VALID
)
458 l
= isl_basic_map_alloc_inequality(bmap
);
460 return isl_basic_map_free(bmap
);
461 isl_seq_cpy(bmap
->ineq
[l
], info
->bmap
->ineq
[k
], len
);
467 /* Is "bmap" defined by a number of (non-redundant) constraints that
468 * is greater than the number of constraints of basic maps i and j combined?
469 * Equalities are counted as two inequalities.
471 static int number_of_constraints_increases(int i
, int j
,
472 struct isl_coalesce_info
*info
,
473 __isl_keep isl_basic_map
*bmap
, struct isl_tab
*tab
)
477 n_old
= 2 * info
[i
].bmap
->n_eq
+ info
[i
].bmap
->n_ineq
;
478 n_old
+= 2 * info
[j
].bmap
->n_eq
+ info
[j
].bmap
->n_ineq
;
480 n_new
= 2 * bmap
->n_eq
;
481 for (k
= 0; k
< bmap
->n_ineq
; ++k
)
482 if (!isl_tab_is_redundant(tab
, bmap
->n_eq
+ k
))
485 return n_new
> n_old
;
488 /* Replace the pair of basic maps i and j by the basic map bounded
489 * by the valid constraints in both basic maps and the constraints
490 * in extra (if not NULL).
491 * Place the fused basic map in the position that is the smallest of i and j.
493 * If "detect_equalities" is set, then look for equalities encoded
494 * as pairs of inequalities.
495 * If "check_number" is set, then the original basic maps are only
496 * replaced if the total number of constraints does not increase.
497 * While the number of integer divisions in the two basic maps
498 * is assumed to be the same, the actual definitions may be different.
499 * We only copy the definition from one of the basic map if it is
500 * the same as that of the other basic map. Otherwise, we mark
501 * the integer division as unknown and simplify the basic map
502 * in an attempt to recover the integer division definition.
503 * If any extra constraints get introduced, then these may
504 * involve integer divisions with a unit coefficient.
505 * Eliminate those that do not appear with any other coefficient
506 * in other constraints, to ensure they get eliminated completely,
507 * improving the chances of further coalescing.
509 static enum isl_change
fuse(int i
, int j
, struct isl_coalesce_info
*info
,
510 __isl_keep isl_mat
*extra
, int detect_equalities
, int check_number
)
513 struct isl_basic_map
*fused
= NULL
;
514 struct isl_tab
*fused_tab
= NULL
;
515 isl_size total
= isl_basic_map_dim(info
[i
].bmap
, isl_dim_all
);
516 unsigned extra_rows
= extra
? extra
->n_row
: 0;
517 unsigned n_eq
, n_ineq
;
521 return isl_change_error
;
523 return fuse(j
, i
, info
, extra
, detect_equalities
, check_number
);
525 n_eq
= info
[i
].bmap
->n_eq
+ info
[j
].bmap
->n_eq
;
526 n_ineq
= info
[i
].bmap
->n_ineq
+ info
[j
].bmap
->n_ineq
;
527 fused
= isl_basic_map_alloc_space(isl_space_copy(info
[i
].bmap
->dim
),
528 info
[i
].bmap
->n_div
, n_eq
, n_eq
+ n_ineq
+ extra_rows
);
529 fused
= add_valid_constraints(fused
, &info
[i
], 1 + total
);
530 fused
= add_valid_constraints(fused
, &info
[j
], 1 + total
);
533 if (ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_RATIONAL
) &&
534 ISL_F_ISSET(info
[j
].bmap
, ISL_BASIC_MAP_RATIONAL
))
535 ISL_F_SET(fused
, ISL_BASIC_MAP_RATIONAL
);
537 for (k
= 0; k
< info
[i
].bmap
->n_div
; ++k
) {
538 int l
= isl_basic_map_alloc_div(fused
);
541 if (isl_seq_eq(info
[i
].bmap
->div
[k
], info
[j
].bmap
->div
[k
],
543 isl_seq_cpy(fused
->div
[l
], info
[i
].bmap
->div
[k
],
546 isl_int_set_si(fused
->div
[l
][0], 0);
551 for (k
= 0; k
< extra_rows
; ++k
) {
552 l
= isl_basic_map_alloc_inequality(fused
);
555 isl_seq_cpy(fused
->ineq
[l
], extra
->row
[k
], 1 + total
);
558 if (detect_equalities
)
559 fused
= isl_basic_map_detect_inequality_pairs(fused
, NULL
);
560 fused
= isl_basic_map_gauss(fused
, NULL
);
561 if (simplify
|| info
[j
].simplify
) {
562 fused
= isl_basic_map_simplify(fused
);
563 info
[i
].simplify
= 0;
564 } else if (extra_rows
> 0) {
565 fused
= isl_basic_map_eliminate_pure_unit_divs(fused
);
567 fused
= isl_basic_map_finalize(fused
);
569 fused_tab
= isl_tab_from_basic_map(fused
, 0);
570 if (isl_tab_detect_redundant(fused_tab
) < 0)
574 number_of_constraints_increases(i
, j
, info
, fused
, fused_tab
)) {
575 isl_tab_free(fused_tab
);
576 isl_basic_map_free(fused
);
577 return isl_change_none
;
581 info
[i
].bmap
= fused
;
582 info
[i
].tab
= fused_tab
;
583 info
[i
].modified
= 1;
586 return isl_change_fuse
;
588 isl_tab_free(fused_tab
);
589 isl_basic_map_free(fused
);
590 return isl_change_error
;
593 /* Given a pair of basic maps i and j such that all constraints are either
594 * "valid" or "cut", check if the facets corresponding to the "cut"
595 * constraints of i lie entirely within basic map j.
596 * If so, replace the pair by the basic map consisting of the valid
597 * constraints in both basic maps.
598 * Checking whether the facet lies entirely within basic map j
599 * is performed by checking whether the constraints of basic map j
600 * are valid for the facet. These tests are performed on a rational
601 * tableau to avoid the theoretical possibility that a constraint
602 * that was considered to be a cut constraint for the entire basic map i
603 * happens to be considered to be a valid constraint for the facet,
604 * even though it cuts off the same rational points.
606 * To see that we are not introducing any extra points, call the
607 * two basic maps A and B and the resulting map U and let x
608 * be an element of U \setminus ( A \cup B ).
609 * A line connecting x with an element of A \cup B meets a facet F
610 * of either A or B. Assume it is a facet of B and let c_1 be
611 * the corresponding facet constraint. We have c_1(x) < 0 and
612 * so c_1 is a cut constraint. This implies that there is some
613 * (possibly rational) point x' satisfying the constraints of A
614 * and the opposite of c_1 as otherwise c_1 would have been marked
615 * valid for A. The line connecting x and x' meets a facet of A
616 * in a (possibly rational) point that also violates c_1, but this
617 * is impossible since all cut constraints of B are valid for all
619 * In case F is a facet of A rather than B, then we can apply the
620 * above reasoning to find a facet of B separating x from A \cup B first.
622 static enum isl_change
check_facets(int i
, int j
,
623 struct isl_coalesce_info
*info
)
626 struct isl_tab_undo
*snap
, *snap2
;
627 unsigned n_eq
= info
[i
].bmap
->n_eq
;
629 snap
= isl_tab_snap(info
[i
].tab
);
630 if (isl_tab_mark_rational(info
[i
].tab
) < 0)
631 return isl_change_error
;
632 snap2
= isl_tab_snap(info
[i
].tab
);
634 for (k
= 0; k
< info
[i
].bmap
->n_ineq
; ++k
) {
635 if (info
[i
].ineq
[k
] != STATUS_CUT
)
637 if (isl_tab_select_facet(info
[i
].tab
, n_eq
+ k
) < 0)
638 return isl_change_error
;
639 for (l
= 0; l
< info
[j
].bmap
->n_ineq
; ++l
) {
641 if (info
[j
].ineq
[l
] != STATUS_CUT
)
643 stat
= status_in(info
[j
].bmap
->ineq
[l
], info
[i
].tab
);
645 return isl_change_error
;
646 if (stat
!= STATUS_VALID
)
649 if (isl_tab_rollback(info
[i
].tab
, snap2
) < 0)
650 return isl_change_error
;
651 if (l
< info
[j
].bmap
->n_ineq
)
655 if (k
< info
[i
].bmap
->n_ineq
) {
656 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
657 return isl_change_error
;
658 return isl_change_none
;
660 return fuse(i
, j
, info
, NULL
, 0, 0);
663 /* Check if info->bmap contains the basic map represented
664 * by the tableau "tab".
665 * For each equality, we check both the constraint itself
666 * (as an inequality) and its negation. Make sure the
667 * equality is returned to its original state before returning.
669 static isl_bool
contains(struct isl_coalesce_info
*info
, struct isl_tab
*tab
)
673 isl_basic_map
*bmap
= info
->bmap
;
675 dim
= isl_basic_map_dim(bmap
, isl_dim_all
);
677 return isl_bool_error
;
678 for (k
= 0; k
< bmap
->n_eq
; ++k
) {
680 isl_seq_neg(bmap
->eq
[k
], bmap
->eq
[k
], 1 + dim
);
681 stat
= status_in(bmap
->eq
[k
], tab
);
682 isl_seq_neg(bmap
->eq
[k
], bmap
->eq
[k
], 1 + dim
);
684 return isl_bool_error
;
685 if (stat
!= STATUS_VALID
)
686 return isl_bool_false
;
687 stat
= status_in(bmap
->eq
[k
], tab
);
689 return isl_bool_error
;
690 if (stat
!= STATUS_VALID
)
691 return isl_bool_false
;
694 for (k
= 0; k
< bmap
->n_ineq
; ++k
) {
696 if (info
->ineq
[k
] == STATUS_REDUNDANT
)
698 stat
= status_in(bmap
->ineq
[k
], tab
);
700 return isl_bool_error
;
701 if (stat
!= STATUS_VALID
)
702 return isl_bool_false
;
704 return isl_bool_true
;
707 /* Basic map "i" has an inequality (say "k") that is adjacent
708 * to some inequality of basic map "j". All the other inequalities
710 * Check if basic map "j" forms an extension of basic map "i".
712 * Note that this function is only called if some of the equalities or
713 * inequalities of basic map "j" do cut basic map "i". The function is
714 * correct even if there are no such cut constraints, but in that case
715 * the additional checks performed by this function are overkill.
717 * In particular, we replace constraint k, say f >= 0, by constraint
718 * f <= -1, add the inequalities of "j" that are valid for "i"
719 * and check if the result is a subset of basic map "j".
720 * To improve the chances of the subset relation being detected,
721 * any variable that only attains a single integer value
722 * in the tableau of "i" is first fixed to that value.
723 * If the result is a subset, then we know that this result is exactly equal
724 * to basic map "j" since all its constraints are valid for basic map "j".
725 * By combining the valid constraints of "i" (all equalities and all
726 * inequalities except "k") and the valid constraints of "j" we therefore
727 * obtain a basic map that is equal to their union.
728 * In this case, there is no need to perform a rollback of the tableau
729 * since it is going to be destroyed in fuse().
735 * |_______| _ |_________\
747 static enum isl_change
is_adj_ineq_extension(int i
, int j
,
748 struct isl_coalesce_info
*info
)
751 struct isl_tab_undo
*snap
;
752 unsigned n_eq
= info
[i
].bmap
->n_eq
;
753 isl_size total
= isl_basic_map_dim(info
[i
].bmap
, isl_dim_all
);
758 return isl_change_error
;
759 if (isl_tab_extend_cons(info
[i
].tab
, 1 + info
[j
].bmap
->n_ineq
) < 0)
760 return isl_change_error
;
762 k
= find_ineq(&info
[i
], STATUS_ADJ_INEQ
);
764 isl_die(isl_basic_map_get_ctx(info
[i
].bmap
), isl_error_internal
,
765 "info[i].ineq should have exactly one STATUS_ADJ_INEQ",
766 return isl_change_error
);
768 snap
= isl_tab_snap(info
[i
].tab
);
770 if (isl_tab_unrestrict(info
[i
].tab
, n_eq
+ k
) < 0)
771 return isl_change_error
;
773 isl_seq_neg(info
[i
].bmap
->ineq
[k
], info
[i
].bmap
->ineq
[k
], 1 + total
);
774 isl_int_sub_ui(info
[i
].bmap
->ineq
[k
][0], info
[i
].bmap
->ineq
[k
][0], 1);
775 r
= isl_tab_add_ineq(info
[i
].tab
, info
[i
].bmap
->ineq
[k
]);
776 isl_seq_neg(info
[i
].bmap
->ineq
[k
], info
[i
].bmap
->ineq
[k
], 1 + total
);
777 isl_int_sub_ui(info
[i
].bmap
->ineq
[k
][0], info
[i
].bmap
->ineq
[k
][0], 1);
779 return isl_change_error
;
781 for (k
= 0; k
< info
[j
].bmap
->n_ineq
; ++k
) {
782 if (info
[j
].ineq
[k
] != STATUS_VALID
)
784 if (isl_tab_add_ineq(info
[i
].tab
, info
[j
].bmap
->ineq
[k
]) < 0)
785 return isl_change_error
;
787 if (isl_tab_detect_constants(info
[i
].tab
) < 0)
788 return isl_change_error
;
790 super
= contains(&info
[j
], info
[i
].tab
);
792 return isl_change_error
;
794 return fuse(i
, j
, info
, NULL
, 0, 0);
796 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
797 return isl_change_error
;
799 return isl_change_none
;
803 /* Both basic maps have at least one inequality with and adjacent
804 * (but opposite) inequality in the other basic map.
805 * Check that there are no cut constraints and that there is only
806 * a single pair of adjacent inequalities.
807 * If so, we can replace the pair by a single basic map described
808 * by all but the pair of adjacent inequalities.
809 * Any additional points introduced lie strictly between the two
810 * adjacent hyperplanes and can therefore be integral.
819 * The test for a single pair of adjancent inequalities is important
820 * for avoiding the combination of two basic maps like the following
830 * If there are some cut constraints on one side, then we may
831 * still be able to fuse the two basic maps, but we need to perform
832 * some additional checks in is_adj_ineq_extension.
834 static enum isl_change
check_adj_ineq(int i
, int j
,
835 struct isl_coalesce_info
*info
)
837 int count_i
, count_j
;
840 count_i
= count_ineq(&info
[i
], STATUS_ADJ_INEQ
);
841 count_j
= count_ineq(&info
[j
], STATUS_ADJ_INEQ
);
843 if (count_i
!= 1 && count_j
!= 1)
844 return isl_change_none
;
846 cut_i
= any_eq(&info
[i
], STATUS_CUT
) || any_ineq(&info
[i
], STATUS_CUT
);
847 cut_j
= any_eq(&info
[j
], STATUS_CUT
) || any_ineq(&info
[j
], STATUS_CUT
);
849 if (!cut_i
&& !cut_j
&& count_i
== 1 && count_j
== 1)
850 return fuse(i
, j
, info
, NULL
, 0, 0);
852 if (count_i
== 1 && !cut_i
)
853 return is_adj_ineq_extension(i
, j
, info
);
855 if (count_j
== 1 && !cut_j
)
856 return is_adj_ineq_extension(j
, i
, info
);
858 return isl_change_none
;
861 /* Given an affine transformation matrix "T", does row "row" represent
862 * anything other than a unit vector (possibly shifted by a constant)
863 * that is not involved in any of the other rows?
865 * That is, if a constraint involves the variable corresponding to
866 * the row, then could its preimage by "T" have any coefficients
867 * that are different from those in the original constraint?
869 static int not_unique_unit_row(__isl_keep isl_mat
*T
, int row
)
872 int len
= T
->n_col
- 1;
874 i
= isl_seq_first_non_zero(T
->row
[row
] + 1, len
);
877 if (!isl_int_is_one(T
->row
[row
][1 + i
]) &&
878 !isl_int_is_negone(T
->row
[row
][1 + i
]))
881 j
= isl_seq_first_non_zero(T
->row
[row
] + 1 + i
+ 1, len
- (i
+ 1));
885 for (j
= 1; j
< T
->n_row
; ++j
) {
888 if (!isl_int_is_zero(T
->row
[j
][1 + i
]))
895 /* Does inequality constraint "ineq" of "bmap" involve any of
896 * the variables marked in "affected"?
897 * "total" is the total number of variables, i.e., the number
898 * of entries in "affected".
900 static isl_bool
is_affected(__isl_keep isl_basic_map
*bmap
, int ineq
,
901 int *affected
, int total
)
905 for (i
= 0; i
< total
; ++i
) {
908 if (!isl_int_is_zero(bmap
->ineq
[ineq
][1 + i
]))
909 return isl_bool_true
;
912 return isl_bool_false
;
915 /* Given the compressed version of inequality constraint "ineq"
916 * of info->bmap in "v", check if the constraint can be tightened,
917 * where the compression is based on an equality constraint valid
919 * If so, add the tightened version of the inequality constraint
920 * to info->tab. "v" may be modified by this function.
922 * That is, if the compressed constraint is of the form
926 * with 0 < c < m, then it is equivalent to
930 * This means that c can also be subtracted from the original,
931 * uncompressed constraint without affecting the integer points
932 * in info->tab. Add this tightened constraint as an extra row
933 * to info->tab to make this information explicitly available.
935 static __isl_give isl_vec
*try_tightening(struct isl_coalesce_info
*info
,
936 int ineq
, __isl_take isl_vec
*v
)
944 ctx
= isl_vec_get_ctx(v
);
945 isl_seq_gcd(v
->el
+ 1, v
->size
- 1, &ctx
->normalize_gcd
);
946 if (isl_int_is_zero(ctx
->normalize_gcd
) ||
947 isl_int_is_one(ctx
->normalize_gcd
)) {
955 isl_int_fdiv_r(v
->el
[0], v
->el
[0], ctx
->normalize_gcd
);
956 if (isl_int_is_zero(v
->el
[0]))
959 if (isl_tab_extend_cons(info
->tab
, 1) < 0)
960 return isl_vec_free(v
);
962 isl_int_sub(info
->bmap
->ineq
[ineq
][0],
963 info
->bmap
->ineq
[ineq
][0], v
->el
[0]);
964 r
= isl_tab_add_ineq(info
->tab
, info
->bmap
->ineq
[ineq
]);
965 isl_int_add(info
->bmap
->ineq
[ineq
][0],
966 info
->bmap
->ineq
[ineq
][0], v
->el
[0]);
969 return isl_vec_free(v
);
974 /* Tighten the (non-redundant) constraints on the facet represented
976 * In particular, on input, info->tab represents the result
977 * of relaxing the "n" inequality constraints of info->bmap in "relaxed"
978 * by one, i.e., replacing f_i >= 0 by f_i + 1 >= 0, and then
979 * replacing the one at index "l" by the corresponding equality,
980 * i.e., f_k + 1 = 0, with k = relaxed[l].
982 * Compute a variable compression from the equality constraint f_k + 1 = 0
983 * and use it to tighten the other constraints of info->bmap
984 * (that is, all constraints that have not been relaxed),
985 * updating info->tab (and leaving info->bmap untouched).
986 * The compression handles essentially two cases, one where a variable
987 * is assigned a fixed value and can therefore be eliminated, and one
988 * where one variable is a shifted multiple of some other variable and
989 * can therefore be replaced by that multiple.
990 * Gaussian elimination would also work for the first case, but for
991 * the second case, the effectiveness would depend on the order
993 * After compression, some of the constraints may have coefficients
994 * with a common divisor. If this divisor does not divide the constant
995 * term, then the constraint can be tightened.
996 * The tightening is performed on the tableau info->tab by introducing
997 * extra (temporary) constraints.
999 * Only constraints that are possibly affected by the compression are
1000 * considered. In particular, if the constraint only involves variables
1001 * that are directly mapped to a distinct set of other variables, then
1002 * no common divisor can be introduced and no tightening can occur.
1004 * It is important to only consider the non-redundant constraints
1005 * since the facet constraint has been relaxed prior to the call
1006 * to this function, meaning that the constraints that were redundant
1007 * prior to the relaxation may no longer be redundant.
1008 * These constraints will be ignored in the fused result, so
1009 * the fusion detection should not exploit them.
1011 static isl_stat
tighten_on_relaxed_facet(struct isl_coalesce_info
*info
,
1012 int n
, int *relaxed
, int l
)
1023 ctx
= isl_basic_map_get_ctx(info
->bmap
);
1024 total
= isl_basic_map_dim(info
->bmap
, isl_dim_all
);
1026 return isl_stat_error
;
1027 isl_int_add_ui(info
->bmap
->ineq
[k
][0], info
->bmap
->ineq
[k
][0], 1);
1028 T
= isl_mat_sub_alloc6(ctx
, info
->bmap
->ineq
, k
, 1, 0, 1 + total
);
1029 T
= isl_mat_variable_compression(T
, NULL
);
1030 isl_int_sub_ui(info
->bmap
->ineq
[k
][0], info
->bmap
->ineq
[k
][0], 1);
1032 return isl_stat_error
;
1033 if (T
->n_col
== 0) {
1038 affected
= isl_alloc_array(ctx
, int, total
);
1042 for (i
= 0; i
< total
; ++i
)
1043 affected
[i
] = not_unique_unit_row(T
, 1 + i
);
1045 for (i
= 0; i
< info
->bmap
->n_ineq
; ++i
) {
1047 if (any(relaxed
, n
, i
))
1049 if (info
->ineq
[i
] == STATUS_REDUNDANT
)
1051 handle
= is_affected(info
->bmap
, i
, affected
, total
);
1056 v
= isl_vec_alloc(ctx
, 1 + total
);
1059 isl_seq_cpy(v
->el
, info
->bmap
->ineq
[i
], 1 + total
);
1060 v
= isl_vec_mat_product(v
, isl_mat_copy(T
));
1061 v
= try_tightening(info
, i
, v
);
1073 return isl_stat_error
;
1076 /* Replace the basic maps "i" and "j" by an extension of "i"
1077 * along the "n" inequality constraints in "relax" by one.
1078 * The tableau info[i].tab has already been extended.
1079 * Extend info[i].bmap accordingly by relaxing all constraints in "relax"
1081 * Each integer division that does not have exactly the same
1082 * definition in "i" and "j" is marked unknown and the basic map
1083 * is scheduled to be simplified in an attempt to recover
1084 * the integer division definition.
1085 * Place the extension in the position that is the smallest of i and j.
1087 static enum isl_change
extend(int i
, int j
, int n
, int *relax
,
1088 struct isl_coalesce_info
*info
)
1093 info
[i
].bmap
= isl_basic_map_cow(info
[i
].bmap
);
1094 total
= isl_basic_map_dim(info
[i
].bmap
, isl_dim_all
);
1096 return isl_change_error
;
1097 for (l
= 0; l
< info
[i
].bmap
->n_div
; ++l
)
1098 if (!isl_seq_eq(info
[i
].bmap
->div
[l
],
1099 info
[j
].bmap
->div
[l
], 1 + 1 + total
)) {
1100 isl_int_set_si(info
[i
].bmap
->div
[l
][0], 0);
1101 info
[i
].simplify
= 1;
1103 for (l
= 0; l
< n
; ++l
)
1104 isl_int_add_ui(info
[i
].bmap
->ineq
[relax
[l
]][0],
1105 info
[i
].bmap
->ineq
[relax
[l
]][0], 1);
1106 ISL_F_CLR(info
[i
].bmap
, ISL_BASIC_MAP_NO_REDUNDANT
);
1107 ISL_F_SET(info
[i
].bmap
, ISL_BASIC_MAP_FINAL
);
1109 info
[i
].modified
= 1;
1111 exchange(&info
[i
], &info
[j
]);
1112 return isl_change_fuse
;
1115 /* Basic map "i" has "n" inequality constraints (collected in "relax")
1116 * that are such that they include basic map "j" if they are relaxed
1117 * by one. All the other inequalities are valid for "j".
1118 * Check if basic map "j" forms an extension of basic map "i".
1120 * In particular, relax the constraints in "relax", compute the corresponding
1121 * facets one by one and check whether each of these is included
1122 * in the other basic map.
1123 * Before testing for inclusion, the constraints on each facet
1124 * are tightened to increase the chance of an inclusion being detected.
1125 * (Adding the valid constraints of "j" to the tableau of "i", as is done
1126 * in is_adj_ineq_extension, may further increase those chances, but this
1127 * is not currently done.)
1128 * If each facet is included, we know that relaxing the constraints extends
1129 * the basic map with exactly the other basic map (we already know that this
1130 * other basic map is included in the extension, because all other
1131 * inequality constraints are valid of "j") and we can replace the
1132 * two basic maps by this extension.
1134 * If any of the relaxed constraints turn out to be redundant, then bail out.
1135 * isl_tab_select_facet refuses to handle such constraints. It may be
1136 * possible to handle them anyway by making a distinction between
1137 * redundant constraints with a corresponding facet that still intersects
1138 * the set (allowing isl_tab_select_facet to handle them) and
1139 * those where the facet does not intersect the set (which can be ignored
1140 * because the empty facet is trivially included in the other disjunct).
1141 * However, relaxed constraints that turn out to be redundant should
1142 * be fairly rare and no such instance has been reported where
1143 * coalescing would be successful.
1159 static enum isl_change
is_relaxed_extension(int i
, int j
, int n
, int *relax
,
1160 struct isl_coalesce_info
*info
)
1164 struct isl_tab_undo
*snap
, *snap2
;
1165 unsigned n_eq
= info
[i
].bmap
->n_eq
;
1167 for (l
= 0; l
< n
; ++l
)
1168 if (isl_tab_is_equality(info
[i
].tab
, n_eq
+ relax
[l
]))
1169 return isl_change_none
;
1171 snap
= isl_tab_snap(info
[i
].tab
);
1172 for (l
= 0; l
< n
; ++l
)
1173 if (isl_tab_relax(info
[i
].tab
, n_eq
+ relax
[l
]) < 0)
1174 return isl_change_error
;
1175 for (l
= 0; l
< n
; ++l
) {
1176 if (!isl_tab_is_redundant(info
[i
].tab
, n_eq
+ relax
[l
]))
1178 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
1179 return isl_change_error
;
1180 return isl_change_none
;
1182 snap2
= isl_tab_snap(info
[i
].tab
);
1183 for (l
= 0; l
< n
; ++l
) {
1184 if (isl_tab_rollback(info
[i
].tab
, snap2
) < 0)
1185 return isl_change_error
;
1186 if (isl_tab_select_facet(info
[i
].tab
, n_eq
+ relax
[l
]) < 0)
1187 return isl_change_error
;
1188 if (tighten_on_relaxed_facet(&info
[i
], n
, relax
, l
) < 0)
1189 return isl_change_error
;
1190 super
= contains(&info
[j
], info
[i
].tab
);
1192 return isl_change_error
;
1195 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
1196 return isl_change_error
;
1197 return isl_change_none
;
1200 if (isl_tab_rollback(info
[i
].tab
, snap2
) < 0)
1201 return isl_change_error
;
1202 return extend(i
, j
, n
, relax
, info
);
1205 /* Data structure that keeps track of the wrapping constraints
1206 * and of information to bound the coefficients of those constraints.
1208 * bound is set if we want to apply a bound on the coefficients
1209 * mat contains the wrapping constraints
1210 * max is the bound on the coefficients (if bound is set)
1218 /* Update wraps->max to be greater than or equal to the coefficients
1219 * in the equalities and inequalities of info->bmap that can be removed
1220 * if we end up applying wrapping.
1222 static isl_stat
wraps_update_max(struct isl_wraps
*wraps
,
1223 struct isl_coalesce_info
*info
)
1227 isl_size total
= isl_basic_map_dim(info
->bmap
, isl_dim_all
);
1230 return isl_stat_error
;
1231 isl_int_init(max_k
);
1233 for (k
= 0; k
< info
->bmap
->n_eq
; ++k
) {
1234 if (info
->eq
[2 * k
] == STATUS_VALID
&&
1235 info
->eq
[2 * k
+ 1] == STATUS_VALID
)
1237 isl_seq_abs_max(info
->bmap
->eq
[k
] + 1, total
, &max_k
);
1238 if (isl_int_abs_gt(max_k
, wraps
->max
))
1239 isl_int_set(wraps
->max
, max_k
);
1242 for (k
= 0; k
< info
->bmap
->n_ineq
; ++k
) {
1243 if (info
->ineq
[k
] == STATUS_VALID
||
1244 info
->ineq
[k
] == STATUS_REDUNDANT
)
1246 isl_seq_abs_max(info
->bmap
->ineq
[k
] + 1, total
, &max_k
);
1247 if (isl_int_abs_gt(max_k
, wraps
->max
))
1248 isl_int_set(wraps
->max
, max_k
);
1251 isl_int_clear(max_k
);
1256 /* Initialize the isl_wraps data structure.
1257 * If we want to bound the coefficients of the wrapping constraints,
1258 * we set wraps->max to the largest coefficient
1259 * in the equalities and inequalities that can be removed if we end up
1260 * applying wrapping.
1262 static isl_stat
wraps_init(struct isl_wraps
*wraps
, __isl_take isl_mat
*mat
,
1263 struct isl_coalesce_info
*info
, int i
, int j
)
1270 return isl_stat_error
;
1271 ctx
= isl_mat_get_ctx(mat
);
1272 wraps
->bound
= isl_options_get_coalesce_bounded_wrapping(ctx
);
1275 isl_int_init(wraps
->max
);
1276 isl_int_set_si(wraps
->max
, 0);
1277 if (wraps_update_max(wraps
, &info
[i
]) < 0)
1278 return isl_stat_error
;
1279 if (wraps_update_max(wraps
, &info
[j
]) < 0)
1280 return isl_stat_error
;
1285 /* Free the contents of the isl_wraps data structure.
1287 static void wraps_free(struct isl_wraps
*wraps
)
1289 isl_mat_free(wraps
->mat
);
1291 isl_int_clear(wraps
->max
);
1294 /* Mark the wrapping as failed by resetting wraps->mat->n_row to zero.
1296 static isl_stat
wraps_mark_failed(struct isl_wraps
*wraps
)
1298 wraps
->mat
->n_row
= 0;
1302 /* Is the wrapping constraint in row "row" allowed?
1304 * If wraps->bound is set, we check that none of the coefficients
1305 * is greater than wraps->max.
1307 static int allow_wrap(struct isl_wraps
*wraps
, int row
)
1314 for (i
= 1; i
< wraps
->mat
->n_col
; ++i
)
1315 if (isl_int_abs_gt(wraps
->mat
->row
[row
][i
], wraps
->max
))
1321 /* Wrap "ineq" (or its opposite if "negate" is set) around "bound"
1322 * to include "set" and add the result in position "w" of "wraps".
1323 * "len" is the total number of coefficients in "bound" and "ineq".
1324 * Return 1 on success, 0 on failure and -1 on error.
1325 * Wrapping can fail if the result of wrapping is equal to "bound"
1326 * or if we want to bound the sizes of the coefficients and
1327 * the wrapped constraint does not satisfy this bound.
1329 static int add_wrap(struct isl_wraps
*wraps
, int w
, isl_int
*bound
,
1330 isl_int
*ineq
, unsigned len
, __isl_keep isl_set
*set
, int negate
)
1332 isl_seq_cpy(wraps
->mat
->row
[w
], bound
, len
);
1334 isl_seq_neg(wraps
->mat
->row
[w
+ 1], ineq
, len
);
1335 ineq
= wraps
->mat
->row
[w
+ 1];
1337 if (!isl_set_wrap_facet(set
, wraps
->mat
->row
[w
], ineq
))
1339 if (isl_seq_eq(wraps
->mat
->row
[w
], bound
, len
))
1341 if (!allow_wrap(wraps
, w
))
1346 /* For each constraint in info->bmap that is not redundant (as determined
1347 * by info->tab) and that is not a valid constraint for the other basic map,
1348 * wrap the constraint around "bound" such that it includes the whole
1349 * set "set" and append the resulting constraint to "wraps".
1350 * Note that the constraints that are valid for the other basic map
1351 * will be added to the combined basic map by default, so there is
1352 * no need to wrap them.
1353 * The caller wrap_in_facets even relies on this function not wrapping
1354 * any constraints that are already valid.
1355 * "wraps" is assumed to have been pre-allocated to the appropriate size.
1356 * wraps->n_row is the number of actual wrapped constraints that have
1358 * If any of the wrapping problems results in a constraint that is
1359 * identical to "bound", then this means that "set" is unbounded in such
1360 * way that no wrapping is possible. If this happens then wraps->n_row
1362 * Similarly, if we want to bound the coefficients of the wrapping
1363 * constraints and a newly added wrapping constraint does not
1364 * satisfy the bound, then wraps->n_row is also reset to zero.
1366 static isl_stat
add_wraps(struct isl_wraps
*wraps
,
1367 struct isl_coalesce_info
*info
, isl_int
*bound
, __isl_keep isl_set
*set
)
1372 isl_basic_map
*bmap
= info
->bmap
;
1373 isl_size total
= isl_basic_map_dim(bmap
, isl_dim_all
);
1374 unsigned len
= 1 + total
;
1377 return isl_stat_error
;
1379 w
= wraps
->mat
->n_row
;
1381 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
1382 if (info
->ineq
[l
] == STATUS_VALID
||
1383 info
->ineq
[l
] == STATUS_REDUNDANT
)
1385 if (isl_seq_is_neg(bound
, bmap
->ineq
[l
], len
))
1387 if (isl_seq_eq(bound
, bmap
->ineq
[l
], len
))
1389 if (isl_tab_is_redundant(info
->tab
, bmap
->n_eq
+ l
))
1392 added
= add_wrap(wraps
, w
, bound
, bmap
->ineq
[l
], len
, set
, 0);
1394 return isl_stat_error
;
1399 for (l
= 0; l
< bmap
->n_eq
; ++l
) {
1400 if (isl_seq_is_neg(bound
, bmap
->eq
[l
], len
))
1402 if (isl_seq_eq(bound
, bmap
->eq
[l
], len
))
1405 for (m
= 0; m
< 2; ++m
) {
1406 if (info
->eq
[2 * l
+ m
] == STATUS_VALID
)
1408 added
= add_wrap(wraps
, w
, bound
, bmap
->eq
[l
], len
,
1411 return isl_stat_error
;
1418 wraps
->mat
->n_row
= w
;
1421 return wraps_mark_failed(wraps
);
1424 /* Check if the constraints in "wraps" from "first" until the last
1425 * are all valid for the basic set represented by "tab".
1426 * If not, wraps->n_row is set to zero.
1428 static int check_wraps(__isl_keep isl_mat
*wraps
, int first
,
1429 struct isl_tab
*tab
)
1433 for (i
= first
; i
< wraps
->n_row
; ++i
) {
1434 enum isl_ineq_type type
;
1435 type
= isl_tab_ineq_type(tab
, wraps
->row
[i
]);
1436 if (type
== isl_ineq_error
)
1438 if (type
== isl_ineq_redundant
)
1447 /* Return a set that corresponds to the non-redundant constraints
1448 * (as recorded in tab) of bmap.
1450 * It's important to remove the redundant constraints as some
1451 * of the other constraints may have been modified after the
1452 * constraints were marked redundant.
1453 * In particular, a constraint may have been relaxed.
1454 * Redundant constraints are ignored when a constraint is relaxed
1455 * and should therefore continue to be ignored ever after.
1456 * Otherwise, the relaxation might be thwarted by some of
1457 * these constraints.
1459 * Update the underlying set to ensure that the dimension doesn't change.
1460 * Otherwise the integer divisions could get dropped if the tab
1461 * turns out to be empty.
1463 static __isl_give isl_set
*set_from_updated_bmap(__isl_keep isl_basic_map
*bmap
,
1464 struct isl_tab
*tab
)
1466 isl_basic_set
*bset
;
1468 bmap
= isl_basic_map_copy(bmap
);
1469 bset
= isl_basic_map_underlying_set(bmap
);
1470 bset
= isl_basic_set_cow(bset
);
1471 bset
= isl_basic_set_update_from_tab(bset
, tab
);
1472 return isl_set_from_basic_set(bset
);
1475 /* Does "info" have any cut constraints that are redundant?
1477 static isl_bool
has_redundant_cuts(struct isl_coalesce_info
*info
)
1480 isl_size n_eq
, n_ineq
;
1482 n_eq
= isl_basic_map_n_equality(info
->bmap
);
1483 n_ineq
= isl_basic_map_n_inequality(info
->bmap
);
1484 if (n_eq
< 0 || n_ineq
< 0)
1485 return isl_bool_error
;
1486 for (l
= 0; l
< n_ineq
; ++l
) {
1489 if (info
->ineq
[l
] != STATUS_CUT
)
1491 red
= isl_tab_is_redundant(info
->tab
, n_eq
+ l
);
1493 return isl_bool_error
;
1495 return isl_bool_true
;
1498 return isl_bool_false
;
1501 /* Wrap the constraints of info->bmap that bound the facet defined
1502 * by inequality "k" around (the opposite of) this inequality to
1503 * include "set". "bound" may be used to store the negated inequality.
1504 * Since the wrapped constraints are not guaranteed to contain the whole
1505 * of info->bmap, we check them in check_wraps.
1506 * If any of the wrapped constraints turn out to be invalid, then
1507 * check_wraps will reset wrap->n_row to zero.
1509 * If any of the cut constraints of info->bmap turn out
1510 * to be redundant with respect to other constraints
1511 * then these will neither be wrapped nor added directly to the result.
1512 * The result may therefore not be correct.
1513 * Skip wrapping and reset wrap->mat->n_row to zero in this case.
1515 static isl_stat
add_wraps_around_facet(struct isl_wraps
*wraps
,
1516 struct isl_coalesce_info
*info
, int k
, isl_int
*bound
,
1517 __isl_keep isl_set
*set
)
1520 struct isl_tab_undo
*snap
;
1522 isl_size total
= isl_basic_map_dim(info
->bmap
, isl_dim_all
);
1525 return isl_stat_error
;
1527 snap
= isl_tab_snap(info
->tab
);
1529 if (isl_tab_select_facet(info
->tab
, info
->bmap
->n_eq
+ k
) < 0)
1530 return isl_stat_error
;
1531 if (isl_tab_detect_redundant(info
->tab
) < 0)
1532 return isl_stat_error
;
1533 nowrap
= has_redundant_cuts(info
);
1535 return isl_stat_error
;
1537 n
= wraps
->mat
->n_row
;
1539 isl_seq_neg(bound
, info
->bmap
->ineq
[k
], 1 + total
);
1541 if (add_wraps(wraps
, info
, bound
, set
) < 0)
1542 return isl_stat_error
;
1545 if (isl_tab_rollback(info
->tab
, snap
) < 0)
1546 return isl_stat_error
;
1548 return wraps_mark_failed(wraps
);
1549 if (check_wraps(wraps
->mat
, n
, info
->tab
) < 0)
1550 return isl_stat_error
;
1555 /* Given a basic set i with a constraint k that is adjacent to
1556 * basic set j, check if we can wrap
1557 * both the facet corresponding to k (if "wrap_facet" is set) and basic map j
1558 * (always) around their ridges to include the other set.
1559 * If so, replace the pair of basic sets by their union.
1561 * All constraints of i (except k) are assumed to be valid or
1562 * cut constraints for j.
1563 * Wrapping the cut constraints to include basic map j may result
1564 * in constraints that are no longer valid of basic map i
1565 * we have to check that the resulting wrapping constraints are valid for i.
1566 * If "wrap_facet" is not set, then all constraints of i (except k)
1567 * are assumed to be valid for j.
1576 static enum isl_change
can_wrap_in_facet(int i
, int j
, int k
,
1577 struct isl_coalesce_info
*info
, int wrap_facet
)
1579 enum isl_change change
= isl_change_none
;
1580 struct isl_wraps wraps
;
1583 struct isl_set
*set_i
= NULL
;
1584 struct isl_set
*set_j
= NULL
;
1585 struct isl_vec
*bound
= NULL
;
1586 isl_size total
= isl_basic_map_dim(info
[i
].bmap
, isl_dim_all
);
1589 return isl_change_error
;
1590 set_i
= set_from_updated_bmap(info
[i
].bmap
, info
[i
].tab
);
1591 set_j
= set_from_updated_bmap(info
[j
].bmap
, info
[j
].tab
);
1592 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
1593 mat
= isl_mat_alloc(ctx
, 2 * (info
[i
].bmap
->n_eq
+ info
[j
].bmap
->n_eq
) +
1594 info
[i
].bmap
->n_ineq
+ info
[j
].bmap
->n_ineq
,
1596 if (wraps_init(&wraps
, mat
, info
, i
, j
) < 0)
1598 bound
= isl_vec_alloc(ctx
, 1 + total
);
1599 if (!set_i
|| !set_j
|| !bound
)
1602 isl_seq_cpy(bound
->el
, info
[i
].bmap
->ineq
[k
], 1 + total
);
1603 isl_int_add_ui(bound
->el
[0], bound
->el
[0], 1);
1604 isl_seq_normalize(ctx
, bound
->el
, 1 + total
);
1606 isl_seq_cpy(wraps
.mat
->row
[0], bound
->el
, 1 + total
);
1607 wraps
.mat
->n_row
= 1;
1609 if (add_wraps(&wraps
, &info
[j
], bound
->el
, set_i
) < 0)
1611 if (!wraps
.mat
->n_row
)
1615 if (add_wraps_around_facet(&wraps
, &info
[i
], k
,
1616 bound
->el
, set_j
) < 0)
1618 if (!wraps
.mat
->n_row
)
1622 change
= fuse(i
, j
, info
, wraps
.mat
, 0, 0);
1627 isl_set_free(set_i
);
1628 isl_set_free(set_j
);
1630 isl_vec_free(bound
);
1635 isl_vec_free(bound
);
1636 isl_set_free(set_i
);
1637 isl_set_free(set_j
);
1638 return isl_change_error
;
1641 /* Given a cut constraint t(x) >= 0 of basic map i, stored in row "w"
1642 * of wrap.mat, replace it by its relaxed version t(x) + 1 >= 0, and
1643 * add wrapping constraints to wrap.mat for all constraints
1644 * of basic map j that bound the part of basic map j that sticks out
1645 * of the cut constraint.
1646 * "set_i" is the underlying set of basic map i.
1647 * If any wrapping fails, then wraps->mat.n_row is reset to zero.
1649 * In particular, we first intersect basic map j with t(x) + 1 = 0.
1650 * If the result is empty, then t(x) >= 0 was actually a valid constraint
1651 * (with respect to the integer points), so we add t(x) >= 0 instead.
1652 * Otherwise, we wrap the constraints of basic map j that are not
1653 * redundant in this intersection and that are not already valid
1654 * for basic map i over basic map i.
1655 * Note that it is sufficient to wrap the constraints to include
1656 * basic map i, because we will only wrap the constraints that do
1657 * not include basic map i already. The wrapped constraint will
1658 * therefore be more relaxed compared to the original constraint.
1659 * Since the original constraint is valid for basic map j, so is
1660 * the wrapped constraint.
1662 static isl_stat
wrap_in_facet(struct isl_wraps
*wraps
, int w
,
1663 struct isl_coalesce_info
*info_j
, __isl_keep isl_set
*set_i
,
1664 struct isl_tab_undo
*snap
)
1666 isl_int_add_ui(wraps
->mat
->row
[w
][0], wraps
->mat
->row
[w
][0], 1);
1667 if (isl_tab_add_eq(info_j
->tab
, wraps
->mat
->row
[w
]) < 0)
1668 return isl_stat_error
;
1669 if (isl_tab_detect_redundant(info_j
->tab
) < 0)
1670 return isl_stat_error
;
1672 if (info_j
->tab
->empty
)
1673 isl_int_sub_ui(wraps
->mat
->row
[w
][0], wraps
->mat
->row
[w
][0], 1);
1674 else if (add_wraps(wraps
, info_j
, wraps
->mat
->row
[w
], set_i
) < 0)
1675 return isl_stat_error
;
1677 if (isl_tab_rollback(info_j
->tab
, snap
) < 0)
1678 return isl_stat_error
;
1683 /* Given a pair of basic maps i and j such that j sticks out
1684 * of i at n cut constraints, each time by at most one,
1685 * try to compute wrapping constraints and replace the two
1686 * basic maps by a single basic map.
1687 * The other constraints of i are assumed to be valid for j.
1688 * "set_i" is the underlying set of basic map i.
1689 * "wraps" has been initialized to be of the right size.
1691 * For each cut constraint t(x) >= 0 of i, we add the relaxed version
1692 * t(x) + 1 >= 0, along with wrapping constraints for all constraints
1693 * of basic map j that bound the part of basic map j that sticks out
1694 * of the cut constraint.
1696 * If any wrapping fails, i.e., if we cannot wrap to touch
1697 * the union, then we give up.
1698 * Otherwise, the pair of basic maps is replaced by their union.
1700 static enum isl_change
try_wrap_in_facets(int i
, int j
,
1701 struct isl_coalesce_info
*info
, struct isl_wraps
*wraps
,
1702 __isl_keep isl_set
*set_i
)
1706 struct isl_tab_undo
*snap
;
1708 total
= isl_basic_map_dim(info
[i
].bmap
, isl_dim_all
);
1710 return isl_change_error
;
1712 snap
= isl_tab_snap(info
[j
].tab
);
1714 wraps
->mat
->n_row
= 0;
1716 for (k
= 0; k
< info
[i
].bmap
->n_eq
; ++k
) {
1717 for (l
= 0; l
< 2; ++l
) {
1718 if (info
[i
].eq
[2 * k
+ l
] != STATUS_CUT
)
1720 w
= wraps
->mat
->n_row
++;
1722 isl_seq_neg(wraps
->mat
->row
[w
],
1723 info
[i
].bmap
->eq
[k
], 1 + total
);
1725 isl_seq_cpy(wraps
->mat
->row
[w
],
1726 info
[i
].bmap
->eq
[k
], 1 + total
);
1727 if (wrap_in_facet(wraps
, w
, &info
[j
], set_i
, snap
) < 0)
1728 return isl_change_error
;
1730 if (!wraps
->mat
->n_row
)
1731 return isl_change_none
;
1735 for (k
= 0; k
< info
[i
].bmap
->n_ineq
; ++k
) {
1736 if (info
[i
].ineq
[k
] != STATUS_CUT
)
1738 w
= wraps
->mat
->n_row
++;
1739 isl_seq_cpy(wraps
->mat
->row
[w
],
1740 info
[i
].bmap
->ineq
[k
], 1 + total
);
1741 if (wrap_in_facet(wraps
, w
, &info
[j
], set_i
, snap
) < 0)
1742 return isl_change_error
;
1744 if (!wraps
->mat
->n_row
)
1745 return isl_change_none
;
1748 return fuse(i
, j
, info
, wraps
->mat
, 0, 1);
1751 /* Given a pair of basic maps i and j such that j sticks out
1752 * of i at n cut constraints, each time by at most one,
1753 * try to compute wrapping constraints and replace the two
1754 * basic maps by a single basic map.
1755 * The other constraints of i are assumed to be valid for j.
1757 * The core computation is performed by try_wrap_in_facets.
1758 * This function simply extracts an underlying set representation
1759 * of basic map i and initializes the data structure for keeping
1760 * track of wrapping constraints.
1762 static enum isl_change
wrap_in_facets(int i
, int j
, int n
,
1763 struct isl_coalesce_info
*info
)
1765 enum isl_change change
= isl_change_none
;
1766 struct isl_wraps wraps
;
1769 isl_set
*set_i
= NULL
;
1770 isl_size total
= isl_basic_map_dim(info
[i
].bmap
, isl_dim_all
);
1774 return isl_change_error
;
1775 if (isl_tab_extend_cons(info
[j
].tab
, 1) < 0)
1776 return isl_change_error
;
1778 max_wrap
= 1 + 2 * info
[j
].bmap
->n_eq
+ info
[j
].bmap
->n_ineq
;
1781 set_i
= set_from_updated_bmap(info
[i
].bmap
, info
[i
].tab
);
1782 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
1783 mat
= isl_mat_alloc(ctx
, max_wrap
, 1 + total
);
1784 if (wraps_init(&wraps
, mat
, info
, i
, j
) < 0)
1789 change
= try_wrap_in_facets(i
, j
, info
, &wraps
, set_i
);
1792 isl_set_free(set_i
);
1797 isl_set_free(set_i
);
1798 return isl_change_error
;
1801 /* Return the effect of inequality "ineq" on the tableau "tab",
1802 * after relaxing the constant term of "ineq" by one.
1804 static enum isl_ineq_type
type_of_relaxed(struct isl_tab
*tab
, isl_int
*ineq
)
1806 enum isl_ineq_type type
;
1808 isl_int_add_ui(ineq
[0], ineq
[0], 1);
1809 type
= isl_tab_ineq_type(tab
, ineq
);
1810 isl_int_sub_ui(ineq
[0], ineq
[0], 1);
1815 /* Given two basic sets i and j,
1816 * check if relaxing all the cut constraints of i by one turns
1817 * them into valid constraint for j and check if we can wrap in
1818 * the bits that are sticking out.
1819 * If so, replace the pair by their union.
1821 * We first check if all relaxed cut inequalities of i are valid for j
1822 * and then try to wrap in the intersections of the relaxed cut inequalities
1825 * During this wrapping, we consider the points of j that lie at a distance
1826 * of exactly 1 from i. In particular, we ignore the points that lie in
1827 * between this lower-dimensional space and the basic map i.
1828 * We can therefore only apply this to integer maps.
1854 * Wrapping can fail if the result of wrapping one of the facets
1855 * around its edges does not produce any new facet constraint.
1856 * In particular, this happens when we try to wrap in unbounded sets.
1858 * _______________________________________________________________________
1862 * |_| |_________________________________________________________________
1865 * The following is not an acceptable result of coalescing the above two
1866 * sets as it includes extra integer points.
1867 * _______________________________________________________________________
1872 * \______________________________________________________________________
1874 static enum isl_change
can_wrap_in_set(int i
, int j
,
1875 struct isl_coalesce_info
*info
)
1881 if (ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_RATIONAL
) ||
1882 ISL_F_ISSET(info
[j
].bmap
, ISL_BASIC_MAP_RATIONAL
))
1883 return isl_change_none
;
1885 n
= count_eq(&info
[i
], STATUS_CUT
) + count_ineq(&info
[i
], STATUS_CUT
);
1887 return isl_change_none
;
1889 total
= isl_basic_map_dim(info
[i
].bmap
, isl_dim_all
);
1891 return isl_change_error
;
1892 for (k
= 0; k
< info
[i
].bmap
->n_eq
; ++k
) {
1893 for (l
= 0; l
< 2; ++l
) {
1894 enum isl_ineq_type type
;
1896 if (info
[i
].eq
[2 * k
+ l
] != STATUS_CUT
)
1900 isl_seq_neg(info
[i
].bmap
->eq
[k
],
1901 info
[i
].bmap
->eq
[k
], 1 + total
);
1902 type
= type_of_relaxed(info
[j
].tab
,
1903 info
[i
].bmap
->eq
[k
]);
1905 isl_seq_neg(info
[i
].bmap
->eq
[k
],
1906 info
[i
].bmap
->eq
[k
], 1 + total
);
1907 if (type
== isl_ineq_error
)
1908 return isl_change_error
;
1909 if (type
!= isl_ineq_redundant
)
1910 return isl_change_none
;
1914 for (k
= 0; k
< info
[i
].bmap
->n_ineq
; ++k
) {
1915 enum isl_ineq_type type
;
1917 if (info
[i
].ineq
[k
] != STATUS_CUT
)
1920 type
= type_of_relaxed(info
[j
].tab
, info
[i
].bmap
->ineq
[k
]);
1921 if (type
== isl_ineq_error
)
1922 return isl_change_error
;
1923 if (type
!= isl_ineq_redundant
)
1924 return isl_change_none
;
1927 return wrap_in_facets(i
, j
, n
, info
);
1930 /* Check if either i or j has only cut constraints that can
1931 * be used to wrap in (a facet of) the other basic set.
1932 * if so, replace the pair by their union.
1934 static enum isl_change
check_wrap(int i
, int j
, struct isl_coalesce_info
*info
)
1936 enum isl_change change
= isl_change_none
;
1938 change
= can_wrap_in_set(i
, j
, info
);
1939 if (change
!= isl_change_none
)
1942 change
= can_wrap_in_set(j
, i
, info
);
1946 /* Check if all inequality constraints of "i" that cut "j" cease
1947 * to be cut constraints if they are relaxed by one.
1948 * If so, collect the cut constraints in "list".
1949 * The caller is responsible for allocating "list".
1951 static isl_bool
all_cut_by_one(int i
, int j
, struct isl_coalesce_info
*info
,
1957 for (l
= 0; l
< info
[i
].bmap
->n_ineq
; ++l
) {
1958 enum isl_ineq_type type
;
1960 if (info
[i
].ineq
[l
] != STATUS_CUT
)
1962 type
= type_of_relaxed(info
[j
].tab
, info
[i
].bmap
->ineq
[l
]);
1963 if (type
== isl_ineq_error
)
1964 return isl_bool_error
;
1965 if (type
!= isl_ineq_redundant
)
1966 return isl_bool_false
;
1970 return isl_bool_true
;
1973 /* Given two basic maps such that "j" has at least one equality constraint
1974 * that is adjacent to an inequality constraint of "i" and such that "i" has
1975 * exactly one inequality constraint that is adjacent to an equality
1976 * constraint of "j", check whether "i" can be extended to include "j" or
1977 * whether "j" can be wrapped into "i".
1978 * All remaining constraints of "i" and "j" are assumed to be valid
1979 * or cut constraints of the other basic map.
1980 * However, none of the equality constraints of "i" are cut constraints.
1982 * If "i" has any "cut" inequality constraints, then check if relaxing
1983 * each of them by one is sufficient for them to become valid.
1984 * If so, check if the inequality constraint adjacent to an equality
1985 * constraint of "j" along with all these cut constraints
1986 * can be relaxed by one to contain exactly "j".
1987 * Otherwise, or if this fails, check if "j" can be wrapped into "i".
1989 static enum isl_change
check_single_adj_eq(int i
, int j
,
1990 struct isl_coalesce_info
*info
)
1992 enum isl_change change
= isl_change_none
;
1999 n_cut
= count_ineq(&info
[i
], STATUS_CUT
);
2001 k
= find_ineq(&info
[i
], STATUS_ADJ_EQ
);
2004 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
2005 relax
= isl_calloc_array(ctx
, int, 1 + n_cut
);
2007 return isl_change_error
;
2009 try_relax
= all_cut_by_one(i
, j
, info
, relax
+ 1);
2011 change
= isl_change_error
;
2013 try_relax
= isl_bool_true
;
2016 if (try_relax
&& change
== isl_change_none
)
2017 change
= is_relaxed_extension(i
, j
, 1 + n_cut
, relax
, info
);
2020 if (change
!= isl_change_none
)
2023 change
= can_wrap_in_facet(i
, j
, k
, info
, n_cut
> 0);
2028 /* At least one of the basic maps has an equality that is adjacent
2029 * to an inequality. Make sure that only one of the basic maps has
2030 * such an equality and that the other basic map has exactly one
2031 * inequality adjacent to an equality.
2032 * If the other basic map does not have such an inequality, then
2033 * check if all its constraints are either valid or cut constraints
2034 * and, if so, try wrapping in the first map into the second.
2035 * Otherwise, try to extend one basic map with the other or
2036 * wrap one basic map in the other.
2038 static enum isl_change
check_adj_eq(int i
, int j
,
2039 struct isl_coalesce_info
*info
)
2041 if (any_eq(&info
[i
], STATUS_ADJ_INEQ
) &&
2042 any_eq(&info
[j
], STATUS_ADJ_INEQ
))
2043 /* ADJ EQ TOO MANY */
2044 return isl_change_none
;
2046 if (any_eq(&info
[i
], STATUS_ADJ_INEQ
))
2047 return check_adj_eq(j
, i
, info
);
2049 /* j has an equality adjacent to an inequality in i */
2051 if (count_ineq(&info
[i
], STATUS_ADJ_EQ
) != 1) {
2052 if (all_valid_or_cut(&info
[i
]))
2053 return can_wrap_in_set(i
, j
, info
);
2054 return isl_change_none
;
2056 if (any_eq(&info
[i
], STATUS_CUT
))
2057 return isl_change_none
;
2058 if (any_ineq(&info
[j
], STATUS_ADJ_EQ
) ||
2059 any_ineq(&info
[i
], STATUS_ADJ_INEQ
) ||
2060 any_ineq(&info
[j
], STATUS_ADJ_INEQ
))
2061 /* ADJ EQ TOO MANY */
2062 return isl_change_none
;
2064 return check_single_adj_eq(i
, j
, info
);
2067 /* Disjunct "j" lies on a hyperplane that is adjacent to disjunct "i".
2068 * In particular, disjunct "i" has an inequality constraint that is adjacent
2069 * to a (combination of) equality constraint(s) of disjunct "j",
2070 * but disjunct "j" has no explicit equality constraint adjacent
2071 * to an inequality constraint of disjunct "i".
2073 * Disjunct "i" is already known not to have any equality constraints
2074 * that are adjacent to an equality or inequality constraint.
2075 * Check that, other than the inequality constraint mentioned above,
2076 * all other constraints of disjunct "i" are valid for disjunct "j".
2077 * If so, try and wrap in disjunct "j".
2079 static enum isl_change
check_ineq_adj_eq(int i
, int j
,
2080 struct isl_coalesce_info
*info
)
2084 if (any_eq(&info
[i
], STATUS_CUT
))
2085 return isl_change_none
;
2086 if (any_ineq(&info
[i
], STATUS_CUT
))
2087 return isl_change_none
;
2088 if (any_ineq(&info
[i
], STATUS_ADJ_INEQ
))
2089 return isl_change_none
;
2090 if (count_ineq(&info
[i
], STATUS_ADJ_EQ
) != 1)
2091 return isl_change_none
;
2093 k
= find_ineq(&info
[i
], STATUS_ADJ_EQ
);
2095 return can_wrap_in_facet(i
, j
, k
, info
, 0);
2098 /* The two basic maps lie on adjacent hyperplanes. In particular,
2099 * basic map "i" has an equality that lies parallel to basic map "j".
2100 * Check if we can wrap the facets around the parallel hyperplanes
2101 * to include the other set.
2103 * We perform basically the same operations as can_wrap_in_facet,
2104 * except that we don't need to select a facet of one of the sets.
2110 * If there is more than one equality of "i" adjacent to an equality of "j",
2111 * then the result will satisfy one or more equalities that are a linear
2112 * combination of these equalities. These will be encoded as pairs
2113 * of inequalities in the wrapping constraints and need to be made
2116 static enum isl_change
check_eq_adj_eq(int i
, int j
,
2117 struct isl_coalesce_info
*info
)
2120 enum isl_change change
= isl_change_none
;
2121 int detect_equalities
= 0;
2122 struct isl_wraps wraps
;
2125 struct isl_set
*set_i
= NULL
;
2126 struct isl_set
*set_j
= NULL
;
2127 struct isl_vec
*bound
= NULL
;
2128 isl_size total
= isl_basic_map_dim(info
[i
].bmap
, isl_dim_all
);
2131 return isl_change_error
;
2132 if (count_eq(&info
[i
], STATUS_ADJ_EQ
) != 1)
2133 detect_equalities
= 1;
2135 k
= find_eq(&info
[i
], STATUS_ADJ_EQ
);
2137 set_i
= set_from_updated_bmap(info
[i
].bmap
, info
[i
].tab
);
2138 set_j
= set_from_updated_bmap(info
[j
].bmap
, info
[j
].tab
);
2139 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
2140 mat
= isl_mat_alloc(ctx
, 2 * (info
[i
].bmap
->n_eq
+ info
[j
].bmap
->n_eq
) +
2141 info
[i
].bmap
->n_ineq
+ info
[j
].bmap
->n_ineq
,
2143 if (wraps_init(&wraps
, mat
, info
, i
, j
) < 0)
2145 bound
= isl_vec_alloc(ctx
, 1 + total
);
2146 if (!set_i
|| !set_j
|| !bound
)
2150 isl_seq_neg(bound
->el
, info
[i
].bmap
->eq
[k
/ 2], 1 + total
);
2152 isl_seq_cpy(bound
->el
, info
[i
].bmap
->eq
[k
/ 2], 1 + total
);
2153 isl_int_add_ui(bound
->el
[0], bound
->el
[0], 1);
2155 isl_seq_cpy(wraps
.mat
->row
[0], bound
->el
, 1 + total
);
2156 wraps
.mat
->n_row
= 1;
2158 if (add_wraps(&wraps
, &info
[j
], bound
->el
, set_i
) < 0)
2160 if (!wraps
.mat
->n_row
)
2163 isl_int_sub_ui(bound
->el
[0], bound
->el
[0], 1);
2164 isl_seq_neg(bound
->el
, bound
->el
, 1 + total
);
2166 isl_seq_cpy(wraps
.mat
->row
[wraps
.mat
->n_row
], bound
->el
, 1 + total
);
2169 if (add_wraps(&wraps
, &info
[i
], bound
->el
, set_j
) < 0)
2171 if (!wraps
.mat
->n_row
)
2174 change
= fuse(i
, j
, info
, wraps
.mat
, detect_equalities
, 0);
2177 error
: change
= isl_change_error
;
2182 isl_set_free(set_i
);
2183 isl_set_free(set_j
);
2184 isl_vec_free(bound
);
2189 /* Initialize the "eq" and "ineq" fields of "info".
2191 static void init_status(struct isl_coalesce_info
*info
)
2193 info
->eq
= info
->ineq
= NULL
;
2196 /* Set info->eq to the positions of the equalities of info->bmap
2197 * with respect to the basic map represented by "tab".
2198 * If info->eq has already been computed, then do not compute it again.
2200 static void set_eq_status_in(struct isl_coalesce_info
*info
,
2201 struct isl_tab
*tab
)
2205 info
->eq
= eq_status_in(info
->bmap
, tab
);
2208 /* Set info->ineq to the positions of the inequalities of info->bmap
2209 * with respect to the basic map represented by "tab".
2210 * If info->ineq has already been computed, then do not compute it again.
2212 static void set_ineq_status_in(struct isl_coalesce_info
*info
,
2213 struct isl_tab
*tab
)
2217 info
->ineq
= ineq_status_in(info
->bmap
, info
->tab
, tab
);
2220 /* Free the memory allocated by the "eq" and "ineq" fields of "info".
2221 * This function assumes that init_status has been called on "info" first,
2222 * after which the "eq" and "ineq" fields may or may not have been
2223 * assigned a newly allocated array.
2225 static void clear_status(struct isl_coalesce_info
*info
)
2231 /* Are all inequality constraints of the basic map represented by "info"
2232 * valid for the other basic map, except for a single constraint
2233 * that is adjacent to an inequality constraint of the other basic map?
2235 static int all_ineq_valid_or_single_adj_ineq(struct isl_coalesce_info
*info
)
2240 for (i
= 0; i
< info
->bmap
->n_ineq
; ++i
) {
2241 if (info
->ineq
[i
] == STATUS_REDUNDANT
)
2243 if (info
->ineq
[i
] == STATUS_VALID
)
2245 if (info
->ineq
[i
] != STATUS_ADJ_INEQ
)
2255 /* Basic map "i" has one or more equality constraints that separate it
2256 * from basic map "j". Check if it happens to be an extension
2258 * In particular, check that all constraints of "j" are valid for "i",
2259 * except for one inequality constraint that is adjacent
2260 * to an inequality constraints of "i".
2261 * If so, check for "i" being an extension of "j" by calling
2262 * is_adj_ineq_extension.
2264 * Clean up the memory allocated for keeping track of the status
2265 * of the constraints before returning.
2267 static enum isl_change
separating_equality(int i
, int j
,
2268 struct isl_coalesce_info
*info
)
2270 enum isl_change change
= isl_change_none
;
2272 if (all(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_VALID
) &&
2273 all_ineq_valid_or_single_adj_ineq(&info
[j
]))
2274 change
= is_adj_ineq_extension(j
, i
, info
);
2276 clear_status(&info
[i
]);
2277 clear_status(&info
[j
]);
2281 /* Check if the union of the given pair of basic maps
2282 * can be represented by a single basic map.
2283 * If so, replace the pair by the single basic map and return
2284 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
2285 * Otherwise, return isl_change_none.
2286 * The two basic maps are assumed to live in the same local space.
2287 * The "eq" and "ineq" fields of info[i] and info[j] are assumed
2288 * to have been initialized by the caller, either to NULL or
2289 * to valid information.
2291 * We first check the effect of each constraint of one basic map
2292 * on the other basic map.
2293 * The constraint may be
2294 * redundant the constraint is redundant in its own
2295 * basic map and should be ignore and removed
2297 * valid all (integer) points of the other basic map
2298 * satisfy the constraint
2299 * separate no (integer) point of the other basic map
2300 * satisfies the constraint
2301 * cut some but not all points of the other basic map
2302 * satisfy the constraint
2303 * adj_eq the given constraint is adjacent (on the outside)
2304 * to an equality of the other basic map
2305 * adj_ineq the given constraint is adjacent (on the outside)
2306 * to an inequality of the other basic map
2308 * We consider seven cases in which we can replace the pair by a single
2309 * basic map. We ignore all "redundant" constraints.
2311 * 1. all constraints of one basic map are valid
2312 * => the other basic map is a subset and can be removed
2314 * 2. all constraints of both basic maps are either "valid" or "cut"
2315 * and the facets corresponding to the "cut" constraints
2316 * of one of the basic maps lies entirely inside the other basic map
2317 * => the pair can be replaced by a basic map consisting
2318 * of the valid constraints in both basic maps
2320 * 3. there is a single pair of adjacent inequalities
2321 * (all other constraints are "valid")
2322 * => the pair can be replaced by a basic map consisting
2323 * of the valid constraints in both basic maps
2325 * 4. one basic map has a single adjacent inequality, while the other
2326 * constraints are "valid". The other basic map has some
2327 * "cut" constraints, but replacing the adjacent inequality by
2328 * its opposite and adding the valid constraints of the other
2329 * basic map results in a subset of the other basic map
2330 * => the pair can be replaced by a basic map consisting
2331 * of the valid constraints in both basic maps
2333 * 5. there is a single adjacent pair of an inequality and an equality,
2334 * the other constraints of the basic map containing the inequality are
2335 * "valid". Moreover, if the inequality the basic map is relaxed
2336 * and then turned into an equality, then resulting facet lies
2337 * entirely inside the other basic map
2338 * => the pair can be replaced by the basic map containing
2339 * the inequality, with the inequality relaxed.
2341 * 6. there is a single inequality adjacent to an equality,
2342 * the other constraints of the basic map containing the inequality are
2343 * "valid". Moreover, the facets corresponding to both
2344 * the inequality and the equality can be wrapped around their
2345 * ridges to include the other basic map
2346 * => the pair can be replaced by a basic map consisting
2347 * of the valid constraints in both basic maps together
2348 * with all wrapping constraints
2350 * 7. one of the basic maps extends beyond the other by at most one.
2351 * Moreover, the facets corresponding to the cut constraints and
2352 * the pieces of the other basic map at offset one from these cut
2353 * constraints can be wrapped around their ridges to include
2354 * the union of the two basic maps
2355 * => the pair can be replaced by a basic map consisting
2356 * of the valid constraints in both basic maps together
2357 * with all wrapping constraints
2359 * 8. the two basic maps live in adjacent hyperplanes. In principle
2360 * such sets can always be combined through wrapping, but we impose
2361 * that there is only one such pair, to avoid overeager coalescing.
2363 * Throughout the computation, we maintain a collection of tableaus
2364 * corresponding to the basic maps. When the basic maps are dropped
2365 * or combined, the tableaus are modified accordingly.
2367 static enum isl_change
coalesce_local_pair_reuse(int i
, int j
,
2368 struct isl_coalesce_info
*info
)
2370 enum isl_change change
= isl_change_none
;
2372 set_ineq_status_in(&info
[i
], info
[j
].tab
);
2373 if (info
[i
].bmap
->n_ineq
&& !info
[i
].ineq
)
2375 if (any_ineq(&info
[i
], STATUS_ERROR
))
2377 if (any_ineq(&info
[i
], STATUS_SEPARATE
))
2380 set_ineq_status_in(&info
[j
], info
[i
].tab
);
2381 if (info
[j
].bmap
->n_ineq
&& !info
[j
].ineq
)
2383 if (any_ineq(&info
[j
], STATUS_ERROR
))
2385 if (any_ineq(&info
[j
], STATUS_SEPARATE
))
2388 set_eq_status_in(&info
[i
], info
[j
].tab
);
2389 if (info
[i
].bmap
->n_eq
&& !info
[i
].eq
)
2391 if (any_eq(&info
[i
], STATUS_ERROR
))
2394 set_eq_status_in(&info
[j
], info
[i
].tab
);
2395 if (info
[j
].bmap
->n_eq
&& !info
[j
].eq
)
2397 if (any_eq(&info
[j
], STATUS_ERROR
))
2400 if (any_eq(&info
[i
], STATUS_SEPARATE
))
2401 return separating_equality(i
, j
, info
);
2402 if (any_eq(&info
[j
], STATUS_SEPARATE
))
2403 return separating_equality(j
, i
, info
);
2405 if (all(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_VALID
) &&
2406 all(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_VALID
)) {
2408 change
= isl_change_drop_second
;
2409 } else if (all(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_VALID
) &&
2410 all(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_VALID
)) {
2412 change
= isl_change_drop_first
;
2413 } else if (any_eq(&info
[i
], STATUS_ADJ_EQ
)) {
2414 change
= check_eq_adj_eq(i
, j
, info
);
2415 } else if (any_eq(&info
[j
], STATUS_ADJ_EQ
)) {
2416 change
= check_eq_adj_eq(j
, i
, info
);
2417 } else if (any_eq(&info
[i
], STATUS_ADJ_INEQ
) ||
2418 any_eq(&info
[j
], STATUS_ADJ_INEQ
)) {
2419 change
= check_adj_eq(i
, j
, info
);
2420 } else if (any_ineq(&info
[i
], STATUS_ADJ_EQ
)) {
2421 change
= check_ineq_adj_eq(i
, j
, info
);
2422 } else if (any_ineq(&info
[j
], STATUS_ADJ_EQ
)) {
2423 change
= check_ineq_adj_eq(j
, i
, info
);
2424 } else if (any_ineq(&info
[i
], STATUS_ADJ_INEQ
) ||
2425 any_ineq(&info
[j
], STATUS_ADJ_INEQ
)) {
2426 change
= check_adj_ineq(i
, j
, info
);
2428 if (!any_eq(&info
[i
], STATUS_CUT
) &&
2429 !any_eq(&info
[j
], STATUS_CUT
))
2430 change
= check_facets(i
, j
, info
);
2431 if (change
== isl_change_none
)
2432 change
= check_wrap(i
, j
, info
);
2436 clear_status(&info
[i
]);
2437 clear_status(&info
[j
]);
2440 clear_status(&info
[i
]);
2441 clear_status(&info
[j
]);
2442 return isl_change_error
;
2445 /* Check if the union of the given pair of basic maps
2446 * can be represented by a single basic map.
2447 * If so, replace the pair by the single basic map and return
2448 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
2449 * Otherwise, return isl_change_none.
2450 * The two basic maps are assumed to live in the same local space.
2452 static enum isl_change
coalesce_local_pair(int i
, int j
,
2453 struct isl_coalesce_info
*info
)
2455 init_status(&info
[i
]);
2456 init_status(&info
[j
]);
2457 return coalesce_local_pair_reuse(i
, j
, info
);
2460 /* Shift the integer division at position "div" of the basic map
2461 * represented by "info" by "shift".
2463 * That is, if the integer division has the form
2467 * then replace it by
2469 * floor((f(x) + shift * d)/d) - shift
2471 static isl_stat
shift_div(struct isl_coalesce_info
*info
, int div
,
2474 isl_size total
, n_div
;
2476 info
->bmap
= isl_basic_map_shift_div(info
->bmap
, div
, 0, shift
);
2478 return isl_stat_error
;
2480 total
= isl_basic_map_dim(info
->bmap
, isl_dim_all
);
2481 n_div
= isl_basic_map_dim(info
->bmap
, isl_dim_div
);
2482 if (total
< 0 || n_div
< 0)
2483 return isl_stat_error
;
2485 if (isl_tab_shift_var(info
->tab
, total
+ div
, shift
) < 0)
2486 return isl_stat_error
;
2491 /* If the integer division at position "div" is defined by an equality,
2492 * i.e., a stride constraint, then change the integer division expression
2493 * to have a constant term equal to zero.
2495 * Let the equality constraint be
2499 * The integer division expression is then typically of the form
2501 * a = floor((-f - c')/m)
2503 * The integer division is first shifted by t = floor(c/m),
2504 * turning the equality constraint into
2506 * c - m floor(c/m) + f + m a' = 0
2510 * (c mod m) + f + m a' = 0
2514 * a' = (-f - (c mod m))/m = floor((-f)/m)
2516 * because a' is an integer and 0 <= (c mod m) < m.
2517 * The constant term of a' can therefore be zeroed out,
2518 * but only if the integer division expression is of the expected form.
2520 static isl_stat
normalize_stride_div(struct isl_coalesce_info
*info
, int div
)
2522 isl_bool defined
, valid
;
2525 isl_int shift
, stride
;
2527 defined
= isl_basic_map_has_defining_equality(info
->bmap
, isl_dim_div
,
2530 return isl_stat_error
;
2534 return isl_stat_error
;
2535 valid
= isl_constraint_is_div_equality(c
, div
);
2536 isl_int_init(shift
);
2537 isl_int_init(stride
);
2538 isl_constraint_get_constant(c
, &shift
);
2539 isl_constraint_get_coefficient(c
, isl_dim_div
, div
, &stride
);
2540 isl_int_fdiv_q(shift
, shift
, stride
);
2541 r
= shift_div(info
, div
, shift
);
2542 isl_int_clear(stride
);
2543 isl_int_clear(shift
);
2544 isl_constraint_free(c
);
2545 if (r
< 0 || valid
< 0)
2546 return isl_stat_error
;
2549 info
->bmap
= isl_basic_map_set_div_expr_constant_num_si_inplace(
2550 info
->bmap
, div
, 0);
2552 return isl_stat_error
;
2556 /* The basic maps represented by "info1" and "info2" are known
2557 * to have the same number of integer divisions.
2558 * Check if pairs of integer divisions are equal to each other
2559 * despite the fact that they differ by a rational constant.
2561 * In particular, look for any pair of integer divisions that
2562 * only differ in their constant terms.
2563 * If either of these integer divisions is defined
2564 * by stride constraints, then modify it to have a zero constant term.
2565 * If both are defined by stride constraints then in the end they will have
2566 * the same (zero) constant term.
2568 static isl_stat
harmonize_stride_divs(struct isl_coalesce_info
*info1
,
2569 struct isl_coalesce_info
*info2
)
2574 n
= isl_basic_map_dim(info1
->bmap
, isl_dim_div
);
2576 return isl_stat_error
;
2577 for (i
= 0; i
< n
; ++i
) {
2578 isl_bool known
, harmonize
;
2580 known
= isl_basic_map_div_is_known(info1
->bmap
, i
);
2581 if (known
>= 0 && known
)
2582 known
= isl_basic_map_div_is_known(info2
->bmap
, i
);
2584 return isl_stat_error
;
2587 harmonize
= isl_basic_map_equal_div_expr_except_constant(
2588 info1
->bmap
, i
, info2
->bmap
, i
);
2590 return isl_stat_error
;
2593 if (normalize_stride_div(info1
, i
) < 0)
2594 return isl_stat_error
;
2595 if (normalize_stride_div(info2
, i
) < 0)
2596 return isl_stat_error
;
2602 /* If "shift" is an integer constant, then shift the integer division
2603 * at position "div" of the basic map represented by "info" by "shift".
2604 * If "shift" is not an integer constant, then do nothing.
2605 * If "shift" is equal to zero, then no shift needs to be performed either.
2607 * That is, if the integer division has the form
2611 * then replace it by
2613 * floor((f(x) + shift * d)/d) - shift
2615 static isl_stat
shift_if_cst_int(struct isl_coalesce_info
*info
, int div
,
2616 __isl_keep isl_aff
*shift
)
2623 cst
= isl_aff_is_cst(shift
);
2624 if (cst
< 0 || !cst
)
2625 return cst
< 0 ? isl_stat_error
: isl_stat_ok
;
2627 c
= isl_aff_get_constant_val(shift
);
2628 cst
= isl_val_is_int(c
);
2629 if (cst
>= 0 && cst
)
2630 cst
= isl_bool_not(isl_val_is_zero(c
));
2631 if (cst
< 0 || !cst
) {
2633 return cst
< 0 ? isl_stat_error
: isl_stat_ok
;
2637 r
= isl_val_get_num_isl_int(c
, &d
);
2639 r
= shift_div(info
, div
, d
);
2647 /* Check if some of the divs in the basic map represented by "info1"
2648 * are shifts of the corresponding divs in the basic map represented
2649 * by "info2", taking into account the equality constraints "eq1" of "info1"
2650 * and "eq2" of "info2". If so, align them with those of "info2".
2651 * "info1" and "info2" are assumed to have the same number
2652 * of integer divisions.
2654 * An integer division is considered to be a shift of another integer
2655 * division if, after simplification with respect to the equality
2656 * constraints of the other basic map, one is equal to the other
2659 * In particular, for each pair of integer divisions, if both are known,
2660 * have the same denominator and are not already equal to each other,
2661 * simplify each with respect to the equality constraints
2662 * of the other basic map. If the difference is an integer constant,
2663 * then move this difference outside.
2664 * That is, if, after simplification, one integer division is of the form
2666 * floor((f(x) + c_1)/d)
2668 * while the other is of the form
2670 * floor((f(x) + c_2)/d)
2672 * and n = (c_2 - c_1)/d is an integer, then replace the first
2673 * integer division by
2675 * floor((f_1(x) + c_1 + n * d)/d) - n,
2677 * where floor((f_1(x) + c_1 + n * d)/d) = floor((f2(x) + c_2)/d)
2678 * after simplification with respect to the equality constraints.
2680 static isl_stat
harmonize_divs_with_hulls(struct isl_coalesce_info
*info1
,
2681 struct isl_coalesce_info
*info2
, __isl_keep isl_basic_set
*eq1
,
2682 __isl_keep isl_basic_set
*eq2
)
2686 isl_local_space
*ls1
, *ls2
;
2688 total
= isl_basic_map_dim(info1
->bmap
, isl_dim_all
);
2690 return isl_stat_error
;
2691 ls1
= isl_local_space_wrap(isl_basic_map_get_local_space(info1
->bmap
));
2692 ls2
= isl_local_space_wrap(isl_basic_map_get_local_space(info2
->bmap
));
2693 for (i
= 0; i
< info1
->bmap
->n_div
; ++i
) {
2695 isl_aff
*div1
, *div2
;
2697 if (!isl_local_space_div_is_known(ls1
, i
) ||
2698 !isl_local_space_div_is_known(ls2
, i
))
2700 if (isl_int_ne(info1
->bmap
->div
[i
][0], info2
->bmap
->div
[i
][0]))
2702 if (isl_seq_eq(info1
->bmap
->div
[i
] + 1,
2703 info2
->bmap
->div
[i
] + 1, 1 + total
))
2705 div1
= isl_local_space_get_div(ls1
, i
);
2706 div2
= isl_local_space_get_div(ls2
, i
);
2707 div1
= isl_aff_substitute_equalities(div1
,
2708 isl_basic_set_copy(eq2
));
2709 div2
= isl_aff_substitute_equalities(div2
,
2710 isl_basic_set_copy(eq1
));
2711 div2
= isl_aff_sub(div2
, div1
);
2712 r
= shift_if_cst_int(info1
, i
, div2
);
2717 isl_local_space_free(ls1
);
2718 isl_local_space_free(ls2
);
2720 if (i
< info1
->bmap
->n_div
)
2721 return isl_stat_error
;
2725 /* Check if some of the divs in the basic map represented by "info1"
2726 * are shifts of the corresponding divs in the basic map represented
2727 * by "info2". If so, align them with those of "info2".
2728 * Only do this if "info1" and "info2" have the same number
2729 * of integer divisions.
2731 * An integer division is considered to be a shift of another integer
2732 * division if, after simplification with respect to the equality
2733 * constraints of the other basic map, one is equal to the other
2736 * First check if pairs of integer divisions are equal to each other
2737 * despite the fact that they differ by a rational constant.
2738 * If so, try and arrange for them to have the same constant term.
2740 * Then, extract the equality constraints and continue with
2741 * harmonize_divs_with_hulls.
2743 * If the equality constraints of both basic maps are the same,
2744 * then there is no need to perform any shifting since
2745 * the coefficients of the integer divisions should have been
2746 * reduced in the same way.
2748 static isl_stat
harmonize_divs(struct isl_coalesce_info
*info1
,
2749 struct isl_coalesce_info
*info2
)
2752 isl_basic_map
*bmap1
, *bmap2
;
2753 isl_basic_set
*eq1
, *eq2
;
2756 if (!info1
->bmap
|| !info2
->bmap
)
2757 return isl_stat_error
;
2759 if (info1
->bmap
->n_div
!= info2
->bmap
->n_div
)
2761 if (info1
->bmap
->n_div
== 0)
2764 if (harmonize_stride_divs(info1
, info2
) < 0)
2765 return isl_stat_error
;
2767 bmap1
= isl_basic_map_copy(info1
->bmap
);
2768 bmap2
= isl_basic_map_copy(info2
->bmap
);
2769 eq1
= isl_basic_map_wrap(isl_basic_map_plain_affine_hull(bmap1
));
2770 eq2
= isl_basic_map_wrap(isl_basic_map_plain_affine_hull(bmap2
));
2771 equal
= isl_basic_set_plain_is_equal(eq1
, eq2
);
2777 r
= harmonize_divs_with_hulls(info1
, info2
, eq1
, eq2
);
2778 isl_basic_set_free(eq1
);
2779 isl_basic_set_free(eq2
);
2784 /* Do the two basic maps live in the same local space, i.e.,
2785 * do they have the same (known) divs?
2786 * If either basic map has any unknown divs, then we can only assume
2787 * that they do not live in the same local space.
2789 static isl_bool
same_divs(__isl_keep isl_basic_map
*bmap1
,
2790 __isl_keep isl_basic_map
*bmap2
)
2796 if (!bmap1
|| !bmap2
)
2797 return isl_bool_error
;
2798 if (bmap1
->n_div
!= bmap2
->n_div
)
2799 return isl_bool_false
;
2801 if (bmap1
->n_div
== 0)
2802 return isl_bool_true
;
2804 known
= isl_basic_map_divs_known(bmap1
);
2805 if (known
< 0 || !known
)
2807 known
= isl_basic_map_divs_known(bmap2
);
2808 if (known
< 0 || !known
)
2811 total
= isl_basic_map_dim(bmap1
, isl_dim_all
);
2813 return isl_bool_error
;
2814 for (i
= 0; i
< bmap1
->n_div
; ++i
)
2815 if (!isl_seq_eq(bmap1
->div
[i
], bmap2
->div
[i
], 2 + total
))
2816 return isl_bool_false
;
2818 return isl_bool_true
;
2821 /* Assuming that "tab" contains the equality constraints and
2822 * the initial inequality constraints of "bmap", copy the remaining
2823 * inequality constraints of "bmap" to "Tab".
2825 static isl_stat
copy_ineq(struct isl_tab
*tab
, __isl_keep isl_basic_map
*bmap
)
2830 return isl_stat_error
;
2832 n_ineq
= tab
->n_con
- tab
->n_eq
;
2833 for (i
= n_ineq
; i
< bmap
->n_ineq
; ++i
)
2834 if (isl_tab_add_ineq(tab
, bmap
->ineq
[i
]) < 0)
2835 return isl_stat_error
;
2840 /* Description of an integer division that is added
2841 * during an expansion.
2842 * "pos" is the position of the corresponding variable.
2843 * "cst" indicates whether this integer division has a fixed value.
2844 * "val" contains the fixed value, if the value is fixed.
2846 struct isl_expanded
{
2852 /* For each of the "n" integer division variables "expanded",
2853 * if the variable has a fixed value, then add two inequality
2854 * constraints expressing the fixed value.
2855 * Otherwise, add the corresponding div constraints.
2856 * The caller is responsible for removing the div constraints
2857 * that it added for all these "n" integer divisions.
2859 * The div constraints and the pair of inequality constraints
2860 * forcing the fixed value cannot both be added for a given variable
2861 * as the combination may render some of the original constraints redundant.
2862 * These would then be ignored during the coalescing detection,
2863 * while they could remain in the fused result.
2865 * The two added inequality constraints are
2870 * with "a" the variable and "v" its fixed value.
2871 * The facet corresponding to one of these two constraints is selected
2872 * in the tableau to ensure that the pair of inequality constraints
2873 * is treated as an equality constraint.
2875 * The information in info->ineq is thrown away because it was
2876 * computed in terms of div constraints, while some of those
2877 * have now been replaced by these pairs of inequality constraints.
2879 static isl_stat
fix_constant_divs(struct isl_coalesce_info
*info
,
2880 int n
, struct isl_expanded
*expanded
)
2886 o_div
= isl_basic_map_offset(info
->bmap
, isl_dim_div
) - 1;
2887 ineq
= isl_vec_alloc(isl_tab_get_ctx(info
->tab
), 1 + info
->tab
->n_var
);
2889 return isl_stat_error
;
2890 isl_seq_clr(ineq
->el
+ 1, info
->tab
->n_var
);
2892 for (i
= 0; i
< n
; ++i
) {
2893 if (!expanded
[i
].cst
) {
2894 info
->bmap
= isl_basic_map_extend_constraints(
2896 info
->bmap
= isl_basic_map_add_div_constraints(
2897 info
->bmap
, expanded
[i
].pos
- o_div
);
2899 isl_int_set_si(ineq
->el
[1 + expanded
[i
].pos
], -1);
2900 isl_int_set(ineq
->el
[0], expanded
[i
].val
);
2901 info
->bmap
= isl_basic_map_add_ineq(info
->bmap
,
2903 isl_int_set_si(ineq
->el
[1 + expanded
[i
].pos
], 1);
2904 isl_int_neg(ineq
->el
[0], expanded
[i
].val
);
2905 info
->bmap
= isl_basic_map_add_ineq(info
->bmap
,
2907 isl_int_set_si(ineq
->el
[1 + expanded
[i
].pos
], 0);
2909 if (copy_ineq(info
->tab
, info
->bmap
) < 0)
2911 if (expanded
[i
].cst
&&
2912 isl_tab_select_facet(info
->tab
, info
->tab
->n_con
- 1) < 0)
2921 return i
< n
? isl_stat_error
: isl_stat_ok
;
2924 /* Insert the "n" integer division variables "expanded"
2925 * into info->tab and info->bmap and
2926 * update info->ineq with respect to the redundant constraints
2927 * in the resulting tableau.
2928 * "bmap" contains the result of this insertion in info->bmap,
2929 * while info->bmap is the original version
2930 * of "bmap", i.e., the one that corresponds to the current
2931 * state of info->tab. The number of constraints in info->bmap
2932 * is assumed to be the same as the number of constraints
2933 * in info->tab. This is required to be able to detect
2934 * the extra constraints in "bmap".
2936 * In particular, introduce extra variables corresponding
2937 * to the extra integer divisions and add the div constraints
2938 * that were added to "bmap" after info->tab was created
2940 * Furthermore, check if these extra integer divisions happen
2941 * to attain a fixed integer value in info->tab.
2942 * If so, replace the corresponding div constraints by pairs
2943 * of inequality constraints that fix these
2944 * integer divisions to their single integer values.
2945 * Replace info->bmap by "bmap" to match the changes to info->tab.
2946 * info->ineq was computed without a tableau and therefore
2947 * does not take into account the redundant constraints
2948 * in the tableau. Mark them here.
2949 * There is no need to check the newly added div constraints
2950 * since they cannot be redundant.
2951 * The redundancy check is not performed when constants have been discovered
2952 * since info->ineq is completely thrown away in this case.
2954 static isl_stat
tab_insert_divs(struct isl_coalesce_info
*info
,
2955 int n
, struct isl_expanded
*expanded
, __isl_take isl_basic_map
*bmap
)
2959 struct isl_tab_undo
*snap
;
2963 return isl_stat_error
;
2964 if (info
->bmap
->n_eq
+ info
->bmap
->n_ineq
!= info
->tab
->n_con
)
2965 isl_die(isl_basic_map_get_ctx(bmap
), isl_error_internal
,
2966 "original tableau does not correspond "
2967 "to original basic map", goto error
);
2969 if (isl_tab_extend_vars(info
->tab
, n
) < 0)
2971 if (isl_tab_extend_cons(info
->tab
, 2 * n
) < 0)
2974 for (i
= 0; i
< n
; ++i
) {
2975 if (isl_tab_insert_var(info
->tab
, expanded
[i
].pos
) < 0)
2979 snap
= isl_tab_snap(info
->tab
);
2981 n_ineq
= info
->tab
->n_con
- info
->tab
->n_eq
;
2982 if (copy_ineq(info
->tab
, bmap
) < 0)
2985 isl_basic_map_free(info
->bmap
);
2989 for (i
= 0; i
< n
; ++i
) {
2990 expanded
[i
].cst
= isl_tab_is_constant(info
->tab
,
2991 expanded
[i
].pos
, &expanded
[i
].val
);
2992 if (expanded
[i
].cst
< 0)
2993 return isl_stat_error
;
2994 if (expanded
[i
].cst
)
2999 if (isl_tab_rollback(info
->tab
, snap
) < 0)
3000 return isl_stat_error
;
3001 info
->bmap
= isl_basic_map_cow(info
->bmap
);
3002 info
->bmap
= isl_basic_map_free_inequality(info
->bmap
, 2 * n
);
3004 return isl_stat_error
;
3006 return fix_constant_divs(info
, n
, expanded
);
3009 n_eq
= info
->bmap
->n_eq
;
3010 for (i
= 0; i
< n_ineq
; ++i
) {
3011 if (isl_tab_is_redundant(info
->tab
, n_eq
+ i
))
3012 info
->ineq
[i
] = STATUS_REDUNDANT
;
3017 isl_basic_map_free(bmap
);
3018 return isl_stat_error
;
3021 /* Expand info->tab and info->bmap in the same way "bmap" was expanded
3022 * in isl_basic_map_expand_divs using the expansion "exp" and
3023 * update info->ineq with respect to the redundant constraints
3024 * in the resulting tableau. info->bmap is the original version
3025 * of "bmap", i.e., the one that corresponds to the current
3026 * state of info->tab. The number of constraints in info->bmap
3027 * is assumed to be the same as the number of constraints
3028 * in info->tab. This is required to be able to detect
3029 * the extra constraints in "bmap".
3031 * Extract the positions where extra local variables are introduced
3032 * from "exp" and call tab_insert_divs.
3034 static isl_stat
expand_tab(struct isl_coalesce_info
*info
, int *exp
,
3035 __isl_take isl_basic_map
*bmap
)
3038 struct isl_expanded
*expanded
;
3041 isl_size total
, n_div
;
3045 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
3046 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
3047 if (total
< 0 || n_div
< 0)
3048 return isl_stat_error
;
3049 pos
= total
- n_div
;
3050 extra_var
= total
- info
->tab
->n_var
;
3051 n
= n_div
- extra_var
;
3053 ctx
= isl_basic_map_get_ctx(bmap
);
3054 expanded
= isl_calloc_array(ctx
, struct isl_expanded
, extra_var
);
3055 if (extra_var
&& !expanded
)
3060 for (j
= 0; j
< n_div
; ++j
) {
3061 if (i
< n
&& exp
[i
] == j
) {
3065 expanded
[k
++].pos
= pos
+ j
;
3068 for (k
= 0; k
< extra_var
; ++k
)
3069 isl_int_init(expanded
[k
].val
);
3071 r
= tab_insert_divs(info
, extra_var
, expanded
, bmap
);
3073 for (k
= 0; k
< extra_var
; ++k
)
3074 isl_int_clear(expanded
[k
].val
);
3079 isl_basic_map_free(bmap
);
3080 return isl_stat_error
;
3083 /* Check if the union of the basic maps represented by info[i] and info[j]
3084 * can be represented by a single basic map,
3085 * after expanding the divs of info[i] to match those of info[j].
3086 * If so, replace the pair by the single basic map and return
3087 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
3088 * Otherwise, return isl_change_none.
3090 * The caller has already checked for info[j] being a subset of info[i].
3091 * If some of the divs of info[j] are unknown, then the expanded info[i]
3092 * will not have the corresponding div constraints. The other patterns
3093 * therefore cannot apply. Skip the computation in this case.
3095 * The expansion is performed using the divs "div" and expansion "exp"
3096 * computed by the caller.
3097 * info[i].bmap has already been expanded and the result is passed in
3099 * The "eq" and "ineq" fields of info[i] reflect the status of
3100 * the constraints of the expanded "bmap" with respect to info[j].tab.
3101 * However, inequality constraints that are redundant in info[i].tab
3102 * have not yet been marked as such because no tableau was available.
3104 * Replace info[i].bmap by "bmap" and expand info[i].tab as well,
3105 * updating info[i].ineq with respect to the redundant constraints.
3106 * Then try and coalesce the expanded info[i] with info[j],
3107 * reusing the information in info[i].eq and info[i].ineq.
3108 * If this does not result in any coalescing or if it results in info[j]
3109 * getting dropped (which should not happen in practice, since the case
3110 * of info[j] being a subset of info[i] has already been checked by
3111 * the caller), then revert info[i] to its original state.
3113 static enum isl_change
coalesce_expand_tab_divs(__isl_take isl_basic_map
*bmap
,
3114 int i
, int j
, struct isl_coalesce_info
*info
, __isl_keep isl_mat
*div
,
3118 isl_basic_map
*bmap_i
;
3119 struct isl_tab_undo
*snap
;
3120 enum isl_change change
= isl_change_none
;
3122 known
= isl_basic_map_divs_known(info
[j
].bmap
);
3123 if (known
< 0 || !known
) {
3124 clear_status(&info
[i
]);
3125 isl_basic_map_free(bmap
);
3126 return known
< 0 ? isl_change_error
: isl_change_none
;
3129 bmap_i
= isl_basic_map_copy(info
[i
].bmap
);
3130 snap
= isl_tab_snap(info
[i
].tab
);
3131 if (expand_tab(&info
[i
], exp
, bmap
) < 0)
3132 change
= isl_change_error
;
3134 init_status(&info
[j
]);
3135 if (change
== isl_change_none
)
3136 change
= coalesce_local_pair_reuse(i
, j
, info
);
3138 clear_status(&info
[i
]);
3139 if (change
!= isl_change_none
&& change
!= isl_change_drop_second
) {
3140 isl_basic_map_free(bmap_i
);
3142 isl_basic_map_free(info
[i
].bmap
);
3143 info
[i
].bmap
= bmap_i
;
3145 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
3146 change
= isl_change_error
;
3152 /* Check if the union of "bmap" and the basic map represented by info[j]
3153 * can be represented by a single basic map,
3154 * after expanding the divs of "bmap" to match those of info[j].
3155 * If so, replace the pair by the single basic map and return
3156 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
3157 * Otherwise, return isl_change_none.
3159 * In particular, check if the expanded "bmap" contains the basic map
3160 * represented by the tableau info[j].tab.
3161 * The expansion is performed using the divs "div" and expansion "exp"
3162 * computed by the caller.
3163 * Then we check if all constraints of the expanded "bmap" are valid for
3166 * If "i" is not equal to -1, then "bmap" is equal to info[i].bmap.
3167 * In this case, the positions of the constraints of info[i].bmap
3168 * with respect to the basic map represented by info[j] are stored
3171 * If the expanded "bmap" does not contain the basic map
3172 * represented by the tableau info[j].tab and if "i" is not -1,
3173 * i.e., if the original "bmap" is info[i].bmap, then expand info[i].tab
3174 * as well and check if that results in coalescing.
3176 static enum isl_change
coalesce_with_expanded_divs(
3177 __isl_keep isl_basic_map
*bmap
, int i
, int j
,
3178 struct isl_coalesce_info
*info
, __isl_keep isl_mat
*div
, int *exp
)
3180 enum isl_change change
= isl_change_none
;
3181 struct isl_coalesce_info info_local
, *info_i
;
3183 info_i
= i
>= 0 ? &info
[i
] : &info_local
;
3184 init_status(info_i
);
3185 bmap
= isl_basic_map_copy(bmap
);
3186 bmap
= isl_basic_map_expand_divs(bmap
, isl_mat_copy(div
), exp
);
3187 bmap
= isl_basic_map_mark_final(bmap
);
3192 info_local
.bmap
= bmap
;
3193 info_i
->eq
= eq_status_in(bmap
, info
[j
].tab
);
3194 if (bmap
->n_eq
&& !info_i
->eq
)
3196 if (any_eq(info_i
, STATUS_ERROR
))
3198 if (any_eq(info_i
, STATUS_SEPARATE
))
3201 info_i
->ineq
= ineq_status_in(bmap
, NULL
, info
[j
].tab
);
3202 if (bmap
->n_ineq
&& !info_i
->ineq
)
3204 if (any_ineq(info_i
, STATUS_ERROR
))
3206 if (any_ineq(info_i
, STATUS_SEPARATE
))
3209 if (all(info_i
->eq
, 2 * bmap
->n_eq
, STATUS_VALID
) &&
3210 all(info_i
->ineq
, bmap
->n_ineq
, STATUS_VALID
)) {
3212 change
= isl_change_drop_second
;
3215 if (change
== isl_change_none
&& i
!= -1)
3216 return coalesce_expand_tab_divs(bmap
, i
, j
, info
, div
, exp
);
3219 isl_basic_map_free(bmap
);
3220 clear_status(info_i
);
3223 isl_basic_map_free(bmap
);
3224 clear_status(info_i
);
3225 return isl_change_error
;
3228 /* Check if the union of "bmap_i" and the basic map represented by info[j]
3229 * can be represented by a single basic map,
3230 * after aligning the divs of "bmap_i" to match those of info[j].
3231 * If so, replace the pair by the single basic map and return
3232 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
3233 * Otherwise, return isl_change_none.
3235 * In particular, check if "bmap_i" contains the basic map represented by
3236 * info[j] after aligning the divs of "bmap_i" to those of info[j].
3237 * Note that this can only succeed if the number of divs of "bmap_i"
3238 * is smaller than (or equal to) the number of divs of info[j].
3240 * We first check if the divs of "bmap_i" are all known and form a subset
3241 * of those of info[j].bmap. If so, we pass control over to
3242 * coalesce_with_expanded_divs.
3244 * If "i" is not equal to -1, then "bmap" is equal to info[i].bmap.
3246 static enum isl_change
coalesce_after_aligning_divs(
3247 __isl_keep isl_basic_map
*bmap_i
, int i
, int j
,
3248 struct isl_coalesce_info
*info
)
3251 isl_mat
*div_i
, *div_j
, *div
;
3255 enum isl_change change
;
3257 known
= isl_basic_map_divs_known(bmap_i
);
3259 return isl_change_error
;
3261 return isl_change_none
;
3263 ctx
= isl_basic_map_get_ctx(bmap_i
);
3265 div_i
= isl_basic_map_get_divs(bmap_i
);
3266 div_j
= isl_basic_map_get_divs(info
[j
].bmap
);
3268 if (!div_i
|| !div_j
)
3271 exp1
= isl_alloc_array(ctx
, int, div_i
->n_row
);
3272 exp2
= isl_alloc_array(ctx
, int, div_j
->n_row
);
3273 if ((div_i
->n_row
&& !exp1
) || (div_j
->n_row
&& !exp2
))
3276 div
= isl_merge_divs(div_i
, div_j
, exp1
, exp2
);
3280 if (div
->n_row
== div_j
->n_row
)
3281 change
= coalesce_with_expanded_divs(bmap_i
,
3282 i
, j
, info
, div
, exp1
);
3284 change
= isl_change_none
;
3288 isl_mat_free(div_i
);
3289 isl_mat_free(div_j
);
3296 isl_mat_free(div_i
);
3297 isl_mat_free(div_j
);
3300 return isl_change_error
;
3303 /* Check if basic map "j" is a subset of basic map "i" after
3304 * exploiting the extra equalities of "j" to simplify the divs of "i".
3305 * If so, remove basic map "j" and return isl_change_drop_second.
3307 * If "j" does not have any equalities or if they are the same
3308 * as those of "i", then we cannot exploit them to simplify the divs.
3309 * Similarly, if there are no divs in "i", then they cannot be simplified.
3310 * If, on the other hand, the affine hulls of "i" and "j" do not intersect,
3311 * then "j" cannot be a subset of "i".
3313 * Otherwise, we intersect "i" with the affine hull of "j" and then
3314 * check if "j" is a subset of the result after aligning the divs.
3315 * If so, then "j" is definitely a subset of "i" and can be removed.
3316 * Note that if after intersection with the affine hull of "j".
3317 * "i" still has more divs than "j", then there is no way we can
3318 * align the divs of "i" to those of "j".
3320 static enum isl_change
coalesce_subset_with_equalities(int i
, int j
,
3321 struct isl_coalesce_info
*info
)
3323 isl_basic_map
*hull_i
, *hull_j
, *bmap_i
;
3325 enum isl_change change
;
3327 if (info
[j
].bmap
->n_eq
== 0)
3328 return isl_change_none
;
3329 if (info
[i
].bmap
->n_div
== 0)
3330 return isl_change_none
;
3332 hull_i
= isl_basic_map_copy(info
[i
].bmap
);
3333 hull_i
= isl_basic_map_plain_affine_hull(hull_i
);
3334 hull_j
= isl_basic_map_copy(info
[j
].bmap
);
3335 hull_j
= isl_basic_map_plain_affine_hull(hull_j
);
3337 hull_j
= isl_basic_map_intersect(hull_j
, isl_basic_map_copy(hull_i
));
3338 equal
= isl_basic_map_plain_is_equal(hull_i
, hull_j
);
3339 empty
= isl_basic_map_plain_is_empty(hull_j
);
3340 isl_basic_map_free(hull_i
);
3342 if (equal
< 0 || equal
|| empty
< 0 || empty
) {
3343 isl_basic_map_free(hull_j
);
3344 if (equal
< 0 || empty
< 0)
3345 return isl_change_error
;
3346 return isl_change_none
;
3349 bmap_i
= isl_basic_map_copy(info
[i
].bmap
);
3350 bmap_i
= isl_basic_map_intersect(bmap_i
, hull_j
);
3352 return isl_change_error
;
3354 if (bmap_i
->n_div
> info
[j
].bmap
->n_div
) {
3355 isl_basic_map_free(bmap_i
);
3356 return isl_change_none
;
3359 change
= coalesce_after_aligning_divs(bmap_i
, -1, j
, info
);
3361 isl_basic_map_free(bmap_i
);
3366 /* Check if the union of and the basic maps represented by info[i] and info[j]
3367 * can be represented by a single basic map, by aligning or equating
3368 * their integer divisions.
3369 * If so, replace the pair by the single basic map and return
3370 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
3371 * Otherwise, return isl_change_none.
3373 * Note that we only perform any test if the number of divs is different
3374 * in the two basic maps. In case the number of divs is the same,
3375 * we have already established that the divs are different
3376 * in the two basic maps.
3377 * In particular, if the number of divs of basic map i is smaller than
3378 * the number of divs of basic map j, then we check if j is a subset of i
3381 static enum isl_change
coalesce_divs(int i
, int j
,
3382 struct isl_coalesce_info
*info
)
3384 enum isl_change change
= isl_change_none
;
3386 if (info
[i
].bmap
->n_div
< info
[j
].bmap
->n_div
)
3387 change
= coalesce_after_aligning_divs(info
[i
].bmap
, i
, j
, info
);
3388 if (change
!= isl_change_none
)
3391 if (info
[j
].bmap
->n_div
< info
[i
].bmap
->n_div
)
3392 change
= coalesce_after_aligning_divs(info
[j
].bmap
, j
, i
, info
);
3393 if (change
!= isl_change_none
)
3394 return invert_change(change
);
3396 change
= coalesce_subset_with_equalities(i
, j
, info
);
3397 if (change
!= isl_change_none
)
3400 change
= coalesce_subset_with_equalities(j
, i
, info
);
3401 if (change
!= isl_change_none
)
3402 return invert_change(change
);
3404 return isl_change_none
;
3407 /* Does "bmap" involve any divs that themselves refer to divs?
3409 static isl_bool
has_nested_div(__isl_keep isl_basic_map
*bmap
)
3415 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
3416 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
3417 if (total
< 0 || n_div
< 0)
3418 return isl_bool_error
;
3421 for (i
= 0; i
< n_div
; ++i
)
3422 if (isl_seq_first_non_zero(bmap
->div
[i
] + 2 + total
,
3424 return isl_bool_true
;
3426 return isl_bool_false
;
3429 /* Return a list of affine expressions, one for each integer division
3430 * in "bmap_i". For each integer division that also appears in "bmap_j",
3431 * the affine expression is set to NaN. The number of NaNs in the list
3432 * is equal to the number of integer divisions in "bmap_j".
3433 * For the other integer divisions of "bmap_i", the corresponding
3434 * element in the list is a purely affine expression equal to the integer
3435 * division in "hull".
3436 * If no such list can be constructed, then the number of elements
3437 * in the returned list is smaller than the number of integer divisions
3440 static __isl_give isl_aff_list
*set_up_substitutions(
3441 __isl_keep isl_basic_map
*bmap_i
, __isl_keep isl_basic_map
*bmap_j
,
3442 __isl_take isl_basic_map
*hull
)
3444 isl_size n_div_i
, n_div_j
, total
;
3446 isl_local_space
*ls
;
3447 isl_basic_set
*wrap_hull
;
3452 n_div_i
= isl_basic_map_dim(bmap_i
, isl_dim_div
);
3453 n_div_j
= isl_basic_map_dim(bmap_j
, isl_dim_div
);
3454 total
= isl_basic_map_dim(bmap_i
, isl_dim_all
);
3455 if (!hull
|| n_div_i
< 0 || n_div_j
< 0 || total
< 0)
3458 ctx
= isl_basic_map_get_ctx(hull
);
3461 ls
= isl_basic_map_get_local_space(bmap_i
);
3462 ls
= isl_local_space_wrap(ls
);
3463 wrap_hull
= isl_basic_map_wrap(hull
);
3465 aff_nan
= isl_aff_nan_on_domain(isl_local_space_copy(ls
));
3466 list
= isl_aff_list_alloc(ctx
, n_div_i
);
3469 for (i
= 0; i
< n_div_i
; ++i
) {
3474 isl_basic_map_equal_div_expr_part(bmap_i
, i
, bmap_j
, j
,
3477 list
= isl_aff_list_add(list
, isl_aff_copy(aff_nan
));
3480 if (n_div_i
- i
<= n_div_j
- j
)
3483 aff
= isl_local_space_get_div(ls
, i
);
3484 aff
= isl_aff_substitute_equalities(aff
,
3485 isl_basic_set_copy(wrap_hull
));
3486 aff
= isl_aff_floor(aff
);
3487 n_div
= isl_aff_dim(aff
, isl_dim_div
);
3495 list
= isl_aff_list_add(list
, aff
);
3498 isl_aff_free(aff_nan
);
3499 isl_local_space_free(ls
);
3500 isl_basic_set_free(wrap_hull
);
3504 isl_aff_free(aff_nan
);
3505 isl_local_space_free(ls
);
3506 isl_basic_set_free(wrap_hull
);
3507 isl_aff_list_free(list
);
3511 /* Add variables to info->bmap and info->tab corresponding to the elements
3512 * in "list" that are not set to NaN.
3513 * "extra_var" is the number of these elements.
3514 * "dim" is the offset in the variables of "tab" where we should
3515 * start considering the elements in "list".
3516 * When this function returns, the total number of variables in "tab"
3517 * is equal to "dim" plus the number of elements in "list".
3519 * The newly added existentially quantified variables are not given
3520 * an explicit representation because the corresponding div constraints
3521 * do not appear in info->bmap. These constraints are not added
3522 * to info->bmap because for internal consistency, they would need to
3523 * be added to info->tab as well, where they could combine with the equality
3524 * that is added later to result in constraints that do not hold
3525 * in the original input.
3527 static isl_stat
add_sub_vars(struct isl_coalesce_info
*info
,
3528 __isl_keep isl_aff_list
*list
, int dim
, int extra_var
)
3533 info
->bmap
= isl_basic_map_cow(info
->bmap
);
3534 info
->bmap
= isl_basic_map_extend(info
->bmap
, extra_var
, 0, 0);
3535 n
= isl_aff_list_n_aff(list
);
3536 if (!info
->bmap
|| n
< 0)
3537 return isl_stat_error
;
3538 for (i
= 0; i
< n
; ++i
) {
3542 aff
= isl_aff_list_get_aff(list
, i
);
3543 is_nan
= isl_aff_is_nan(aff
);
3546 return isl_stat_error
;
3550 if (isl_tab_insert_var(info
->tab
, dim
+ i
) < 0)
3551 return isl_stat_error
;
3552 d
= isl_basic_map_alloc_div(info
->bmap
);
3554 return isl_stat_error
;
3555 info
->bmap
= isl_basic_map_mark_div_unknown(info
->bmap
, d
);
3556 for (j
= d
; j
> i
; --j
)
3557 info
->bmap
= isl_basic_map_swap_div(info
->bmap
,
3560 return isl_stat_error
;
3566 /* For each element in "list" that is not set to NaN, fix the corresponding
3567 * variable in "tab" to the purely affine expression defined by the element.
3568 * "dim" is the offset in the variables of "tab" where we should
3569 * start considering the elements in "list".
3571 * This function assumes that a sufficient number of rows and
3572 * elements in the constraint array are available in the tableau.
3574 static isl_stat
add_sub_equalities(struct isl_tab
*tab
,
3575 __isl_keep isl_aff_list
*list
, int dim
)
3583 n
= isl_aff_list_n_aff(list
);
3585 return isl_stat_error
;
3587 ctx
= isl_tab_get_ctx(tab
);
3588 sub
= isl_vec_alloc(ctx
, 1 + dim
+ n
);
3590 return isl_stat_error
;
3591 isl_seq_clr(sub
->el
+ 1 + dim
, n
);
3593 for (i
= 0; i
< n
; ++i
) {
3594 aff
= isl_aff_list_get_aff(list
, i
);
3597 if (isl_aff_is_nan(aff
)) {
3601 isl_seq_cpy(sub
->el
, aff
->v
->el
+ 1, 1 + dim
);
3602 isl_int_neg(sub
->el
[1 + dim
+ i
], aff
->v
->el
[0]);
3603 if (isl_tab_add_eq(tab
, sub
->el
) < 0)
3605 isl_int_set_si(sub
->el
[1 + dim
+ i
], 0);
3614 return isl_stat_error
;
3617 /* Add variables to info->tab and info->bmap corresponding to the elements
3618 * in "list" that are not set to NaN. The value of the added variable
3619 * in info->tab is fixed to the purely affine expression defined by the element.
3620 * "dim" is the offset in the variables of info->tab where we should
3621 * start considering the elements in "list".
3622 * When this function returns, the total number of variables in info->tab
3623 * is equal to "dim" plus the number of elements in "list".
3625 static isl_stat
add_subs(struct isl_coalesce_info
*info
,
3626 __isl_keep isl_aff_list
*list
, int dim
)
3631 n
= isl_aff_list_n_aff(list
);
3633 return isl_stat_error
;
3635 extra_var
= n
- (info
->tab
->n_var
- dim
);
3637 if (isl_tab_extend_vars(info
->tab
, extra_var
) < 0)
3638 return isl_stat_error
;
3639 if (isl_tab_extend_cons(info
->tab
, 2 * extra_var
) < 0)
3640 return isl_stat_error
;
3641 if (add_sub_vars(info
, list
, dim
, extra_var
) < 0)
3642 return isl_stat_error
;
3644 return add_sub_equalities(info
->tab
, list
, dim
);
3647 /* Coalesce basic map "j" into basic map "i" after adding the extra integer
3648 * divisions in "i" but not in "j" to basic map "j", with values
3649 * specified by "list". The total number of elements in "list"
3650 * is equal to the number of integer divisions in "i", while the number
3651 * of NaN elements in the list is equal to the number of integer divisions
3654 * If no coalescing can be performed, then we need to revert basic map "j"
3655 * to its original state. We do the same if basic map "i" gets dropped
3656 * during the coalescing, even though this should not happen in practice
3657 * since we have already checked for "j" being a subset of "i"
3658 * before we reach this stage.
3660 static enum isl_change
coalesce_with_subs(int i
, int j
,
3661 struct isl_coalesce_info
*info
, __isl_keep isl_aff_list
*list
)
3663 isl_basic_map
*bmap_j
;
3664 struct isl_tab_undo
*snap
;
3665 isl_size dim
, n_div
;
3666 enum isl_change change
;
3668 bmap_j
= isl_basic_map_copy(info
[j
].bmap
);
3669 snap
= isl_tab_snap(info
[j
].tab
);
3671 dim
= isl_basic_map_dim(bmap_j
, isl_dim_all
);
3672 n_div
= isl_basic_map_dim(bmap_j
, isl_dim_div
);
3673 if (dim
< 0 || n_div
< 0)
3676 if (add_subs(&info
[j
], list
, dim
) < 0)
3679 change
= coalesce_local_pair(i
, j
, info
);
3680 if (change
!= isl_change_none
&& change
!= isl_change_drop_first
) {
3681 isl_basic_map_free(bmap_j
);
3683 isl_basic_map_free(info
[j
].bmap
);
3684 info
[j
].bmap
= bmap_j
;
3686 if (isl_tab_rollback(info
[j
].tab
, snap
) < 0)
3687 return isl_change_error
;
3692 isl_basic_map_free(bmap_j
);
3693 return isl_change_error
;
3696 /* Check if we can coalesce basic map "j" into basic map "i" after copying
3697 * those extra integer divisions in "i" that can be simplified away
3698 * using the extra equalities in "j".
3699 * All divs are assumed to be known and not contain any nested divs.
3701 * We first check if there are any extra equalities in "j" that we
3702 * can exploit. Then we check if every integer division in "i"
3703 * either already appears in "j" or can be simplified using the
3704 * extra equalities to a purely affine expression.
3705 * If these tests succeed, then we try to coalesce the two basic maps
3706 * by introducing extra dimensions in "j" corresponding to
3707 * the extra integer divisions "i" fixed to the corresponding
3708 * purely affine expression.
3710 static enum isl_change
check_coalesce_into_eq(int i
, int j
,
3711 struct isl_coalesce_info
*info
)
3713 isl_size n_div_i
, n_div_j
, n
;
3714 isl_basic_map
*hull_i
, *hull_j
;
3715 isl_bool equal
, empty
;
3717 enum isl_change change
;
3719 n_div_i
= isl_basic_map_dim(info
[i
].bmap
, isl_dim_div
);
3720 n_div_j
= isl_basic_map_dim(info
[j
].bmap
, isl_dim_div
);
3721 if (n_div_i
< 0 || n_div_j
< 0)
3722 return isl_change_error
;
3723 if (n_div_i
<= n_div_j
)
3724 return isl_change_none
;
3725 if (info
[j
].bmap
->n_eq
== 0)
3726 return isl_change_none
;
3728 hull_i
= isl_basic_map_copy(info
[i
].bmap
);
3729 hull_i
= isl_basic_map_plain_affine_hull(hull_i
);
3730 hull_j
= isl_basic_map_copy(info
[j
].bmap
);
3731 hull_j
= isl_basic_map_plain_affine_hull(hull_j
);
3733 hull_j
= isl_basic_map_intersect(hull_j
, isl_basic_map_copy(hull_i
));
3734 equal
= isl_basic_map_plain_is_equal(hull_i
, hull_j
);
3735 empty
= isl_basic_map_plain_is_empty(hull_j
);
3736 isl_basic_map_free(hull_i
);
3738 if (equal
< 0 || empty
< 0)
3740 if (equal
|| empty
) {
3741 isl_basic_map_free(hull_j
);
3742 return isl_change_none
;
3745 list
= set_up_substitutions(info
[i
].bmap
, info
[j
].bmap
, hull_j
);
3747 return isl_change_error
;
3748 n
= isl_aff_list_n_aff(list
);
3750 change
= isl_change_error
;
3751 else if (n
< n_div_i
)
3752 change
= isl_change_none
;
3754 change
= coalesce_with_subs(i
, j
, info
, list
);
3756 isl_aff_list_free(list
);
3760 isl_basic_map_free(hull_j
);
3761 return isl_change_error
;
3764 /* Check if we can coalesce basic maps "i" and "j" after copying
3765 * those extra integer divisions in one of the basic maps that can
3766 * be simplified away using the extra equalities in the other basic map.
3767 * We require all divs to be known in both basic maps.
3768 * Furthermore, to simplify the comparison of div expressions,
3769 * we do not allow any nested integer divisions.
3771 static enum isl_change
check_coalesce_eq(int i
, int j
,
3772 struct isl_coalesce_info
*info
)
3774 isl_bool known
, nested
;
3775 enum isl_change change
;
3777 known
= isl_basic_map_divs_known(info
[i
].bmap
);
3778 if (known
< 0 || !known
)
3779 return known
< 0 ? isl_change_error
: isl_change_none
;
3780 known
= isl_basic_map_divs_known(info
[j
].bmap
);
3781 if (known
< 0 || !known
)
3782 return known
< 0 ? isl_change_error
: isl_change_none
;
3783 nested
= has_nested_div(info
[i
].bmap
);
3784 if (nested
< 0 || nested
)
3785 return nested
< 0 ? isl_change_error
: isl_change_none
;
3786 nested
= has_nested_div(info
[j
].bmap
);
3787 if (nested
< 0 || nested
)
3788 return nested
< 0 ? isl_change_error
: isl_change_none
;
3790 change
= check_coalesce_into_eq(i
, j
, info
);
3791 if (change
!= isl_change_none
)
3793 change
= check_coalesce_into_eq(j
, i
, info
);
3794 if (change
!= isl_change_none
)
3795 return invert_change(change
);
3797 return isl_change_none
;
3800 /* Check if the union of the given pair of basic maps
3801 * can be represented by a single basic map.
3802 * If so, replace the pair by the single basic map and return
3803 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
3804 * Otherwise, return isl_change_none.
3806 * We first check if the two basic maps live in the same local space,
3807 * after aligning the divs that differ by only an integer constant.
3808 * If so, we do the complete check. Otherwise, we check if they have
3809 * the same number of integer divisions and can be coalesced, if one is
3810 * an obvious subset of the other or if the extra integer divisions
3811 * of one basic map can be simplified away using the extra equalities
3812 * of the other basic map.
3814 * Note that trying to coalesce pairs of disjuncts with the same
3815 * number, but different local variables may drop the explicit
3816 * representation of some of these local variables.
3817 * This operation is therefore not performed when
3818 * the "coalesce_preserve_locals" option is set.
3820 static enum isl_change
coalesce_pair(int i
, int j
,
3821 struct isl_coalesce_info
*info
)
3825 enum isl_change change
;
3828 if (harmonize_divs(&info
[i
], &info
[j
]) < 0)
3829 return isl_change_error
;
3830 same
= same_divs(info
[i
].bmap
, info
[j
].bmap
);
3832 return isl_change_error
;
3834 return coalesce_local_pair(i
, j
, info
);
3836 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
3837 preserve
= isl_options_get_coalesce_preserve_locals(ctx
);
3838 if (!preserve
&& info
[i
].bmap
->n_div
== info
[j
].bmap
->n_div
) {
3839 change
= coalesce_local_pair(i
, j
, info
);
3840 if (change
!= isl_change_none
)
3844 change
= coalesce_divs(i
, j
, info
);
3845 if (change
!= isl_change_none
)
3848 return check_coalesce_eq(i
, j
, info
);
3851 /* Return the maximum of "a" and "b".
3853 static int isl_max(int a
, int b
)
3855 return a
> b
? a
: b
;
3858 /* Pairwise coalesce the basic maps in the range [start1, end1[ of "info"
3859 * with those in the range [start2, end2[, skipping basic maps
3860 * that have been removed (either before or within this function).
3862 * For each basic map i in the first range, we check if it can be coalesced
3863 * with respect to any previously considered basic map j in the second range.
3864 * If i gets dropped (because it was a subset of some j), then
3865 * we can move on to the next basic map.
3866 * If j gets dropped, we need to continue checking against the other
3867 * previously considered basic maps.
3868 * If the two basic maps got fused, then we recheck the fused basic map
3869 * against the previously considered basic maps, starting at i + 1
3870 * (even if start2 is greater than i + 1).
3872 static int coalesce_range(isl_ctx
*ctx
, struct isl_coalesce_info
*info
,
3873 int start1
, int end1
, int start2
, int end2
)
3877 for (i
= end1
- 1; i
>= start1
; --i
) {
3878 if (info
[i
].removed
)
3880 for (j
= isl_max(i
+ 1, start2
); j
< end2
; ++j
) {
3881 enum isl_change changed
;
3883 if (info
[j
].removed
)
3885 if (info
[i
].removed
)
3886 isl_die(ctx
, isl_error_internal
,
3887 "basic map unexpectedly removed",
3889 changed
= coalesce_pair(i
, j
, info
);
3891 case isl_change_error
:
3893 case isl_change_none
:
3894 case isl_change_drop_second
:
3896 case isl_change_drop_first
:
3899 case isl_change_fuse
:
3909 /* Pairwise coalesce the basic maps described by the "n" elements of "info".
3911 * We consider groups of basic maps that live in the same apparent
3912 * affine hull and we first coalesce within such a group before we
3913 * coalesce the elements in the group with elements of previously
3914 * considered groups. If a fuse happens during the second phase,
3915 * then we also reconsider the elements within the group.
3917 static int coalesce(isl_ctx
*ctx
, int n
, struct isl_coalesce_info
*info
)
3921 for (end
= n
; end
> 0; end
= start
) {
3923 while (start
>= 1 &&
3924 info
[start
- 1].hull_hash
== info
[start
].hull_hash
)
3926 if (coalesce_range(ctx
, info
, start
, end
, start
, end
) < 0)
3928 if (coalesce_range(ctx
, info
, start
, end
, end
, n
) < 0)
3935 /* Update the basic maps in "map" based on the information in "info".
3936 * In particular, remove the basic maps that have been marked removed and
3937 * update the others based on the information in the corresponding tableau.
3938 * Since we detected implicit equalities without calling
3939 * isl_basic_map_gauss, we need to do it now.
3940 * Also call isl_basic_map_simplify if we may have lost the definition
3941 * of one or more integer divisions.
3942 * If a basic map is still equal to the one from which the corresponding "info"
3943 * entry was created, then redundant constraint and
3944 * implicit equality constraint detection have been performed
3945 * on the corresponding tableau and the basic map can be marked as such.
3947 static __isl_give isl_map
*update_basic_maps(__isl_take isl_map
*map
,
3948 int n
, struct isl_coalesce_info
*info
)
3955 for (i
= n
- 1; i
>= 0; --i
) {
3956 if (info
[i
].removed
) {
3957 isl_basic_map_free(map
->p
[i
]);
3958 if (i
!= map
->n
- 1)
3959 map
->p
[i
] = map
->p
[map
->n
- 1];
3964 info
[i
].bmap
= isl_basic_map_update_from_tab(info
[i
].bmap
,
3966 info
[i
].bmap
= isl_basic_map_gauss(info
[i
].bmap
, NULL
);
3967 if (info
[i
].simplify
)
3968 info
[i
].bmap
= isl_basic_map_simplify(info
[i
].bmap
);
3969 info
[i
].bmap
= isl_basic_map_finalize(info
[i
].bmap
);
3971 return isl_map_free(map
);
3972 if (!info
[i
].modified
) {
3973 ISL_F_SET(info
[i
].bmap
, ISL_BASIC_MAP_NO_IMPLICIT
);
3974 ISL_F_SET(info
[i
].bmap
, ISL_BASIC_MAP_NO_REDUNDANT
);
3976 isl_basic_map_free(map
->p
[i
]);
3977 map
->p
[i
] = info
[i
].bmap
;
3978 info
[i
].bmap
= NULL
;
3984 /* For each pair of basic maps in the map, check if the union of the two
3985 * can be represented by a single basic map.
3986 * If so, replace the pair by the single basic map and start over.
3988 * We factor out any (hidden) common factor from the constraint
3989 * coefficients to improve the detection of adjacent constraints.
3990 * Note that this function does not call isl_basic_map_gauss,
3991 * but it does make sure that only a single copy of the basic map
3992 * is affected. This means that isl_basic_map_gauss may have
3993 * to be called at the end of the computation (in update_basic_maps)
3994 * on this single copy to ensure that
3995 * the basic maps are not left in an unexpected state.
3997 * Since we are constructing the tableaus of the basic maps anyway,
3998 * we exploit them to detect implicit equalities and redundant constraints.
3999 * This also helps the coalescing as it can ignore the redundant constraints.
4000 * In order to avoid confusion, we make all implicit equalities explicit
4001 * in the basic maps. If the basic map only has a single reference
4002 * (this happens in particular if it was modified by
4003 * isl_basic_map_reduce_coefficients), then isl_basic_map_gauss
4004 * does not get called on the result. The call to
4005 * isl_basic_map_gauss in update_basic_maps resolves this as well.
4006 * For each basic map, we also compute the hash of the apparent affine hull
4007 * for use in coalesce.
4009 __isl_give isl_map
*isl_map_coalesce(__isl_take isl_map
*map
)
4014 struct isl_coalesce_info
*info
= NULL
;
4016 map
= isl_map_remove_empty_parts(map
);
4023 ctx
= isl_map_get_ctx(map
);
4024 map
= isl_map_sort_divs(map
);
4025 map
= isl_map_cow(map
);
4032 info
= isl_calloc_array(map
->ctx
, struct isl_coalesce_info
, n
);
4036 for (i
= 0; i
< map
->n
; ++i
) {
4037 map
->p
[i
] = isl_basic_map_reduce_coefficients(map
->p
[i
]);
4040 info
[i
].bmap
= isl_basic_map_copy(map
->p
[i
]);
4041 info
[i
].tab
= isl_tab_from_basic_map(info
[i
].bmap
, 0);
4044 if (!ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_NO_IMPLICIT
))
4045 if (isl_tab_detect_implicit_equalities(info
[i
].tab
) < 0)
4047 info
[i
].bmap
= isl_tab_make_equalities_explicit(info
[i
].tab
,
4051 if (!ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_NO_REDUNDANT
))
4052 if (isl_tab_detect_redundant(info
[i
].tab
) < 0)
4054 if (coalesce_info_set_hull_hash(&info
[i
]) < 0)
4057 for (i
= map
->n
- 1; i
>= 0; --i
)
4058 if (info
[i
].tab
->empty
)
4061 if (coalesce(ctx
, n
, info
) < 0)
4064 map
= update_basic_maps(map
, n
, info
);
4066 clear_coalesce_info(n
, info
);
4070 clear_coalesce_info(n
, info
);
4075 /* For each pair of basic sets in the set, check if the union of the two
4076 * can be represented by a single basic set.
4077 * If so, replace the pair by the single basic set and start over.
4079 __isl_give isl_set
*isl_set_coalesce(__isl_take isl_set
*set
)
4081 return set_from_map(isl_map_coalesce(set_to_map(set
)));