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.
504 static enum isl_change
fuse(int i
, int j
, struct isl_coalesce_info
*info
,
505 __isl_keep isl_mat
*extra
, int detect_equalities
, int check_number
)
508 struct isl_basic_map
*fused
= NULL
;
509 struct isl_tab
*fused_tab
= NULL
;
510 isl_size total
= isl_basic_map_dim(info
[i
].bmap
, isl_dim_all
);
511 unsigned extra_rows
= extra
? extra
->n_row
: 0;
512 unsigned n_eq
, n_ineq
;
516 return isl_change_error
;
518 return fuse(j
, i
, info
, extra
, detect_equalities
, check_number
);
520 n_eq
= info
[i
].bmap
->n_eq
+ info
[j
].bmap
->n_eq
;
521 n_ineq
= info
[i
].bmap
->n_ineq
+ info
[j
].bmap
->n_ineq
;
522 fused
= isl_basic_map_alloc_space(isl_space_copy(info
[i
].bmap
->dim
),
523 info
[i
].bmap
->n_div
, n_eq
, n_eq
+ n_ineq
+ extra_rows
);
524 fused
= add_valid_constraints(fused
, &info
[i
], 1 + total
);
525 fused
= add_valid_constraints(fused
, &info
[j
], 1 + total
);
528 if (ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_RATIONAL
) &&
529 ISL_F_ISSET(info
[j
].bmap
, ISL_BASIC_MAP_RATIONAL
))
530 ISL_F_SET(fused
, ISL_BASIC_MAP_RATIONAL
);
532 for (k
= 0; k
< info
[i
].bmap
->n_div
; ++k
) {
533 int l
= isl_basic_map_alloc_div(fused
);
536 if (isl_seq_eq(info
[i
].bmap
->div
[k
], info
[j
].bmap
->div
[k
],
538 isl_seq_cpy(fused
->div
[l
], info
[i
].bmap
->div
[k
],
541 isl_int_set_si(fused
->div
[l
][0], 0);
546 for (k
= 0; k
< extra_rows
; ++k
) {
547 l
= isl_basic_map_alloc_inequality(fused
);
550 isl_seq_cpy(fused
->ineq
[l
], extra
->row
[k
], 1 + total
);
553 if (detect_equalities
)
554 fused
= isl_basic_map_detect_inequality_pairs(fused
, NULL
);
555 fused
= isl_basic_map_gauss(fused
, NULL
);
556 if (simplify
|| info
[j
].simplify
) {
557 fused
= isl_basic_map_simplify(fused
);
558 info
[i
].simplify
= 0;
560 fused
= isl_basic_map_finalize(fused
);
562 fused_tab
= isl_tab_from_basic_map(fused
, 0);
563 if (isl_tab_detect_redundant(fused_tab
) < 0)
567 number_of_constraints_increases(i
, j
, info
, fused
, fused_tab
)) {
568 isl_tab_free(fused_tab
);
569 isl_basic_map_free(fused
);
570 return isl_change_none
;
574 info
[i
].bmap
= fused
;
575 info
[i
].tab
= fused_tab
;
576 info
[i
].modified
= 1;
579 return isl_change_fuse
;
581 isl_tab_free(fused_tab
);
582 isl_basic_map_free(fused
);
583 return isl_change_error
;
586 /* Given a pair of basic maps i and j such that all constraints are either
587 * "valid" or "cut", check if the facets corresponding to the "cut"
588 * constraints of i lie entirely within basic map j.
589 * If so, replace the pair by the basic map consisting of the valid
590 * constraints in both basic maps.
591 * Checking whether the facet lies entirely within basic map j
592 * is performed by checking whether the constraints of basic map j
593 * are valid for the facet. These tests are performed on a rational
594 * tableau to avoid the theoretical possibility that a constraint
595 * that was considered to be a cut constraint for the entire basic map i
596 * happens to be considered to be a valid constraint for the facet,
597 * even though it cuts off the same rational points.
599 * To see that we are not introducing any extra points, call the
600 * two basic maps A and B and the resulting map U and let x
601 * be an element of U \setminus ( A \cup B ).
602 * A line connecting x with an element of A \cup B meets a facet F
603 * of either A or B. Assume it is a facet of B and let c_1 be
604 * the corresponding facet constraint. We have c_1(x) < 0 and
605 * so c_1 is a cut constraint. This implies that there is some
606 * (possibly rational) point x' satisfying the constraints of A
607 * and the opposite of c_1 as otherwise c_1 would have been marked
608 * valid for A. The line connecting x and x' meets a facet of A
609 * in a (possibly rational) point that also violates c_1, but this
610 * is impossible since all cut constraints of B are valid for all
612 * In case F is a facet of A rather than B, then we can apply the
613 * above reasoning to find a facet of B separating x from A \cup B first.
615 static enum isl_change
check_facets(int i
, int j
,
616 struct isl_coalesce_info
*info
)
619 struct isl_tab_undo
*snap
, *snap2
;
620 unsigned n_eq
= info
[i
].bmap
->n_eq
;
622 snap
= isl_tab_snap(info
[i
].tab
);
623 if (isl_tab_mark_rational(info
[i
].tab
) < 0)
624 return isl_change_error
;
625 snap2
= isl_tab_snap(info
[i
].tab
);
627 for (k
= 0; k
< info
[i
].bmap
->n_ineq
; ++k
) {
628 if (info
[i
].ineq
[k
] != STATUS_CUT
)
630 if (isl_tab_select_facet(info
[i
].tab
, n_eq
+ k
) < 0)
631 return isl_change_error
;
632 for (l
= 0; l
< info
[j
].bmap
->n_ineq
; ++l
) {
634 if (info
[j
].ineq
[l
] != STATUS_CUT
)
636 stat
= status_in(info
[j
].bmap
->ineq
[l
], info
[i
].tab
);
638 return isl_change_error
;
639 if (stat
!= STATUS_VALID
)
642 if (isl_tab_rollback(info
[i
].tab
, snap2
) < 0)
643 return isl_change_error
;
644 if (l
< info
[j
].bmap
->n_ineq
)
648 if (k
< info
[i
].bmap
->n_ineq
) {
649 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
650 return isl_change_error
;
651 return isl_change_none
;
653 return fuse(i
, j
, info
, NULL
, 0, 0);
656 /* Check if info->bmap contains the basic map represented
657 * by the tableau "tab".
658 * For each equality, we check both the constraint itself
659 * (as an inequality) and its negation. Make sure the
660 * equality is returned to its original state before returning.
662 static isl_bool
contains(struct isl_coalesce_info
*info
, struct isl_tab
*tab
)
666 isl_basic_map
*bmap
= info
->bmap
;
668 dim
= isl_basic_map_dim(bmap
, isl_dim_all
);
670 return isl_bool_error
;
671 for (k
= 0; k
< bmap
->n_eq
; ++k
) {
673 isl_seq_neg(bmap
->eq
[k
], bmap
->eq
[k
], 1 + dim
);
674 stat
= status_in(bmap
->eq
[k
], tab
);
675 isl_seq_neg(bmap
->eq
[k
], bmap
->eq
[k
], 1 + dim
);
677 return isl_bool_error
;
678 if (stat
!= STATUS_VALID
)
679 return isl_bool_false
;
680 stat
= status_in(bmap
->eq
[k
], tab
);
682 return isl_bool_error
;
683 if (stat
!= STATUS_VALID
)
684 return isl_bool_false
;
687 for (k
= 0; k
< bmap
->n_ineq
; ++k
) {
689 if (info
->ineq
[k
] == STATUS_REDUNDANT
)
691 stat
= status_in(bmap
->ineq
[k
], tab
);
693 return isl_bool_error
;
694 if (stat
!= STATUS_VALID
)
695 return isl_bool_false
;
697 return isl_bool_true
;
700 /* Basic map "i" has an inequality (say "k") that is adjacent
701 * to some inequality of basic map "j". All the other inequalities
703 * Check if basic map "j" forms an extension of basic map "i".
705 * Note that this function is only called if some of the equalities or
706 * inequalities of basic map "j" do cut basic map "i". The function is
707 * correct even if there are no such cut constraints, but in that case
708 * the additional checks performed by this function are overkill.
710 * In particular, we replace constraint k, say f >= 0, by constraint
711 * f <= -1, add the inequalities of "j" that are valid for "i"
712 * and check if the result is a subset of basic map "j".
713 * To improve the chances of the subset relation being detected,
714 * any variable that only attains a single integer value
715 * in the tableau of "i" is first fixed to that value.
716 * If the result is a subset, then we know that this result is exactly equal
717 * to basic map "j" since all its constraints are valid for basic map "j".
718 * By combining the valid constraints of "i" (all equalities and all
719 * inequalities except "k") and the valid constraints of "j" we therefore
720 * obtain a basic map that is equal to their union.
721 * In this case, there is no need to perform a rollback of the tableau
722 * since it is going to be destroyed in fuse().
728 * |_______| _ |_________\
740 static enum isl_change
is_adj_ineq_extension(int i
, int j
,
741 struct isl_coalesce_info
*info
)
744 struct isl_tab_undo
*snap
;
745 unsigned n_eq
= info
[i
].bmap
->n_eq
;
746 isl_size total
= isl_basic_map_dim(info
[i
].bmap
, isl_dim_all
);
751 return isl_change_error
;
752 if (isl_tab_extend_cons(info
[i
].tab
, 1 + info
[j
].bmap
->n_ineq
) < 0)
753 return isl_change_error
;
755 k
= find_ineq(&info
[i
], STATUS_ADJ_INEQ
);
757 isl_die(isl_basic_map_get_ctx(info
[i
].bmap
), isl_error_internal
,
758 "info[i].ineq should have exactly one STATUS_ADJ_INEQ",
759 return isl_change_error
);
761 snap
= isl_tab_snap(info
[i
].tab
);
763 if (isl_tab_unrestrict(info
[i
].tab
, n_eq
+ k
) < 0)
764 return isl_change_error
;
766 isl_seq_neg(info
[i
].bmap
->ineq
[k
], info
[i
].bmap
->ineq
[k
], 1 + total
);
767 isl_int_sub_ui(info
[i
].bmap
->ineq
[k
][0], info
[i
].bmap
->ineq
[k
][0], 1);
768 r
= isl_tab_add_ineq(info
[i
].tab
, info
[i
].bmap
->ineq
[k
]);
769 isl_seq_neg(info
[i
].bmap
->ineq
[k
], info
[i
].bmap
->ineq
[k
], 1 + total
);
770 isl_int_sub_ui(info
[i
].bmap
->ineq
[k
][0], info
[i
].bmap
->ineq
[k
][0], 1);
772 return isl_change_error
;
774 for (k
= 0; k
< info
[j
].bmap
->n_ineq
; ++k
) {
775 if (info
[j
].ineq
[k
] != STATUS_VALID
)
777 if (isl_tab_add_ineq(info
[i
].tab
, info
[j
].bmap
->ineq
[k
]) < 0)
778 return isl_change_error
;
780 if (isl_tab_detect_constants(info
[i
].tab
) < 0)
781 return isl_change_error
;
783 super
= contains(&info
[j
], info
[i
].tab
);
785 return isl_change_error
;
787 return fuse(i
, j
, info
, NULL
, 0, 0);
789 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
790 return isl_change_error
;
792 return isl_change_none
;
796 /* Both basic maps have at least one inequality with and adjacent
797 * (but opposite) inequality in the other basic map.
798 * Check that there are no cut constraints and that there is only
799 * a single pair of adjacent inequalities.
800 * If so, we can replace the pair by a single basic map described
801 * by all but the pair of adjacent inequalities.
802 * Any additional points introduced lie strictly between the two
803 * adjacent hyperplanes and can therefore be integral.
812 * The test for a single pair of adjancent inequalities is important
813 * for avoiding the combination of two basic maps like the following
823 * If there are some cut constraints on one side, then we may
824 * still be able to fuse the two basic maps, but we need to perform
825 * some additional checks in is_adj_ineq_extension.
827 static enum isl_change
check_adj_ineq(int i
, int j
,
828 struct isl_coalesce_info
*info
)
830 int count_i
, count_j
;
833 count_i
= count_ineq(&info
[i
], STATUS_ADJ_INEQ
);
834 count_j
= count_ineq(&info
[j
], STATUS_ADJ_INEQ
);
836 if (count_i
!= 1 && count_j
!= 1)
837 return isl_change_none
;
839 cut_i
= any_eq(&info
[i
], STATUS_CUT
) || any_ineq(&info
[i
], STATUS_CUT
);
840 cut_j
= any_eq(&info
[j
], STATUS_CUT
) || any_ineq(&info
[j
], STATUS_CUT
);
842 if (!cut_i
&& !cut_j
&& count_i
== 1 && count_j
== 1)
843 return fuse(i
, j
, info
, NULL
, 0, 0);
845 if (count_i
== 1 && !cut_i
)
846 return is_adj_ineq_extension(i
, j
, info
);
848 if (count_j
== 1 && !cut_j
)
849 return is_adj_ineq_extension(j
, i
, info
);
851 return isl_change_none
;
854 /* Given an affine transformation matrix "T", does row "row" represent
855 * anything other than a unit vector (possibly shifted by a constant)
856 * that is not involved in any of the other rows?
858 * That is, if a constraint involves the variable corresponding to
859 * the row, then could its preimage by "T" have any coefficients
860 * that are different from those in the original constraint?
862 static int not_unique_unit_row(__isl_keep isl_mat
*T
, int row
)
865 int len
= T
->n_col
- 1;
867 i
= isl_seq_first_non_zero(T
->row
[row
] + 1, len
);
870 if (!isl_int_is_one(T
->row
[row
][1 + i
]) &&
871 !isl_int_is_negone(T
->row
[row
][1 + i
]))
874 j
= isl_seq_first_non_zero(T
->row
[row
] + 1 + i
+ 1, len
- (i
+ 1));
878 for (j
= 1; j
< T
->n_row
; ++j
) {
881 if (!isl_int_is_zero(T
->row
[j
][1 + i
]))
888 /* Does inequality constraint "ineq" of "bmap" involve any of
889 * the variables marked in "affected"?
890 * "total" is the total number of variables, i.e., the number
891 * of entries in "affected".
893 static isl_bool
is_affected(__isl_keep isl_basic_map
*bmap
, int ineq
,
894 int *affected
, int total
)
898 for (i
= 0; i
< total
; ++i
) {
901 if (!isl_int_is_zero(bmap
->ineq
[ineq
][1 + i
]))
902 return isl_bool_true
;
905 return isl_bool_false
;
908 /* Given the compressed version of inequality constraint "ineq"
909 * of info->bmap in "v", check if the constraint can be tightened,
910 * where the compression is based on an equality constraint valid
912 * If so, add the tightened version of the inequality constraint
913 * to info->tab. "v" may be modified by this function.
915 * That is, if the compressed constraint is of the form
919 * with 0 < c < m, then it is equivalent to
923 * This means that c can also be subtracted from the original,
924 * uncompressed constraint without affecting the integer points
925 * in info->tab. Add this tightened constraint as an extra row
926 * to info->tab to make this information explicitly available.
928 static __isl_give isl_vec
*try_tightening(struct isl_coalesce_info
*info
,
929 int ineq
, __isl_take isl_vec
*v
)
937 ctx
= isl_vec_get_ctx(v
);
938 isl_seq_gcd(v
->el
+ 1, v
->size
- 1, &ctx
->normalize_gcd
);
939 if (isl_int_is_zero(ctx
->normalize_gcd
) ||
940 isl_int_is_one(ctx
->normalize_gcd
)) {
948 isl_int_fdiv_r(v
->el
[0], v
->el
[0], ctx
->normalize_gcd
);
949 if (isl_int_is_zero(v
->el
[0]))
952 if (isl_tab_extend_cons(info
->tab
, 1) < 0)
953 return isl_vec_free(v
);
955 isl_int_sub(info
->bmap
->ineq
[ineq
][0],
956 info
->bmap
->ineq
[ineq
][0], v
->el
[0]);
957 r
= isl_tab_add_ineq(info
->tab
, info
->bmap
->ineq
[ineq
]);
958 isl_int_add(info
->bmap
->ineq
[ineq
][0],
959 info
->bmap
->ineq
[ineq
][0], v
->el
[0]);
962 return isl_vec_free(v
);
967 /* Tighten the (non-redundant) constraints on the facet represented
969 * In particular, on input, info->tab represents the result
970 * of relaxing the "n" inequality constraints of info->bmap in "relaxed"
971 * by one, i.e., replacing f_i >= 0 by f_i + 1 >= 0, and then
972 * replacing the one at index "l" by the corresponding equality,
973 * i.e., f_k + 1 = 0, with k = relaxed[l].
975 * Compute a variable compression from the equality constraint f_k + 1 = 0
976 * and use it to tighten the other constraints of info->bmap
977 * (that is, all constraints that have not been relaxed),
978 * updating info->tab (and leaving info->bmap untouched).
979 * The compression handles essentially two cases, one where a variable
980 * is assigned a fixed value and can therefore be eliminated, and one
981 * where one variable is a shifted multiple of some other variable and
982 * can therefore be replaced by that multiple.
983 * Gaussian elimination would also work for the first case, but for
984 * the second case, the effectiveness would depend on the order
986 * After compression, some of the constraints may have coefficients
987 * with a common divisor. If this divisor does not divide the constant
988 * term, then the constraint can be tightened.
989 * The tightening is performed on the tableau info->tab by introducing
990 * extra (temporary) constraints.
992 * Only constraints that are possibly affected by the compression are
993 * considered. In particular, if the constraint only involves variables
994 * that are directly mapped to a distinct set of other variables, then
995 * no common divisor can be introduced and no tightening can occur.
997 * It is important to only consider the non-redundant constraints
998 * since the facet constraint has been relaxed prior to the call
999 * to this function, meaning that the constraints that were redundant
1000 * prior to the relaxation may no longer be redundant.
1001 * These constraints will be ignored in the fused result, so
1002 * the fusion detection should not exploit them.
1004 static isl_stat
tighten_on_relaxed_facet(struct isl_coalesce_info
*info
,
1005 int n
, int *relaxed
, int l
)
1016 ctx
= isl_basic_map_get_ctx(info
->bmap
);
1017 total
= isl_basic_map_dim(info
->bmap
, isl_dim_all
);
1019 return isl_stat_error
;
1020 isl_int_add_ui(info
->bmap
->ineq
[k
][0], info
->bmap
->ineq
[k
][0], 1);
1021 T
= isl_mat_sub_alloc6(ctx
, info
->bmap
->ineq
, k
, 1, 0, 1 + total
);
1022 T
= isl_mat_variable_compression(T
, NULL
);
1023 isl_int_sub_ui(info
->bmap
->ineq
[k
][0], info
->bmap
->ineq
[k
][0], 1);
1025 return isl_stat_error
;
1026 if (T
->n_col
== 0) {
1031 affected
= isl_alloc_array(ctx
, int, total
);
1035 for (i
= 0; i
< total
; ++i
)
1036 affected
[i
] = not_unique_unit_row(T
, 1 + i
);
1038 for (i
= 0; i
< info
->bmap
->n_ineq
; ++i
) {
1040 if (any(relaxed
, n
, i
))
1042 if (info
->ineq
[i
] == STATUS_REDUNDANT
)
1044 handle
= is_affected(info
->bmap
, i
, affected
, total
);
1049 v
= isl_vec_alloc(ctx
, 1 + total
);
1052 isl_seq_cpy(v
->el
, info
->bmap
->ineq
[i
], 1 + total
);
1053 v
= isl_vec_mat_product(v
, isl_mat_copy(T
));
1054 v
= try_tightening(info
, i
, v
);
1066 return isl_stat_error
;
1069 /* Replace the basic maps "i" and "j" by an extension of "i"
1070 * along the "n" inequality constraints in "relax" by one.
1071 * The tableau info[i].tab has already been extended.
1072 * Extend info[i].bmap accordingly by relaxing all constraints in "relax"
1074 * Each integer division that does not have exactly the same
1075 * definition in "i" and "j" is marked unknown and the basic map
1076 * is scheduled to be simplified in an attempt to recover
1077 * the integer division definition.
1078 * Place the extension in the position that is the smallest of i and j.
1080 static enum isl_change
extend(int i
, int j
, int n
, int *relax
,
1081 struct isl_coalesce_info
*info
)
1086 info
[i
].bmap
= isl_basic_map_cow(info
[i
].bmap
);
1087 total
= isl_basic_map_dim(info
[i
].bmap
, isl_dim_all
);
1089 return isl_change_error
;
1090 for (l
= 0; l
< info
[i
].bmap
->n_div
; ++l
)
1091 if (!isl_seq_eq(info
[i
].bmap
->div
[l
],
1092 info
[j
].bmap
->div
[l
], 1 + 1 + total
)) {
1093 isl_int_set_si(info
[i
].bmap
->div
[l
][0], 0);
1094 info
[i
].simplify
= 1;
1096 for (l
= 0; l
< n
; ++l
)
1097 isl_int_add_ui(info
[i
].bmap
->ineq
[relax
[l
]][0],
1098 info
[i
].bmap
->ineq
[relax
[l
]][0], 1);
1099 ISL_F_CLR(info
[i
].bmap
, ISL_BASIC_MAP_NO_REDUNDANT
);
1100 ISL_F_SET(info
[i
].bmap
, ISL_BASIC_MAP_FINAL
);
1102 info
[i
].modified
= 1;
1104 exchange(&info
[i
], &info
[j
]);
1105 return isl_change_fuse
;
1108 /* Basic map "i" has "n" inequality constraints (collected in "relax")
1109 * that are such that they include basic map "j" if they are relaxed
1110 * by one. All the other inequalities are valid for "j".
1111 * Check if basic map "j" forms an extension of basic map "i".
1113 * In particular, relax the constraints in "relax", compute the corresponding
1114 * facets one by one and check whether each of these is included
1115 * in the other basic map.
1116 * Before testing for inclusion, the constraints on each facet
1117 * are tightened to increase the chance of an inclusion being detected.
1118 * (Adding the valid constraints of "j" to the tableau of "i", as is done
1119 * in is_adj_ineq_extension, may further increase those chances, but this
1120 * is not currently done.)
1121 * If each facet is included, we know that relaxing the constraints extends
1122 * the basic map with exactly the other basic map (we already know that this
1123 * other basic map is included in the extension, because all other
1124 * inequality constraints are valid of "j") and we can replace the
1125 * two basic maps by this extension.
1127 * If any of the relaxed constraints turn out to be redundant, then bail out.
1128 * isl_tab_select_facet refuses to handle such constraints. It may be
1129 * possible to handle them anyway by making a distinction between
1130 * redundant constraints with a corresponding facet that still intersects
1131 * the set (allowing isl_tab_select_facet to handle them) and
1132 * those where the facet does not intersect the set (which can be ignored
1133 * because the empty facet is trivially included in the other disjunct).
1134 * However, relaxed constraints that turn out to be redundant should
1135 * be fairly rare and no such instance has been reported where
1136 * coalescing would be successful.
1152 static enum isl_change
is_relaxed_extension(int i
, int j
, int n
, int *relax
,
1153 struct isl_coalesce_info
*info
)
1157 struct isl_tab_undo
*snap
, *snap2
;
1158 unsigned n_eq
= info
[i
].bmap
->n_eq
;
1160 for (l
= 0; l
< n
; ++l
)
1161 if (isl_tab_is_equality(info
[i
].tab
, n_eq
+ relax
[l
]))
1162 return isl_change_none
;
1164 snap
= isl_tab_snap(info
[i
].tab
);
1165 for (l
= 0; l
< n
; ++l
)
1166 if (isl_tab_relax(info
[i
].tab
, n_eq
+ relax
[l
]) < 0)
1167 return isl_change_error
;
1168 for (l
= 0; l
< n
; ++l
) {
1169 if (!isl_tab_is_redundant(info
[i
].tab
, n_eq
+ relax
[l
]))
1171 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
1172 return isl_change_error
;
1173 return isl_change_none
;
1175 snap2
= isl_tab_snap(info
[i
].tab
);
1176 for (l
= 0; l
< n
; ++l
) {
1177 if (isl_tab_rollback(info
[i
].tab
, snap2
) < 0)
1178 return isl_change_error
;
1179 if (isl_tab_select_facet(info
[i
].tab
, n_eq
+ relax
[l
]) < 0)
1180 return isl_change_error
;
1181 if (tighten_on_relaxed_facet(&info
[i
], n
, relax
, l
) < 0)
1182 return isl_change_error
;
1183 super
= contains(&info
[j
], info
[i
].tab
);
1185 return isl_change_error
;
1188 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
1189 return isl_change_error
;
1190 return isl_change_none
;
1193 if (isl_tab_rollback(info
[i
].tab
, snap2
) < 0)
1194 return isl_change_error
;
1195 return extend(i
, j
, n
, relax
, info
);
1198 /* Data structure that keeps track of the wrapping constraints
1199 * and of information to bound the coefficients of those constraints.
1201 * bound is set if we want to apply a bound on the coefficients
1202 * mat contains the wrapping constraints
1203 * max is the bound on the coefficients (if bound is set)
1211 /* Update wraps->max to be greater than or equal to the coefficients
1212 * in the equalities and inequalities of info->bmap that can be removed
1213 * if we end up applying wrapping.
1215 static isl_stat
wraps_update_max(struct isl_wraps
*wraps
,
1216 struct isl_coalesce_info
*info
)
1220 isl_size total
= isl_basic_map_dim(info
->bmap
, isl_dim_all
);
1223 return isl_stat_error
;
1224 isl_int_init(max_k
);
1226 for (k
= 0; k
< info
->bmap
->n_eq
; ++k
) {
1227 if (info
->eq
[2 * k
] == STATUS_VALID
&&
1228 info
->eq
[2 * k
+ 1] == STATUS_VALID
)
1230 isl_seq_abs_max(info
->bmap
->eq
[k
] + 1, total
, &max_k
);
1231 if (isl_int_abs_gt(max_k
, wraps
->max
))
1232 isl_int_set(wraps
->max
, max_k
);
1235 for (k
= 0; k
< info
->bmap
->n_ineq
; ++k
) {
1236 if (info
->ineq
[k
] == STATUS_VALID
||
1237 info
->ineq
[k
] == STATUS_REDUNDANT
)
1239 isl_seq_abs_max(info
->bmap
->ineq
[k
] + 1, total
, &max_k
);
1240 if (isl_int_abs_gt(max_k
, wraps
->max
))
1241 isl_int_set(wraps
->max
, max_k
);
1244 isl_int_clear(max_k
);
1249 /* Initialize the isl_wraps data structure.
1250 * If we want to bound the coefficients of the wrapping constraints,
1251 * we set wraps->max to the largest coefficient
1252 * in the equalities and inequalities that can be removed if we end up
1253 * applying wrapping.
1255 static isl_stat
wraps_init(struct isl_wraps
*wraps
, __isl_take isl_mat
*mat
,
1256 struct isl_coalesce_info
*info
, int i
, int j
)
1263 return isl_stat_error
;
1264 ctx
= isl_mat_get_ctx(mat
);
1265 wraps
->bound
= isl_options_get_coalesce_bounded_wrapping(ctx
);
1268 isl_int_init(wraps
->max
);
1269 isl_int_set_si(wraps
->max
, 0);
1270 if (wraps_update_max(wraps
, &info
[i
]) < 0)
1271 return isl_stat_error
;
1272 if (wraps_update_max(wraps
, &info
[j
]) < 0)
1273 return isl_stat_error
;
1278 /* Free the contents of the isl_wraps data structure.
1280 static void wraps_free(struct isl_wraps
*wraps
)
1282 isl_mat_free(wraps
->mat
);
1284 isl_int_clear(wraps
->max
);
1287 /* Is the wrapping constraint in row "row" allowed?
1289 * If wraps->bound is set, we check that none of the coefficients
1290 * is greater than wraps->max.
1292 static int allow_wrap(struct isl_wraps
*wraps
, int row
)
1299 for (i
= 1; i
< wraps
->mat
->n_col
; ++i
)
1300 if (isl_int_abs_gt(wraps
->mat
->row
[row
][i
], wraps
->max
))
1306 /* Wrap "ineq" (or its opposite if "negate" is set) around "bound"
1307 * to include "set" and add the result in position "w" of "wraps".
1308 * "len" is the total number of coefficients in "bound" and "ineq".
1309 * Return 1 on success, 0 on failure and -1 on error.
1310 * Wrapping can fail if the result of wrapping is equal to "bound"
1311 * or if we want to bound the sizes of the coefficients and
1312 * the wrapped constraint does not satisfy this bound.
1314 static int add_wrap(struct isl_wraps
*wraps
, int w
, isl_int
*bound
,
1315 isl_int
*ineq
, unsigned len
, __isl_keep isl_set
*set
, int negate
)
1317 isl_seq_cpy(wraps
->mat
->row
[w
], bound
, len
);
1319 isl_seq_neg(wraps
->mat
->row
[w
+ 1], ineq
, len
);
1320 ineq
= wraps
->mat
->row
[w
+ 1];
1322 if (!isl_set_wrap_facet(set
, wraps
->mat
->row
[w
], ineq
))
1324 if (isl_seq_eq(wraps
->mat
->row
[w
], bound
, len
))
1326 if (!allow_wrap(wraps
, w
))
1331 /* For each constraint in info->bmap that is not redundant (as determined
1332 * by info->tab) and that is not a valid constraint for the other basic map,
1333 * wrap the constraint around "bound" such that it includes the whole
1334 * set "set" and append the resulting constraint to "wraps".
1335 * Note that the constraints that are valid for the other basic map
1336 * will be added to the combined basic map by default, so there is
1337 * no need to wrap them.
1338 * The caller wrap_in_facets even relies on this function not wrapping
1339 * any constraints that are already valid.
1340 * "wraps" is assumed to have been pre-allocated to the appropriate size.
1341 * wraps->n_row is the number of actual wrapped constraints that have
1343 * If any of the wrapping problems results in a constraint that is
1344 * identical to "bound", then this means that "set" is unbounded in such
1345 * way that no wrapping is possible. If this happens then wraps->n_row
1347 * Similarly, if we want to bound the coefficients of the wrapping
1348 * constraints and a newly added wrapping constraint does not
1349 * satisfy the bound, then wraps->n_row is also reset to zero.
1351 static isl_stat
add_wraps(struct isl_wraps
*wraps
,
1352 struct isl_coalesce_info
*info
, isl_int
*bound
, __isl_keep isl_set
*set
)
1357 isl_basic_map
*bmap
= info
->bmap
;
1358 isl_size total
= isl_basic_map_dim(bmap
, isl_dim_all
);
1359 unsigned len
= 1 + total
;
1362 return isl_stat_error
;
1364 w
= wraps
->mat
->n_row
;
1366 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
1367 if (info
->ineq
[l
] == STATUS_VALID
||
1368 info
->ineq
[l
] == STATUS_REDUNDANT
)
1370 if (isl_seq_is_neg(bound
, bmap
->ineq
[l
], len
))
1372 if (isl_seq_eq(bound
, bmap
->ineq
[l
], len
))
1374 if (isl_tab_is_redundant(info
->tab
, bmap
->n_eq
+ l
))
1377 added
= add_wrap(wraps
, w
, bound
, bmap
->ineq
[l
], len
, set
, 0);
1379 return isl_stat_error
;
1384 for (l
= 0; l
< bmap
->n_eq
; ++l
) {
1385 if (isl_seq_is_neg(bound
, bmap
->eq
[l
], len
))
1387 if (isl_seq_eq(bound
, bmap
->eq
[l
], len
))
1390 for (m
= 0; m
< 2; ++m
) {
1391 if (info
->eq
[2 * l
+ m
] == STATUS_VALID
)
1393 added
= add_wrap(wraps
, w
, bound
, bmap
->eq
[l
], len
,
1396 return isl_stat_error
;
1403 wraps
->mat
->n_row
= w
;
1406 wraps
->mat
->n_row
= 0;
1410 /* Check if the constraints in "wraps" from "first" until the last
1411 * are all valid for the basic set represented by "tab".
1412 * If not, wraps->n_row is set to zero.
1414 static int check_wraps(__isl_keep isl_mat
*wraps
, int first
,
1415 struct isl_tab
*tab
)
1419 for (i
= first
; i
< wraps
->n_row
; ++i
) {
1420 enum isl_ineq_type type
;
1421 type
= isl_tab_ineq_type(tab
, wraps
->row
[i
]);
1422 if (type
== isl_ineq_error
)
1424 if (type
== isl_ineq_redundant
)
1433 /* Return a set that corresponds to the non-redundant constraints
1434 * (as recorded in tab) of bmap.
1436 * It's important to remove the redundant constraints as some
1437 * of the other constraints may have been modified after the
1438 * constraints were marked redundant.
1439 * In particular, a constraint may have been relaxed.
1440 * Redundant constraints are ignored when a constraint is relaxed
1441 * and should therefore continue to be ignored ever after.
1442 * Otherwise, the relaxation might be thwarted by some of
1443 * these constraints.
1445 * Update the underlying set to ensure that the dimension doesn't change.
1446 * Otherwise the integer divisions could get dropped if the tab
1447 * turns out to be empty.
1449 static __isl_give isl_set
*set_from_updated_bmap(__isl_keep isl_basic_map
*bmap
,
1450 struct isl_tab
*tab
)
1452 isl_basic_set
*bset
;
1454 bmap
= isl_basic_map_copy(bmap
);
1455 bset
= isl_basic_map_underlying_set(bmap
);
1456 bset
= isl_basic_set_cow(bset
);
1457 bset
= isl_basic_set_update_from_tab(bset
, tab
);
1458 return isl_set_from_basic_set(bset
);
1461 /* Wrap the constraints of info->bmap that bound the facet defined
1462 * by inequality "k" around (the opposite of) this inequality to
1463 * include "set". "bound" may be used to store the negated inequality.
1464 * Since the wrapped constraints are not guaranteed to contain the whole
1465 * of info->bmap, we check them in check_wraps.
1466 * If any of the wrapped constraints turn out to be invalid, then
1467 * check_wraps will reset wrap->n_row to zero.
1469 static isl_stat
add_wraps_around_facet(struct isl_wraps
*wraps
,
1470 struct isl_coalesce_info
*info
, int k
, isl_int
*bound
,
1471 __isl_keep isl_set
*set
)
1473 struct isl_tab_undo
*snap
;
1475 isl_size total
= isl_basic_map_dim(info
->bmap
, isl_dim_all
);
1478 return isl_stat_error
;
1480 snap
= isl_tab_snap(info
->tab
);
1482 if (isl_tab_select_facet(info
->tab
, info
->bmap
->n_eq
+ k
) < 0)
1483 return isl_stat_error
;
1484 if (isl_tab_detect_redundant(info
->tab
) < 0)
1485 return isl_stat_error
;
1487 isl_seq_neg(bound
, info
->bmap
->ineq
[k
], 1 + total
);
1489 n
= wraps
->mat
->n_row
;
1490 if (add_wraps(wraps
, info
, bound
, set
) < 0)
1491 return isl_stat_error
;
1493 if (isl_tab_rollback(info
->tab
, snap
) < 0)
1494 return isl_stat_error
;
1495 if (check_wraps(wraps
->mat
, n
, info
->tab
) < 0)
1496 return isl_stat_error
;
1501 /* Given a basic set i with a constraint k that is adjacent to
1502 * basic set j, check if we can wrap
1503 * both the facet corresponding to k (if "wrap_facet" is set) and basic map j
1504 * (always) around their ridges to include the other set.
1505 * If so, replace the pair of basic sets by their union.
1507 * All constraints of i (except k) are assumed to be valid or
1508 * cut constraints for j.
1509 * Wrapping the cut constraints to include basic map j may result
1510 * in constraints that are no longer valid of basic map i
1511 * we have to check that the resulting wrapping constraints are valid for i.
1512 * If "wrap_facet" is not set, then all constraints of i (except k)
1513 * are assumed to be valid for j.
1522 static enum isl_change
can_wrap_in_facet(int i
, int j
, int k
,
1523 struct isl_coalesce_info
*info
, int wrap_facet
)
1525 enum isl_change change
= isl_change_none
;
1526 struct isl_wraps wraps
;
1529 struct isl_set
*set_i
= NULL
;
1530 struct isl_set
*set_j
= NULL
;
1531 struct isl_vec
*bound
= NULL
;
1532 isl_size total
= isl_basic_map_dim(info
[i
].bmap
, isl_dim_all
);
1535 return isl_change_error
;
1536 set_i
= set_from_updated_bmap(info
[i
].bmap
, info
[i
].tab
);
1537 set_j
= set_from_updated_bmap(info
[j
].bmap
, info
[j
].tab
);
1538 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
1539 mat
= isl_mat_alloc(ctx
, 2 * (info
[i
].bmap
->n_eq
+ info
[j
].bmap
->n_eq
) +
1540 info
[i
].bmap
->n_ineq
+ info
[j
].bmap
->n_ineq
,
1542 if (wraps_init(&wraps
, mat
, info
, i
, j
) < 0)
1544 bound
= isl_vec_alloc(ctx
, 1 + total
);
1545 if (!set_i
|| !set_j
|| !bound
)
1548 isl_seq_cpy(bound
->el
, info
[i
].bmap
->ineq
[k
], 1 + total
);
1549 isl_int_add_ui(bound
->el
[0], bound
->el
[0], 1);
1550 isl_seq_normalize(ctx
, bound
->el
, 1 + total
);
1552 isl_seq_cpy(wraps
.mat
->row
[0], bound
->el
, 1 + total
);
1553 wraps
.mat
->n_row
= 1;
1555 if (add_wraps(&wraps
, &info
[j
], bound
->el
, set_i
) < 0)
1557 if (!wraps
.mat
->n_row
)
1561 if (add_wraps_around_facet(&wraps
, &info
[i
], k
,
1562 bound
->el
, set_j
) < 0)
1564 if (!wraps
.mat
->n_row
)
1568 change
= fuse(i
, j
, info
, wraps
.mat
, 0, 0);
1573 isl_set_free(set_i
);
1574 isl_set_free(set_j
);
1576 isl_vec_free(bound
);
1581 isl_vec_free(bound
);
1582 isl_set_free(set_i
);
1583 isl_set_free(set_j
);
1584 return isl_change_error
;
1587 /* Given a cut constraint t(x) >= 0 of basic map i, stored in row "w"
1588 * of wrap.mat, replace it by its relaxed version t(x) + 1 >= 0, and
1589 * add wrapping constraints to wrap.mat for all constraints
1590 * of basic map j that bound the part of basic map j that sticks out
1591 * of the cut constraint.
1592 * "set_i" is the underlying set of basic map i.
1593 * If any wrapping fails, then wraps->mat.n_row is reset to zero.
1595 * In particular, we first intersect basic map j with t(x) + 1 = 0.
1596 * If the result is empty, then t(x) >= 0 was actually a valid constraint
1597 * (with respect to the integer points), so we add t(x) >= 0 instead.
1598 * Otherwise, we wrap the constraints of basic map j that are not
1599 * redundant in this intersection and that are not already valid
1600 * for basic map i over basic map i.
1601 * Note that it is sufficient to wrap the constraints to include
1602 * basic map i, because we will only wrap the constraints that do
1603 * not include basic map i already. The wrapped constraint will
1604 * therefore be more relaxed compared to the original constraint.
1605 * Since the original constraint is valid for basic map j, so is
1606 * the wrapped constraint.
1608 static isl_stat
wrap_in_facet(struct isl_wraps
*wraps
, int w
,
1609 struct isl_coalesce_info
*info_j
, __isl_keep isl_set
*set_i
,
1610 struct isl_tab_undo
*snap
)
1612 isl_int_add_ui(wraps
->mat
->row
[w
][0], wraps
->mat
->row
[w
][0], 1);
1613 if (isl_tab_add_eq(info_j
->tab
, wraps
->mat
->row
[w
]) < 0)
1614 return isl_stat_error
;
1615 if (isl_tab_detect_redundant(info_j
->tab
) < 0)
1616 return isl_stat_error
;
1618 if (info_j
->tab
->empty
)
1619 isl_int_sub_ui(wraps
->mat
->row
[w
][0], wraps
->mat
->row
[w
][0], 1);
1620 else if (add_wraps(wraps
, info_j
, wraps
->mat
->row
[w
], set_i
) < 0)
1621 return isl_stat_error
;
1623 if (isl_tab_rollback(info_j
->tab
, snap
) < 0)
1624 return isl_stat_error
;
1629 /* Given a pair of basic maps i and j such that j sticks out
1630 * of i at n cut constraints, each time by at most one,
1631 * try to compute wrapping constraints and replace the two
1632 * basic maps by a single basic map.
1633 * The other constraints of i are assumed to be valid for j.
1634 * "set_i" is the underlying set of basic map i.
1635 * "wraps" has been initialized to be of the right size.
1637 * For each cut constraint t(x) >= 0 of i, we add the relaxed version
1638 * t(x) + 1 >= 0, along with wrapping constraints for all constraints
1639 * of basic map j that bound the part of basic map j that sticks out
1640 * of the cut constraint.
1642 * If any wrapping fails, i.e., if we cannot wrap to touch
1643 * the union, then we give up.
1644 * Otherwise, the pair of basic maps is replaced by their union.
1646 static enum isl_change
try_wrap_in_facets(int i
, int j
,
1647 struct isl_coalesce_info
*info
, struct isl_wraps
*wraps
,
1648 __isl_keep isl_set
*set_i
)
1652 struct isl_tab_undo
*snap
;
1654 total
= isl_basic_map_dim(info
[i
].bmap
, isl_dim_all
);
1656 return isl_change_error
;
1658 snap
= isl_tab_snap(info
[j
].tab
);
1660 wraps
->mat
->n_row
= 0;
1662 for (k
= 0; k
< info
[i
].bmap
->n_eq
; ++k
) {
1663 for (l
= 0; l
< 2; ++l
) {
1664 if (info
[i
].eq
[2 * k
+ l
] != STATUS_CUT
)
1666 w
= wraps
->mat
->n_row
++;
1668 isl_seq_neg(wraps
->mat
->row
[w
],
1669 info
[i
].bmap
->eq
[k
], 1 + total
);
1671 isl_seq_cpy(wraps
->mat
->row
[w
],
1672 info
[i
].bmap
->eq
[k
], 1 + total
);
1673 if (wrap_in_facet(wraps
, w
, &info
[j
], set_i
, snap
) < 0)
1674 return isl_change_error
;
1676 if (!wraps
->mat
->n_row
)
1677 return isl_change_none
;
1681 for (k
= 0; k
< info
[i
].bmap
->n_ineq
; ++k
) {
1682 if (info
[i
].ineq
[k
] != STATUS_CUT
)
1684 w
= wraps
->mat
->n_row
++;
1685 isl_seq_cpy(wraps
->mat
->row
[w
],
1686 info
[i
].bmap
->ineq
[k
], 1 + total
);
1687 if (wrap_in_facet(wraps
, w
, &info
[j
], set_i
, snap
) < 0)
1688 return isl_change_error
;
1690 if (!wraps
->mat
->n_row
)
1691 return isl_change_none
;
1694 return fuse(i
, j
, info
, wraps
->mat
, 0, 1);
1697 /* Given a pair of basic maps i and j such that j sticks out
1698 * of i at n cut constraints, each time by at most one,
1699 * try to compute wrapping constraints and replace the two
1700 * basic maps by a single basic map.
1701 * The other constraints of i are assumed to be valid for j.
1703 * The core computation is performed by try_wrap_in_facets.
1704 * This function simply extracts an underlying set representation
1705 * of basic map i and initializes the data structure for keeping
1706 * track of wrapping constraints.
1708 static enum isl_change
wrap_in_facets(int i
, int j
, int n
,
1709 struct isl_coalesce_info
*info
)
1711 enum isl_change change
= isl_change_none
;
1712 struct isl_wraps wraps
;
1715 isl_set
*set_i
= NULL
;
1716 isl_size total
= isl_basic_map_dim(info
[i
].bmap
, isl_dim_all
);
1720 return isl_change_error
;
1721 if (isl_tab_extend_cons(info
[j
].tab
, 1) < 0)
1722 return isl_change_error
;
1724 max_wrap
= 1 + 2 * info
[j
].bmap
->n_eq
+ info
[j
].bmap
->n_ineq
;
1727 set_i
= set_from_updated_bmap(info
[i
].bmap
, info
[i
].tab
);
1728 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
1729 mat
= isl_mat_alloc(ctx
, max_wrap
, 1 + total
);
1730 if (wraps_init(&wraps
, mat
, info
, i
, j
) < 0)
1735 change
= try_wrap_in_facets(i
, j
, info
, &wraps
, set_i
);
1738 isl_set_free(set_i
);
1743 isl_set_free(set_i
);
1744 return isl_change_error
;
1747 /* Return the effect of inequality "ineq" on the tableau "tab",
1748 * after relaxing the constant term of "ineq" by one.
1750 static enum isl_ineq_type
type_of_relaxed(struct isl_tab
*tab
, isl_int
*ineq
)
1752 enum isl_ineq_type type
;
1754 isl_int_add_ui(ineq
[0], ineq
[0], 1);
1755 type
= isl_tab_ineq_type(tab
, ineq
);
1756 isl_int_sub_ui(ineq
[0], ineq
[0], 1);
1761 /* Given two basic sets i and j,
1762 * check if relaxing all the cut constraints of i by one turns
1763 * them into valid constraint for j and check if we can wrap in
1764 * the bits that are sticking out.
1765 * If so, replace the pair by their union.
1767 * We first check if all relaxed cut inequalities of i are valid for j
1768 * and then try to wrap in the intersections of the relaxed cut inequalities
1771 * During this wrapping, we consider the points of j that lie at a distance
1772 * of exactly 1 from i. In particular, we ignore the points that lie in
1773 * between this lower-dimensional space and the basic map i.
1774 * We can therefore only apply this to integer maps.
1800 * Wrapping can fail if the result of wrapping one of the facets
1801 * around its edges does not produce any new facet constraint.
1802 * In particular, this happens when we try to wrap in unbounded sets.
1804 * _______________________________________________________________________
1808 * |_| |_________________________________________________________________
1811 * The following is not an acceptable result of coalescing the above two
1812 * sets as it includes extra integer points.
1813 * _______________________________________________________________________
1818 * \______________________________________________________________________
1820 static enum isl_change
can_wrap_in_set(int i
, int j
,
1821 struct isl_coalesce_info
*info
)
1827 if (ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_RATIONAL
) ||
1828 ISL_F_ISSET(info
[j
].bmap
, ISL_BASIC_MAP_RATIONAL
))
1829 return isl_change_none
;
1831 n
= count_eq(&info
[i
], STATUS_CUT
) + count_ineq(&info
[i
], STATUS_CUT
);
1833 return isl_change_none
;
1835 total
= isl_basic_map_dim(info
[i
].bmap
, isl_dim_all
);
1837 return isl_change_error
;
1838 for (k
= 0; k
< info
[i
].bmap
->n_eq
; ++k
) {
1839 for (l
= 0; l
< 2; ++l
) {
1840 enum isl_ineq_type type
;
1842 if (info
[i
].eq
[2 * k
+ l
] != STATUS_CUT
)
1846 isl_seq_neg(info
[i
].bmap
->eq
[k
],
1847 info
[i
].bmap
->eq
[k
], 1 + total
);
1848 type
= type_of_relaxed(info
[j
].tab
,
1849 info
[i
].bmap
->eq
[k
]);
1851 isl_seq_neg(info
[i
].bmap
->eq
[k
],
1852 info
[i
].bmap
->eq
[k
], 1 + total
);
1853 if (type
== isl_ineq_error
)
1854 return isl_change_error
;
1855 if (type
!= isl_ineq_redundant
)
1856 return isl_change_none
;
1860 for (k
= 0; k
< info
[i
].bmap
->n_ineq
; ++k
) {
1861 enum isl_ineq_type type
;
1863 if (info
[i
].ineq
[k
] != STATUS_CUT
)
1866 type
= type_of_relaxed(info
[j
].tab
, info
[i
].bmap
->ineq
[k
]);
1867 if (type
== isl_ineq_error
)
1868 return isl_change_error
;
1869 if (type
!= isl_ineq_redundant
)
1870 return isl_change_none
;
1873 return wrap_in_facets(i
, j
, n
, info
);
1876 /* Check if either i or j has only cut constraints that can
1877 * be used to wrap in (a facet of) the other basic set.
1878 * if so, replace the pair by their union.
1880 static enum isl_change
check_wrap(int i
, int j
, struct isl_coalesce_info
*info
)
1882 enum isl_change change
= isl_change_none
;
1884 change
= can_wrap_in_set(i
, j
, info
);
1885 if (change
!= isl_change_none
)
1888 change
= can_wrap_in_set(j
, i
, info
);
1892 /* Check if all inequality constraints of "i" that cut "j" cease
1893 * to be cut constraints if they are relaxed by one.
1894 * If so, collect the cut constraints in "list".
1895 * The caller is responsible for allocating "list".
1897 static isl_bool
all_cut_by_one(int i
, int j
, struct isl_coalesce_info
*info
,
1903 for (l
= 0; l
< info
[i
].bmap
->n_ineq
; ++l
) {
1904 enum isl_ineq_type type
;
1906 if (info
[i
].ineq
[l
] != STATUS_CUT
)
1908 type
= type_of_relaxed(info
[j
].tab
, info
[i
].bmap
->ineq
[l
]);
1909 if (type
== isl_ineq_error
)
1910 return isl_bool_error
;
1911 if (type
!= isl_ineq_redundant
)
1912 return isl_bool_false
;
1916 return isl_bool_true
;
1919 /* Given two basic maps such that "j" has at least one equality constraint
1920 * that is adjacent to an inequality constraint of "i" and such that "i" has
1921 * exactly one inequality constraint that is adjacent to an equality
1922 * constraint of "j", check whether "i" can be extended to include "j" or
1923 * whether "j" can be wrapped into "i".
1924 * All remaining constraints of "i" and "j" are assumed to be valid
1925 * or cut constraints of the other basic map.
1926 * However, none of the equality constraints of "i" are cut constraints.
1928 * If "i" has any "cut" inequality constraints, then check if relaxing
1929 * each of them by one is sufficient for them to become valid.
1930 * If so, check if the inequality constraint adjacent to an equality
1931 * constraint of "j" along with all these cut constraints
1932 * can be relaxed by one to contain exactly "j".
1933 * Otherwise, or if this fails, check if "j" can be wrapped into "i".
1935 static enum isl_change
check_single_adj_eq(int i
, int j
,
1936 struct isl_coalesce_info
*info
)
1938 enum isl_change change
= isl_change_none
;
1945 n_cut
= count_ineq(&info
[i
], STATUS_CUT
);
1947 k
= find_ineq(&info
[i
], STATUS_ADJ_EQ
);
1950 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
1951 relax
= isl_calloc_array(ctx
, int, 1 + n_cut
);
1953 return isl_change_error
;
1955 try_relax
= all_cut_by_one(i
, j
, info
, relax
+ 1);
1957 change
= isl_change_error
;
1959 try_relax
= isl_bool_true
;
1962 if (try_relax
&& change
== isl_change_none
)
1963 change
= is_relaxed_extension(i
, j
, 1 + n_cut
, relax
, info
);
1966 if (change
!= isl_change_none
)
1969 change
= can_wrap_in_facet(i
, j
, k
, info
, n_cut
> 0);
1974 /* At least one of the basic maps has an equality that is adjacent
1975 * to an inequality. Make sure that only one of the basic maps has
1976 * such an equality and that the other basic map has exactly one
1977 * inequality adjacent to an equality.
1978 * If the other basic map does not have such an inequality, then
1979 * check if all its constraints are either valid or cut constraints
1980 * and, if so, try wrapping in the first map into the second.
1981 * Otherwise, try to extend one basic map with the other or
1982 * wrap one basic map in the other.
1984 static enum isl_change
check_adj_eq(int i
, int j
,
1985 struct isl_coalesce_info
*info
)
1987 if (any_eq(&info
[i
], STATUS_ADJ_INEQ
) &&
1988 any_eq(&info
[j
], STATUS_ADJ_INEQ
))
1989 /* ADJ EQ TOO MANY */
1990 return isl_change_none
;
1992 if (any_eq(&info
[i
], STATUS_ADJ_INEQ
))
1993 return check_adj_eq(j
, i
, info
);
1995 /* j has an equality adjacent to an inequality in i */
1997 if (count_ineq(&info
[i
], STATUS_ADJ_EQ
) != 1) {
1998 if (all_valid_or_cut(&info
[i
]))
1999 return can_wrap_in_set(i
, j
, info
);
2000 return isl_change_none
;
2002 if (any_eq(&info
[i
], STATUS_CUT
))
2003 return isl_change_none
;
2004 if (any_ineq(&info
[j
], STATUS_ADJ_EQ
) ||
2005 any_ineq(&info
[i
], STATUS_ADJ_INEQ
) ||
2006 any_ineq(&info
[j
], STATUS_ADJ_INEQ
))
2007 /* ADJ EQ TOO MANY */
2008 return isl_change_none
;
2010 return check_single_adj_eq(i
, j
, info
);
2013 /* Disjunct "j" lies on a hyperplane that is adjacent to disjunct "i".
2014 * In particular, disjunct "i" has an inequality constraint that is adjacent
2015 * to a (combination of) equality constraint(s) of disjunct "j",
2016 * but disjunct "j" has no explicit equality constraint adjacent
2017 * to an inequality constraint of disjunct "i".
2019 * Disjunct "i" is already known not to have any equality constraints
2020 * that are adjacent to an equality or inequality constraint.
2021 * Check that, other than the inequality constraint mentioned above,
2022 * all other constraints of disjunct "i" are valid for disjunct "j".
2023 * If so, try and wrap in disjunct "j".
2025 static enum isl_change
check_ineq_adj_eq(int i
, int j
,
2026 struct isl_coalesce_info
*info
)
2030 if (any_eq(&info
[i
], STATUS_CUT
))
2031 return isl_change_none
;
2032 if (any_ineq(&info
[i
], STATUS_CUT
))
2033 return isl_change_none
;
2034 if (any_ineq(&info
[i
], STATUS_ADJ_INEQ
))
2035 return isl_change_none
;
2036 if (count_ineq(&info
[i
], STATUS_ADJ_EQ
) != 1)
2037 return isl_change_none
;
2039 k
= find_ineq(&info
[i
], STATUS_ADJ_EQ
);
2041 return can_wrap_in_facet(i
, j
, k
, info
, 0);
2044 /* The two basic maps lie on adjacent hyperplanes. In particular,
2045 * basic map "i" has an equality that lies parallel to basic map "j".
2046 * Check if we can wrap the facets around the parallel hyperplanes
2047 * to include the other set.
2049 * We perform basically the same operations as can_wrap_in_facet,
2050 * except that we don't need to select a facet of one of the sets.
2056 * If there is more than one equality of "i" adjacent to an equality of "j",
2057 * then the result will satisfy one or more equalities that are a linear
2058 * combination of these equalities. These will be encoded as pairs
2059 * of inequalities in the wrapping constraints and need to be made
2062 static enum isl_change
check_eq_adj_eq(int i
, int j
,
2063 struct isl_coalesce_info
*info
)
2066 enum isl_change change
= isl_change_none
;
2067 int detect_equalities
= 0;
2068 struct isl_wraps wraps
;
2071 struct isl_set
*set_i
= NULL
;
2072 struct isl_set
*set_j
= NULL
;
2073 struct isl_vec
*bound
= NULL
;
2074 isl_size total
= isl_basic_map_dim(info
[i
].bmap
, isl_dim_all
);
2077 return isl_change_error
;
2078 if (count_eq(&info
[i
], STATUS_ADJ_EQ
) != 1)
2079 detect_equalities
= 1;
2081 k
= find_eq(&info
[i
], STATUS_ADJ_EQ
);
2083 set_i
= set_from_updated_bmap(info
[i
].bmap
, info
[i
].tab
);
2084 set_j
= set_from_updated_bmap(info
[j
].bmap
, info
[j
].tab
);
2085 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
2086 mat
= isl_mat_alloc(ctx
, 2 * (info
[i
].bmap
->n_eq
+ info
[j
].bmap
->n_eq
) +
2087 info
[i
].bmap
->n_ineq
+ info
[j
].bmap
->n_ineq
,
2089 if (wraps_init(&wraps
, mat
, info
, i
, j
) < 0)
2091 bound
= isl_vec_alloc(ctx
, 1 + total
);
2092 if (!set_i
|| !set_j
|| !bound
)
2096 isl_seq_neg(bound
->el
, info
[i
].bmap
->eq
[k
/ 2], 1 + total
);
2098 isl_seq_cpy(bound
->el
, info
[i
].bmap
->eq
[k
/ 2], 1 + total
);
2099 isl_int_add_ui(bound
->el
[0], bound
->el
[0], 1);
2101 isl_seq_cpy(wraps
.mat
->row
[0], bound
->el
, 1 + total
);
2102 wraps
.mat
->n_row
= 1;
2104 if (add_wraps(&wraps
, &info
[j
], bound
->el
, set_i
) < 0)
2106 if (!wraps
.mat
->n_row
)
2109 isl_int_sub_ui(bound
->el
[0], bound
->el
[0], 1);
2110 isl_seq_neg(bound
->el
, bound
->el
, 1 + total
);
2112 isl_seq_cpy(wraps
.mat
->row
[wraps
.mat
->n_row
], bound
->el
, 1 + total
);
2115 if (add_wraps(&wraps
, &info
[i
], bound
->el
, set_j
) < 0)
2117 if (!wraps
.mat
->n_row
)
2120 change
= fuse(i
, j
, info
, wraps
.mat
, detect_equalities
, 0);
2123 error
: change
= isl_change_error
;
2128 isl_set_free(set_i
);
2129 isl_set_free(set_j
);
2130 isl_vec_free(bound
);
2135 /* Initialize the "eq" and "ineq" fields of "info".
2137 static void init_status(struct isl_coalesce_info
*info
)
2139 info
->eq
= info
->ineq
= NULL
;
2142 /* Set info->eq to the positions of the equalities of info->bmap
2143 * with respect to the basic map represented by "tab".
2144 * If info->eq has already been computed, then do not compute it again.
2146 static void set_eq_status_in(struct isl_coalesce_info
*info
,
2147 struct isl_tab
*tab
)
2151 info
->eq
= eq_status_in(info
->bmap
, tab
);
2154 /* Set info->ineq to the positions of the inequalities of info->bmap
2155 * with respect to the basic map represented by "tab".
2156 * If info->ineq has already been computed, then do not compute it again.
2158 static void set_ineq_status_in(struct isl_coalesce_info
*info
,
2159 struct isl_tab
*tab
)
2163 info
->ineq
= ineq_status_in(info
->bmap
, info
->tab
, tab
);
2166 /* Free the memory allocated by the "eq" and "ineq" fields of "info".
2167 * This function assumes that init_status has been called on "info" first,
2168 * after which the "eq" and "ineq" fields may or may not have been
2169 * assigned a newly allocated array.
2171 static void clear_status(struct isl_coalesce_info
*info
)
2177 /* Are all inequality constraints of the basic map represented by "info"
2178 * valid for the other basic map, except for a single constraint
2179 * that is adjacent to an inequality constraint of the other basic map?
2181 static int all_ineq_valid_or_single_adj_ineq(struct isl_coalesce_info
*info
)
2186 for (i
= 0; i
< info
->bmap
->n_ineq
; ++i
) {
2187 if (info
->ineq
[i
] == STATUS_REDUNDANT
)
2189 if (info
->ineq
[i
] == STATUS_VALID
)
2191 if (info
->ineq
[i
] != STATUS_ADJ_INEQ
)
2201 /* Basic map "i" has one or more equality constraints that separate it
2202 * from basic map "j". Check if it happens to be an extension
2204 * In particular, check that all constraints of "j" are valid for "i",
2205 * except for one inequality constraint that is adjacent
2206 * to an inequality constraints of "i".
2207 * If so, check for "i" being an extension of "j" by calling
2208 * is_adj_ineq_extension.
2210 * Clean up the memory allocated for keeping track of the status
2211 * of the constraints before returning.
2213 static enum isl_change
separating_equality(int i
, int j
,
2214 struct isl_coalesce_info
*info
)
2216 enum isl_change change
= isl_change_none
;
2218 if (all(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_VALID
) &&
2219 all_ineq_valid_or_single_adj_ineq(&info
[j
]))
2220 change
= is_adj_ineq_extension(j
, i
, info
);
2222 clear_status(&info
[i
]);
2223 clear_status(&info
[j
]);
2227 /* Check if the union of the given pair of basic maps
2228 * can be represented by a single basic map.
2229 * If so, replace the pair by the single basic map and return
2230 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
2231 * Otherwise, return isl_change_none.
2232 * The two basic maps are assumed to live in the same local space.
2233 * The "eq" and "ineq" fields of info[i] and info[j] are assumed
2234 * to have been initialized by the caller, either to NULL or
2235 * to valid information.
2237 * We first check the effect of each constraint of one basic map
2238 * on the other basic map.
2239 * The constraint may be
2240 * redundant the constraint is redundant in its own
2241 * basic map and should be ignore and removed
2243 * valid all (integer) points of the other basic map
2244 * satisfy the constraint
2245 * separate no (integer) point of the other basic map
2246 * satisfies the constraint
2247 * cut some but not all points of the other basic map
2248 * satisfy the constraint
2249 * adj_eq the given constraint is adjacent (on the outside)
2250 * to an equality of the other basic map
2251 * adj_ineq the given constraint is adjacent (on the outside)
2252 * to an inequality of the other basic map
2254 * We consider seven cases in which we can replace the pair by a single
2255 * basic map. We ignore all "redundant" constraints.
2257 * 1. all constraints of one basic map are valid
2258 * => the other basic map is a subset and can be removed
2260 * 2. all constraints of both basic maps are either "valid" or "cut"
2261 * and the facets corresponding to the "cut" constraints
2262 * of one of the basic maps lies entirely inside the other basic map
2263 * => the pair can be replaced by a basic map consisting
2264 * of the valid constraints in both basic maps
2266 * 3. there is a single pair of adjacent inequalities
2267 * (all other constraints are "valid")
2268 * => the pair can be replaced by a basic map consisting
2269 * of the valid constraints in both basic maps
2271 * 4. one basic map has a single adjacent inequality, while the other
2272 * constraints are "valid". The other basic map has some
2273 * "cut" constraints, but replacing the adjacent inequality by
2274 * its opposite and adding the valid constraints of the other
2275 * basic map results in a subset of the other basic map
2276 * => the pair can be replaced by a basic map consisting
2277 * of the valid constraints in both basic maps
2279 * 5. there is a single adjacent pair of an inequality and an equality,
2280 * the other constraints of the basic map containing the inequality are
2281 * "valid". Moreover, if the inequality the basic map is relaxed
2282 * and then turned into an equality, then resulting facet lies
2283 * entirely inside the other basic map
2284 * => the pair can be replaced by the basic map containing
2285 * the inequality, with the inequality relaxed.
2287 * 6. there is a single inequality adjacent to an equality,
2288 * the other constraints of the basic map containing the inequality are
2289 * "valid". Moreover, the facets corresponding to both
2290 * the inequality and the equality can be wrapped around their
2291 * ridges to include the other basic map
2292 * => the pair can be replaced by a basic map consisting
2293 * of the valid constraints in both basic maps together
2294 * with all wrapping constraints
2296 * 7. one of the basic maps extends beyond the other by at most one.
2297 * Moreover, the facets corresponding to the cut constraints and
2298 * the pieces of the other basic map at offset one from these cut
2299 * constraints can be wrapped around their ridges to include
2300 * the union of the two basic maps
2301 * => the pair can be replaced by a basic map consisting
2302 * of the valid constraints in both basic maps together
2303 * with all wrapping constraints
2305 * 8. the two basic maps live in adjacent hyperplanes. In principle
2306 * such sets can always be combined through wrapping, but we impose
2307 * that there is only one such pair, to avoid overeager coalescing.
2309 * Throughout the computation, we maintain a collection of tableaus
2310 * corresponding to the basic maps. When the basic maps are dropped
2311 * or combined, the tableaus are modified accordingly.
2313 static enum isl_change
coalesce_local_pair_reuse(int i
, int j
,
2314 struct isl_coalesce_info
*info
)
2316 enum isl_change change
= isl_change_none
;
2318 set_ineq_status_in(&info
[i
], info
[j
].tab
);
2319 if (info
[i
].bmap
->n_ineq
&& !info
[i
].ineq
)
2321 if (any_ineq(&info
[i
], STATUS_ERROR
))
2323 if (any_ineq(&info
[i
], STATUS_SEPARATE
))
2326 set_ineq_status_in(&info
[j
], info
[i
].tab
);
2327 if (info
[j
].bmap
->n_ineq
&& !info
[j
].ineq
)
2329 if (any_ineq(&info
[j
], STATUS_ERROR
))
2331 if (any_ineq(&info
[j
], STATUS_SEPARATE
))
2334 set_eq_status_in(&info
[i
], info
[j
].tab
);
2335 if (info
[i
].bmap
->n_eq
&& !info
[i
].eq
)
2337 if (any_eq(&info
[i
], STATUS_ERROR
))
2340 set_eq_status_in(&info
[j
], info
[i
].tab
);
2341 if (info
[j
].bmap
->n_eq
&& !info
[j
].eq
)
2343 if (any_eq(&info
[j
], STATUS_ERROR
))
2346 if (any_eq(&info
[i
], STATUS_SEPARATE
))
2347 return separating_equality(i
, j
, info
);
2348 if (any_eq(&info
[j
], STATUS_SEPARATE
))
2349 return separating_equality(j
, i
, info
);
2351 if (all(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_VALID
) &&
2352 all(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_VALID
)) {
2354 change
= isl_change_drop_second
;
2355 } else if (all(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_VALID
) &&
2356 all(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_VALID
)) {
2358 change
= isl_change_drop_first
;
2359 } else if (any_eq(&info
[i
], STATUS_ADJ_EQ
)) {
2360 change
= check_eq_adj_eq(i
, j
, info
);
2361 } else if (any_eq(&info
[j
], STATUS_ADJ_EQ
)) {
2362 change
= check_eq_adj_eq(j
, i
, info
);
2363 } else if (any_eq(&info
[i
], STATUS_ADJ_INEQ
) ||
2364 any_eq(&info
[j
], STATUS_ADJ_INEQ
)) {
2365 change
= check_adj_eq(i
, j
, info
);
2366 } else if (any_ineq(&info
[i
], STATUS_ADJ_EQ
)) {
2367 change
= check_ineq_adj_eq(i
, j
, info
);
2368 } else if (any_ineq(&info
[j
], STATUS_ADJ_EQ
)) {
2369 change
= check_ineq_adj_eq(j
, i
, info
);
2370 } else if (any_ineq(&info
[i
], STATUS_ADJ_INEQ
) ||
2371 any_ineq(&info
[j
], STATUS_ADJ_INEQ
)) {
2372 change
= check_adj_ineq(i
, j
, info
);
2374 if (!any_eq(&info
[i
], STATUS_CUT
) &&
2375 !any_eq(&info
[j
], STATUS_CUT
))
2376 change
= check_facets(i
, j
, info
);
2377 if (change
== isl_change_none
)
2378 change
= check_wrap(i
, j
, info
);
2382 clear_status(&info
[i
]);
2383 clear_status(&info
[j
]);
2386 clear_status(&info
[i
]);
2387 clear_status(&info
[j
]);
2388 return isl_change_error
;
2391 /* Check if the union of the given pair of basic maps
2392 * can be represented by a single basic map.
2393 * If so, replace the pair by the single basic map and return
2394 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
2395 * Otherwise, return isl_change_none.
2396 * The two basic maps are assumed to live in the same local space.
2398 static enum isl_change
coalesce_local_pair(int i
, int j
,
2399 struct isl_coalesce_info
*info
)
2401 init_status(&info
[i
]);
2402 init_status(&info
[j
]);
2403 return coalesce_local_pair_reuse(i
, j
, info
);
2406 /* Shift the integer division at position "div" of the basic map
2407 * represented by "info" by "shift".
2409 * That is, if the integer division has the form
2413 * then replace it by
2415 * floor((f(x) + shift * d)/d) - shift
2417 static isl_stat
shift_div(struct isl_coalesce_info
*info
, int div
,
2420 isl_size total
, n_div
;
2422 info
->bmap
= isl_basic_map_shift_div(info
->bmap
, div
, 0, shift
);
2424 return isl_stat_error
;
2426 total
= isl_basic_map_dim(info
->bmap
, isl_dim_all
);
2427 n_div
= isl_basic_map_dim(info
->bmap
, isl_dim_div
);
2428 if (total
< 0 || n_div
< 0)
2429 return isl_stat_error
;
2431 if (isl_tab_shift_var(info
->tab
, total
+ div
, shift
) < 0)
2432 return isl_stat_error
;
2437 /* If the integer division at position "div" is defined by an equality,
2438 * i.e., a stride constraint, then change the integer division expression
2439 * to have a constant term equal to zero.
2441 * Let the equality constraint be
2445 * The integer division expression is then typically of the form
2447 * a = floor((-f - c')/m)
2449 * The integer division is first shifted by t = floor(c/m),
2450 * turning the equality constraint into
2452 * c - m floor(c/m) + f + m a' = 0
2456 * (c mod m) + f + m a' = 0
2460 * a' = (-f - (c mod m))/m = floor((-f)/m)
2462 * because a' is an integer and 0 <= (c mod m) < m.
2463 * The constant term of a' can therefore be zeroed out,
2464 * but only if the integer division expression is of the expected form.
2466 static isl_stat
normalize_stride_div(struct isl_coalesce_info
*info
, int div
)
2468 isl_bool defined
, valid
;
2471 isl_int shift
, stride
;
2473 defined
= isl_basic_map_has_defining_equality(info
->bmap
, isl_dim_div
,
2476 return isl_stat_error
;
2480 return isl_stat_error
;
2481 valid
= isl_constraint_is_div_equality(c
, div
);
2482 isl_int_init(shift
);
2483 isl_int_init(stride
);
2484 isl_constraint_get_constant(c
, &shift
);
2485 isl_constraint_get_coefficient(c
, isl_dim_div
, div
, &stride
);
2486 isl_int_fdiv_q(shift
, shift
, stride
);
2487 r
= shift_div(info
, div
, shift
);
2488 isl_int_clear(stride
);
2489 isl_int_clear(shift
);
2490 isl_constraint_free(c
);
2491 if (r
< 0 || valid
< 0)
2492 return isl_stat_error
;
2495 info
->bmap
= isl_basic_map_set_div_expr_constant_num_si_inplace(
2496 info
->bmap
, div
, 0);
2498 return isl_stat_error
;
2502 /* The basic maps represented by "info1" and "info2" are known
2503 * to have the same number of integer divisions.
2504 * Check if pairs of integer divisions are equal to each other
2505 * despite the fact that they differ by a rational constant.
2507 * In particular, look for any pair of integer divisions that
2508 * only differ in their constant terms.
2509 * If either of these integer divisions is defined
2510 * by stride constraints, then modify it to have a zero constant term.
2511 * If both are defined by stride constraints then in the end they will have
2512 * the same (zero) constant term.
2514 static isl_stat
harmonize_stride_divs(struct isl_coalesce_info
*info1
,
2515 struct isl_coalesce_info
*info2
)
2520 n
= isl_basic_map_dim(info1
->bmap
, isl_dim_div
);
2522 return isl_stat_error
;
2523 for (i
= 0; i
< n
; ++i
) {
2524 isl_bool known
, harmonize
;
2526 known
= isl_basic_map_div_is_known(info1
->bmap
, i
);
2527 if (known
>= 0 && known
)
2528 known
= isl_basic_map_div_is_known(info2
->bmap
, i
);
2530 return isl_stat_error
;
2533 harmonize
= isl_basic_map_equal_div_expr_except_constant(
2534 info1
->bmap
, i
, info2
->bmap
, i
);
2536 return isl_stat_error
;
2539 if (normalize_stride_div(info1
, i
) < 0)
2540 return isl_stat_error
;
2541 if (normalize_stride_div(info2
, i
) < 0)
2542 return isl_stat_error
;
2548 /* If "shift" is an integer constant, then shift the integer division
2549 * at position "div" of the basic map represented by "info" by "shift".
2550 * If "shift" is not an integer constant, then do nothing.
2551 * If "shift" is equal to zero, then no shift needs to be performed either.
2553 * That is, if the integer division has the form
2557 * then replace it by
2559 * floor((f(x) + shift * d)/d) - shift
2561 static isl_stat
shift_if_cst_int(struct isl_coalesce_info
*info
, int div
,
2562 __isl_keep isl_aff
*shift
)
2569 cst
= isl_aff_is_cst(shift
);
2570 if (cst
< 0 || !cst
)
2571 return cst
< 0 ? isl_stat_error
: isl_stat_ok
;
2573 c
= isl_aff_get_constant_val(shift
);
2574 cst
= isl_val_is_int(c
);
2575 if (cst
>= 0 && cst
)
2576 cst
= isl_bool_not(isl_val_is_zero(c
));
2577 if (cst
< 0 || !cst
) {
2579 return cst
< 0 ? isl_stat_error
: isl_stat_ok
;
2583 r
= isl_val_get_num_isl_int(c
, &d
);
2585 r
= shift_div(info
, div
, d
);
2593 /* Check if some of the divs in the basic map represented by "info1"
2594 * are shifts of the corresponding divs in the basic map represented
2595 * by "info2", taking into account the equality constraints "eq1" of "info1"
2596 * and "eq2" of "info2". If so, align them with those of "info2".
2597 * "info1" and "info2" are assumed to have the same number
2598 * of integer divisions.
2600 * An integer division is considered to be a shift of another integer
2601 * division if, after simplification with respect to the equality
2602 * constraints of the other basic map, one is equal to the other
2605 * In particular, for each pair of integer divisions, if both are known,
2606 * have the same denominator and are not already equal to each other,
2607 * simplify each with respect to the equality constraints
2608 * of the other basic map. If the difference is an integer constant,
2609 * then move this difference outside.
2610 * That is, if, after simplification, one integer division is of the form
2612 * floor((f(x) + c_1)/d)
2614 * while the other is of the form
2616 * floor((f(x) + c_2)/d)
2618 * and n = (c_2 - c_1)/d is an integer, then replace the first
2619 * integer division by
2621 * floor((f_1(x) + c_1 + n * d)/d) - n,
2623 * where floor((f_1(x) + c_1 + n * d)/d) = floor((f2(x) + c_2)/d)
2624 * after simplification with respect to the equality constraints.
2626 static isl_stat
harmonize_divs_with_hulls(struct isl_coalesce_info
*info1
,
2627 struct isl_coalesce_info
*info2
, __isl_keep isl_basic_set
*eq1
,
2628 __isl_keep isl_basic_set
*eq2
)
2632 isl_local_space
*ls1
, *ls2
;
2634 total
= isl_basic_map_dim(info1
->bmap
, isl_dim_all
);
2636 return isl_stat_error
;
2637 ls1
= isl_local_space_wrap(isl_basic_map_get_local_space(info1
->bmap
));
2638 ls2
= isl_local_space_wrap(isl_basic_map_get_local_space(info2
->bmap
));
2639 for (i
= 0; i
< info1
->bmap
->n_div
; ++i
) {
2641 isl_aff
*div1
, *div2
;
2643 if (!isl_local_space_div_is_known(ls1
, i
) ||
2644 !isl_local_space_div_is_known(ls2
, i
))
2646 if (isl_int_ne(info1
->bmap
->div
[i
][0], info2
->bmap
->div
[i
][0]))
2648 if (isl_seq_eq(info1
->bmap
->div
[i
] + 1,
2649 info2
->bmap
->div
[i
] + 1, 1 + total
))
2651 div1
= isl_local_space_get_div(ls1
, i
);
2652 div2
= isl_local_space_get_div(ls2
, i
);
2653 div1
= isl_aff_substitute_equalities(div1
,
2654 isl_basic_set_copy(eq2
));
2655 div2
= isl_aff_substitute_equalities(div2
,
2656 isl_basic_set_copy(eq1
));
2657 div2
= isl_aff_sub(div2
, div1
);
2658 r
= shift_if_cst_int(info1
, i
, div2
);
2663 isl_local_space_free(ls1
);
2664 isl_local_space_free(ls2
);
2666 if (i
< info1
->bmap
->n_div
)
2667 return isl_stat_error
;
2671 /* Check if some of the divs in the basic map represented by "info1"
2672 * are shifts of the corresponding divs in the basic map represented
2673 * by "info2". If so, align them with those of "info2".
2674 * Only do this if "info1" and "info2" have the same number
2675 * of integer divisions.
2677 * An integer division is considered to be a shift of another integer
2678 * division if, after simplification with respect to the equality
2679 * constraints of the other basic map, one is equal to the other
2682 * First check if pairs of integer divisions are equal to each other
2683 * despite the fact that they differ by a rational constant.
2684 * If so, try and arrange for them to have the same constant term.
2686 * Then, extract the equality constraints and continue with
2687 * harmonize_divs_with_hulls.
2689 * If the equality constraints of both basic maps are the same,
2690 * then there is no need to perform any shifting since
2691 * the coefficients of the integer divisions should have been
2692 * reduced in the same way.
2694 static isl_stat
harmonize_divs(struct isl_coalesce_info
*info1
,
2695 struct isl_coalesce_info
*info2
)
2698 isl_basic_map
*bmap1
, *bmap2
;
2699 isl_basic_set
*eq1
, *eq2
;
2702 if (!info1
->bmap
|| !info2
->bmap
)
2703 return isl_stat_error
;
2705 if (info1
->bmap
->n_div
!= info2
->bmap
->n_div
)
2707 if (info1
->bmap
->n_div
== 0)
2710 if (harmonize_stride_divs(info1
, info2
) < 0)
2711 return isl_stat_error
;
2713 bmap1
= isl_basic_map_copy(info1
->bmap
);
2714 bmap2
= isl_basic_map_copy(info2
->bmap
);
2715 eq1
= isl_basic_map_wrap(isl_basic_map_plain_affine_hull(bmap1
));
2716 eq2
= isl_basic_map_wrap(isl_basic_map_plain_affine_hull(bmap2
));
2717 equal
= isl_basic_set_plain_is_equal(eq1
, eq2
);
2723 r
= harmonize_divs_with_hulls(info1
, info2
, eq1
, eq2
);
2724 isl_basic_set_free(eq1
);
2725 isl_basic_set_free(eq2
);
2730 /* Do the two basic maps live in the same local space, i.e.,
2731 * do they have the same (known) divs?
2732 * If either basic map has any unknown divs, then we can only assume
2733 * that they do not live in the same local space.
2735 static isl_bool
same_divs(__isl_keep isl_basic_map
*bmap1
,
2736 __isl_keep isl_basic_map
*bmap2
)
2742 if (!bmap1
|| !bmap2
)
2743 return isl_bool_error
;
2744 if (bmap1
->n_div
!= bmap2
->n_div
)
2745 return isl_bool_false
;
2747 if (bmap1
->n_div
== 0)
2748 return isl_bool_true
;
2750 known
= isl_basic_map_divs_known(bmap1
);
2751 if (known
< 0 || !known
)
2753 known
= isl_basic_map_divs_known(bmap2
);
2754 if (known
< 0 || !known
)
2757 total
= isl_basic_map_dim(bmap1
, isl_dim_all
);
2759 return isl_bool_error
;
2760 for (i
= 0; i
< bmap1
->n_div
; ++i
)
2761 if (!isl_seq_eq(bmap1
->div
[i
], bmap2
->div
[i
], 2 + total
))
2762 return isl_bool_false
;
2764 return isl_bool_true
;
2767 /* Assuming that "tab" contains the equality constraints and
2768 * the initial inequality constraints of "bmap", copy the remaining
2769 * inequality constraints of "bmap" to "Tab".
2771 static isl_stat
copy_ineq(struct isl_tab
*tab
, __isl_keep isl_basic_map
*bmap
)
2776 return isl_stat_error
;
2778 n_ineq
= tab
->n_con
- tab
->n_eq
;
2779 for (i
= n_ineq
; i
< bmap
->n_ineq
; ++i
)
2780 if (isl_tab_add_ineq(tab
, bmap
->ineq
[i
]) < 0)
2781 return isl_stat_error
;
2786 /* Description of an integer division that is added
2787 * during an expansion.
2788 * "pos" is the position of the corresponding variable.
2789 * "cst" indicates whether this integer division has a fixed value.
2790 * "val" contains the fixed value, if the value is fixed.
2792 struct isl_expanded
{
2798 /* For each of the "n" integer division variables "expanded",
2799 * if the variable has a fixed value, then add two inequality
2800 * constraints expressing the fixed value.
2801 * Otherwise, add the corresponding div constraints.
2802 * The caller is responsible for removing the div constraints
2803 * that it added for all these "n" integer divisions.
2805 * The div constraints and the pair of inequality constraints
2806 * forcing the fixed value cannot both be added for a given variable
2807 * as the combination may render some of the original constraints redundant.
2808 * These would then be ignored during the coalescing detection,
2809 * while they could remain in the fused result.
2811 * The two added inequality constraints are
2816 * with "a" the variable and "v" its fixed value.
2817 * The facet corresponding to one of these two constraints is selected
2818 * in the tableau to ensure that the pair of inequality constraints
2819 * is treated as an equality constraint.
2821 * The information in info->ineq is thrown away because it was
2822 * computed in terms of div constraints, while some of those
2823 * have now been replaced by these pairs of inequality constraints.
2825 static isl_stat
fix_constant_divs(struct isl_coalesce_info
*info
,
2826 int n
, struct isl_expanded
*expanded
)
2832 o_div
= isl_basic_map_offset(info
->bmap
, isl_dim_div
) - 1;
2833 ineq
= isl_vec_alloc(isl_tab_get_ctx(info
->tab
), 1 + info
->tab
->n_var
);
2835 return isl_stat_error
;
2836 isl_seq_clr(ineq
->el
+ 1, info
->tab
->n_var
);
2838 for (i
= 0; i
< n
; ++i
) {
2839 if (!expanded
[i
].cst
) {
2840 info
->bmap
= isl_basic_map_extend_constraints(
2842 info
->bmap
= isl_basic_map_add_div_constraints(
2843 info
->bmap
, expanded
[i
].pos
- o_div
);
2845 isl_int_set_si(ineq
->el
[1 + expanded
[i
].pos
], -1);
2846 isl_int_set(ineq
->el
[0], expanded
[i
].val
);
2847 info
->bmap
= isl_basic_map_add_ineq(info
->bmap
,
2849 isl_int_set_si(ineq
->el
[1 + expanded
[i
].pos
], 1);
2850 isl_int_neg(ineq
->el
[0], expanded
[i
].val
);
2851 info
->bmap
= isl_basic_map_add_ineq(info
->bmap
,
2853 isl_int_set_si(ineq
->el
[1 + expanded
[i
].pos
], 0);
2855 if (copy_ineq(info
->tab
, info
->bmap
) < 0)
2857 if (expanded
[i
].cst
&&
2858 isl_tab_select_facet(info
->tab
, info
->tab
->n_con
- 1) < 0)
2867 return i
< n
? isl_stat_error
: isl_stat_ok
;
2870 /* Insert the "n" integer division variables "expanded"
2871 * into info->tab and info->bmap and
2872 * update info->ineq with respect to the redundant constraints
2873 * in the resulting tableau.
2874 * "bmap" contains the result of this insertion in info->bmap,
2875 * while info->bmap is the original version
2876 * of "bmap", i.e., the one that corresponds to the current
2877 * state of info->tab. The number of constraints in info->bmap
2878 * is assumed to be the same as the number of constraints
2879 * in info->tab. This is required to be able to detect
2880 * the extra constraints in "bmap".
2882 * In particular, introduce extra variables corresponding
2883 * to the extra integer divisions and add the div constraints
2884 * that were added to "bmap" after info->tab was created
2886 * Furthermore, check if these extra integer divisions happen
2887 * to attain a fixed integer value in info->tab.
2888 * If so, replace the corresponding div constraints by pairs
2889 * of inequality constraints that fix these
2890 * integer divisions to their single integer values.
2891 * Replace info->bmap by "bmap" to match the changes to info->tab.
2892 * info->ineq was computed without a tableau and therefore
2893 * does not take into account the redundant constraints
2894 * in the tableau. Mark them here.
2895 * There is no need to check the newly added div constraints
2896 * since they cannot be redundant.
2897 * The redundancy check is not performed when constants have been discovered
2898 * since info->ineq is completely thrown away in this case.
2900 static isl_stat
tab_insert_divs(struct isl_coalesce_info
*info
,
2901 int n
, struct isl_expanded
*expanded
, __isl_take isl_basic_map
*bmap
)
2905 struct isl_tab_undo
*snap
;
2909 return isl_stat_error
;
2910 if (info
->bmap
->n_eq
+ info
->bmap
->n_ineq
!= info
->tab
->n_con
)
2911 isl_die(isl_basic_map_get_ctx(bmap
), isl_error_internal
,
2912 "original tableau does not correspond "
2913 "to original basic map", goto error
);
2915 if (isl_tab_extend_vars(info
->tab
, n
) < 0)
2917 if (isl_tab_extend_cons(info
->tab
, 2 * n
) < 0)
2920 for (i
= 0; i
< n
; ++i
) {
2921 if (isl_tab_insert_var(info
->tab
, expanded
[i
].pos
) < 0)
2925 snap
= isl_tab_snap(info
->tab
);
2927 n_ineq
= info
->tab
->n_con
- info
->tab
->n_eq
;
2928 if (copy_ineq(info
->tab
, bmap
) < 0)
2931 isl_basic_map_free(info
->bmap
);
2935 for (i
= 0; i
< n
; ++i
) {
2936 expanded
[i
].cst
= isl_tab_is_constant(info
->tab
,
2937 expanded
[i
].pos
, &expanded
[i
].val
);
2938 if (expanded
[i
].cst
< 0)
2939 return isl_stat_error
;
2940 if (expanded
[i
].cst
)
2945 if (isl_tab_rollback(info
->tab
, snap
) < 0)
2946 return isl_stat_error
;
2947 info
->bmap
= isl_basic_map_cow(info
->bmap
);
2948 info
->bmap
= isl_basic_map_free_inequality(info
->bmap
, 2 * n
);
2950 return isl_stat_error
;
2952 return fix_constant_divs(info
, n
, expanded
);
2955 n_eq
= info
->bmap
->n_eq
;
2956 for (i
= 0; i
< n_ineq
; ++i
) {
2957 if (isl_tab_is_redundant(info
->tab
, n_eq
+ i
))
2958 info
->ineq
[i
] = STATUS_REDUNDANT
;
2963 isl_basic_map_free(bmap
);
2964 return isl_stat_error
;
2967 /* Expand info->tab and info->bmap in the same way "bmap" was expanded
2968 * in isl_basic_map_expand_divs using the expansion "exp" and
2969 * update info->ineq with respect to the redundant constraints
2970 * in the resulting tableau. info->bmap is the original version
2971 * of "bmap", i.e., the one that corresponds to the current
2972 * state of info->tab. The number of constraints in info->bmap
2973 * is assumed to be the same as the number of constraints
2974 * in info->tab. This is required to be able to detect
2975 * the extra constraints in "bmap".
2977 * Extract the positions where extra local variables are introduced
2978 * from "exp" and call tab_insert_divs.
2980 static isl_stat
expand_tab(struct isl_coalesce_info
*info
, int *exp
,
2981 __isl_take isl_basic_map
*bmap
)
2984 struct isl_expanded
*expanded
;
2987 isl_size total
, n_div
;
2991 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
2992 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
2993 if (total
< 0 || n_div
< 0)
2994 return isl_stat_error
;
2995 pos
= total
- n_div
;
2996 extra_var
= total
- info
->tab
->n_var
;
2997 n
= n_div
- extra_var
;
2999 ctx
= isl_basic_map_get_ctx(bmap
);
3000 expanded
= isl_calloc_array(ctx
, struct isl_expanded
, extra_var
);
3001 if (extra_var
&& !expanded
)
3006 for (j
= 0; j
< n_div
; ++j
) {
3007 if (i
< n
&& exp
[i
] == j
) {
3011 expanded
[k
++].pos
= pos
+ j
;
3014 for (k
= 0; k
< extra_var
; ++k
)
3015 isl_int_init(expanded
[k
].val
);
3017 r
= tab_insert_divs(info
, extra_var
, expanded
, bmap
);
3019 for (k
= 0; k
< extra_var
; ++k
)
3020 isl_int_clear(expanded
[k
].val
);
3025 isl_basic_map_free(bmap
);
3026 return isl_stat_error
;
3029 /* Check if the union of the basic maps represented by info[i] and info[j]
3030 * can be represented by a single basic map,
3031 * after expanding the divs of info[i] to match those of info[j].
3032 * If so, replace the pair by the single basic map and return
3033 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
3034 * Otherwise, return isl_change_none.
3036 * The caller has already checked for info[j] being a subset of info[i].
3037 * If some of the divs of info[j] are unknown, then the expanded info[i]
3038 * will not have the corresponding div constraints. The other patterns
3039 * therefore cannot apply. Skip the computation in this case.
3041 * The expansion is performed using the divs "div" and expansion "exp"
3042 * computed by the caller.
3043 * info[i].bmap has already been expanded and the result is passed in
3045 * The "eq" and "ineq" fields of info[i] reflect the status of
3046 * the constraints of the expanded "bmap" with respect to info[j].tab.
3047 * However, inequality constraints that are redundant in info[i].tab
3048 * have not yet been marked as such because no tableau was available.
3050 * Replace info[i].bmap by "bmap" and expand info[i].tab as well,
3051 * updating info[i].ineq with respect to the redundant constraints.
3052 * Then try and coalesce the expanded info[i] with info[j],
3053 * reusing the information in info[i].eq and info[i].ineq.
3054 * If this does not result in any coalescing or if it results in info[j]
3055 * getting dropped (which should not happen in practice, since the case
3056 * of info[j] being a subset of info[i] has already been checked by
3057 * the caller), then revert info[i] to its original state.
3059 static enum isl_change
coalesce_expand_tab_divs(__isl_take isl_basic_map
*bmap
,
3060 int i
, int j
, struct isl_coalesce_info
*info
, __isl_keep isl_mat
*div
,
3064 isl_basic_map
*bmap_i
;
3065 struct isl_tab_undo
*snap
;
3066 enum isl_change change
= isl_change_none
;
3068 known
= isl_basic_map_divs_known(info
[j
].bmap
);
3069 if (known
< 0 || !known
) {
3070 clear_status(&info
[i
]);
3071 isl_basic_map_free(bmap
);
3072 return known
< 0 ? isl_change_error
: isl_change_none
;
3075 bmap_i
= isl_basic_map_copy(info
[i
].bmap
);
3076 snap
= isl_tab_snap(info
[i
].tab
);
3077 if (expand_tab(&info
[i
], exp
, bmap
) < 0)
3078 change
= isl_change_error
;
3080 init_status(&info
[j
]);
3081 if (change
== isl_change_none
)
3082 change
= coalesce_local_pair_reuse(i
, j
, info
);
3084 clear_status(&info
[i
]);
3085 if (change
!= isl_change_none
&& change
!= isl_change_drop_second
) {
3086 isl_basic_map_free(bmap_i
);
3088 isl_basic_map_free(info
[i
].bmap
);
3089 info
[i
].bmap
= bmap_i
;
3091 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
3092 change
= isl_change_error
;
3098 /* Check if the union of "bmap" and the basic map represented by info[j]
3099 * can be represented by a single basic map,
3100 * after expanding the divs of "bmap" to match those of info[j].
3101 * If so, replace the pair by the single basic map and return
3102 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
3103 * Otherwise, return isl_change_none.
3105 * In particular, check if the expanded "bmap" contains the basic map
3106 * represented by the tableau info[j].tab.
3107 * The expansion is performed using the divs "div" and expansion "exp"
3108 * computed by the caller.
3109 * Then we check if all constraints of the expanded "bmap" are valid for
3112 * If "i" is not equal to -1, then "bmap" is equal to info[i].bmap.
3113 * In this case, the positions of the constraints of info[i].bmap
3114 * with respect to the basic map represented by info[j] are stored
3117 * If the expanded "bmap" does not contain the basic map
3118 * represented by the tableau info[j].tab and if "i" is not -1,
3119 * i.e., if the original "bmap" is info[i].bmap, then expand info[i].tab
3120 * as well and check if that results in coalescing.
3122 static enum isl_change
coalesce_with_expanded_divs(
3123 __isl_keep isl_basic_map
*bmap
, int i
, int j
,
3124 struct isl_coalesce_info
*info
, __isl_keep isl_mat
*div
, int *exp
)
3126 enum isl_change change
= isl_change_none
;
3127 struct isl_coalesce_info info_local
, *info_i
;
3129 info_i
= i
>= 0 ? &info
[i
] : &info_local
;
3130 init_status(info_i
);
3131 bmap
= isl_basic_map_copy(bmap
);
3132 bmap
= isl_basic_map_expand_divs(bmap
, isl_mat_copy(div
), exp
);
3133 bmap
= isl_basic_map_mark_final(bmap
);
3138 info_local
.bmap
= bmap
;
3139 info_i
->eq
= eq_status_in(bmap
, info
[j
].tab
);
3140 if (bmap
->n_eq
&& !info_i
->eq
)
3142 if (any_eq(info_i
, STATUS_ERROR
))
3144 if (any_eq(info_i
, STATUS_SEPARATE
))
3147 info_i
->ineq
= ineq_status_in(bmap
, NULL
, info
[j
].tab
);
3148 if (bmap
->n_ineq
&& !info_i
->ineq
)
3150 if (any_ineq(info_i
, STATUS_ERROR
))
3152 if (any_ineq(info_i
, STATUS_SEPARATE
))
3155 if (all(info_i
->eq
, 2 * bmap
->n_eq
, STATUS_VALID
) &&
3156 all(info_i
->ineq
, bmap
->n_ineq
, STATUS_VALID
)) {
3158 change
= isl_change_drop_second
;
3161 if (change
== isl_change_none
&& i
!= -1)
3162 return coalesce_expand_tab_divs(bmap
, i
, j
, info
, div
, exp
);
3165 isl_basic_map_free(bmap
);
3166 clear_status(info_i
);
3169 isl_basic_map_free(bmap
);
3170 clear_status(info_i
);
3171 return isl_change_error
;
3174 /* Check if the union of "bmap_i" and the basic map represented by info[j]
3175 * can be represented by a single basic map,
3176 * after aligning the divs of "bmap_i" to match those of info[j].
3177 * If so, replace the pair by the single basic map and return
3178 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
3179 * Otherwise, return isl_change_none.
3181 * In particular, check if "bmap_i" contains the basic map represented by
3182 * info[j] after aligning the divs of "bmap_i" to those of info[j].
3183 * Note that this can only succeed if the number of divs of "bmap_i"
3184 * is smaller than (or equal to) the number of divs of info[j].
3186 * We first check if the divs of "bmap_i" are all known and form a subset
3187 * of those of info[j].bmap. If so, we pass control over to
3188 * coalesce_with_expanded_divs.
3190 * If "i" is not equal to -1, then "bmap" is equal to info[i].bmap.
3192 static enum isl_change
coalesce_after_aligning_divs(
3193 __isl_keep isl_basic_map
*bmap_i
, int i
, int j
,
3194 struct isl_coalesce_info
*info
)
3197 isl_mat
*div_i
, *div_j
, *div
;
3201 enum isl_change change
;
3203 known
= isl_basic_map_divs_known(bmap_i
);
3205 return isl_change_error
;
3207 return isl_change_none
;
3209 ctx
= isl_basic_map_get_ctx(bmap_i
);
3211 div_i
= isl_basic_map_get_divs(bmap_i
);
3212 div_j
= isl_basic_map_get_divs(info
[j
].bmap
);
3214 if (!div_i
|| !div_j
)
3217 exp1
= isl_alloc_array(ctx
, int, div_i
->n_row
);
3218 exp2
= isl_alloc_array(ctx
, int, div_j
->n_row
);
3219 if ((div_i
->n_row
&& !exp1
) || (div_j
->n_row
&& !exp2
))
3222 div
= isl_merge_divs(div_i
, div_j
, exp1
, exp2
);
3226 if (div
->n_row
== div_j
->n_row
)
3227 change
= coalesce_with_expanded_divs(bmap_i
,
3228 i
, j
, info
, div
, exp1
);
3230 change
= isl_change_none
;
3234 isl_mat_free(div_i
);
3235 isl_mat_free(div_j
);
3242 isl_mat_free(div_i
);
3243 isl_mat_free(div_j
);
3246 return isl_change_error
;
3249 /* Check if basic map "j" is a subset of basic map "i" after
3250 * exploiting the extra equalities of "j" to simplify the divs of "i".
3251 * If so, remove basic map "j" and return isl_change_drop_second.
3253 * If "j" does not have any equalities or if they are the same
3254 * as those of "i", then we cannot exploit them to simplify the divs.
3255 * Similarly, if there are no divs in "i", then they cannot be simplified.
3256 * If, on the other hand, the affine hulls of "i" and "j" do not intersect,
3257 * then "j" cannot be a subset of "i".
3259 * Otherwise, we intersect "i" with the affine hull of "j" and then
3260 * check if "j" is a subset of the result after aligning the divs.
3261 * If so, then "j" is definitely a subset of "i" and can be removed.
3262 * Note that if after intersection with the affine hull of "j".
3263 * "i" still has more divs than "j", then there is no way we can
3264 * align the divs of "i" to those of "j".
3266 static enum isl_change
coalesce_subset_with_equalities(int i
, int j
,
3267 struct isl_coalesce_info
*info
)
3269 isl_basic_map
*hull_i
, *hull_j
, *bmap_i
;
3271 enum isl_change change
;
3273 if (info
[j
].bmap
->n_eq
== 0)
3274 return isl_change_none
;
3275 if (info
[i
].bmap
->n_div
== 0)
3276 return isl_change_none
;
3278 hull_i
= isl_basic_map_copy(info
[i
].bmap
);
3279 hull_i
= isl_basic_map_plain_affine_hull(hull_i
);
3280 hull_j
= isl_basic_map_copy(info
[j
].bmap
);
3281 hull_j
= isl_basic_map_plain_affine_hull(hull_j
);
3283 hull_j
= isl_basic_map_intersect(hull_j
, isl_basic_map_copy(hull_i
));
3284 equal
= isl_basic_map_plain_is_equal(hull_i
, hull_j
);
3285 empty
= isl_basic_map_plain_is_empty(hull_j
);
3286 isl_basic_map_free(hull_i
);
3288 if (equal
< 0 || equal
|| empty
< 0 || empty
) {
3289 isl_basic_map_free(hull_j
);
3290 if (equal
< 0 || empty
< 0)
3291 return isl_change_error
;
3292 return isl_change_none
;
3295 bmap_i
= isl_basic_map_copy(info
[i
].bmap
);
3296 bmap_i
= isl_basic_map_intersect(bmap_i
, hull_j
);
3298 return isl_change_error
;
3300 if (bmap_i
->n_div
> info
[j
].bmap
->n_div
) {
3301 isl_basic_map_free(bmap_i
);
3302 return isl_change_none
;
3305 change
= coalesce_after_aligning_divs(bmap_i
, -1, j
, info
);
3307 isl_basic_map_free(bmap_i
);
3312 /* Check if the union of and the basic maps represented by info[i] and info[j]
3313 * can be represented by a single basic map, by aligning or equating
3314 * their integer divisions.
3315 * If so, replace the pair by the single basic map and return
3316 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
3317 * Otherwise, return isl_change_none.
3319 * Note that we only perform any test if the number of divs is different
3320 * in the two basic maps. In case the number of divs is the same,
3321 * we have already established that the divs are different
3322 * in the two basic maps.
3323 * In particular, if the number of divs of basic map i is smaller than
3324 * the number of divs of basic map j, then we check if j is a subset of i
3327 static enum isl_change
coalesce_divs(int i
, int j
,
3328 struct isl_coalesce_info
*info
)
3330 enum isl_change change
= isl_change_none
;
3332 if (info
[i
].bmap
->n_div
< info
[j
].bmap
->n_div
)
3333 change
= coalesce_after_aligning_divs(info
[i
].bmap
, i
, j
, info
);
3334 if (change
!= isl_change_none
)
3337 if (info
[j
].bmap
->n_div
< info
[i
].bmap
->n_div
)
3338 change
= coalesce_after_aligning_divs(info
[j
].bmap
, j
, i
, info
);
3339 if (change
!= isl_change_none
)
3340 return invert_change(change
);
3342 change
= coalesce_subset_with_equalities(i
, j
, info
);
3343 if (change
!= isl_change_none
)
3346 change
= coalesce_subset_with_equalities(j
, i
, info
);
3347 if (change
!= isl_change_none
)
3348 return invert_change(change
);
3350 return isl_change_none
;
3353 /* Does "bmap" involve any divs that themselves refer to divs?
3355 static isl_bool
has_nested_div(__isl_keep isl_basic_map
*bmap
)
3361 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
3362 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
3363 if (total
< 0 || n_div
< 0)
3364 return isl_bool_error
;
3367 for (i
= 0; i
< n_div
; ++i
)
3368 if (isl_seq_first_non_zero(bmap
->div
[i
] + 2 + total
,
3370 return isl_bool_true
;
3372 return isl_bool_false
;
3375 /* Return a list of affine expressions, one for each integer division
3376 * in "bmap_i". For each integer division that also appears in "bmap_j",
3377 * the affine expression is set to NaN. The number of NaNs in the list
3378 * is equal to the number of integer divisions in "bmap_j".
3379 * For the other integer divisions of "bmap_i", the corresponding
3380 * element in the list is a purely affine expression equal to the integer
3381 * division in "hull".
3382 * If no such list can be constructed, then the number of elements
3383 * in the returned list is smaller than the number of integer divisions
3386 static __isl_give isl_aff_list
*set_up_substitutions(
3387 __isl_keep isl_basic_map
*bmap_i
, __isl_keep isl_basic_map
*bmap_j
,
3388 __isl_take isl_basic_map
*hull
)
3390 isl_size n_div_i
, n_div_j
, total
;
3392 isl_local_space
*ls
;
3393 isl_basic_set
*wrap_hull
;
3398 n_div_i
= isl_basic_map_dim(bmap_i
, isl_dim_div
);
3399 n_div_j
= isl_basic_map_dim(bmap_j
, isl_dim_div
);
3400 total
= isl_basic_map_dim(bmap_i
, isl_dim_all
);
3401 if (!hull
|| n_div_i
< 0 || n_div_j
< 0 || total
< 0)
3404 ctx
= isl_basic_map_get_ctx(hull
);
3407 ls
= isl_basic_map_get_local_space(bmap_i
);
3408 ls
= isl_local_space_wrap(ls
);
3409 wrap_hull
= isl_basic_map_wrap(hull
);
3411 aff_nan
= isl_aff_nan_on_domain(isl_local_space_copy(ls
));
3412 list
= isl_aff_list_alloc(ctx
, n_div_i
);
3415 for (i
= 0; i
< n_div_i
; ++i
) {
3420 isl_basic_map_equal_div_expr_part(bmap_i
, i
, bmap_j
, j
,
3423 list
= isl_aff_list_add(list
, isl_aff_copy(aff_nan
));
3426 if (n_div_i
- i
<= n_div_j
- j
)
3429 aff
= isl_local_space_get_div(ls
, i
);
3430 aff
= isl_aff_substitute_equalities(aff
,
3431 isl_basic_set_copy(wrap_hull
));
3432 aff
= isl_aff_floor(aff
);
3433 n_div
= isl_aff_dim(aff
, isl_dim_div
);
3441 list
= isl_aff_list_add(list
, aff
);
3444 isl_aff_free(aff_nan
);
3445 isl_local_space_free(ls
);
3446 isl_basic_set_free(wrap_hull
);
3450 isl_aff_free(aff_nan
);
3451 isl_local_space_free(ls
);
3452 isl_basic_set_free(wrap_hull
);
3453 isl_aff_list_free(list
);
3457 /* Add variables to info->bmap and info->tab corresponding to the elements
3458 * in "list" that are not set to NaN.
3459 * "extra_var" is the number of these elements.
3460 * "dim" is the offset in the variables of "tab" where we should
3461 * start considering the elements in "list".
3462 * When this function returns, the total number of variables in "tab"
3463 * is equal to "dim" plus the number of elements in "list".
3465 * The newly added existentially quantified variables are not given
3466 * an explicit representation because the corresponding div constraints
3467 * do not appear in info->bmap. These constraints are not added
3468 * to info->bmap because for internal consistency, they would need to
3469 * be added to info->tab as well, where they could combine with the equality
3470 * that is added later to result in constraints that do not hold
3471 * in the original input.
3473 static isl_stat
add_sub_vars(struct isl_coalesce_info
*info
,
3474 __isl_keep isl_aff_list
*list
, int dim
, int extra_var
)
3480 space
= isl_basic_map_get_space(info
->bmap
);
3481 info
->bmap
= isl_basic_map_cow(info
->bmap
);
3482 info
->bmap
= isl_basic_map_extend_space(info
->bmap
, space
,
3484 n
= isl_aff_list_n_aff(list
);
3485 if (!info
->bmap
|| n
< 0)
3486 return isl_stat_error
;
3487 for (i
= 0; i
< n
; ++i
) {
3491 aff
= isl_aff_list_get_aff(list
, i
);
3492 is_nan
= isl_aff_is_nan(aff
);
3495 return isl_stat_error
;
3499 if (isl_tab_insert_var(info
->tab
, dim
+ i
) < 0)
3500 return isl_stat_error
;
3501 d
= isl_basic_map_alloc_div(info
->bmap
);
3503 return isl_stat_error
;
3504 info
->bmap
= isl_basic_map_mark_div_unknown(info
->bmap
, d
);
3505 for (j
= d
; j
> i
; --j
)
3506 info
->bmap
= isl_basic_map_swap_div(info
->bmap
,
3509 return isl_stat_error
;
3515 /* For each element in "list" that is not set to NaN, fix the corresponding
3516 * variable in "tab" to the purely affine expression defined by the element.
3517 * "dim" is the offset in the variables of "tab" where we should
3518 * start considering the elements in "list".
3520 * This function assumes that a sufficient number of rows and
3521 * elements in the constraint array are available in the tableau.
3523 static isl_stat
add_sub_equalities(struct isl_tab
*tab
,
3524 __isl_keep isl_aff_list
*list
, int dim
)
3532 n
= isl_aff_list_n_aff(list
);
3534 return isl_stat_error
;
3536 ctx
= isl_tab_get_ctx(tab
);
3537 sub
= isl_vec_alloc(ctx
, 1 + dim
+ n
);
3539 return isl_stat_error
;
3540 isl_seq_clr(sub
->el
+ 1 + dim
, n
);
3542 for (i
= 0; i
< n
; ++i
) {
3543 aff
= isl_aff_list_get_aff(list
, i
);
3546 if (isl_aff_is_nan(aff
)) {
3550 isl_seq_cpy(sub
->el
, aff
->v
->el
+ 1, 1 + dim
);
3551 isl_int_neg(sub
->el
[1 + dim
+ i
], aff
->v
->el
[0]);
3552 if (isl_tab_add_eq(tab
, sub
->el
) < 0)
3554 isl_int_set_si(sub
->el
[1 + dim
+ i
], 0);
3563 return isl_stat_error
;
3566 /* Add variables to info->tab and info->bmap corresponding to the elements
3567 * in "list" that are not set to NaN. The value of the added variable
3568 * in info->tab is fixed to the purely affine expression defined by the element.
3569 * "dim" is the offset in the variables of info->tab where we should
3570 * start considering the elements in "list".
3571 * When this function returns, the total number of variables in info->tab
3572 * is equal to "dim" plus the number of elements in "list".
3574 static isl_stat
add_subs(struct isl_coalesce_info
*info
,
3575 __isl_keep isl_aff_list
*list
, int dim
)
3580 n
= isl_aff_list_n_aff(list
);
3582 return isl_stat_error
;
3584 extra_var
= n
- (info
->tab
->n_var
- dim
);
3586 if (isl_tab_extend_vars(info
->tab
, extra_var
) < 0)
3587 return isl_stat_error
;
3588 if (isl_tab_extend_cons(info
->tab
, 2 * extra_var
) < 0)
3589 return isl_stat_error
;
3590 if (add_sub_vars(info
, list
, dim
, extra_var
) < 0)
3591 return isl_stat_error
;
3593 return add_sub_equalities(info
->tab
, list
, dim
);
3596 /* Coalesce basic map "j" into basic map "i" after adding the extra integer
3597 * divisions in "i" but not in "j" to basic map "j", with values
3598 * specified by "list". The total number of elements in "list"
3599 * is equal to the number of integer divisions in "i", while the number
3600 * of NaN elements in the list is equal to the number of integer divisions
3603 * If no coalescing can be performed, then we need to revert basic map "j"
3604 * to its original state. We do the same if basic map "i" gets dropped
3605 * during the coalescing, even though this should not happen in practice
3606 * since we have already checked for "j" being a subset of "i"
3607 * before we reach this stage.
3609 static enum isl_change
coalesce_with_subs(int i
, int j
,
3610 struct isl_coalesce_info
*info
, __isl_keep isl_aff_list
*list
)
3612 isl_basic_map
*bmap_j
;
3613 struct isl_tab_undo
*snap
;
3614 isl_size dim
, n_div
;
3615 enum isl_change change
;
3617 bmap_j
= isl_basic_map_copy(info
[j
].bmap
);
3618 snap
= isl_tab_snap(info
[j
].tab
);
3620 dim
= isl_basic_map_dim(bmap_j
, isl_dim_all
);
3621 n_div
= isl_basic_map_dim(bmap_j
, isl_dim_div
);
3622 if (dim
< 0 || n_div
< 0)
3625 if (add_subs(&info
[j
], list
, dim
) < 0)
3628 change
= coalesce_local_pair(i
, j
, info
);
3629 if (change
!= isl_change_none
&& change
!= isl_change_drop_first
) {
3630 isl_basic_map_free(bmap_j
);
3632 isl_basic_map_free(info
[j
].bmap
);
3633 info
[j
].bmap
= bmap_j
;
3635 if (isl_tab_rollback(info
[j
].tab
, snap
) < 0)
3636 return isl_change_error
;
3641 isl_basic_map_free(bmap_j
);
3642 return isl_change_error
;
3645 /* Check if we can coalesce basic map "j" into basic map "i" after copying
3646 * those extra integer divisions in "i" that can be simplified away
3647 * using the extra equalities in "j".
3648 * All divs are assumed to be known and not contain any nested divs.
3650 * We first check if there are any extra equalities in "j" that we
3651 * can exploit. Then we check if every integer division in "i"
3652 * either already appears in "j" or can be simplified using the
3653 * extra equalities to a purely affine expression.
3654 * If these tests succeed, then we try to coalesce the two basic maps
3655 * by introducing extra dimensions in "j" corresponding to
3656 * the extra integer divisions "i" fixed to the corresponding
3657 * purely affine expression.
3659 static enum isl_change
check_coalesce_into_eq(int i
, int j
,
3660 struct isl_coalesce_info
*info
)
3662 isl_size n_div_i
, n_div_j
, n
;
3663 isl_basic_map
*hull_i
, *hull_j
;
3664 isl_bool equal
, empty
;
3666 enum isl_change change
;
3668 n_div_i
= isl_basic_map_dim(info
[i
].bmap
, isl_dim_div
);
3669 n_div_j
= isl_basic_map_dim(info
[j
].bmap
, isl_dim_div
);
3670 if (n_div_i
< 0 || n_div_j
< 0)
3671 return isl_change_error
;
3672 if (n_div_i
<= n_div_j
)
3673 return isl_change_none
;
3674 if (info
[j
].bmap
->n_eq
== 0)
3675 return isl_change_none
;
3677 hull_i
= isl_basic_map_copy(info
[i
].bmap
);
3678 hull_i
= isl_basic_map_plain_affine_hull(hull_i
);
3679 hull_j
= isl_basic_map_copy(info
[j
].bmap
);
3680 hull_j
= isl_basic_map_plain_affine_hull(hull_j
);
3682 hull_j
= isl_basic_map_intersect(hull_j
, isl_basic_map_copy(hull_i
));
3683 equal
= isl_basic_map_plain_is_equal(hull_i
, hull_j
);
3684 empty
= isl_basic_map_plain_is_empty(hull_j
);
3685 isl_basic_map_free(hull_i
);
3687 if (equal
< 0 || empty
< 0)
3689 if (equal
|| empty
) {
3690 isl_basic_map_free(hull_j
);
3691 return isl_change_none
;
3694 list
= set_up_substitutions(info
[i
].bmap
, info
[j
].bmap
, hull_j
);
3696 return isl_change_error
;
3697 n
= isl_aff_list_n_aff(list
);
3699 change
= isl_change_error
;
3700 else if (n
< n_div_i
)
3701 change
= isl_change_none
;
3703 change
= coalesce_with_subs(i
, j
, info
, list
);
3705 isl_aff_list_free(list
);
3709 isl_basic_map_free(hull_j
);
3710 return isl_change_error
;
3713 /* Check if we can coalesce basic maps "i" and "j" after copying
3714 * those extra integer divisions in one of the basic maps that can
3715 * be simplified away using the extra equalities in the other basic map.
3716 * We require all divs to be known in both basic maps.
3717 * Furthermore, to simplify the comparison of div expressions,
3718 * we do not allow any nested integer divisions.
3720 static enum isl_change
check_coalesce_eq(int i
, int j
,
3721 struct isl_coalesce_info
*info
)
3723 isl_bool known
, nested
;
3724 enum isl_change change
;
3726 known
= isl_basic_map_divs_known(info
[i
].bmap
);
3727 if (known
< 0 || !known
)
3728 return known
< 0 ? isl_change_error
: isl_change_none
;
3729 known
= isl_basic_map_divs_known(info
[j
].bmap
);
3730 if (known
< 0 || !known
)
3731 return known
< 0 ? isl_change_error
: isl_change_none
;
3732 nested
= has_nested_div(info
[i
].bmap
);
3733 if (nested
< 0 || nested
)
3734 return nested
< 0 ? isl_change_error
: isl_change_none
;
3735 nested
= has_nested_div(info
[j
].bmap
);
3736 if (nested
< 0 || nested
)
3737 return nested
< 0 ? isl_change_error
: isl_change_none
;
3739 change
= check_coalesce_into_eq(i
, j
, info
);
3740 if (change
!= isl_change_none
)
3742 change
= check_coalesce_into_eq(j
, i
, info
);
3743 if (change
!= isl_change_none
)
3744 return invert_change(change
);
3746 return isl_change_none
;
3749 /* Check if the union of the given pair of basic maps
3750 * can be represented by a single basic map.
3751 * If so, replace the pair by the single basic map and return
3752 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
3753 * Otherwise, return isl_change_none.
3755 * We first check if the two basic maps live in the same local space,
3756 * after aligning the divs that differ by only an integer constant.
3757 * If so, we do the complete check. Otherwise, we check if they have
3758 * the same number of integer divisions and can be coalesced, if one is
3759 * an obvious subset of the other or if the extra integer divisions
3760 * of one basic map can be simplified away using the extra equalities
3761 * of the other basic map.
3763 * Note that trying to coalesce pairs of disjuncts with the same
3764 * number, but different local variables may drop the explicit
3765 * representation of some of these local variables.
3766 * This operation is therefore not performed when
3767 * the "coalesce_preserve_locals" option is set.
3769 static enum isl_change
coalesce_pair(int i
, int j
,
3770 struct isl_coalesce_info
*info
)
3774 enum isl_change change
;
3777 if (harmonize_divs(&info
[i
], &info
[j
]) < 0)
3778 return isl_change_error
;
3779 same
= same_divs(info
[i
].bmap
, info
[j
].bmap
);
3781 return isl_change_error
;
3783 return coalesce_local_pair(i
, j
, info
);
3785 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
3786 preserve
= isl_options_get_coalesce_preserve_locals(ctx
);
3787 if (!preserve
&& info
[i
].bmap
->n_div
== info
[j
].bmap
->n_div
) {
3788 change
= coalesce_local_pair(i
, j
, info
);
3789 if (change
!= isl_change_none
)
3793 change
= coalesce_divs(i
, j
, info
);
3794 if (change
!= isl_change_none
)
3797 return check_coalesce_eq(i
, j
, info
);
3800 /* Return the maximum of "a" and "b".
3802 static int isl_max(int a
, int b
)
3804 return a
> b
? a
: b
;
3807 /* Pairwise coalesce the basic maps in the range [start1, end1[ of "info"
3808 * with those in the range [start2, end2[, skipping basic maps
3809 * that have been removed (either before or within this function).
3811 * For each basic map i in the first range, we check if it can be coalesced
3812 * with respect to any previously considered basic map j in the second range.
3813 * If i gets dropped (because it was a subset of some j), then
3814 * we can move on to the next basic map.
3815 * If j gets dropped, we need to continue checking against the other
3816 * previously considered basic maps.
3817 * If the two basic maps got fused, then we recheck the fused basic map
3818 * against the previously considered basic maps, starting at i + 1
3819 * (even if start2 is greater than i + 1).
3821 static int coalesce_range(isl_ctx
*ctx
, struct isl_coalesce_info
*info
,
3822 int start1
, int end1
, int start2
, int end2
)
3826 for (i
= end1
- 1; i
>= start1
; --i
) {
3827 if (info
[i
].removed
)
3829 for (j
= isl_max(i
+ 1, start2
); j
< end2
; ++j
) {
3830 enum isl_change changed
;
3832 if (info
[j
].removed
)
3834 if (info
[i
].removed
)
3835 isl_die(ctx
, isl_error_internal
,
3836 "basic map unexpectedly removed",
3838 changed
= coalesce_pair(i
, j
, info
);
3840 case isl_change_error
:
3842 case isl_change_none
:
3843 case isl_change_drop_second
:
3845 case isl_change_drop_first
:
3848 case isl_change_fuse
:
3858 /* Pairwise coalesce the basic maps described by the "n" elements of "info".
3860 * We consider groups of basic maps that live in the same apparent
3861 * affine hull and we first coalesce within such a group before we
3862 * coalesce the elements in the group with elements of previously
3863 * considered groups. If a fuse happens during the second phase,
3864 * then we also reconsider the elements within the group.
3866 static int coalesce(isl_ctx
*ctx
, int n
, struct isl_coalesce_info
*info
)
3870 for (end
= n
; end
> 0; end
= start
) {
3872 while (start
>= 1 &&
3873 info
[start
- 1].hull_hash
== info
[start
].hull_hash
)
3875 if (coalesce_range(ctx
, info
, start
, end
, start
, end
) < 0)
3877 if (coalesce_range(ctx
, info
, start
, end
, end
, n
) < 0)
3884 /* Update the basic maps in "map" based on the information in "info".
3885 * In particular, remove the basic maps that have been marked removed and
3886 * update the others based on the information in the corresponding tableau.
3887 * Since we detected implicit equalities without calling
3888 * isl_basic_map_gauss, we need to do it now.
3889 * Also call isl_basic_map_simplify if we may have lost the definition
3890 * of one or more integer divisions.
3891 * If a basic map is still equal to the one from which the corresponding "info"
3892 * entry was created, then redundant constraint and
3893 * implicit equality constraint detection have been performed
3894 * on the corresponding tableau and the basic map can be marked as such.
3896 static __isl_give isl_map
*update_basic_maps(__isl_take isl_map
*map
,
3897 int n
, struct isl_coalesce_info
*info
)
3904 for (i
= n
- 1; i
>= 0; --i
) {
3905 if (info
[i
].removed
) {
3906 isl_basic_map_free(map
->p
[i
]);
3907 if (i
!= map
->n
- 1)
3908 map
->p
[i
] = map
->p
[map
->n
- 1];
3913 info
[i
].bmap
= isl_basic_map_update_from_tab(info
[i
].bmap
,
3915 info
[i
].bmap
= isl_basic_map_gauss(info
[i
].bmap
, NULL
);
3916 if (info
[i
].simplify
)
3917 info
[i
].bmap
= isl_basic_map_simplify(info
[i
].bmap
);
3918 info
[i
].bmap
= isl_basic_map_finalize(info
[i
].bmap
);
3920 return isl_map_free(map
);
3921 if (!info
[i
].modified
) {
3922 ISL_F_SET(info
[i
].bmap
, ISL_BASIC_MAP_NO_IMPLICIT
);
3923 ISL_F_SET(info
[i
].bmap
, ISL_BASIC_MAP_NO_REDUNDANT
);
3925 isl_basic_map_free(map
->p
[i
]);
3926 map
->p
[i
] = info
[i
].bmap
;
3927 info
[i
].bmap
= NULL
;
3933 /* For each pair of basic maps in the map, check if the union of the two
3934 * can be represented by a single basic map.
3935 * If so, replace the pair by the single basic map and start over.
3937 * We factor out any (hidden) common factor from the constraint
3938 * coefficients to improve the detection of adjacent constraints.
3939 * Note that this function does not call isl_basic_map_gauss,
3940 * but it does make sure that only a single copy of the basic map
3941 * is affected. This means that isl_basic_map_gauss may have
3942 * to be called at the end of the computation (in update_basic_maps)
3943 * on this single copy to ensure that
3944 * the basic maps are not left in an unexpected state.
3946 * Since we are constructing the tableaus of the basic maps anyway,
3947 * we exploit them to detect implicit equalities and redundant constraints.
3948 * This also helps the coalescing as it can ignore the redundant constraints.
3949 * In order to avoid confusion, we make all implicit equalities explicit
3950 * in the basic maps. If the basic map only has a single reference
3951 * (this happens in particular if it was modified by
3952 * isl_basic_map_reduce_coefficients), then isl_basic_map_gauss
3953 * does not get called on the result. The call to
3954 * isl_basic_map_gauss in update_basic_maps resolves this as well.
3955 * For each basic map, we also compute the hash of the apparent affine hull
3956 * for use in coalesce.
3958 __isl_give isl_map
*isl_map_coalesce(__isl_take isl_map
*map
)
3963 struct isl_coalesce_info
*info
= NULL
;
3965 map
= isl_map_remove_empty_parts(map
);
3972 ctx
= isl_map_get_ctx(map
);
3973 map
= isl_map_sort_divs(map
);
3974 map
= isl_map_cow(map
);
3981 info
= isl_calloc_array(map
->ctx
, struct isl_coalesce_info
, n
);
3985 for (i
= 0; i
< map
->n
; ++i
) {
3986 map
->p
[i
] = isl_basic_map_reduce_coefficients(map
->p
[i
]);
3989 info
[i
].bmap
= isl_basic_map_copy(map
->p
[i
]);
3990 info
[i
].tab
= isl_tab_from_basic_map(info
[i
].bmap
, 0);
3993 if (!ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_NO_IMPLICIT
))
3994 if (isl_tab_detect_implicit_equalities(info
[i
].tab
) < 0)
3996 info
[i
].bmap
= isl_tab_make_equalities_explicit(info
[i
].tab
,
4000 if (!ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_NO_REDUNDANT
))
4001 if (isl_tab_detect_redundant(info
[i
].tab
) < 0)
4003 if (coalesce_info_set_hull_hash(&info
[i
]) < 0)
4006 for (i
= map
->n
- 1; i
>= 0; --i
)
4007 if (info
[i
].tab
->empty
)
4010 if (coalesce(ctx
, n
, info
) < 0)
4013 map
= update_basic_maps(map
, n
, info
);
4015 clear_coalesce_info(n
, info
);
4019 clear_coalesce_info(n
, info
);
4024 /* For each pair of basic sets in the set, check if the union of the two
4025 * can be represented by a single basic set.
4026 * If so, replace the pair by the single basic set and start over.
4028 struct isl_set
*isl_set_coalesce(struct isl_set
*set
)
4030 return set_from_map(isl_map_coalesce(set_to_map(set
)));