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 * "removed" is set if this basic map has been removed from the map
181 * "simplify" is set if this basic map may have some unknown integer
182 * divisions that were not present in the input basic maps. The basic
183 * map should then be simplified such that we may be able to find
184 * a definition among the constraints.
186 * "eq" and "ineq" are only set if we are currently trying to coalesce
187 * this basic map with another basic map, in which case they represent
188 * the position of the inequalities of this basic map with respect to
189 * the other basic map. The number of elements in the "eq" array
190 * is twice the number of equalities in the "bmap", corresponding
191 * to the two inequalities that make up each equality.
193 struct isl_coalesce_info
{
203 /* Is there any (half of an) equality constraint in the description
204 * of the basic map represented by "info" that
205 * has position "status" with respect to the other basic map?
207 static int any_eq(struct isl_coalesce_info
*info
, int status
)
211 n_eq
= isl_basic_map_n_equality(info
->bmap
);
212 return any(info
->eq
, 2 * n_eq
, status
);
215 /* Is there any inequality constraint in the description
216 * of the basic map represented by "info" that
217 * has position "status" with respect to the other basic map?
219 static int any_ineq(struct isl_coalesce_info
*info
, int status
)
223 n_ineq
= isl_basic_map_n_inequality(info
->bmap
);
224 return any(info
->ineq
, n_ineq
, status
);
227 /* Return the position of the first half on an equality constraint
228 * in the description of the basic map represented by "info" that
229 * has position "status" with respect to the other basic map.
230 * The returned value is twice the position of the equality constraint
231 * plus zero for the negative half and plus one for the positive half.
232 * Return -1 if there is no such entry.
234 static int find_eq(struct isl_coalesce_info
*info
, int status
)
238 n_eq
= isl_basic_map_n_equality(info
->bmap
);
239 return find(info
->eq
, 2 * n_eq
, status
);
242 /* Return the position of the first inequality constraint in the description
243 * of the basic map represented by "info" that
244 * has position "status" with respect to the other basic map.
245 * Return -1 if there is no such entry.
247 static int find_ineq(struct isl_coalesce_info
*info
, int status
)
251 n_ineq
= isl_basic_map_n_inequality(info
->bmap
);
252 return find(info
->ineq
, n_ineq
, status
);
255 /* Return the number of (halves of) equality constraints in the description
256 * of the basic map represented by "info" that
257 * have position "status" with respect to the other basic map.
259 static int count_eq(struct isl_coalesce_info
*info
, int status
)
263 n_eq
= isl_basic_map_n_equality(info
->bmap
);
264 return count(info
->eq
, 2 * n_eq
, status
);
267 /* Return the number of inequality constraints in the description
268 * of the basic map represented by "info" that
269 * have position "status" with respect to the other basic map.
271 static int count_ineq(struct isl_coalesce_info
*info
, int status
)
275 n_ineq
= isl_basic_map_n_inequality(info
->bmap
);
276 return count(info
->ineq
, n_ineq
, status
);
279 /* Are all non-redundant constraints of the basic map represented by "info"
280 * either valid or cut constraints with respect to the other basic map?
282 static int all_valid_or_cut(struct isl_coalesce_info
*info
)
286 for (i
= 0; i
< 2 * info
->bmap
->n_eq
; ++i
) {
287 if (info
->eq
[i
] == STATUS_REDUNDANT
)
289 if (info
->eq
[i
] == STATUS_VALID
)
291 if (info
->eq
[i
] == STATUS_CUT
)
296 for (i
= 0; i
< info
->bmap
->n_ineq
; ++i
) {
297 if (info
->ineq
[i
] == STATUS_REDUNDANT
)
299 if (info
->ineq
[i
] == STATUS_VALID
)
301 if (info
->ineq
[i
] == STATUS_CUT
)
309 /* Compute the hash of the (apparent) affine hull of info->bmap (with
310 * the existentially quantified variables removed) and store it
313 static int coalesce_info_set_hull_hash(struct isl_coalesce_info
*info
)
318 hull
= isl_basic_map_copy(info
->bmap
);
319 hull
= isl_basic_map_plain_affine_hull(hull
);
320 n_div
= isl_basic_map_dim(hull
, isl_dim_div
);
322 hull
= isl_basic_map_free(hull
);
323 hull
= isl_basic_map_drop_constraints_involving_dims(hull
,
324 isl_dim_div
, 0, n_div
);
325 info
->hull_hash
= isl_basic_map_get_hash(hull
);
326 isl_basic_map_free(hull
);
328 return hull
? 0 : -1;
331 /* Free all the allocated memory in an array
332 * of "n" isl_coalesce_info elements.
334 static void clear_coalesce_info(int n
, struct isl_coalesce_info
*info
)
341 for (i
= 0; i
< n
; ++i
) {
342 isl_basic_map_free(info
[i
].bmap
);
343 isl_tab_free(info
[i
].tab
);
349 /* Drop the basic map represented by "info".
350 * That is, clear the memory associated to the entry and
351 * mark it as having been removed.
352 * Gaussian elimination needs to be performed on the basic map
353 * before it gets freed because it may have been put
354 * in an inconsistent state in isl_map_coalesce while it may
355 * be shared with other maps.
357 static void drop(struct isl_coalesce_info
*info
)
359 info
->bmap
= isl_basic_map_gauss(info
->bmap
, NULL
);
360 info
->bmap
= isl_basic_map_free(info
->bmap
);
361 isl_tab_free(info
->tab
);
366 /* Exchange the information in "info1" with that in "info2".
368 static void exchange(struct isl_coalesce_info
*info1
,
369 struct isl_coalesce_info
*info2
)
371 struct isl_coalesce_info info
;
378 /* This type represents the kind of change that has been performed
379 * while trying to coalesce two basic maps.
381 * isl_change_none: nothing was changed
382 * isl_change_drop_first: the first basic map was removed
383 * isl_change_drop_second: the second basic map was removed
384 * isl_change_fuse: the two basic maps were replaced by a new basic map.
387 isl_change_error
= -1,
389 isl_change_drop_first
,
390 isl_change_drop_second
,
394 /* Update "change" based on an interchange of the first and the second
395 * basic map. That is, interchange isl_change_drop_first and
396 * isl_change_drop_second.
398 static enum isl_change
invert_change(enum isl_change change
)
401 case isl_change_error
:
402 return isl_change_error
;
403 case isl_change_none
:
404 return isl_change_none
;
405 case isl_change_drop_first
:
406 return isl_change_drop_second
;
407 case isl_change_drop_second
:
408 return isl_change_drop_first
;
409 case isl_change_fuse
:
410 return isl_change_fuse
;
413 return isl_change_error
;
416 /* Add the valid constraints of the basic map represented by "info"
417 * to "bmap". "len" is the size of the constraints.
418 * If only one of the pair of inequalities that make up an equality
419 * is valid, then add that inequality.
421 static __isl_give isl_basic_map
*add_valid_constraints(
422 __isl_take isl_basic_map
*bmap
, struct isl_coalesce_info
*info
,
430 for (k
= 0; k
< info
->bmap
->n_eq
; ++k
) {
431 if (info
->eq
[2 * k
] == STATUS_VALID
&&
432 info
->eq
[2 * k
+ 1] == STATUS_VALID
) {
433 l
= isl_basic_map_alloc_equality(bmap
);
435 return isl_basic_map_free(bmap
);
436 isl_seq_cpy(bmap
->eq
[l
], info
->bmap
->eq
[k
], len
);
437 } else if (info
->eq
[2 * k
] == STATUS_VALID
) {
438 l
= isl_basic_map_alloc_inequality(bmap
);
440 return isl_basic_map_free(bmap
);
441 isl_seq_neg(bmap
->ineq
[l
], info
->bmap
->eq
[k
], len
);
442 } else if (info
->eq
[2 * k
+ 1] == STATUS_VALID
) {
443 l
= isl_basic_map_alloc_inequality(bmap
);
445 return isl_basic_map_free(bmap
);
446 isl_seq_cpy(bmap
->ineq
[l
], info
->bmap
->eq
[k
], len
);
450 for (k
= 0; k
< info
->bmap
->n_ineq
; ++k
) {
451 if (info
->ineq
[k
] != STATUS_VALID
)
453 l
= isl_basic_map_alloc_inequality(bmap
);
455 return isl_basic_map_free(bmap
);
456 isl_seq_cpy(bmap
->ineq
[l
], info
->bmap
->ineq
[k
], len
);
462 /* Is "bmap" defined by a number of (non-redundant) constraints that
463 * is greater than the number of constraints of basic maps i and j combined?
464 * Equalities are counted as two inequalities.
466 static int number_of_constraints_increases(int i
, int j
,
467 struct isl_coalesce_info
*info
,
468 __isl_keep isl_basic_map
*bmap
, struct isl_tab
*tab
)
472 n_old
= 2 * info
[i
].bmap
->n_eq
+ info
[i
].bmap
->n_ineq
;
473 n_old
+= 2 * info
[j
].bmap
->n_eq
+ info
[j
].bmap
->n_ineq
;
475 n_new
= 2 * bmap
->n_eq
;
476 for (k
= 0; k
< bmap
->n_ineq
; ++k
)
477 if (!isl_tab_is_redundant(tab
, bmap
->n_eq
+ k
))
480 return n_new
> n_old
;
483 /* Replace the pair of basic maps i and j by the basic map bounded
484 * by the valid constraints in both basic maps and the constraints
485 * in extra (if not NULL).
486 * Place the fused basic map in the position that is the smallest of i and j.
488 * If "detect_equalities" is set, then look for equalities encoded
489 * as pairs of inequalities.
490 * If "check_number" is set, then the original basic maps are only
491 * replaced if the total number of constraints does not increase.
492 * While the number of integer divisions in the two basic maps
493 * is assumed to be the same, the actual definitions may be different.
494 * We only copy the definition from one of the basic map if it is
495 * the same as that of the other basic map. Otherwise, we mark
496 * the integer division as unknown and simplify the basic map
497 * in an attempt to recover the integer division definition.
499 static enum isl_change
fuse(int i
, int j
, struct isl_coalesce_info
*info
,
500 __isl_keep isl_mat
*extra
, int detect_equalities
, int check_number
)
503 struct isl_basic_map
*fused
= NULL
;
504 struct isl_tab
*fused_tab
= NULL
;
505 isl_size total
= isl_basic_map_dim(info
[i
].bmap
, isl_dim_all
);
506 unsigned extra_rows
= extra
? extra
->n_row
: 0;
507 unsigned n_eq
, n_ineq
;
511 return isl_change_error
;
513 return fuse(j
, i
, info
, extra
, detect_equalities
, check_number
);
515 n_eq
= info
[i
].bmap
->n_eq
+ info
[j
].bmap
->n_eq
;
516 n_ineq
= info
[i
].bmap
->n_ineq
+ info
[j
].bmap
->n_ineq
;
517 fused
= isl_basic_map_alloc_space(isl_space_copy(info
[i
].bmap
->dim
),
518 info
[i
].bmap
->n_div
, n_eq
, n_eq
+ n_ineq
+ extra_rows
);
519 fused
= add_valid_constraints(fused
, &info
[i
], 1 + total
);
520 fused
= add_valid_constraints(fused
, &info
[j
], 1 + total
);
523 if (ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_RATIONAL
) &&
524 ISL_F_ISSET(info
[j
].bmap
, ISL_BASIC_MAP_RATIONAL
))
525 ISL_F_SET(fused
, ISL_BASIC_MAP_RATIONAL
);
527 for (k
= 0; k
< info
[i
].bmap
->n_div
; ++k
) {
528 int l
= isl_basic_map_alloc_div(fused
);
531 if (isl_seq_eq(info
[i
].bmap
->div
[k
], info
[j
].bmap
->div
[k
],
533 isl_seq_cpy(fused
->div
[l
], info
[i
].bmap
->div
[k
],
536 isl_int_set_si(fused
->div
[l
][0], 0);
541 for (k
= 0; k
< extra_rows
; ++k
) {
542 l
= isl_basic_map_alloc_inequality(fused
);
545 isl_seq_cpy(fused
->ineq
[l
], extra
->row
[k
], 1 + total
);
548 if (detect_equalities
)
549 fused
= isl_basic_map_detect_inequality_pairs(fused
, NULL
);
550 fused
= isl_basic_map_gauss(fused
, NULL
);
551 if (simplify
|| info
[j
].simplify
) {
552 fused
= isl_basic_map_simplify(fused
);
553 info
[i
].simplify
= 0;
555 fused
= isl_basic_map_finalize(fused
);
557 fused_tab
= isl_tab_from_basic_map(fused
, 0);
558 if (isl_tab_detect_redundant(fused_tab
) < 0)
562 number_of_constraints_increases(i
, j
, info
, fused
, fused_tab
)) {
563 isl_tab_free(fused_tab
);
564 isl_basic_map_free(fused
);
565 return isl_change_none
;
568 isl_basic_map_free(info
[i
].bmap
);
569 info
[i
].bmap
= fused
;
570 isl_tab_free(info
[i
].tab
);
571 info
[i
].tab
= fused_tab
;
574 return isl_change_fuse
;
576 isl_tab_free(fused_tab
);
577 isl_basic_map_free(fused
);
578 return isl_change_error
;
581 /* Given a pair of basic maps i and j such that all constraints are either
582 * "valid" or "cut", check if the facets corresponding to the "cut"
583 * constraints of i lie entirely within basic map j.
584 * If so, replace the pair by the basic map consisting of the valid
585 * constraints in both basic maps.
586 * Checking whether the facet lies entirely within basic map j
587 * is performed by checking whether the constraints of basic map j
588 * are valid for the facet. These tests are performed on a rational
589 * tableau to avoid the theoretical possibility that a constraint
590 * that was considered to be a cut constraint for the entire basic map i
591 * happens to be considered to be a valid constraint for the facet,
592 * even though it cuts off the same rational points.
594 * To see that we are not introducing any extra points, call the
595 * two basic maps A and B and the resulting map U and let x
596 * be an element of U \setminus ( A \cup B ).
597 * A line connecting x with an element of A \cup B meets a facet F
598 * of either A or B. Assume it is a facet of B and let c_1 be
599 * the corresponding facet constraint. We have c_1(x) < 0 and
600 * so c_1 is a cut constraint. This implies that there is some
601 * (possibly rational) point x' satisfying the constraints of A
602 * and the opposite of c_1 as otherwise c_1 would have been marked
603 * valid for A. The line connecting x and x' meets a facet of A
604 * in a (possibly rational) point that also violates c_1, but this
605 * is impossible since all cut constraints of B are valid for all
607 * In case F is a facet of A rather than B, then we can apply the
608 * above reasoning to find a facet of B separating x from A \cup B first.
610 static enum isl_change
check_facets(int i
, int j
,
611 struct isl_coalesce_info
*info
)
614 struct isl_tab_undo
*snap
, *snap2
;
615 unsigned n_eq
= info
[i
].bmap
->n_eq
;
617 snap
= isl_tab_snap(info
[i
].tab
);
618 if (isl_tab_mark_rational(info
[i
].tab
) < 0)
619 return isl_change_error
;
620 snap2
= isl_tab_snap(info
[i
].tab
);
622 for (k
= 0; k
< info
[i
].bmap
->n_ineq
; ++k
) {
623 if (info
[i
].ineq
[k
] != STATUS_CUT
)
625 if (isl_tab_select_facet(info
[i
].tab
, n_eq
+ k
) < 0)
626 return isl_change_error
;
627 for (l
= 0; l
< info
[j
].bmap
->n_ineq
; ++l
) {
629 if (info
[j
].ineq
[l
] != STATUS_CUT
)
631 stat
= status_in(info
[j
].bmap
->ineq
[l
], info
[i
].tab
);
633 return isl_change_error
;
634 if (stat
!= STATUS_VALID
)
637 if (isl_tab_rollback(info
[i
].tab
, snap2
) < 0)
638 return isl_change_error
;
639 if (l
< info
[j
].bmap
->n_ineq
)
643 if (k
< info
[i
].bmap
->n_ineq
) {
644 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
645 return isl_change_error
;
646 return isl_change_none
;
648 return fuse(i
, j
, info
, NULL
, 0, 0);
651 /* Check if info->bmap contains the basic map represented
652 * by the tableau "tab".
653 * For each equality, we check both the constraint itself
654 * (as an inequality) and its negation. Make sure the
655 * equality is returned to its original state before returning.
657 static isl_bool
contains(struct isl_coalesce_info
*info
, struct isl_tab
*tab
)
661 isl_basic_map
*bmap
= info
->bmap
;
663 dim
= isl_basic_map_dim(bmap
, isl_dim_all
);
665 return isl_bool_error
;
666 for (k
= 0; k
< bmap
->n_eq
; ++k
) {
668 isl_seq_neg(bmap
->eq
[k
], bmap
->eq
[k
], 1 + dim
);
669 stat
= status_in(bmap
->eq
[k
], tab
);
670 isl_seq_neg(bmap
->eq
[k
], bmap
->eq
[k
], 1 + dim
);
672 return isl_bool_error
;
673 if (stat
!= STATUS_VALID
)
674 return isl_bool_false
;
675 stat
= status_in(bmap
->eq
[k
], tab
);
677 return isl_bool_error
;
678 if (stat
!= STATUS_VALID
)
679 return isl_bool_false
;
682 for (k
= 0; k
< bmap
->n_ineq
; ++k
) {
684 if (info
->ineq
[k
] == STATUS_REDUNDANT
)
686 stat
= status_in(bmap
->ineq
[k
], tab
);
688 return isl_bool_error
;
689 if (stat
!= STATUS_VALID
)
690 return isl_bool_false
;
692 return isl_bool_true
;
695 /* Basic map "i" has an inequality (say "k") that is adjacent
696 * to some inequality of basic map "j". All the other inequalities
698 * Check if basic map "j" forms an extension of basic map "i".
700 * Note that this function is only called if some of the equalities or
701 * inequalities of basic map "j" do cut basic map "i". The function is
702 * correct even if there are no such cut constraints, but in that case
703 * the additional checks performed by this function are overkill.
705 * In particular, we replace constraint k, say f >= 0, by constraint
706 * f <= -1, add the inequalities of "j" that are valid for "i"
707 * and check if the result is a subset of basic map "j".
708 * To improve the chances of the subset relation being detected,
709 * any variable that only attains a single integer value
710 * in the tableau of "i" is first fixed to that value.
711 * If the result is a subset, then we know that this result is exactly equal
712 * to basic map "j" since all its constraints are valid for basic map "j".
713 * By combining the valid constraints of "i" (all equalities and all
714 * inequalities except "k") and the valid constraints of "j" we therefore
715 * obtain a basic map that is equal to their union.
716 * In this case, there is no need to perform a rollback of the tableau
717 * since it is going to be destroyed in fuse().
723 * |_______| _ |_________\
735 static enum isl_change
is_adj_ineq_extension(int i
, int j
,
736 struct isl_coalesce_info
*info
)
739 struct isl_tab_undo
*snap
;
740 unsigned n_eq
= info
[i
].bmap
->n_eq
;
741 isl_size total
= isl_basic_map_dim(info
[i
].bmap
, isl_dim_all
);
746 return isl_change_error
;
747 if (isl_tab_extend_cons(info
[i
].tab
, 1 + info
[j
].bmap
->n_ineq
) < 0)
748 return isl_change_error
;
750 k
= find_ineq(&info
[i
], STATUS_ADJ_INEQ
);
752 isl_die(isl_basic_map_get_ctx(info
[i
].bmap
), isl_error_internal
,
753 "info[i].ineq should have exactly one STATUS_ADJ_INEQ",
754 return isl_change_error
);
756 snap
= isl_tab_snap(info
[i
].tab
);
758 if (isl_tab_unrestrict(info
[i
].tab
, n_eq
+ k
) < 0)
759 return isl_change_error
;
761 isl_seq_neg(info
[i
].bmap
->ineq
[k
], info
[i
].bmap
->ineq
[k
], 1 + total
);
762 isl_int_sub_ui(info
[i
].bmap
->ineq
[k
][0], info
[i
].bmap
->ineq
[k
][0], 1);
763 r
= isl_tab_add_ineq(info
[i
].tab
, info
[i
].bmap
->ineq
[k
]);
764 isl_seq_neg(info
[i
].bmap
->ineq
[k
], info
[i
].bmap
->ineq
[k
], 1 + total
);
765 isl_int_sub_ui(info
[i
].bmap
->ineq
[k
][0], info
[i
].bmap
->ineq
[k
][0], 1);
767 return isl_change_error
;
769 for (k
= 0; k
< info
[j
].bmap
->n_ineq
; ++k
) {
770 if (info
[j
].ineq
[k
] != STATUS_VALID
)
772 if (isl_tab_add_ineq(info
[i
].tab
, info
[j
].bmap
->ineq
[k
]) < 0)
773 return isl_change_error
;
775 if (isl_tab_detect_constants(info
[i
].tab
) < 0)
776 return isl_change_error
;
778 super
= contains(&info
[j
], info
[i
].tab
);
780 return isl_change_error
;
782 return fuse(i
, j
, info
, NULL
, 0, 0);
784 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
785 return isl_change_error
;
787 return isl_change_none
;
791 /* Both basic maps have at least one inequality with and adjacent
792 * (but opposite) inequality in the other basic map.
793 * Check that there are no cut constraints and that there is only
794 * a single pair of adjacent inequalities.
795 * If so, we can replace the pair by a single basic map described
796 * by all but the pair of adjacent inequalities.
797 * Any additional points introduced lie strictly between the two
798 * adjacent hyperplanes and can therefore be integral.
807 * The test for a single pair of adjancent inequalities is important
808 * for avoiding the combination of two basic maps like the following
818 * If there are some cut constraints on one side, then we may
819 * still be able to fuse the two basic maps, but we need to perform
820 * some additional checks in is_adj_ineq_extension.
822 static enum isl_change
check_adj_ineq(int i
, int j
,
823 struct isl_coalesce_info
*info
)
825 int count_i
, count_j
;
828 count_i
= count_ineq(&info
[i
], STATUS_ADJ_INEQ
);
829 count_j
= count_ineq(&info
[j
], STATUS_ADJ_INEQ
);
831 if (count_i
!= 1 && count_j
!= 1)
832 return isl_change_none
;
834 cut_i
= any_eq(&info
[i
], STATUS_CUT
) || any_ineq(&info
[i
], STATUS_CUT
);
835 cut_j
= any_eq(&info
[j
], STATUS_CUT
) || any_ineq(&info
[j
], STATUS_CUT
);
837 if (!cut_i
&& !cut_j
&& count_i
== 1 && count_j
== 1)
838 return fuse(i
, j
, info
, NULL
, 0, 0);
840 if (count_i
== 1 && !cut_i
)
841 return is_adj_ineq_extension(i
, j
, info
);
843 if (count_j
== 1 && !cut_j
)
844 return is_adj_ineq_extension(j
, i
, info
);
846 return isl_change_none
;
849 /* Given an affine transformation matrix "T", does row "row" represent
850 * anything other than a unit vector (possibly shifted by a constant)
851 * that is not involved in any of the other rows?
853 * That is, if a constraint involves the variable corresponding to
854 * the row, then could its preimage by "T" have any coefficients
855 * that are different from those in the original constraint?
857 static int not_unique_unit_row(__isl_keep isl_mat
*T
, int row
)
860 int len
= T
->n_col
- 1;
862 i
= isl_seq_first_non_zero(T
->row
[row
] + 1, len
);
865 if (!isl_int_is_one(T
->row
[row
][1 + i
]) &&
866 !isl_int_is_negone(T
->row
[row
][1 + i
]))
869 j
= isl_seq_first_non_zero(T
->row
[row
] + 1 + i
+ 1, len
- (i
+ 1));
873 for (j
= 1; j
< T
->n_row
; ++j
) {
876 if (!isl_int_is_zero(T
->row
[j
][1 + i
]))
883 /* Does inequality constraint "ineq" of "bmap" involve any of
884 * the variables marked in "affected"?
885 * "total" is the total number of variables, i.e., the number
886 * of entries in "affected".
888 static isl_bool
is_affected(__isl_keep isl_basic_map
*bmap
, int ineq
,
889 int *affected
, int total
)
893 for (i
= 0; i
< total
; ++i
) {
896 if (!isl_int_is_zero(bmap
->ineq
[ineq
][1 + i
]))
897 return isl_bool_true
;
900 return isl_bool_false
;
903 /* Given the compressed version of inequality constraint "ineq"
904 * of info->bmap in "v", check if the constraint can be tightened,
905 * where the compression is based on an equality constraint valid
907 * If so, add the tightened version of the inequality constraint
908 * to info->tab. "v" may be modified by this function.
910 * That is, if the compressed constraint is of the form
914 * with 0 < c < m, then it is equivalent to
918 * This means that c can also be subtracted from the original,
919 * uncompressed constraint without affecting the integer points
920 * in info->tab. Add this tightened constraint as an extra row
921 * to info->tab to make this information explicitly available.
923 static __isl_give isl_vec
*try_tightening(struct isl_coalesce_info
*info
,
924 int ineq
, __isl_take isl_vec
*v
)
932 ctx
= isl_vec_get_ctx(v
);
933 isl_seq_gcd(v
->el
+ 1, v
->size
- 1, &ctx
->normalize_gcd
);
934 if (isl_int_is_zero(ctx
->normalize_gcd
) ||
935 isl_int_is_one(ctx
->normalize_gcd
)) {
943 isl_int_fdiv_r(v
->el
[0], v
->el
[0], ctx
->normalize_gcd
);
944 if (isl_int_is_zero(v
->el
[0]))
947 if (isl_tab_extend_cons(info
->tab
, 1) < 0)
948 return isl_vec_free(v
);
950 isl_int_sub(info
->bmap
->ineq
[ineq
][0],
951 info
->bmap
->ineq
[ineq
][0], v
->el
[0]);
952 r
= isl_tab_add_ineq(info
->tab
, info
->bmap
->ineq
[ineq
]);
953 isl_int_add(info
->bmap
->ineq
[ineq
][0],
954 info
->bmap
->ineq
[ineq
][0], v
->el
[0]);
957 return isl_vec_free(v
);
962 /* Tighten the (non-redundant) constraints on the facet represented
964 * In particular, on input, info->tab represents the result
965 * of relaxing the "n" inequality constraints of info->bmap in "relaxed"
966 * by one, i.e., replacing f_i >= 0 by f_i + 1 >= 0, and then
967 * replacing the one at index "l" by the corresponding equality,
968 * i.e., f_k + 1 = 0, with k = relaxed[l].
970 * Compute a variable compression from the equality constraint f_k + 1 = 0
971 * and use it to tighten the other constraints of info->bmap
972 * (that is, all constraints that have not been relaxed),
973 * updating info->tab (and leaving info->bmap untouched).
974 * The compression handles essentially two cases, one where a variable
975 * is assigned a fixed value and can therefore be eliminated, and one
976 * where one variable is a shifted multiple of some other variable and
977 * can therefore be replaced by that multiple.
978 * Gaussian elimination would also work for the first case, but for
979 * the second case, the effectiveness would depend on the order
981 * After compression, some of the constraints may have coefficients
982 * with a common divisor. If this divisor does not divide the constant
983 * term, then the constraint can be tightened.
984 * The tightening is performed on the tableau info->tab by introducing
985 * extra (temporary) constraints.
987 * Only constraints that are possibly affected by the compression are
988 * considered. In particular, if the constraint only involves variables
989 * that are directly mapped to a distinct set of other variables, then
990 * no common divisor can be introduced and no tightening can occur.
992 * It is important to only consider the non-redundant constraints
993 * since the facet constraint has been relaxed prior to the call
994 * to this function, meaning that the constraints that were redundant
995 * prior to the relaxation may no longer be redundant.
996 * These constraints will be ignored in the fused result, so
997 * the fusion detection should not exploit them.
999 static isl_stat
tighten_on_relaxed_facet(struct isl_coalesce_info
*info
,
1000 int n
, int *relaxed
, int l
)
1011 ctx
= isl_basic_map_get_ctx(info
->bmap
);
1012 total
= isl_basic_map_dim(info
->bmap
, isl_dim_all
);
1014 return isl_stat_error
;
1015 isl_int_add_ui(info
->bmap
->ineq
[k
][0], info
->bmap
->ineq
[k
][0], 1);
1016 T
= isl_mat_sub_alloc6(ctx
, info
->bmap
->ineq
, k
, 1, 0, 1 + total
);
1017 T
= isl_mat_variable_compression(T
, NULL
);
1018 isl_int_sub_ui(info
->bmap
->ineq
[k
][0], info
->bmap
->ineq
[k
][0], 1);
1020 return isl_stat_error
;
1021 if (T
->n_col
== 0) {
1026 affected
= isl_alloc_array(ctx
, int, total
);
1030 for (i
= 0; i
< total
; ++i
)
1031 affected
[i
] = not_unique_unit_row(T
, 1 + i
);
1033 for (i
= 0; i
< info
->bmap
->n_ineq
; ++i
) {
1035 if (any(relaxed
, n
, i
))
1037 if (info
->ineq
[i
] == STATUS_REDUNDANT
)
1039 handle
= is_affected(info
->bmap
, i
, affected
, total
);
1044 v
= isl_vec_alloc(ctx
, 1 + total
);
1047 isl_seq_cpy(v
->el
, info
->bmap
->ineq
[i
], 1 + total
);
1048 v
= isl_vec_mat_product(v
, isl_mat_copy(T
));
1049 v
= try_tightening(info
, i
, v
);
1061 return isl_stat_error
;
1064 /* Replace the basic maps "i" and "j" by an extension of "i"
1065 * along the "n" inequality constraints in "relax" by one.
1066 * The tableau info[i].tab has already been extended.
1067 * Extend info[i].bmap accordingly by relaxing all constraints in "relax"
1069 * Each integer division that does not have exactly the same
1070 * definition in "i" and "j" is marked unknown and the basic map
1071 * is scheduled to be simplified in an attempt to recover
1072 * the integer division definition.
1073 * Place the extension in the position that is the smallest of i and j.
1075 static enum isl_change
extend(int i
, int j
, int n
, int *relax
,
1076 struct isl_coalesce_info
*info
)
1081 info
[i
].bmap
= isl_basic_map_cow(info
[i
].bmap
);
1082 total
= isl_basic_map_dim(info
[i
].bmap
, isl_dim_all
);
1084 return isl_change_error
;
1085 for (l
= 0; l
< info
[i
].bmap
->n_div
; ++l
)
1086 if (!isl_seq_eq(info
[i
].bmap
->div
[l
],
1087 info
[j
].bmap
->div
[l
], 1 + 1 + total
)) {
1088 isl_int_set_si(info
[i
].bmap
->div
[l
][0], 0);
1089 info
[i
].simplify
= 1;
1091 for (l
= 0; l
< n
; ++l
)
1092 isl_int_add_ui(info
[i
].bmap
->ineq
[relax
[l
]][0],
1093 info
[i
].bmap
->ineq
[relax
[l
]][0], 1);
1094 ISL_F_SET(info
[i
].bmap
, ISL_BASIC_MAP_FINAL
);
1097 exchange(&info
[i
], &info
[j
]);
1098 return isl_change_fuse
;
1101 /* Basic map "i" has "n" inequality constraints (collected in "relax")
1102 * that are such that they include basic map "j" if they are relaxed
1103 * by one. All the other inequalities are valid for "j".
1104 * Check if basic map "j" forms an extension of basic map "i".
1106 * In particular, relax the constraints in "relax", compute the corresponding
1107 * facets one by one and check whether each of these is included
1108 * in the other basic map.
1109 * Before testing for inclusion, the constraints on each facet
1110 * are tightened to increase the chance of an inclusion being detected.
1111 * (Adding the valid constraints of "j" to the tableau of "i", as is done
1112 * in is_adj_ineq_extension, may further increase those chances, but this
1113 * is not currently done.)
1114 * If each facet is included, we know that relaxing the constraints extends
1115 * the basic map with exactly the other basic map (we already know that this
1116 * other basic map is included in the extension, because all other
1117 * inequality constraints are valid of "j") and we can replace the
1118 * two basic maps by this extension.
1120 * If any of the relaxed constraints turn out to be redundant, then bail out.
1121 * isl_tab_select_facet refuses to handle such constraints. It may be
1122 * possible to handle them anyway by making a distinction between
1123 * redundant constraints with a corresponding facet that still intersects
1124 * the set (allowing isl_tab_select_facet to handle them) and
1125 * those where the facet does not intersect the set (which can be ignored
1126 * because the empty facet is trivially included in the other disjunct).
1127 * However, relaxed constraints that turn out to be redundant should
1128 * be fairly rare and no such instance has been reported where
1129 * coalescing would be successful.
1145 static enum isl_change
is_relaxed_extension(int i
, int j
, int n
, int *relax
,
1146 struct isl_coalesce_info
*info
)
1150 struct isl_tab_undo
*snap
, *snap2
;
1151 unsigned n_eq
= info
[i
].bmap
->n_eq
;
1153 for (l
= 0; l
< n
; ++l
)
1154 if (isl_tab_is_equality(info
[i
].tab
, n_eq
+ relax
[l
]))
1155 return isl_change_none
;
1157 snap
= isl_tab_snap(info
[i
].tab
);
1158 for (l
= 0; l
< n
; ++l
)
1159 if (isl_tab_relax(info
[i
].tab
, n_eq
+ relax
[l
]) < 0)
1160 return isl_change_error
;
1161 for (l
= 0; l
< n
; ++l
) {
1162 if (!isl_tab_is_redundant(info
[i
].tab
, n_eq
+ relax
[l
]))
1164 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
1165 return isl_change_error
;
1166 return isl_change_none
;
1168 snap2
= isl_tab_snap(info
[i
].tab
);
1169 for (l
= 0; l
< n
; ++l
) {
1170 if (isl_tab_rollback(info
[i
].tab
, snap2
) < 0)
1171 return isl_change_error
;
1172 if (isl_tab_select_facet(info
[i
].tab
, n_eq
+ relax
[l
]) < 0)
1173 return isl_change_error
;
1174 if (tighten_on_relaxed_facet(&info
[i
], n
, relax
, l
) < 0)
1175 return isl_change_error
;
1176 super
= contains(&info
[j
], info
[i
].tab
);
1178 return isl_change_error
;
1181 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
1182 return isl_change_error
;
1183 return isl_change_none
;
1186 if (isl_tab_rollback(info
[i
].tab
, snap2
) < 0)
1187 return isl_change_error
;
1188 return extend(i
, j
, n
, relax
, info
);
1191 /* Data structure that keeps track of the wrapping constraints
1192 * and of information to bound the coefficients of those constraints.
1194 * bound is set if we want to apply a bound on the coefficients
1195 * mat contains the wrapping constraints
1196 * max is the bound on the coefficients (if bound is set)
1204 /* Update wraps->max to be greater than or equal to the coefficients
1205 * in the equalities and inequalities of info->bmap that can be removed
1206 * if we end up applying wrapping.
1208 static isl_stat
wraps_update_max(struct isl_wraps
*wraps
,
1209 struct isl_coalesce_info
*info
)
1213 isl_size total
= isl_basic_map_dim(info
->bmap
, isl_dim_all
);
1216 return isl_stat_error
;
1217 isl_int_init(max_k
);
1219 for (k
= 0; k
< info
->bmap
->n_eq
; ++k
) {
1220 if (info
->eq
[2 * k
] == STATUS_VALID
&&
1221 info
->eq
[2 * k
+ 1] == STATUS_VALID
)
1223 isl_seq_abs_max(info
->bmap
->eq
[k
] + 1, total
, &max_k
);
1224 if (isl_int_abs_gt(max_k
, wraps
->max
))
1225 isl_int_set(wraps
->max
, max_k
);
1228 for (k
= 0; k
< info
->bmap
->n_ineq
; ++k
) {
1229 if (info
->ineq
[k
] == STATUS_VALID
||
1230 info
->ineq
[k
] == STATUS_REDUNDANT
)
1232 isl_seq_abs_max(info
->bmap
->ineq
[k
] + 1, total
, &max_k
);
1233 if (isl_int_abs_gt(max_k
, wraps
->max
))
1234 isl_int_set(wraps
->max
, max_k
);
1237 isl_int_clear(max_k
);
1242 /* Initialize the isl_wraps data structure.
1243 * If we want to bound the coefficients of the wrapping constraints,
1244 * we set wraps->max to the largest coefficient
1245 * in the equalities and inequalities that can be removed if we end up
1246 * applying wrapping.
1248 static isl_stat
wraps_init(struct isl_wraps
*wraps
, __isl_take isl_mat
*mat
,
1249 struct isl_coalesce_info
*info
, int i
, int j
)
1256 return isl_stat_error
;
1257 ctx
= isl_mat_get_ctx(mat
);
1258 wraps
->bound
= isl_options_get_coalesce_bounded_wrapping(ctx
);
1261 isl_int_init(wraps
->max
);
1262 isl_int_set_si(wraps
->max
, 0);
1263 if (wraps_update_max(wraps
, &info
[i
]) < 0)
1264 return isl_stat_error
;
1265 if (wraps_update_max(wraps
, &info
[j
]) < 0)
1266 return isl_stat_error
;
1271 /* Free the contents of the isl_wraps data structure.
1273 static void wraps_free(struct isl_wraps
*wraps
)
1275 isl_mat_free(wraps
->mat
);
1277 isl_int_clear(wraps
->max
);
1280 /* Is the wrapping constraint in row "row" allowed?
1282 * If wraps->bound is set, we check that none of the coefficients
1283 * is greater than wraps->max.
1285 static int allow_wrap(struct isl_wraps
*wraps
, int row
)
1292 for (i
= 1; i
< wraps
->mat
->n_col
; ++i
)
1293 if (isl_int_abs_gt(wraps
->mat
->row
[row
][i
], wraps
->max
))
1299 /* Wrap "ineq" (or its opposite if "negate" is set) around "bound"
1300 * to include "set" and add the result in position "w" of "wraps".
1301 * "len" is the total number of coefficients in "bound" and "ineq".
1302 * Return 1 on success, 0 on failure and -1 on error.
1303 * Wrapping can fail if the result of wrapping is equal to "bound"
1304 * or if we want to bound the sizes of the coefficients and
1305 * the wrapped constraint does not satisfy this bound.
1307 static int add_wrap(struct isl_wraps
*wraps
, int w
, isl_int
*bound
,
1308 isl_int
*ineq
, unsigned len
, __isl_keep isl_set
*set
, int negate
)
1310 isl_seq_cpy(wraps
->mat
->row
[w
], bound
, len
);
1312 isl_seq_neg(wraps
->mat
->row
[w
+ 1], ineq
, len
);
1313 ineq
= wraps
->mat
->row
[w
+ 1];
1315 if (!isl_set_wrap_facet(set
, wraps
->mat
->row
[w
], ineq
))
1317 if (isl_seq_eq(wraps
->mat
->row
[w
], bound
, len
))
1319 if (!allow_wrap(wraps
, w
))
1324 /* For each constraint in info->bmap that is not redundant (as determined
1325 * by info->tab) and that is not a valid constraint for the other basic map,
1326 * wrap the constraint around "bound" such that it includes the whole
1327 * set "set" and append the resulting constraint to "wraps".
1328 * Note that the constraints that are valid for the other basic map
1329 * will be added to the combined basic map by default, so there is
1330 * no need to wrap them.
1331 * The caller wrap_in_facets even relies on this function not wrapping
1332 * any constraints that are already valid.
1333 * "wraps" is assumed to have been pre-allocated to the appropriate size.
1334 * wraps->n_row is the number of actual wrapped constraints that have
1336 * If any of the wrapping problems results in a constraint that is
1337 * identical to "bound", then this means that "set" is unbounded in such
1338 * way that no wrapping is possible. If this happens then wraps->n_row
1340 * Similarly, if we want to bound the coefficients of the wrapping
1341 * constraints and a newly added wrapping constraint does not
1342 * satisfy the bound, then wraps->n_row is also reset to zero.
1344 static isl_stat
add_wraps(struct isl_wraps
*wraps
,
1345 struct isl_coalesce_info
*info
, isl_int
*bound
, __isl_keep isl_set
*set
)
1350 isl_basic_map
*bmap
= info
->bmap
;
1351 isl_size total
= isl_basic_map_dim(bmap
, isl_dim_all
);
1352 unsigned len
= 1 + total
;
1355 return isl_stat_error
;
1357 w
= wraps
->mat
->n_row
;
1359 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
1360 if (info
->ineq
[l
] == STATUS_VALID
||
1361 info
->ineq
[l
] == STATUS_REDUNDANT
)
1363 if (isl_seq_is_neg(bound
, bmap
->ineq
[l
], len
))
1365 if (isl_seq_eq(bound
, bmap
->ineq
[l
], len
))
1367 if (isl_tab_is_redundant(info
->tab
, bmap
->n_eq
+ l
))
1370 added
= add_wrap(wraps
, w
, bound
, bmap
->ineq
[l
], len
, set
, 0);
1372 return isl_stat_error
;
1377 for (l
= 0; l
< bmap
->n_eq
; ++l
) {
1378 if (isl_seq_is_neg(bound
, bmap
->eq
[l
], len
))
1380 if (isl_seq_eq(bound
, bmap
->eq
[l
], len
))
1383 for (m
= 0; m
< 2; ++m
) {
1384 if (info
->eq
[2 * l
+ m
] == STATUS_VALID
)
1386 added
= add_wrap(wraps
, w
, bound
, bmap
->eq
[l
], len
,
1389 return isl_stat_error
;
1396 wraps
->mat
->n_row
= w
;
1399 wraps
->mat
->n_row
= 0;
1403 /* Check if the constraints in "wraps" from "first" until the last
1404 * are all valid for the basic set represented by "tab".
1405 * If not, wraps->n_row is set to zero.
1407 static int check_wraps(__isl_keep isl_mat
*wraps
, int first
,
1408 struct isl_tab
*tab
)
1412 for (i
= first
; i
< wraps
->n_row
; ++i
) {
1413 enum isl_ineq_type type
;
1414 type
= isl_tab_ineq_type(tab
, wraps
->row
[i
]);
1415 if (type
== isl_ineq_error
)
1417 if (type
== isl_ineq_redundant
)
1426 /* Return a set that corresponds to the non-redundant constraints
1427 * (as recorded in tab) of bmap.
1429 * It's important to remove the redundant constraints as some
1430 * of the other constraints may have been modified after the
1431 * constraints were marked redundant.
1432 * In particular, a constraint may have been relaxed.
1433 * Redundant constraints are ignored when a constraint is relaxed
1434 * and should therefore continue to be ignored ever after.
1435 * Otherwise, the relaxation might be thwarted by some of
1436 * these constraints.
1438 * Update the underlying set to ensure that the dimension doesn't change.
1439 * Otherwise the integer divisions could get dropped if the tab
1440 * turns out to be empty.
1442 static __isl_give isl_set
*set_from_updated_bmap(__isl_keep isl_basic_map
*bmap
,
1443 struct isl_tab
*tab
)
1445 isl_basic_set
*bset
;
1447 bmap
= isl_basic_map_copy(bmap
);
1448 bset
= isl_basic_map_underlying_set(bmap
);
1449 bset
= isl_basic_set_cow(bset
);
1450 bset
= isl_basic_set_update_from_tab(bset
, tab
);
1451 return isl_set_from_basic_set(bset
);
1454 /* Wrap the constraints of info->bmap that bound the facet defined
1455 * by inequality "k" around (the opposite of) this inequality to
1456 * include "set". "bound" may be used to store the negated inequality.
1457 * Since the wrapped constraints are not guaranteed to contain the whole
1458 * of info->bmap, we check them in check_wraps.
1459 * If any of the wrapped constraints turn out to be invalid, then
1460 * check_wraps will reset wrap->n_row to zero.
1462 static isl_stat
add_wraps_around_facet(struct isl_wraps
*wraps
,
1463 struct isl_coalesce_info
*info
, int k
, isl_int
*bound
,
1464 __isl_keep isl_set
*set
)
1466 struct isl_tab_undo
*snap
;
1468 isl_size total
= isl_basic_map_dim(info
->bmap
, isl_dim_all
);
1471 return isl_stat_error
;
1473 snap
= isl_tab_snap(info
->tab
);
1475 if (isl_tab_select_facet(info
->tab
, info
->bmap
->n_eq
+ k
) < 0)
1476 return isl_stat_error
;
1477 if (isl_tab_detect_redundant(info
->tab
) < 0)
1478 return isl_stat_error
;
1480 isl_seq_neg(bound
, info
->bmap
->ineq
[k
], 1 + total
);
1482 n
= wraps
->mat
->n_row
;
1483 if (add_wraps(wraps
, info
, bound
, set
) < 0)
1484 return isl_stat_error
;
1486 if (isl_tab_rollback(info
->tab
, snap
) < 0)
1487 return isl_stat_error
;
1488 if (check_wraps(wraps
->mat
, n
, info
->tab
) < 0)
1489 return isl_stat_error
;
1494 /* Given a basic set i with a constraint k that is adjacent to
1495 * basic set j, check if we can wrap
1496 * both the facet corresponding to k (if "wrap_facet" is set) and basic map j
1497 * (always) around their ridges to include the other set.
1498 * If so, replace the pair of basic sets by their union.
1500 * All constraints of i (except k) are assumed to be valid or
1501 * cut constraints for j.
1502 * Wrapping the cut constraints to include basic map j may result
1503 * in constraints that are no longer valid of basic map i
1504 * we have to check that the resulting wrapping constraints are valid for i.
1505 * If "wrap_facet" is not set, then all constraints of i (except k)
1506 * are assumed to be valid for j.
1515 static enum isl_change
can_wrap_in_facet(int i
, int j
, int k
,
1516 struct isl_coalesce_info
*info
, int wrap_facet
)
1518 enum isl_change change
= isl_change_none
;
1519 struct isl_wraps wraps
;
1522 struct isl_set
*set_i
= NULL
;
1523 struct isl_set
*set_j
= NULL
;
1524 struct isl_vec
*bound
= NULL
;
1525 isl_size total
= isl_basic_map_dim(info
[i
].bmap
, isl_dim_all
);
1528 return isl_change_error
;
1529 set_i
= set_from_updated_bmap(info
[i
].bmap
, info
[i
].tab
);
1530 set_j
= set_from_updated_bmap(info
[j
].bmap
, info
[j
].tab
);
1531 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
1532 mat
= isl_mat_alloc(ctx
, 2 * (info
[i
].bmap
->n_eq
+ info
[j
].bmap
->n_eq
) +
1533 info
[i
].bmap
->n_ineq
+ info
[j
].bmap
->n_ineq
,
1535 if (wraps_init(&wraps
, mat
, info
, i
, j
) < 0)
1537 bound
= isl_vec_alloc(ctx
, 1 + total
);
1538 if (!set_i
|| !set_j
|| !bound
)
1541 isl_seq_cpy(bound
->el
, info
[i
].bmap
->ineq
[k
], 1 + total
);
1542 isl_int_add_ui(bound
->el
[0], bound
->el
[0], 1);
1543 isl_seq_normalize(ctx
, bound
->el
, 1 + total
);
1545 isl_seq_cpy(wraps
.mat
->row
[0], bound
->el
, 1 + total
);
1546 wraps
.mat
->n_row
= 1;
1548 if (add_wraps(&wraps
, &info
[j
], bound
->el
, set_i
) < 0)
1550 if (!wraps
.mat
->n_row
)
1554 if (add_wraps_around_facet(&wraps
, &info
[i
], k
,
1555 bound
->el
, set_j
) < 0)
1557 if (!wraps
.mat
->n_row
)
1561 change
= fuse(i
, j
, info
, wraps
.mat
, 0, 0);
1566 isl_set_free(set_i
);
1567 isl_set_free(set_j
);
1569 isl_vec_free(bound
);
1574 isl_vec_free(bound
);
1575 isl_set_free(set_i
);
1576 isl_set_free(set_j
);
1577 return isl_change_error
;
1580 /* Given a cut constraint t(x) >= 0 of basic map i, stored in row "w"
1581 * of wrap.mat, replace it by its relaxed version t(x) + 1 >= 0, and
1582 * add wrapping constraints to wrap.mat for all constraints
1583 * of basic map j that bound the part of basic map j that sticks out
1584 * of the cut constraint.
1585 * "set_i" is the underlying set of basic map i.
1586 * If any wrapping fails, then wraps->mat.n_row is reset to zero.
1588 * In particular, we first intersect basic map j with t(x) + 1 = 0.
1589 * If the result is empty, then t(x) >= 0 was actually a valid constraint
1590 * (with respect to the integer points), so we add t(x) >= 0 instead.
1591 * Otherwise, we wrap the constraints of basic map j that are not
1592 * redundant in this intersection and that are not already valid
1593 * for basic map i over basic map i.
1594 * Note that it is sufficient to wrap the constraints to include
1595 * basic map i, because we will only wrap the constraints that do
1596 * not include basic map i already. The wrapped constraint will
1597 * therefore be more relaxed compared to the original constraint.
1598 * Since the original constraint is valid for basic map j, so is
1599 * the wrapped constraint.
1601 static isl_stat
wrap_in_facet(struct isl_wraps
*wraps
, int w
,
1602 struct isl_coalesce_info
*info_j
, __isl_keep isl_set
*set_i
,
1603 struct isl_tab_undo
*snap
)
1605 isl_int_add_ui(wraps
->mat
->row
[w
][0], wraps
->mat
->row
[w
][0], 1);
1606 if (isl_tab_add_eq(info_j
->tab
, wraps
->mat
->row
[w
]) < 0)
1607 return isl_stat_error
;
1608 if (isl_tab_detect_redundant(info_j
->tab
) < 0)
1609 return isl_stat_error
;
1611 if (info_j
->tab
->empty
)
1612 isl_int_sub_ui(wraps
->mat
->row
[w
][0], wraps
->mat
->row
[w
][0], 1);
1613 else if (add_wraps(wraps
, info_j
, wraps
->mat
->row
[w
], set_i
) < 0)
1614 return isl_stat_error
;
1616 if (isl_tab_rollback(info_j
->tab
, snap
) < 0)
1617 return isl_stat_error
;
1622 /* Given a pair of basic maps i and j such that j sticks out
1623 * of i at n cut constraints, each time by at most one,
1624 * try to compute wrapping constraints and replace the two
1625 * basic maps by a single basic map.
1626 * The other constraints of i are assumed to be valid for j.
1627 * "set_i" is the underlying set of basic map i.
1628 * "wraps" has been initialized to be of the right size.
1630 * For each cut constraint t(x) >= 0 of i, we add the relaxed version
1631 * t(x) + 1 >= 0, along with wrapping constraints for all constraints
1632 * of basic map j that bound the part of basic map j that sticks out
1633 * of the cut constraint.
1635 * If any wrapping fails, i.e., if we cannot wrap to touch
1636 * the union, then we give up.
1637 * Otherwise, the pair of basic maps is replaced by their union.
1639 static enum isl_change
try_wrap_in_facets(int i
, int j
,
1640 struct isl_coalesce_info
*info
, struct isl_wraps
*wraps
,
1641 __isl_keep isl_set
*set_i
)
1645 struct isl_tab_undo
*snap
;
1647 total
= isl_basic_map_dim(info
[i
].bmap
, isl_dim_all
);
1649 return isl_change_error
;
1651 snap
= isl_tab_snap(info
[j
].tab
);
1653 wraps
->mat
->n_row
= 0;
1655 for (k
= 0; k
< info
[i
].bmap
->n_eq
; ++k
) {
1656 for (l
= 0; l
< 2; ++l
) {
1657 if (info
[i
].eq
[2 * k
+ l
] != STATUS_CUT
)
1659 w
= wraps
->mat
->n_row
++;
1661 isl_seq_neg(wraps
->mat
->row
[w
],
1662 info
[i
].bmap
->eq
[k
], 1 + total
);
1664 isl_seq_cpy(wraps
->mat
->row
[w
],
1665 info
[i
].bmap
->eq
[k
], 1 + total
);
1666 if (wrap_in_facet(wraps
, w
, &info
[j
], set_i
, snap
) < 0)
1667 return isl_change_error
;
1669 if (!wraps
->mat
->n_row
)
1670 return isl_change_none
;
1674 for (k
= 0; k
< info
[i
].bmap
->n_ineq
; ++k
) {
1675 if (info
[i
].ineq
[k
] != STATUS_CUT
)
1677 w
= wraps
->mat
->n_row
++;
1678 isl_seq_cpy(wraps
->mat
->row
[w
],
1679 info
[i
].bmap
->ineq
[k
], 1 + total
);
1680 if (wrap_in_facet(wraps
, w
, &info
[j
], set_i
, snap
) < 0)
1681 return isl_change_error
;
1683 if (!wraps
->mat
->n_row
)
1684 return isl_change_none
;
1687 return fuse(i
, j
, info
, wraps
->mat
, 0, 1);
1690 /* Given a pair of basic maps i and j such that j sticks out
1691 * of i at n cut constraints, each time by at most one,
1692 * try to compute wrapping constraints and replace the two
1693 * basic maps by a single basic map.
1694 * The other constraints of i are assumed to be valid for j.
1696 * The core computation is performed by try_wrap_in_facets.
1697 * This function simply extracts an underlying set representation
1698 * of basic map i and initializes the data structure for keeping
1699 * track of wrapping constraints.
1701 static enum isl_change
wrap_in_facets(int i
, int j
, int n
,
1702 struct isl_coalesce_info
*info
)
1704 enum isl_change change
= isl_change_none
;
1705 struct isl_wraps wraps
;
1708 isl_set
*set_i
= NULL
;
1709 isl_size total
= isl_basic_map_dim(info
[i
].bmap
, isl_dim_all
);
1713 return isl_change_error
;
1714 if (isl_tab_extend_cons(info
[j
].tab
, 1) < 0)
1715 return isl_change_error
;
1717 max_wrap
= 1 + 2 * info
[j
].bmap
->n_eq
+ info
[j
].bmap
->n_ineq
;
1720 set_i
= set_from_updated_bmap(info
[i
].bmap
, info
[i
].tab
);
1721 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
1722 mat
= isl_mat_alloc(ctx
, max_wrap
, 1 + total
);
1723 if (wraps_init(&wraps
, mat
, info
, i
, j
) < 0)
1728 change
= try_wrap_in_facets(i
, j
, info
, &wraps
, set_i
);
1731 isl_set_free(set_i
);
1736 isl_set_free(set_i
);
1737 return isl_change_error
;
1740 /* Return the effect of inequality "ineq" on the tableau "tab",
1741 * after relaxing the constant term of "ineq" by one.
1743 static enum isl_ineq_type
type_of_relaxed(struct isl_tab
*tab
, isl_int
*ineq
)
1745 enum isl_ineq_type type
;
1747 isl_int_add_ui(ineq
[0], ineq
[0], 1);
1748 type
= isl_tab_ineq_type(tab
, ineq
);
1749 isl_int_sub_ui(ineq
[0], ineq
[0], 1);
1754 /* Given two basic sets i and j,
1755 * check if relaxing all the cut constraints of i by one turns
1756 * them into valid constraint for j and check if we can wrap in
1757 * the bits that are sticking out.
1758 * If so, replace the pair by their union.
1760 * We first check if all relaxed cut inequalities of i are valid for j
1761 * and then try to wrap in the intersections of the relaxed cut inequalities
1764 * During this wrapping, we consider the points of j that lie at a distance
1765 * of exactly 1 from i. In particular, we ignore the points that lie in
1766 * between this lower-dimensional space and the basic map i.
1767 * We can therefore only apply this to integer maps.
1793 * Wrapping can fail if the result of wrapping one of the facets
1794 * around its edges does not produce any new facet constraint.
1795 * In particular, this happens when we try to wrap in unbounded sets.
1797 * _______________________________________________________________________
1801 * |_| |_________________________________________________________________
1804 * The following is not an acceptable result of coalescing the above two
1805 * sets as it includes extra integer points.
1806 * _______________________________________________________________________
1811 * \______________________________________________________________________
1813 static enum isl_change
can_wrap_in_set(int i
, int j
,
1814 struct isl_coalesce_info
*info
)
1820 if (ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_RATIONAL
) ||
1821 ISL_F_ISSET(info
[j
].bmap
, ISL_BASIC_MAP_RATIONAL
))
1822 return isl_change_none
;
1824 n
= count_eq(&info
[i
], STATUS_CUT
) + count_ineq(&info
[i
], STATUS_CUT
);
1826 return isl_change_none
;
1828 total
= isl_basic_map_dim(info
[i
].bmap
, isl_dim_all
);
1830 return isl_change_error
;
1831 for (k
= 0; k
< info
[i
].bmap
->n_eq
; ++k
) {
1832 for (l
= 0; l
< 2; ++l
) {
1833 enum isl_ineq_type type
;
1835 if (info
[i
].eq
[2 * k
+ l
] != STATUS_CUT
)
1839 isl_seq_neg(info
[i
].bmap
->eq
[k
],
1840 info
[i
].bmap
->eq
[k
], 1 + total
);
1841 type
= type_of_relaxed(info
[j
].tab
,
1842 info
[i
].bmap
->eq
[k
]);
1844 isl_seq_neg(info
[i
].bmap
->eq
[k
],
1845 info
[i
].bmap
->eq
[k
], 1 + total
);
1846 if (type
== isl_ineq_error
)
1847 return isl_change_error
;
1848 if (type
!= isl_ineq_redundant
)
1849 return isl_change_none
;
1853 for (k
= 0; k
< info
[i
].bmap
->n_ineq
; ++k
) {
1854 enum isl_ineq_type type
;
1856 if (info
[i
].ineq
[k
] != STATUS_CUT
)
1859 type
= type_of_relaxed(info
[j
].tab
, info
[i
].bmap
->ineq
[k
]);
1860 if (type
== isl_ineq_error
)
1861 return isl_change_error
;
1862 if (type
!= isl_ineq_redundant
)
1863 return isl_change_none
;
1866 return wrap_in_facets(i
, j
, n
, info
);
1869 /* Check if either i or j has only cut constraints that can
1870 * be used to wrap in (a facet of) the other basic set.
1871 * if so, replace the pair by their union.
1873 static enum isl_change
check_wrap(int i
, int j
, struct isl_coalesce_info
*info
)
1875 enum isl_change change
= isl_change_none
;
1877 change
= can_wrap_in_set(i
, j
, info
);
1878 if (change
!= isl_change_none
)
1881 change
= can_wrap_in_set(j
, i
, info
);
1885 /* Check if all inequality constraints of "i" that cut "j" cease
1886 * to be cut constraints if they are relaxed by one.
1887 * If so, collect the cut constraints in "list".
1888 * The caller is responsible for allocating "list".
1890 static isl_bool
all_cut_by_one(int i
, int j
, struct isl_coalesce_info
*info
,
1896 for (l
= 0; l
< info
[i
].bmap
->n_ineq
; ++l
) {
1897 enum isl_ineq_type type
;
1899 if (info
[i
].ineq
[l
] != STATUS_CUT
)
1901 type
= type_of_relaxed(info
[j
].tab
, info
[i
].bmap
->ineq
[l
]);
1902 if (type
== isl_ineq_error
)
1903 return isl_bool_error
;
1904 if (type
!= isl_ineq_redundant
)
1905 return isl_bool_false
;
1909 return isl_bool_true
;
1912 /* Given two basic maps such that "j" has at least one equality constraint
1913 * that is adjacent to an inequality constraint of "i" and such that "i" has
1914 * exactly one inequality constraint that is adjacent to an equality
1915 * constraint of "j", check whether "i" can be extended to include "j" or
1916 * whether "j" can be wrapped into "i".
1917 * All remaining constraints of "i" and "j" are assumed to be valid
1918 * or cut constraints of the other basic map.
1919 * However, none of the equality constraints of "i" are cut constraints.
1921 * If "i" has any "cut" inequality constraints, then check if relaxing
1922 * each of them by one is sufficient for them to become valid.
1923 * If so, check if the inequality constraint adjacent to an equality
1924 * constraint of "j" along with all these cut constraints
1925 * can be relaxed by one to contain exactly "j".
1926 * Otherwise, or if this fails, check if "j" can be wrapped into "i".
1928 static enum isl_change
check_single_adj_eq(int i
, int j
,
1929 struct isl_coalesce_info
*info
)
1931 enum isl_change change
= isl_change_none
;
1938 n_cut
= count_ineq(&info
[i
], STATUS_CUT
);
1940 k
= find_ineq(&info
[i
], STATUS_ADJ_EQ
);
1943 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
1944 relax
= isl_calloc_array(ctx
, int, 1 + n_cut
);
1946 return isl_change_error
;
1948 try_relax
= all_cut_by_one(i
, j
, info
, relax
+ 1);
1950 change
= isl_change_error
;
1952 try_relax
= isl_bool_true
;
1955 if (try_relax
&& change
== isl_change_none
)
1956 change
= is_relaxed_extension(i
, j
, 1 + n_cut
, relax
, info
);
1959 if (change
!= isl_change_none
)
1962 change
= can_wrap_in_facet(i
, j
, k
, info
, n_cut
> 0);
1967 /* At least one of the basic maps has an equality that is adjacent
1968 * to an inequality. Make sure that only one of the basic maps has
1969 * such an equality and that the other basic map has exactly one
1970 * inequality adjacent to an equality.
1971 * If the other basic map does not have such an inequality, then
1972 * check if all its constraints are either valid or cut constraints
1973 * and, if so, try wrapping in the first map into the second.
1974 * Otherwise, try to extend one basic map with the other or
1975 * wrap one basic map in the other.
1977 static enum isl_change
check_adj_eq(int i
, int j
,
1978 struct isl_coalesce_info
*info
)
1980 if (any_eq(&info
[i
], STATUS_ADJ_INEQ
) &&
1981 any_eq(&info
[j
], STATUS_ADJ_INEQ
))
1982 /* ADJ EQ TOO MANY */
1983 return isl_change_none
;
1985 if (any_eq(&info
[i
], STATUS_ADJ_INEQ
))
1986 return check_adj_eq(j
, i
, info
);
1988 /* j has an equality adjacent to an inequality in i */
1990 if (count_ineq(&info
[i
], STATUS_ADJ_EQ
) != 1) {
1991 if (all_valid_or_cut(&info
[i
]))
1992 return can_wrap_in_set(i
, j
, info
);
1993 return isl_change_none
;
1995 if (any_eq(&info
[i
], STATUS_CUT
))
1996 return isl_change_none
;
1997 if (any_ineq(&info
[j
], STATUS_ADJ_EQ
) ||
1998 any_ineq(&info
[i
], STATUS_ADJ_INEQ
) ||
1999 any_ineq(&info
[j
], STATUS_ADJ_INEQ
))
2000 /* ADJ EQ TOO MANY */
2001 return isl_change_none
;
2003 return check_single_adj_eq(i
, j
, info
);
2006 /* Disjunct "j" lies on a hyperplane that is adjacent to disjunct "i".
2007 * In particular, disjunct "i" has an inequality constraint that is adjacent
2008 * to a (combination of) equality constraint(s) of disjunct "j",
2009 * but disjunct "j" has no explicit equality constraint adjacent
2010 * to an inequality constraint of disjunct "i".
2012 * Disjunct "i" is already known not to have any equality constraints
2013 * that are adjacent to an equality or inequality constraint.
2014 * Check that, other than the inequality constraint mentioned above,
2015 * all other constraints of disjunct "i" are valid for disjunct "j".
2016 * If so, try and wrap in disjunct "j".
2018 static enum isl_change
check_ineq_adj_eq(int i
, int j
,
2019 struct isl_coalesce_info
*info
)
2023 if (any_eq(&info
[i
], STATUS_CUT
))
2024 return isl_change_none
;
2025 if (any_ineq(&info
[i
], STATUS_CUT
))
2026 return isl_change_none
;
2027 if (any_ineq(&info
[i
], STATUS_ADJ_INEQ
))
2028 return isl_change_none
;
2029 if (count_ineq(&info
[i
], STATUS_ADJ_EQ
) != 1)
2030 return isl_change_none
;
2032 k
= find_ineq(&info
[i
], STATUS_ADJ_EQ
);
2034 return can_wrap_in_facet(i
, j
, k
, info
, 0);
2037 /* The two basic maps lie on adjacent hyperplanes. In particular,
2038 * basic map "i" has an equality that lies parallel to basic map "j".
2039 * Check if we can wrap the facets around the parallel hyperplanes
2040 * to include the other set.
2042 * We perform basically the same operations as can_wrap_in_facet,
2043 * except that we don't need to select a facet of one of the sets.
2049 * If there is more than one equality of "i" adjacent to an equality of "j",
2050 * then the result will satisfy one or more equalities that are a linear
2051 * combination of these equalities. These will be encoded as pairs
2052 * of inequalities in the wrapping constraints and need to be made
2055 static enum isl_change
check_eq_adj_eq(int i
, int j
,
2056 struct isl_coalesce_info
*info
)
2059 enum isl_change change
= isl_change_none
;
2060 int detect_equalities
= 0;
2061 struct isl_wraps wraps
;
2064 struct isl_set
*set_i
= NULL
;
2065 struct isl_set
*set_j
= NULL
;
2066 struct isl_vec
*bound
= NULL
;
2067 isl_size total
= isl_basic_map_dim(info
[i
].bmap
, isl_dim_all
);
2070 return isl_change_error
;
2071 if (count_eq(&info
[i
], STATUS_ADJ_EQ
) != 1)
2072 detect_equalities
= 1;
2074 k
= find_eq(&info
[i
], STATUS_ADJ_EQ
);
2076 set_i
= set_from_updated_bmap(info
[i
].bmap
, info
[i
].tab
);
2077 set_j
= set_from_updated_bmap(info
[j
].bmap
, info
[j
].tab
);
2078 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
2079 mat
= isl_mat_alloc(ctx
, 2 * (info
[i
].bmap
->n_eq
+ info
[j
].bmap
->n_eq
) +
2080 info
[i
].bmap
->n_ineq
+ info
[j
].bmap
->n_ineq
,
2082 if (wraps_init(&wraps
, mat
, info
, i
, j
) < 0)
2084 bound
= isl_vec_alloc(ctx
, 1 + total
);
2085 if (!set_i
|| !set_j
|| !bound
)
2089 isl_seq_neg(bound
->el
, info
[i
].bmap
->eq
[k
/ 2], 1 + total
);
2091 isl_seq_cpy(bound
->el
, info
[i
].bmap
->eq
[k
/ 2], 1 + total
);
2092 isl_int_add_ui(bound
->el
[0], bound
->el
[0], 1);
2094 isl_seq_cpy(wraps
.mat
->row
[0], bound
->el
, 1 + total
);
2095 wraps
.mat
->n_row
= 1;
2097 if (add_wraps(&wraps
, &info
[j
], bound
->el
, set_i
) < 0)
2099 if (!wraps
.mat
->n_row
)
2102 isl_int_sub_ui(bound
->el
[0], bound
->el
[0], 1);
2103 isl_seq_neg(bound
->el
, bound
->el
, 1 + total
);
2105 isl_seq_cpy(wraps
.mat
->row
[wraps
.mat
->n_row
], bound
->el
, 1 + total
);
2108 if (add_wraps(&wraps
, &info
[i
], bound
->el
, set_j
) < 0)
2110 if (!wraps
.mat
->n_row
)
2113 change
= fuse(i
, j
, info
, wraps
.mat
, detect_equalities
, 0);
2116 error
: change
= isl_change_error
;
2121 isl_set_free(set_i
);
2122 isl_set_free(set_j
);
2123 isl_vec_free(bound
);
2128 /* Initialize the "eq" and "ineq" fields of "info".
2130 static void init_status(struct isl_coalesce_info
*info
)
2132 info
->eq
= info
->ineq
= NULL
;
2135 /* Set info->eq to the positions of the equalities of info->bmap
2136 * with respect to the basic map represented by "tab".
2137 * If info->eq has already been computed, then do not compute it again.
2139 static void set_eq_status_in(struct isl_coalesce_info
*info
,
2140 struct isl_tab
*tab
)
2144 info
->eq
= eq_status_in(info
->bmap
, tab
);
2147 /* Set info->ineq to the positions of the inequalities of info->bmap
2148 * with respect to the basic map represented by "tab".
2149 * If info->ineq has already been computed, then do not compute it again.
2151 static void set_ineq_status_in(struct isl_coalesce_info
*info
,
2152 struct isl_tab
*tab
)
2156 info
->ineq
= ineq_status_in(info
->bmap
, info
->tab
, tab
);
2159 /* Free the memory allocated by the "eq" and "ineq" fields of "info".
2160 * This function assumes that init_status has been called on "info" first,
2161 * after which the "eq" and "ineq" fields may or may not have been
2162 * assigned a newly allocated array.
2164 static void clear_status(struct isl_coalesce_info
*info
)
2170 /* Are all inequality constraints of the basic map represented by "info"
2171 * valid for the other basic map, except for a single constraint
2172 * that is adjacent to an inequality constraint of the other basic map?
2174 static int all_ineq_valid_or_single_adj_ineq(struct isl_coalesce_info
*info
)
2179 for (i
= 0; i
< info
->bmap
->n_ineq
; ++i
) {
2180 if (info
->ineq
[i
] == STATUS_REDUNDANT
)
2182 if (info
->ineq
[i
] == STATUS_VALID
)
2184 if (info
->ineq
[i
] != STATUS_ADJ_INEQ
)
2194 /* Basic map "i" has one or more equality constraints that separate it
2195 * from basic map "j". Check if it happens to be an extension
2197 * In particular, check that all constraints of "j" are valid for "i",
2198 * except for one inequality constraint that is adjacent
2199 * to an inequality constraints of "i".
2200 * If so, check for "i" being an extension of "j" by calling
2201 * is_adj_ineq_extension.
2203 * Clean up the memory allocated for keeping track of the status
2204 * of the constraints before returning.
2206 static enum isl_change
separating_equality(int i
, int j
,
2207 struct isl_coalesce_info
*info
)
2209 enum isl_change change
= isl_change_none
;
2211 if (all(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_VALID
) &&
2212 all_ineq_valid_or_single_adj_ineq(&info
[j
]))
2213 change
= is_adj_ineq_extension(j
, i
, info
);
2215 clear_status(&info
[i
]);
2216 clear_status(&info
[j
]);
2220 /* Check if the union of the given pair of basic maps
2221 * can be represented by a single basic map.
2222 * If so, replace the pair by the single basic map and return
2223 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
2224 * Otherwise, return isl_change_none.
2225 * The two basic maps are assumed to live in the same local space.
2226 * The "eq" and "ineq" fields of info[i] and info[j] are assumed
2227 * to have been initialized by the caller, either to NULL or
2228 * to valid information.
2230 * We first check the effect of each constraint of one basic map
2231 * on the other basic map.
2232 * The constraint may be
2233 * redundant the constraint is redundant in its own
2234 * basic map and should be ignore and removed
2236 * valid all (integer) points of the other basic map
2237 * satisfy the constraint
2238 * separate no (integer) point of the other basic map
2239 * satisfies the constraint
2240 * cut some but not all points of the other basic map
2241 * satisfy the constraint
2242 * adj_eq the given constraint is adjacent (on the outside)
2243 * to an equality of the other basic map
2244 * adj_ineq the given constraint is adjacent (on the outside)
2245 * to an inequality of the other basic map
2247 * We consider seven cases in which we can replace the pair by a single
2248 * basic map. We ignore all "redundant" constraints.
2250 * 1. all constraints of one basic map are valid
2251 * => the other basic map is a subset and can be removed
2253 * 2. all constraints of both basic maps are either "valid" or "cut"
2254 * and the facets corresponding to the "cut" constraints
2255 * of one of the basic maps lies entirely inside the other basic map
2256 * => the pair can be replaced by a basic map consisting
2257 * of the valid constraints in both basic maps
2259 * 3. there is a single pair of adjacent inequalities
2260 * (all other constraints are "valid")
2261 * => the pair can be replaced by a basic map consisting
2262 * of the valid constraints in both basic maps
2264 * 4. one basic map has a single adjacent inequality, while the other
2265 * constraints are "valid". The other basic map has some
2266 * "cut" constraints, but replacing the adjacent inequality by
2267 * its opposite and adding the valid constraints of the other
2268 * basic map results in a subset of the other basic map
2269 * => the pair can be replaced by a basic map consisting
2270 * of the valid constraints in both basic maps
2272 * 5. there is a single adjacent pair of an inequality and an equality,
2273 * the other constraints of the basic map containing the inequality are
2274 * "valid". Moreover, if the inequality the basic map is relaxed
2275 * and then turned into an equality, then resulting facet lies
2276 * entirely inside the other basic map
2277 * => the pair can be replaced by the basic map containing
2278 * the inequality, with the inequality relaxed.
2280 * 6. there is a single inequality adjacent to an equality,
2281 * the other constraints of the basic map containing the inequality are
2282 * "valid". Moreover, the facets corresponding to both
2283 * the inequality and the equality can be wrapped around their
2284 * ridges to include the other basic map
2285 * => the pair can be replaced by a basic map consisting
2286 * of the valid constraints in both basic maps together
2287 * with all wrapping constraints
2289 * 7. one of the basic maps extends beyond the other by at most one.
2290 * Moreover, the facets corresponding to the cut constraints and
2291 * the pieces of the other basic map at offset one from these cut
2292 * constraints can be wrapped around their ridges to include
2293 * the union of the two basic maps
2294 * => the pair can be replaced by a basic map consisting
2295 * of the valid constraints in both basic maps together
2296 * with all wrapping constraints
2298 * 8. the two basic maps live in adjacent hyperplanes. In principle
2299 * such sets can always be combined through wrapping, but we impose
2300 * that there is only one such pair, to avoid overeager coalescing.
2302 * Throughout the computation, we maintain a collection of tableaus
2303 * corresponding to the basic maps. When the basic maps are dropped
2304 * or combined, the tableaus are modified accordingly.
2306 static enum isl_change
coalesce_local_pair_reuse(int i
, int j
,
2307 struct isl_coalesce_info
*info
)
2309 enum isl_change change
= isl_change_none
;
2311 set_ineq_status_in(&info
[i
], info
[j
].tab
);
2312 if (info
[i
].bmap
->n_ineq
&& !info
[i
].ineq
)
2314 if (any_ineq(&info
[i
], STATUS_ERROR
))
2316 if (any_ineq(&info
[i
], STATUS_SEPARATE
))
2319 set_ineq_status_in(&info
[j
], info
[i
].tab
);
2320 if (info
[j
].bmap
->n_ineq
&& !info
[j
].ineq
)
2322 if (any_ineq(&info
[j
], STATUS_ERROR
))
2324 if (any_ineq(&info
[j
], STATUS_SEPARATE
))
2327 set_eq_status_in(&info
[i
], info
[j
].tab
);
2328 if (info
[i
].bmap
->n_eq
&& !info
[i
].eq
)
2330 if (any_eq(&info
[i
], STATUS_ERROR
))
2333 set_eq_status_in(&info
[j
], info
[i
].tab
);
2334 if (info
[j
].bmap
->n_eq
&& !info
[j
].eq
)
2336 if (any_eq(&info
[j
], STATUS_ERROR
))
2339 if (any_eq(&info
[i
], STATUS_SEPARATE
))
2340 return separating_equality(i
, j
, info
);
2341 if (any_eq(&info
[j
], STATUS_SEPARATE
))
2342 return separating_equality(j
, i
, info
);
2344 if (all(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_VALID
) &&
2345 all(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_VALID
)) {
2347 change
= isl_change_drop_second
;
2348 } else if (all(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_VALID
) &&
2349 all(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_VALID
)) {
2351 change
= isl_change_drop_first
;
2352 } else if (any_eq(&info
[i
], STATUS_ADJ_EQ
)) {
2353 change
= check_eq_adj_eq(i
, j
, info
);
2354 } else if (any_eq(&info
[j
], STATUS_ADJ_EQ
)) {
2355 change
= check_eq_adj_eq(j
, i
, info
);
2356 } else if (any_eq(&info
[i
], STATUS_ADJ_INEQ
) ||
2357 any_eq(&info
[j
], STATUS_ADJ_INEQ
)) {
2358 change
= check_adj_eq(i
, j
, info
);
2359 } else if (any_ineq(&info
[i
], STATUS_ADJ_EQ
)) {
2360 change
= check_ineq_adj_eq(i
, j
, info
);
2361 } else if (any_ineq(&info
[j
], STATUS_ADJ_EQ
)) {
2362 change
= check_ineq_adj_eq(j
, i
, info
);
2363 } else if (any_ineq(&info
[i
], STATUS_ADJ_INEQ
) ||
2364 any_ineq(&info
[j
], STATUS_ADJ_INEQ
)) {
2365 change
= check_adj_ineq(i
, j
, info
);
2367 if (!any_eq(&info
[i
], STATUS_CUT
) &&
2368 !any_eq(&info
[j
], STATUS_CUT
))
2369 change
= check_facets(i
, j
, info
);
2370 if (change
== isl_change_none
)
2371 change
= check_wrap(i
, j
, info
);
2375 clear_status(&info
[i
]);
2376 clear_status(&info
[j
]);
2379 clear_status(&info
[i
]);
2380 clear_status(&info
[j
]);
2381 return isl_change_error
;
2384 /* Check if the union of the given pair of basic maps
2385 * can be represented by a single basic map.
2386 * If so, replace the pair by the single basic map and return
2387 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
2388 * Otherwise, return isl_change_none.
2389 * The two basic maps are assumed to live in the same local space.
2391 static enum isl_change
coalesce_local_pair(int i
, int j
,
2392 struct isl_coalesce_info
*info
)
2394 init_status(&info
[i
]);
2395 init_status(&info
[j
]);
2396 return coalesce_local_pair_reuse(i
, j
, info
);
2399 /* Shift the integer division at position "div" of the basic map
2400 * represented by "info" by "shift".
2402 * That is, if the integer division has the form
2406 * then replace it by
2408 * floor((f(x) + shift * d)/d) - shift
2410 static isl_stat
shift_div(struct isl_coalesce_info
*info
, int div
,
2413 isl_size total
, n_div
;
2415 info
->bmap
= isl_basic_map_shift_div(info
->bmap
, div
, 0, shift
);
2417 return isl_stat_error
;
2419 total
= isl_basic_map_dim(info
->bmap
, isl_dim_all
);
2420 n_div
= isl_basic_map_dim(info
->bmap
, isl_dim_div
);
2421 if (total
< 0 || n_div
< 0)
2422 return isl_stat_error
;
2424 if (isl_tab_shift_var(info
->tab
, total
+ div
, shift
) < 0)
2425 return isl_stat_error
;
2430 /* If the integer division at position "div" is defined by an equality,
2431 * i.e., a stride constraint, then change the integer division expression
2432 * to have a constant term equal to zero.
2434 * Let the equality constraint be
2438 * The integer division expression is then typically of the form
2440 * a = floor((-f - c')/m)
2442 * The integer division is first shifted by t = floor(c/m),
2443 * turning the equality constraint into
2445 * c - m floor(c/m) + f + m a' = 0
2449 * (c mod m) + f + m a' = 0
2453 * a' = (-f - (c mod m))/m = floor((-f)/m)
2455 * because a' is an integer and 0 <= (c mod m) < m.
2456 * The constant term of a' can therefore be zeroed out,
2457 * but only if the integer division expression is of the expected form.
2459 static isl_stat
normalize_stride_div(struct isl_coalesce_info
*info
, int div
)
2461 isl_bool defined
, valid
;
2464 isl_int shift
, stride
;
2466 defined
= isl_basic_map_has_defining_equality(info
->bmap
, isl_dim_div
,
2469 return isl_stat_error
;
2473 return isl_stat_error
;
2474 valid
= isl_constraint_is_div_equality(c
, div
);
2475 isl_int_init(shift
);
2476 isl_int_init(stride
);
2477 isl_constraint_get_constant(c
, &shift
);
2478 isl_constraint_get_coefficient(c
, isl_dim_div
, div
, &stride
);
2479 isl_int_fdiv_q(shift
, shift
, stride
);
2480 r
= shift_div(info
, div
, shift
);
2481 isl_int_clear(stride
);
2482 isl_int_clear(shift
);
2483 isl_constraint_free(c
);
2484 if (r
< 0 || valid
< 0)
2485 return isl_stat_error
;
2488 info
->bmap
= isl_basic_map_set_div_expr_constant_num_si_inplace(
2489 info
->bmap
, div
, 0);
2491 return isl_stat_error
;
2495 /* The basic maps represented by "info1" and "info2" are known
2496 * to have the same number of integer divisions.
2497 * Check if pairs of integer divisions are equal to each other
2498 * despite the fact that they differ by a rational constant.
2500 * In particular, look for any pair of integer divisions that
2501 * only differ in their constant terms.
2502 * If either of these integer divisions is defined
2503 * by stride constraints, then modify it to have a zero constant term.
2504 * If both are defined by stride constraints then in the end they will have
2505 * the same (zero) constant term.
2507 static isl_stat
harmonize_stride_divs(struct isl_coalesce_info
*info1
,
2508 struct isl_coalesce_info
*info2
)
2513 n
= isl_basic_map_dim(info1
->bmap
, isl_dim_div
);
2515 return isl_stat_error
;
2516 for (i
= 0; i
< n
; ++i
) {
2517 isl_bool known
, harmonize
;
2519 known
= isl_basic_map_div_is_known(info1
->bmap
, i
);
2520 if (known
>= 0 && known
)
2521 known
= isl_basic_map_div_is_known(info2
->bmap
, i
);
2523 return isl_stat_error
;
2526 harmonize
= isl_basic_map_equal_div_expr_except_constant(
2527 info1
->bmap
, i
, info2
->bmap
, i
);
2529 return isl_stat_error
;
2532 if (normalize_stride_div(info1
, i
) < 0)
2533 return isl_stat_error
;
2534 if (normalize_stride_div(info2
, i
) < 0)
2535 return isl_stat_error
;
2541 /* If "shift" is an integer constant, then shift the integer division
2542 * at position "div" of the basic map represented by "info" by "shift".
2543 * If "shift" is not an integer constant, then do nothing.
2544 * If "shift" is equal to zero, then no shift needs to be performed either.
2546 * That is, if the integer division has the form
2550 * then replace it by
2552 * floor((f(x) + shift * d)/d) - shift
2554 static isl_stat
shift_if_cst_int(struct isl_coalesce_info
*info
, int div
,
2555 __isl_keep isl_aff
*shift
)
2562 cst
= isl_aff_is_cst(shift
);
2563 if (cst
< 0 || !cst
)
2564 return cst
< 0 ? isl_stat_error
: isl_stat_ok
;
2566 c
= isl_aff_get_constant_val(shift
);
2567 cst
= isl_val_is_int(c
);
2568 if (cst
>= 0 && cst
)
2569 cst
= isl_bool_not(isl_val_is_zero(c
));
2570 if (cst
< 0 || !cst
) {
2572 return cst
< 0 ? isl_stat_error
: isl_stat_ok
;
2576 r
= isl_val_get_num_isl_int(c
, &d
);
2578 r
= shift_div(info
, div
, d
);
2586 /* Check if some of the divs in the basic map represented by "info1"
2587 * are shifts of the corresponding divs in the basic map represented
2588 * by "info2", taking into account the equality constraints "eq1" of "info1"
2589 * and "eq2" of "info2". If so, align them with those of "info2".
2590 * "info1" and "info2" are assumed to have the same number
2591 * of integer divisions.
2593 * An integer division is considered to be a shift of another integer
2594 * division if, after simplification with respect to the equality
2595 * constraints of the other basic map, one is equal to the other
2598 * In particular, for each pair of integer divisions, if both are known,
2599 * have the same denominator and are not already equal to each other,
2600 * simplify each with respect to the equality constraints
2601 * of the other basic map. If the difference is an integer constant,
2602 * then move this difference outside.
2603 * That is, if, after simplification, one integer division is of the form
2605 * floor((f(x) + c_1)/d)
2607 * while the other is of the form
2609 * floor((f(x) + c_2)/d)
2611 * and n = (c_2 - c_1)/d is an integer, then replace the first
2612 * integer division by
2614 * floor((f_1(x) + c_1 + n * d)/d) - n,
2616 * where floor((f_1(x) + c_1 + n * d)/d) = floor((f2(x) + c_2)/d)
2617 * after simplification with respect to the equality constraints.
2619 static isl_stat
harmonize_divs_with_hulls(struct isl_coalesce_info
*info1
,
2620 struct isl_coalesce_info
*info2
, __isl_keep isl_basic_set
*eq1
,
2621 __isl_keep isl_basic_set
*eq2
)
2625 isl_local_space
*ls1
, *ls2
;
2627 total
= isl_basic_map_dim(info1
->bmap
, isl_dim_all
);
2629 return isl_stat_error
;
2630 ls1
= isl_local_space_wrap(isl_basic_map_get_local_space(info1
->bmap
));
2631 ls2
= isl_local_space_wrap(isl_basic_map_get_local_space(info2
->bmap
));
2632 for (i
= 0; i
< info1
->bmap
->n_div
; ++i
) {
2634 isl_aff
*div1
, *div2
;
2636 if (!isl_local_space_div_is_known(ls1
, i
) ||
2637 !isl_local_space_div_is_known(ls2
, i
))
2639 if (isl_int_ne(info1
->bmap
->div
[i
][0], info2
->bmap
->div
[i
][0]))
2641 if (isl_seq_eq(info1
->bmap
->div
[i
] + 1,
2642 info2
->bmap
->div
[i
] + 1, 1 + total
))
2644 div1
= isl_local_space_get_div(ls1
, i
);
2645 div2
= isl_local_space_get_div(ls2
, i
);
2646 div1
= isl_aff_substitute_equalities(div1
,
2647 isl_basic_set_copy(eq2
));
2648 div2
= isl_aff_substitute_equalities(div2
,
2649 isl_basic_set_copy(eq1
));
2650 div2
= isl_aff_sub(div2
, div1
);
2651 r
= shift_if_cst_int(info1
, i
, div2
);
2656 isl_local_space_free(ls1
);
2657 isl_local_space_free(ls2
);
2659 if (i
< info1
->bmap
->n_div
)
2660 return isl_stat_error
;
2664 /* Check if some of the divs in the basic map represented by "info1"
2665 * are shifts of the corresponding divs in the basic map represented
2666 * by "info2". If so, align them with those of "info2".
2667 * Only do this if "info1" and "info2" have the same number
2668 * of integer divisions.
2670 * An integer division is considered to be a shift of another integer
2671 * division if, after simplification with respect to the equality
2672 * constraints of the other basic map, one is equal to the other
2675 * First check if pairs of integer divisions are equal to each other
2676 * despite the fact that they differ by a rational constant.
2677 * If so, try and arrange for them to have the same constant term.
2679 * Then, extract the equality constraints and continue with
2680 * harmonize_divs_with_hulls.
2682 * If the equality constraints of both basic maps are the same,
2683 * then there is no need to perform any shifting since
2684 * the coefficients of the integer divisions should have been
2685 * reduced in the same way.
2687 static isl_stat
harmonize_divs(struct isl_coalesce_info
*info1
,
2688 struct isl_coalesce_info
*info2
)
2691 isl_basic_map
*bmap1
, *bmap2
;
2692 isl_basic_set
*eq1
, *eq2
;
2695 if (!info1
->bmap
|| !info2
->bmap
)
2696 return isl_stat_error
;
2698 if (info1
->bmap
->n_div
!= info2
->bmap
->n_div
)
2700 if (info1
->bmap
->n_div
== 0)
2703 if (harmonize_stride_divs(info1
, info2
) < 0)
2704 return isl_stat_error
;
2706 bmap1
= isl_basic_map_copy(info1
->bmap
);
2707 bmap2
= isl_basic_map_copy(info2
->bmap
);
2708 eq1
= isl_basic_map_wrap(isl_basic_map_plain_affine_hull(bmap1
));
2709 eq2
= isl_basic_map_wrap(isl_basic_map_plain_affine_hull(bmap2
));
2710 equal
= isl_basic_set_plain_is_equal(eq1
, eq2
);
2716 r
= harmonize_divs_with_hulls(info1
, info2
, eq1
, eq2
);
2717 isl_basic_set_free(eq1
);
2718 isl_basic_set_free(eq2
);
2723 /* Do the two basic maps live in the same local space, i.e.,
2724 * do they have the same (known) divs?
2725 * If either basic map has any unknown divs, then we can only assume
2726 * that they do not live in the same local space.
2728 static isl_bool
same_divs(__isl_keep isl_basic_map
*bmap1
,
2729 __isl_keep isl_basic_map
*bmap2
)
2735 if (!bmap1
|| !bmap2
)
2736 return isl_bool_error
;
2737 if (bmap1
->n_div
!= bmap2
->n_div
)
2738 return isl_bool_false
;
2740 if (bmap1
->n_div
== 0)
2741 return isl_bool_true
;
2743 known
= isl_basic_map_divs_known(bmap1
);
2744 if (known
< 0 || !known
)
2746 known
= isl_basic_map_divs_known(bmap2
);
2747 if (known
< 0 || !known
)
2750 total
= isl_basic_map_dim(bmap1
, isl_dim_all
);
2752 return isl_bool_error
;
2753 for (i
= 0; i
< bmap1
->n_div
; ++i
)
2754 if (!isl_seq_eq(bmap1
->div
[i
], bmap2
->div
[i
], 2 + total
))
2755 return isl_bool_false
;
2757 return isl_bool_true
;
2760 /* Assuming that "tab" contains the equality constraints and
2761 * the initial inequality constraints of "bmap", copy the remaining
2762 * inequality constraints of "bmap" to "Tab".
2764 static isl_stat
copy_ineq(struct isl_tab
*tab
, __isl_keep isl_basic_map
*bmap
)
2769 return isl_stat_error
;
2771 n_ineq
= tab
->n_con
- tab
->n_eq
;
2772 for (i
= n_ineq
; i
< bmap
->n_ineq
; ++i
)
2773 if (isl_tab_add_ineq(tab
, bmap
->ineq
[i
]) < 0)
2774 return isl_stat_error
;
2779 /* Description of an integer division that is added
2780 * during an expansion.
2781 * "pos" is the position of the corresponding variable.
2782 * "cst" indicates whether this integer division has a fixed value.
2783 * "val" contains the fixed value, if the value is fixed.
2785 struct isl_expanded
{
2791 /* For each of the "n" integer division variables "expanded",
2792 * if the variable has a fixed value, then add two inequality
2793 * constraints expressing the fixed value.
2794 * Otherwise, add the corresponding div constraints.
2795 * The caller is responsible for removing the div constraints
2796 * that it added for all these "n" integer divisions.
2798 * The div constraints and the pair of inequality constraints
2799 * forcing the fixed value cannot both be added for a given variable
2800 * as the combination may render some of the original constraints redundant.
2801 * These would then be ignored during the coalescing detection,
2802 * while they could remain in the fused result.
2804 * The two added inequality constraints are
2809 * with "a" the variable and "v" its fixed value.
2810 * The facet corresponding to one of these two constraints is selected
2811 * in the tableau to ensure that the pair of inequality constraints
2812 * is treated as an equality constraint.
2814 * The information in info->ineq is thrown away because it was
2815 * computed in terms of div constraints, while some of those
2816 * have now been replaced by these pairs of inequality constraints.
2818 static isl_stat
fix_constant_divs(struct isl_coalesce_info
*info
,
2819 int n
, struct isl_expanded
*expanded
)
2825 o_div
= isl_basic_map_offset(info
->bmap
, isl_dim_div
) - 1;
2826 ineq
= isl_vec_alloc(isl_tab_get_ctx(info
->tab
), 1 + info
->tab
->n_var
);
2828 return isl_stat_error
;
2829 isl_seq_clr(ineq
->el
+ 1, info
->tab
->n_var
);
2831 for (i
= 0; i
< n
; ++i
) {
2832 if (!expanded
[i
].cst
) {
2833 info
->bmap
= isl_basic_map_extend_constraints(
2835 info
->bmap
= isl_basic_map_add_div_constraints(
2836 info
->bmap
, expanded
[i
].pos
- o_div
);
2838 isl_int_set_si(ineq
->el
[1 + expanded
[i
].pos
], -1);
2839 isl_int_set(ineq
->el
[0], expanded
[i
].val
);
2840 info
->bmap
= isl_basic_map_add_ineq(info
->bmap
,
2842 isl_int_set_si(ineq
->el
[1 + expanded
[i
].pos
], 1);
2843 isl_int_neg(ineq
->el
[0], expanded
[i
].val
);
2844 info
->bmap
= isl_basic_map_add_ineq(info
->bmap
,
2846 isl_int_set_si(ineq
->el
[1 + expanded
[i
].pos
], 0);
2848 if (copy_ineq(info
->tab
, info
->bmap
) < 0)
2850 if (expanded
[i
].cst
&&
2851 isl_tab_select_facet(info
->tab
, info
->tab
->n_con
- 1) < 0)
2860 return i
< n
? isl_stat_error
: isl_stat_ok
;
2863 /* Insert the "n" integer division variables "expanded"
2864 * into info->tab and info->bmap and
2865 * update info->ineq with respect to the redundant constraints
2866 * in the resulting tableau.
2867 * "bmap" contains the result of this insertion in info->bmap,
2868 * while info->bmap is the original version
2869 * of "bmap", i.e., the one that corresponds to the current
2870 * state of info->tab. The number of constraints in info->bmap
2871 * is assumed to be the same as the number of constraints
2872 * in info->tab. This is required to be able to detect
2873 * the extra constraints in "bmap".
2875 * In particular, introduce extra variables corresponding
2876 * to the extra integer divisions and add the div constraints
2877 * that were added to "bmap" after info->tab was created
2879 * Furthermore, check if these extra integer divisions happen
2880 * to attain a fixed integer value in info->tab.
2881 * If so, replace the corresponding div constraints by pairs
2882 * of inequality constraints that fix these
2883 * integer divisions to their single integer values.
2884 * Replace info->bmap by "bmap" to match the changes to info->tab.
2885 * info->ineq was computed without a tableau and therefore
2886 * does not take into account the redundant constraints
2887 * in the tableau. Mark them here.
2888 * There is no need to check the newly added div constraints
2889 * since they cannot be redundant.
2890 * The redundancy check is not performed when constants have been discovered
2891 * since info->ineq is completely thrown away in this case.
2893 static isl_stat
tab_insert_divs(struct isl_coalesce_info
*info
,
2894 int n
, struct isl_expanded
*expanded
, __isl_take isl_basic_map
*bmap
)
2898 struct isl_tab_undo
*snap
;
2902 return isl_stat_error
;
2903 if (info
->bmap
->n_eq
+ info
->bmap
->n_ineq
!= info
->tab
->n_con
)
2904 isl_die(isl_basic_map_get_ctx(bmap
), isl_error_internal
,
2905 "original tableau does not correspond "
2906 "to original basic map", goto error
);
2908 if (isl_tab_extend_vars(info
->tab
, n
) < 0)
2910 if (isl_tab_extend_cons(info
->tab
, 2 * n
) < 0)
2913 for (i
= 0; i
< n
; ++i
) {
2914 if (isl_tab_insert_var(info
->tab
, expanded
[i
].pos
) < 0)
2918 snap
= isl_tab_snap(info
->tab
);
2920 n_ineq
= info
->tab
->n_con
- info
->tab
->n_eq
;
2921 if (copy_ineq(info
->tab
, bmap
) < 0)
2924 isl_basic_map_free(info
->bmap
);
2928 for (i
= 0; i
< n
; ++i
) {
2929 expanded
[i
].cst
= isl_tab_is_constant(info
->tab
,
2930 expanded
[i
].pos
, &expanded
[i
].val
);
2931 if (expanded
[i
].cst
< 0)
2932 return isl_stat_error
;
2933 if (expanded
[i
].cst
)
2938 if (isl_tab_rollback(info
->tab
, snap
) < 0)
2939 return isl_stat_error
;
2940 info
->bmap
= isl_basic_map_cow(info
->bmap
);
2941 if (isl_basic_map_free_inequality(info
->bmap
, 2 * n
) < 0)
2942 return isl_stat_error
;
2944 return fix_constant_divs(info
, n
, expanded
);
2947 n_eq
= info
->bmap
->n_eq
;
2948 for (i
= 0; i
< n_ineq
; ++i
) {
2949 if (isl_tab_is_redundant(info
->tab
, n_eq
+ i
))
2950 info
->ineq
[i
] = STATUS_REDUNDANT
;
2955 isl_basic_map_free(bmap
);
2956 return isl_stat_error
;
2959 /* Expand info->tab and info->bmap in the same way "bmap" was expanded
2960 * in isl_basic_map_expand_divs using the expansion "exp" and
2961 * update info->ineq with respect to the redundant constraints
2962 * in the resulting tableau. info->bmap is the original version
2963 * of "bmap", i.e., the one that corresponds to the current
2964 * state of info->tab. The number of constraints in info->bmap
2965 * is assumed to be the same as the number of constraints
2966 * in info->tab. This is required to be able to detect
2967 * the extra constraints in "bmap".
2969 * Extract the positions where extra local variables are introduced
2970 * from "exp" and call tab_insert_divs.
2972 static isl_stat
expand_tab(struct isl_coalesce_info
*info
, int *exp
,
2973 __isl_take isl_basic_map
*bmap
)
2976 struct isl_expanded
*expanded
;
2979 isl_size total
, n_div
;
2983 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
2984 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
2985 if (total
< 0 || n_div
< 0)
2986 return isl_stat_error
;
2987 pos
= total
- n_div
;
2988 extra_var
= total
- info
->tab
->n_var
;
2989 n
= n_div
- extra_var
;
2991 ctx
= isl_basic_map_get_ctx(bmap
);
2992 expanded
= isl_calloc_array(ctx
, struct isl_expanded
, extra_var
);
2993 if (extra_var
&& !expanded
)
2998 for (j
= 0; j
< n_div
; ++j
) {
2999 if (i
< n
&& exp
[i
] == j
) {
3003 expanded
[k
++].pos
= pos
+ j
;
3006 for (k
= 0; k
< extra_var
; ++k
)
3007 isl_int_init(expanded
[k
].val
);
3009 r
= tab_insert_divs(info
, extra_var
, expanded
, bmap
);
3011 for (k
= 0; k
< extra_var
; ++k
)
3012 isl_int_clear(expanded
[k
].val
);
3017 isl_basic_map_free(bmap
);
3018 return isl_stat_error
;
3021 /* Check if the union of the basic maps represented by info[i] and info[j]
3022 * can be represented by a single basic map,
3023 * after expanding the divs of info[i] to match those of info[j].
3024 * If so, replace the pair by the single basic map and return
3025 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
3026 * Otherwise, return isl_change_none.
3028 * The caller has already checked for info[j] being a subset of info[i].
3029 * If some of the divs of info[j] are unknown, then the expanded info[i]
3030 * will not have the corresponding div constraints. The other patterns
3031 * therefore cannot apply. Skip the computation in this case.
3033 * The expansion is performed using the divs "div" and expansion "exp"
3034 * computed by the caller.
3035 * info[i].bmap has already been expanded and the result is passed in
3037 * The "eq" and "ineq" fields of info[i] reflect the status of
3038 * the constraints of the expanded "bmap" with respect to info[j].tab.
3039 * However, inequality constraints that are redundant in info[i].tab
3040 * have not yet been marked as such because no tableau was available.
3042 * Replace info[i].bmap by "bmap" and expand info[i].tab as well,
3043 * updating info[i].ineq with respect to the redundant constraints.
3044 * Then try and coalesce the expanded info[i] with info[j],
3045 * reusing the information in info[i].eq and info[i].ineq.
3046 * If this does not result in any coalescing or if it results in info[j]
3047 * getting dropped (which should not happen in practice, since the case
3048 * of info[j] being a subset of info[i] has already been checked by
3049 * the caller), then revert info[i] to its original state.
3051 static enum isl_change
coalesce_expand_tab_divs(__isl_take isl_basic_map
*bmap
,
3052 int i
, int j
, struct isl_coalesce_info
*info
, __isl_keep isl_mat
*div
,
3056 isl_basic_map
*bmap_i
;
3057 struct isl_tab_undo
*snap
;
3058 enum isl_change change
= isl_change_none
;
3060 known
= isl_basic_map_divs_known(info
[j
].bmap
);
3061 if (known
< 0 || !known
) {
3062 clear_status(&info
[i
]);
3063 isl_basic_map_free(bmap
);
3064 return known
< 0 ? isl_change_error
: isl_change_none
;
3067 bmap_i
= isl_basic_map_copy(info
[i
].bmap
);
3068 snap
= isl_tab_snap(info
[i
].tab
);
3069 if (expand_tab(&info
[i
], exp
, bmap
) < 0)
3070 change
= isl_change_error
;
3072 init_status(&info
[j
]);
3073 if (change
== isl_change_none
)
3074 change
= coalesce_local_pair_reuse(i
, j
, info
);
3076 clear_status(&info
[i
]);
3077 if (change
!= isl_change_none
&& change
!= isl_change_drop_second
) {
3078 isl_basic_map_free(bmap_i
);
3080 isl_basic_map_free(info
[i
].bmap
);
3081 info
[i
].bmap
= bmap_i
;
3083 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
3084 change
= isl_change_error
;
3090 /* Check if the union of "bmap" and the basic map represented by info[j]
3091 * can be represented by a single basic map,
3092 * after expanding the divs of "bmap" to match those of info[j].
3093 * If so, replace the pair by the single basic map and return
3094 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
3095 * Otherwise, return isl_change_none.
3097 * In particular, check if the expanded "bmap" contains the basic map
3098 * represented by the tableau info[j].tab.
3099 * The expansion is performed using the divs "div" and expansion "exp"
3100 * computed by the caller.
3101 * Then we check if all constraints of the expanded "bmap" are valid for
3104 * If "i" is not equal to -1, then "bmap" is equal to info[i].bmap.
3105 * In this case, the positions of the constraints of info[i].bmap
3106 * with respect to the basic map represented by info[j] are stored
3109 * If the expanded "bmap" does not contain the basic map
3110 * represented by the tableau info[j].tab and if "i" is not -1,
3111 * i.e., if the original "bmap" is info[i].bmap, then expand info[i].tab
3112 * as well and check if that results in coalescing.
3114 static enum isl_change
coalesce_with_expanded_divs(
3115 __isl_keep isl_basic_map
*bmap
, int i
, int j
,
3116 struct isl_coalesce_info
*info
, __isl_keep isl_mat
*div
, int *exp
)
3118 enum isl_change change
= isl_change_none
;
3119 struct isl_coalesce_info info_local
, *info_i
;
3121 info_i
= i
>= 0 ? &info
[i
] : &info_local
;
3122 init_status(info_i
);
3123 bmap
= isl_basic_map_copy(bmap
);
3124 bmap
= isl_basic_map_expand_divs(bmap
, isl_mat_copy(div
), exp
);
3125 bmap
= isl_basic_map_mark_final(bmap
);
3130 info_local
.bmap
= bmap
;
3131 info_i
->eq
= eq_status_in(bmap
, info
[j
].tab
);
3132 if (bmap
->n_eq
&& !info_i
->eq
)
3134 if (any_eq(info_i
, STATUS_ERROR
))
3136 if (any_eq(info_i
, STATUS_SEPARATE
))
3139 info_i
->ineq
= ineq_status_in(bmap
, NULL
, info
[j
].tab
);
3140 if (bmap
->n_ineq
&& !info_i
->ineq
)
3142 if (any_ineq(info_i
, STATUS_ERROR
))
3144 if (any_ineq(info_i
, STATUS_SEPARATE
))
3147 if (all(info_i
->eq
, 2 * bmap
->n_eq
, STATUS_VALID
) &&
3148 all(info_i
->ineq
, bmap
->n_ineq
, STATUS_VALID
)) {
3150 change
= isl_change_drop_second
;
3153 if (change
== isl_change_none
&& i
!= -1)
3154 return coalesce_expand_tab_divs(bmap
, i
, j
, info
, div
, exp
);
3157 isl_basic_map_free(bmap
);
3158 clear_status(info_i
);
3161 isl_basic_map_free(bmap
);
3162 clear_status(info_i
);
3163 return isl_change_error
;
3166 /* Check if the union of "bmap_i" and the basic map represented by info[j]
3167 * can be represented by a single basic map,
3168 * after aligning the divs of "bmap_i" to match those of info[j].
3169 * If so, replace the pair by the single basic map and return
3170 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
3171 * Otherwise, return isl_change_none.
3173 * In particular, check if "bmap_i" contains the basic map represented by
3174 * info[j] after aligning the divs of "bmap_i" to those of info[j].
3175 * Note that this can only succeed if the number of divs of "bmap_i"
3176 * is smaller than (or equal to) the number of divs of info[j].
3178 * We first check if the divs of "bmap_i" are all known and form a subset
3179 * of those of info[j].bmap. If so, we pass control over to
3180 * coalesce_with_expanded_divs.
3182 * If "i" is not equal to -1, then "bmap" is equal to info[i].bmap.
3184 static enum isl_change
coalesce_after_aligning_divs(
3185 __isl_keep isl_basic_map
*bmap_i
, int i
, int j
,
3186 struct isl_coalesce_info
*info
)
3189 isl_mat
*div_i
, *div_j
, *div
;
3193 enum isl_change change
;
3195 known
= isl_basic_map_divs_known(bmap_i
);
3197 return isl_change_error
;
3199 return isl_change_none
;
3201 ctx
= isl_basic_map_get_ctx(bmap_i
);
3203 div_i
= isl_basic_map_get_divs(bmap_i
);
3204 div_j
= isl_basic_map_get_divs(info
[j
].bmap
);
3206 if (!div_i
|| !div_j
)
3209 exp1
= isl_alloc_array(ctx
, int, div_i
->n_row
);
3210 exp2
= isl_alloc_array(ctx
, int, div_j
->n_row
);
3211 if ((div_i
->n_row
&& !exp1
) || (div_j
->n_row
&& !exp2
))
3214 div
= isl_merge_divs(div_i
, div_j
, exp1
, exp2
);
3218 if (div
->n_row
== div_j
->n_row
)
3219 change
= coalesce_with_expanded_divs(bmap_i
,
3220 i
, j
, info
, div
, exp1
);
3222 change
= isl_change_none
;
3226 isl_mat_free(div_i
);
3227 isl_mat_free(div_j
);
3234 isl_mat_free(div_i
);
3235 isl_mat_free(div_j
);
3238 return isl_change_error
;
3241 /* Check if basic map "j" is a subset of basic map "i" after
3242 * exploiting the extra equalities of "j" to simplify the divs of "i".
3243 * If so, remove basic map "j" and return isl_change_drop_second.
3245 * If "j" does not have any equalities or if they are the same
3246 * as those of "i", then we cannot exploit them to simplify the divs.
3247 * Similarly, if there are no divs in "i", then they cannot be simplified.
3248 * If, on the other hand, the affine hulls of "i" and "j" do not intersect,
3249 * then "j" cannot be a subset of "i".
3251 * Otherwise, we intersect "i" with the affine hull of "j" and then
3252 * check if "j" is a subset of the result after aligning the divs.
3253 * If so, then "j" is definitely a subset of "i" and can be removed.
3254 * Note that if after intersection with the affine hull of "j".
3255 * "i" still has more divs than "j", then there is no way we can
3256 * align the divs of "i" to those of "j".
3258 static enum isl_change
coalesce_subset_with_equalities(int i
, int j
,
3259 struct isl_coalesce_info
*info
)
3261 isl_basic_map
*hull_i
, *hull_j
, *bmap_i
;
3263 enum isl_change change
;
3265 if (info
[j
].bmap
->n_eq
== 0)
3266 return isl_change_none
;
3267 if (info
[i
].bmap
->n_div
== 0)
3268 return isl_change_none
;
3270 hull_i
= isl_basic_map_copy(info
[i
].bmap
);
3271 hull_i
= isl_basic_map_plain_affine_hull(hull_i
);
3272 hull_j
= isl_basic_map_copy(info
[j
].bmap
);
3273 hull_j
= isl_basic_map_plain_affine_hull(hull_j
);
3275 hull_j
= isl_basic_map_intersect(hull_j
, isl_basic_map_copy(hull_i
));
3276 equal
= isl_basic_map_plain_is_equal(hull_i
, hull_j
);
3277 empty
= isl_basic_map_plain_is_empty(hull_j
);
3278 isl_basic_map_free(hull_i
);
3280 if (equal
< 0 || equal
|| empty
< 0 || empty
) {
3281 isl_basic_map_free(hull_j
);
3282 if (equal
< 0 || empty
< 0)
3283 return isl_change_error
;
3284 return isl_change_none
;
3287 bmap_i
= isl_basic_map_copy(info
[i
].bmap
);
3288 bmap_i
= isl_basic_map_intersect(bmap_i
, hull_j
);
3290 return isl_change_error
;
3292 if (bmap_i
->n_div
> info
[j
].bmap
->n_div
) {
3293 isl_basic_map_free(bmap_i
);
3294 return isl_change_none
;
3297 change
= coalesce_after_aligning_divs(bmap_i
, -1, j
, info
);
3299 isl_basic_map_free(bmap_i
);
3304 /* Check if the union of and the basic maps represented by info[i] and info[j]
3305 * can be represented by a single basic map, by aligning or equating
3306 * their integer divisions.
3307 * If so, replace the pair by the single basic map and return
3308 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
3309 * Otherwise, return isl_change_none.
3311 * Note that we only perform any test if the number of divs is different
3312 * in the two basic maps. In case the number of divs is the same,
3313 * we have already established that the divs are different
3314 * in the two basic maps.
3315 * In particular, if the number of divs of basic map i is smaller than
3316 * the number of divs of basic map j, then we check if j is a subset of i
3319 static enum isl_change
coalesce_divs(int i
, int j
,
3320 struct isl_coalesce_info
*info
)
3322 enum isl_change change
= isl_change_none
;
3324 if (info
[i
].bmap
->n_div
< info
[j
].bmap
->n_div
)
3325 change
= coalesce_after_aligning_divs(info
[i
].bmap
, i
, j
, info
);
3326 if (change
!= isl_change_none
)
3329 if (info
[j
].bmap
->n_div
< info
[i
].bmap
->n_div
)
3330 change
= coalesce_after_aligning_divs(info
[j
].bmap
, j
, i
, info
);
3331 if (change
!= isl_change_none
)
3332 return invert_change(change
);
3334 change
= coalesce_subset_with_equalities(i
, j
, info
);
3335 if (change
!= isl_change_none
)
3338 change
= coalesce_subset_with_equalities(j
, i
, info
);
3339 if (change
!= isl_change_none
)
3340 return invert_change(change
);
3342 return isl_change_none
;
3345 /* Does "bmap" involve any divs that themselves refer to divs?
3347 static isl_bool
has_nested_div(__isl_keep isl_basic_map
*bmap
)
3353 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
3354 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
3355 if (total
< 0 || n_div
< 0)
3356 return isl_bool_error
;
3359 for (i
= 0; i
< n_div
; ++i
)
3360 if (isl_seq_first_non_zero(bmap
->div
[i
] + 2 + total
,
3362 return isl_bool_true
;
3364 return isl_bool_false
;
3367 /* Return a list of affine expressions, one for each integer division
3368 * in "bmap_i". For each integer division that also appears in "bmap_j",
3369 * the affine expression is set to NaN. The number of NaNs in the list
3370 * is equal to the number of integer divisions in "bmap_j".
3371 * For the other integer divisions of "bmap_i", the corresponding
3372 * element in the list is a purely affine expression equal to the integer
3373 * division in "hull".
3374 * If no such list can be constructed, then the number of elements
3375 * in the returned list is smaller than the number of integer divisions
3378 static __isl_give isl_aff_list
*set_up_substitutions(
3379 __isl_keep isl_basic_map
*bmap_i
, __isl_keep isl_basic_map
*bmap_j
,
3380 __isl_take isl_basic_map
*hull
)
3382 isl_size n_div_i
, n_div_j
, total
;
3384 isl_local_space
*ls
;
3385 isl_basic_set
*wrap_hull
;
3390 n_div_i
= isl_basic_map_dim(bmap_i
, isl_dim_div
);
3391 n_div_j
= isl_basic_map_dim(bmap_j
, isl_dim_div
);
3392 total
= isl_basic_map_dim(bmap_i
, isl_dim_all
);
3393 if (!hull
|| n_div_i
< 0 || n_div_j
< 0 || total
< 0)
3396 ctx
= isl_basic_map_get_ctx(hull
);
3399 ls
= isl_basic_map_get_local_space(bmap_i
);
3400 ls
= isl_local_space_wrap(ls
);
3401 wrap_hull
= isl_basic_map_wrap(hull
);
3403 aff_nan
= isl_aff_nan_on_domain(isl_local_space_copy(ls
));
3404 list
= isl_aff_list_alloc(ctx
, n_div_i
);
3407 for (i
= 0; i
< n_div_i
; ++i
) {
3412 isl_basic_map_equal_div_expr_part(bmap_i
, i
, bmap_j
, j
,
3415 list
= isl_aff_list_add(list
, isl_aff_copy(aff_nan
));
3418 if (n_div_i
- i
<= n_div_j
- j
)
3421 aff
= isl_local_space_get_div(ls
, i
);
3422 aff
= isl_aff_substitute_equalities(aff
,
3423 isl_basic_set_copy(wrap_hull
));
3424 aff
= isl_aff_floor(aff
);
3425 n_div
= isl_aff_dim(aff
, isl_dim_div
);
3433 list
= isl_aff_list_add(list
, aff
);
3436 isl_aff_free(aff_nan
);
3437 isl_local_space_free(ls
);
3438 isl_basic_set_free(wrap_hull
);
3442 isl_aff_free(aff_nan
);
3443 isl_local_space_free(ls
);
3444 isl_basic_set_free(wrap_hull
);
3445 isl_aff_list_free(list
);
3449 /* Add variables to info->bmap and info->tab corresponding to the elements
3450 * in "list" that are not set to NaN.
3451 * "extra_var" is the number of these elements.
3452 * "dim" is the offset in the variables of "tab" where we should
3453 * start considering the elements in "list".
3454 * When this function returns, the total number of variables in "tab"
3455 * is equal to "dim" plus the number of elements in "list".
3457 * The newly added existentially quantified variables are not given
3458 * an explicit representation because the corresponding div constraints
3459 * do not appear in info->bmap. These constraints are not added
3460 * to info->bmap because for internal consistency, they would need to
3461 * be added to info->tab as well, where they could combine with the equality
3462 * that is added later to result in constraints that do not hold
3463 * in the original input.
3465 static isl_stat
add_sub_vars(struct isl_coalesce_info
*info
,
3466 __isl_keep isl_aff_list
*list
, int dim
, int extra_var
)
3471 space
= isl_basic_map_get_space(info
->bmap
);
3472 info
->bmap
= isl_basic_map_cow(info
->bmap
);
3473 info
->bmap
= isl_basic_map_extend_space(info
->bmap
, space
,
3476 return isl_stat_error
;
3477 n
= isl_aff_list_n_aff(list
);
3478 for (i
= 0; i
< n
; ++i
) {
3482 aff
= isl_aff_list_get_aff(list
, i
);
3483 is_nan
= isl_aff_is_nan(aff
);
3486 return isl_stat_error
;
3490 if (isl_tab_insert_var(info
->tab
, dim
+ i
) < 0)
3491 return isl_stat_error
;
3492 d
= isl_basic_map_alloc_div(info
->bmap
);
3494 return isl_stat_error
;
3495 info
->bmap
= isl_basic_map_mark_div_unknown(info
->bmap
, d
);
3496 for (j
= d
; j
> i
; --j
)
3497 info
->bmap
= isl_basic_map_swap_div(info
->bmap
,
3500 return isl_stat_error
;
3506 /* For each element in "list" that is not set to NaN, fix the corresponding
3507 * variable in "tab" to the purely affine expression defined by the element.
3508 * "dim" is the offset in the variables of "tab" where we should
3509 * start considering the elements in "list".
3511 * This function assumes that a sufficient number of rows and
3512 * elements in the constraint array are available in the tableau.
3514 static isl_stat
add_sub_equalities(struct isl_tab
*tab
,
3515 __isl_keep isl_aff_list
*list
, int dim
)
3522 n
= isl_aff_list_n_aff(list
);
3524 ctx
= isl_tab_get_ctx(tab
);
3525 sub
= isl_vec_alloc(ctx
, 1 + dim
+ n
);
3527 return isl_stat_error
;
3528 isl_seq_clr(sub
->el
+ 1 + dim
, n
);
3530 for (i
= 0; i
< n
; ++i
) {
3531 aff
= isl_aff_list_get_aff(list
, i
);
3534 if (isl_aff_is_nan(aff
)) {
3538 isl_seq_cpy(sub
->el
, aff
->v
->el
+ 1, 1 + dim
);
3539 isl_int_neg(sub
->el
[1 + dim
+ i
], aff
->v
->el
[0]);
3540 if (isl_tab_add_eq(tab
, sub
->el
) < 0)
3542 isl_int_set_si(sub
->el
[1 + dim
+ i
], 0);
3551 return isl_stat_error
;
3554 /* Add variables to info->tab and info->bmap corresponding to the elements
3555 * in "list" that are not set to NaN. The value of the added variable
3556 * in info->tab is fixed to the purely affine expression defined by the element.
3557 * "dim" is the offset in the variables of info->tab where we should
3558 * start considering the elements in "list".
3559 * When this function returns, the total number of variables in info->tab
3560 * is equal to "dim" plus the number of elements in "list".
3562 static isl_stat
add_subs(struct isl_coalesce_info
*info
,
3563 __isl_keep isl_aff_list
*list
, int dim
)
3569 return isl_stat_error
;
3571 n
= isl_aff_list_n_aff(list
);
3572 extra_var
= n
- (info
->tab
->n_var
- dim
);
3574 if (isl_tab_extend_vars(info
->tab
, extra_var
) < 0)
3575 return isl_stat_error
;
3576 if (isl_tab_extend_cons(info
->tab
, 2 * extra_var
) < 0)
3577 return isl_stat_error
;
3578 if (add_sub_vars(info
, list
, dim
, extra_var
) < 0)
3579 return isl_stat_error
;
3581 return add_sub_equalities(info
->tab
, list
, dim
);
3584 /* Coalesce basic map "j" into basic map "i" after adding the extra integer
3585 * divisions in "i" but not in "j" to basic map "j", with values
3586 * specified by "list". The total number of elements in "list"
3587 * is equal to the number of integer divisions in "i", while the number
3588 * of NaN elements in the list is equal to the number of integer divisions
3591 * If no coalescing can be performed, then we need to revert basic map "j"
3592 * to its original state. We do the same if basic map "i" gets dropped
3593 * during the coalescing, even though this should not happen in practice
3594 * since we have already checked for "j" being a subset of "i"
3595 * before we reach this stage.
3597 static enum isl_change
coalesce_with_subs(int i
, int j
,
3598 struct isl_coalesce_info
*info
, __isl_keep isl_aff_list
*list
)
3600 isl_basic_map
*bmap_j
;
3601 struct isl_tab_undo
*snap
;
3602 isl_size dim
, n_div
;
3603 enum isl_change change
;
3605 bmap_j
= isl_basic_map_copy(info
[j
].bmap
);
3606 snap
= isl_tab_snap(info
[j
].tab
);
3608 dim
= isl_basic_map_dim(bmap_j
, isl_dim_all
);
3609 n_div
= isl_basic_map_dim(bmap_j
, isl_dim_div
);
3610 if (dim
< 0 || n_div
< 0)
3613 if (add_subs(&info
[j
], list
, dim
) < 0)
3616 change
= coalesce_local_pair(i
, j
, info
);
3617 if (change
!= isl_change_none
&& change
!= isl_change_drop_first
) {
3618 isl_basic_map_free(bmap_j
);
3620 isl_basic_map_free(info
[j
].bmap
);
3621 info
[j
].bmap
= bmap_j
;
3623 if (isl_tab_rollback(info
[j
].tab
, snap
) < 0)
3624 return isl_change_error
;
3629 isl_basic_map_free(bmap_j
);
3630 return isl_change_error
;
3633 /* Check if we can coalesce basic map "j" into basic map "i" after copying
3634 * those extra integer divisions in "i" that can be simplified away
3635 * using the extra equalities in "j".
3636 * All divs are assumed to be known and not contain any nested divs.
3638 * We first check if there are any extra equalities in "j" that we
3639 * can exploit. Then we check if every integer division in "i"
3640 * either already appears in "j" or can be simplified using the
3641 * extra equalities to a purely affine expression.
3642 * If these tests succeed, then we try to coalesce the two basic maps
3643 * by introducing extra dimensions in "j" corresponding to
3644 * the extra integer divsisions "i" fixed to the corresponding
3645 * purely affine expression.
3647 static enum isl_change
check_coalesce_into_eq(int i
, int j
,
3648 struct isl_coalesce_info
*info
)
3650 isl_size n_div_i
, n_div_j
;
3651 isl_basic_map
*hull_i
, *hull_j
;
3652 isl_bool equal
, empty
;
3654 enum isl_change change
;
3656 n_div_i
= isl_basic_map_dim(info
[i
].bmap
, isl_dim_div
);
3657 n_div_j
= isl_basic_map_dim(info
[j
].bmap
, isl_dim_div
);
3658 if (n_div_i
< 0 || n_div_j
< 0)
3659 return isl_change_error
;
3660 if (n_div_i
<= n_div_j
)
3661 return isl_change_none
;
3662 if (info
[j
].bmap
->n_eq
== 0)
3663 return isl_change_none
;
3665 hull_i
= isl_basic_map_copy(info
[i
].bmap
);
3666 hull_i
= isl_basic_map_plain_affine_hull(hull_i
);
3667 hull_j
= isl_basic_map_copy(info
[j
].bmap
);
3668 hull_j
= isl_basic_map_plain_affine_hull(hull_j
);
3670 hull_j
= isl_basic_map_intersect(hull_j
, isl_basic_map_copy(hull_i
));
3671 equal
= isl_basic_map_plain_is_equal(hull_i
, hull_j
);
3672 empty
= isl_basic_map_plain_is_empty(hull_j
);
3673 isl_basic_map_free(hull_i
);
3675 if (equal
< 0 || empty
< 0)
3677 if (equal
|| empty
) {
3678 isl_basic_map_free(hull_j
);
3679 return isl_change_none
;
3682 list
= set_up_substitutions(info
[i
].bmap
, info
[j
].bmap
, hull_j
);
3684 return isl_change_error
;
3685 if (isl_aff_list_n_aff(list
) < n_div_i
)
3686 change
= isl_change_none
;
3688 change
= coalesce_with_subs(i
, j
, info
, list
);
3690 isl_aff_list_free(list
);
3694 isl_basic_map_free(hull_j
);
3695 return isl_change_error
;
3698 /* Check if we can coalesce basic maps "i" and "j" after copying
3699 * those extra integer divisions in one of the basic maps that can
3700 * be simplified away using the extra equalities in the other basic map.
3701 * We require all divs to be known in both basic maps.
3702 * Furthermore, to simplify the comparison of div expressions,
3703 * we do not allow any nested integer divisions.
3705 static enum isl_change
check_coalesce_eq(int i
, int j
,
3706 struct isl_coalesce_info
*info
)
3708 isl_bool known
, nested
;
3709 enum isl_change change
;
3711 known
= isl_basic_map_divs_known(info
[i
].bmap
);
3712 if (known
< 0 || !known
)
3713 return known
< 0 ? isl_change_error
: isl_change_none
;
3714 known
= isl_basic_map_divs_known(info
[j
].bmap
);
3715 if (known
< 0 || !known
)
3716 return known
< 0 ? isl_change_error
: isl_change_none
;
3717 nested
= has_nested_div(info
[i
].bmap
);
3718 if (nested
< 0 || nested
)
3719 return nested
< 0 ? isl_change_error
: isl_change_none
;
3720 nested
= has_nested_div(info
[j
].bmap
);
3721 if (nested
< 0 || nested
)
3722 return nested
< 0 ? isl_change_error
: isl_change_none
;
3724 change
= check_coalesce_into_eq(i
, j
, info
);
3725 if (change
!= isl_change_none
)
3727 change
= check_coalesce_into_eq(j
, i
, info
);
3728 if (change
!= isl_change_none
)
3729 return invert_change(change
);
3731 return isl_change_none
;
3734 /* Check if the union of the given pair of basic maps
3735 * can be represented by a single basic map.
3736 * If so, replace the pair by the single basic map and return
3737 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
3738 * Otherwise, return isl_change_none.
3740 * We first check if the two basic maps live in the same local space,
3741 * after aligning the divs that differ by only an integer constant.
3742 * If so, we do the complete check. Otherwise, we check if they have
3743 * the same number of integer divisions and can be coalesced, if one is
3744 * an obvious subset of the other or if the extra integer divisions
3745 * of one basic map can be simplified away using the extra equalities
3746 * of the other basic map.
3748 * Note that trying to coalesce pairs of disjuncts with the same
3749 * number, but different local variables may drop the explicit
3750 * representation of some of these local variables.
3751 * This operation is therefore not performed when
3752 * the "coalesce_preserve_locals" option is set.
3754 static enum isl_change
coalesce_pair(int i
, int j
,
3755 struct isl_coalesce_info
*info
)
3759 enum isl_change change
;
3762 if (harmonize_divs(&info
[i
], &info
[j
]) < 0)
3763 return isl_change_error
;
3764 same
= same_divs(info
[i
].bmap
, info
[j
].bmap
);
3766 return isl_change_error
;
3768 return coalesce_local_pair(i
, j
, info
);
3770 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
3771 preserve
= isl_options_get_coalesce_preserve_locals(ctx
);
3772 if (!preserve
&& info
[i
].bmap
->n_div
== info
[j
].bmap
->n_div
) {
3773 change
= coalesce_local_pair(i
, j
, info
);
3774 if (change
!= isl_change_none
)
3778 change
= coalesce_divs(i
, j
, info
);
3779 if (change
!= isl_change_none
)
3782 return check_coalesce_eq(i
, j
, info
);
3785 /* Return the maximum of "a" and "b".
3787 static int isl_max(int a
, int b
)
3789 return a
> b
? a
: b
;
3792 /* Pairwise coalesce the basic maps in the range [start1, end1[ of "info"
3793 * with those in the range [start2, end2[, skipping basic maps
3794 * that have been removed (either before or within this function).
3796 * For each basic map i in the first range, we check if it can be coalesced
3797 * with respect to any previously considered basic map j in the second range.
3798 * If i gets dropped (because it was a subset of some j), then
3799 * we can move on to the next basic map.
3800 * If j gets dropped, we need to continue checking against the other
3801 * previously considered basic maps.
3802 * If the two basic maps got fused, then we recheck the fused basic map
3803 * against the previously considered basic maps, starting at i + 1
3804 * (even if start2 is greater than i + 1).
3806 static int coalesce_range(isl_ctx
*ctx
, struct isl_coalesce_info
*info
,
3807 int start1
, int end1
, int start2
, int end2
)
3811 for (i
= end1
- 1; i
>= start1
; --i
) {
3812 if (info
[i
].removed
)
3814 for (j
= isl_max(i
+ 1, start2
); j
< end2
; ++j
) {
3815 enum isl_change changed
;
3817 if (info
[j
].removed
)
3819 if (info
[i
].removed
)
3820 isl_die(ctx
, isl_error_internal
,
3821 "basic map unexpectedly removed",
3823 changed
= coalesce_pair(i
, j
, info
);
3825 case isl_change_error
:
3827 case isl_change_none
:
3828 case isl_change_drop_second
:
3830 case isl_change_drop_first
:
3833 case isl_change_fuse
:
3843 /* Pairwise coalesce the basic maps described by the "n" elements of "info".
3845 * We consider groups of basic maps that live in the same apparent
3846 * affine hull and we first coalesce within such a group before we
3847 * coalesce the elements in the group with elements of previously
3848 * considered groups. If a fuse happens during the second phase,
3849 * then we also reconsider the elements within the group.
3851 static int coalesce(isl_ctx
*ctx
, int n
, struct isl_coalesce_info
*info
)
3855 for (end
= n
; end
> 0; end
= start
) {
3857 while (start
>= 1 &&
3858 info
[start
- 1].hull_hash
== info
[start
].hull_hash
)
3860 if (coalesce_range(ctx
, info
, start
, end
, start
, end
) < 0)
3862 if (coalesce_range(ctx
, info
, start
, end
, end
, n
) < 0)
3869 /* Update the basic maps in "map" based on the information in "info".
3870 * In particular, remove the basic maps that have been marked removed and
3871 * update the others based on the information in the corresponding tableau.
3872 * Since we detected implicit equalities without calling
3873 * isl_basic_map_gauss, we need to do it now.
3874 * Also call isl_basic_map_simplify if we may have lost the definition
3875 * of one or more integer divisions.
3877 static __isl_give isl_map
*update_basic_maps(__isl_take isl_map
*map
,
3878 int n
, struct isl_coalesce_info
*info
)
3885 for (i
= n
- 1; i
>= 0; --i
) {
3886 if (info
[i
].removed
) {
3887 isl_basic_map_free(map
->p
[i
]);
3888 if (i
!= map
->n
- 1)
3889 map
->p
[i
] = map
->p
[map
->n
- 1];
3894 info
[i
].bmap
= isl_basic_map_update_from_tab(info
[i
].bmap
,
3896 info
[i
].bmap
= isl_basic_map_gauss(info
[i
].bmap
, NULL
);
3897 if (info
[i
].simplify
)
3898 info
[i
].bmap
= isl_basic_map_simplify(info
[i
].bmap
);
3899 info
[i
].bmap
= isl_basic_map_finalize(info
[i
].bmap
);
3901 return isl_map_free(map
);
3902 ISL_F_SET(info
[i
].bmap
, ISL_BASIC_MAP_NO_IMPLICIT
);
3903 ISL_F_SET(info
[i
].bmap
, ISL_BASIC_MAP_NO_REDUNDANT
);
3904 isl_basic_map_free(map
->p
[i
]);
3905 map
->p
[i
] = info
[i
].bmap
;
3906 info
[i
].bmap
= NULL
;
3912 /* For each pair of basic maps in the map, check if the union of the two
3913 * can be represented by a single basic map.
3914 * If so, replace the pair by the single basic map and start over.
3916 * We factor out any (hidden) common factor from the constraint
3917 * coefficients to improve the detection of adjacent constraints.
3919 * Since we are constructing the tableaus of the basic maps anyway,
3920 * we exploit them to detect implicit equalities and redundant constraints.
3921 * This also helps the coalescing as it can ignore the redundant constraints.
3922 * In order to avoid confusion, we make all implicit equalities explicit
3923 * in the basic maps. We don't call isl_basic_map_gauss, though,
3924 * as that may affect the number of constraints.
3925 * This means that we have to call isl_basic_map_gauss at the end
3926 * of the computation (in update_basic_maps and in drop) to ensure that
3927 * the basic maps are not left in an unexpected state.
3928 * For each basic map, we also compute the hash of the apparent affine hull
3929 * for use in coalesce.
3931 __isl_give isl_map
*isl_map_coalesce(__isl_take isl_map
*map
)
3936 struct isl_coalesce_info
*info
= NULL
;
3938 map
= isl_map_remove_empty_parts(map
);
3945 ctx
= isl_map_get_ctx(map
);
3946 map
= isl_map_sort_divs(map
);
3947 map
= isl_map_cow(map
);
3954 info
= isl_calloc_array(map
->ctx
, struct isl_coalesce_info
, n
);
3958 for (i
= 0; i
< map
->n
; ++i
) {
3959 map
->p
[i
] = isl_basic_map_reduce_coefficients(map
->p
[i
]);
3962 info
[i
].bmap
= isl_basic_map_copy(map
->p
[i
]);
3963 info
[i
].tab
= isl_tab_from_basic_map(info
[i
].bmap
, 0);
3966 if (!ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_NO_IMPLICIT
))
3967 if (isl_tab_detect_implicit_equalities(info
[i
].tab
) < 0)
3969 info
[i
].bmap
= isl_tab_make_equalities_explicit(info
[i
].tab
,
3973 if (!ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_NO_REDUNDANT
))
3974 if (isl_tab_detect_redundant(info
[i
].tab
) < 0)
3976 if (coalesce_info_set_hull_hash(&info
[i
]) < 0)
3979 for (i
= map
->n
- 1; i
>= 0; --i
)
3980 if (info
[i
].tab
->empty
)
3983 if (coalesce(ctx
, n
, info
) < 0)
3986 map
= update_basic_maps(map
, n
, info
);
3988 clear_coalesce_info(n
, info
);
3992 clear_coalesce_info(n
, info
);
3997 /* For each pair of basic sets in the set, check if the union of the two
3998 * can be represented by a single basic set.
3999 * If so, replace the pair by the single basic set and start over.
4001 struct isl_set
*isl_set_coalesce(struct isl_set
*set
)
4003 return set_from_map(isl_map_coalesce(set_to_map(set
)));