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
)
69 int *eq
= isl_calloc_array(bmap_i
->ctx
, int, 2 * bmap_i
->n_eq
);
75 dim
= isl_basic_map_total_dim(bmap_i
);
76 for (k
= 0; k
< bmap_i
->n_eq
; ++k
) {
77 for (l
= 0; l
< 2; ++l
) {
78 isl_seq_neg(bmap_i
->eq
[k
], bmap_i
->eq
[k
], 1+dim
);
79 eq
[2 * k
+ l
] = status_in(bmap_i
->eq
[k
], tab_j
);
80 if (eq
[2 * k
+ l
] == STATUS_ERROR
)
91 /* Compute the position of the inequalities of basic map "bmap_i"
92 * (also represented by "tab_i", if not NULL) with respect to the basic map
93 * represented by "tab_j".
95 static int *ineq_status_in(__isl_keep isl_basic_map
*bmap_i
,
96 struct isl_tab
*tab_i
, struct isl_tab
*tab_j
)
99 unsigned n_eq
= bmap_i
->n_eq
;
100 int *ineq
= isl_calloc_array(bmap_i
->ctx
, int, bmap_i
->n_ineq
);
105 for (k
= 0; k
< bmap_i
->n_ineq
; ++k
) {
106 if (tab_i
&& isl_tab_is_redundant(tab_i
, n_eq
+ k
)) {
107 ineq
[k
] = STATUS_REDUNDANT
;
110 ineq
[k
] = status_in(bmap_i
->ineq
[k
], tab_j
);
111 if (ineq
[k
] == STATUS_ERROR
)
113 if (ineq
[k
] == STATUS_SEPARATE
)
123 static int any(int *con
, unsigned len
, int status
)
127 for (i
= 0; i
< len
; ++i
)
128 if (con
[i
] == status
)
133 /* Return the first position of "status" in the list "con" of length "len".
134 * Return -1 if there is no such entry.
136 static int find(int *con
, unsigned len
, int status
)
140 for (i
= 0; i
< len
; ++i
)
141 if (con
[i
] == status
)
146 static int count(int *con
, unsigned len
, int status
)
151 for (i
= 0; i
< len
; ++i
)
152 if (con
[i
] == status
)
157 static int all(int *con
, unsigned len
, int status
)
161 for (i
= 0; i
< len
; ++i
) {
162 if (con
[i
] == STATUS_REDUNDANT
)
164 if (con
[i
] != status
)
170 /* Internal information associated to a basic map in a map
171 * that is to be coalesced by isl_map_coalesce.
173 * "bmap" is the basic map itself (or NULL if "removed" is set)
174 * "tab" is the corresponding tableau (or NULL if "removed" is set)
175 * "hull_hash" identifies the affine space in which "bmap" lives.
176 * "removed" is set if this basic map has been removed from the map
177 * "simplify" is set if this basic map may have some unknown integer
178 * divisions that were not present in the input basic maps. The basic
179 * map should then be simplified such that we may be able to find
180 * a definition among the constraints.
182 * "eq" and "ineq" are only set if we are currently trying to coalesce
183 * this basic map with another basic map, in which case they represent
184 * the position of the inequalities of this basic map with respect to
185 * the other basic map. The number of elements in the "eq" array
186 * is twice the number of equalities in the "bmap", corresponding
187 * to the two inequalities that make up each equality.
189 struct isl_coalesce_info
{
199 /* Is there any (half of an) equality constraint in the description
200 * of the basic map represented by "info" that
201 * has position "status" with respect to the other basic map?
203 static int any_eq(struct isl_coalesce_info
*info
, int status
)
207 n_eq
= isl_basic_map_n_equality(info
->bmap
);
208 return any(info
->eq
, 2 * n_eq
, status
);
211 /* Is there any inequality constraint in the description
212 * of the basic map represented by "info" that
213 * has position "status" with respect to the other basic map?
215 static int any_ineq(struct isl_coalesce_info
*info
, int status
)
219 n_ineq
= isl_basic_map_n_inequality(info
->bmap
);
220 return any(info
->ineq
, n_ineq
, status
);
223 /* Are all non-redundant constraints of the basic map represented by "info"
224 * either valid or cut constraints with respect to the other basic map?
226 static int all_valid_or_cut(struct isl_coalesce_info
*info
)
230 for (i
= 0; i
< 2 * info
->bmap
->n_eq
; ++i
) {
231 if (info
->eq
[i
] == STATUS_REDUNDANT
)
233 if (info
->eq
[i
] == STATUS_VALID
)
235 if (info
->eq
[i
] == STATUS_CUT
)
240 for (i
= 0; i
< info
->bmap
->n_ineq
; ++i
) {
241 if (info
->ineq
[i
] == STATUS_REDUNDANT
)
243 if (info
->ineq
[i
] == STATUS_VALID
)
245 if (info
->ineq
[i
] == STATUS_CUT
)
253 /* Compute the hash of the (apparent) affine hull of info->bmap (with
254 * the existentially quantified variables removed) and store it
257 static int coalesce_info_set_hull_hash(struct isl_coalesce_info
*info
)
262 hull
= isl_basic_map_copy(info
->bmap
);
263 hull
= isl_basic_map_plain_affine_hull(hull
);
264 n_div
= isl_basic_map_dim(hull
, isl_dim_div
);
265 hull
= isl_basic_map_drop_constraints_involving_dims(hull
,
266 isl_dim_div
, 0, n_div
);
267 info
->hull_hash
= isl_basic_map_get_hash(hull
);
268 isl_basic_map_free(hull
);
270 return hull
? 0 : -1;
273 /* Free all the allocated memory in an array
274 * of "n" isl_coalesce_info elements.
276 static void clear_coalesce_info(int n
, struct isl_coalesce_info
*info
)
283 for (i
= 0; i
< n
; ++i
) {
284 isl_basic_map_free(info
[i
].bmap
);
285 isl_tab_free(info
[i
].tab
);
291 /* Drop the basic map represented by "info".
292 * That is, clear the memory associated to the entry and
293 * mark it as having been removed.
295 static void drop(struct isl_coalesce_info
*info
)
297 info
->bmap
= isl_basic_map_free(info
->bmap
);
298 isl_tab_free(info
->tab
);
303 /* Exchange the information in "info1" with that in "info2".
305 static void exchange(struct isl_coalesce_info
*info1
,
306 struct isl_coalesce_info
*info2
)
308 struct isl_coalesce_info info
;
315 /* This type represents the kind of change that has been performed
316 * while trying to coalesce two basic maps.
318 * isl_change_none: nothing was changed
319 * isl_change_drop_first: the first basic map was removed
320 * isl_change_drop_second: the second basic map was removed
321 * isl_change_fuse: the two basic maps were replaced by a new basic map.
324 isl_change_error
= -1,
326 isl_change_drop_first
,
327 isl_change_drop_second
,
331 /* Update "change" based on an interchange of the first and the second
332 * basic map. That is, interchange isl_change_drop_first and
333 * isl_change_drop_second.
335 static enum isl_change
invert_change(enum isl_change change
)
338 case isl_change_error
:
339 return isl_change_error
;
340 case isl_change_none
:
341 return isl_change_none
;
342 case isl_change_drop_first
:
343 return isl_change_drop_second
;
344 case isl_change_drop_second
:
345 return isl_change_drop_first
;
346 case isl_change_fuse
:
347 return isl_change_fuse
;
350 return isl_change_error
;
353 /* Add the valid constraints of the basic map represented by "info"
354 * to "bmap". "len" is the size of the constraints.
355 * If only one of the pair of inequalities that make up an equality
356 * is valid, then add that inequality.
358 static __isl_give isl_basic_map
*add_valid_constraints(
359 __isl_take isl_basic_map
*bmap
, struct isl_coalesce_info
*info
,
367 for (k
= 0; k
< info
->bmap
->n_eq
; ++k
) {
368 if (info
->eq
[2 * k
] == STATUS_VALID
&&
369 info
->eq
[2 * k
+ 1] == STATUS_VALID
) {
370 l
= isl_basic_map_alloc_equality(bmap
);
372 return isl_basic_map_free(bmap
);
373 isl_seq_cpy(bmap
->eq
[l
], info
->bmap
->eq
[k
], len
);
374 } else if (info
->eq
[2 * k
] == STATUS_VALID
) {
375 l
= isl_basic_map_alloc_inequality(bmap
);
377 return isl_basic_map_free(bmap
);
378 isl_seq_neg(bmap
->ineq
[l
], info
->bmap
->eq
[k
], len
);
379 } else if (info
->eq
[2 * k
+ 1] == STATUS_VALID
) {
380 l
= isl_basic_map_alloc_inequality(bmap
);
382 return isl_basic_map_free(bmap
);
383 isl_seq_cpy(bmap
->ineq
[l
], info
->bmap
->eq
[k
], len
);
387 for (k
= 0; k
< info
->bmap
->n_ineq
; ++k
) {
388 if (info
->ineq
[k
] != STATUS_VALID
)
390 l
= isl_basic_map_alloc_inequality(bmap
);
392 return isl_basic_map_free(bmap
);
393 isl_seq_cpy(bmap
->ineq
[l
], info
->bmap
->ineq
[k
], len
);
399 /* Is "bmap" defined by a number of (non-redundant) constraints that
400 * is greater than the number of constraints of basic maps i and j combined?
401 * Equalities are counted as two inequalities.
403 static int number_of_constraints_increases(int i
, int j
,
404 struct isl_coalesce_info
*info
,
405 __isl_keep isl_basic_map
*bmap
, struct isl_tab
*tab
)
409 n_old
= 2 * info
[i
].bmap
->n_eq
+ info
[i
].bmap
->n_ineq
;
410 n_old
+= 2 * info
[j
].bmap
->n_eq
+ info
[j
].bmap
->n_ineq
;
412 n_new
= 2 * bmap
->n_eq
;
413 for (k
= 0; k
< bmap
->n_ineq
; ++k
)
414 if (!isl_tab_is_redundant(tab
, bmap
->n_eq
+ k
))
417 return n_new
> n_old
;
420 /* Replace the pair of basic maps i and j by the basic map bounded
421 * by the valid constraints in both basic maps and the constraints
422 * in extra (if not NULL).
423 * Place the fused basic map in the position that is the smallest of i and j.
425 * If "detect_equalities" is set, then look for equalities encoded
426 * as pairs of inequalities.
427 * If "check_number" is set, then the original basic maps are only
428 * replaced if the total number of constraints does not increase.
429 * While the number of integer divisions in the two basic maps
430 * is assumed to be the same, the actual definitions may be different.
431 * We only copy the definition from one of the basic map if it is
432 * the same as that of the other basic map. Otherwise, we mark
433 * the integer division as unknown and simplify the basic map
434 * in an attempt to recover the integer division definition.
436 static enum isl_change
fuse(int i
, int j
, struct isl_coalesce_info
*info
,
437 __isl_keep isl_mat
*extra
, int detect_equalities
, int check_number
)
440 struct isl_basic_map
*fused
= NULL
;
441 struct isl_tab
*fused_tab
= NULL
;
442 unsigned total
= isl_basic_map_total_dim(info
[i
].bmap
);
443 unsigned extra_rows
= extra
? extra
->n_row
: 0;
444 unsigned n_eq
, n_ineq
;
448 return fuse(j
, i
, info
, extra
, detect_equalities
, check_number
);
450 n_eq
= info
[i
].bmap
->n_eq
+ info
[j
].bmap
->n_eq
;
451 n_ineq
= info
[i
].bmap
->n_ineq
+ info
[j
].bmap
->n_ineq
;
452 fused
= isl_basic_map_alloc_space(isl_space_copy(info
[i
].bmap
->dim
),
453 info
[i
].bmap
->n_div
, n_eq
, n_eq
+ n_ineq
+ extra_rows
);
454 fused
= add_valid_constraints(fused
, &info
[i
], 1 + total
);
455 fused
= add_valid_constraints(fused
, &info
[j
], 1 + total
);
458 if (ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_RATIONAL
) &&
459 ISL_F_ISSET(info
[j
].bmap
, ISL_BASIC_MAP_RATIONAL
))
460 ISL_F_SET(fused
, ISL_BASIC_MAP_RATIONAL
);
462 for (k
= 0; k
< info
[i
].bmap
->n_div
; ++k
) {
463 int l
= isl_basic_map_alloc_div(fused
);
466 if (isl_seq_eq(info
[i
].bmap
->div
[k
], info
[j
].bmap
->div
[k
],
468 isl_seq_cpy(fused
->div
[l
], info
[i
].bmap
->div
[k
],
471 isl_int_set_si(fused
->div
[l
][0], 0);
476 for (k
= 0; k
< extra_rows
; ++k
) {
477 l
= isl_basic_map_alloc_inequality(fused
);
480 isl_seq_cpy(fused
->ineq
[l
], extra
->row
[k
], 1 + total
);
483 if (detect_equalities
)
484 fused
= isl_basic_map_detect_inequality_pairs(fused
, NULL
);
485 fused
= isl_basic_map_gauss(fused
, NULL
);
486 if (simplify
|| info
[j
].simplify
) {
487 fused
= isl_basic_map_simplify(fused
);
488 info
[i
].simplify
= 0;
490 fused
= isl_basic_map_finalize(fused
);
492 fused_tab
= isl_tab_from_basic_map(fused
, 0);
493 if (isl_tab_detect_redundant(fused_tab
) < 0)
497 number_of_constraints_increases(i
, j
, info
, fused
, fused_tab
)) {
498 isl_tab_free(fused_tab
);
499 isl_basic_map_free(fused
);
500 return isl_change_none
;
503 isl_basic_map_free(info
[i
].bmap
);
504 info
[i
].bmap
= fused
;
505 isl_tab_free(info
[i
].tab
);
506 info
[i
].tab
= fused_tab
;
509 return isl_change_fuse
;
511 isl_tab_free(fused_tab
);
512 isl_basic_map_free(fused
);
513 return isl_change_error
;
516 /* Given a pair of basic maps i and j such that all constraints are either
517 * "valid" or "cut", check if the facets corresponding to the "cut"
518 * constraints of i lie entirely within basic map j.
519 * If so, replace the pair by the basic map consisting of the valid
520 * constraints in both basic maps.
521 * Checking whether the facet lies entirely within basic map j
522 * is performed by checking whether the constraints of basic map j
523 * are valid for the facet. These tests are performed on a rational
524 * tableau to avoid the theoretical possibility that a constraint
525 * that was considered to be a cut constraint for the entire basic map i
526 * happens to be considered to be a valid constraint for the facet,
527 * even though it cuts off the same rational points.
529 * To see that we are not introducing any extra points, call the
530 * two basic maps A and B and the resulting map U and let x
531 * be an element of U \setminus ( A \cup B ).
532 * A line connecting x with an element of A \cup B meets a facet F
533 * of either A or B. Assume it is a facet of B and let c_1 be
534 * the corresponding facet constraint. We have c_1(x) < 0 and
535 * so c_1 is a cut constraint. This implies that there is some
536 * (possibly rational) point x' satisfying the constraints of A
537 * and the opposite of c_1 as otherwise c_1 would have been marked
538 * valid for A. The line connecting x and x' meets a facet of A
539 * in a (possibly rational) point that also violates c_1, but this
540 * is impossible since all cut constraints of B are valid for all
542 * In case F is a facet of A rather than B, then we can apply the
543 * above reasoning to find a facet of B separating x from A \cup B first.
545 static enum isl_change
check_facets(int i
, int j
,
546 struct isl_coalesce_info
*info
)
549 struct isl_tab_undo
*snap
, *snap2
;
550 unsigned n_eq
= info
[i
].bmap
->n_eq
;
552 snap
= isl_tab_snap(info
[i
].tab
);
553 if (isl_tab_mark_rational(info
[i
].tab
) < 0)
554 return isl_change_error
;
555 snap2
= isl_tab_snap(info
[i
].tab
);
557 for (k
= 0; k
< info
[i
].bmap
->n_ineq
; ++k
) {
558 if (info
[i
].ineq
[k
] != STATUS_CUT
)
560 if (isl_tab_select_facet(info
[i
].tab
, n_eq
+ k
) < 0)
561 return isl_change_error
;
562 for (l
= 0; l
< info
[j
].bmap
->n_ineq
; ++l
) {
564 if (info
[j
].ineq
[l
] != STATUS_CUT
)
566 stat
= status_in(info
[j
].bmap
->ineq
[l
], info
[i
].tab
);
568 return isl_change_error
;
569 if (stat
!= STATUS_VALID
)
572 if (isl_tab_rollback(info
[i
].tab
, snap2
) < 0)
573 return isl_change_error
;
574 if (l
< info
[j
].bmap
->n_ineq
)
578 if (k
< info
[i
].bmap
->n_ineq
) {
579 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
580 return isl_change_error
;
581 return isl_change_none
;
583 return fuse(i
, j
, info
, NULL
, 0, 0);
586 /* Check if info->bmap contains the basic map represented
587 * by the tableau "tab".
588 * For each equality, we check both the constraint itself
589 * (as an inequality) and its negation. Make sure the
590 * equality is returned to its original state before returning.
592 static isl_bool
contains(struct isl_coalesce_info
*info
, struct isl_tab
*tab
)
596 isl_basic_map
*bmap
= info
->bmap
;
598 dim
= isl_basic_map_total_dim(bmap
);
599 for (k
= 0; k
< bmap
->n_eq
; ++k
) {
601 isl_seq_neg(bmap
->eq
[k
], bmap
->eq
[k
], 1 + dim
);
602 stat
= status_in(bmap
->eq
[k
], tab
);
603 isl_seq_neg(bmap
->eq
[k
], bmap
->eq
[k
], 1 + dim
);
605 return isl_bool_error
;
606 if (stat
!= STATUS_VALID
)
607 return isl_bool_false
;
608 stat
= status_in(bmap
->eq
[k
], tab
);
610 return isl_bool_error
;
611 if (stat
!= STATUS_VALID
)
612 return isl_bool_false
;
615 for (k
= 0; k
< bmap
->n_ineq
; ++k
) {
617 if (info
->ineq
[k
] == STATUS_REDUNDANT
)
619 stat
= status_in(bmap
->ineq
[k
], tab
);
621 return isl_bool_error
;
622 if (stat
!= STATUS_VALID
)
623 return isl_bool_false
;
625 return isl_bool_true
;
628 /* Basic map "i" has an inequality (say "k") that is adjacent
629 * to some inequality of basic map "j". All the other inequalities
631 * Check if basic map "j" forms an extension of basic map "i".
633 * Note that this function is only called if some of the equalities or
634 * inequalities of basic map "j" do cut basic map "i". The function is
635 * correct even if there are no such cut constraints, but in that case
636 * the additional checks performed by this function are overkill.
638 * In particular, we replace constraint k, say f >= 0, by constraint
639 * f <= -1, add the inequalities of "j" that are valid for "i"
640 * and check if the result is a subset of basic map "j".
641 * To improve the chances of the subset relation being detected,
642 * any variable that only attains a single integer value
643 * in the tableau of "i" is first fixed to that value.
644 * If the result is a subset, then we know that this result is exactly equal
645 * to basic map "j" since all its constraints are valid for basic map "j".
646 * By combining the valid constraints of "i" (all equalities and all
647 * inequalities except "k") and the valid constraints of "j" we therefore
648 * obtain a basic map that is equal to their union.
649 * In this case, there is no need to perform a rollback of the tableau
650 * since it is going to be destroyed in fuse().
656 * |_______| _ |_________\
668 static enum isl_change
is_adj_ineq_extension(int i
, int j
,
669 struct isl_coalesce_info
*info
)
672 struct isl_tab_undo
*snap
;
673 unsigned n_eq
= info
[i
].bmap
->n_eq
;
674 unsigned total
= isl_basic_map_total_dim(info
[i
].bmap
);
678 if (isl_tab_extend_cons(info
[i
].tab
, 1 + info
[j
].bmap
->n_ineq
) < 0)
679 return isl_change_error
;
681 k
= find(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ADJ_INEQ
);
683 isl_die(isl_basic_map_get_ctx(info
[i
].bmap
), isl_error_internal
,
684 "info[i].ineq should have exactly one STATUS_ADJ_INEQ",
685 return isl_change_error
);
687 snap
= isl_tab_snap(info
[i
].tab
);
689 if (isl_tab_unrestrict(info
[i
].tab
, n_eq
+ k
) < 0)
690 return isl_change_error
;
692 isl_seq_neg(info
[i
].bmap
->ineq
[k
], info
[i
].bmap
->ineq
[k
], 1 + total
);
693 isl_int_sub_ui(info
[i
].bmap
->ineq
[k
][0], info
[i
].bmap
->ineq
[k
][0], 1);
694 r
= isl_tab_add_ineq(info
[i
].tab
, info
[i
].bmap
->ineq
[k
]);
695 isl_seq_neg(info
[i
].bmap
->ineq
[k
], info
[i
].bmap
->ineq
[k
], 1 + total
);
696 isl_int_sub_ui(info
[i
].bmap
->ineq
[k
][0], info
[i
].bmap
->ineq
[k
][0], 1);
698 return isl_change_error
;
700 for (k
= 0; k
< info
[j
].bmap
->n_ineq
; ++k
) {
701 if (info
[j
].ineq
[k
] != STATUS_VALID
)
703 if (isl_tab_add_ineq(info
[i
].tab
, info
[j
].bmap
->ineq
[k
]) < 0)
704 return isl_change_error
;
706 if (isl_tab_detect_constants(info
[i
].tab
) < 0)
707 return isl_change_error
;
709 super
= contains(&info
[j
], info
[i
].tab
);
711 return isl_change_error
;
713 return fuse(i
, j
, info
, NULL
, 0, 0);
715 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
716 return isl_change_error
;
718 return isl_change_none
;
722 /* Both basic maps have at least one inequality with and adjacent
723 * (but opposite) inequality in the other basic map.
724 * Check that there are no cut constraints and that there is only
725 * a single pair of adjacent inequalities.
726 * If so, we can replace the pair by a single basic map described
727 * by all but the pair of adjacent inequalities.
728 * Any additional points introduced lie strictly between the two
729 * adjacent hyperplanes and can therefore be integral.
738 * The test for a single pair of adjancent inequalities is important
739 * for avoiding the combination of two basic maps like the following
749 * If there are some cut constraints on one side, then we may
750 * still be able to fuse the two basic maps, but we need to perform
751 * some additional checks in is_adj_ineq_extension.
753 static enum isl_change
check_adj_ineq(int i
, int j
,
754 struct isl_coalesce_info
*info
)
756 int count_i
, count_j
;
759 count_i
= count(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ADJ_INEQ
);
760 count_j
= count(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_ADJ_INEQ
);
762 if (count_i
!= 1 && count_j
!= 1)
763 return isl_change_none
;
765 cut_i
= any_eq(&info
[i
], STATUS_CUT
) || any_ineq(&info
[i
], STATUS_CUT
);
766 cut_j
= any_eq(&info
[j
], STATUS_CUT
) || any_ineq(&info
[j
], STATUS_CUT
);
768 if (!cut_i
&& !cut_j
&& count_i
== 1 && count_j
== 1)
769 return fuse(i
, j
, info
, NULL
, 0, 0);
771 if (count_i
== 1 && !cut_i
)
772 return is_adj_ineq_extension(i
, j
, info
);
774 if (count_j
== 1 && !cut_j
)
775 return is_adj_ineq_extension(j
, i
, info
);
777 return isl_change_none
;
780 /* Given an affine transformation matrix "T", does row "row" represent
781 * anything other than a unit vector (possibly shifted by a constant)
782 * that is not involved in any of the other rows?
784 * That is, if a constraint involves the variable corresponding to
785 * the row, then could its preimage by "T" have any coefficients
786 * that are different from those in the original constraint?
788 static int not_unique_unit_row(__isl_keep isl_mat
*T
, int row
)
791 int len
= T
->n_col
- 1;
793 i
= isl_seq_first_non_zero(T
->row
[row
] + 1, len
);
796 if (!isl_int_is_one(T
->row
[row
][1 + i
]) &&
797 !isl_int_is_negone(T
->row
[row
][1 + i
]))
800 j
= isl_seq_first_non_zero(T
->row
[row
] + 1 + i
+ 1, len
- (i
+ 1));
804 for (j
= 1; j
< T
->n_row
; ++j
) {
807 if (!isl_int_is_zero(T
->row
[j
][1 + i
]))
814 /* Does inequality constraint "ineq" of "bmap" involve any of
815 * the variables marked in "affected"?
816 * "total" is the total number of variables, i.e., the number
817 * of entries in "affected".
819 static isl_bool
is_affected(__isl_keep isl_basic_map
*bmap
, int ineq
,
820 int *affected
, int total
)
824 for (i
= 0; i
< total
; ++i
) {
827 if (!isl_int_is_zero(bmap
->ineq
[ineq
][1 + i
]))
828 return isl_bool_true
;
831 return isl_bool_false
;
834 /* Given the compressed version of inequality constraint "ineq"
835 * of info->bmap in "v", check if the constraint can be tightened,
836 * where the compression is based on an equality constraint valid
838 * If so, add the tightened version of the inequality constraint
839 * to info->tab. "v" may be modified by this function.
841 * That is, if the compressed constraint is of the form
845 * with 0 < c < m, then it is equivalent to
849 * This means that c can also be subtracted from the original,
850 * uncompressed constraint without affecting the integer points
851 * in info->tab. Add this tightened constraint as an extra row
852 * to info->tab to make this information explicitly available.
854 static __isl_give isl_vec
*try_tightening(struct isl_coalesce_info
*info
,
855 int ineq
, __isl_take isl_vec
*v
)
863 ctx
= isl_vec_get_ctx(v
);
864 isl_seq_gcd(v
->el
+ 1, v
->size
- 1, &ctx
->normalize_gcd
);
865 if (isl_int_is_zero(ctx
->normalize_gcd
) ||
866 isl_int_is_one(ctx
->normalize_gcd
)) {
874 isl_int_fdiv_r(v
->el
[0], v
->el
[0], ctx
->normalize_gcd
);
875 if (isl_int_is_zero(v
->el
[0]))
878 if (isl_tab_extend_cons(info
->tab
, 1) < 0)
879 return isl_vec_free(v
);
881 isl_int_sub(info
->bmap
->ineq
[ineq
][0],
882 info
->bmap
->ineq
[ineq
][0], v
->el
[0]);
883 r
= isl_tab_add_ineq(info
->tab
, info
->bmap
->ineq
[ineq
]);
884 isl_int_add(info
->bmap
->ineq
[ineq
][0],
885 info
->bmap
->ineq
[ineq
][0], v
->el
[0]);
888 return isl_vec_free(v
);
893 /* Tighten the (non-redundant) constraints on the facet represented
895 * In particular, on input, info->tab represents the result
896 * of relaxing the "n" inequality constraints of info->bmap in "relaxed"
897 * by one, i.e., replacing f_i >= 0 by f_i + 1 >= 0, and then
898 * replacing the one at index "l" by the corresponding equality,
899 * i.e., f_k + 1 = 0, with k = relaxed[l].
901 * Compute a variable compression from the equality constraint f_k + 1 = 0
902 * and use it to tighten the other constraints of info->bmap
903 * (that is, all constraints that have not been relaxed),
904 * updating info->tab (and leaving info->bmap untouched).
905 * The compression handles essentially two cases, one where a variable
906 * is assigned a fixed value and can therefore be eliminated, and one
907 * where one variable is a shifted multiple of some other variable and
908 * can therefore be replaced by that multiple.
909 * Gaussian elimination would also work for the first case, but for
910 * the second case, the effectiveness would depend on the order
912 * After compression, some of the constraints may have coefficients
913 * with a common divisor. If this divisor does not divide the constant
914 * term, then the constraint can be tightened.
915 * The tightening is performed on the tableau info->tab by introducing
916 * extra (temporary) constraints.
918 * Only constraints that are possibly affected by the compression are
919 * considered. In particular, if the constraint only involves variables
920 * that are directly mapped to a distinct set of other variables, then
921 * no common divisor can be introduced and no tightening can occur.
923 * It is important to only consider the non-redundant constraints
924 * since the facet constraint has been relaxed prior to the call
925 * to this function, meaning that the constraints that were redundant
926 * prior to the relaxation may no longer be redundant.
927 * These constraints will be ignored in the fused result, so
928 * the fusion detection should not exploit them.
930 static isl_stat
tighten_on_relaxed_facet(struct isl_coalesce_info
*info
,
931 int n
, int *relaxed
, int l
)
942 ctx
= isl_basic_map_get_ctx(info
->bmap
);
943 total
= isl_basic_map_total_dim(info
->bmap
);
944 isl_int_add_ui(info
->bmap
->ineq
[k
][0], info
->bmap
->ineq
[k
][0], 1);
945 T
= isl_mat_sub_alloc6(ctx
, info
->bmap
->ineq
, k
, 1, 0, 1 + total
);
946 T
= isl_mat_variable_compression(T
, NULL
);
947 isl_int_sub_ui(info
->bmap
->ineq
[k
][0], info
->bmap
->ineq
[k
][0], 1);
949 return isl_stat_error
;
955 affected
= isl_alloc_array(ctx
, int, total
);
959 for (i
= 0; i
< total
; ++i
)
960 affected
[i
] = not_unique_unit_row(T
, 1 + i
);
962 for (i
= 0; i
< info
->bmap
->n_ineq
; ++i
) {
964 if (any(relaxed
, n
, i
))
966 if (info
->ineq
[i
] == STATUS_REDUNDANT
)
968 handle
= is_affected(info
->bmap
, i
, affected
, total
);
973 v
= isl_vec_alloc(ctx
, 1 + total
);
976 isl_seq_cpy(v
->el
, info
->bmap
->ineq
[i
], 1 + total
);
977 v
= isl_vec_mat_product(v
, isl_mat_copy(T
));
978 v
= try_tightening(info
, i
, v
);
990 return isl_stat_error
;
993 /* Replace the basic maps "i" and "j" by an extension of "i"
994 * along the "n" inequality constraints in "relax" by one.
995 * The tableau info[i].tab has already been extended.
996 * Extend info[i].bmap accordingly by relaxing all constraints in "relax"
998 * Each integer division that does not have exactly the same
999 * definition in "i" and "j" is marked unknown and the basic map
1000 * is scheduled to be simplified in an attempt to recover
1001 * the integer division definition.
1002 * Place the extension in the position that is the smallest of i and j.
1004 static enum isl_change
extend(int i
, int j
, int n
, int *relax
,
1005 struct isl_coalesce_info
*info
)
1010 info
[i
].bmap
= isl_basic_map_cow(info
[i
].bmap
);
1012 return isl_change_error
;
1013 total
= isl_basic_map_total_dim(info
[i
].bmap
);
1014 for (l
= 0; l
< info
[i
].bmap
->n_div
; ++l
)
1015 if (!isl_seq_eq(info
[i
].bmap
->div
[l
],
1016 info
[j
].bmap
->div
[l
], 1 + 1 + total
)) {
1017 isl_int_set_si(info
[i
].bmap
->div
[l
][0], 0);
1018 info
[i
].simplify
= 1;
1020 for (l
= 0; l
< n
; ++l
)
1021 isl_int_add_ui(info
[i
].bmap
->ineq
[relax
[l
]][0],
1022 info
[i
].bmap
->ineq
[relax
[l
]][0], 1);
1023 ISL_F_SET(info
[i
].bmap
, ISL_BASIC_MAP_FINAL
);
1026 exchange(&info
[i
], &info
[j
]);
1027 return isl_change_fuse
;
1030 /* Basic map "i" has "n" inequality constraints (collected in "relax")
1031 * that are such that they include basic map "j" if they are relaxed
1032 * by one. All the other inequalities are valid for "j".
1033 * Check if basic map "j" forms an extension of basic map "i".
1035 * In particular, relax the constraints in "relax", compute the corresponding
1036 * facets one by one and check whether each of these is included
1037 * in the other basic map.
1038 * Before testing for inclusion, the constraints on each facet
1039 * are tightened to increase the chance of an inclusion being detected.
1040 * (Adding the valid constraints of "j" to the tableau of "i", as is done
1041 * in is_adj_ineq_extension, may further increase those chances, but this
1042 * is not currently done.)
1043 * If each facet is included, we know that relaxing the constraints extends
1044 * the basic map with exactly the other basic map (we already know that this
1045 * other basic map is included in the extension, because all other
1046 * inequality constraints are valid of "j") and we can replace the
1047 * two basic maps by this extension.
1049 * If any of the relaxed constraints turn out to be redundant, then bail out.
1050 * isl_tab_select_facet refuses to handle such constraints. It may be
1051 * possible to handle them anyway by making a distinction between
1052 * redundant constraints with a corresponding facet that still intersects
1053 * the set (allowing isl_tab_select_facet to handle them) and
1054 * those where the facet does not intersect the set (which can be ignored
1055 * because the empty facet is trivially included in the other disjunct).
1056 * However, relaxed constraints that turn out to be redundant should
1057 * be fairly rare and no such instance has been reported where
1058 * coalescing would be successful.
1074 static enum isl_change
is_relaxed_extension(int i
, int j
, int n
, int *relax
,
1075 struct isl_coalesce_info
*info
)
1079 struct isl_tab_undo
*snap
, *snap2
;
1080 unsigned n_eq
= info
[i
].bmap
->n_eq
;
1082 for (l
= 0; l
< n
; ++l
)
1083 if (isl_tab_is_equality(info
[i
].tab
, n_eq
+ relax
[l
]))
1084 return isl_change_none
;
1086 snap
= isl_tab_snap(info
[i
].tab
);
1087 for (l
= 0; l
< n
; ++l
)
1088 if (isl_tab_relax(info
[i
].tab
, n_eq
+ relax
[l
]) < 0)
1089 return isl_change_error
;
1090 for (l
= 0; l
< n
; ++l
) {
1091 if (!isl_tab_is_redundant(info
[i
].tab
, n_eq
+ relax
[l
]))
1093 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
1094 return isl_change_error
;
1095 return isl_change_none
;
1097 snap2
= isl_tab_snap(info
[i
].tab
);
1098 for (l
= 0; l
< n
; ++l
) {
1099 if (isl_tab_rollback(info
[i
].tab
, snap2
) < 0)
1100 return isl_change_error
;
1101 if (isl_tab_select_facet(info
[i
].tab
, n_eq
+ relax
[l
]) < 0)
1102 return isl_change_error
;
1103 if (tighten_on_relaxed_facet(&info
[i
], n
, relax
, l
) < 0)
1104 return isl_change_error
;
1105 super
= contains(&info
[j
], info
[i
].tab
);
1107 return isl_change_error
;
1110 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
1111 return isl_change_error
;
1112 return isl_change_none
;
1115 if (isl_tab_rollback(info
[i
].tab
, snap2
) < 0)
1116 return isl_change_error
;
1117 return extend(i
, j
, n
, relax
, info
);
1120 /* Data structure that keeps track of the wrapping constraints
1121 * and of information to bound the coefficients of those constraints.
1123 * bound is set if we want to apply a bound on the coefficients
1124 * mat contains the wrapping constraints
1125 * max is the bound on the coefficients (if bound is set)
1133 /* Update wraps->max to be greater than or equal to the coefficients
1134 * in the equalities and inequalities of info->bmap that can be removed
1135 * if we end up applying wrapping.
1137 static isl_stat
wraps_update_max(struct isl_wraps
*wraps
,
1138 struct isl_coalesce_info
*info
)
1142 unsigned total
= isl_basic_map_total_dim(info
->bmap
);
1144 isl_int_init(max_k
);
1146 for (k
= 0; k
< info
->bmap
->n_eq
; ++k
) {
1147 if (info
->eq
[2 * k
] == STATUS_VALID
&&
1148 info
->eq
[2 * k
+ 1] == STATUS_VALID
)
1150 isl_seq_abs_max(info
->bmap
->eq
[k
] + 1, total
, &max_k
);
1151 if (isl_int_abs_gt(max_k
, wraps
->max
))
1152 isl_int_set(wraps
->max
, max_k
);
1155 for (k
= 0; k
< info
->bmap
->n_ineq
; ++k
) {
1156 if (info
->ineq
[k
] == STATUS_VALID
||
1157 info
->ineq
[k
] == STATUS_REDUNDANT
)
1159 isl_seq_abs_max(info
->bmap
->ineq
[k
] + 1, total
, &max_k
);
1160 if (isl_int_abs_gt(max_k
, wraps
->max
))
1161 isl_int_set(wraps
->max
, max_k
);
1164 isl_int_clear(max_k
);
1169 /* Initialize the isl_wraps data structure.
1170 * If we want to bound the coefficients of the wrapping constraints,
1171 * we set wraps->max to the largest coefficient
1172 * in the equalities and inequalities that can be removed if we end up
1173 * applying wrapping.
1175 static isl_stat
wraps_init(struct isl_wraps
*wraps
, __isl_take isl_mat
*mat
,
1176 struct isl_coalesce_info
*info
, int i
, int j
)
1183 return isl_stat_error
;
1184 ctx
= isl_mat_get_ctx(mat
);
1185 wraps
->bound
= isl_options_get_coalesce_bounded_wrapping(ctx
);
1188 isl_int_init(wraps
->max
);
1189 isl_int_set_si(wraps
->max
, 0);
1190 if (wraps_update_max(wraps
, &info
[i
]) < 0)
1191 return isl_stat_error
;
1192 if (wraps_update_max(wraps
, &info
[j
]) < 0)
1193 return isl_stat_error
;
1198 /* Free the contents of the isl_wraps data structure.
1200 static void wraps_free(struct isl_wraps
*wraps
)
1202 isl_mat_free(wraps
->mat
);
1204 isl_int_clear(wraps
->max
);
1207 /* Is the wrapping constraint in row "row" allowed?
1209 * If wraps->bound is set, we check that none of the coefficients
1210 * is greater than wraps->max.
1212 static int allow_wrap(struct isl_wraps
*wraps
, int row
)
1219 for (i
= 1; i
< wraps
->mat
->n_col
; ++i
)
1220 if (isl_int_abs_gt(wraps
->mat
->row
[row
][i
], wraps
->max
))
1226 /* Wrap "ineq" (or its opposite if "negate" is set) around "bound"
1227 * to include "set" and add the result in position "w" of "wraps".
1228 * "len" is the total number of coefficients in "bound" and "ineq".
1229 * Return 1 on success, 0 on failure and -1 on error.
1230 * Wrapping can fail if the result of wrapping is equal to "bound"
1231 * or if we want to bound the sizes of the coefficients and
1232 * the wrapped constraint does not satisfy this bound.
1234 static int add_wrap(struct isl_wraps
*wraps
, int w
, isl_int
*bound
,
1235 isl_int
*ineq
, unsigned len
, __isl_keep isl_set
*set
, int negate
)
1237 isl_seq_cpy(wraps
->mat
->row
[w
], bound
, len
);
1239 isl_seq_neg(wraps
->mat
->row
[w
+ 1], ineq
, len
);
1240 ineq
= wraps
->mat
->row
[w
+ 1];
1242 if (!isl_set_wrap_facet(set
, wraps
->mat
->row
[w
], ineq
))
1244 if (isl_seq_eq(wraps
->mat
->row
[w
], bound
, len
))
1246 if (!allow_wrap(wraps
, w
))
1251 /* For each constraint in info->bmap that is not redundant (as determined
1252 * by info->tab) and that is not a valid constraint for the other basic map,
1253 * wrap the constraint around "bound" such that it includes the whole
1254 * set "set" and append the resulting constraint to "wraps".
1255 * Note that the constraints that are valid for the other basic map
1256 * will be added to the combined basic map by default, so there is
1257 * no need to wrap them.
1258 * The caller wrap_in_facets even relies on this function not wrapping
1259 * any constraints that are already valid.
1260 * "wraps" is assumed to have been pre-allocated to the appropriate size.
1261 * wraps->n_row is the number of actual wrapped constraints that have
1263 * If any of the wrapping problems results in a constraint that is
1264 * identical to "bound", then this means that "set" is unbounded in such
1265 * way that no wrapping is possible. If this happens then wraps->n_row
1267 * Similarly, if we want to bound the coefficients of the wrapping
1268 * constraints and a newly added wrapping constraint does not
1269 * satisfy the bound, then wraps->n_row is also reset to zero.
1271 static isl_stat
add_wraps(struct isl_wraps
*wraps
,
1272 struct isl_coalesce_info
*info
, isl_int
*bound
, __isl_keep isl_set
*set
)
1277 isl_basic_map
*bmap
= info
->bmap
;
1278 unsigned len
= 1 + isl_basic_map_total_dim(bmap
);
1280 w
= wraps
->mat
->n_row
;
1282 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
1283 if (info
->ineq
[l
] == STATUS_VALID
||
1284 info
->ineq
[l
] == STATUS_REDUNDANT
)
1286 if (isl_seq_is_neg(bound
, bmap
->ineq
[l
], len
))
1288 if (isl_seq_eq(bound
, bmap
->ineq
[l
], len
))
1290 if (isl_tab_is_redundant(info
->tab
, bmap
->n_eq
+ l
))
1293 added
= add_wrap(wraps
, w
, bound
, bmap
->ineq
[l
], len
, set
, 0);
1295 return isl_stat_error
;
1300 for (l
= 0; l
< bmap
->n_eq
; ++l
) {
1301 if (isl_seq_is_neg(bound
, bmap
->eq
[l
], len
))
1303 if (isl_seq_eq(bound
, bmap
->eq
[l
], len
))
1306 for (m
= 0; m
< 2; ++m
) {
1307 if (info
->eq
[2 * l
+ m
] == STATUS_VALID
)
1309 added
= add_wrap(wraps
, w
, bound
, bmap
->eq
[l
], len
,
1312 return isl_stat_error
;
1319 wraps
->mat
->n_row
= w
;
1322 wraps
->mat
->n_row
= 0;
1326 /* Check if the constraints in "wraps" from "first" until the last
1327 * are all valid for the basic set represented by "tab".
1328 * If not, wraps->n_row is set to zero.
1330 static int check_wraps(__isl_keep isl_mat
*wraps
, int first
,
1331 struct isl_tab
*tab
)
1335 for (i
= first
; i
< wraps
->n_row
; ++i
) {
1336 enum isl_ineq_type type
;
1337 type
= isl_tab_ineq_type(tab
, wraps
->row
[i
]);
1338 if (type
== isl_ineq_error
)
1340 if (type
== isl_ineq_redundant
)
1349 /* Return a set that corresponds to the non-redundant constraints
1350 * (as recorded in tab) of bmap.
1352 * It's important to remove the redundant constraints as some
1353 * of the other constraints may have been modified after the
1354 * constraints were marked redundant.
1355 * In particular, a constraint may have been relaxed.
1356 * Redundant constraints are ignored when a constraint is relaxed
1357 * and should therefore continue to be ignored ever after.
1358 * Otherwise, the relaxation might be thwarted by some of
1359 * these constraints.
1361 * Update the underlying set to ensure that the dimension doesn't change.
1362 * Otherwise the integer divisions could get dropped if the tab
1363 * turns out to be empty.
1365 static __isl_give isl_set
*set_from_updated_bmap(__isl_keep isl_basic_map
*bmap
,
1366 struct isl_tab
*tab
)
1368 isl_basic_set
*bset
;
1370 bmap
= isl_basic_map_copy(bmap
);
1371 bset
= isl_basic_map_underlying_set(bmap
);
1372 bset
= isl_basic_set_cow(bset
);
1373 bset
= isl_basic_set_update_from_tab(bset
, tab
);
1374 return isl_set_from_basic_set(bset
);
1377 /* Wrap the constraints of info->bmap that bound the facet defined
1378 * by inequality "k" around (the opposite of) this inequality to
1379 * include "set". "bound" may be used to store the negated inequality.
1380 * Since the wrapped constraints are not guaranteed to contain the whole
1381 * of info->bmap, we check them in check_wraps.
1382 * If any of the wrapped constraints turn out to be invalid, then
1383 * check_wraps will reset wrap->n_row to zero.
1385 static isl_stat
add_wraps_around_facet(struct isl_wraps
*wraps
,
1386 struct isl_coalesce_info
*info
, int k
, isl_int
*bound
,
1387 __isl_keep isl_set
*set
)
1389 struct isl_tab_undo
*snap
;
1391 unsigned total
= isl_basic_map_total_dim(info
->bmap
);
1393 snap
= isl_tab_snap(info
->tab
);
1395 if (isl_tab_select_facet(info
->tab
, info
->bmap
->n_eq
+ k
) < 0)
1396 return isl_stat_error
;
1397 if (isl_tab_detect_redundant(info
->tab
) < 0)
1398 return isl_stat_error
;
1400 isl_seq_neg(bound
, info
->bmap
->ineq
[k
], 1 + total
);
1402 n
= wraps
->mat
->n_row
;
1403 if (add_wraps(wraps
, info
, bound
, set
) < 0)
1404 return isl_stat_error
;
1406 if (isl_tab_rollback(info
->tab
, snap
) < 0)
1407 return isl_stat_error
;
1408 if (check_wraps(wraps
->mat
, n
, info
->tab
) < 0)
1409 return isl_stat_error
;
1414 /* Given a basic set i with a constraint k that is adjacent to
1415 * basic set j, check if we can wrap
1416 * both the facet corresponding to k (if "wrap_facet" is set) and basic map j
1417 * (always) around their ridges to include the other set.
1418 * If so, replace the pair of basic sets by their union.
1420 * All constraints of i (except k) are assumed to be valid or
1421 * cut constraints for j.
1422 * Wrapping the cut constraints to include basic map j may result
1423 * in constraints that are no longer valid of basic map i
1424 * we have to check that the resulting wrapping constraints are valid for i.
1425 * If "wrap_facet" is not set, then all constraints of i (except k)
1426 * are assumed to be valid for j.
1435 static enum isl_change
can_wrap_in_facet(int i
, int j
, int k
,
1436 struct isl_coalesce_info
*info
, int wrap_facet
)
1438 enum isl_change change
= isl_change_none
;
1439 struct isl_wraps wraps
;
1442 struct isl_set
*set_i
= NULL
;
1443 struct isl_set
*set_j
= NULL
;
1444 struct isl_vec
*bound
= NULL
;
1445 unsigned total
= isl_basic_map_total_dim(info
[i
].bmap
);
1447 set_i
= set_from_updated_bmap(info
[i
].bmap
, info
[i
].tab
);
1448 set_j
= set_from_updated_bmap(info
[j
].bmap
, info
[j
].tab
);
1449 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
1450 mat
= isl_mat_alloc(ctx
, 2 * (info
[i
].bmap
->n_eq
+ info
[j
].bmap
->n_eq
) +
1451 info
[i
].bmap
->n_ineq
+ info
[j
].bmap
->n_ineq
,
1453 if (wraps_init(&wraps
, mat
, info
, i
, j
) < 0)
1455 bound
= isl_vec_alloc(ctx
, 1 + total
);
1456 if (!set_i
|| !set_j
|| !bound
)
1459 isl_seq_cpy(bound
->el
, info
[i
].bmap
->ineq
[k
], 1 + total
);
1460 isl_int_add_ui(bound
->el
[0], bound
->el
[0], 1);
1462 isl_seq_cpy(wraps
.mat
->row
[0], bound
->el
, 1 + total
);
1463 wraps
.mat
->n_row
= 1;
1465 if (add_wraps(&wraps
, &info
[j
], bound
->el
, set_i
) < 0)
1467 if (!wraps
.mat
->n_row
)
1471 if (add_wraps_around_facet(&wraps
, &info
[i
], k
,
1472 bound
->el
, set_j
) < 0)
1474 if (!wraps
.mat
->n_row
)
1478 change
= fuse(i
, j
, info
, wraps
.mat
, 0, 0);
1483 isl_set_free(set_i
);
1484 isl_set_free(set_j
);
1486 isl_vec_free(bound
);
1491 isl_vec_free(bound
);
1492 isl_set_free(set_i
);
1493 isl_set_free(set_j
);
1494 return isl_change_error
;
1497 /* Given a cut constraint t(x) >= 0 of basic map i, stored in row "w"
1498 * of wrap.mat, replace it by its relaxed version t(x) + 1 >= 0, and
1499 * add wrapping constraints to wrap.mat for all constraints
1500 * of basic map j that bound the part of basic map j that sticks out
1501 * of the cut constraint.
1502 * "set_i" is the underlying set of basic map i.
1503 * If any wrapping fails, then wraps->mat.n_row is reset to zero.
1505 * In particular, we first intersect basic map j with t(x) + 1 = 0.
1506 * If the result is empty, then t(x) >= 0 was actually a valid constraint
1507 * (with respect to the integer points), so we add t(x) >= 0 instead.
1508 * Otherwise, we wrap the constraints of basic map j that are not
1509 * redundant in this intersection and that are not already valid
1510 * for basic map i over basic map i.
1511 * Note that it is sufficient to wrap the constraints to include
1512 * basic map i, because we will only wrap the constraints that do
1513 * not include basic map i already. The wrapped constraint will
1514 * therefore be more relaxed compared to the original constraint.
1515 * Since the original constraint is valid for basic map j, so is
1516 * the wrapped constraint.
1518 static isl_stat
wrap_in_facet(struct isl_wraps
*wraps
, int w
,
1519 struct isl_coalesce_info
*info_j
, __isl_keep isl_set
*set_i
,
1520 struct isl_tab_undo
*snap
)
1522 isl_int_add_ui(wraps
->mat
->row
[w
][0], wraps
->mat
->row
[w
][0], 1);
1523 if (isl_tab_add_eq(info_j
->tab
, wraps
->mat
->row
[w
]) < 0)
1524 return isl_stat_error
;
1525 if (isl_tab_detect_redundant(info_j
->tab
) < 0)
1526 return isl_stat_error
;
1528 if (info_j
->tab
->empty
)
1529 isl_int_sub_ui(wraps
->mat
->row
[w
][0], wraps
->mat
->row
[w
][0], 1);
1530 else if (add_wraps(wraps
, info_j
, wraps
->mat
->row
[w
], set_i
) < 0)
1531 return isl_stat_error
;
1533 if (isl_tab_rollback(info_j
->tab
, snap
) < 0)
1534 return isl_stat_error
;
1539 /* Given a pair of basic maps i and j such that j sticks out
1540 * of i at n cut constraints, each time by at most one,
1541 * try to compute wrapping constraints and replace the two
1542 * basic maps by a single basic map.
1543 * The other constraints of i are assumed to be valid for j.
1544 * "set_i" is the underlying set of basic map i.
1545 * "wraps" has been initialized to be of the right size.
1547 * For each cut constraint t(x) >= 0 of i, we add the relaxed version
1548 * t(x) + 1 >= 0, along with wrapping constraints for all constraints
1549 * of basic map j that bound the part of basic map j that sticks out
1550 * of the cut constraint.
1552 * If any wrapping fails, i.e., if we cannot wrap to touch
1553 * the union, then we give up.
1554 * Otherwise, the pair of basic maps is replaced by their union.
1556 static enum isl_change
try_wrap_in_facets(int i
, int j
,
1557 struct isl_coalesce_info
*info
, struct isl_wraps
*wraps
,
1558 __isl_keep isl_set
*set_i
)
1562 struct isl_tab_undo
*snap
;
1564 total
= isl_basic_map_total_dim(info
[i
].bmap
);
1566 snap
= isl_tab_snap(info
[j
].tab
);
1568 wraps
->mat
->n_row
= 0;
1570 for (k
= 0; k
< info
[i
].bmap
->n_eq
; ++k
) {
1571 for (l
= 0; l
< 2; ++l
) {
1572 if (info
[i
].eq
[2 * k
+ l
] != STATUS_CUT
)
1574 w
= wraps
->mat
->n_row
++;
1576 isl_seq_neg(wraps
->mat
->row
[w
],
1577 info
[i
].bmap
->eq
[k
], 1 + total
);
1579 isl_seq_cpy(wraps
->mat
->row
[w
],
1580 info
[i
].bmap
->eq
[k
], 1 + total
);
1581 if (wrap_in_facet(wraps
, w
, &info
[j
], set_i
, snap
) < 0)
1582 return isl_change_error
;
1584 if (!wraps
->mat
->n_row
)
1585 return isl_change_none
;
1589 for (k
= 0; k
< info
[i
].bmap
->n_ineq
; ++k
) {
1590 if (info
[i
].ineq
[k
] != STATUS_CUT
)
1592 w
= wraps
->mat
->n_row
++;
1593 isl_seq_cpy(wraps
->mat
->row
[w
],
1594 info
[i
].bmap
->ineq
[k
], 1 + total
);
1595 if (wrap_in_facet(wraps
, w
, &info
[j
], set_i
, snap
) < 0)
1596 return isl_change_error
;
1598 if (!wraps
->mat
->n_row
)
1599 return isl_change_none
;
1602 return fuse(i
, j
, info
, wraps
->mat
, 0, 1);
1605 /* Given a pair of basic maps i and j such that j sticks out
1606 * of i at n cut constraints, each time by at most one,
1607 * try to compute wrapping constraints and replace the two
1608 * basic maps by a single basic map.
1609 * The other constraints of i are assumed to be valid for j.
1611 * The core computation is performed by try_wrap_in_facets.
1612 * This function simply extracts an underlying set representation
1613 * of basic map i and initializes the data structure for keeping
1614 * track of wrapping constraints.
1616 static enum isl_change
wrap_in_facets(int i
, int j
, int n
,
1617 struct isl_coalesce_info
*info
)
1619 enum isl_change change
= isl_change_none
;
1620 struct isl_wraps wraps
;
1623 isl_set
*set_i
= NULL
;
1624 unsigned total
= isl_basic_map_total_dim(info
[i
].bmap
);
1627 if (isl_tab_extend_cons(info
[j
].tab
, 1) < 0)
1628 return isl_change_error
;
1630 max_wrap
= 1 + 2 * info
[j
].bmap
->n_eq
+ info
[j
].bmap
->n_ineq
;
1633 set_i
= set_from_updated_bmap(info
[i
].bmap
, info
[i
].tab
);
1634 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
1635 mat
= isl_mat_alloc(ctx
, max_wrap
, 1 + total
);
1636 if (wraps_init(&wraps
, mat
, info
, i
, j
) < 0)
1641 change
= try_wrap_in_facets(i
, j
, info
, &wraps
, set_i
);
1644 isl_set_free(set_i
);
1649 isl_set_free(set_i
);
1650 return isl_change_error
;
1653 /* Return the effect of inequality "ineq" on the tableau "tab",
1654 * after relaxing the constant term of "ineq" by one.
1656 static enum isl_ineq_type
type_of_relaxed(struct isl_tab
*tab
, isl_int
*ineq
)
1658 enum isl_ineq_type type
;
1660 isl_int_add_ui(ineq
[0], ineq
[0], 1);
1661 type
= isl_tab_ineq_type(tab
, ineq
);
1662 isl_int_sub_ui(ineq
[0], ineq
[0], 1);
1667 /* Given two basic sets i and j,
1668 * check if relaxing all the cut constraints of i by one turns
1669 * them into valid constraint for j and check if we can wrap in
1670 * the bits that are sticking out.
1671 * If so, replace the pair by their union.
1673 * We first check if all relaxed cut inequalities of i are valid for j
1674 * and then try to wrap in the intersections of the relaxed cut inequalities
1677 * During this wrapping, we consider the points of j that lie at a distance
1678 * of exactly 1 from i. In particular, we ignore the points that lie in
1679 * between this lower-dimensional space and the basic map i.
1680 * We can therefore only apply this to integer maps.
1706 * Wrapping can fail if the result of wrapping one of the facets
1707 * around its edges does not produce any new facet constraint.
1708 * In particular, this happens when we try to wrap in unbounded sets.
1710 * _______________________________________________________________________
1714 * |_| |_________________________________________________________________
1717 * The following is not an acceptable result of coalescing the above two
1718 * sets as it includes extra integer points.
1719 * _______________________________________________________________________
1724 * \______________________________________________________________________
1726 static enum isl_change
can_wrap_in_set(int i
, int j
,
1727 struct isl_coalesce_info
*info
)
1733 if (ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_RATIONAL
) ||
1734 ISL_F_ISSET(info
[j
].bmap
, ISL_BASIC_MAP_RATIONAL
))
1735 return isl_change_none
;
1737 n
= count(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_CUT
);
1738 n
+= count(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_CUT
);
1740 return isl_change_none
;
1742 total
= isl_basic_map_total_dim(info
[i
].bmap
);
1743 for (k
= 0; k
< info
[i
].bmap
->n_eq
; ++k
) {
1744 for (l
= 0; l
< 2; ++l
) {
1745 enum isl_ineq_type type
;
1747 if (info
[i
].eq
[2 * k
+ l
] != STATUS_CUT
)
1751 isl_seq_neg(info
[i
].bmap
->eq
[k
],
1752 info
[i
].bmap
->eq
[k
], 1 + total
);
1753 type
= type_of_relaxed(info
[j
].tab
,
1754 info
[i
].bmap
->eq
[k
]);
1756 isl_seq_neg(info
[i
].bmap
->eq
[k
],
1757 info
[i
].bmap
->eq
[k
], 1 + total
);
1758 if (type
== isl_ineq_error
)
1759 return isl_change_error
;
1760 if (type
!= isl_ineq_redundant
)
1761 return isl_change_none
;
1765 for (k
= 0; k
< info
[i
].bmap
->n_ineq
; ++k
) {
1766 enum isl_ineq_type type
;
1768 if (info
[i
].ineq
[k
] != STATUS_CUT
)
1771 type
= type_of_relaxed(info
[j
].tab
, info
[i
].bmap
->ineq
[k
]);
1772 if (type
== isl_ineq_error
)
1773 return isl_change_error
;
1774 if (type
!= isl_ineq_redundant
)
1775 return isl_change_none
;
1778 return wrap_in_facets(i
, j
, n
, info
);
1781 /* Check if either i or j has only cut constraints that can
1782 * be used to wrap in (a facet of) the other basic set.
1783 * if so, replace the pair by their union.
1785 static enum isl_change
check_wrap(int i
, int j
, struct isl_coalesce_info
*info
)
1787 enum isl_change change
= isl_change_none
;
1789 change
= can_wrap_in_set(i
, j
, info
);
1790 if (change
!= isl_change_none
)
1793 change
= can_wrap_in_set(j
, i
, info
);
1797 /* Check if all inequality constraints of "i" that cut "j" cease
1798 * to be cut constraints if they are relaxed by one.
1799 * If so, collect the cut constraints in "list".
1800 * The caller is responsible for allocating "list".
1802 static isl_bool
all_cut_by_one(int i
, int j
, struct isl_coalesce_info
*info
,
1808 for (l
= 0; l
< info
[i
].bmap
->n_ineq
; ++l
) {
1809 enum isl_ineq_type type
;
1811 if (info
[i
].ineq
[l
] != STATUS_CUT
)
1813 type
= type_of_relaxed(info
[j
].tab
, info
[i
].bmap
->ineq
[l
]);
1814 if (type
== isl_ineq_error
)
1815 return isl_bool_error
;
1816 if (type
!= isl_ineq_redundant
)
1817 return isl_bool_false
;
1821 return isl_bool_true
;
1824 /* Given two basic maps such that "j" has at least one equality constraint
1825 * that is adjacent to an inequality constraint of "i" and such that "i" has
1826 * exactly one inequality constraint that is adjacent to an equality
1827 * constraint of "j", check whether "i" can be extended to include "j" or
1828 * whether "j" can be wrapped into "i".
1829 * All remaining constraints of "i" and "j" are assumed to be valid
1830 * or cut constraints of the other basic map.
1831 * However, none of the equality constraints of "i" are cut constraints.
1833 * If "i" has any "cut" inequality constraints, then check if relaxing
1834 * each of them by one is sufficient for them to become valid.
1835 * If so, check if the inequality constraint adjacent to an equality
1836 * constraint of "j" along with all these cut constraints
1837 * can be relaxed by one to contain exactly "j".
1838 * Otherwise, or if this fails, check if "j" can be wrapped into "i".
1840 static enum isl_change
check_single_adj_eq(int i
, int j
,
1841 struct isl_coalesce_info
*info
)
1843 enum isl_change change
= isl_change_none
;
1850 n_cut
= count(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_CUT
);
1852 k
= find(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ADJ_EQ
);
1855 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
1856 relax
= isl_calloc_array(ctx
, int, 1 + n_cut
);
1858 return isl_change_error
;
1860 try_relax
= all_cut_by_one(i
, j
, info
, relax
+ 1);
1862 change
= isl_change_error
;
1864 try_relax
= isl_bool_true
;
1867 if (try_relax
&& change
== isl_change_none
)
1868 change
= is_relaxed_extension(i
, j
, 1 + n_cut
, relax
, info
);
1871 if (change
!= isl_change_none
)
1874 change
= can_wrap_in_facet(i
, j
, k
, info
, n_cut
> 0);
1879 /* At least one of the basic maps has an equality that is adjacent
1880 * to an inequality. Make sure that only one of the basic maps has
1881 * such an equality and that the other basic map has exactly one
1882 * inequality adjacent to an equality.
1883 * If the other basic map does not have such an inequality, then
1884 * check if all its constraints are either valid or cut constraints
1885 * and, if so, try wrapping in the first map into the second.
1886 * Otherwise, try to extend one basic map with the other or
1887 * wrap one basic map in the other.
1889 static enum isl_change
check_adj_eq(int i
, int j
,
1890 struct isl_coalesce_info
*info
)
1892 if (any_eq(&info
[i
], STATUS_ADJ_INEQ
) &&
1893 any_eq(&info
[j
], STATUS_ADJ_INEQ
))
1894 /* ADJ EQ TOO MANY */
1895 return isl_change_none
;
1897 if (any_eq(&info
[i
], STATUS_ADJ_INEQ
))
1898 return check_adj_eq(j
, i
, info
);
1900 /* j has an equality adjacent to an inequality in i */
1902 if (count(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ADJ_EQ
) != 1) {
1903 if (all_valid_or_cut(&info
[i
]))
1904 return can_wrap_in_set(i
, j
, info
);
1905 return isl_change_none
;
1907 if (any_eq(&info
[i
], STATUS_CUT
))
1908 return isl_change_none
;
1909 if (any_ineq(&info
[j
], STATUS_ADJ_EQ
) ||
1910 any_ineq(&info
[i
], STATUS_ADJ_INEQ
) ||
1911 any_ineq(&info
[j
], STATUS_ADJ_INEQ
))
1912 /* ADJ EQ TOO MANY */
1913 return isl_change_none
;
1915 return check_single_adj_eq(i
, j
, info
);
1918 /* The two basic maps lie on adjacent hyperplanes. In particular,
1919 * basic map "i" has an equality that lies parallel to basic map "j".
1920 * Check if we can wrap the facets around the parallel hyperplanes
1921 * to include the other set.
1923 * We perform basically the same operations as can_wrap_in_facet,
1924 * except that we don't need to select a facet of one of the sets.
1930 * If there is more than one equality of "i" adjacent to an equality of "j",
1931 * then the result will satisfy one or more equalities that are a linear
1932 * combination of these equalities. These will be encoded as pairs
1933 * of inequalities in the wrapping constraints and need to be made
1936 static enum isl_change
check_eq_adj_eq(int i
, int j
,
1937 struct isl_coalesce_info
*info
)
1940 enum isl_change change
= isl_change_none
;
1941 int detect_equalities
= 0;
1942 struct isl_wraps wraps
;
1945 struct isl_set
*set_i
= NULL
;
1946 struct isl_set
*set_j
= NULL
;
1947 struct isl_vec
*bound
= NULL
;
1948 unsigned total
= isl_basic_map_total_dim(info
[i
].bmap
);
1950 if (count(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_ADJ_EQ
) != 1)
1951 detect_equalities
= 1;
1953 k
= find(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_ADJ_EQ
);
1955 set_i
= set_from_updated_bmap(info
[i
].bmap
, info
[i
].tab
);
1956 set_j
= set_from_updated_bmap(info
[j
].bmap
, info
[j
].tab
);
1957 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
1958 mat
= isl_mat_alloc(ctx
, 2 * (info
[i
].bmap
->n_eq
+ info
[j
].bmap
->n_eq
) +
1959 info
[i
].bmap
->n_ineq
+ info
[j
].bmap
->n_ineq
,
1961 if (wraps_init(&wraps
, mat
, info
, i
, j
) < 0)
1963 bound
= isl_vec_alloc(ctx
, 1 + total
);
1964 if (!set_i
|| !set_j
|| !bound
)
1968 isl_seq_neg(bound
->el
, info
[i
].bmap
->eq
[k
/ 2], 1 + total
);
1970 isl_seq_cpy(bound
->el
, info
[i
].bmap
->eq
[k
/ 2], 1 + total
);
1971 isl_int_add_ui(bound
->el
[0], bound
->el
[0], 1);
1973 isl_seq_cpy(wraps
.mat
->row
[0], bound
->el
, 1 + total
);
1974 wraps
.mat
->n_row
= 1;
1976 if (add_wraps(&wraps
, &info
[j
], bound
->el
, set_i
) < 0)
1978 if (!wraps
.mat
->n_row
)
1981 isl_int_sub_ui(bound
->el
[0], bound
->el
[0], 1);
1982 isl_seq_neg(bound
->el
, bound
->el
, 1 + total
);
1984 isl_seq_cpy(wraps
.mat
->row
[wraps
.mat
->n_row
], bound
->el
, 1 + total
);
1987 if (add_wraps(&wraps
, &info
[i
], bound
->el
, set_j
) < 0)
1989 if (!wraps
.mat
->n_row
)
1992 change
= fuse(i
, j
, info
, wraps
.mat
, detect_equalities
, 0);
1995 error
: change
= isl_change_error
;
2000 isl_set_free(set_i
);
2001 isl_set_free(set_j
);
2002 isl_vec_free(bound
);
2007 /* Initialize the "eq" and "ineq" fields of "info".
2009 static void init_status(struct isl_coalesce_info
*info
)
2011 info
->eq
= info
->ineq
= NULL
;
2014 /* Set info->eq to the positions of the equalities of info->bmap
2015 * with respect to the basic map represented by "tab".
2016 * If info->eq has already been computed, then do not compute it again.
2018 static void set_eq_status_in(struct isl_coalesce_info
*info
,
2019 struct isl_tab
*tab
)
2023 info
->eq
= eq_status_in(info
->bmap
, tab
);
2026 /* Set info->ineq to the positions of the inequalities of info->bmap
2027 * with respect to the basic map represented by "tab".
2028 * If info->ineq has already been computed, then do not compute it again.
2030 static void set_ineq_status_in(struct isl_coalesce_info
*info
,
2031 struct isl_tab
*tab
)
2035 info
->ineq
= ineq_status_in(info
->bmap
, info
->tab
, tab
);
2038 /* Free the memory allocated by the "eq" and "ineq" fields of "info".
2039 * This function assumes that init_status has been called on "info" first,
2040 * after which the "eq" and "ineq" fields may or may not have been
2041 * assigned a newly allocated array.
2043 static void clear_status(struct isl_coalesce_info
*info
)
2049 /* Are all inequality constraints of the basic map represented by "info"
2050 * valid for the other basic map, except for a single constraint
2051 * that is adjacent to an inequality constraint of the other basic map?
2053 static int all_ineq_valid_or_single_adj_ineq(struct isl_coalesce_info
*info
)
2058 for (i
= 0; i
< info
->bmap
->n_ineq
; ++i
) {
2059 if (info
->ineq
[i
] == STATUS_REDUNDANT
)
2061 if (info
->ineq
[i
] == STATUS_VALID
)
2063 if (info
->ineq
[i
] != STATUS_ADJ_INEQ
)
2073 /* Basic map "i" has one or more equality constraints that separate it
2074 * from basic map "j". Check if it happens to be an extension
2076 * In particular, check that all constraints of "j" are valid for "i",
2077 * except for one inequality constraint that is adjacent
2078 * to an inequality constraints of "i".
2079 * If so, check for "i" being an extension of "j" by calling
2080 * is_adj_ineq_extension.
2082 * Clean up the memory allocated for keeping track of the status
2083 * of the constraints before returning.
2085 static enum isl_change
separating_equality(int i
, int j
,
2086 struct isl_coalesce_info
*info
)
2088 enum isl_change change
= isl_change_none
;
2090 if (all(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_VALID
) &&
2091 all_ineq_valid_or_single_adj_ineq(&info
[j
]))
2092 change
= is_adj_ineq_extension(j
, i
, info
);
2094 clear_status(&info
[i
]);
2095 clear_status(&info
[j
]);
2099 /* Check if the union of the given pair of basic maps
2100 * can be represented by a single basic map.
2101 * If so, replace the pair by the single basic map and return
2102 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
2103 * Otherwise, return isl_change_none.
2104 * The two basic maps are assumed to live in the same local space.
2105 * The "eq" and "ineq" fields of info[i] and info[j] are assumed
2106 * to have been initialized by the caller, either to NULL or
2107 * to valid information.
2109 * We first check the effect of each constraint of one basic map
2110 * on the other basic map.
2111 * The constraint may be
2112 * redundant the constraint is redundant in its own
2113 * basic map and should be ignore and removed
2115 * valid all (integer) points of the other basic map
2116 * satisfy the constraint
2117 * separate no (integer) point of the other basic map
2118 * satisfies the constraint
2119 * cut some but not all points of the other basic map
2120 * satisfy the constraint
2121 * adj_eq the given constraint is adjacent (on the outside)
2122 * to an equality of the other basic map
2123 * adj_ineq the given constraint is adjacent (on the outside)
2124 * to an inequality of the other basic map
2126 * We consider seven cases in which we can replace the pair by a single
2127 * basic map. We ignore all "redundant" constraints.
2129 * 1. all constraints of one basic map are valid
2130 * => the other basic map is a subset and can be removed
2132 * 2. all constraints of both basic maps are either "valid" or "cut"
2133 * and the facets corresponding to the "cut" constraints
2134 * of one of the basic maps lies entirely inside the other basic map
2135 * => the pair can be replaced by a basic map consisting
2136 * of the valid constraints in both basic maps
2138 * 3. there is a single pair of adjacent inequalities
2139 * (all other constraints are "valid")
2140 * => the pair can be replaced by a basic map consisting
2141 * of the valid constraints in both basic maps
2143 * 4. one basic map has a single adjacent inequality, while the other
2144 * constraints are "valid". The other basic map has some
2145 * "cut" constraints, but replacing the adjacent inequality by
2146 * its opposite and adding the valid constraints of the other
2147 * basic map results in a subset of the other basic map
2148 * => the pair can be replaced by a basic map consisting
2149 * of the valid constraints in both basic maps
2151 * 5. there is a single adjacent pair of an inequality and an equality,
2152 * the other constraints of the basic map containing the inequality are
2153 * "valid". Moreover, if the inequality the basic map is relaxed
2154 * and then turned into an equality, then resulting facet lies
2155 * entirely inside the other basic map
2156 * => the pair can be replaced by the basic map containing
2157 * the inequality, with the inequality relaxed.
2159 * 6. there is a single adjacent pair of an inequality and an equality,
2160 * the other constraints of the basic map containing the inequality are
2161 * "valid". Moreover, the facets corresponding to both
2162 * the inequality and the equality can be wrapped around their
2163 * ridges to include the other basic map
2164 * => the pair can be replaced by a basic map consisting
2165 * of the valid constraints in both basic maps together
2166 * with all wrapping constraints
2168 * 7. one of the basic maps extends beyond the other by at most one.
2169 * Moreover, the facets corresponding to the cut constraints and
2170 * the pieces of the other basic map at offset one from these cut
2171 * constraints can be wrapped around their ridges to include
2172 * the union of the two basic maps
2173 * => the pair can be replaced by a basic map consisting
2174 * of the valid constraints in both basic maps together
2175 * with all wrapping constraints
2177 * 8. the two basic maps live in adjacent hyperplanes. In principle
2178 * such sets can always be combined through wrapping, but we impose
2179 * that there is only one such pair, to avoid overeager coalescing.
2181 * Throughout the computation, we maintain a collection of tableaus
2182 * corresponding to the basic maps. When the basic maps are dropped
2183 * or combined, the tableaus are modified accordingly.
2185 static enum isl_change
coalesce_local_pair_reuse(int i
, int j
,
2186 struct isl_coalesce_info
*info
)
2188 enum isl_change change
= isl_change_none
;
2190 set_ineq_status_in(&info
[i
], info
[j
].tab
);
2191 if (info
[i
].bmap
->n_ineq
&& !info
[i
].ineq
)
2193 if (any_ineq(&info
[i
], STATUS_ERROR
))
2195 if (any_ineq(&info
[i
], STATUS_SEPARATE
))
2198 set_ineq_status_in(&info
[j
], info
[i
].tab
);
2199 if (info
[j
].bmap
->n_ineq
&& !info
[j
].ineq
)
2201 if (any_ineq(&info
[j
], STATUS_ERROR
))
2203 if (any_ineq(&info
[j
], STATUS_SEPARATE
))
2206 set_eq_status_in(&info
[i
], info
[j
].tab
);
2207 if (info
[i
].bmap
->n_eq
&& !info
[i
].eq
)
2209 if (any_eq(&info
[i
], STATUS_ERROR
))
2212 set_eq_status_in(&info
[j
], info
[i
].tab
);
2213 if (info
[j
].bmap
->n_eq
&& !info
[j
].eq
)
2215 if (any_eq(&info
[j
], STATUS_ERROR
))
2218 if (any_eq(&info
[i
], STATUS_SEPARATE
))
2219 return separating_equality(i
, j
, info
);
2220 if (any_eq(&info
[j
], STATUS_SEPARATE
))
2221 return separating_equality(j
, i
, info
);
2223 if (all(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_VALID
) &&
2224 all(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_VALID
)) {
2226 change
= isl_change_drop_second
;
2227 } else if (all(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_VALID
) &&
2228 all(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_VALID
)) {
2230 change
= isl_change_drop_first
;
2231 } else if (any_eq(&info
[i
], STATUS_ADJ_EQ
)) {
2232 change
= check_eq_adj_eq(i
, j
, info
);
2233 } else if (any_eq(&info
[j
], STATUS_ADJ_EQ
)) {
2234 change
= check_eq_adj_eq(j
, i
, info
);
2235 } else if (any_eq(&info
[i
], STATUS_ADJ_INEQ
) ||
2236 any_eq(&info
[j
], STATUS_ADJ_INEQ
)) {
2237 change
= check_adj_eq(i
, j
, info
);
2238 } else if (any_ineq(&info
[i
], STATUS_ADJ_EQ
) ||
2239 any_ineq(&info
[j
], STATUS_ADJ_EQ
)) {
2242 } else if (any_ineq(&info
[i
], STATUS_ADJ_INEQ
) ||
2243 any_ineq(&info
[j
], STATUS_ADJ_INEQ
)) {
2244 change
= check_adj_ineq(i
, j
, info
);
2246 if (!any_eq(&info
[i
], STATUS_CUT
) &&
2247 !any_eq(&info
[j
], STATUS_CUT
))
2248 change
= check_facets(i
, j
, info
);
2249 if (change
== isl_change_none
)
2250 change
= check_wrap(i
, j
, info
);
2254 clear_status(&info
[i
]);
2255 clear_status(&info
[j
]);
2258 clear_status(&info
[i
]);
2259 clear_status(&info
[j
]);
2260 return isl_change_error
;
2263 /* Check if the union of the given pair of basic maps
2264 * can be represented by a single basic map.
2265 * If so, replace the pair by the single basic map and return
2266 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
2267 * Otherwise, return isl_change_none.
2268 * The two basic maps are assumed to live in the same local space.
2270 static enum isl_change
coalesce_local_pair(int i
, int j
,
2271 struct isl_coalesce_info
*info
)
2273 init_status(&info
[i
]);
2274 init_status(&info
[j
]);
2275 return coalesce_local_pair_reuse(i
, j
, info
);
2278 /* Shift the integer division at position "div" of the basic map
2279 * represented by "info" by "shift".
2281 * That is, if the integer division has the form
2285 * then replace it by
2287 * floor((f(x) + shift * d)/d) - shift
2289 static isl_stat
shift_div(struct isl_coalesce_info
*info
, int div
,
2294 info
->bmap
= isl_basic_map_shift_div(info
->bmap
, div
, 0, shift
);
2296 return isl_stat_error
;
2298 total
= isl_basic_map_dim(info
->bmap
, isl_dim_all
);
2299 total
-= isl_basic_map_dim(info
->bmap
, isl_dim_div
);
2300 if (isl_tab_shift_var(info
->tab
, total
+ div
, shift
) < 0)
2301 return isl_stat_error
;
2306 /* If the integer division at position "div" is defined by an equality,
2307 * i.e., a stride constraint, then change the integer division expression
2308 * to have a constant term equal to zero.
2310 * Let the equality constraint be
2314 * The integer division expression is then of the form
2316 * a = floor((-f - c')/m)
2318 * The integer division is first shifted by t = floor(c/m),
2319 * turning the equality constraint into
2321 * c - m floor(c/m) + f + m a' = 0
2325 * (c mod m) + f + m a' = 0
2329 * a' = (-f - (c mod m))/m = floor((-f)/m)
2331 * because a' is an integer and 0 <= (c mod m) < m.
2332 * The constant term of a' can therefore be zeroed out.
2334 static isl_stat
normalize_stride_div(struct isl_coalesce_info
*info
, int div
)
2339 isl_int shift
, stride
;
2341 defined
= isl_basic_map_has_defining_equality(info
->bmap
, isl_dim_div
,
2344 return isl_stat_error
;
2348 return isl_stat_error
;
2349 isl_int_init(shift
);
2350 isl_int_init(stride
);
2351 isl_constraint_get_constant(c
, &shift
);
2352 isl_constraint_get_coefficient(c
, isl_dim_div
, div
, &stride
);
2353 isl_int_fdiv_q(shift
, shift
, stride
);
2354 r
= shift_div(info
, div
, shift
);
2355 isl_int_clear(stride
);
2356 isl_int_clear(shift
);
2357 isl_constraint_free(c
);
2359 return isl_stat_error
;
2360 info
->bmap
= isl_basic_map_set_div_expr_constant_num_si_inplace(
2361 info
->bmap
, div
, 0);
2363 return isl_stat_error
;
2367 /* The basic maps represented by "info1" and "info2" are known
2368 * to have the same number of integer divisions.
2369 * Check if pairs of integer divisions are equal to each other
2370 * despite the fact that they differ by a rational constant.
2372 * In particular, look for any pair of integer divisions that
2373 * only differ in their constant terms.
2374 * If either of these integer divisions is defined
2375 * by stride constraints, then modify it to have a zero constant term.
2376 * If both are defined by stride constraints then in the end they will have
2377 * the same (zero) constant term.
2379 static isl_stat
harmonize_stride_divs(struct isl_coalesce_info
*info1
,
2380 struct isl_coalesce_info
*info2
)
2384 n
= isl_basic_map_dim(info1
->bmap
, isl_dim_div
);
2385 for (i
= 0; i
< n
; ++i
) {
2386 isl_bool known
, harmonize
;
2388 known
= isl_basic_map_div_is_known(info1
->bmap
, i
);
2389 if (known
>= 0 && known
)
2390 known
= isl_basic_map_div_is_known(info2
->bmap
, i
);
2392 return isl_stat_error
;
2395 harmonize
= isl_basic_map_equal_div_expr_except_constant(
2396 info1
->bmap
, i
, info2
->bmap
, i
);
2398 return isl_stat_error
;
2401 if (normalize_stride_div(info1
, i
) < 0)
2402 return isl_stat_error
;
2403 if (normalize_stride_div(info2
, i
) < 0)
2404 return isl_stat_error
;
2410 /* If "shift" is an integer constant, then shift the integer division
2411 * at position "div" of the basic map represented by "info" by "shift".
2412 * If "shift" is not an integer constant, then do nothing.
2413 * If "shift" is equal to zero, then no shift needs to be performed either.
2415 * That is, if the integer division has the form
2419 * then replace it by
2421 * floor((f(x) + shift * d)/d) - shift
2423 static isl_stat
shift_if_cst_int(struct isl_coalesce_info
*info
, int div
,
2424 __isl_keep isl_aff
*shift
)
2431 cst
= isl_aff_is_cst(shift
);
2432 if (cst
< 0 || !cst
)
2433 return cst
< 0 ? isl_stat_error
: isl_stat_ok
;
2435 c
= isl_aff_get_constant_val(shift
);
2436 cst
= isl_val_is_int(c
);
2437 if (cst
>= 0 && cst
)
2438 cst
= isl_bool_not(isl_val_is_zero(c
));
2439 if (cst
< 0 || !cst
) {
2441 return cst
< 0 ? isl_stat_error
: isl_stat_ok
;
2445 r
= isl_val_get_num_isl_int(c
, &d
);
2447 r
= shift_div(info
, div
, d
);
2455 /* Check if some of the divs in the basic map represented by "info1"
2456 * are shifts of the corresponding divs in the basic map represented
2457 * by "info2", taking into account the equality constraints "eq1" of "info1"
2458 * and "eq2" of "info2". If so, align them with those of "info2".
2459 * "info1" and "info2" are assumed to have the same number
2460 * of integer divisions.
2462 * An integer division is considered to be a shift of another integer
2463 * division if, after simplification with respect to the equality
2464 * constraints of the other basic map, one is equal to the other
2467 * In particular, for each pair of integer divisions, if both are known,
2468 * have the same denominator and are not already equal to each other,
2469 * simplify each with respect to the equality constraints
2470 * of the other basic map. If the difference is an integer constant,
2471 * then move this difference outside.
2472 * That is, if, after simplification, one integer division is of the form
2474 * floor((f(x) + c_1)/d)
2476 * while the other is of the form
2478 * floor((f(x) + c_2)/d)
2480 * and n = (c_2 - c_1)/d is an integer, then replace the first
2481 * integer division by
2483 * floor((f_1(x) + c_1 + n * d)/d) - n,
2485 * where floor((f_1(x) + c_1 + n * d)/d) = floor((f2(x) + c_2)/d)
2486 * after simplification with respect to the equality constraints.
2488 static isl_stat
harmonize_divs_with_hulls(struct isl_coalesce_info
*info1
,
2489 struct isl_coalesce_info
*info2
, __isl_keep isl_basic_set
*eq1
,
2490 __isl_keep isl_basic_set
*eq2
)
2494 isl_local_space
*ls1
, *ls2
;
2496 total
= isl_basic_map_total_dim(info1
->bmap
);
2497 ls1
= isl_local_space_wrap(isl_basic_map_get_local_space(info1
->bmap
));
2498 ls2
= isl_local_space_wrap(isl_basic_map_get_local_space(info2
->bmap
));
2499 for (i
= 0; i
< info1
->bmap
->n_div
; ++i
) {
2501 isl_aff
*div1
, *div2
;
2503 if (!isl_local_space_div_is_known(ls1
, i
) ||
2504 !isl_local_space_div_is_known(ls2
, i
))
2506 if (isl_int_ne(info1
->bmap
->div
[i
][0], info2
->bmap
->div
[i
][0]))
2508 if (isl_seq_eq(info1
->bmap
->div
[i
] + 1,
2509 info2
->bmap
->div
[i
] + 1, 1 + total
))
2511 div1
= isl_local_space_get_div(ls1
, i
);
2512 div2
= isl_local_space_get_div(ls2
, i
);
2513 div1
= isl_aff_substitute_equalities(div1
,
2514 isl_basic_set_copy(eq2
));
2515 div2
= isl_aff_substitute_equalities(div2
,
2516 isl_basic_set_copy(eq1
));
2517 div2
= isl_aff_sub(div2
, div1
);
2518 r
= shift_if_cst_int(info1
, i
, div2
);
2523 isl_local_space_free(ls1
);
2524 isl_local_space_free(ls2
);
2526 if (i
< info1
->bmap
->n_div
)
2527 return isl_stat_error
;
2531 /* Check if some of the divs in the basic map represented by "info1"
2532 * are shifts of the corresponding divs in the basic map represented
2533 * by "info2". If so, align them with those of "info2".
2534 * Only do this if "info1" and "info2" have the same number
2535 * of integer divisions.
2537 * An integer division is considered to be a shift of another integer
2538 * division if, after simplification with respect to the equality
2539 * constraints of the other basic map, one is equal to the other
2542 * First check if pairs of integer divisions are equal to each other
2543 * despite the fact that they differ by a rational constant.
2544 * If so, try and arrange for them to have the same constant term.
2546 * Then, extract the equality constraints and continue with
2547 * harmonize_divs_with_hulls.
2549 * If the equality constraints of both basic maps are the same,
2550 * then there is no need to perform any shifting since
2551 * the coefficients of the integer divisions should have been
2552 * reduced in the same way.
2554 static isl_stat
harmonize_divs(struct isl_coalesce_info
*info1
,
2555 struct isl_coalesce_info
*info2
)
2558 isl_basic_map
*bmap1
, *bmap2
;
2559 isl_basic_set
*eq1
, *eq2
;
2562 if (!info1
->bmap
|| !info2
->bmap
)
2563 return isl_stat_error
;
2565 if (info1
->bmap
->n_div
!= info2
->bmap
->n_div
)
2567 if (info1
->bmap
->n_div
== 0)
2570 if (harmonize_stride_divs(info1
, info2
) < 0)
2571 return isl_stat_error
;
2573 bmap1
= isl_basic_map_copy(info1
->bmap
);
2574 bmap2
= isl_basic_map_copy(info2
->bmap
);
2575 eq1
= isl_basic_map_wrap(isl_basic_map_plain_affine_hull(bmap1
));
2576 eq2
= isl_basic_map_wrap(isl_basic_map_plain_affine_hull(bmap2
));
2577 equal
= isl_basic_set_plain_is_equal(eq1
, eq2
);
2583 r
= harmonize_divs_with_hulls(info1
, info2
, eq1
, eq2
);
2584 isl_basic_set_free(eq1
);
2585 isl_basic_set_free(eq2
);
2590 /* Do the two basic maps live in the same local space, i.e.,
2591 * do they have the same (known) divs?
2592 * If either basic map has any unknown divs, then we can only assume
2593 * that they do not live in the same local space.
2595 static isl_bool
same_divs(__isl_keep isl_basic_map
*bmap1
,
2596 __isl_keep isl_basic_map
*bmap2
)
2602 if (!bmap1
|| !bmap2
)
2603 return isl_bool_error
;
2604 if (bmap1
->n_div
!= bmap2
->n_div
)
2605 return isl_bool_false
;
2607 if (bmap1
->n_div
== 0)
2608 return isl_bool_true
;
2610 known
= isl_basic_map_divs_known(bmap1
);
2611 if (known
< 0 || !known
)
2613 known
= isl_basic_map_divs_known(bmap2
);
2614 if (known
< 0 || !known
)
2617 total
= isl_basic_map_total_dim(bmap1
);
2618 for (i
= 0; i
< bmap1
->n_div
; ++i
)
2619 if (!isl_seq_eq(bmap1
->div
[i
], bmap2
->div
[i
], 2 + total
))
2625 /* Assuming that "tab" contains the equality constraints and
2626 * the initial inequality constraints of "bmap", copy the remaining
2627 * inequality constraints of "bmap" to "Tab".
2629 static isl_stat
copy_ineq(struct isl_tab
*tab
, __isl_keep isl_basic_map
*bmap
)
2634 return isl_stat_error
;
2636 n_ineq
= tab
->n_con
- tab
->n_eq
;
2637 for (i
= n_ineq
; i
< bmap
->n_ineq
; ++i
)
2638 if (isl_tab_add_ineq(tab
, bmap
->ineq
[i
]) < 0)
2639 return isl_stat_error
;
2644 /* Description of an integer division that is added
2645 * during an expansion.
2646 * "pos" is the position of the corresponding variable.
2647 * "cst" indicates whether this integer division has a fixed value.
2648 * "val" contains the fixed value, if the value is fixed.
2650 struct isl_expanded
{
2656 /* For each of the "n" integer division variables "expanded",
2657 * if the variable has a fixed value, then add two inequality
2658 * constraints expressing the fixed value.
2659 * Otherwise, add the corresponding div constraints.
2660 * The caller is responsible for removing the div constraints
2661 * that it added for all these "n" integer divisions.
2663 * The div constraints and the pair of inequality constraints
2664 * forcing the fixed value cannot both be added for a given variable
2665 * as the combination may render some of the original constraints redundant.
2666 * These would then be ignored during the coalescing detection,
2667 * while they could remain in the fused result.
2669 * The two added inequality constraints are
2674 * with "a" the variable and "v" its fixed value.
2675 * The facet corresponding to one of these two constraints is selected
2676 * in the tableau to ensure that the pair of inequality constraints
2677 * is treated as an equality constraint.
2679 * The information in info->ineq is thrown away because it was
2680 * computed in terms of div constraints, while some of those
2681 * have now been replaced by these pairs of inequality constraints.
2683 static isl_stat
fix_constant_divs(struct isl_coalesce_info
*info
,
2684 int n
, struct isl_expanded
*expanded
)
2690 o_div
= isl_basic_map_offset(info
->bmap
, isl_dim_div
) - 1;
2691 ineq
= isl_vec_alloc(isl_tab_get_ctx(info
->tab
), 1 + info
->tab
->n_var
);
2693 return isl_stat_error
;
2694 isl_seq_clr(ineq
->el
+ 1, info
->tab
->n_var
);
2696 for (i
= 0; i
< n
; ++i
) {
2697 if (!expanded
[i
].cst
) {
2698 info
->bmap
= isl_basic_map_extend_constraints(
2700 if (isl_basic_map_add_div_constraints(info
->bmap
,
2701 expanded
[i
].pos
- o_div
) < 0)
2704 isl_int_set_si(ineq
->el
[1 + expanded
[i
].pos
], -1);
2705 isl_int_set(ineq
->el
[0], expanded
[i
].val
);
2706 info
->bmap
= isl_basic_map_add_ineq(info
->bmap
,
2708 isl_int_set_si(ineq
->el
[1 + expanded
[i
].pos
], 1);
2709 isl_int_neg(ineq
->el
[0], expanded
[i
].val
);
2710 info
->bmap
= isl_basic_map_add_ineq(info
->bmap
,
2712 isl_int_set_si(ineq
->el
[1 + expanded
[i
].pos
], 0);
2714 if (copy_ineq(info
->tab
, info
->bmap
) < 0)
2716 if (expanded
[i
].cst
&&
2717 isl_tab_select_facet(info
->tab
, info
->tab
->n_con
- 1) < 0)
2726 return i
< n
? isl_stat_error
: isl_stat_ok
;
2729 /* Insert the "n" integer division variables "expanded"
2730 * into info->tab and info->bmap and
2731 * update info->ineq with respect to the redundant constraints
2732 * in the resulting tableau.
2733 * "bmap" contains the result of this insertion in info->bmap,
2734 * while info->bmap is the original version
2735 * of "bmap", i.e., the one that corresponds to the current
2736 * state of info->tab. The number of constraints in info->bmap
2737 * is assumed to be the same as the number of constraints
2738 * in info->tab. This is required to be able to detect
2739 * the extra constraints in "bmap".
2741 * In particular, introduce extra variables corresponding
2742 * to the extra integer divisions and add the div constraints
2743 * that were added to "bmap" after info->tab was created
2745 * Furthermore, check if these extra integer divisions happen
2746 * to attain a fixed integer value in info->tab.
2747 * If so, replace the corresponding div constraints by pairs
2748 * of inequality constraints that fix these
2749 * integer divisions to their single integer values.
2750 * Replace info->bmap by "bmap" to match the changes to info->tab.
2751 * info->ineq was computed without a tableau and therefore
2752 * does not take into account the redundant constraints
2753 * in the tableau. Mark them here.
2754 * There is no need to check the newly added div constraints
2755 * since they cannot be redundant.
2756 * The redundancy check is not performed when constants have been discovered
2757 * since info->ineq is completely thrown away in this case.
2759 static isl_stat
tab_insert_divs(struct isl_coalesce_info
*info
,
2760 int n
, struct isl_expanded
*expanded
, __isl_take isl_basic_map
*bmap
)
2764 struct isl_tab_undo
*snap
;
2768 return isl_stat_error
;
2769 if (info
->bmap
->n_eq
+ info
->bmap
->n_ineq
!= info
->tab
->n_con
)
2770 isl_die(isl_basic_map_get_ctx(bmap
), isl_error_internal
,
2771 "original tableau does not correspond "
2772 "to original basic map", goto error
);
2774 if (isl_tab_extend_vars(info
->tab
, n
) < 0)
2776 if (isl_tab_extend_cons(info
->tab
, 2 * n
) < 0)
2779 for (i
= 0; i
< n
; ++i
) {
2780 if (isl_tab_insert_var(info
->tab
, expanded
[i
].pos
) < 0)
2784 snap
= isl_tab_snap(info
->tab
);
2786 n_ineq
= info
->tab
->n_con
- info
->tab
->n_eq
;
2787 if (copy_ineq(info
->tab
, bmap
) < 0)
2790 isl_basic_map_free(info
->bmap
);
2794 for (i
= 0; i
< n
; ++i
) {
2795 expanded
[i
].cst
= isl_tab_is_constant(info
->tab
,
2796 expanded
[i
].pos
, &expanded
[i
].val
);
2797 if (expanded
[i
].cst
< 0)
2798 return isl_stat_error
;
2799 if (expanded
[i
].cst
)
2804 if (isl_tab_rollback(info
->tab
, snap
) < 0)
2805 return isl_stat_error
;
2806 info
->bmap
= isl_basic_map_cow(info
->bmap
);
2807 if (isl_basic_map_free_inequality(info
->bmap
, 2 * n
) < 0)
2808 return isl_stat_error
;
2810 return fix_constant_divs(info
, n
, expanded
);
2813 n_eq
= info
->bmap
->n_eq
;
2814 for (i
= 0; i
< n_ineq
; ++i
) {
2815 if (isl_tab_is_redundant(info
->tab
, n_eq
+ i
))
2816 info
->ineq
[i
] = STATUS_REDUNDANT
;
2821 isl_basic_map_free(bmap
);
2822 return isl_stat_error
;
2825 /* Expand info->tab and info->bmap in the same way "bmap" was expanded
2826 * in isl_basic_map_expand_divs using the expansion "exp" and
2827 * update info->ineq with respect to the redundant constraints
2828 * in the resulting tableau. info->bmap is the original version
2829 * of "bmap", i.e., the one that corresponds to the current
2830 * state of info->tab. The number of constraints in info->bmap
2831 * is assumed to be the same as the number of constraints
2832 * in info->tab. This is required to be able to detect
2833 * the extra constraints in "bmap".
2835 * Extract the positions where extra local variables are introduced
2836 * from "exp" and call tab_insert_divs.
2838 static isl_stat
expand_tab(struct isl_coalesce_info
*info
, int *exp
,
2839 __isl_take isl_basic_map
*bmap
)
2842 struct isl_expanded
*expanded
;
2845 unsigned total
, pos
, n_div
;
2848 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
2849 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
2850 pos
= total
- n_div
;
2851 extra_var
= total
- info
->tab
->n_var
;
2852 n
= n_div
- extra_var
;
2854 ctx
= isl_basic_map_get_ctx(bmap
);
2855 expanded
= isl_calloc_array(ctx
, struct isl_expanded
, extra_var
);
2856 if (extra_var
&& !expanded
)
2861 for (j
= 0; j
< n_div
; ++j
) {
2862 if (i
< n
&& exp
[i
] == j
) {
2866 expanded
[k
++].pos
= pos
+ j
;
2869 for (k
= 0; k
< extra_var
; ++k
)
2870 isl_int_init(expanded
[k
].val
);
2872 r
= tab_insert_divs(info
, extra_var
, expanded
, bmap
);
2874 for (k
= 0; k
< extra_var
; ++k
)
2875 isl_int_clear(expanded
[k
].val
);
2880 isl_basic_map_free(bmap
);
2881 return isl_stat_error
;
2884 /* Check if the union of the basic maps represented by info[i] and info[j]
2885 * can be represented by a single basic map,
2886 * after expanding the divs of info[i] to match those of info[j].
2887 * If so, replace the pair by the single basic map and return
2888 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
2889 * Otherwise, return isl_change_none.
2891 * The caller has already checked for info[j] being a subset of info[i].
2892 * If some of the divs of info[j] are unknown, then the expanded info[i]
2893 * will not have the corresponding div constraints. The other patterns
2894 * therefore cannot apply. Skip the computation in this case.
2896 * The expansion is performed using the divs "div" and expansion "exp"
2897 * computed by the caller.
2898 * info[i].bmap has already been expanded and the result is passed in
2900 * The "eq" and "ineq" fields of info[i] reflect the status of
2901 * the constraints of the expanded "bmap" with respect to info[j].tab.
2902 * However, inequality constraints that are redundant in info[i].tab
2903 * have not yet been marked as such because no tableau was available.
2905 * Replace info[i].bmap by "bmap" and expand info[i].tab as well,
2906 * updating info[i].ineq with respect to the redundant constraints.
2907 * Then try and coalesce the expanded info[i] with info[j],
2908 * reusing the information in info[i].eq and info[i].ineq.
2909 * If this does not result in any coalescing or if it results in info[j]
2910 * getting dropped (which should not happen in practice, since the case
2911 * of info[j] being a subset of info[i] has already been checked by
2912 * the caller), then revert info[i] to its original state.
2914 static enum isl_change
coalesce_expand_tab_divs(__isl_take isl_basic_map
*bmap
,
2915 int i
, int j
, struct isl_coalesce_info
*info
, __isl_keep isl_mat
*div
,
2919 isl_basic_map
*bmap_i
;
2920 struct isl_tab_undo
*snap
;
2921 enum isl_change change
= isl_change_none
;
2923 known
= isl_basic_map_divs_known(info
[j
].bmap
);
2924 if (known
< 0 || !known
) {
2925 clear_status(&info
[i
]);
2926 isl_basic_map_free(bmap
);
2927 return known
< 0 ? isl_change_error
: isl_change_none
;
2930 bmap_i
= isl_basic_map_copy(info
[i
].bmap
);
2931 snap
= isl_tab_snap(info
[i
].tab
);
2932 if (expand_tab(&info
[i
], exp
, bmap
) < 0)
2933 change
= isl_change_error
;
2935 init_status(&info
[j
]);
2936 if (change
== isl_change_none
)
2937 change
= coalesce_local_pair_reuse(i
, j
, info
);
2939 clear_status(&info
[i
]);
2940 if (change
!= isl_change_none
&& change
!= isl_change_drop_second
) {
2941 isl_basic_map_free(bmap_i
);
2943 isl_basic_map_free(info
[i
].bmap
);
2944 info
[i
].bmap
= bmap_i
;
2946 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
2947 change
= isl_change_error
;
2953 /* Check if the union of "bmap" and the basic map represented by info[j]
2954 * can be represented by a single basic map,
2955 * after expanding the divs of "bmap" to match those of info[j].
2956 * If so, replace the pair by the single basic map and return
2957 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
2958 * Otherwise, return isl_change_none.
2960 * In particular, check if the expanded "bmap" contains the basic map
2961 * represented by the tableau info[j].tab.
2962 * The expansion is performed using the divs "div" and expansion "exp"
2963 * computed by the caller.
2964 * Then we check if all constraints of the expanded "bmap" are valid for
2967 * If "i" is not equal to -1, then "bmap" is equal to info[i].bmap.
2968 * In this case, the positions of the constraints of info[i].bmap
2969 * with respect to the basic map represented by info[j] are stored
2972 * If the expanded "bmap" does not contain the basic map
2973 * represented by the tableau info[j].tab and if "i" is not -1,
2974 * i.e., if the original "bmap" is info[i].bmap, then expand info[i].tab
2975 * as well and check if that results in coalescing.
2977 static enum isl_change
coalesce_with_expanded_divs(
2978 __isl_keep isl_basic_map
*bmap
, int i
, int j
,
2979 struct isl_coalesce_info
*info
, __isl_keep isl_mat
*div
, int *exp
)
2981 enum isl_change change
= isl_change_none
;
2982 struct isl_coalesce_info info_local
, *info_i
;
2984 info_i
= i
>= 0 ? &info
[i
] : &info_local
;
2985 init_status(info_i
);
2986 bmap
= isl_basic_map_copy(bmap
);
2987 bmap
= isl_basic_map_expand_divs(bmap
, isl_mat_copy(div
), exp
);
2988 bmap
= isl_basic_map_mark_final(bmap
);
2993 info_local
.bmap
= bmap
;
2994 info_i
->eq
= eq_status_in(bmap
, info
[j
].tab
);
2995 if (bmap
->n_eq
&& !info_i
->eq
)
2997 if (any_eq(info_i
, STATUS_ERROR
))
2999 if (any_eq(info_i
, STATUS_SEPARATE
))
3002 info_i
->ineq
= ineq_status_in(bmap
, NULL
, info
[j
].tab
);
3003 if (bmap
->n_ineq
&& !info_i
->ineq
)
3005 if (any_ineq(info_i
, STATUS_ERROR
))
3007 if (any_ineq(info_i
, STATUS_SEPARATE
))
3010 if (all(info_i
->eq
, 2 * bmap
->n_eq
, STATUS_VALID
) &&
3011 all(info_i
->ineq
, bmap
->n_ineq
, STATUS_VALID
)) {
3013 change
= isl_change_drop_second
;
3016 if (change
== isl_change_none
&& i
!= -1)
3017 return coalesce_expand_tab_divs(bmap
, i
, j
, info
, div
, exp
);
3020 isl_basic_map_free(bmap
);
3021 clear_status(info_i
);
3024 isl_basic_map_free(bmap
);
3025 clear_status(info_i
);
3026 return isl_change_error
;
3029 /* Check if the union of "bmap_i" and the basic map represented by info[j]
3030 * can be represented by a single basic map,
3031 * after aligning the divs of "bmap_i" to match those of info[j].
3032 * If so, replace the pair by the single basic map and return
3033 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
3034 * Otherwise, return isl_change_none.
3036 * In particular, check if "bmap_i" contains the basic map represented by
3037 * info[j] after aligning the divs of "bmap_i" to those of info[j].
3038 * Note that this can only succeed if the number of divs of "bmap_i"
3039 * is smaller than (or equal to) the number of divs of info[j].
3041 * We first check if the divs of "bmap_i" are all known and form a subset
3042 * of those of info[j].bmap. If so, we pass control over to
3043 * coalesce_with_expanded_divs.
3045 * If "i" is not equal to -1, then "bmap" is equal to info[i].bmap.
3047 static enum isl_change
coalesce_after_aligning_divs(
3048 __isl_keep isl_basic_map
*bmap_i
, int i
, int j
,
3049 struct isl_coalesce_info
*info
)
3052 isl_mat
*div_i
, *div_j
, *div
;
3056 enum isl_change change
;
3058 known
= isl_basic_map_divs_known(bmap_i
);
3059 if (known
< 0 || !known
)
3062 ctx
= isl_basic_map_get_ctx(bmap_i
);
3064 div_i
= isl_basic_map_get_divs(bmap_i
);
3065 div_j
= isl_basic_map_get_divs(info
[j
].bmap
);
3067 if (!div_i
|| !div_j
)
3070 exp1
= isl_alloc_array(ctx
, int, div_i
->n_row
);
3071 exp2
= isl_alloc_array(ctx
, int, div_j
->n_row
);
3072 if ((div_i
->n_row
&& !exp1
) || (div_j
->n_row
&& !exp2
))
3075 div
= isl_merge_divs(div_i
, div_j
, exp1
, exp2
);
3079 if (div
->n_row
== div_j
->n_row
)
3080 change
= coalesce_with_expanded_divs(bmap_i
,
3081 i
, j
, info
, div
, exp1
);
3083 change
= isl_change_none
;
3087 isl_mat_free(div_i
);
3088 isl_mat_free(div_j
);
3095 isl_mat_free(div_i
);
3096 isl_mat_free(div_j
);
3099 return isl_change_error
;
3102 /* Check if basic map "j" is a subset of basic map "i" after
3103 * exploiting the extra equalities of "j" to simplify the divs of "i".
3104 * If so, remove basic map "j" and return isl_change_drop_second.
3106 * If "j" does not have any equalities or if they are the same
3107 * as those of "i", then we cannot exploit them to simplify the divs.
3108 * Similarly, if there are no divs in "i", then they cannot be simplified.
3109 * If, on the other hand, the affine hulls of "i" and "j" do not intersect,
3110 * then "j" cannot be a subset of "i".
3112 * Otherwise, we intersect "i" with the affine hull of "j" and then
3113 * check if "j" is a subset of the result after aligning the divs.
3114 * If so, then "j" is definitely a subset of "i" and can be removed.
3115 * Note that if after intersection with the affine hull of "j".
3116 * "i" still has more divs than "j", then there is no way we can
3117 * align the divs of "i" to those of "j".
3119 static enum isl_change
coalesce_subset_with_equalities(int i
, int j
,
3120 struct isl_coalesce_info
*info
)
3122 isl_basic_map
*hull_i
, *hull_j
, *bmap_i
;
3124 enum isl_change change
;
3126 if (info
[j
].bmap
->n_eq
== 0)
3127 return isl_change_none
;
3128 if (info
[i
].bmap
->n_div
== 0)
3129 return isl_change_none
;
3131 hull_i
= isl_basic_map_copy(info
[i
].bmap
);
3132 hull_i
= isl_basic_map_plain_affine_hull(hull_i
);
3133 hull_j
= isl_basic_map_copy(info
[j
].bmap
);
3134 hull_j
= isl_basic_map_plain_affine_hull(hull_j
);
3136 hull_j
= isl_basic_map_intersect(hull_j
, isl_basic_map_copy(hull_i
));
3137 equal
= isl_basic_map_plain_is_equal(hull_i
, hull_j
);
3138 empty
= isl_basic_map_plain_is_empty(hull_j
);
3139 isl_basic_map_free(hull_i
);
3141 if (equal
< 0 || equal
|| empty
< 0 || empty
) {
3142 isl_basic_map_free(hull_j
);
3143 if (equal
< 0 || empty
< 0)
3144 return isl_change_error
;
3145 return isl_change_none
;
3148 bmap_i
= isl_basic_map_copy(info
[i
].bmap
);
3149 bmap_i
= isl_basic_map_intersect(bmap_i
, hull_j
);
3151 return isl_change_error
;
3153 if (bmap_i
->n_div
> info
[j
].bmap
->n_div
) {
3154 isl_basic_map_free(bmap_i
);
3155 return isl_change_none
;
3158 change
= coalesce_after_aligning_divs(bmap_i
, -1, j
, info
);
3160 isl_basic_map_free(bmap_i
);
3165 /* Check if the union of and the basic maps represented by info[i] and info[j]
3166 * can be represented by a single basic map, by aligning or equating
3167 * their integer divisions.
3168 * If so, replace the pair by the single basic map and return
3169 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
3170 * Otherwise, return isl_change_none.
3172 * Note that we only perform any test if the number of divs is different
3173 * in the two basic maps. In case the number of divs is the same,
3174 * we have already established that the divs are different
3175 * in the two basic maps.
3176 * In particular, if the number of divs of basic map i is smaller than
3177 * the number of divs of basic map j, then we check if j is a subset of i
3180 static enum isl_change
coalesce_divs(int i
, int j
,
3181 struct isl_coalesce_info
*info
)
3183 enum isl_change change
= isl_change_none
;
3185 if (info
[i
].bmap
->n_div
< info
[j
].bmap
->n_div
)
3186 change
= coalesce_after_aligning_divs(info
[i
].bmap
, i
, j
, info
);
3187 if (change
!= isl_change_none
)
3190 if (info
[j
].bmap
->n_div
< info
[i
].bmap
->n_div
)
3191 change
= coalesce_after_aligning_divs(info
[j
].bmap
, j
, i
, info
);
3192 if (change
!= isl_change_none
)
3193 return invert_change(change
);
3195 change
= coalesce_subset_with_equalities(i
, j
, info
);
3196 if (change
!= isl_change_none
)
3199 change
= coalesce_subset_with_equalities(j
, i
, info
);
3200 if (change
!= isl_change_none
)
3201 return invert_change(change
);
3203 return isl_change_none
;
3206 /* Does "bmap" involve any divs that themselves refer to divs?
3208 static isl_bool
has_nested_div(__isl_keep isl_basic_map
*bmap
)
3214 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
3215 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
3218 for (i
= 0; i
< n_div
; ++i
)
3219 if (isl_seq_first_non_zero(bmap
->div
[i
] + 2 + total
,
3221 return isl_bool_true
;
3223 return isl_bool_false
;
3226 /* Return a list of affine expressions, one for each integer division
3227 * in "bmap_i". For each integer division that also appears in "bmap_j",
3228 * the affine expression is set to NaN. The number of NaNs in the list
3229 * is equal to the number of integer divisions in "bmap_j".
3230 * For the other integer divisions of "bmap_i", the corresponding
3231 * element in the list is a purely affine expression equal to the integer
3232 * division in "hull".
3233 * If no such list can be constructed, then the number of elements
3234 * in the returned list is smaller than the number of integer divisions
3237 static __isl_give isl_aff_list
*set_up_substitutions(
3238 __isl_keep isl_basic_map
*bmap_i
, __isl_keep isl_basic_map
*bmap_j
,
3239 __isl_take isl_basic_map
*hull
)
3241 unsigned n_div_i
, n_div_j
, total
;
3243 isl_local_space
*ls
;
3244 isl_basic_set
*wrap_hull
;
3252 ctx
= isl_basic_map_get_ctx(hull
);
3254 n_div_i
= isl_basic_map_dim(bmap_i
, isl_dim_div
);
3255 n_div_j
= isl_basic_map_dim(bmap_j
, isl_dim_div
);
3256 total
= isl_basic_map_total_dim(bmap_i
) - n_div_i
;
3258 ls
= isl_basic_map_get_local_space(bmap_i
);
3259 ls
= isl_local_space_wrap(ls
);
3260 wrap_hull
= isl_basic_map_wrap(hull
);
3262 aff_nan
= isl_aff_nan_on_domain(isl_local_space_copy(ls
));
3263 list
= isl_aff_list_alloc(ctx
, n_div_i
);
3266 for (i
= 0; i
< n_div_i
; ++i
) {
3270 isl_basic_map_equal_div_expr_part(bmap_i
, i
, bmap_j
, j
,
3273 list
= isl_aff_list_add(list
, isl_aff_copy(aff_nan
));
3276 if (n_div_i
- i
<= n_div_j
- j
)
3279 aff
= isl_local_space_get_div(ls
, i
);
3280 aff
= isl_aff_substitute_equalities(aff
,
3281 isl_basic_set_copy(wrap_hull
));
3282 aff
= isl_aff_floor(aff
);
3285 if (isl_aff_dim(aff
, isl_dim_div
) != 0) {
3290 list
= isl_aff_list_add(list
, aff
);
3293 isl_aff_free(aff_nan
);
3294 isl_local_space_free(ls
);
3295 isl_basic_set_free(wrap_hull
);
3299 isl_aff_free(aff_nan
);
3300 isl_local_space_free(ls
);
3301 isl_basic_set_free(wrap_hull
);
3302 isl_aff_list_free(list
);
3306 /* Add variables to info->bmap and info->tab corresponding to the elements
3307 * in "list" that are not set to NaN.
3308 * "extra_var" is the number of these elements.
3309 * "dim" is the offset in the variables of "tab" where we should
3310 * start considering the elements in "list".
3311 * When this function returns, the total number of variables in "tab"
3312 * is equal to "dim" plus the number of elements in "list".
3314 * The newly added existentially quantified variables are not given
3315 * an explicit representation because the corresponding div constraints
3316 * do not appear in info->bmap. These constraints are not added
3317 * to info->bmap because for internal consistency, they would need to
3318 * be added to info->tab as well, where they could combine with the equality
3319 * that is added later to result in constraints that do not hold
3320 * in the original input.
3322 static isl_stat
add_sub_vars(struct isl_coalesce_info
*info
,
3323 __isl_keep isl_aff_list
*list
, int dim
, int extra_var
)
3328 space
= isl_basic_map_get_space(info
->bmap
);
3329 info
->bmap
= isl_basic_map_cow(info
->bmap
);
3330 info
->bmap
= isl_basic_map_extend_space(info
->bmap
, space
,
3333 return isl_stat_error
;
3334 n
= isl_aff_list_n_aff(list
);
3335 for (i
= 0; i
< n
; ++i
) {
3339 aff
= isl_aff_list_get_aff(list
, i
);
3340 is_nan
= isl_aff_is_nan(aff
);
3343 return isl_stat_error
;
3347 if (isl_tab_insert_var(info
->tab
, dim
+ i
) < 0)
3348 return isl_stat_error
;
3349 d
= isl_basic_map_alloc_div(info
->bmap
);
3351 return isl_stat_error
;
3352 info
->bmap
= isl_basic_map_mark_div_unknown(info
->bmap
, d
);
3354 return isl_stat_error
;
3355 for (j
= d
; j
> i
; --j
)
3356 isl_basic_map_swap_div(info
->bmap
, j
- 1, j
);
3362 /* For each element in "list" that is not set to NaN, fix the corresponding
3363 * variable in "tab" to the purely affine expression defined by the element.
3364 * "dim" is the offset in the variables of "tab" where we should
3365 * start considering the elements in "list".
3367 * This function assumes that a sufficient number of rows and
3368 * elements in the constraint array are available in the tableau.
3370 static int add_sub_equalities(struct isl_tab
*tab
,
3371 __isl_keep isl_aff_list
*list
, int dim
)
3378 n
= isl_aff_list_n_aff(list
);
3380 ctx
= isl_tab_get_ctx(tab
);
3381 sub
= isl_vec_alloc(ctx
, 1 + dim
+ n
);
3384 isl_seq_clr(sub
->el
+ 1 + dim
, n
);
3386 for (i
= 0; i
< n
; ++i
) {
3387 aff
= isl_aff_list_get_aff(list
, i
);
3390 if (isl_aff_is_nan(aff
)) {
3394 isl_seq_cpy(sub
->el
, aff
->v
->el
+ 1, 1 + dim
);
3395 isl_int_neg(sub
->el
[1 + dim
+ i
], aff
->v
->el
[0]);
3396 if (isl_tab_add_eq(tab
, sub
->el
) < 0)
3398 isl_int_set_si(sub
->el
[1 + dim
+ i
], 0);
3410 /* Add variables to info->tab and info->bmap corresponding to the elements
3411 * in "list" that are not set to NaN. The value of the added variable
3412 * in info->tab is fixed to the purely affine expression defined by the element.
3413 * "dim" is the offset in the variables of info->tab where we should
3414 * start considering the elements in "list".
3415 * When this function returns, the total number of variables in info->tab
3416 * is equal to "dim" plus the number of elements in "list".
3418 static int add_subs(struct isl_coalesce_info
*info
,
3419 __isl_keep isl_aff_list
*list
, int dim
)
3427 n
= isl_aff_list_n_aff(list
);
3428 extra_var
= n
- (info
->tab
->n_var
- dim
);
3430 if (isl_tab_extend_vars(info
->tab
, extra_var
) < 0)
3432 if (isl_tab_extend_cons(info
->tab
, 2 * extra_var
) < 0)
3434 if (add_sub_vars(info
, list
, dim
, extra_var
) < 0)
3437 return add_sub_equalities(info
->tab
, list
, dim
);
3440 /* Coalesce basic map "j" into basic map "i" after adding the extra integer
3441 * divisions in "i" but not in "j" to basic map "j", with values
3442 * specified by "list". The total number of elements in "list"
3443 * is equal to the number of integer divisions in "i", while the number
3444 * of NaN elements in the list is equal to the number of integer divisions
3447 * If no coalescing can be performed, then we need to revert basic map "j"
3448 * to its original state. We do the same if basic map "i" gets dropped
3449 * during the coalescing, even though this should not happen in practice
3450 * since we have already checked for "j" being a subset of "i"
3451 * before we reach this stage.
3453 static enum isl_change
coalesce_with_subs(int i
, int j
,
3454 struct isl_coalesce_info
*info
, __isl_keep isl_aff_list
*list
)
3456 isl_basic_map
*bmap_j
;
3457 struct isl_tab_undo
*snap
;
3459 enum isl_change change
;
3461 bmap_j
= isl_basic_map_copy(info
[j
].bmap
);
3462 snap
= isl_tab_snap(info
[j
].tab
);
3464 dim
= isl_basic_map_dim(bmap_j
, isl_dim_all
);
3465 dim
-= isl_basic_map_dim(bmap_j
, isl_dim_div
);
3466 if (add_subs(&info
[j
], list
, dim
) < 0)
3469 change
= coalesce_local_pair(i
, j
, info
);
3470 if (change
!= isl_change_none
&& change
!= isl_change_drop_first
) {
3471 isl_basic_map_free(bmap_j
);
3473 isl_basic_map_free(info
[j
].bmap
);
3474 info
[j
].bmap
= bmap_j
;
3476 if (isl_tab_rollback(info
[j
].tab
, snap
) < 0)
3477 return isl_change_error
;
3482 isl_basic_map_free(bmap_j
);
3483 return isl_change_error
;
3486 /* Check if we can coalesce basic map "j" into basic map "i" after copying
3487 * those extra integer divisions in "i" that can be simplified away
3488 * using the extra equalities in "j".
3489 * All divs are assumed to be known and not contain any nested divs.
3491 * We first check if there are any extra equalities in "j" that we
3492 * can exploit. Then we check if every integer division in "i"
3493 * either already appears in "j" or can be simplified using the
3494 * extra equalities to a purely affine expression.
3495 * If these tests succeed, then we try to coalesce the two basic maps
3496 * by introducing extra dimensions in "j" corresponding to
3497 * the extra integer divsisions "i" fixed to the corresponding
3498 * purely affine expression.
3500 static enum isl_change
check_coalesce_into_eq(int i
, int j
,
3501 struct isl_coalesce_info
*info
)
3503 unsigned n_div_i
, n_div_j
;
3504 isl_basic_map
*hull_i
, *hull_j
;
3507 enum isl_change change
;
3509 n_div_i
= isl_basic_map_dim(info
[i
].bmap
, isl_dim_div
);
3510 n_div_j
= isl_basic_map_dim(info
[j
].bmap
, isl_dim_div
);
3511 if (n_div_i
<= n_div_j
)
3512 return isl_change_none
;
3513 if (info
[j
].bmap
->n_eq
== 0)
3514 return isl_change_none
;
3516 hull_i
= isl_basic_map_copy(info
[i
].bmap
);
3517 hull_i
= isl_basic_map_plain_affine_hull(hull_i
);
3518 hull_j
= isl_basic_map_copy(info
[j
].bmap
);
3519 hull_j
= isl_basic_map_plain_affine_hull(hull_j
);
3521 hull_j
= isl_basic_map_intersect(hull_j
, isl_basic_map_copy(hull_i
));
3522 equal
= isl_basic_map_plain_is_equal(hull_i
, hull_j
);
3523 empty
= isl_basic_map_plain_is_empty(hull_j
);
3524 isl_basic_map_free(hull_i
);
3526 if (equal
< 0 || empty
< 0)
3528 if (equal
|| empty
) {
3529 isl_basic_map_free(hull_j
);
3530 return isl_change_none
;
3533 list
= set_up_substitutions(info
[i
].bmap
, info
[j
].bmap
, hull_j
);
3535 return isl_change_error
;
3536 if (isl_aff_list_n_aff(list
) < n_div_i
)
3537 change
= isl_change_none
;
3539 change
= coalesce_with_subs(i
, j
, info
, list
);
3541 isl_aff_list_free(list
);
3545 isl_basic_map_free(hull_j
);
3546 return isl_change_error
;
3549 /* Check if we can coalesce basic maps "i" and "j" after copying
3550 * those extra integer divisions in one of the basic maps that can
3551 * be simplified away using the extra equalities in the other basic map.
3552 * We require all divs to be known in both basic maps.
3553 * Furthermore, to simplify the comparison of div expressions,
3554 * we do not allow any nested integer divisions.
3556 static enum isl_change
check_coalesce_eq(int i
, int j
,
3557 struct isl_coalesce_info
*info
)
3559 isl_bool known
, nested
;
3560 enum isl_change change
;
3562 known
= isl_basic_map_divs_known(info
[i
].bmap
);
3563 if (known
< 0 || !known
)
3564 return known
< 0 ? isl_change_error
: isl_change_none
;
3565 known
= isl_basic_map_divs_known(info
[j
].bmap
);
3566 if (known
< 0 || !known
)
3567 return known
< 0 ? isl_change_error
: isl_change_none
;
3568 nested
= has_nested_div(info
[i
].bmap
);
3569 if (nested
< 0 || nested
)
3570 return nested
< 0 ? isl_change_error
: isl_change_none
;
3571 nested
= has_nested_div(info
[j
].bmap
);
3572 if (nested
< 0 || nested
)
3573 return nested
< 0 ? isl_change_error
: isl_change_none
;
3575 change
= check_coalesce_into_eq(i
, j
, info
);
3576 if (change
!= isl_change_none
)
3578 change
= check_coalesce_into_eq(j
, i
, info
);
3579 if (change
!= isl_change_none
)
3580 return invert_change(change
);
3582 return isl_change_none
;
3585 /* Check if the union of the given pair of basic maps
3586 * can be represented by a single basic map.
3587 * If so, replace the pair by the single basic map and return
3588 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
3589 * Otherwise, return isl_change_none.
3591 * We first check if the two basic maps live in the same local space,
3592 * after aligning the divs that differ by only an integer constant.
3593 * If so, we do the complete check. Otherwise, we check if they have
3594 * the same number of integer divisions and can be coalesced, if one is
3595 * an obvious subset of the other or if the extra integer divisions
3596 * of one basic map can be simplified away using the extra equalities
3597 * of the other basic map.
3599 static enum isl_change
coalesce_pair(int i
, int j
,
3600 struct isl_coalesce_info
*info
)
3603 enum isl_change change
;
3605 if (harmonize_divs(&info
[i
], &info
[j
]) < 0)
3606 return isl_change_error
;
3607 same
= same_divs(info
[i
].bmap
, info
[j
].bmap
);
3609 return isl_change_error
;
3611 return coalesce_local_pair(i
, j
, info
);
3613 if (info
[i
].bmap
->n_div
== info
[j
].bmap
->n_div
) {
3614 change
= coalesce_local_pair(i
, j
, info
);
3615 if (change
!= isl_change_none
)
3619 change
= coalesce_divs(i
, j
, info
);
3620 if (change
!= isl_change_none
)
3623 return check_coalesce_eq(i
, j
, info
);
3626 /* Return the maximum of "a" and "b".
3628 static int isl_max(int a
, int b
)
3630 return a
> b
? a
: b
;
3633 /* Pairwise coalesce the basic maps in the range [start1, end1[ of "info"
3634 * with those in the range [start2, end2[, skipping basic maps
3635 * that have been removed (either before or within this function).
3637 * For each basic map i in the first range, we check if it can be coalesced
3638 * with respect to any previously considered basic map j in the second range.
3639 * If i gets dropped (because it was a subset of some j), then
3640 * we can move on to the next basic map.
3641 * If j gets dropped, we need to continue checking against the other
3642 * previously considered basic maps.
3643 * If the two basic maps got fused, then we recheck the fused basic map
3644 * against the previously considered basic maps, starting at i + 1
3645 * (even if start2 is greater than i + 1).
3647 static int coalesce_range(isl_ctx
*ctx
, struct isl_coalesce_info
*info
,
3648 int start1
, int end1
, int start2
, int end2
)
3652 for (i
= end1
- 1; i
>= start1
; --i
) {
3653 if (info
[i
].removed
)
3655 for (j
= isl_max(i
+ 1, start2
); j
< end2
; ++j
) {
3656 enum isl_change changed
;
3658 if (info
[j
].removed
)
3660 if (info
[i
].removed
)
3661 isl_die(ctx
, isl_error_internal
,
3662 "basic map unexpectedly removed",
3664 changed
= coalesce_pair(i
, j
, info
);
3666 case isl_change_error
:
3668 case isl_change_none
:
3669 case isl_change_drop_second
:
3671 case isl_change_drop_first
:
3674 case isl_change_fuse
:
3684 /* Pairwise coalesce the basic maps described by the "n" elements of "info".
3686 * We consider groups of basic maps that live in the same apparent
3687 * affine hull and we first coalesce within such a group before we
3688 * coalesce the elements in the group with elements of previously
3689 * considered groups. If a fuse happens during the second phase,
3690 * then we also reconsider the elements within the group.
3692 static int coalesce(isl_ctx
*ctx
, int n
, struct isl_coalesce_info
*info
)
3696 for (end
= n
; end
> 0; end
= start
) {
3698 while (start
>= 1 &&
3699 info
[start
- 1].hull_hash
== info
[start
].hull_hash
)
3701 if (coalesce_range(ctx
, info
, start
, end
, start
, end
) < 0)
3703 if (coalesce_range(ctx
, info
, start
, end
, end
, n
) < 0)
3710 /* Update the basic maps in "map" based on the information in "info".
3711 * In particular, remove the basic maps that have been marked removed and
3712 * update the others based on the information in the corresponding tableau.
3713 * Since we detected implicit equalities without calling
3714 * isl_basic_map_gauss, we need to do it now.
3715 * Also call isl_basic_map_simplify if we may have lost the definition
3716 * of one or more integer divisions.
3718 static __isl_give isl_map
*update_basic_maps(__isl_take isl_map
*map
,
3719 int n
, struct isl_coalesce_info
*info
)
3726 for (i
= n
- 1; i
>= 0; --i
) {
3727 if (info
[i
].removed
) {
3728 isl_basic_map_free(map
->p
[i
]);
3729 if (i
!= map
->n
- 1)
3730 map
->p
[i
] = map
->p
[map
->n
- 1];
3735 info
[i
].bmap
= isl_basic_map_update_from_tab(info
[i
].bmap
,
3737 info
[i
].bmap
= isl_basic_map_gauss(info
[i
].bmap
, NULL
);
3738 if (info
[i
].simplify
)
3739 info
[i
].bmap
= isl_basic_map_simplify(info
[i
].bmap
);
3740 info
[i
].bmap
= isl_basic_map_finalize(info
[i
].bmap
);
3742 return isl_map_free(map
);
3743 ISL_F_SET(info
[i
].bmap
, ISL_BASIC_MAP_NO_IMPLICIT
);
3744 ISL_F_SET(info
[i
].bmap
, ISL_BASIC_MAP_NO_REDUNDANT
);
3745 isl_basic_map_free(map
->p
[i
]);
3746 map
->p
[i
] = info
[i
].bmap
;
3747 info
[i
].bmap
= NULL
;
3753 /* For each pair of basic maps in the map, check if the union of the two
3754 * can be represented by a single basic map.
3755 * If so, replace the pair by the single basic map and start over.
3757 * We factor out any (hidden) common factor from the constraint
3758 * coefficients to improve the detection of adjacent constraints.
3760 * Since we are constructing the tableaus of the basic maps anyway,
3761 * we exploit them to detect implicit equalities and redundant constraints.
3762 * This also helps the coalescing as it can ignore the redundant constraints.
3763 * In order to avoid confusion, we make all implicit equalities explicit
3764 * in the basic maps. We don't call isl_basic_map_gauss, though,
3765 * as that may affect the number of constraints.
3766 * This means that we have to call isl_basic_map_gauss at the end
3767 * of the computation (in update_basic_maps) to ensure that
3768 * the basic maps are not left in an unexpected state.
3769 * For each basic map, we also compute the hash of the apparent affine hull
3770 * for use in coalesce.
3772 __isl_give isl_map
*isl_map_coalesce(__isl_take isl_map
*map
)
3777 struct isl_coalesce_info
*info
= NULL
;
3779 map
= isl_map_remove_empty_parts(map
);
3786 ctx
= isl_map_get_ctx(map
);
3787 map
= isl_map_sort_divs(map
);
3788 map
= isl_map_cow(map
);
3795 info
= isl_calloc_array(map
->ctx
, struct isl_coalesce_info
, n
);
3799 for (i
= 0; i
< map
->n
; ++i
) {
3800 map
->p
[i
] = isl_basic_map_reduce_coefficients(map
->p
[i
]);
3803 info
[i
].bmap
= isl_basic_map_copy(map
->p
[i
]);
3804 info
[i
].tab
= isl_tab_from_basic_map(info
[i
].bmap
, 0);
3807 if (!ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_NO_IMPLICIT
))
3808 if (isl_tab_detect_implicit_equalities(info
[i
].tab
) < 0)
3810 info
[i
].bmap
= isl_tab_make_equalities_explicit(info
[i
].tab
,
3814 if (!ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_NO_REDUNDANT
))
3815 if (isl_tab_detect_redundant(info
[i
].tab
) < 0)
3817 if (coalesce_info_set_hull_hash(&info
[i
]) < 0)
3820 for (i
= map
->n
- 1; i
>= 0; --i
)
3821 if (info
[i
].tab
->empty
)
3824 if (coalesce(ctx
, n
, info
) < 0)
3827 map
= update_basic_maps(map
, n
, info
);
3829 clear_coalesce_info(n
, info
);
3833 clear_coalesce_info(n
, info
);
3838 /* For each pair of basic sets in the set, check if the union of the two
3839 * can be represented by a single basic set.
3840 * If so, replace the pair by the single basic set and start over.
3842 struct isl_set
*isl_set_coalesce(struct isl_set
*set
)
3844 return set_from_map(isl_map_coalesce(set_to_map(set
)));