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
7 * Copyright 2020 Cerebras Systems
9 * Use of this software is governed by the MIT license
11 * Written by Sven Verdoolaege, K.U.Leuven, Departement
12 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
13 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
14 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
15 * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
16 * and Inria Paris - Rocquencourt, Domaine de Voluceau - Rocquencourt,
17 * B.P. 105 - 78153 Le Chesnay, France
18 * and Centre de Recherche Inria de Paris, 2 rue Simone Iff - Voie DQ12,
19 * CS 42112, 75589 Paris Cedex 12, France
20 * and Cerebras Systems, 175 S San Antonio Rd, Los Altos, CA, USA
23 #include <isl_ctx_private.h>
24 #include "isl_map_private.h"
26 #include <isl/options.h>
28 #include <isl_mat_private.h>
29 #include <isl_local_space_private.h>
30 #include <isl_val_private.h>
31 #include <isl_vec_private.h>
32 #include <isl_aff_private.h>
33 #include <isl_equalities.h>
34 #include <isl_constraint_private.h>
36 #include <set_to_map.c>
37 #include <set_from_map.c>
39 #define STATUS_ERROR -1
40 #define STATUS_REDUNDANT 1
41 #define STATUS_VALID 2
42 #define STATUS_SEPARATE 3
44 #define STATUS_ADJ_EQ 5
45 #define STATUS_ADJ_INEQ 6
47 static int status_in(isl_int
*ineq
, struct isl_tab
*tab
)
49 enum isl_ineq_type type
= isl_tab_ineq_type(tab
, ineq
);
52 case isl_ineq_error
: return STATUS_ERROR
;
53 case isl_ineq_redundant
: return STATUS_VALID
;
54 case isl_ineq_separate
: return STATUS_SEPARATE
;
55 case isl_ineq_cut
: return STATUS_CUT
;
56 case isl_ineq_adj_eq
: return STATUS_ADJ_EQ
;
57 case isl_ineq_adj_ineq
: return STATUS_ADJ_INEQ
;
61 /* Compute the position of the equalities of basic map "bmap_i"
62 * with respect to the basic map represented by "tab_j".
63 * The resulting array has twice as many entries as the number
64 * of equalities corresponding to the two inequalities to which
65 * each equality corresponds.
67 static int *eq_status_in(__isl_keep isl_basic_map
*bmap_i
,
68 struct isl_tab
*tab_j
)
74 dim
= isl_basic_map_dim(bmap_i
, isl_dim_all
);
78 eq
= isl_calloc_array(bmap_i
->ctx
, int, 2 * bmap_i
->n_eq
);
82 for (k
= 0; k
< bmap_i
->n_eq
; ++k
) {
83 for (l
= 0; l
< 2; ++l
) {
84 isl_seq_neg(bmap_i
->eq
[k
], bmap_i
->eq
[k
], 1+dim
);
85 eq
[2 * k
+ l
] = status_in(bmap_i
->eq
[k
], tab_j
);
86 if (eq
[2 * k
+ l
] == STATUS_ERROR
)
97 /* Compute the position of the inequalities of basic map "bmap_i"
98 * (also represented by "tab_i", if not NULL) with respect to the basic map
99 * represented by "tab_j".
101 static int *ineq_status_in(__isl_keep isl_basic_map
*bmap_i
,
102 struct isl_tab
*tab_i
, struct isl_tab
*tab_j
)
105 unsigned n_eq
= bmap_i
->n_eq
;
106 int *ineq
= isl_calloc_array(bmap_i
->ctx
, int, bmap_i
->n_ineq
);
111 for (k
= 0; k
< bmap_i
->n_ineq
; ++k
) {
112 if (tab_i
&& isl_tab_is_redundant(tab_i
, n_eq
+ k
)) {
113 ineq
[k
] = STATUS_REDUNDANT
;
116 ineq
[k
] = status_in(bmap_i
->ineq
[k
], tab_j
);
117 if (ineq
[k
] == STATUS_ERROR
)
119 if (ineq
[k
] == STATUS_SEPARATE
)
129 static int any(int *con
, unsigned len
, int status
)
133 for (i
= 0; i
< len
; ++i
)
134 if (con
[i
] == status
)
139 /* Return the first position of "status" in the list "con" of length "len".
140 * Return -1 if there is no such entry.
142 static int find(int *con
, unsigned len
, int status
)
146 for (i
= 0; i
< len
; ++i
)
147 if (con
[i
] == status
)
152 static int count(int *con
, unsigned len
, int status
)
157 for (i
= 0; i
< len
; ++i
)
158 if (con
[i
] == status
)
163 static int all(int *con
, unsigned len
, int status
)
167 for (i
= 0; i
< len
; ++i
) {
168 if (con
[i
] == STATUS_REDUNDANT
)
170 if (con
[i
] != status
)
176 /* Internal information associated to a basic map in a map
177 * that is to be coalesced by isl_map_coalesce.
179 * "bmap" is the basic map itself (or NULL if "removed" is set)
180 * "tab" is the corresponding tableau (or NULL if "removed" is set)
181 * "hull_hash" identifies the affine space in which "bmap" lives.
182 * "modified" is set if this basic map may not be identical
183 * to any of the basic maps in the input.
184 * "removed" is set if this basic map has been removed from the map
185 * "simplify" is set if this basic map may have some unknown integer
186 * divisions that were not present in the input basic maps. The basic
187 * map should then be simplified such that we may be able to find
188 * a definition among the constraints.
190 * "eq" and "ineq" are only set if we are currently trying to coalesce
191 * this basic map with another basic map, in which case they represent
192 * the position of the inequalities of this basic map with respect to
193 * the other basic map. The number of elements in the "eq" array
194 * is twice the number of equalities in the "bmap", corresponding
195 * to the two inequalities that make up each equality.
197 struct isl_coalesce_info
{
208 /* Is there any (half of an) equality constraint in the description
209 * of the basic map represented by "info" that
210 * has position "status" with respect to the other basic map?
212 static int any_eq(struct isl_coalesce_info
*info
, int status
)
216 n_eq
= isl_basic_map_n_equality(info
->bmap
);
217 return any(info
->eq
, 2 * n_eq
, status
);
220 /* Is there any inequality constraint in the description
221 * of the basic map represented by "info" that
222 * has position "status" with respect to the other basic map?
224 static int any_ineq(struct isl_coalesce_info
*info
, int status
)
228 n_ineq
= isl_basic_map_n_inequality(info
->bmap
);
229 return any(info
->ineq
, n_ineq
, status
);
232 /* Return the position of the first half on an equality constraint
233 * in the description of the basic map represented by "info" that
234 * has position "status" with respect to the other basic map.
235 * The returned value is twice the position of the equality constraint
236 * plus zero for the negative half and plus one for the positive half.
237 * Return -1 if there is no such entry.
239 static int find_eq(struct isl_coalesce_info
*info
, int status
)
243 n_eq
= isl_basic_map_n_equality(info
->bmap
);
244 return find(info
->eq
, 2 * n_eq
, status
);
247 /* Return the position of the first inequality constraint in the description
248 * of the basic map represented by "info" that
249 * has position "status" with respect to the other basic map.
250 * Return -1 if there is no such entry.
252 static int find_ineq(struct isl_coalesce_info
*info
, int status
)
256 n_ineq
= isl_basic_map_n_inequality(info
->bmap
);
257 return find(info
->ineq
, n_ineq
, status
);
260 /* Return the number of (halves of) equality constraints in the description
261 * of the basic map represented by "info" that
262 * have position "status" with respect to the other basic map.
264 static int count_eq(struct isl_coalesce_info
*info
, int status
)
268 n_eq
= isl_basic_map_n_equality(info
->bmap
);
269 return count(info
->eq
, 2 * n_eq
, status
);
272 /* Return the number of inequality constraints in the description
273 * of the basic map represented by "info" that
274 * have position "status" with respect to the other basic map.
276 static int count_ineq(struct isl_coalesce_info
*info
, int status
)
280 n_ineq
= isl_basic_map_n_inequality(info
->bmap
);
281 return count(info
->ineq
, n_ineq
, status
);
284 /* Are all non-redundant constraints of the basic map represented by "info"
285 * either valid or cut constraints with respect to the other basic map?
287 static int all_valid_or_cut(struct isl_coalesce_info
*info
)
291 for (i
= 0; i
< 2 * info
->bmap
->n_eq
; ++i
) {
292 if (info
->eq
[i
] == STATUS_REDUNDANT
)
294 if (info
->eq
[i
] == STATUS_VALID
)
296 if (info
->eq
[i
] == STATUS_CUT
)
301 for (i
= 0; i
< info
->bmap
->n_ineq
; ++i
) {
302 if (info
->ineq
[i
] == STATUS_REDUNDANT
)
304 if (info
->ineq
[i
] == STATUS_VALID
)
306 if (info
->ineq
[i
] == STATUS_CUT
)
314 /* Compute the hash of the (apparent) affine hull of info->bmap (with
315 * the existentially quantified variables removed) and store it
318 static int coalesce_info_set_hull_hash(struct isl_coalesce_info
*info
)
323 hull
= isl_basic_map_copy(info
->bmap
);
324 hull
= isl_basic_map_plain_affine_hull(hull
);
325 n_div
= isl_basic_map_dim(hull
, isl_dim_div
);
327 hull
= isl_basic_map_free(hull
);
328 hull
= isl_basic_map_drop_constraints_involving_dims(hull
,
329 isl_dim_div
, 0, n_div
);
330 info
->hull_hash
= isl_basic_map_get_hash(hull
);
331 isl_basic_map_free(hull
);
333 return hull
? 0 : -1;
336 /* Free all the allocated memory in an array
337 * of "n" isl_coalesce_info elements.
339 static void clear_coalesce_info(int n
, struct isl_coalesce_info
*info
)
346 for (i
= 0; i
< n
; ++i
) {
347 isl_basic_map_free(info
[i
].bmap
);
348 isl_tab_free(info
[i
].tab
);
354 /* Clear the memory associated to "info".
356 static void clear(struct isl_coalesce_info
*info
)
358 info
->bmap
= isl_basic_map_free(info
->bmap
);
359 isl_tab_free(info
->tab
);
363 /* Drop the basic map represented by "info".
364 * That is, clear the memory associated to the entry and
365 * mark it as having been removed.
367 static void drop(struct isl_coalesce_info
*info
)
373 /* Exchange the information in "info1" with that in "info2".
375 static void exchange(struct isl_coalesce_info
*info1
,
376 struct isl_coalesce_info
*info2
)
378 struct isl_coalesce_info info
;
385 /* This type represents the kind of change that has been performed
386 * while trying to coalesce two basic maps.
388 * isl_change_none: nothing was changed
389 * isl_change_drop_first: the first basic map was removed
390 * isl_change_drop_second: the second basic map was removed
391 * isl_change_fuse: the two basic maps were replaced by a new basic map.
394 isl_change_error
= -1,
396 isl_change_drop_first
,
397 isl_change_drop_second
,
401 /* Update "change" based on an interchange of the first and the second
402 * basic map. That is, interchange isl_change_drop_first and
403 * isl_change_drop_second.
405 static enum isl_change
invert_change(enum isl_change change
)
408 case isl_change_error
:
409 return isl_change_error
;
410 case isl_change_none
:
411 return isl_change_none
;
412 case isl_change_drop_first
:
413 return isl_change_drop_second
;
414 case isl_change_drop_second
:
415 return isl_change_drop_first
;
416 case isl_change_fuse
:
417 return isl_change_fuse
;
420 return isl_change_error
;
423 /* Add the valid constraints of the basic map represented by "info"
424 * to "bmap". "len" is the size of the constraints.
425 * If only one of the pair of inequalities that make up an equality
426 * is valid, then add that inequality.
428 static __isl_give isl_basic_map
*add_valid_constraints(
429 __isl_take isl_basic_map
*bmap
, struct isl_coalesce_info
*info
,
437 for (k
= 0; k
< info
->bmap
->n_eq
; ++k
) {
438 if (info
->eq
[2 * k
] == STATUS_VALID
&&
439 info
->eq
[2 * k
+ 1] == STATUS_VALID
) {
440 l
= isl_basic_map_alloc_equality(bmap
);
442 return isl_basic_map_free(bmap
);
443 isl_seq_cpy(bmap
->eq
[l
], info
->bmap
->eq
[k
], len
);
444 } else if (info
->eq
[2 * k
] == STATUS_VALID
) {
445 l
= isl_basic_map_alloc_inequality(bmap
);
447 return isl_basic_map_free(bmap
);
448 isl_seq_neg(bmap
->ineq
[l
], info
->bmap
->eq
[k
], len
);
449 } else if (info
->eq
[2 * k
+ 1] == STATUS_VALID
) {
450 l
= isl_basic_map_alloc_inequality(bmap
);
452 return isl_basic_map_free(bmap
);
453 isl_seq_cpy(bmap
->ineq
[l
], info
->bmap
->eq
[k
], len
);
457 for (k
= 0; k
< info
->bmap
->n_ineq
; ++k
) {
458 if (info
->ineq
[k
] != STATUS_VALID
)
460 l
= isl_basic_map_alloc_inequality(bmap
);
462 return isl_basic_map_free(bmap
);
463 isl_seq_cpy(bmap
->ineq
[l
], info
->bmap
->ineq
[k
], len
);
469 /* Is "bmap" defined by a number of (non-redundant) constraints that
470 * is greater than the number of constraints of basic maps i and j combined?
471 * Equalities are counted as two inequalities.
473 static int number_of_constraints_increases(int i
, int j
,
474 struct isl_coalesce_info
*info
,
475 __isl_keep isl_basic_map
*bmap
, struct isl_tab
*tab
)
479 n_old
= 2 * info
[i
].bmap
->n_eq
+ info
[i
].bmap
->n_ineq
;
480 n_old
+= 2 * info
[j
].bmap
->n_eq
+ info
[j
].bmap
->n_ineq
;
482 n_new
= 2 * bmap
->n_eq
;
483 for (k
= 0; k
< bmap
->n_ineq
; ++k
)
484 if (!isl_tab_is_redundant(tab
, bmap
->n_eq
+ k
))
487 return n_new
> n_old
;
490 /* Replace the pair of basic maps i and j by the basic map bounded
491 * by the valid constraints in both basic maps and the constraints
492 * in extra (if not NULL).
493 * Place the fused basic map in the position that is the smallest of i and j.
495 * If "detect_equalities" is set, then look for equalities encoded
496 * as pairs of inequalities.
497 * If "check_number" is set, then the original basic maps are only
498 * replaced if the total number of constraints does not increase.
499 * While the number of integer divisions in the two basic maps
500 * is assumed to be the same, the actual definitions may be different.
501 * We only copy the definition from one of the basic maps if it is
502 * the same as that of the other basic map. Otherwise, we mark
503 * the integer division as unknown and simplify the basic map
504 * in an attempt to recover the integer division definition.
505 * If any extra constraints get introduced, then these may
506 * involve integer divisions with a unit coefficient.
507 * Eliminate those that do not appear with any other coefficient
508 * in other constraints, to ensure they get eliminated completely,
509 * improving the chances of further coalescing.
511 static enum isl_change
fuse(int i
, int j
, struct isl_coalesce_info
*info
,
512 __isl_keep isl_mat
*extra
, int detect_equalities
, int check_number
)
515 struct isl_basic_map
*fused
= NULL
;
516 struct isl_tab
*fused_tab
= NULL
;
517 isl_size total
= isl_basic_map_dim(info
[i
].bmap
, isl_dim_all
);
518 unsigned extra_rows
= extra
? extra
->n_row
: 0;
519 unsigned n_eq
, n_ineq
;
523 return isl_change_error
;
525 return fuse(j
, i
, info
, extra
, detect_equalities
, check_number
);
527 n_eq
= info
[i
].bmap
->n_eq
+ info
[j
].bmap
->n_eq
;
528 n_ineq
= info
[i
].bmap
->n_ineq
+ info
[j
].bmap
->n_ineq
;
529 fused
= isl_basic_map_alloc_space(isl_space_copy(info
[i
].bmap
->dim
),
530 info
[i
].bmap
->n_div
, n_eq
, n_eq
+ n_ineq
+ extra_rows
);
531 fused
= add_valid_constraints(fused
, &info
[i
], 1 + total
);
532 fused
= add_valid_constraints(fused
, &info
[j
], 1 + total
);
535 if (ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_RATIONAL
) &&
536 ISL_F_ISSET(info
[j
].bmap
, ISL_BASIC_MAP_RATIONAL
))
537 ISL_F_SET(fused
, ISL_BASIC_MAP_RATIONAL
);
539 for (k
= 0; k
< info
[i
].bmap
->n_div
; ++k
) {
540 int l
= isl_basic_map_alloc_div(fused
);
543 if (isl_seq_eq(info
[i
].bmap
->div
[k
], info
[j
].bmap
->div
[k
],
545 isl_seq_cpy(fused
->div
[l
], info
[i
].bmap
->div
[k
],
548 isl_int_set_si(fused
->div
[l
][0], 0);
553 for (k
= 0; k
< extra_rows
; ++k
) {
554 l
= isl_basic_map_alloc_inequality(fused
);
557 isl_seq_cpy(fused
->ineq
[l
], extra
->row
[k
], 1 + total
);
560 if (detect_equalities
)
561 fused
= isl_basic_map_detect_inequality_pairs(fused
, NULL
);
562 fused
= isl_basic_map_gauss(fused
, NULL
);
563 if (simplify
|| info
[j
].simplify
) {
564 fused
= isl_basic_map_simplify(fused
);
565 info
[i
].simplify
= 0;
566 } else if (extra_rows
> 0) {
567 fused
= isl_basic_map_eliminate_pure_unit_divs(fused
);
569 fused
= isl_basic_map_finalize(fused
);
571 fused_tab
= isl_tab_from_basic_map(fused
, 0);
572 if (isl_tab_detect_redundant(fused_tab
) < 0)
576 number_of_constraints_increases(i
, j
, info
, fused
, fused_tab
)) {
577 isl_tab_free(fused_tab
);
578 isl_basic_map_free(fused
);
579 return isl_change_none
;
583 info
[i
].bmap
= fused
;
584 info
[i
].tab
= fused_tab
;
585 info
[i
].modified
= 1;
588 return isl_change_fuse
;
590 isl_tab_free(fused_tab
);
591 isl_basic_map_free(fused
);
592 return isl_change_error
;
595 /* Given a pair of basic maps i and j such that all constraints are either
596 * "valid" or "cut", check if the facets corresponding to the "cut"
597 * constraints of i lie entirely within basic map j.
598 * If so, replace the pair by the basic map consisting of the valid
599 * constraints in both basic maps.
600 * Checking whether the facet lies entirely within basic map j
601 * is performed by checking whether the constraints of basic map j
602 * are valid for the facet. These tests are performed on a rational
603 * tableau to avoid the theoretical possibility that a constraint
604 * that was considered to be a cut constraint for the entire basic map i
605 * happens to be considered to be a valid constraint for the facet,
606 * even though it cuts off the same rational points.
608 * To see that we are not introducing any extra points, call the
609 * two basic maps A and B and the resulting map U and let x
610 * be an element of U \setminus ( A \cup B ).
611 * A line connecting x with an element of A \cup B meets a facet F
612 * of either A or B. Assume it is a facet of B and let c_1 be
613 * the corresponding facet constraint. We have c_1(x) < 0 and
614 * so c_1 is a cut constraint. This implies that there is some
615 * (possibly rational) point x' satisfying the constraints of A
616 * and the opposite of c_1 as otherwise c_1 would have been marked
617 * valid for A. The line connecting x and x' meets a facet of A
618 * in a (possibly rational) point that also violates c_1, but this
619 * is impossible since all cut constraints of B are valid for all
621 * In case F is a facet of A rather than B, then we can apply the
622 * above reasoning to find a facet of B separating x from A \cup B first.
624 static enum isl_change
check_facets(int i
, int j
,
625 struct isl_coalesce_info
*info
)
628 struct isl_tab_undo
*snap
, *snap2
;
629 unsigned n_eq
= info
[i
].bmap
->n_eq
;
631 snap
= isl_tab_snap(info
[i
].tab
);
632 if (isl_tab_mark_rational(info
[i
].tab
) < 0)
633 return isl_change_error
;
634 snap2
= isl_tab_snap(info
[i
].tab
);
636 for (k
= 0; k
< info
[i
].bmap
->n_ineq
; ++k
) {
637 if (info
[i
].ineq
[k
] != STATUS_CUT
)
639 if (isl_tab_select_facet(info
[i
].tab
, n_eq
+ k
) < 0)
640 return isl_change_error
;
641 for (l
= 0; l
< info
[j
].bmap
->n_ineq
; ++l
) {
643 if (info
[j
].ineq
[l
] != STATUS_CUT
)
645 stat
= status_in(info
[j
].bmap
->ineq
[l
], info
[i
].tab
);
647 return isl_change_error
;
648 if (stat
!= STATUS_VALID
)
651 if (isl_tab_rollback(info
[i
].tab
, snap2
) < 0)
652 return isl_change_error
;
653 if (l
< info
[j
].bmap
->n_ineq
)
657 if (k
< info
[i
].bmap
->n_ineq
) {
658 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
659 return isl_change_error
;
660 return isl_change_none
;
662 return fuse(i
, j
, info
, NULL
, 0, 0);
665 /* Check if info->bmap contains the basic map represented
666 * by the tableau "tab".
667 * For each equality, we check both the constraint itself
668 * (as an inequality) and its negation. Make sure the
669 * equality is returned to its original state before returning.
671 static isl_bool
contains(struct isl_coalesce_info
*info
, struct isl_tab
*tab
)
675 isl_basic_map
*bmap
= info
->bmap
;
677 dim
= isl_basic_map_dim(bmap
, isl_dim_all
);
679 return isl_bool_error
;
680 for (k
= 0; k
< bmap
->n_eq
; ++k
) {
682 isl_seq_neg(bmap
->eq
[k
], bmap
->eq
[k
], 1 + dim
);
683 stat
= status_in(bmap
->eq
[k
], tab
);
684 isl_seq_neg(bmap
->eq
[k
], bmap
->eq
[k
], 1 + dim
);
686 return isl_bool_error
;
687 if (stat
!= STATUS_VALID
)
688 return isl_bool_false
;
689 stat
= status_in(bmap
->eq
[k
], tab
);
691 return isl_bool_error
;
692 if (stat
!= STATUS_VALID
)
693 return isl_bool_false
;
696 for (k
= 0; k
< bmap
->n_ineq
; ++k
) {
698 if (info
->ineq
[k
] == STATUS_REDUNDANT
)
700 stat
= status_in(bmap
->ineq
[k
], tab
);
702 return isl_bool_error
;
703 if (stat
!= STATUS_VALID
)
704 return isl_bool_false
;
706 return isl_bool_true
;
709 /* Basic map "i" has an inequality "k" that is adjacent
710 * to some inequality of basic map "j". All the other inequalities
712 * If not NULL, then "extra" contains extra wrapping constraints that are valid
713 * for both "i" and "j".
714 * Check if basic map "j" forms an extension of basic map "i",
715 * taking into account the extra constraints, if any.
717 * Note that this function is only called if some of the equalities or
718 * inequalities of basic map "j" do cut basic map "i". The function is
719 * correct even if there are no such cut constraints, but in that case
720 * the additional checks performed by this function are overkill.
722 * In particular, we replace constraint k, say f >= 0, by constraint
723 * f <= -1, add the inequalities of "j" that are valid for "i",
724 * as well as the "extra" constraints, if any,
725 * and check if the result is a subset of basic map "j".
726 * To improve the chances of the subset relation being detected,
727 * any variable that only attains a single integer value
728 * in the tableau of "i" is first fixed to that value.
729 * If the result is a subset, then we know that this result is exactly equal
730 * to basic map "j" since all its constraints are valid for basic map "j".
731 * By combining the valid constraints of "i" (all equalities and all
732 * inequalities except "k"), the valid constraints of "j" and
733 * the "extra" constraints, if any, we therefore
734 * obtain a basic map that is equal to their union.
735 * In this case, there is no need to perform a rollback of the tableau
736 * since it is going to be destroyed in fuse().
742 * |_______| _ |_________\
758 * |_______| |_______/
760 static enum isl_change
is_adj_ineq_extension_with_wraps(int i
, int j
, int k
,
761 struct isl_coalesce_info
*info
, __isl_keep isl_mat
*extra
)
763 struct isl_tab_undo
*snap
;
764 isl_size n_eq_i
, n_ineq_j
, n_extra
;
765 isl_size total
= isl_basic_map_dim(info
[i
].bmap
, isl_dim_all
);
770 return isl_change_error
;
772 n_eq_i
= isl_basic_map_n_equality(info
[i
].bmap
);
773 n_ineq_j
= isl_basic_map_n_inequality(info
[j
].bmap
);
774 n_extra
= isl_mat_rows(extra
);
775 if (n_eq_i
< 0 || n_ineq_j
< 0 || n_extra
< 0)
776 return isl_change_error
;
778 if (isl_tab_extend_cons(info
[i
].tab
, 1 + n_ineq_j
+ n_extra
) < 0)
779 return isl_change_error
;
781 snap
= isl_tab_snap(info
[i
].tab
);
783 if (isl_tab_unrestrict(info
[i
].tab
, n_eq_i
+ k
) < 0)
784 return isl_change_error
;
786 isl_seq_neg(info
[i
].bmap
->ineq
[k
], info
[i
].bmap
->ineq
[k
], 1 + total
);
787 isl_int_sub_ui(info
[i
].bmap
->ineq
[k
][0], info
[i
].bmap
->ineq
[k
][0], 1);
788 r
= isl_tab_add_ineq(info
[i
].tab
, info
[i
].bmap
->ineq
[k
]);
789 isl_seq_neg(info
[i
].bmap
->ineq
[k
], info
[i
].bmap
->ineq
[k
], 1 + total
);
790 isl_int_sub_ui(info
[i
].bmap
->ineq
[k
][0], info
[i
].bmap
->ineq
[k
][0], 1);
792 return isl_change_error
;
794 for (k
= 0; k
< n_ineq_j
; ++k
) {
795 if (info
[j
].ineq
[k
] != STATUS_VALID
)
797 if (isl_tab_add_ineq(info
[i
].tab
, info
[j
].bmap
->ineq
[k
]) < 0)
798 return isl_change_error
;
800 for (k
= 0; k
< n_extra
; ++k
) {
801 if (isl_tab_add_ineq(info
[i
].tab
, extra
->row
[k
]) < 0)
802 return isl_change_error
;
804 if (isl_tab_detect_constants(info
[i
].tab
) < 0)
805 return isl_change_error
;
807 super
= contains(&info
[j
], info
[i
].tab
);
809 return isl_change_error
;
811 return fuse(i
, j
, info
, extra
, 0, 0);
813 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
814 return isl_change_error
;
816 return isl_change_none
;
819 /* Given an affine transformation matrix "T", does row "row" represent
820 * anything other than a unit vector (possibly shifted by a constant)
821 * that is not involved in any of the other rows?
823 * That is, if a constraint involves the variable corresponding to
824 * the row, then could its preimage by "T" have any coefficients
825 * that are different from those in the original constraint?
827 static int not_unique_unit_row(__isl_keep isl_mat
*T
, int row
)
830 int len
= T
->n_col
- 1;
832 i
= isl_seq_first_non_zero(T
->row
[row
] + 1, len
);
835 if (!isl_int_is_one(T
->row
[row
][1 + i
]) &&
836 !isl_int_is_negone(T
->row
[row
][1 + i
]))
839 j
= isl_seq_first_non_zero(T
->row
[row
] + 1 + i
+ 1, len
- (i
+ 1));
843 for (j
= 1; j
< T
->n_row
; ++j
) {
846 if (!isl_int_is_zero(T
->row
[j
][1 + i
]))
853 /* Does inequality constraint "ineq" of "bmap" involve any of
854 * the variables marked in "affected"?
855 * "total" is the total number of variables, i.e., the number
856 * of entries in "affected".
858 static isl_bool
is_affected(__isl_keep isl_basic_map
*bmap
, int ineq
,
859 int *affected
, int total
)
863 for (i
= 0; i
< total
; ++i
) {
866 if (!isl_int_is_zero(bmap
->ineq
[ineq
][1 + i
]))
867 return isl_bool_true
;
870 return isl_bool_false
;
873 /* Given the compressed version of inequality constraint "ineq"
874 * of info->bmap in "v", check if the constraint can be tightened,
875 * where the compression is based on an equality constraint valid
877 * If so, add the tightened version of the inequality constraint
878 * to info->tab. "v" may be modified by this function.
880 * That is, if the compressed constraint is of the form
884 * with 0 < c < m, then it is equivalent to
888 * This means that c can also be subtracted from the original,
889 * uncompressed constraint without affecting the integer points
890 * in info->tab. Add this tightened constraint as an extra row
891 * to info->tab to make this information explicitly available.
893 static __isl_give isl_vec
*try_tightening(struct isl_coalesce_info
*info
,
894 int ineq
, __isl_take isl_vec
*v
)
902 ctx
= isl_vec_get_ctx(v
);
903 isl_seq_gcd(v
->el
+ 1, v
->size
- 1, &ctx
->normalize_gcd
);
904 if (isl_int_is_zero(ctx
->normalize_gcd
) ||
905 isl_int_is_one(ctx
->normalize_gcd
)) {
913 isl_int_fdiv_r(v
->el
[0], v
->el
[0], ctx
->normalize_gcd
);
914 if (isl_int_is_zero(v
->el
[0]))
917 if (isl_tab_extend_cons(info
->tab
, 1) < 0)
918 return isl_vec_free(v
);
920 isl_int_sub(info
->bmap
->ineq
[ineq
][0],
921 info
->bmap
->ineq
[ineq
][0], v
->el
[0]);
922 r
= isl_tab_add_ineq(info
->tab
, info
->bmap
->ineq
[ineq
]);
923 isl_int_add(info
->bmap
->ineq
[ineq
][0],
924 info
->bmap
->ineq
[ineq
][0], v
->el
[0]);
927 return isl_vec_free(v
);
932 /* Tighten the (non-redundant) constraints on the facet represented
934 * In particular, on input, info->tab represents the result
935 * of relaxing the "n" inequality constraints of info->bmap in "relaxed"
936 * by one, i.e., replacing f_i >= 0 by f_i + 1 >= 0, and then
937 * replacing the one at index "l" by the corresponding equality,
938 * i.e., f_k + 1 = 0, with k = relaxed[l].
940 * Compute a variable compression from the equality constraint f_k + 1 = 0
941 * and use it to tighten the other constraints of info->bmap
942 * (that is, all constraints that have not been relaxed),
943 * updating info->tab (and leaving info->bmap untouched).
944 * The compression handles essentially two cases, one where a variable
945 * is assigned a fixed value and can therefore be eliminated, and one
946 * where one variable is a shifted multiple of some other variable and
947 * can therefore be replaced by that multiple.
948 * Gaussian elimination would also work for the first case, but for
949 * the second case, the effectiveness would depend on the order
951 * After compression, some of the constraints may have coefficients
952 * with a common divisor. If this divisor does not divide the constant
953 * term, then the constraint can be tightened.
954 * The tightening is performed on the tableau info->tab by introducing
955 * extra (temporary) constraints.
957 * Only constraints that are possibly affected by the compression are
958 * considered. In particular, if the constraint only involves variables
959 * that are directly mapped to a distinct set of other variables, then
960 * no common divisor can be introduced and no tightening can occur.
962 * It is important to only consider the non-redundant constraints
963 * since the facet constraint has been relaxed prior to the call
964 * to this function, meaning that the constraints that were redundant
965 * prior to the relaxation may no longer be redundant.
966 * These constraints will be ignored in the fused result, so
967 * the fusion detection should not exploit them.
969 static isl_stat
tighten_on_relaxed_facet(struct isl_coalesce_info
*info
,
970 int n
, int *relaxed
, int l
)
981 ctx
= isl_basic_map_get_ctx(info
->bmap
);
982 total
= isl_basic_map_dim(info
->bmap
, isl_dim_all
);
984 return isl_stat_error
;
985 isl_int_add_ui(info
->bmap
->ineq
[k
][0], info
->bmap
->ineq
[k
][0], 1);
986 T
= isl_mat_sub_alloc6(ctx
, info
->bmap
->ineq
, k
, 1, 0, 1 + total
);
987 T
= isl_mat_variable_compression(T
, NULL
);
988 isl_int_sub_ui(info
->bmap
->ineq
[k
][0], info
->bmap
->ineq
[k
][0], 1);
990 return isl_stat_error
;
996 affected
= isl_alloc_array(ctx
, int, total
);
1000 for (i
= 0; i
< total
; ++i
)
1001 affected
[i
] = not_unique_unit_row(T
, 1 + i
);
1003 for (i
= 0; i
< info
->bmap
->n_ineq
; ++i
) {
1005 if (any(relaxed
, n
, i
))
1007 if (info
->ineq
[i
] == STATUS_REDUNDANT
)
1009 handle
= is_affected(info
->bmap
, i
, affected
, total
);
1014 v
= isl_vec_alloc(ctx
, 1 + total
);
1017 isl_seq_cpy(v
->el
, info
->bmap
->ineq
[i
], 1 + total
);
1018 v
= isl_vec_mat_product(v
, isl_mat_copy(T
));
1019 v
= try_tightening(info
, i
, v
);
1031 return isl_stat_error
;
1034 /* Replace the basic maps "i" and "j" by an extension of "i"
1035 * along the "n" inequality constraints in "relax" by one.
1036 * The tableau info[i].tab has already been extended.
1037 * Extend info[i].bmap accordingly by relaxing all constraints in "relax"
1039 * Each integer division that does not have exactly the same
1040 * definition in "i" and "j" is marked unknown and the basic map
1041 * is scheduled to be simplified in an attempt to recover
1042 * the integer division definition.
1043 * Place the extension in the position that is the smallest of i and j.
1045 static enum isl_change
extend(int i
, int j
, int n
, int *relax
,
1046 struct isl_coalesce_info
*info
)
1051 info
[i
].bmap
= isl_basic_map_cow(info
[i
].bmap
);
1052 total
= isl_basic_map_dim(info
[i
].bmap
, isl_dim_all
);
1054 return isl_change_error
;
1055 for (l
= 0; l
< info
[i
].bmap
->n_div
; ++l
)
1056 if (!isl_seq_eq(info
[i
].bmap
->div
[l
],
1057 info
[j
].bmap
->div
[l
], 1 + 1 + total
)) {
1058 isl_int_set_si(info
[i
].bmap
->div
[l
][0], 0);
1059 info
[i
].simplify
= 1;
1061 for (l
= 0; l
< n
; ++l
)
1062 isl_int_add_ui(info
[i
].bmap
->ineq
[relax
[l
]][0],
1063 info
[i
].bmap
->ineq
[relax
[l
]][0], 1);
1064 ISL_F_CLR(info
[i
].bmap
, ISL_BASIC_MAP_NO_REDUNDANT
);
1065 ISL_F_SET(info
[i
].bmap
, ISL_BASIC_MAP_FINAL
);
1067 info
[i
].modified
= 1;
1069 exchange(&info
[i
], &info
[j
]);
1070 return isl_change_fuse
;
1073 /* Basic map "i" has "n" inequality constraints (collected in "relax")
1074 * that are such that they include basic map "j" if they are relaxed
1075 * by one. All the other inequalities are valid for "j".
1076 * Check if basic map "j" forms an extension of basic map "i".
1078 * In particular, relax the constraints in "relax", compute the corresponding
1079 * facets one by one and check whether each of these is included
1080 * in the other basic map.
1081 * Before testing for inclusion, the constraints on each facet
1082 * are tightened to increase the chance of an inclusion being detected.
1083 * (Adding the valid constraints of "j" to the tableau of "i", as is done
1084 * in is_adj_ineq_extension, may further increase those chances, but this
1085 * is not currently done.)
1086 * If each facet is included, we know that relaxing the constraints extends
1087 * the basic map with exactly the other basic map (we already know that this
1088 * other basic map is included in the extension, because all other
1089 * inequality constraints are valid of "j") and we can replace the
1090 * two basic maps by this extension.
1092 * If any of the relaxed constraints turn out to be redundant, then bail out.
1093 * isl_tab_select_facet refuses to handle such constraints. It may be
1094 * possible to handle them anyway by making a distinction between
1095 * redundant constraints with a corresponding facet that still intersects
1096 * the set (allowing isl_tab_select_facet to handle them) and
1097 * those where the facet does not intersect the set (which can be ignored
1098 * because the empty facet is trivially included in the other disjunct).
1099 * However, relaxed constraints that turn out to be redundant should
1100 * be fairly rare and no such instance has been reported where
1101 * coalescing would be successful.
1117 static enum isl_change
is_relaxed_extension(int i
, int j
, int n
, int *relax
,
1118 struct isl_coalesce_info
*info
)
1122 struct isl_tab_undo
*snap
, *snap2
;
1123 unsigned n_eq
= info
[i
].bmap
->n_eq
;
1125 for (l
= 0; l
< n
; ++l
)
1126 if (isl_tab_is_equality(info
[i
].tab
, n_eq
+ relax
[l
]))
1127 return isl_change_none
;
1129 snap
= isl_tab_snap(info
[i
].tab
);
1130 for (l
= 0; l
< n
; ++l
)
1131 if (isl_tab_relax(info
[i
].tab
, n_eq
+ relax
[l
]) < 0)
1132 return isl_change_error
;
1133 for (l
= 0; l
< n
; ++l
) {
1134 if (!isl_tab_is_redundant(info
[i
].tab
, n_eq
+ relax
[l
]))
1136 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
1137 return isl_change_error
;
1138 return isl_change_none
;
1140 snap2
= isl_tab_snap(info
[i
].tab
);
1141 for (l
= 0; l
< n
; ++l
) {
1142 if (isl_tab_rollback(info
[i
].tab
, snap2
) < 0)
1143 return isl_change_error
;
1144 if (isl_tab_select_facet(info
[i
].tab
, n_eq
+ relax
[l
]) < 0)
1145 return isl_change_error
;
1146 if (tighten_on_relaxed_facet(&info
[i
], n
, relax
, l
) < 0)
1147 return isl_change_error
;
1148 super
= contains(&info
[j
], info
[i
].tab
);
1150 return isl_change_error
;
1153 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
1154 return isl_change_error
;
1155 return isl_change_none
;
1158 if (isl_tab_rollback(info
[i
].tab
, snap2
) < 0)
1159 return isl_change_error
;
1160 return extend(i
, j
, n
, relax
, info
);
1163 /* Data structure that keeps track of the wrapping constraints
1164 * and of information to bound the coefficients of those constraints.
1166 * "failed" is set if wrapping has failed.
1167 * bound is set if we want to apply a bound on the coefficients
1168 * mat contains the wrapping constraints
1169 * max is the bound on the coefficients (if bound is set)
1178 /* Update wraps->max to be greater than or equal to the coefficients
1179 * in the equalities and inequalities of info->bmap that can be removed
1180 * if we end up applying wrapping.
1182 static isl_stat
wraps_update_max(struct isl_wraps
*wraps
,
1183 struct isl_coalesce_info
*info
)
1187 isl_size total
= isl_basic_map_dim(info
->bmap
, isl_dim_all
);
1190 return isl_stat_error
;
1191 isl_int_init(max_k
);
1193 for (k
= 0; k
< info
->bmap
->n_eq
; ++k
) {
1194 if (info
->eq
[2 * k
] == STATUS_VALID
&&
1195 info
->eq
[2 * k
+ 1] == STATUS_VALID
)
1197 isl_seq_abs_max(info
->bmap
->eq
[k
] + 1, total
, &max_k
);
1198 if (isl_int_abs_gt(max_k
, wraps
->max
))
1199 isl_int_set(wraps
->max
, max_k
);
1202 for (k
= 0; k
< info
->bmap
->n_ineq
; ++k
) {
1203 if (info
->ineq
[k
] == STATUS_VALID
||
1204 info
->ineq
[k
] == STATUS_REDUNDANT
)
1206 isl_seq_abs_max(info
->bmap
->ineq
[k
] + 1, total
, &max_k
);
1207 if (isl_int_abs_gt(max_k
, wraps
->max
))
1208 isl_int_set(wraps
->max
, max_k
);
1211 isl_int_clear(max_k
);
1216 /* Initialize the isl_wraps data structure.
1217 * If we want to bound the coefficients of the wrapping constraints,
1218 * we set wraps->max to the largest coefficient
1219 * in the equalities and inequalities that can be removed if we end up
1220 * applying wrapping.
1222 static isl_stat
wraps_init(struct isl_wraps
*wraps
, __isl_take isl_mat
*mat
,
1223 struct isl_coalesce_info
*info
, int i
, int j
)
1231 return isl_stat_error
;
1232 wraps
->mat
->n_row
= 0;
1233 ctx
= isl_mat_get_ctx(mat
);
1234 wraps
->bound
= isl_options_get_coalesce_bounded_wrapping(ctx
);
1237 isl_int_init(wraps
->max
);
1238 isl_int_set_si(wraps
->max
, 0);
1239 if (wraps_update_max(wraps
, &info
[i
]) < 0)
1240 return isl_stat_error
;
1241 if (wraps_update_max(wraps
, &info
[j
]) < 0)
1242 return isl_stat_error
;
1247 /* Free the contents of the isl_wraps data structure.
1249 static void wraps_free(struct isl_wraps
*wraps
)
1251 isl_mat_free(wraps
->mat
);
1253 isl_int_clear(wraps
->max
);
1256 /* Mark the wrapping as failed.
1258 static isl_stat
wraps_mark_failed(struct isl_wraps
*wraps
)
1264 /* Is the wrapping constraint in row "row" allowed?
1266 * If wraps->bound is set, we check that none of the coefficients
1267 * is greater than wraps->max.
1269 static int allow_wrap(struct isl_wraps
*wraps
, int row
)
1276 for (i
= 1; i
< wraps
->mat
->n_col
; ++i
)
1277 if (isl_int_abs_gt(wraps
->mat
->row
[row
][i
], wraps
->max
))
1283 /* Wrap "ineq" (or its opposite if "negate" is set) around "bound"
1284 * to include "set" and add the result in position "w" of "wraps".
1285 * "len" is the total number of coefficients in "bound" and "ineq".
1286 * Return isl_bool_true on success, isl_bool_false on failure and
1287 * isl_bool_error on error.
1288 * Wrapping can fail if the result of wrapping is equal to "bound"
1289 * or if we want to bound the sizes of the coefficients and
1290 * the wrapped constraint does not satisfy this bound.
1292 static isl_bool
add_wrap(struct isl_wraps
*wraps
, int w
, isl_int
*bound
,
1293 isl_int
*ineq
, unsigned len
, __isl_keep isl_set
*set
, int negate
)
1295 isl_seq_cpy(wraps
->mat
->row
[w
], bound
, len
);
1297 isl_seq_neg(wraps
->mat
->row
[w
+ 1], ineq
, len
);
1298 ineq
= wraps
->mat
->row
[w
+ 1];
1300 if (!isl_set_wrap_facet(set
, wraps
->mat
->row
[w
], ineq
))
1301 return isl_bool_error
;
1302 if (isl_seq_eq(wraps
->mat
->row
[w
], bound
, len
))
1303 return isl_bool_false
;
1304 if (!allow_wrap(wraps
, w
))
1305 return isl_bool_false
;
1306 return isl_bool_true
;
1309 /* This function has two modes of operations.
1311 * If "add_valid" is set, then all the constraints of info->bmap
1312 * (except the opposite of "bound") are valid for the other basic map.
1313 * In this case, attempts are made to wrap some of these valid constraints
1314 * to more tightly fit around "set". Only successful wrappings are recorded
1315 * and failed wrappings are ignored.
1317 * If "add_valid" is not set, then some of the constraints of info->bmap
1318 * are not valid for the other basic map, and only those are considered
1319 * for wrapping. In this case all attempted wrappings need to succeed.
1320 * Otherwise "wraps" is marked as failed.
1321 * Note that the constraints that are valid for the other basic map
1322 * will be added to the combined basic map by default, so there is
1323 * no need to wrap them.
1324 * The caller wrap_in_facets even relies on this function not wrapping
1325 * any constraints that are already valid.
1327 * Only consider constraints that are not redundant (as determined
1328 * by info->tab) and that are valid or invalid depending on "add_valid".
1329 * Wrap each constraint around "bound" such that it includes the whole
1330 * set "set" and append the resulting constraint to "wraps".
1331 * "wraps" is assumed to have been pre-allocated to the appropriate size.
1332 * wraps->n_row is the number of actual wrapped constraints that have
1334 * If any of the wrapping problems results in a constraint that is
1335 * identical to "bound", then this means that "set" is unbounded in such
1336 * a way that no wrapping is possible.
1337 * Similarly, if we want to bound the coefficients of the wrapping
1338 * constraints and a newly added wrapping constraint does not
1339 * satisfy the bound, then the wrapping is considered to have failed.
1340 * Note though that "wraps" is only marked failed if "add_valid" is not set.
1342 static isl_stat
add_selected_wraps(struct isl_wraps
*wraps
,
1343 struct isl_coalesce_info
*info
, isl_int
*bound
, __isl_keep isl_set
*set
,
1349 isl_basic_map
*bmap
= info
->bmap
;
1350 isl_size total
= isl_basic_map_dim(bmap
, isl_dim_all
);
1351 unsigned len
= 1 + total
;
1354 return isl_stat_error
;
1356 w
= wraps
->mat
->n_row
;
1358 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
1359 int is_valid
= info
->ineq
[l
] == STATUS_VALID
;
1360 if ((!add_valid
&& is_valid
) ||
1361 info
->ineq
[l
] == STATUS_REDUNDANT
)
1363 if (isl_seq_is_neg(bound
, bmap
->ineq
[l
], len
))
1365 if (isl_seq_eq(bound
, bmap
->ineq
[l
], len
))
1367 if (isl_tab_is_redundant(info
->tab
, bmap
->n_eq
+ l
))
1370 added
= add_wrap(wraps
, w
, bound
, bmap
->ineq
[l
], len
, set
, 0);
1372 return isl_stat_error
;
1373 if (!added
&& !is_valid
)
1378 for (l
= 0; l
< bmap
->n_eq
; ++l
) {
1379 if (isl_seq_is_neg(bound
, bmap
->eq
[l
], len
))
1381 if (isl_seq_eq(bound
, bmap
->eq
[l
], len
))
1384 for (m
= 0; m
< 2; ++m
) {
1385 if (info
->eq
[2 * l
+ m
] == STATUS_VALID
)
1387 added
= add_wrap(wraps
, w
, bound
, bmap
->eq
[l
], len
,
1390 return isl_stat_error
;
1397 wraps
->mat
->n_row
= w
;
1400 return wraps_mark_failed(wraps
);
1403 /* For each constraint in info->bmap that is not redundant (as determined
1404 * by info->tab) and that is not a valid constraint for the other basic map,
1405 * wrap the constraint around "bound" such that it includes the whole
1406 * set "set" and append the resulting constraint to "wraps".
1407 * Note that the constraints that are valid for the other basic map
1408 * will be added to the combined basic map by default, so there is
1409 * no need to wrap them.
1410 * The caller wrap_in_facets even relies on this function not wrapping
1411 * any constraints that are already valid.
1412 * "wraps" is assumed to have been pre-allocated to the appropriate size.
1413 * wraps->n_row is the number of actual wrapped constraints that have
1415 * If any of the wrapping problems results in a constraint that is
1416 * identical to "bound", then this means that "set" is unbounded in such
1417 * a way that no wrapping is possible. If this happens then "wraps"
1418 * is marked as failed.
1419 * Similarly, if we want to bound the coefficients of the wrapping
1420 * constraints and a newly added wrapping constraint does not
1421 * satisfy the bound, then "wraps" is also marked as failed.
1423 static isl_stat
add_wraps(struct isl_wraps
*wraps
,
1424 struct isl_coalesce_info
*info
, isl_int
*bound
, __isl_keep isl_set
*set
)
1426 return add_selected_wraps(wraps
, info
, bound
, set
, 0);
1429 /* Check if the constraints in "wraps" from "first" until the last
1430 * are all valid for the basic set represented by "tab",
1431 * dropping the invalid constraints if "keep" is set and
1432 * marking the wrapping as failed if "keep" is not set and
1433 * any constraint turns out to be invalid.
1435 static isl_stat
check_wraps(struct isl_wraps
*wraps
, int first
,
1436 struct isl_tab
*tab
, int keep
)
1440 for (i
= wraps
->mat
->n_row
- 1; i
>= first
; --i
) {
1441 enum isl_ineq_type type
;
1442 type
= isl_tab_ineq_type(tab
, wraps
->mat
->row
[i
]);
1443 if (type
== isl_ineq_error
)
1444 return isl_stat_error
;
1445 if (type
== isl_ineq_redundant
)
1448 return wraps_mark_failed(wraps
);
1449 wraps
->mat
= isl_mat_drop_rows(wraps
->mat
, i
, 1);
1451 return isl_stat_error
;
1457 /* Return a set that corresponds to the non-redundant constraints
1458 * (as recorded in tab) of bmap.
1460 * It's important to remove the redundant constraints as some
1461 * of the other constraints may have been modified after the
1462 * constraints were marked redundant.
1463 * In particular, a constraint may have been relaxed.
1464 * Redundant constraints are ignored when a constraint is relaxed
1465 * and should therefore continue to be ignored ever after.
1466 * Otherwise, the relaxation might be thwarted by some of
1467 * these constraints.
1469 * Update the underlying set to ensure that the dimension doesn't change.
1470 * Otherwise the integer divisions could get dropped if the tab
1471 * turns out to be empty.
1473 static __isl_give isl_set
*set_from_updated_bmap(__isl_keep isl_basic_map
*bmap
,
1474 struct isl_tab
*tab
)
1476 isl_basic_set
*bset
;
1478 bmap
= isl_basic_map_copy(bmap
);
1479 bset
= isl_basic_map_underlying_set(bmap
);
1480 bset
= isl_basic_set_cow(bset
);
1481 bset
= isl_basic_set_update_from_tab(bset
, tab
);
1482 return isl_set_from_basic_set(bset
);
1485 /* Does "info" have any cut constraints that are redundant?
1487 static isl_bool
has_redundant_cuts(struct isl_coalesce_info
*info
)
1490 isl_size n_eq
, n_ineq
;
1492 n_eq
= isl_basic_map_n_equality(info
->bmap
);
1493 n_ineq
= isl_basic_map_n_inequality(info
->bmap
);
1494 if (n_eq
< 0 || n_ineq
< 0)
1495 return isl_bool_error
;
1496 for (l
= 0; l
< n_ineq
; ++l
) {
1499 if (info
->ineq
[l
] != STATUS_CUT
)
1501 red
= isl_tab_is_redundant(info
->tab
, n_eq
+ l
);
1503 return isl_bool_error
;
1505 return isl_bool_true
;
1508 return isl_bool_false
;
1511 /* Wrap some constraints of info->bmap that bound the facet defined
1512 * by inequality "k" around (the opposite of) this inequality to
1513 * include "set". "bound" may be used to store the negated inequality.
1515 * If "add_valid" is set, then all ridges are already valid and
1516 * the purpose is to wrap "set" more tightly. In this case,
1517 * wrapping doesn't fail, although it is possible that no constraint
1520 * If "add_valid" is not set, then some of the ridges are cut constraints
1521 * and only those are wrapped around "set".
1523 * Since the wrapped constraints are not guaranteed to contain the whole
1524 * of info->bmap, we check them in check_wraps.
1525 * If any of the wrapped constraints turn out to be invalid, then
1526 * check_wraps will mark "wraps" as failed if "add_valid" is not set.
1527 * If "add_valid" is set, then the offending constraints are
1530 * If the facet turns out to be empty, then no wrapping can be performed.
1531 * This is considered a failure, unless "add_valid" is set.
1533 * If any of the cut constraints of info->bmap turn out
1534 * to be redundant with respect to other constraints
1535 * then these will neither be wrapped nor added directly to the result.
1536 * The result may therefore not be correct.
1537 * Skip wrapping and mark "wraps" as failed in this case.
1539 static isl_stat
add_selected_wraps_around_facet(struct isl_wraps
*wraps
,
1540 struct isl_coalesce_info
*info
, int k
, isl_int
*bound
,
1541 __isl_keep isl_set
*set
, int add_valid
)
1544 struct isl_tab_undo
*snap
;
1546 isl_size total
= isl_basic_map_dim(info
->bmap
, isl_dim_all
);
1549 return isl_stat_error
;
1551 snap
= isl_tab_snap(info
->tab
);
1553 if (isl_tab_select_facet(info
->tab
, info
->bmap
->n_eq
+ k
) < 0)
1554 return isl_stat_error
;
1555 if (isl_tab_detect_redundant(info
->tab
) < 0)
1556 return isl_stat_error
;
1557 if (info
->tab
->empty
) {
1558 if (isl_tab_rollback(info
->tab
, snap
) < 0)
1559 return isl_stat_error
;
1561 return wraps_mark_failed(wraps
);
1564 nowrap
= has_redundant_cuts(info
);
1566 return isl_stat_error
;
1568 n
= wraps
->mat
->n_row
;
1570 isl_seq_neg(bound
, info
->bmap
->ineq
[k
], 1 + total
);
1572 if (add_selected_wraps(wraps
, info
, bound
, set
, add_valid
) < 0)
1573 return isl_stat_error
;
1576 if (isl_tab_rollback(info
->tab
, snap
) < 0)
1577 return isl_stat_error
;
1579 return wraps_mark_failed(wraps
);
1580 if (check_wraps(wraps
, n
, info
->tab
, add_valid
) < 0)
1581 return isl_stat_error
;
1586 /* Wrap the constraints of info->bmap that bound the facet defined
1587 * by inequality "k" around (the opposite of) this inequality to
1588 * include "set". "bound" may be used to store the negated inequality.
1589 * If any of the wrapped constraints turn out to be invalid for info->bmap
1590 * itself, then mark "wraps" as failed.
1592 static isl_stat
add_wraps_around_facet(struct isl_wraps
*wraps
,
1593 struct isl_coalesce_info
*info
, int k
, isl_int
*bound
,
1594 __isl_keep isl_set
*set
)
1596 return add_selected_wraps_around_facet(wraps
, info
, k
, bound
, set
, 0);
1599 /* Wrap the (valid) constraints of info->bmap that bound the facet defined
1600 * by inequality "k" around (the opposite of) this inequality to
1601 * include "set" more tightly.
1602 * "bound" may be used to store the negated inequality.
1603 * Remove any wrapping constraints that turn out to be invalid
1604 * for info->bmap itself.
1606 static isl_stat
add_valid_wraps_around_facet(struct isl_wraps
*wraps
,
1607 struct isl_coalesce_info
*info
, int k
, isl_int
*bound
,
1608 __isl_keep isl_set
*set
)
1610 return add_selected_wraps_around_facet(wraps
, info
, k
, bound
, set
, 1);
1613 /* Basic map "i" has an inequality (say "k") that is adjacent
1614 * to some inequality of basic map "j". All the other inequalities
1615 * are valid for "j".
1616 * Check if basic map "j" forms an extension of basic map "i".
1618 * Note that this function is only called if some of the equalities or
1619 * inequalities of basic map "j" do cut basic map "i". The function is
1620 * correct even if there are no such cut constraints, but in that case
1621 * the additional checks performed by this function are overkill.
1623 * First try and wrap the ridges of "k" around "j".
1624 * Note that those ridges are already valid for "j",
1625 * but the wrapped versions may wrap "j" more tightly,
1626 * increasing the chances of "j" being detected as an extension of "i"
1628 static enum isl_change
is_adj_ineq_extension(int i
, int j
,
1629 struct isl_coalesce_info
*info
)
1632 enum isl_change change
;
1634 isl_size n_eq_i
, n_ineq_i
;
1635 struct isl_wraps wraps
;
1642 k
= find_ineq(&info
[i
], STATUS_ADJ_INEQ
);
1644 isl_die(isl_basic_map_get_ctx(info
[i
].bmap
), isl_error_internal
,
1645 "info[i].ineq should have exactly one STATUS_ADJ_INEQ",
1646 return isl_change_error
);
1648 total
= isl_basic_map_dim(info
[i
].bmap
, isl_dim_all
);
1649 n_eq_i
= isl_basic_map_n_equality(info
[i
].bmap
);
1650 n_ineq_i
= isl_basic_map_n_inequality(info
[i
].bmap
);
1651 if (total
< 0 || n_eq_i
< 0 || n_ineq_i
< 0)
1652 return isl_change_error
;
1654 set_j
= set_from_updated_bmap(info
[j
].bmap
, info
[j
].tab
);
1655 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
1656 bound
= isl_vec_alloc(ctx
, 1 + total
);
1657 mat
= isl_mat_alloc(ctx
, 2 * n_eq_i
+ n_ineq_i
, 1 + total
);
1658 if (wraps_init(&wraps
, mat
, info
, i
, j
) < 0)
1660 if (!bound
|| !set_j
)
1662 r
= add_valid_wraps_around_facet(&wraps
, &info
[i
], k
, bound
->el
, set_j
);
1666 change
= is_adj_ineq_extension_with_wraps(i
, j
, k
, info
, wraps
.mat
);
1669 isl_vec_free(bound
);
1670 isl_set_free(set_j
);
1675 isl_vec_free(bound
);
1676 isl_set_free(set_j
);
1677 return isl_change_error
;
1680 /* Both basic maps have at least one inequality with and adjacent
1681 * (but opposite) inequality in the other basic map.
1682 * Check that there are no cut constraints and that there is only
1683 * a single pair of adjacent inequalities.
1684 * If so, we can replace the pair by a single basic map described
1685 * by all but the pair of adjacent inequalities.
1686 * Any additional points introduced lie strictly between the two
1687 * adjacent hyperplanes and can therefore be integral.
1696 * The test for a single pair of adjacent inequalities is important
1697 * for avoiding the combination of two basic maps like the following
1707 * If there are some cut constraints on one side, then we may
1708 * still be able to fuse the two basic maps, but we need to perform
1709 * some additional checks in is_adj_ineq_extension.
1711 static enum isl_change
check_adj_ineq(int i
, int j
,
1712 struct isl_coalesce_info
*info
)
1714 int count_i
, count_j
;
1717 count_i
= count_ineq(&info
[i
], STATUS_ADJ_INEQ
);
1718 count_j
= count_ineq(&info
[j
], STATUS_ADJ_INEQ
);
1720 if (count_i
!= 1 && count_j
!= 1)
1721 return isl_change_none
;
1723 cut_i
= any_eq(&info
[i
], STATUS_CUT
) || any_ineq(&info
[i
], STATUS_CUT
);
1724 cut_j
= any_eq(&info
[j
], STATUS_CUT
) || any_ineq(&info
[j
], STATUS_CUT
);
1726 if (!cut_i
&& !cut_j
&& count_i
== 1 && count_j
== 1)
1727 return fuse(i
, j
, info
, NULL
, 0, 0);
1729 if (count_i
== 1 && !cut_i
)
1730 return is_adj_ineq_extension(i
, j
, info
);
1732 if (count_j
== 1 && !cut_j
)
1733 return is_adj_ineq_extension(j
, i
, info
);
1735 return isl_change_none
;
1738 /* Given a basic set i with a constraint k that is adjacent to
1739 * basic set j, check if we can wrap
1740 * both the facet corresponding to k (if "wrap_facet" is set) and basic map j
1741 * (always) around their ridges to include the other set.
1742 * If so, replace the pair of basic sets by their union.
1744 * All constraints of i (except k) are assumed to be valid or
1745 * cut constraints for j.
1746 * Wrapping the cut constraints to include basic map j may result
1747 * in constraints that are no longer valid of basic map i
1748 * we have to check that the resulting wrapping constraints are valid for i.
1749 * If "wrap_facet" is not set, then all constraints of i (except k)
1750 * are assumed to be valid for j.
1759 static enum isl_change
can_wrap_in_facet(int i
, int j
, int k
,
1760 struct isl_coalesce_info
*info
, int wrap_facet
)
1762 enum isl_change change
= isl_change_none
;
1763 struct isl_wraps wraps
;
1766 struct isl_set
*set_i
= NULL
;
1767 struct isl_set
*set_j
= NULL
;
1768 struct isl_vec
*bound
= NULL
;
1769 isl_size total
= isl_basic_map_dim(info
[i
].bmap
, isl_dim_all
);
1772 return isl_change_error
;
1773 set_i
= set_from_updated_bmap(info
[i
].bmap
, info
[i
].tab
);
1774 set_j
= set_from_updated_bmap(info
[j
].bmap
, info
[j
].tab
);
1775 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
1776 mat
= isl_mat_alloc(ctx
, 2 * (info
[i
].bmap
->n_eq
+ info
[j
].bmap
->n_eq
) +
1777 info
[i
].bmap
->n_ineq
+ info
[j
].bmap
->n_ineq
,
1779 if (wraps_init(&wraps
, mat
, info
, i
, j
) < 0)
1781 bound
= isl_vec_alloc(ctx
, 1 + total
);
1782 if (!set_i
|| !set_j
|| !bound
)
1785 isl_seq_cpy(bound
->el
, info
[i
].bmap
->ineq
[k
], 1 + total
);
1786 isl_int_add_ui(bound
->el
[0], bound
->el
[0], 1);
1787 isl_seq_normalize(ctx
, bound
->el
, 1 + total
);
1789 isl_seq_cpy(wraps
.mat
->row
[0], bound
->el
, 1 + total
);
1790 wraps
.mat
->n_row
= 1;
1792 if (add_wraps(&wraps
, &info
[j
], bound
->el
, set_i
) < 0)
1798 if (add_wraps_around_facet(&wraps
, &info
[i
], k
,
1799 bound
->el
, set_j
) < 0)
1805 change
= fuse(i
, j
, info
, wraps
.mat
, 0, 0);
1810 isl_set_free(set_i
);
1811 isl_set_free(set_j
);
1813 isl_vec_free(bound
);
1818 isl_vec_free(bound
);
1819 isl_set_free(set_i
);
1820 isl_set_free(set_j
);
1821 return isl_change_error
;
1824 /* Given a cut constraint t(x) >= 0 of basic map i, stored in row "w"
1825 * of wrap.mat, replace it by its relaxed version t(x) + 1 >= 0, and
1826 * add wrapping constraints to wrap.mat for all constraints
1827 * of basic map j that bound the part of basic map j that sticks out
1828 * of the cut constraint.
1829 * "set_i" is the underlying set of basic map i.
1830 * If any wrapping fails, then wraps->mat.n_row is reset to zero.
1832 * In particular, we first intersect basic map j with t(x) + 1 = 0.
1833 * If the result is empty, then t(x) >= 0 was actually a valid constraint
1834 * (with respect to the integer points), so we add t(x) >= 0 instead.
1835 * Otherwise, we wrap the constraints of basic map j that are not
1836 * redundant in this intersection and that are not already valid
1837 * for basic map i over basic map i.
1838 * Note that it is sufficient to wrap the constraints to include
1839 * basic map i, because we will only wrap the constraints that do
1840 * not include basic map i already. The wrapped constraint will
1841 * therefore be more relaxed compared to the original constraint.
1842 * Since the original constraint is valid for basic map j, so is
1843 * the wrapped constraint.
1845 static isl_stat
wrap_in_facet(struct isl_wraps
*wraps
, int w
,
1846 struct isl_coalesce_info
*info_j
, __isl_keep isl_set
*set_i
,
1847 struct isl_tab_undo
*snap
)
1849 isl_int_add_ui(wraps
->mat
->row
[w
][0], wraps
->mat
->row
[w
][0], 1);
1850 if (isl_tab_add_eq(info_j
->tab
, wraps
->mat
->row
[w
]) < 0)
1851 return isl_stat_error
;
1852 if (isl_tab_detect_redundant(info_j
->tab
) < 0)
1853 return isl_stat_error
;
1855 if (info_j
->tab
->empty
)
1856 isl_int_sub_ui(wraps
->mat
->row
[w
][0], wraps
->mat
->row
[w
][0], 1);
1857 else if (add_wraps(wraps
, info_j
, wraps
->mat
->row
[w
], set_i
) < 0)
1858 return isl_stat_error
;
1860 if (isl_tab_rollback(info_j
->tab
, snap
) < 0)
1861 return isl_stat_error
;
1866 /* Given a pair of basic maps i and j such that j sticks out
1867 * of i at n cut constraints, each time by at most one,
1868 * try to compute wrapping constraints and replace the two
1869 * basic maps by a single basic map.
1870 * The other constraints of i are assumed to be valid for j.
1871 * "set_i" is the underlying set of basic map i.
1872 * "wraps" has been initialized to be of the right size.
1874 * For each cut constraint t(x) >= 0 of i, we add the relaxed version
1875 * t(x) + 1 >= 0, along with wrapping constraints for all constraints
1876 * of basic map j that bound the part of basic map j that sticks out
1877 * of the cut constraint.
1879 * If any wrapping fails, i.e., if we cannot wrap to touch
1880 * the union, then we give up.
1881 * Otherwise, the pair of basic maps is replaced by their union.
1883 static enum isl_change
try_wrap_in_facets(int i
, int j
,
1884 struct isl_coalesce_info
*info
, struct isl_wraps
*wraps
,
1885 __isl_keep isl_set
*set_i
)
1889 struct isl_tab_undo
*snap
;
1891 total
= isl_basic_map_dim(info
[i
].bmap
, isl_dim_all
);
1893 return isl_change_error
;
1895 snap
= isl_tab_snap(info
[j
].tab
);
1897 for (k
= 0; k
< info
[i
].bmap
->n_eq
; ++k
) {
1898 for (l
= 0; l
< 2; ++l
) {
1899 if (info
[i
].eq
[2 * k
+ l
] != STATUS_CUT
)
1901 w
= wraps
->mat
->n_row
++;
1903 isl_seq_neg(wraps
->mat
->row
[w
],
1904 info
[i
].bmap
->eq
[k
], 1 + total
);
1906 isl_seq_cpy(wraps
->mat
->row
[w
],
1907 info
[i
].bmap
->eq
[k
], 1 + total
);
1908 if (wrap_in_facet(wraps
, w
, &info
[j
], set_i
, snap
) < 0)
1909 return isl_change_error
;
1912 return isl_change_none
;
1916 for (k
= 0; k
< info
[i
].bmap
->n_ineq
; ++k
) {
1917 if (info
[i
].ineq
[k
] != STATUS_CUT
)
1919 w
= wraps
->mat
->n_row
++;
1920 isl_seq_cpy(wraps
->mat
->row
[w
],
1921 info
[i
].bmap
->ineq
[k
], 1 + total
);
1922 if (wrap_in_facet(wraps
, w
, &info
[j
], set_i
, snap
) < 0)
1923 return isl_change_error
;
1926 return isl_change_none
;
1929 return fuse(i
, j
, info
, wraps
->mat
, 0, 1);
1932 /* Given a pair of basic maps i and j such that j sticks out
1933 * of i at n cut constraints, each time by at most one,
1934 * try to compute wrapping constraints and replace the two
1935 * basic maps by a single basic map.
1936 * The other constraints of i are assumed to be valid for j.
1938 * The core computation is performed by try_wrap_in_facets.
1939 * This function simply extracts an underlying set representation
1940 * of basic map i and initializes the data structure for keeping
1941 * track of wrapping constraints.
1943 static enum isl_change
wrap_in_facets(int i
, int j
, int n
,
1944 struct isl_coalesce_info
*info
)
1946 enum isl_change change
= isl_change_none
;
1947 struct isl_wraps wraps
;
1950 isl_set
*set_i
= NULL
;
1951 isl_size total
= isl_basic_map_dim(info
[i
].bmap
, isl_dim_all
);
1955 return isl_change_error
;
1956 if (isl_tab_extend_cons(info
[j
].tab
, 1) < 0)
1957 return isl_change_error
;
1959 max_wrap
= 1 + 2 * info
[j
].bmap
->n_eq
+ info
[j
].bmap
->n_ineq
;
1962 set_i
= set_from_updated_bmap(info
[i
].bmap
, info
[i
].tab
);
1963 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
1964 mat
= isl_mat_alloc(ctx
, max_wrap
, 1 + total
);
1965 if (wraps_init(&wraps
, mat
, info
, i
, j
) < 0)
1970 change
= try_wrap_in_facets(i
, j
, info
, &wraps
, set_i
);
1973 isl_set_free(set_i
);
1978 isl_set_free(set_i
);
1979 return isl_change_error
;
1982 /* Return the effect of inequality "ineq" on the tableau "tab",
1983 * after relaxing the constant term of "ineq" by one.
1985 static enum isl_ineq_type
type_of_relaxed(struct isl_tab
*tab
, isl_int
*ineq
)
1987 enum isl_ineq_type type
;
1989 isl_int_add_ui(ineq
[0], ineq
[0], 1);
1990 type
= isl_tab_ineq_type(tab
, ineq
);
1991 isl_int_sub_ui(ineq
[0], ineq
[0], 1);
1996 /* Given two basic sets i and j,
1997 * check if relaxing all the cut constraints of i by one turns
1998 * them into valid constraint for j and check if we can wrap in
1999 * the bits that are sticking out.
2000 * If so, replace the pair by their union.
2002 * We first check if all relaxed cut inequalities of i are valid for j
2003 * and then try to wrap in the intersections of the relaxed cut inequalities
2006 * During this wrapping, we consider the points of j that lie at a distance
2007 * of exactly 1 from i. In particular, we ignore the points that lie in
2008 * between this lower-dimensional space and the basic map i.
2009 * We can therefore only apply this to integer maps.
2035 * Wrapping can fail if the result of wrapping one of the facets
2036 * around its edges does not produce any new facet constraint.
2037 * In particular, this happens when we try to wrap in unbounded sets.
2039 * _______________________________________________________________________
2043 * |_| |_________________________________________________________________
2046 * The following is not an acceptable result of coalescing the above two
2047 * sets as it includes extra integer points.
2048 * _______________________________________________________________________
2053 * \______________________________________________________________________
2055 static enum isl_change
can_wrap_in_set(int i
, int j
,
2056 struct isl_coalesce_info
*info
)
2062 if (ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_RATIONAL
) ||
2063 ISL_F_ISSET(info
[j
].bmap
, ISL_BASIC_MAP_RATIONAL
))
2064 return isl_change_none
;
2066 n
= count_eq(&info
[i
], STATUS_CUT
) + count_ineq(&info
[i
], STATUS_CUT
);
2068 return isl_change_none
;
2070 total
= isl_basic_map_dim(info
[i
].bmap
, isl_dim_all
);
2072 return isl_change_error
;
2073 for (k
= 0; k
< info
[i
].bmap
->n_eq
; ++k
) {
2074 for (l
= 0; l
< 2; ++l
) {
2075 enum isl_ineq_type type
;
2077 if (info
[i
].eq
[2 * k
+ l
] != STATUS_CUT
)
2081 isl_seq_neg(info
[i
].bmap
->eq
[k
],
2082 info
[i
].bmap
->eq
[k
], 1 + total
);
2083 type
= type_of_relaxed(info
[j
].tab
,
2084 info
[i
].bmap
->eq
[k
]);
2086 isl_seq_neg(info
[i
].bmap
->eq
[k
],
2087 info
[i
].bmap
->eq
[k
], 1 + total
);
2088 if (type
== isl_ineq_error
)
2089 return isl_change_error
;
2090 if (type
!= isl_ineq_redundant
)
2091 return isl_change_none
;
2095 for (k
= 0; k
< info
[i
].bmap
->n_ineq
; ++k
) {
2096 enum isl_ineq_type type
;
2098 if (info
[i
].ineq
[k
] != STATUS_CUT
)
2101 type
= type_of_relaxed(info
[j
].tab
, info
[i
].bmap
->ineq
[k
]);
2102 if (type
== isl_ineq_error
)
2103 return isl_change_error
;
2104 if (type
!= isl_ineq_redundant
)
2105 return isl_change_none
;
2108 return wrap_in_facets(i
, j
, n
, info
);
2111 /* Check if either i or j has only cut constraints that can
2112 * be used to wrap in (a facet of) the other basic set.
2113 * if so, replace the pair by their union.
2115 static enum isl_change
check_wrap(int i
, int j
, struct isl_coalesce_info
*info
)
2117 enum isl_change change
= isl_change_none
;
2119 change
= can_wrap_in_set(i
, j
, info
);
2120 if (change
!= isl_change_none
)
2123 change
= can_wrap_in_set(j
, i
, info
);
2127 /* Check if all inequality constraints of "i" that cut "j" cease
2128 * to be cut constraints if they are relaxed by one.
2129 * If so, collect the cut constraints in "list".
2130 * The caller is responsible for allocating "list".
2132 static isl_bool
all_cut_by_one(int i
, int j
, struct isl_coalesce_info
*info
,
2138 for (l
= 0; l
< info
[i
].bmap
->n_ineq
; ++l
) {
2139 enum isl_ineq_type type
;
2141 if (info
[i
].ineq
[l
] != STATUS_CUT
)
2143 type
= type_of_relaxed(info
[j
].tab
, info
[i
].bmap
->ineq
[l
]);
2144 if (type
== isl_ineq_error
)
2145 return isl_bool_error
;
2146 if (type
!= isl_ineq_redundant
)
2147 return isl_bool_false
;
2151 return isl_bool_true
;
2154 /* Given two basic maps such that "j" has at least one equality constraint
2155 * that is adjacent to an inequality constraint of "i" and such that "i" has
2156 * exactly one inequality constraint that is adjacent to an equality
2157 * constraint of "j", check whether "i" can be extended to include "j" or
2158 * whether "j" can be wrapped into "i".
2159 * All remaining constraints of "i" and "j" are assumed to be valid
2160 * or cut constraints of the other basic map.
2161 * However, none of the equality constraints of "i" are cut constraints.
2163 * If "i" has any "cut" inequality constraints, then check if relaxing
2164 * each of them by one is sufficient for them to become valid.
2165 * If so, check if the inequality constraint adjacent to an equality
2166 * constraint of "j" along with all these cut constraints
2167 * can be relaxed by one to contain exactly "j".
2168 * Otherwise, or if this fails, check if "j" can be wrapped into "i".
2170 static enum isl_change
check_single_adj_eq(int i
, int j
,
2171 struct isl_coalesce_info
*info
)
2173 enum isl_change change
= isl_change_none
;
2180 n_cut
= count_ineq(&info
[i
], STATUS_CUT
);
2182 k
= find_ineq(&info
[i
], STATUS_ADJ_EQ
);
2185 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
2186 relax
= isl_calloc_array(ctx
, int, 1 + n_cut
);
2188 return isl_change_error
;
2190 try_relax
= all_cut_by_one(i
, j
, info
, relax
+ 1);
2192 change
= isl_change_error
;
2194 try_relax
= isl_bool_true
;
2197 if (try_relax
&& change
== isl_change_none
)
2198 change
= is_relaxed_extension(i
, j
, 1 + n_cut
, relax
, info
);
2201 if (change
!= isl_change_none
)
2204 change
= can_wrap_in_facet(i
, j
, k
, info
, n_cut
> 0);
2209 /* At least one of the basic maps has an equality that is adjacent
2210 * to an inequality. Make sure that only one of the basic maps has
2211 * such an equality and that the other basic map has exactly one
2212 * inequality adjacent to an equality.
2213 * If the other basic map does not have such an inequality, then
2214 * check if all its constraints are either valid or cut constraints
2215 * and, if so, try wrapping in the first map into the second.
2216 * Otherwise, try to extend one basic map with the other or
2217 * wrap one basic map in the other.
2219 static enum isl_change
check_adj_eq(int i
, int j
,
2220 struct isl_coalesce_info
*info
)
2222 if (any_eq(&info
[i
], STATUS_ADJ_INEQ
) &&
2223 any_eq(&info
[j
], STATUS_ADJ_INEQ
))
2224 /* ADJ EQ TOO MANY */
2225 return isl_change_none
;
2227 if (any_eq(&info
[i
], STATUS_ADJ_INEQ
))
2228 return check_adj_eq(j
, i
, info
);
2230 /* j has an equality adjacent to an inequality in i */
2232 if (count_ineq(&info
[i
], STATUS_ADJ_EQ
) != 1) {
2233 if (all_valid_or_cut(&info
[i
]))
2234 return can_wrap_in_set(i
, j
, info
);
2235 return isl_change_none
;
2237 if (any_eq(&info
[i
], STATUS_CUT
))
2238 return isl_change_none
;
2239 if (any_ineq(&info
[j
], STATUS_ADJ_EQ
) ||
2240 any_ineq(&info
[i
], STATUS_ADJ_INEQ
) ||
2241 any_ineq(&info
[j
], STATUS_ADJ_INEQ
))
2242 /* ADJ EQ TOO MANY */
2243 return isl_change_none
;
2245 return check_single_adj_eq(i
, j
, info
);
2248 /* Disjunct "j" lies on a hyperplane that is adjacent to disjunct "i".
2249 * In particular, disjunct "i" has an inequality constraint that is adjacent
2250 * to a (combination of) equality constraint(s) of disjunct "j",
2251 * but disjunct "j" has no explicit equality constraint adjacent
2252 * to an inequality constraint of disjunct "i".
2254 * Disjunct "i" is already known not to have any equality constraints
2255 * that are adjacent to an equality or inequality constraint.
2256 * Check that, other than the inequality constraint mentioned above,
2257 * all other constraints of disjunct "i" are valid for disjunct "j".
2258 * If so, try and wrap in disjunct "j".
2260 static enum isl_change
check_ineq_adj_eq(int i
, int j
,
2261 struct isl_coalesce_info
*info
)
2265 if (any_eq(&info
[i
], STATUS_CUT
))
2266 return isl_change_none
;
2267 if (any_ineq(&info
[i
], STATUS_CUT
))
2268 return isl_change_none
;
2269 if (any_ineq(&info
[i
], STATUS_ADJ_INEQ
))
2270 return isl_change_none
;
2271 if (count_ineq(&info
[i
], STATUS_ADJ_EQ
) != 1)
2272 return isl_change_none
;
2274 k
= find_ineq(&info
[i
], STATUS_ADJ_EQ
);
2276 return can_wrap_in_facet(i
, j
, k
, info
, 0);
2279 /* The two basic maps lie on adjacent hyperplanes. In particular,
2280 * basic map "i" has an equality that lies parallel to basic map "j".
2281 * Check if we can wrap the facets around the parallel hyperplanes
2282 * to include the other set.
2284 * We perform basically the same operations as can_wrap_in_facet,
2285 * except that we don't need to select a facet of one of the sets.
2291 * If there is more than one equality of "i" adjacent to an equality of "j",
2292 * then the result will satisfy one or more equalities that are a linear
2293 * combination of these equalities. These will be encoded as pairs
2294 * of inequalities in the wrapping constraints and need to be made
2297 static enum isl_change
check_eq_adj_eq(int i
, int j
,
2298 struct isl_coalesce_info
*info
)
2301 enum isl_change change
= isl_change_none
;
2302 int detect_equalities
= 0;
2303 struct isl_wraps wraps
;
2306 struct isl_set
*set_i
= NULL
;
2307 struct isl_set
*set_j
= NULL
;
2308 struct isl_vec
*bound
= NULL
;
2309 isl_size total
= isl_basic_map_dim(info
[i
].bmap
, isl_dim_all
);
2312 return isl_change_error
;
2313 if (count_eq(&info
[i
], STATUS_ADJ_EQ
) != 1)
2314 detect_equalities
= 1;
2316 k
= find_eq(&info
[i
], STATUS_ADJ_EQ
);
2318 set_i
= set_from_updated_bmap(info
[i
].bmap
, info
[i
].tab
);
2319 set_j
= set_from_updated_bmap(info
[j
].bmap
, info
[j
].tab
);
2320 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
2321 mat
= isl_mat_alloc(ctx
, 2 * (info
[i
].bmap
->n_eq
+ info
[j
].bmap
->n_eq
) +
2322 info
[i
].bmap
->n_ineq
+ info
[j
].bmap
->n_ineq
,
2324 if (wraps_init(&wraps
, mat
, info
, i
, j
) < 0)
2326 bound
= isl_vec_alloc(ctx
, 1 + total
);
2327 if (!set_i
|| !set_j
|| !bound
)
2331 isl_seq_neg(bound
->el
, info
[i
].bmap
->eq
[k
/ 2], 1 + total
);
2333 isl_seq_cpy(bound
->el
, info
[i
].bmap
->eq
[k
/ 2], 1 + total
);
2334 isl_int_add_ui(bound
->el
[0], bound
->el
[0], 1);
2336 isl_seq_cpy(wraps
.mat
->row
[0], bound
->el
, 1 + total
);
2337 wraps
.mat
->n_row
= 1;
2339 if (add_wraps(&wraps
, &info
[j
], bound
->el
, set_i
) < 0)
2344 isl_int_sub_ui(bound
->el
[0], bound
->el
[0], 1);
2345 isl_seq_neg(bound
->el
, bound
->el
, 1 + total
);
2347 isl_seq_cpy(wraps
.mat
->row
[wraps
.mat
->n_row
], bound
->el
, 1 + total
);
2350 if (add_wraps(&wraps
, &info
[i
], bound
->el
, set_j
) < 0)
2355 change
= fuse(i
, j
, info
, wraps
.mat
, detect_equalities
, 0);
2358 error
: change
= isl_change_error
;
2363 isl_set_free(set_i
);
2364 isl_set_free(set_j
);
2365 isl_vec_free(bound
);
2370 /* Initialize the "eq" and "ineq" fields of "info".
2372 static void init_status(struct isl_coalesce_info
*info
)
2374 info
->eq
= info
->ineq
= NULL
;
2377 /* Set info->eq to the positions of the equalities of info->bmap
2378 * with respect to the basic map represented by "tab".
2379 * If info->eq has already been computed, then do not compute it again.
2381 static void set_eq_status_in(struct isl_coalesce_info
*info
,
2382 struct isl_tab
*tab
)
2386 info
->eq
= eq_status_in(info
->bmap
, tab
);
2389 /* Set info->ineq to the positions of the inequalities of info->bmap
2390 * with respect to the basic map represented by "tab".
2391 * If info->ineq has already been computed, then do not compute it again.
2393 static void set_ineq_status_in(struct isl_coalesce_info
*info
,
2394 struct isl_tab
*tab
)
2398 info
->ineq
= ineq_status_in(info
->bmap
, info
->tab
, tab
);
2401 /* Free the memory allocated by the "eq" and "ineq" fields of "info".
2402 * This function assumes that init_status has been called on "info" first,
2403 * after which the "eq" and "ineq" fields may or may not have been
2404 * assigned a newly allocated array.
2406 static void clear_status(struct isl_coalesce_info
*info
)
2412 /* Are all inequality constraints of the basic map represented by "info"
2413 * valid for the other basic map, except for a single constraint
2414 * that is adjacent to an inequality constraint of the other basic map?
2416 static int all_ineq_valid_or_single_adj_ineq(struct isl_coalesce_info
*info
)
2421 for (i
= 0; i
< info
->bmap
->n_ineq
; ++i
) {
2422 if (info
->ineq
[i
] == STATUS_REDUNDANT
)
2424 if (info
->ineq
[i
] == STATUS_VALID
)
2426 if (info
->ineq
[i
] != STATUS_ADJ_INEQ
)
2436 /* Basic map "i" has one or more equality constraints that separate it
2437 * from basic map "j". Check if it happens to be an extension
2439 * In particular, check that all constraints of "j" are valid for "i",
2440 * except for one inequality constraint that is adjacent
2441 * to an inequality constraints of "i".
2442 * If so, check for "i" being an extension of "j" by calling
2443 * is_adj_ineq_extension.
2445 * Clean up the memory allocated for keeping track of the status
2446 * of the constraints before returning.
2448 static enum isl_change
separating_equality(int i
, int j
,
2449 struct isl_coalesce_info
*info
)
2451 enum isl_change change
= isl_change_none
;
2453 if (all(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_VALID
) &&
2454 all_ineq_valid_or_single_adj_ineq(&info
[j
]))
2455 change
= is_adj_ineq_extension(j
, i
, info
);
2457 clear_status(&info
[i
]);
2458 clear_status(&info
[j
]);
2462 /* Check if the union of the given pair of basic maps
2463 * can be represented by a single basic map.
2464 * If so, replace the pair by the single basic map and return
2465 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
2466 * Otherwise, return isl_change_none.
2467 * The two basic maps are assumed to live in the same local space.
2468 * The "eq" and "ineq" fields of info[i] and info[j] are assumed
2469 * to have been initialized by the caller, either to NULL or
2470 * to valid information.
2472 * We first check the effect of each constraint of one basic map
2473 * on the other basic map.
2474 * The constraint may be
2475 * redundant the constraint is redundant in its own
2476 * basic map and should be ignore and removed
2478 * valid all (integer) points of the other basic map
2479 * satisfy the constraint
2480 * separate no (integer) point of the other basic map
2481 * satisfies the constraint
2482 * cut some but not all points of the other basic map
2483 * satisfy the constraint
2484 * adj_eq the given constraint is adjacent (on the outside)
2485 * to an equality of the other basic map
2486 * adj_ineq the given constraint is adjacent (on the outside)
2487 * to an inequality of the other basic map
2489 * We consider seven cases in which we can replace the pair by a single
2490 * basic map. We ignore all "redundant" constraints.
2492 * 1. all constraints of one basic map are valid
2493 * => the other basic map is a subset and can be removed
2495 * 2. all constraints of both basic maps are either "valid" or "cut"
2496 * and the facets corresponding to the "cut" constraints
2497 * of one of the basic maps lies entirely inside the other basic map
2498 * => the pair can be replaced by a basic map consisting
2499 * of the valid constraints in both basic maps
2501 * 3. there is a single pair of adjacent inequalities
2502 * (all other constraints are "valid")
2503 * => the pair can be replaced by a basic map consisting
2504 * of the valid constraints in both basic maps
2506 * 4. one basic map has a single adjacent inequality, while the other
2507 * constraints are "valid". The other basic map has some
2508 * "cut" constraints, but replacing the adjacent inequality by
2509 * its opposite and adding the valid constraints of the other
2510 * basic map results in a subset of the other basic map
2511 * => the pair can be replaced by a basic map consisting
2512 * of the valid constraints in both basic maps
2514 * 5. there is a single adjacent pair of an inequality and an equality,
2515 * the other constraints of the basic map containing the inequality are
2516 * "valid". Moreover, if the inequality the basic map is relaxed
2517 * and then turned into an equality, then resulting facet lies
2518 * entirely inside the other basic map
2519 * => the pair can be replaced by the basic map containing
2520 * the inequality, with the inequality relaxed.
2522 * 6. there is a single inequality adjacent to an equality,
2523 * the other constraints of the basic map containing the inequality are
2524 * "valid". Moreover, the facets corresponding to both
2525 * the inequality and the equality can be wrapped around their
2526 * ridges to include the other basic map
2527 * => the pair can be replaced by a basic map consisting
2528 * of the valid constraints in both basic maps together
2529 * with all wrapping constraints
2531 * 7. one of the basic maps extends beyond the other by at most one.
2532 * Moreover, the facets corresponding to the cut constraints and
2533 * the pieces of the other basic map at offset one from these cut
2534 * constraints can be wrapped around their ridges to include
2535 * the union of the two basic maps
2536 * => the pair can be replaced by a basic map consisting
2537 * of the valid constraints in both basic maps together
2538 * with all wrapping constraints
2540 * 8. the two basic maps live in adjacent hyperplanes. In principle
2541 * such sets can always be combined through wrapping, but we impose
2542 * that there is only one such pair, to avoid overeager coalescing.
2544 * Throughout the computation, we maintain a collection of tableaus
2545 * corresponding to the basic maps. When the basic maps are dropped
2546 * or combined, the tableaus are modified accordingly.
2548 static enum isl_change
coalesce_local_pair_reuse(int i
, int j
,
2549 struct isl_coalesce_info
*info
)
2551 enum isl_change change
= isl_change_none
;
2553 set_ineq_status_in(&info
[i
], info
[j
].tab
);
2554 if (info
[i
].bmap
->n_ineq
&& !info
[i
].ineq
)
2556 if (any_ineq(&info
[i
], STATUS_ERROR
))
2558 if (any_ineq(&info
[i
], STATUS_SEPARATE
))
2561 set_ineq_status_in(&info
[j
], info
[i
].tab
);
2562 if (info
[j
].bmap
->n_ineq
&& !info
[j
].ineq
)
2564 if (any_ineq(&info
[j
], STATUS_ERROR
))
2566 if (any_ineq(&info
[j
], STATUS_SEPARATE
))
2569 set_eq_status_in(&info
[i
], info
[j
].tab
);
2570 if (info
[i
].bmap
->n_eq
&& !info
[i
].eq
)
2572 if (any_eq(&info
[i
], STATUS_ERROR
))
2575 set_eq_status_in(&info
[j
], info
[i
].tab
);
2576 if (info
[j
].bmap
->n_eq
&& !info
[j
].eq
)
2578 if (any_eq(&info
[j
], STATUS_ERROR
))
2581 if (any_eq(&info
[i
], STATUS_SEPARATE
))
2582 return separating_equality(i
, j
, info
);
2583 if (any_eq(&info
[j
], STATUS_SEPARATE
))
2584 return separating_equality(j
, i
, info
);
2586 if (all(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_VALID
) &&
2587 all(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_VALID
)) {
2589 change
= isl_change_drop_second
;
2590 } else if (all(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_VALID
) &&
2591 all(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_VALID
)) {
2593 change
= isl_change_drop_first
;
2594 } else if (any_eq(&info
[i
], STATUS_ADJ_EQ
)) {
2595 change
= check_eq_adj_eq(i
, j
, info
);
2596 } else if (any_eq(&info
[j
], STATUS_ADJ_EQ
)) {
2597 change
= check_eq_adj_eq(j
, i
, info
);
2598 } else if (any_eq(&info
[i
], STATUS_ADJ_INEQ
) ||
2599 any_eq(&info
[j
], STATUS_ADJ_INEQ
)) {
2600 change
= check_adj_eq(i
, j
, info
);
2601 } else if (any_ineq(&info
[i
], STATUS_ADJ_EQ
)) {
2602 change
= check_ineq_adj_eq(i
, j
, info
);
2603 } else if (any_ineq(&info
[j
], STATUS_ADJ_EQ
)) {
2604 change
= check_ineq_adj_eq(j
, i
, info
);
2605 } else if (any_ineq(&info
[i
], STATUS_ADJ_INEQ
) ||
2606 any_ineq(&info
[j
], STATUS_ADJ_INEQ
)) {
2607 change
= check_adj_ineq(i
, j
, info
);
2609 if (!any_eq(&info
[i
], STATUS_CUT
) &&
2610 !any_eq(&info
[j
], STATUS_CUT
))
2611 change
= check_facets(i
, j
, info
);
2612 if (change
== isl_change_none
)
2613 change
= check_wrap(i
, j
, info
);
2617 clear_status(&info
[i
]);
2618 clear_status(&info
[j
]);
2621 clear_status(&info
[i
]);
2622 clear_status(&info
[j
]);
2623 return isl_change_error
;
2626 /* Check if the union of the given pair of basic maps
2627 * can be represented by a single basic map.
2628 * If so, replace the pair by the single basic map and return
2629 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
2630 * Otherwise, return isl_change_none.
2631 * The two basic maps are assumed to live in the same local space.
2633 static enum isl_change
coalesce_local_pair(int i
, int j
,
2634 struct isl_coalesce_info
*info
)
2636 init_status(&info
[i
]);
2637 init_status(&info
[j
]);
2638 return coalesce_local_pair_reuse(i
, j
, info
);
2641 /* Shift the integer division at position "div" of the basic map
2642 * represented by "info" by "shift".
2644 * That is, if the integer division has the form
2648 * then replace it by
2650 * floor((f(x) + shift * d)/d) - shift
2652 static isl_stat
shift_div(struct isl_coalesce_info
*info
, int div
,
2655 isl_size total
, n_div
;
2657 info
->bmap
= isl_basic_map_shift_div(info
->bmap
, div
, 0, shift
);
2659 return isl_stat_error
;
2661 total
= isl_basic_map_dim(info
->bmap
, isl_dim_all
);
2662 n_div
= isl_basic_map_dim(info
->bmap
, isl_dim_div
);
2663 if (total
< 0 || n_div
< 0)
2664 return isl_stat_error
;
2666 if (isl_tab_shift_var(info
->tab
, total
+ div
, shift
) < 0)
2667 return isl_stat_error
;
2672 /* If the integer division at position "div" is defined by an equality,
2673 * i.e., a stride constraint, then change the integer division expression
2674 * to have a constant term equal to zero.
2676 * Let the equality constraint be
2680 * The integer division expression is then typically of the form
2682 * a = floor((-f - c')/m)
2684 * The integer division is first shifted by t = floor(c/m),
2685 * turning the equality constraint into
2687 * c - m floor(c/m) + f + m a' = 0
2691 * (c mod m) + f + m a' = 0
2695 * a' = (-f - (c mod m))/m = floor((-f)/m)
2697 * because a' is an integer and 0 <= (c mod m) < m.
2698 * The constant term of a' can therefore be zeroed out,
2699 * but only if the integer division expression is of the expected form.
2701 static isl_stat
normalize_stride_div(struct isl_coalesce_info
*info
, int div
)
2703 isl_bool defined
, valid
;
2706 isl_int shift
, stride
;
2708 defined
= isl_basic_map_has_defining_equality(info
->bmap
, isl_dim_div
,
2711 return isl_stat_error
;
2715 return isl_stat_error
;
2716 valid
= isl_constraint_is_div_equality(c
, div
);
2717 isl_int_init(shift
);
2718 isl_int_init(stride
);
2719 isl_constraint_get_constant(c
, &shift
);
2720 isl_constraint_get_coefficient(c
, isl_dim_div
, div
, &stride
);
2721 isl_int_fdiv_q(shift
, shift
, stride
);
2722 r
= shift_div(info
, div
, shift
);
2723 isl_int_clear(stride
);
2724 isl_int_clear(shift
);
2725 isl_constraint_free(c
);
2726 if (r
< 0 || valid
< 0)
2727 return isl_stat_error
;
2730 info
->bmap
= isl_basic_map_set_div_expr_constant_num_si_inplace(
2731 info
->bmap
, div
, 0);
2733 return isl_stat_error
;
2737 /* The basic maps represented by "info1" and "info2" are known
2738 * to have the same number of integer divisions.
2739 * Check if pairs of integer divisions are equal to each other
2740 * despite the fact that they differ by a rational constant.
2742 * In particular, look for any pair of integer divisions that
2743 * only differ in their constant terms.
2744 * If either of these integer divisions is defined
2745 * by stride constraints, then modify it to have a zero constant term.
2746 * If both are defined by stride constraints then in the end they will have
2747 * the same (zero) constant term.
2749 static isl_stat
harmonize_stride_divs(struct isl_coalesce_info
*info1
,
2750 struct isl_coalesce_info
*info2
)
2755 n
= isl_basic_map_dim(info1
->bmap
, isl_dim_div
);
2757 return isl_stat_error
;
2758 for (i
= 0; i
< n
; ++i
) {
2759 isl_bool known
, harmonize
;
2761 known
= isl_basic_map_div_is_known(info1
->bmap
, i
);
2762 if (known
>= 0 && known
)
2763 known
= isl_basic_map_div_is_known(info2
->bmap
, i
);
2765 return isl_stat_error
;
2768 harmonize
= isl_basic_map_equal_div_expr_except_constant(
2769 info1
->bmap
, i
, info2
->bmap
, i
);
2771 return isl_stat_error
;
2774 if (normalize_stride_div(info1
, i
) < 0)
2775 return isl_stat_error
;
2776 if (normalize_stride_div(info2
, i
) < 0)
2777 return isl_stat_error
;
2783 /* If "shift" is an integer constant, then shift the integer division
2784 * at position "div" of the basic map represented by "info" by "shift".
2785 * If "shift" is not an integer constant, then do nothing.
2786 * If "shift" is equal to zero, then no shift needs to be performed either.
2788 * That is, if the integer division has the form
2792 * then replace it by
2794 * floor((f(x) + shift * d)/d) - shift
2796 static isl_stat
shift_if_cst_int(struct isl_coalesce_info
*info
, int div
,
2797 __isl_keep isl_aff
*shift
)
2804 cst
= isl_aff_is_cst(shift
);
2805 if (cst
< 0 || !cst
)
2806 return cst
< 0 ? isl_stat_error
: isl_stat_ok
;
2808 c
= isl_aff_get_constant_val(shift
);
2809 cst
= isl_val_is_int(c
);
2810 if (cst
>= 0 && cst
)
2811 cst
= isl_bool_not(isl_val_is_zero(c
));
2812 if (cst
< 0 || !cst
) {
2814 return cst
< 0 ? isl_stat_error
: isl_stat_ok
;
2818 r
= isl_val_get_num_isl_int(c
, &d
);
2820 r
= shift_div(info
, div
, d
);
2828 /* Check if some of the divs in the basic map represented by "info1"
2829 * are shifts of the corresponding divs in the basic map represented
2830 * by "info2", taking into account the equality constraints "eq1" of "info1"
2831 * and "eq2" of "info2". If so, align them with those of "info2".
2832 * "info1" and "info2" are assumed to have the same number
2833 * of integer divisions.
2835 * An integer division is considered to be a shift of another integer
2836 * division if, after simplification with respect to the equality
2837 * constraints of the other basic map, one is equal to the other
2840 * In particular, for each pair of integer divisions, if both are known,
2841 * have the same denominator and are not already equal to each other,
2842 * simplify each with respect to the equality constraints
2843 * of the other basic map. If the difference is an integer constant,
2844 * then move this difference outside.
2845 * That is, if, after simplification, one integer division is of the form
2847 * floor((f(x) + c_1)/d)
2849 * while the other is of the form
2851 * floor((f(x) + c_2)/d)
2853 * and n = (c_2 - c_1)/d is an integer, then replace the first
2854 * integer division by
2856 * floor((f_1(x) + c_1 + n * d)/d) - n,
2858 * where floor((f_1(x) + c_1 + n * d)/d) = floor((f2(x) + c_2)/d)
2859 * after simplification with respect to the equality constraints.
2861 static isl_stat
harmonize_divs_with_hulls(struct isl_coalesce_info
*info1
,
2862 struct isl_coalesce_info
*info2
, __isl_keep isl_basic_set
*eq1
,
2863 __isl_keep isl_basic_set
*eq2
)
2867 isl_local_space
*ls1
, *ls2
;
2869 total
= isl_basic_map_dim(info1
->bmap
, isl_dim_all
);
2871 return isl_stat_error
;
2872 ls1
= isl_local_space_wrap(isl_basic_map_get_local_space(info1
->bmap
));
2873 ls2
= isl_local_space_wrap(isl_basic_map_get_local_space(info2
->bmap
));
2874 for (i
= 0; i
< info1
->bmap
->n_div
; ++i
) {
2876 isl_aff
*div1
, *div2
;
2878 if (!isl_local_space_div_is_known(ls1
, i
) ||
2879 !isl_local_space_div_is_known(ls2
, i
))
2881 if (isl_int_ne(info1
->bmap
->div
[i
][0], info2
->bmap
->div
[i
][0]))
2883 if (isl_seq_eq(info1
->bmap
->div
[i
] + 1,
2884 info2
->bmap
->div
[i
] + 1, 1 + total
))
2886 div1
= isl_local_space_get_div(ls1
, i
);
2887 div2
= isl_local_space_get_div(ls2
, i
);
2888 div1
= isl_aff_substitute_equalities(div1
,
2889 isl_basic_set_copy(eq2
));
2890 div2
= isl_aff_substitute_equalities(div2
,
2891 isl_basic_set_copy(eq1
));
2892 div2
= isl_aff_sub(div2
, div1
);
2893 r
= shift_if_cst_int(info1
, i
, div2
);
2898 isl_local_space_free(ls1
);
2899 isl_local_space_free(ls2
);
2901 if (i
< info1
->bmap
->n_div
)
2902 return isl_stat_error
;
2906 /* Check if some of the divs in the basic map represented by "info1"
2907 * are shifts of the corresponding divs in the basic map represented
2908 * by "info2". If so, align them with those of "info2".
2909 * Only do this if "info1" and "info2" have the same number
2910 * of integer divisions.
2912 * An integer division is considered to be a shift of another integer
2913 * division if, after simplification with respect to the equality
2914 * constraints of the other basic map, one is equal to the other
2917 * First check if pairs of integer divisions are equal to each other
2918 * despite the fact that they differ by a rational constant.
2919 * If so, try and arrange for them to have the same constant term.
2921 * Then, extract the equality constraints and continue with
2922 * harmonize_divs_with_hulls.
2924 * If the equality constraints of both basic maps are the same,
2925 * then there is no need to perform any shifting since
2926 * the coefficients of the integer divisions should have been
2927 * reduced in the same way.
2929 static isl_stat
harmonize_divs(struct isl_coalesce_info
*info1
,
2930 struct isl_coalesce_info
*info2
)
2933 isl_basic_map
*bmap1
, *bmap2
;
2934 isl_basic_set
*eq1
, *eq2
;
2937 if (!info1
->bmap
|| !info2
->bmap
)
2938 return isl_stat_error
;
2940 if (info1
->bmap
->n_div
!= info2
->bmap
->n_div
)
2942 if (info1
->bmap
->n_div
== 0)
2945 if (harmonize_stride_divs(info1
, info2
) < 0)
2946 return isl_stat_error
;
2948 bmap1
= isl_basic_map_copy(info1
->bmap
);
2949 bmap2
= isl_basic_map_copy(info2
->bmap
);
2950 eq1
= isl_basic_map_wrap(isl_basic_map_plain_affine_hull(bmap1
));
2951 eq2
= isl_basic_map_wrap(isl_basic_map_plain_affine_hull(bmap2
));
2952 equal
= isl_basic_set_plain_is_equal(eq1
, eq2
);
2958 r
= harmonize_divs_with_hulls(info1
, info2
, eq1
, eq2
);
2959 isl_basic_set_free(eq1
);
2960 isl_basic_set_free(eq2
);
2965 /* Do the two basic maps live in the same local space, i.e.,
2966 * do they have the same (known) divs?
2967 * If either basic map has any unknown divs, then we can only assume
2968 * that they do not live in the same local space.
2970 static isl_bool
same_divs(__isl_keep isl_basic_map
*bmap1
,
2971 __isl_keep isl_basic_map
*bmap2
)
2977 if (!bmap1
|| !bmap2
)
2978 return isl_bool_error
;
2979 if (bmap1
->n_div
!= bmap2
->n_div
)
2980 return isl_bool_false
;
2982 if (bmap1
->n_div
== 0)
2983 return isl_bool_true
;
2985 known
= isl_basic_map_divs_known(bmap1
);
2986 if (known
< 0 || !known
)
2988 known
= isl_basic_map_divs_known(bmap2
);
2989 if (known
< 0 || !known
)
2992 total
= isl_basic_map_dim(bmap1
, isl_dim_all
);
2994 return isl_bool_error
;
2995 for (i
= 0; i
< bmap1
->n_div
; ++i
)
2996 if (!isl_seq_eq(bmap1
->div
[i
], bmap2
->div
[i
], 2 + total
))
2997 return isl_bool_false
;
2999 return isl_bool_true
;
3002 /* Assuming that "tab" contains the equality constraints and
3003 * the initial inequality constraints of "bmap", copy the remaining
3004 * inequality constraints of "bmap" to "Tab".
3006 static isl_stat
copy_ineq(struct isl_tab
*tab
, __isl_keep isl_basic_map
*bmap
)
3011 return isl_stat_error
;
3013 n_ineq
= tab
->n_con
- tab
->n_eq
;
3014 for (i
= n_ineq
; i
< bmap
->n_ineq
; ++i
)
3015 if (isl_tab_add_ineq(tab
, bmap
->ineq
[i
]) < 0)
3016 return isl_stat_error
;
3021 /* Description of an integer division that is added
3022 * during an expansion.
3023 * "pos" is the position of the corresponding variable.
3024 * "cst" indicates whether this integer division has a fixed value.
3025 * "val" contains the fixed value, if the value is fixed.
3027 struct isl_expanded
{
3033 /* For each of the "n" integer division variables "expanded",
3034 * if the variable has a fixed value, then add two inequality
3035 * constraints expressing the fixed value.
3036 * Otherwise, add the corresponding div constraints.
3037 * The caller is responsible for removing the div constraints
3038 * that it added for all these "n" integer divisions.
3040 * The div constraints and the pair of inequality constraints
3041 * forcing the fixed value cannot both be added for a given variable
3042 * as the combination may render some of the original constraints redundant.
3043 * These would then be ignored during the coalescing detection,
3044 * while they could remain in the fused result.
3046 * The two added inequality constraints are
3051 * with "a" the variable and "v" its fixed value.
3052 * The facet corresponding to one of these two constraints is selected
3053 * in the tableau to ensure that the pair of inequality constraints
3054 * is treated as an equality constraint.
3055 * Such implicit equality constraints need to be turned
3056 * into explicit equality constraints to ensure both sides
3057 * of the equality constraints are taken into account.
3059 * The information in info->ineq is thrown away because it was
3060 * computed in terms of div constraints, while some of those
3061 * have now been replaced by these pairs of inequality constraints.
3063 static isl_stat
fix_constant_divs(struct isl_coalesce_info
*info
,
3064 int n
, struct isl_expanded
*expanded
)
3070 o_div
= isl_basic_map_offset(info
->bmap
, isl_dim_div
) - 1;
3071 ineq
= isl_vec_alloc(isl_tab_get_ctx(info
->tab
), 1 + info
->tab
->n_var
);
3073 return isl_stat_error
;
3074 isl_seq_clr(ineq
->el
+ 1, info
->tab
->n_var
);
3076 for (i
= 0; i
< n
; ++i
) {
3077 if (!expanded
[i
].cst
) {
3078 info
->bmap
= isl_basic_map_extend_constraints(
3080 info
->bmap
= isl_basic_map_add_div_constraints(
3081 info
->bmap
, expanded
[i
].pos
- o_div
);
3083 isl_int_set_si(ineq
->el
[1 + expanded
[i
].pos
], -1);
3084 isl_int_set(ineq
->el
[0], expanded
[i
].val
);
3085 info
->bmap
= isl_basic_map_add_ineq(info
->bmap
,
3087 isl_int_set_si(ineq
->el
[1 + expanded
[i
].pos
], 1);
3088 isl_int_neg(ineq
->el
[0], expanded
[i
].val
);
3089 info
->bmap
= isl_basic_map_add_ineq(info
->bmap
,
3091 isl_int_set_si(ineq
->el
[1 + expanded
[i
].pos
], 0);
3093 if (copy_ineq(info
->tab
, info
->bmap
) < 0)
3095 if (expanded
[i
].cst
&&
3096 isl_tab_select_facet(info
->tab
, info
->tab
->n_con
- 1) < 0)
3105 info
->bmap
= isl_tab_make_equalities_explicit(info
->tab
, info
->bmap
);
3107 return i
< n
? isl_stat_error
: isl_stat_ok
;
3110 /* Insert the "n" integer division variables "expanded"
3111 * into info->tab and info->bmap and
3112 * update info->ineq with respect to the redundant constraints
3113 * in the resulting tableau.
3114 * "bmap" contains the result of this insertion in info->bmap,
3115 * while info->bmap is the original version
3116 * of "bmap", i.e., the one that corresponds to the current
3117 * state of info->tab. The number of constraints in info->bmap
3118 * is assumed to be the same as the number of constraints
3119 * in info->tab. This is required to be able to detect
3120 * the extra constraints in "bmap".
3122 * In particular, introduce extra variables corresponding
3123 * to the extra integer divisions and add the div constraints
3124 * that were added to "bmap" after info->tab was created
3126 * Furthermore, check if these extra integer divisions happen
3127 * to attain a fixed integer value in info->tab.
3128 * If so, replace the corresponding div constraints by pairs
3129 * of inequality constraints that fix these
3130 * integer divisions to their single integer values.
3131 * Replace info->bmap by "bmap" to match the changes to info->tab.
3132 * info->ineq was computed without a tableau and therefore
3133 * does not take into account the redundant constraints
3134 * in the tableau. Mark them here.
3135 * There is no need to check the newly added div constraints
3136 * since they cannot be redundant.
3137 * The redundancy check is not performed when constants have been discovered
3138 * since info->ineq is completely thrown away in this case.
3140 static isl_stat
tab_insert_divs(struct isl_coalesce_info
*info
,
3141 int n
, struct isl_expanded
*expanded
, __isl_take isl_basic_map
*bmap
)
3145 struct isl_tab_undo
*snap
;
3149 return isl_stat_error
;
3150 if (info
->bmap
->n_eq
+ info
->bmap
->n_ineq
!= info
->tab
->n_con
)
3151 isl_die(isl_basic_map_get_ctx(bmap
), isl_error_internal
,
3152 "original tableau does not correspond "
3153 "to original basic map", goto error
);
3155 if (isl_tab_extend_vars(info
->tab
, n
) < 0)
3157 if (isl_tab_extend_cons(info
->tab
, 2 * n
) < 0)
3160 for (i
= 0; i
< n
; ++i
) {
3161 if (isl_tab_insert_var(info
->tab
, expanded
[i
].pos
) < 0)
3165 snap
= isl_tab_snap(info
->tab
);
3167 n_ineq
= info
->tab
->n_con
- info
->tab
->n_eq
;
3168 if (copy_ineq(info
->tab
, bmap
) < 0)
3171 isl_basic_map_free(info
->bmap
);
3175 for (i
= 0; i
< n
; ++i
) {
3176 expanded
[i
].cst
= isl_tab_is_constant(info
->tab
,
3177 expanded
[i
].pos
, &expanded
[i
].val
);
3178 if (expanded
[i
].cst
< 0)
3179 return isl_stat_error
;
3180 if (expanded
[i
].cst
)
3185 if (isl_tab_rollback(info
->tab
, snap
) < 0)
3186 return isl_stat_error
;
3187 info
->bmap
= isl_basic_map_cow(info
->bmap
);
3188 info
->bmap
= isl_basic_map_free_inequality(info
->bmap
, 2 * n
);
3190 return isl_stat_error
;
3192 return fix_constant_divs(info
, n
, expanded
);
3195 n_eq
= info
->bmap
->n_eq
;
3196 for (i
= 0; i
< n_ineq
; ++i
) {
3197 if (isl_tab_is_redundant(info
->tab
, n_eq
+ i
))
3198 info
->ineq
[i
] = STATUS_REDUNDANT
;
3203 isl_basic_map_free(bmap
);
3204 return isl_stat_error
;
3207 /* Expand info->tab and info->bmap in the same way "bmap" was expanded
3208 * in isl_basic_map_expand_divs using the expansion "exp" and
3209 * update info->ineq with respect to the redundant constraints
3210 * in the resulting tableau. info->bmap is the original version
3211 * of "bmap", i.e., the one that corresponds to the current
3212 * state of info->tab. The number of constraints in info->bmap
3213 * is assumed to be the same as the number of constraints
3214 * in info->tab. This is required to be able to detect
3215 * the extra constraints in "bmap".
3217 * Extract the positions where extra local variables are introduced
3218 * from "exp" and call tab_insert_divs.
3220 static isl_stat
expand_tab(struct isl_coalesce_info
*info
, int *exp
,
3221 __isl_take isl_basic_map
*bmap
)
3224 struct isl_expanded
*expanded
;
3227 isl_size total
, n_div
;
3231 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
3232 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
3233 if (total
< 0 || n_div
< 0)
3234 return isl_stat_error
;
3235 pos
= total
- n_div
;
3236 extra_var
= total
- info
->tab
->n_var
;
3237 n
= n_div
- extra_var
;
3239 ctx
= isl_basic_map_get_ctx(bmap
);
3240 expanded
= isl_calloc_array(ctx
, struct isl_expanded
, extra_var
);
3241 if (extra_var
&& !expanded
)
3246 for (j
= 0; j
< n_div
; ++j
) {
3247 if (i
< n
&& exp
[i
] == j
) {
3251 expanded
[k
++].pos
= pos
+ j
;
3254 for (k
= 0; k
< extra_var
; ++k
)
3255 isl_int_init(expanded
[k
].val
);
3257 r
= tab_insert_divs(info
, extra_var
, expanded
, bmap
);
3259 for (k
= 0; k
< extra_var
; ++k
)
3260 isl_int_clear(expanded
[k
].val
);
3265 isl_basic_map_free(bmap
);
3266 return isl_stat_error
;
3269 /* Check if the union of the basic maps represented by info[i] and info[j]
3270 * can be represented by a single basic map,
3271 * after expanding the divs of info[i] to match those of info[j].
3272 * If so, replace the pair by the single basic map and return
3273 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
3274 * Otherwise, return isl_change_none.
3276 * The caller has already checked for info[j] being a subset of info[i].
3277 * If some of the divs of info[j] are unknown, then the expanded info[i]
3278 * will not have the corresponding div constraints. The other patterns
3279 * therefore cannot apply. Skip the computation in this case.
3281 * The expansion is performed using the divs "div" and expansion "exp"
3282 * computed by the caller.
3283 * info[i].bmap has already been expanded and the result is passed in
3285 * The "eq" and "ineq" fields of info[i] reflect the status of
3286 * the constraints of the expanded "bmap" with respect to info[j].tab.
3287 * However, inequality constraints that are redundant in info[i].tab
3288 * have not yet been marked as such because no tableau was available.
3290 * Replace info[i].bmap by "bmap" and expand info[i].tab as well,
3291 * updating info[i].ineq with respect to the redundant constraints.
3292 * Then try and coalesce the expanded info[i] with info[j],
3293 * reusing the information in info[i].eq and info[i].ineq.
3294 * If this does not result in any coalescing or if it results in info[j]
3295 * getting dropped (which should not happen in practice, since the case
3296 * of info[j] being a subset of info[i] has already been checked by
3297 * the caller), then revert info[i] to its original state.
3299 static enum isl_change
coalesce_expand_tab_divs(__isl_take isl_basic_map
*bmap
,
3300 int i
, int j
, struct isl_coalesce_info
*info
, __isl_keep isl_mat
*div
,
3304 isl_basic_map
*bmap_i
;
3305 struct isl_tab_undo
*snap
;
3306 enum isl_change change
= isl_change_none
;
3308 known
= isl_basic_map_divs_known(info
[j
].bmap
);
3309 if (known
< 0 || !known
) {
3310 clear_status(&info
[i
]);
3311 isl_basic_map_free(bmap
);
3312 return known
< 0 ? isl_change_error
: isl_change_none
;
3315 bmap_i
= isl_basic_map_copy(info
[i
].bmap
);
3316 snap
= isl_tab_snap(info
[i
].tab
);
3317 if (expand_tab(&info
[i
], exp
, bmap
) < 0)
3318 change
= isl_change_error
;
3320 init_status(&info
[j
]);
3321 if (change
== isl_change_none
)
3322 change
= coalesce_local_pair_reuse(i
, j
, info
);
3324 clear_status(&info
[i
]);
3325 if (change
!= isl_change_none
&& change
!= isl_change_drop_second
) {
3326 isl_basic_map_free(bmap_i
);
3328 isl_basic_map_free(info
[i
].bmap
);
3329 info
[i
].bmap
= bmap_i
;
3331 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
3332 change
= isl_change_error
;
3338 /* Check if the union of "bmap" and the basic map represented by info[j]
3339 * can be represented by a single basic map,
3340 * after expanding the divs of "bmap" to match those of info[j].
3341 * If so, replace the pair by the single basic map and return
3342 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
3343 * Otherwise, return isl_change_none.
3345 * In particular, check if the expanded "bmap" contains the basic map
3346 * represented by the tableau info[j].tab.
3347 * The expansion is performed using the divs "div" and expansion "exp"
3348 * computed by the caller.
3349 * Then we check if all constraints of the expanded "bmap" are valid for
3352 * If "i" is not equal to -1, then "bmap" is equal to info[i].bmap.
3353 * In this case, the positions of the constraints of info[i].bmap
3354 * with respect to the basic map represented by info[j] are stored
3357 * If the expanded "bmap" does not contain the basic map
3358 * represented by the tableau info[j].tab and if "i" is not -1,
3359 * i.e., if the original "bmap" is info[i].bmap, then expand info[i].tab
3360 * as well and check if that results in coalescing.
3362 static enum isl_change
coalesce_with_expanded_divs(
3363 __isl_keep isl_basic_map
*bmap
, int i
, int j
,
3364 struct isl_coalesce_info
*info
, __isl_keep isl_mat
*div
, int *exp
)
3366 enum isl_change change
= isl_change_none
;
3367 struct isl_coalesce_info info_local
, *info_i
;
3369 info_i
= i
>= 0 ? &info
[i
] : &info_local
;
3370 init_status(info_i
);
3371 bmap
= isl_basic_map_copy(bmap
);
3372 bmap
= isl_basic_map_expand_divs(bmap
, isl_mat_copy(div
), exp
);
3373 bmap
= isl_basic_map_mark_final(bmap
);
3378 info_local
.bmap
= bmap
;
3379 info_i
->eq
= eq_status_in(bmap
, info
[j
].tab
);
3380 if (bmap
->n_eq
&& !info_i
->eq
)
3382 if (any_eq(info_i
, STATUS_ERROR
))
3384 if (any_eq(info_i
, STATUS_SEPARATE
))
3387 info_i
->ineq
= ineq_status_in(bmap
, NULL
, info
[j
].tab
);
3388 if (bmap
->n_ineq
&& !info_i
->ineq
)
3390 if (any_ineq(info_i
, STATUS_ERROR
))
3392 if (any_ineq(info_i
, STATUS_SEPARATE
))
3395 if (all(info_i
->eq
, 2 * bmap
->n_eq
, STATUS_VALID
) &&
3396 all(info_i
->ineq
, bmap
->n_ineq
, STATUS_VALID
)) {
3398 change
= isl_change_drop_second
;
3401 if (change
== isl_change_none
&& i
!= -1)
3402 return coalesce_expand_tab_divs(bmap
, i
, j
, info
, div
, exp
);
3405 isl_basic_map_free(bmap
);
3406 clear_status(info_i
);
3409 isl_basic_map_free(bmap
);
3410 clear_status(info_i
);
3411 return isl_change_error
;
3414 /* Check if the union of "bmap_i" and the basic map represented by info[j]
3415 * can be represented by a single basic map,
3416 * after aligning the divs of "bmap_i" to match those of info[j].
3417 * If so, replace the pair by the single basic map and return
3418 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
3419 * Otherwise, return isl_change_none.
3421 * In particular, check if "bmap_i" contains the basic map represented by
3422 * info[j] after aligning the divs of "bmap_i" to those of info[j].
3423 * Note that this can only succeed if the number of divs of "bmap_i"
3424 * is smaller than (or equal to) the number of divs of info[j].
3426 * We first check if the divs of "bmap_i" are all known and form a subset
3427 * of those of info[j].bmap. If so, we pass control over to
3428 * coalesce_with_expanded_divs.
3430 * If "i" is not equal to -1, then "bmap" is equal to info[i].bmap.
3432 static enum isl_change
coalesce_after_aligning_divs(
3433 __isl_keep isl_basic_map
*bmap_i
, int i
, int j
,
3434 struct isl_coalesce_info
*info
)
3437 isl_mat
*div_i
, *div_j
, *div
;
3441 enum isl_change change
;
3443 known
= isl_basic_map_divs_known(bmap_i
);
3445 return isl_change_error
;
3447 return isl_change_none
;
3449 ctx
= isl_basic_map_get_ctx(bmap_i
);
3451 div_i
= isl_basic_map_get_divs(bmap_i
);
3452 div_j
= isl_basic_map_get_divs(info
[j
].bmap
);
3454 if (!div_i
|| !div_j
)
3457 exp1
= isl_alloc_array(ctx
, int, div_i
->n_row
);
3458 exp2
= isl_alloc_array(ctx
, int, div_j
->n_row
);
3459 if ((div_i
->n_row
&& !exp1
) || (div_j
->n_row
&& !exp2
))
3462 div
= isl_merge_divs(div_i
, div_j
, exp1
, exp2
);
3466 if (div
->n_row
== div_j
->n_row
)
3467 change
= coalesce_with_expanded_divs(bmap_i
,
3468 i
, j
, info
, div
, exp1
);
3470 change
= isl_change_none
;
3474 isl_mat_free(div_i
);
3475 isl_mat_free(div_j
);
3482 isl_mat_free(div_i
);
3483 isl_mat_free(div_j
);
3486 return isl_change_error
;
3489 /* Check if basic map "j" is a subset of basic map "i" after
3490 * exploiting the extra equalities of "j" to simplify the divs of "i".
3491 * If so, remove basic map "j" and return isl_change_drop_second.
3493 * If "j" does not have any equalities or if they are the same
3494 * as those of "i", then we cannot exploit them to simplify the divs.
3495 * Similarly, if there are no divs in "i", then they cannot be simplified.
3496 * If, on the other hand, the affine hulls of "i" and "j" do not intersect,
3497 * then "j" cannot be a subset of "i".
3499 * Otherwise, we intersect "i" with the affine hull of "j" and then
3500 * check if "j" is a subset of the result after aligning the divs.
3501 * If so, then "j" is definitely a subset of "i" and can be removed.
3502 * Note that if after intersection with the affine hull of "j".
3503 * "i" still has more divs than "j", then there is no way we can
3504 * align the divs of "i" to those of "j".
3506 static enum isl_change
coalesce_subset_with_equalities(int i
, int j
,
3507 struct isl_coalesce_info
*info
)
3509 isl_basic_map
*hull_i
, *hull_j
, *bmap_i
;
3511 enum isl_change change
;
3513 if (info
[j
].bmap
->n_eq
== 0)
3514 return isl_change_none
;
3515 if (info
[i
].bmap
->n_div
== 0)
3516 return isl_change_none
;
3518 hull_i
= isl_basic_map_copy(info
[i
].bmap
);
3519 hull_i
= isl_basic_map_plain_affine_hull(hull_i
);
3520 hull_j
= isl_basic_map_copy(info
[j
].bmap
);
3521 hull_j
= isl_basic_map_plain_affine_hull(hull_j
);
3523 hull_j
= isl_basic_map_intersect(hull_j
, isl_basic_map_copy(hull_i
));
3524 equal
= isl_basic_map_plain_is_equal(hull_i
, hull_j
);
3525 empty
= isl_basic_map_plain_is_empty(hull_j
);
3526 isl_basic_map_free(hull_i
);
3528 if (equal
< 0 || equal
|| empty
< 0 || empty
) {
3529 isl_basic_map_free(hull_j
);
3530 if (equal
< 0 || empty
< 0)
3531 return isl_change_error
;
3532 return isl_change_none
;
3535 bmap_i
= isl_basic_map_copy(info
[i
].bmap
);
3536 bmap_i
= isl_basic_map_intersect(bmap_i
, hull_j
);
3538 return isl_change_error
;
3540 if (bmap_i
->n_div
> info
[j
].bmap
->n_div
) {
3541 isl_basic_map_free(bmap_i
);
3542 return isl_change_none
;
3545 change
= coalesce_after_aligning_divs(bmap_i
, -1, j
, info
);
3547 isl_basic_map_free(bmap_i
);
3552 /* Check if the union of the basic maps represented by info[i] and info[j]
3553 * can be represented by a single basic map, by aligning or equating
3554 * their integer divisions.
3555 * If so, replace the pair by the single basic map and return
3556 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
3557 * Otherwise, return isl_change_none.
3559 * Note that we only perform any test if the number of divs is different
3560 * in the two basic maps. In case the number of divs is the same,
3561 * we have already established that the divs are different
3562 * in the two basic maps.
3563 * In particular, if the number of divs of basic map i is smaller than
3564 * the number of divs of basic map j, then we check if j is a subset of i
3567 static enum isl_change
coalesce_divs(int i
, int j
,
3568 struct isl_coalesce_info
*info
)
3570 enum isl_change change
= isl_change_none
;
3572 if (info
[i
].bmap
->n_div
< info
[j
].bmap
->n_div
)
3573 change
= coalesce_after_aligning_divs(info
[i
].bmap
, i
, j
, info
);
3574 if (change
!= isl_change_none
)
3577 if (info
[j
].bmap
->n_div
< info
[i
].bmap
->n_div
)
3578 change
= coalesce_after_aligning_divs(info
[j
].bmap
, j
, i
, info
);
3579 if (change
!= isl_change_none
)
3580 return invert_change(change
);
3582 change
= coalesce_subset_with_equalities(i
, j
, info
);
3583 if (change
!= isl_change_none
)
3586 change
= coalesce_subset_with_equalities(j
, i
, info
);
3587 if (change
!= isl_change_none
)
3588 return invert_change(change
);
3590 return isl_change_none
;
3593 /* Does "bmap" involve any divs that themselves refer to divs?
3595 static isl_bool
has_nested_div(__isl_keep isl_basic_map
*bmap
)
3601 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
3602 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
3603 if (total
< 0 || n_div
< 0)
3604 return isl_bool_error
;
3607 for (i
= 0; i
< n_div
; ++i
)
3608 if (isl_seq_first_non_zero(bmap
->div
[i
] + 2 + total
,
3610 return isl_bool_true
;
3612 return isl_bool_false
;
3615 /* Return a list of affine expressions, one for each integer division
3616 * in "bmap_i". For each integer division that also appears in "bmap_j",
3617 * the affine expression is set to NaN. The number of NaNs in the list
3618 * is equal to the number of integer divisions in "bmap_j".
3619 * For the other integer divisions of "bmap_i", the corresponding
3620 * element in the list is a purely affine expression equal to the integer
3621 * division in "hull".
3622 * If no such list can be constructed, then the number of elements
3623 * in the returned list is smaller than the number of integer divisions
3625 * The integer division of "bmap_i" and "bmap_j" are assumed to be known and
3626 * not contain any nested divs.
3628 static __isl_give isl_aff_list
*set_up_substitutions(
3629 __isl_keep isl_basic_map
*bmap_i
, __isl_keep isl_basic_map
*bmap_j
,
3630 __isl_take isl_basic_map
*hull
)
3632 isl_size n_div_i
, n_div_j
, total
;
3634 isl_local_space
*ls
;
3635 isl_basic_set
*wrap_hull
;
3640 n_div_i
= isl_basic_map_dim(bmap_i
, isl_dim_div
);
3641 n_div_j
= isl_basic_map_dim(bmap_j
, isl_dim_div
);
3642 total
= isl_basic_map_dim(bmap_i
, isl_dim_all
);
3643 if (!hull
|| n_div_i
< 0 || n_div_j
< 0 || total
< 0)
3646 ctx
= isl_basic_map_get_ctx(hull
);
3649 ls
= isl_basic_map_get_local_space(bmap_i
);
3650 ls
= isl_local_space_wrap(ls
);
3651 wrap_hull
= isl_basic_map_wrap(hull
);
3653 aff_nan
= isl_aff_nan_on_domain(isl_local_space_copy(ls
));
3654 list
= isl_aff_list_alloc(ctx
, n_div_i
);
3657 for (i
= 0; i
< n_div_i
; ++i
) {
3662 isl_basic_map_equal_div_expr_part(bmap_i
, i
, bmap_j
, j
,
3665 list
= isl_aff_list_add(list
, isl_aff_copy(aff_nan
));
3668 if (n_div_i
- i
<= n_div_j
- j
)
3671 aff
= isl_local_space_get_div(ls
, i
);
3672 aff
= isl_aff_substitute_equalities(aff
,
3673 isl_basic_set_copy(wrap_hull
));
3674 aff
= isl_aff_floor(aff
);
3675 n_div
= isl_aff_dim(aff
, isl_dim_div
);
3683 list
= isl_aff_list_add(list
, aff
);
3686 isl_aff_free(aff_nan
);
3687 isl_local_space_free(ls
);
3688 isl_basic_set_free(wrap_hull
);
3692 isl_aff_free(aff_nan
);
3693 isl_local_space_free(ls
);
3694 isl_basic_set_free(wrap_hull
);
3695 isl_aff_list_free(list
);
3699 /* Add variables to info->bmap and info->tab corresponding to the elements
3700 * in "list" that are not set to NaN.
3701 * "extra_var" is the number of these elements.
3702 * "dim" is the offset in the variables of "tab" where we should
3703 * start considering the elements in "list".
3704 * When this function returns, the total number of variables in "tab"
3705 * is equal to "dim" plus the number of elements in "list".
3707 * The newly added existentially quantified variables are not given
3708 * an explicit representation because the corresponding div constraints
3709 * do not appear in info->bmap. These constraints are not added
3710 * to info->bmap because for internal consistency, they would need to
3711 * be added to info->tab as well, where they could combine with the equality
3712 * that is added later to result in constraints that do not hold
3713 * in the original input.
3715 static isl_stat
add_sub_vars(struct isl_coalesce_info
*info
,
3716 __isl_keep isl_aff_list
*list
, int dim
, int extra_var
)
3721 info
->bmap
= isl_basic_map_cow(info
->bmap
);
3722 info
->bmap
= isl_basic_map_extend(info
->bmap
, extra_var
, 0, 0);
3723 n
= isl_aff_list_n_aff(list
);
3724 if (!info
->bmap
|| n
< 0)
3725 return isl_stat_error
;
3726 for (i
= 0; i
< n
; ++i
) {
3730 aff
= isl_aff_list_get_aff(list
, i
);
3731 is_nan
= isl_aff_is_nan(aff
);
3734 return isl_stat_error
;
3738 if (isl_tab_insert_var(info
->tab
, dim
+ i
) < 0)
3739 return isl_stat_error
;
3740 d
= isl_basic_map_alloc_div(info
->bmap
);
3742 return isl_stat_error
;
3743 info
->bmap
= isl_basic_map_mark_div_unknown(info
->bmap
, d
);
3744 for (j
= d
; j
> i
; --j
)
3745 info
->bmap
= isl_basic_map_swap_div(info
->bmap
,
3748 return isl_stat_error
;
3754 /* For each element in "list" that is not set to NaN, fix the corresponding
3755 * variable in "tab" to the purely affine expression defined by the element.
3756 * "dim" is the offset in the variables of "tab" where we should
3757 * start considering the elements in "list".
3759 * This function assumes that a sufficient number of rows and
3760 * elements in the constraint array are available in the tableau.
3762 static isl_stat
add_sub_equalities(struct isl_tab
*tab
,
3763 __isl_keep isl_aff_list
*list
, int dim
)
3771 n
= isl_aff_list_n_aff(list
);
3773 return isl_stat_error
;
3775 ctx
= isl_tab_get_ctx(tab
);
3776 sub
= isl_vec_alloc(ctx
, 1 + dim
+ n
);
3778 return isl_stat_error
;
3779 isl_seq_clr(sub
->el
+ 1 + dim
, n
);
3781 for (i
= 0; i
< n
; ++i
) {
3782 aff
= isl_aff_list_get_aff(list
, i
);
3785 if (isl_aff_is_nan(aff
)) {
3789 isl_seq_cpy(sub
->el
, aff
->v
->el
+ 1, 1 + dim
);
3790 isl_int_neg(sub
->el
[1 + dim
+ i
], aff
->v
->el
[0]);
3791 if (isl_tab_add_eq(tab
, sub
->el
) < 0)
3793 isl_int_set_si(sub
->el
[1 + dim
+ i
], 0);
3802 return isl_stat_error
;
3805 /* Add variables to info->tab and info->bmap corresponding to the elements
3806 * in "list" that are not set to NaN. The value of the added variable
3807 * in info->tab is fixed to the purely affine expression defined by the element.
3808 * "dim" is the offset in the variables of info->tab where we should
3809 * start considering the elements in "list".
3810 * When this function returns, the total number of variables in info->tab
3811 * is equal to "dim" plus the number of elements in "list".
3813 static isl_stat
add_subs(struct isl_coalesce_info
*info
,
3814 __isl_keep isl_aff_list
*list
, int dim
)
3819 n
= isl_aff_list_n_aff(list
);
3821 return isl_stat_error
;
3823 extra_var
= n
- (info
->tab
->n_var
- dim
);
3825 if (isl_tab_extend_vars(info
->tab
, extra_var
) < 0)
3826 return isl_stat_error
;
3827 if (isl_tab_extend_cons(info
->tab
, 2 * extra_var
) < 0)
3828 return isl_stat_error
;
3829 if (add_sub_vars(info
, list
, dim
, extra_var
) < 0)
3830 return isl_stat_error
;
3832 return add_sub_equalities(info
->tab
, list
, dim
);
3835 /* Coalesce basic map "j" into basic map "i" after adding the extra integer
3836 * divisions in "i" but not in "j" to basic map "j", with values
3837 * specified by "list". The total number of elements in "list"
3838 * is equal to the number of integer divisions in "i", while the number
3839 * of NaN elements in the list is equal to the number of integer divisions
3842 * If no coalescing can be performed, then we need to revert basic map "j"
3843 * to its original state. We do the same if basic map "i" gets dropped
3844 * during the coalescing, even though this should not happen in practice
3845 * since we have already checked for "j" being a subset of "i"
3846 * before we reach this stage.
3848 static enum isl_change
coalesce_with_subs(int i
, int j
,
3849 struct isl_coalesce_info
*info
, __isl_keep isl_aff_list
*list
)
3851 isl_basic_map
*bmap_j
;
3852 struct isl_tab_undo
*snap
;
3853 isl_size dim
, n_div
;
3854 enum isl_change change
;
3856 bmap_j
= isl_basic_map_copy(info
[j
].bmap
);
3857 snap
= isl_tab_snap(info
[j
].tab
);
3859 dim
= isl_basic_map_dim(bmap_j
, isl_dim_all
);
3860 n_div
= isl_basic_map_dim(bmap_j
, isl_dim_div
);
3861 if (dim
< 0 || n_div
< 0)
3864 if (add_subs(&info
[j
], list
, dim
) < 0)
3867 change
= coalesce_local_pair(i
, j
, info
);
3868 if (change
!= isl_change_none
&& change
!= isl_change_drop_first
) {
3869 isl_basic_map_free(bmap_j
);
3871 isl_basic_map_free(info
[j
].bmap
);
3872 info
[j
].bmap
= bmap_j
;
3874 if (isl_tab_rollback(info
[j
].tab
, snap
) < 0)
3875 return isl_change_error
;
3880 isl_basic_map_free(bmap_j
);
3881 return isl_change_error
;
3884 /* Check if we can coalesce basic map "j" into basic map "i" after copying
3885 * those extra integer divisions in "i" that can be simplified away
3886 * using the extra equalities in "j".
3887 * All divs are assumed to be known and not contain any nested divs.
3889 * We first check if there are any extra equalities in "j" that we
3890 * can exploit. Then we check if every integer division in "i"
3891 * either already appears in "j" or can be simplified using the
3892 * extra equalities to a purely affine expression.
3893 * If these tests succeed, then we try to coalesce the two basic maps
3894 * by introducing extra dimensions in "j" corresponding to
3895 * the extra integer divisions "i" fixed to the corresponding
3896 * purely affine expression.
3898 static enum isl_change
check_coalesce_into_eq(int i
, int j
,
3899 struct isl_coalesce_info
*info
)
3901 isl_size n_div_i
, n_div_j
, n
;
3902 isl_basic_map
*hull_i
, *hull_j
;
3903 isl_bool equal
, empty
;
3905 enum isl_change change
;
3907 n_div_i
= isl_basic_map_dim(info
[i
].bmap
, isl_dim_div
);
3908 n_div_j
= isl_basic_map_dim(info
[j
].bmap
, isl_dim_div
);
3909 if (n_div_i
< 0 || n_div_j
< 0)
3910 return isl_change_error
;
3911 if (n_div_i
<= n_div_j
)
3912 return isl_change_none
;
3913 if (info
[j
].bmap
->n_eq
== 0)
3914 return isl_change_none
;
3916 hull_i
= isl_basic_map_copy(info
[i
].bmap
);
3917 hull_i
= isl_basic_map_plain_affine_hull(hull_i
);
3918 hull_j
= isl_basic_map_copy(info
[j
].bmap
);
3919 hull_j
= isl_basic_map_plain_affine_hull(hull_j
);
3921 hull_j
= isl_basic_map_intersect(hull_j
, isl_basic_map_copy(hull_i
));
3922 equal
= isl_basic_map_plain_is_equal(hull_i
, hull_j
);
3923 empty
= isl_basic_map_plain_is_empty(hull_j
);
3924 isl_basic_map_free(hull_i
);
3926 if (equal
< 0 || empty
< 0)
3928 if (equal
|| empty
) {
3929 isl_basic_map_free(hull_j
);
3930 return isl_change_none
;
3933 list
= set_up_substitutions(info
[i
].bmap
, info
[j
].bmap
, hull_j
);
3935 return isl_change_error
;
3936 n
= isl_aff_list_n_aff(list
);
3938 change
= isl_change_error
;
3939 else if (n
< n_div_i
)
3940 change
= isl_change_none
;
3942 change
= coalesce_with_subs(i
, j
, info
, list
);
3944 isl_aff_list_free(list
);
3948 isl_basic_map_free(hull_j
);
3949 return isl_change_error
;
3952 /* Check if we can coalesce basic maps "i" and "j" after copying
3953 * those extra integer divisions in one of the basic maps that can
3954 * be simplified away using the extra equalities in the other basic map.
3955 * We require all divs to be known in both basic maps.
3956 * Furthermore, to simplify the comparison of div expressions,
3957 * we do not allow any nested integer divisions.
3959 static enum isl_change
check_coalesce_eq(int i
, int j
,
3960 struct isl_coalesce_info
*info
)
3962 isl_bool known
, nested
;
3963 enum isl_change change
;
3965 known
= isl_basic_map_divs_known(info
[i
].bmap
);
3966 if (known
< 0 || !known
)
3967 return known
< 0 ? isl_change_error
: isl_change_none
;
3968 known
= isl_basic_map_divs_known(info
[j
].bmap
);
3969 if (known
< 0 || !known
)
3970 return known
< 0 ? isl_change_error
: isl_change_none
;
3971 nested
= has_nested_div(info
[i
].bmap
);
3972 if (nested
< 0 || nested
)
3973 return nested
< 0 ? isl_change_error
: isl_change_none
;
3974 nested
= has_nested_div(info
[j
].bmap
);
3975 if (nested
< 0 || nested
)
3976 return nested
< 0 ? isl_change_error
: isl_change_none
;
3978 change
= check_coalesce_into_eq(i
, j
, info
);
3979 if (change
!= isl_change_none
)
3981 change
= check_coalesce_into_eq(j
, i
, info
);
3982 if (change
!= isl_change_none
)
3983 return invert_change(change
);
3985 return isl_change_none
;
3988 /* Check if the union of the given pair of basic maps
3989 * can be represented by a single basic map.
3990 * If so, replace the pair by the single basic map and return
3991 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
3992 * Otherwise, return isl_change_none.
3994 * We first check if the two basic maps live in the same local space,
3995 * after aligning the divs that differ by only an integer constant.
3996 * If so, we do the complete check. Otherwise, we check if they have
3997 * the same number of integer divisions and can be coalesced, if one is
3998 * an obvious subset of the other or if the extra integer divisions
3999 * of one basic map can be simplified away using the extra equalities
4000 * of the other basic map.
4002 * Note that trying to coalesce pairs of disjuncts with the same
4003 * number, but different local variables may drop the explicit
4004 * representation of some of these local variables.
4005 * This operation is therefore not performed when
4006 * the "coalesce_preserve_locals" option is set.
4008 static enum isl_change
coalesce_pair(int i
, int j
,
4009 struct isl_coalesce_info
*info
)
4013 enum isl_change change
;
4016 if (harmonize_divs(&info
[i
], &info
[j
]) < 0)
4017 return isl_change_error
;
4018 same
= same_divs(info
[i
].bmap
, info
[j
].bmap
);
4020 return isl_change_error
;
4022 return coalesce_local_pair(i
, j
, info
);
4024 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
4025 preserve
= isl_options_get_coalesce_preserve_locals(ctx
);
4026 if (!preserve
&& info
[i
].bmap
->n_div
== info
[j
].bmap
->n_div
) {
4027 change
= coalesce_local_pair(i
, j
, info
);
4028 if (change
!= isl_change_none
)
4032 change
= coalesce_divs(i
, j
, info
);
4033 if (change
!= isl_change_none
)
4036 return check_coalesce_eq(i
, j
, info
);
4039 /* Return the maximum of "a" and "b".
4041 static int isl_max(int a
, int b
)
4043 return a
> b
? a
: b
;
4046 /* Pairwise coalesce the basic maps in the range [start1, end1[ of "info"
4047 * with those in the range [start2, end2[, skipping basic maps
4048 * that have been removed (either before or within this function).
4050 * For each basic map i in the first range, we check if it can be coalesced
4051 * with respect to any previously considered basic map j in the second range.
4052 * If i gets dropped (because it was a subset of some j), then
4053 * we can move on to the next basic map.
4054 * If j gets dropped, we need to continue checking against the other
4055 * previously considered basic maps.
4056 * If the two basic maps got fused, then we recheck the fused basic map
4057 * against the previously considered basic maps, starting at i + 1
4058 * (even if start2 is greater than i + 1).
4060 static int coalesce_range(isl_ctx
*ctx
, struct isl_coalesce_info
*info
,
4061 int start1
, int end1
, int start2
, int end2
)
4065 for (i
= end1
- 1; i
>= start1
; --i
) {
4066 if (info
[i
].removed
)
4068 for (j
= isl_max(i
+ 1, start2
); j
< end2
; ++j
) {
4069 enum isl_change changed
;
4071 if (info
[j
].removed
)
4073 if (info
[i
].removed
)
4074 isl_die(ctx
, isl_error_internal
,
4075 "basic map unexpectedly removed",
4077 changed
= coalesce_pair(i
, j
, info
);
4079 case isl_change_error
:
4081 case isl_change_none
:
4082 case isl_change_drop_second
:
4084 case isl_change_drop_first
:
4087 case isl_change_fuse
:
4097 /* Pairwise coalesce the basic maps described by the "n" elements of "info".
4099 * We consider groups of basic maps that live in the same apparent
4100 * affine hull and we first coalesce within such a group before we
4101 * coalesce the elements in the group with elements of previously
4102 * considered groups. If a fuse happens during the second phase,
4103 * then we also reconsider the elements within the group.
4105 static int coalesce(isl_ctx
*ctx
, int n
, struct isl_coalesce_info
*info
)
4109 for (end
= n
; end
> 0; end
= start
) {
4111 while (start
>= 1 &&
4112 info
[start
- 1].hull_hash
== info
[start
].hull_hash
)
4114 if (coalesce_range(ctx
, info
, start
, end
, start
, end
) < 0)
4116 if (coalesce_range(ctx
, info
, start
, end
, end
, n
) < 0)
4123 /* Update the basic maps in "map" based on the information in "info".
4124 * In particular, remove the basic maps that have been marked removed and
4125 * update the others based on the information in the corresponding tableau.
4126 * Since we detected implicit equalities without calling
4127 * isl_basic_map_gauss, we need to do it now.
4128 * Also call isl_basic_map_simplify if we may have lost the definition
4129 * of one or more integer divisions.
4130 * If a basic map is still equal to the one from which the corresponding "info"
4131 * entry was created, then redundant constraint and
4132 * implicit equality constraint detection have been performed
4133 * on the corresponding tableau and the basic map can be marked as such.
4135 static __isl_give isl_map
*update_basic_maps(__isl_take isl_map
*map
,
4136 int n
, struct isl_coalesce_info
*info
)
4143 for (i
= n
- 1; i
>= 0; --i
) {
4144 if (info
[i
].removed
) {
4145 isl_basic_map_free(map
->p
[i
]);
4146 if (i
!= map
->n
- 1)
4147 map
->p
[i
] = map
->p
[map
->n
- 1];
4152 info
[i
].bmap
= isl_basic_map_update_from_tab(info
[i
].bmap
,
4154 info
[i
].bmap
= isl_basic_map_gauss(info
[i
].bmap
, NULL
);
4155 if (info
[i
].simplify
)
4156 info
[i
].bmap
= isl_basic_map_simplify(info
[i
].bmap
);
4157 info
[i
].bmap
= isl_basic_map_finalize(info
[i
].bmap
);
4159 return isl_map_free(map
);
4160 if (!info
[i
].modified
) {
4161 ISL_F_SET(info
[i
].bmap
, ISL_BASIC_MAP_NO_IMPLICIT
);
4162 ISL_F_SET(info
[i
].bmap
, ISL_BASIC_MAP_NO_REDUNDANT
);
4164 isl_basic_map_free(map
->p
[i
]);
4165 map
->p
[i
] = info
[i
].bmap
;
4166 info
[i
].bmap
= NULL
;
4172 /* For each pair of basic maps in the map, check if the union of the two
4173 * can be represented by a single basic map.
4174 * If so, replace the pair by the single basic map and start over.
4176 * We factor out any (hidden) common factor from the constraint
4177 * coefficients to improve the detection of adjacent constraints.
4178 * Note that this function does not call isl_basic_map_gauss,
4179 * but it does make sure that only a single copy of the basic map
4180 * is affected. This means that isl_basic_map_gauss may have
4181 * to be called at the end of the computation (in update_basic_maps)
4182 * on this single copy to ensure that
4183 * the basic maps are not left in an unexpected state.
4185 * Since we are constructing the tableaus of the basic maps anyway,
4186 * we exploit them to detect implicit equalities and redundant constraints.
4187 * This also helps the coalescing as it can ignore the redundant constraints.
4188 * In order to avoid confusion, we make all implicit equalities explicit
4189 * in the basic maps. If the basic map only has a single reference
4190 * (this happens in particular if it was modified by
4191 * isl_basic_map_reduce_coefficients), then isl_basic_map_gauss
4192 * does not get called on the result. The call to
4193 * isl_basic_map_gauss in update_basic_maps resolves this as well.
4194 * For each basic map, we also compute the hash of the apparent affine hull
4195 * for use in coalesce.
4197 __isl_give isl_map
*isl_map_coalesce(__isl_take isl_map
*map
)
4202 struct isl_coalesce_info
*info
= NULL
;
4204 map
= isl_map_remove_empty_parts(map
);
4211 ctx
= isl_map_get_ctx(map
);
4212 map
= isl_map_sort_divs(map
);
4213 map
= isl_map_cow(map
);
4220 info
= isl_calloc_array(map
->ctx
, struct isl_coalesce_info
, n
);
4224 for (i
= 0; i
< map
->n
; ++i
) {
4225 map
->p
[i
] = isl_basic_map_reduce_coefficients(map
->p
[i
]);
4228 info
[i
].bmap
= isl_basic_map_copy(map
->p
[i
]);
4229 info
[i
].tab
= isl_tab_from_basic_map(info
[i
].bmap
, 0);
4232 if (!ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_NO_IMPLICIT
))
4233 if (isl_tab_detect_implicit_equalities(info
[i
].tab
) < 0)
4235 info
[i
].bmap
= isl_tab_make_equalities_explicit(info
[i
].tab
,
4239 if (!ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_NO_REDUNDANT
))
4240 if (isl_tab_detect_redundant(info
[i
].tab
) < 0)
4242 if (coalesce_info_set_hull_hash(&info
[i
]) < 0)
4245 for (i
= map
->n
- 1; i
>= 0; --i
)
4246 if (info
[i
].tab
->empty
)
4249 if (coalesce(ctx
, n
, info
) < 0)
4252 map
= update_basic_maps(map
, n
, info
);
4254 clear_coalesce_info(n
, info
);
4258 clear_coalesce_info(n
, info
);
4263 /* For each pair of basic sets in the set, check if the union of the two
4264 * can be represented by a single basic set.
4265 * If so, replace the pair by the single basic set and start over.
4267 __isl_give isl_set
*isl_set_coalesce(__isl_take isl_set
*set
)
4269 return set_from_map(isl_map_coalesce(set_to_map(set
)));