2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2010 INRIA Saclay
4 * Copyright 2012-2013 Ecole Normale Superieure
5 * Copyright 2014 INRIA Rocquencourt
6 * Copyright 2016 INRIA Paris
8 * Use of this software is governed by the MIT license
10 * Written by Sven Verdoolaege, K.U.Leuven, Departement
11 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
12 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
13 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
14 * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
15 * and Inria Paris - Rocquencourt, Domaine de Voluceau - Rocquencourt,
16 * B.P. 105 - 78153 Le Chesnay, France
17 * and Centre de Recherche Inria de Paris, 2 rue Simone Iff - Voie DQ12,
18 * CS 42112, 75589 Paris Cedex 12, France
21 #include <isl_ctx_private.h>
22 #include "isl_map_private.h"
24 #include <isl/options.h>
26 #include <isl_mat_private.h>
27 #include <isl_local_space_private.h>
28 #include <isl_vec_private.h>
29 #include <isl_aff_private.h>
30 #include <isl_equalities.h>
32 #include <set_to_map.c>
33 #include <set_from_map.c>
35 #define STATUS_ERROR -1
36 #define STATUS_REDUNDANT 1
37 #define STATUS_VALID 2
38 #define STATUS_SEPARATE 3
40 #define STATUS_ADJ_EQ 5
41 #define STATUS_ADJ_INEQ 6
43 static int status_in(isl_int
*ineq
, struct isl_tab
*tab
)
45 enum isl_ineq_type type
= isl_tab_ineq_type(tab
, ineq
);
48 case isl_ineq_error
: return STATUS_ERROR
;
49 case isl_ineq_redundant
: return STATUS_VALID
;
50 case isl_ineq_separate
: return STATUS_SEPARATE
;
51 case isl_ineq_cut
: return STATUS_CUT
;
52 case isl_ineq_adj_eq
: return STATUS_ADJ_EQ
;
53 case isl_ineq_adj_ineq
: return STATUS_ADJ_INEQ
;
57 /* Compute the position of the equalities of basic map "bmap_i"
58 * with respect to the basic map represented by "tab_j".
59 * The resulting array has twice as many entries as the number
60 * of equalities corresponding to the two inequalties to which
61 * each equality corresponds.
63 static int *eq_status_in(__isl_keep isl_basic_map
*bmap_i
,
64 struct isl_tab
*tab_j
)
67 int *eq
= isl_calloc_array(bmap_i
->ctx
, int, 2 * bmap_i
->n_eq
);
73 dim
= isl_basic_map_total_dim(bmap_i
);
74 for (k
= 0; k
< bmap_i
->n_eq
; ++k
) {
75 for (l
= 0; l
< 2; ++l
) {
76 isl_seq_neg(bmap_i
->eq
[k
], bmap_i
->eq
[k
], 1+dim
);
77 eq
[2 * k
+ l
] = status_in(bmap_i
->eq
[k
], tab_j
);
78 if (eq
[2 * k
+ l
] == STATUS_ERROR
)
81 if (eq
[2 * k
] == STATUS_SEPARATE
||
82 eq
[2 * k
+ 1] == STATUS_SEPARATE
)
92 /* Compute the position of the inequalities of basic map "bmap_i"
93 * (also represented by "tab_i", if not NULL) with respect to the basic map
94 * represented by "tab_j".
96 static int *ineq_status_in(__isl_keep isl_basic_map
*bmap_i
,
97 struct isl_tab
*tab_i
, struct isl_tab
*tab_j
)
100 unsigned n_eq
= bmap_i
->n_eq
;
101 int *ineq
= isl_calloc_array(bmap_i
->ctx
, int, bmap_i
->n_ineq
);
106 for (k
= 0; k
< bmap_i
->n_ineq
; ++k
) {
107 if (tab_i
&& isl_tab_is_redundant(tab_i
, n_eq
+ k
)) {
108 ineq
[k
] = STATUS_REDUNDANT
;
111 ineq
[k
] = status_in(bmap_i
->ineq
[k
], tab_j
);
112 if (ineq
[k
] == STATUS_ERROR
)
114 if (ineq
[k
] == STATUS_SEPARATE
)
124 static int any(int *con
, unsigned len
, int status
)
128 for (i
= 0; i
< len
; ++i
)
129 if (con
[i
] == status
)
134 /* Return the first position of "status" in the list "con" of length "len".
135 * Return -1 if there is no such entry.
137 static int find(int *con
, unsigned len
, int status
)
141 for (i
= 0; i
< len
; ++i
)
142 if (con
[i
] == status
)
147 static int count(int *con
, unsigned len
, int status
)
152 for (i
= 0; i
< len
; ++i
)
153 if (con
[i
] == status
)
158 static int all(int *con
, unsigned len
, int status
)
162 for (i
= 0; i
< len
; ++i
) {
163 if (con
[i
] == STATUS_REDUNDANT
)
165 if (con
[i
] != status
)
171 /* Internal information associated to a basic map in a map
172 * that is to be coalesced by isl_map_coalesce.
174 * "bmap" is the basic map itself (or NULL if "removed" is set)
175 * "tab" is the corresponding tableau (or NULL if "removed" is set)
176 * "hull_hash" identifies the affine space in which "bmap" lives.
177 * "removed" is set if this basic map has been removed from the map
178 * "simplify" is set if this basic map may have some unknown integer
179 * divisions that were not present in the input basic maps. The basic
180 * map should then be simplified such that we may be able to find
181 * a definition among the constraints.
183 * "eq" and "ineq" are only set if we are currently trying to coalesce
184 * this basic map with another basic map, in which case they represent
185 * the position of the inequalities of this basic map with respect to
186 * the other basic map. The number of elements in the "eq" array
187 * is twice the number of equalities in the "bmap", corresponding
188 * to the two inequalities that make up each equality.
190 struct isl_coalesce_info
{
200 /* Are all non-redundant constraints of the basic map represented by "info"
201 * either valid or cut constraints with respect to the other basic map?
203 static int all_valid_or_cut(struct isl_coalesce_info
*info
)
207 for (i
= 0; i
< 2 * info
->bmap
->n_eq
; ++i
) {
208 if (info
->eq
[i
] == STATUS_REDUNDANT
)
210 if (info
->eq
[i
] == STATUS_VALID
)
212 if (info
->eq
[i
] == STATUS_CUT
)
217 for (i
= 0; i
< info
->bmap
->n_ineq
; ++i
) {
218 if (info
->ineq
[i
] == STATUS_REDUNDANT
)
220 if (info
->ineq
[i
] == STATUS_VALID
)
222 if (info
->ineq
[i
] == STATUS_CUT
)
230 /* Compute the hash of the (apparent) affine hull of info->bmap (with
231 * the existentially quantified variables removed) and store it
234 static int coalesce_info_set_hull_hash(struct isl_coalesce_info
*info
)
239 hull
= isl_basic_map_copy(info
->bmap
);
240 hull
= isl_basic_map_plain_affine_hull(hull
);
241 n_div
= isl_basic_map_dim(hull
, isl_dim_div
);
242 hull
= isl_basic_map_drop_constraints_involving_dims(hull
,
243 isl_dim_div
, 0, n_div
);
244 info
->hull_hash
= isl_basic_map_get_hash(hull
);
245 isl_basic_map_free(hull
);
247 return hull
? 0 : -1;
250 /* Free all the allocated memory in an array
251 * of "n" isl_coalesce_info elements.
253 static void clear_coalesce_info(int n
, struct isl_coalesce_info
*info
)
260 for (i
= 0; i
< n
; ++i
) {
261 isl_basic_map_free(info
[i
].bmap
);
262 isl_tab_free(info
[i
].tab
);
268 /* Drop the basic map represented by "info".
269 * That is, clear the memory associated to the entry and
270 * mark it as having been removed.
272 static void drop(struct isl_coalesce_info
*info
)
274 info
->bmap
= isl_basic_map_free(info
->bmap
);
275 isl_tab_free(info
->tab
);
280 /* Exchange the information in "info1" with that in "info2".
282 static void exchange(struct isl_coalesce_info
*info1
,
283 struct isl_coalesce_info
*info2
)
285 struct isl_coalesce_info info
;
292 /* This type represents the kind of change that has been performed
293 * while trying to coalesce two basic maps.
295 * isl_change_none: nothing was changed
296 * isl_change_drop_first: the first basic map was removed
297 * isl_change_drop_second: the second basic map was removed
298 * isl_change_fuse: the two basic maps were replaced by a new basic map.
301 isl_change_error
= -1,
303 isl_change_drop_first
,
304 isl_change_drop_second
,
308 /* Update "change" based on an interchange of the first and the second
309 * basic map. That is, interchange isl_change_drop_first and
310 * isl_change_drop_second.
312 static enum isl_change
invert_change(enum isl_change change
)
315 case isl_change_error
:
316 return isl_change_error
;
317 case isl_change_none
:
318 return isl_change_none
;
319 case isl_change_drop_first
:
320 return isl_change_drop_second
;
321 case isl_change_drop_second
:
322 return isl_change_drop_first
;
323 case isl_change_fuse
:
324 return isl_change_fuse
;
327 return isl_change_error
;
330 /* Add the valid constraints of the basic map represented by "info"
331 * to "bmap". "len" is the size of the constraints.
332 * If only one of the pair of inequalities that make up an equality
333 * is valid, then add that inequality.
335 static __isl_give isl_basic_map
*add_valid_constraints(
336 __isl_take isl_basic_map
*bmap
, struct isl_coalesce_info
*info
,
344 for (k
= 0; k
< info
->bmap
->n_eq
; ++k
) {
345 if (info
->eq
[2 * k
] == STATUS_VALID
&&
346 info
->eq
[2 * k
+ 1] == STATUS_VALID
) {
347 l
= isl_basic_map_alloc_equality(bmap
);
349 return isl_basic_map_free(bmap
);
350 isl_seq_cpy(bmap
->eq
[l
], info
->bmap
->eq
[k
], len
);
351 } else if (info
->eq
[2 * k
] == STATUS_VALID
) {
352 l
= isl_basic_map_alloc_inequality(bmap
);
354 return isl_basic_map_free(bmap
);
355 isl_seq_neg(bmap
->ineq
[l
], info
->bmap
->eq
[k
], len
);
356 } else if (info
->eq
[2 * k
+ 1] == STATUS_VALID
) {
357 l
= isl_basic_map_alloc_inequality(bmap
);
359 return isl_basic_map_free(bmap
);
360 isl_seq_cpy(bmap
->ineq
[l
], info
->bmap
->eq
[k
], len
);
364 for (k
= 0; k
< info
->bmap
->n_ineq
; ++k
) {
365 if (info
->ineq
[k
] != STATUS_VALID
)
367 l
= isl_basic_map_alloc_inequality(bmap
);
369 return isl_basic_map_free(bmap
);
370 isl_seq_cpy(bmap
->ineq
[l
], info
->bmap
->ineq
[k
], len
);
376 /* Is "bmap" defined by a number of (non-redundant) constraints that
377 * is greater than the number of constraints of basic maps i and j combined?
378 * Equalities are counted as two inequalities.
380 static int number_of_constraints_increases(int i
, int j
,
381 struct isl_coalesce_info
*info
,
382 __isl_keep isl_basic_map
*bmap
, struct isl_tab
*tab
)
386 n_old
= 2 * info
[i
].bmap
->n_eq
+ info
[i
].bmap
->n_ineq
;
387 n_old
+= 2 * info
[j
].bmap
->n_eq
+ info
[j
].bmap
->n_ineq
;
389 n_new
= 2 * bmap
->n_eq
;
390 for (k
= 0; k
< bmap
->n_ineq
; ++k
)
391 if (!isl_tab_is_redundant(tab
, bmap
->n_eq
+ k
))
394 return n_new
> n_old
;
397 /* Replace the pair of basic maps i and j by the basic map bounded
398 * by the valid constraints in both basic maps and the constraints
399 * in extra (if not NULL).
400 * Place the fused basic map in the position that is the smallest of i and j.
402 * If "detect_equalities" is set, then look for equalities encoded
403 * as pairs of inequalities.
404 * If "check_number" is set, then the original basic maps are only
405 * replaced if the total number of constraints does not increase.
406 * While the number of integer divisions in the two basic maps
407 * is assumed to be the same, the actual definitions may be different.
408 * We only copy the definition from one of the basic map if it is
409 * the same as that of the other basic map. Otherwise, we mark
410 * the integer division as unknown and simplify the basic map
411 * in an attempt to recover the integer division definition.
413 static enum isl_change
fuse(int i
, int j
, struct isl_coalesce_info
*info
,
414 __isl_keep isl_mat
*extra
, int detect_equalities
, int check_number
)
417 struct isl_basic_map
*fused
= NULL
;
418 struct isl_tab
*fused_tab
= NULL
;
419 unsigned total
= isl_basic_map_total_dim(info
[i
].bmap
);
420 unsigned extra_rows
= extra
? extra
->n_row
: 0;
421 unsigned n_eq
, n_ineq
;
425 return fuse(j
, i
, info
, extra
, detect_equalities
, check_number
);
427 n_eq
= info
[i
].bmap
->n_eq
+ info
[j
].bmap
->n_eq
;
428 n_ineq
= info
[i
].bmap
->n_ineq
+ info
[j
].bmap
->n_ineq
;
429 fused
= isl_basic_map_alloc_space(isl_space_copy(info
[i
].bmap
->dim
),
430 info
[i
].bmap
->n_div
, n_eq
, n_eq
+ n_ineq
+ extra_rows
);
431 fused
= add_valid_constraints(fused
, &info
[i
], 1 + total
);
432 fused
= add_valid_constraints(fused
, &info
[j
], 1 + total
);
435 if (ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_RATIONAL
) &&
436 ISL_F_ISSET(info
[j
].bmap
, ISL_BASIC_MAP_RATIONAL
))
437 ISL_F_SET(fused
, ISL_BASIC_MAP_RATIONAL
);
439 for (k
= 0; k
< info
[i
].bmap
->n_div
; ++k
) {
440 int l
= isl_basic_map_alloc_div(fused
);
443 if (isl_seq_eq(info
[i
].bmap
->div
[k
], info
[j
].bmap
->div
[k
],
445 isl_seq_cpy(fused
->div
[l
], info
[i
].bmap
->div
[k
],
448 isl_int_set_si(fused
->div
[l
][0], 0);
453 for (k
= 0; k
< extra_rows
; ++k
) {
454 l
= isl_basic_map_alloc_inequality(fused
);
457 isl_seq_cpy(fused
->ineq
[l
], extra
->row
[k
], 1 + total
);
460 if (detect_equalities
)
461 fused
= isl_basic_map_detect_inequality_pairs(fused
, NULL
);
462 fused
= isl_basic_map_gauss(fused
, NULL
);
463 if (simplify
|| info
[j
].simplify
) {
464 fused
= isl_basic_map_simplify(fused
);
465 info
[i
].simplify
= 0;
467 fused
= isl_basic_map_finalize(fused
);
469 fused_tab
= isl_tab_from_basic_map(fused
, 0);
470 if (isl_tab_detect_redundant(fused_tab
) < 0)
474 number_of_constraints_increases(i
, j
, info
, fused
, fused_tab
)) {
475 isl_tab_free(fused_tab
);
476 isl_basic_map_free(fused
);
477 return isl_change_none
;
480 isl_basic_map_free(info
[i
].bmap
);
481 info
[i
].bmap
= fused
;
482 isl_tab_free(info
[i
].tab
);
483 info
[i
].tab
= fused_tab
;
486 return isl_change_fuse
;
488 isl_tab_free(fused_tab
);
489 isl_basic_map_free(fused
);
490 return isl_change_error
;
493 /* Given a pair of basic maps i and j such that all constraints are either
494 * "valid" or "cut", check if the facets corresponding to the "cut"
495 * constraints of i lie entirely within basic map j.
496 * If so, replace the pair by the basic map consisting of the valid
497 * constraints in both basic maps.
498 * Checking whether the facet lies entirely within basic map j
499 * is performed by checking whether the constraints of basic map j
500 * are valid for the facet. These tests are performed on a rational
501 * tableau to avoid the theoretical possibility that a constraint
502 * that was considered to be a cut constraint for the entire basic map i
503 * happens to be considered to be a valid constraint for the facet,
504 * even though it cuts off the same rational points.
506 * To see that we are not introducing any extra points, call the
507 * two basic maps A and B and the resulting map U and let x
508 * be an element of U \setminus ( A \cup B ).
509 * A line connecting x with an element of A \cup B meets a facet F
510 * of either A or B. Assume it is a facet of B and let c_1 be
511 * the corresponding facet constraint. We have c_1(x) < 0 and
512 * so c_1 is a cut constraint. This implies that there is some
513 * (possibly rational) point x' satisfying the constraints of A
514 * and the opposite of c_1 as otherwise c_1 would have been marked
515 * valid for A. The line connecting x and x' meets a facet of A
516 * in a (possibly rational) point that also violates c_1, but this
517 * is impossible since all cut constraints of B are valid for all
519 * In case F is a facet of A rather than B, then we can apply the
520 * above reasoning to find a facet of B separating x from A \cup B first.
522 static enum isl_change
check_facets(int i
, int j
,
523 struct isl_coalesce_info
*info
)
526 struct isl_tab_undo
*snap
, *snap2
;
527 unsigned n_eq
= info
[i
].bmap
->n_eq
;
529 snap
= isl_tab_snap(info
[i
].tab
);
530 if (isl_tab_mark_rational(info
[i
].tab
) < 0)
531 return isl_change_error
;
532 snap2
= isl_tab_snap(info
[i
].tab
);
534 for (k
= 0; k
< info
[i
].bmap
->n_ineq
; ++k
) {
535 if (info
[i
].ineq
[k
] != STATUS_CUT
)
537 if (isl_tab_select_facet(info
[i
].tab
, n_eq
+ k
) < 0)
538 return isl_change_error
;
539 for (l
= 0; l
< info
[j
].bmap
->n_ineq
; ++l
) {
541 if (info
[j
].ineq
[l
] != STATUS_CUT
)
543 stat
= status_in(info
[j
].bmap
->ineq
[l
], info
[i
].tab
);
545 return isl_change_error
;
546 if (stat
!= STATUS_VALID
)
549 if (isl_tab_rollback(info
[i
].tab
, snap2
) < 0)
550 return isl_change_error
;
551 if (l
< info
[j
].bmap
->n_ineq
)
555 if (k
< info
[i
].bmap
->n_ineq
) {
556 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
557 return isl_change_error
;
558 return isl_change_none
;
560 return fuse(i
, j
, info
, NULL
, 0, 0);
563 /* Check if info->bmap contains the basic map represented
564 * by the tableau "tab".
565 * For each equality, we check both the constraint itself
566 * (as an inequality) and its negation. Make sure the
567 * equality is returned to its original state before returning.
569 static int contains(struct isl_coalesce_info
*info
, struct isl_tab
*tab
)
573 isl_basic_map
*bmap
= info
->bmap
;
575 dim
= isl_basic_map_total_dim(bmap
);
576 for (k
= 0; k
< bmap
->n_eq
; ++k
) {
578 isl_seq_neg(bmap
->eq
[k
], bmap
->eq
[k
], 1 + dim
);
579 stat
= status_in(bmap
->eq
[k
], tab
);
580 isl_seq_neg(bmap
->eq
[k
], bmap
->eq
[k
], 1 + dim
);
583 if (stat
!= STATUS_VALID
)
585 stat
= status_in(bmap
->eq
[k
], tab
);
588 if (stat
!= STATUS_VALID
)
592 for (k
= 0; k
< bmap
->n_ineq
; ++k
) {
594 if (info
->ineq
[k
] == STATUS_REDUNDANT
)
596 stat
= status_in(bmap
->ineq
[k
], tab
);
599 if (stat
!= STATUS_VALID
)
605 /* Basic map "i" has an inequality (say "k") that is adjacent
606 * to some inequality of basic map "j". All the other inequalities
608 * Check if basic map "j" forms an extension of basic map "i".
610 * Note that this function is only called if some of the equalities or
611 * inequalities of basic map "j" do cut basic map "i". The function is
612 * correct even if there are no such cut constraints, but in that case
613 * the additional checks performed by this function are overkill.
615 * In particular, we replace constraint k, say f >= 0, by constraint
616 * f <= -1, add the inequalities of "j" that are valid for "i"
617 * and check if the result is a subset of basic map "j".
618 * If so, then we know that this result is exactly equal to basic map "j"
619 * since all its constraints are valid for basic map "j".
620 * By combining the valid constraints of "i" (all equalities and all
621 * inequalities except "k") and the valid constraints of "j" we therefore
622 * obtain a basic map that is equal to their union.
623 * In this case, there is no need to perform a rollback of the tableau
624 * since it is going to be destroyed in fuse().
630 * |_______| _ |_________\
642 static enum isl_change
is_adj_ineq_extension(int i
, int j
,
643 struct isl_coalesce_info
*info
)
646 struct isl_tab_undo
*snap
;
647 unsigned n_eq
= info
[i
].bmap
->n_eq
;
648 unsigned total
= isl_basic_map_total_dim(info
[i
].bmap
);
652 if (isl_tab_extend_cons(info
[i
].tab
, 1 + info
[j
].bmap
->n_ineq
) < 0)
653 return isl_change_error
;
655 k
= find(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ADJ_INEQ
);
657 isl_die(isl_basic_map_get_ctx(info
[i
].bmap
), isl_error_internal
,
658 "info[i].ineq should have exactly one STATUS_ADJ_INEQ",
659 return isl_change_error
);
661 snap
= isl_tab_snap(info
[i
].tab
);
663 if (isl_tab_unrestrict(info
[i
].tab
, n_eq
+ k
) < 0)
664 return isl_change_error
;
666 isl_seq_neg(info
[i
].bmap
->ineq
[k
], info
[i
].bmap
->ineq
[k
], 1 + total
);
667 isl_int_sub_ui(info
[i
].bmap
->ineq
[k
][0], info
[i
].bmap
->ineq
[k
][0], 1);
668 r
= isl_tab_add_ineq(info
[i
].tab
, info
[i
].bmap
->ineq
[k
]);
669 isl_seq_neg(info
[i
].bmap
->ineq
[k
], info
[i
].bmap
->ineq
[k
], 1 + total
);
670 isl_int_sub_ui(info
[i
].bmap
->ineq
[k
][0], info
[i
].bmap
->ineq
[k
][0], 1);
672 return isl_change_error
;
674 for (k
= 0; k
< info
[j
].bmap
->n_ineq
; ++k
) {
675 if (info
[j
].ineq
[k
] != STATUS_VALID
)
677 if (isl_tab_add_ineq(info
[i
].tab
, info
[j
].bmap
->ineq
[k
]) < 0)
678 return isl_change_error
;
681 super
= contains(&info
[j
], info
[i
].tab
);
683 return isl_change_error
;
685 return fuse(i
, j
, info
, NULL
, 0, 0);
687 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
688 return isl_change_error
;
690 return isl_change_none
;
694 /* Both basic maps have at least one inequality with and adjacent
695 * (but opposite) inequality in the other basic map.
696 * Check that there are no cut constraints and that there is only
697 * a single pair of adjacent inequalities.
698 * If so, we can replace the pair by a single basic map described
699 * by all but the pair of adjacent inequalities.
700 * Any additional points introduced lie strictly between the two
701 * adjacent hyperplanes and can therefore be integral.
710 * The test for a single pair of adjancent inequalities is important
711 * for avoiding the combination of two basic maps like the following
721 * If there are some cut constraints on one side, then we may
722 * still be able to fuse the two basic maps, but we need to perform
723 * some additional checks in is_adj_ineq_extension.
725 static enum isl_change
check_adj_ineq(int i
, int j
,
726 struct isl_coalesce_info
*info
)
728 int count_i
, count_j
;
731 count_i
= count(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ADJ_INEQ
);
732 count_j
= count(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_ADJ_INEQ
);
734 if (count_i
!= 1 && count_j
!= 1)
735 return isl_change_none
;
737 cut_i
= any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_CUT
) ||
738 any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_CUT
);
739 cut_j
= any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_CUT
) ||
740 any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_CUT
);
742 if (!cut_i
&& !cut_j
&& count_i
== 1 && count_j
== 1)
743 return fuse(i
, j
, info
, NULL
, 0, 0);
745 if (count_i
== 1 && !cut_i
)
746 return is_adj_ineq_extension(i
, j
, info
);
748 if (count_j
== 1 && !cut_j
)
749 return is_adj_ineq_extension(j
, i
, info
);
751 return isl_change_none
;
754 /* Given an affine transformation matrix "T", does row "row" represent
755 * anything other than a unit vector (possibly shifted by a constant)
756 * that is not involved in any of the other rows?
758 * That is, if a constraint involves the variable corresponding to
759 * the row, then could its preimage by "T" have any coefficients
760 * that are different from those in the original constraint?
762 static int not_unique_unit_row(__isl_keep isl_mat
*T
, int row
)
765 int len
= T
->n_col
- 1;
767 i
= isl_seq_first_non_zero(T
->row
[row
] + 1, len
);
770 if (!isl_int_is_one(T
->row
[row
][1 + i
]) &&
771 !isl_int_is_negone(T
->row
[row
][1 + i
]))
774 j
= isl_seq_first_non_zero(T
->row
[row
] + 1 + i
+ 1, len
- (i
+ 1));
778 for (j
= 1; j
< T
->n_row
; ++j
) {
781 if (!isl_int_is_zero(T
->row
[j
][1 + i
]))
788 /* Does inequality constraint "ineq" of "bmap" involve any of
789 * the variables marked in "affected"?
790 * "total" is the total number of variables, i.e., the number
791 * of entries in "affected".
793 static int is_affected(__isl_keep isl_basic_map
*bmap
, int ineq
, int *affected
,
798 for (i
= 0; i
< total
; ++i
) {
801 if (!isl_int_is_zero(bmap
->ineq
[ineq
][1 + i
]))
808 /* Given the compressed version of inequality constraint "ineq"
809 * of info->bmap in "v", check if the constraint can be tightened,
810 * where the compression is based on an equality constraint valid
812 * If so, add the tightened version of the inequality constraint
813 * to info->tab. "v" may be modified by this function.
815 * That is, if the compressed constraint is of the form
819 * with 0 < c < m, then it is equivalent to
823 * This means that c can also be subtracted from the original,
824 * uncompressed constraint without affecting the integer points
825 * in info->tab. Add this tightened constraint as an extra row
826 * to info->tab to make this information explicitly available.
828 static __isl_give isl_vec
*try_tightening(struct isl_coalesce_info
*info
,
829 int ineq
, __isl_take isl_vec
*v
)
837 ctx
= isl_vec_get_ctx(v
);
838 isl_seq_gcd(v
->el
+ 1, v
->size
- 1, &ctx
->normalize_gcd
);
839 if (isl_int_is_zero(ctx
->normalize_gcd
) ||
840 isl_int_is_one(ctx
->normalize_gcd
)) {
848 isl_int_fdiv_r(v
->el
[0], v
->el
[0], ctx
->normalize_gcd
);
849 if (isl_int_is_zero(v
->el
[0]))
852 if (isl_tab_extend_cons(info
->tab
, 1) < 0)
853 return isl_vec_free(v
);
855 isl_int_sub(info
->bmap
->ineq
[ineq
][0],
856 info
->bmap
->ineq
[ineq
][0], v
->el
[0]);
857 r
= isl_tab_add_ineq(info
->tab
, info
->bmap
->ineq
[ineq
]);
858 isl_int_add(info
->bmap
->ineq
[ineq
][0],
859 info
->bmap
->ineq
[ineq
][0], v
->el
[0]);
862 return isl_vec_free(v
);
867 /* Tighten the (non-redundant) constraints on the facet represented
869 * In particular, on input, info->tab represents the result
870 * of relaxing the "n" inequality constraints of info->bmap in "relaxed"
871 * by one, i.e., replacing f_i >= 0 by f_i + 1 >= 0, and then
872 * replacing the one at index "l" by the corresponding equality,
873 * i.e., f_k + 1 = 0, with k = relaxed[l].
875 * Compute a variable compression from the equality constraint f_k + 1 = 0
876 * and use it to tighten the other constraints of info->bmap
877 * (that is, all constraints that have not been relaxed),
878 * updating info->tab (and leaving info->bmap untouched).
879 * The compression handles essentially two cases, one where a variable
880 * is assigned a fixed value and can therefore be eliminated, and one
881 * where one variable is a shifted multiple of some other variable and
882 * can therefore be replaced by that multiple.
883 * Gaussian elimination would also work for the first case, but for
884 * the second case, the effectiveness would depend on the order
886 * After compression, some of the constraints may have coefficients
887 * with a common divisor. If this divisor does not divide the constant
888 * term, then the constraint can be tightened.
889 * The tightening is performed on the tableau info->tab by introducing
890 * extra (temporary) constraints.
892 * Only constraints that are possibly affected by the compression are
893 * considered. In particular, if the constraint only involves variables
894 * that are directly mapped to a distinct set of other variables, then
895 * no common divisor can be introduced and no tightening can occur.
897 * It is important to only consider the non-redundant constraints
898 * since the facet constraint has been relaxed prior to the call
899 * to this function, meaning that the constraints that were redundant
900 * prior to the relaxation may no longer be redundant.
901 * These constraints will be ignored in the fused result, so
902 * the fusion detection should not exploit them.
904 static isl_stat
tighten_on_relaxed_facet(struct isl_coalesce_info
*info
,
905 int n
, int *relaxed
, int l
)
916 ctx
= isl_basic_map_get_ctx(info
->bmap
);
917 total
= isl_basic_map_total_dim(info
->bmap
);
918 isl_int_add_ui(info
->bmap
->ineq
[k
][0], info
->bmap
->ineq
[k
][0], 1);
919 T
= isl_mat_sub_alloc6(ctx
, info
->bmap
->ineq
, k
, 1, 0, 1 + total
);
920 T
= isl_mat_variable_compression(T
, NULL
);
921 isl_int_sub_ui(info
->bmap
->ineq
[k
][0], info
->bmap
->ineq
[k
][0], 1);
923 return isl_stat_error
;
929 affected
= isl_alloc_array(ctx
, int, total
);
933 for (i
= 0; i
< total
; ++i
)
934 affected
[i
] = not_unique_unit_row(T
, 1 + i
);
936 for (i
= 0; i
< info
->bmap
->n_ineq
; ++i
) {
937 if (any(relaxed
, n
, i
))
939 if (info
->ineq
[i
] == STATUS_REDUNDANT
)
941 if (!is_affected(info
->bmap
, i
, affected
, total
))
943 v
= isl_vec_alloc(ctx
, 1 + total
);
946 isl_seq_cpy(v
->el
, info
->bmap
->ineq
[i
], 1 + total
);
947 v
= isl_vec_mat_product(v
, isl_mat_copy(T
));
948 v
= try_tightening(info
, i
, v
);
960 return isl_stat_error
;
963 /* Replace the basic maps "i" and "j" by an extension of "i"
964 * along the "n" inequality constraints in "relax" by one.
965 * The tableau info[i].tab has already been extended.
966 * Extend info[i].bmap accordingly by relaxing all constraints in "relax"
968 * Each integer division that does not have exactly the same
969 * definition in "i" and "j" is marked unknown and the basic map
970 * is scheduled to be simplified in an attempt to recover
971 * the integer division definition.
972 * Place the extension in the position that is the smallest of i and j.
974 static enum isl_change
extend(int i
, int j
, int n
, int *relax
,
975 struct isl_coalesce_info
*info
)
980 info
[i
].bmap
= isl_basic_map_cow(info
[i
].bmap
);
982 return isl_change_error
;
983 total
= isl_basic_map_total_dim(info
[i
].bmap
);
984 for (l
= 0; l
< info
[i
].bmap
->n_div
; ++l
)
985 if (!isl_seq_eq(info
[i
].bmap
->div
[l
],
986 info
[j
].bmap
->div
[l
], 1 + 1 + total
)) {
987 isl_int_set_si(info
[i
].bmap
->div
[l
][0], 0);
988 info
[i
].simplify
= 1;
990 for (l
= 0; l
< n
; ++l
)
991 isl_int_add_ui(info
[i
].bmap
->ineq
[relax
[l
]][0],
992 info
[i
].bmap
->ineq
[relax
[l
]][0], 1);
993 ISL_F_SET(info
[i
].bmap
, ISL_BASIC_MAP_FINAL
);
996 exchange(&info
[i
], &info
[j
]);
997 return isl_change_fuse
;
1000 /* Basic map "i" has "n" inequality constraints (collected in "relax")
1001 * that are such that they include basic map "j" if they are relaxed
1002 * by one. All the other inequalities are valid for "j".
1003 * Check if basic map "j" forms an extension of basic map "i".
1005 * In particular, relax the constraints in "relax", compute the corresponding
1006 * facets one by one and check whether each of these is included
1007 * in the other basic map.
1008 * Before testing for inclusion, the constraints on each facet
1009 * are tightened to increase the chance of an inclusion being detected.
1010 * (Adding the valid constraints of "j" to the tableau of "i", as is done
1011 * in is_adj_ineq_extension, may further increase those chances, but this
1012 * is not currently done.)
1013 * If each facet is included, we know that relaxing the constraints extends
1014 * the basic map with exactly the other basic map (we already know that this
1015 * other basic map is included in the extension, because all other
1016 * inequality constraints are valid of "j") and we can replace the
1017 * two basic maps by this extension.
1033 static enum isl_change
is_relaxed_extension(int i
, int j
, int n
, int *relax
,
1034 struct isl_coalesce_info
*info
)
1038 struct isl_tab_undo
*snap
, *snap2
;
1039 unsigned n_eq
= info
[i
].bmap
->n_eq
;
1041 for (l
= 0; l
< n
; ++l
)
1042 if (isl_tab_is_equality(info
[i
].tab
, n_eq
+ relax
[l
]))
1043 return isl_change_none
;
1045 snap
= isl_tab_snap(info
[i
].tab
);
1046 for (l
= 0; l
< n
; ++l
)
1047 if (isl_tab_relax(info
[i
].tab
, n_eq
+ relax
[l
]) < 0)
1048 return isl_change_error
;
1049 snap2
= isl_tab_snap(info
[i
].tab
);
1050 for (l
= 0; l
< n
; ++l
) {
1051 if (isl_tab_rollback(info
[i
].tab
, snap2
) < 0)
1052 return isl_change_error
;
1053 if (isl_tab_select_facet(info
[i
].tab
, n_eq
+ relax
[l
]) < 0)
1054 return isl_change_error
;
1055 if (tighten_on_relaxed_facet(&info
[i
], n
, relax
, l
) < 0)
1056 return isl_change_error
;
1057 super
= contains(&info
[j
], info
[i
].tab
);
1059 return isl_change_error
;
1062 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
1063 return isl_change_error
;
1064 return isl_change_none
;
1067 if (isl_tab_rollback(info
[i
].tab
, snap2
) < 0)
1068 return isl_change_error
;
1069 return extend(i
, j
, n
, relax
, info
);
1072 /* Data structure that keeps track of the wrapping constraints
1073 * and of information to bound the coefficients of those constraints.
1075 * bound is set if we want to apply a bound on the coefficients
1076 * mat contains the wrapping constraints
1077 * max is the bound on the coefficients (if bound is set)
1085 /* Update wraps->max to be greater than or equal to the coefficients
1086 * in the equalities and inequalities of info->bmap that can be removed
1087 * if we end up applying wrapping.
1089 static void wraps_update_max(struct isl_wraps
*wraps
,
1090 struct isl_coalesce_info
*info
)
1094 unsigned total
= isl_basic_map_total_dim(info
->bmap
);
1096 isl_int_init(max_k
);
1098 for (k
= 0; k
< info
->bmap
->n_eq
; ++k
) {
1099 if (info
->eq
[2 * k
] == STATUS_VALID
&&
1100 info
->eq
[2 * k
+ 1] == STATUS_VALID
)
1102 isl_seq_abs_max(info
->bmap
->eq
[k
] + 1, total
, &max_k
);
1103 if (isl_int_abs_gt(max_k
, wraps
->max
))
1104 isl_int_set(wraps
->max
, max_k
);
1107 for (k
= 0; k
< info
->bmap
->n_ineq
; ++k
) {
1108 if (info
->ineq
[k
] == STATUS_VALID
||
1109 info
->ineq
[k
] == STATUS_REDUNDANT
)
1111 isl_seq_abs_max(info
->bmap
->ineq
[k
] + 1, total
, &max_k
);
1112 if (isl_int_abs_gt(max_k
, wraps
->max
))
1113 isl_int_set(wraps
->max
, max_k
);
1116 isl_int_clear(max_k
);
1119 /* Initialize the isl_wraps data structure.
1120 * If we want to bound the coefficients of the wrapping constraints,
1121 * we set wraps->max to the largest coefficient
1122 * in the equalities and inequalities that can be removed if we end up
1123 * applying wrapping.
1125 static void wraps_init(struct isl_wraps
*wraps
, __isl_take isl_mat
*mat
,
1126 struct isl_coalesce_info
*info
, int i
, int j
)
1134 ctx
= isl_mat_get_ctx(mat
);
1135 wraps
->bound
= isl_options_get_coalesce_bounded_wrapping(ctx
);
1138 isl_int_init(wraps
->max
);
1139 isl_int_set_si(wraps
->max
, 0);
1140 wraps_update_max(wraps
, &info
[i
]);
1141 wraps_update_max(wraps
, &info
[j
]);
1144 /* Free the contents of the isl_wraps data structure.
1146 static void wraps_free(struct isl_wraps
*wraps
)
1148 isl_mat_free(wraps
->mat
);
1150 isl_int_clear(wraps
->max
);
1153 /* Is the wrapping constraint in row "row" allowed?
1155 * If wraps->bound is set, we check that none of the coefficients
1156 * is greater than wraps->max.
1158 static int allow_wrap(struct isl_wraps
*wraps
, int row
)
1165 for (i
= 1; i
< wraps
->mat
->n_col
; ++i
)
1166 if (isl_int_abs_gt(wraps
->mat
->row
[row
][i
], wraps
->max
))
1172 /* Wrap "ineq" (or its opposite if "negate" is set) around "bound"
1173 * to include "set" and add the result in position "w" of "wraps".
1174 * "len" is the total number of coefficients in "bound" and "ineq".
1175 * Return 1 on success, 0 on failure and -1 on error.
1176 * Wrapping can fail if the result of wrapping is equal to "bound"
1177 * or if we want to bound the sizes of the coefficients and
1178 * the wrapped constraint does not satisfy this bound.
1180 static int add_wrap(struct isl_wraps
*wraps
, int w
, isl_int
*bound
,
1181 isl_int
*ineq
, unsigned len
, __isl_keep isl_set
*set
, int negate
)
1183 isl_seq_cpy(wraps
->mat
->row
[w
], bound
, len
);
1185 isl_seq_neg(wraps
->mat
->row
[w
+ 1], ineq
, len
);
1186 ineq
= wraps
->mat
->row
[w
+ 1];
1188 if (!isl_set_wrap_facet(set
, wraps
->mat
->row
[w
], ineq
))
1190 if (isl_seq_eq(wraps
->mat
->row
[w
], bound
, len
))
1192 if (!allow_wrap(wraps
, w
))
1197 /* For each constraint in info->bmap that is not redundant (as determined
1198 * by info->tab) and that is not a valid constraint for the other basic map,
1199 * wrap the constraint around "bound" such that it includes the whole
1200 * set "set" and append the resulting constraint to "wraps".
1201 * Note that the constraints that are valid for the other basic map
1202 * will be added to the combined basic map by default, so there is
1203 * no need to wrap them.
1204 * The caller wrap_in_facets even relies on this function not wrapping
1205 * any constraints that are already valid.
1206 * "wraps" is assumed to have been pre-allocated to the appropriate size.
1207 * wraps->n_row is the number of actual wrapped constraints that have
1209 * If any of the wrapping problems results in a constraint that is
1210 * identical to "bound", then this means that "set" is unbounded in such
1211 * way that no wrapping is possible. If this happens then wraps->n_row
1213 * Similarly, if we want to bound the coefficients of the wrapping
1214 * constraints and a newly added wrapping constraint does not
1215 * satisfy the bound, then wraps->n_row is also reset to zero.
1217 static int add_wraps(struct isl_wraps
*wraps
, struct isl_coalesce_info
*info
,
1218 isl_int
*bound
, __isl_keep isl_set
*set
)
1223 isl_basic_map
*bmap
= info
->bmap
;
1224 unsigned len
= 1 + isl_basic_map_total_dim(bmap
);
1226 w
= wraps
->mat
->n_row
;
1228 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
1229 if (info
->ineq
[l
] == STATUS_VALID
||
1230 info
->ineq
[l
] == STATUS_REDUNDANT
)
1232 if (isl_seq_is_neg(bound
, bmap
->ineq
[l
], len
))
1234 if (isl_seq_eq(bound
, bmap
->ineq
[l
], len
))
1236 if (isl_tab_is_redundant(info
->tab
, bmap
->n_eq
+ l
))
1239 added
= add_wrap(wraps
, w
, bound
, bmap
->ineq
[l
], len
, set
, 0);
1246 for (l
= 0; l
< bmap
->n_eq
; ++l
) {
1247 if (isl_seq_is_neg(bound
, bmap
->eq
[l
], len
))
1249 if (isl_seq_eq(bound
, bmap
->eq
[l
], len
))
1252 for (m
= 0; m
< 2; ++m
) {
1253 if (info
->eq
[2 * l
+ m
] == STATUS_VALID
)
1255 added
= add_wrap(wraps
, w
, bound
, bmap
->eq
[l
], len
,
1265 wraps
->mat
->n_row
= w
;
1268 wraps
->mat
->n_row
= 0;
1272 /* Check if the constraints in "wraps" from "first" until the last
1273 * are all valid for the basic set represented by "tab".
1274 * If not, wraps->n_row is set to zero.
1276 static int check_wraps(__isl_keep isl_mat
*wraps
, int first
,
1277 struct isl_tab
*tab
)
1281 for (i
= first
; i
< wraps
->n_row
; ++i
) {
1282 enum isl_ineq_type type
;
1283 type
= isl_tab_ineq_type(tab
, wraps
->row
[i
]);
1284 if (type
== isl_ineq_error
)
1286 if (type
== isl_ineq_redundant
)
1295 /* Return a set that corresponds to the non-redundant constraints
1296 * (as recorded in tab) of bmap.
1298 * It's important to remove the redundant constraints as some
1299 * of the other constraints may have been modified after the
1300 * constraints were marked redundant.
1301 * In particular, a constraint may have been relaxed.
1302 * Redundant constraints are ignored when a constraint is relaxed
1303 * and should therefore continue to be ignored ever after.
1304 * Otherwise, the relaxation might be thwarted by some of
1305 * these constraints.
1307 * Update the underlying set to ensure that the dimension doesn't change.
1308 * Otherwise the integer divisions could get dropped if the tab
1309 * turns out to be empty.
1311 static __isl_give isl_set
*set_from_updated_bmap(__isl_keep isl_basic_map
*bmap
,
1312 struct isl_tab
*tab
)
1314 isl_basic_set
*bset
;
1316 bmap
= isl_basic_map_copy(bmap
);
1317 bset
= isl_basic_map_underlying_set(bmap
);
1318 bset
= isl_basic_set_cow(bset
);
1319 bset
= isl_basic_set_update_from_tab(bset
, tab
);
1320 return isl_set_from_basic_set(bset
);
1323 /* Wrap the constraints of info->bmap that bound the facet defined
1324 * by inequality "k" around (the opposite of) this inequality to
1325 * include "set". "bound" may be used to store the negated inequality.
1326 * Since the wrapped constraints are not guaranteed to contain the whole
1327 * of info->bmap, we check them in check_wraps.
1328 * If any of the wrapped constraints turn out to be invalid, then
1329 * check_wraps will reset wrap->n_row to zero.
1331 static int add_wraps_around_facet(struct isl_wraps
*wraps
,
1332 struct isl_coalesce_info
*info
, int k
, isl_int
*bound
,
1333 __isl_keep isl_set
*set
)
1335 struct isl_tab_undo
*snap
;
1337 unsigned total
= isl_basic_map_total_dim(info
->bmap
);
1339 snap
= isl_tab_snap(info
->tab
);
1341 if (isl_tab_select_facet(info
->tab
, info
->bmap
->n_eq
+ k
) < 0)
1343 if (isl_tab_detect_redundant(info
->tab
) < 0)
1346 isl_seq_neg(bound
, info
->bmap
->ineq
[k
], 1 + total
);
1348 n
= wraps
->mat
->n_row
;
1349 if (add_wraps(wraps
, info
, bound
, set
) < 0)
1352 if (isl_tab_rollback(info
->tab
, snap
) < 0)
1354 if (check_wraps(wraps
->mat
, n
, info
->tab
) < 0)
1360 /* Given a basic set i with a constraint k that is adjacent to
1361 * basic set j, check if we can wrap
1362 * both the facet corresponding to k (if "wrap_facet" is set) and basic map j
1363 * (always) around their ridges to include the other set.
1364 * If so, replace the pair of basic sets by their union.
1366 * All constraints of i (except k) are assumed to be valid or
1367 * cut constraints for j.
1368 * Wrapping the cut constraints to include basic map j may result
1369 * in constraints that are no longer valid of basic map i
1370 * we have to check that the resulting wrapping constraints are valid for i.
1371 * If "wrap_facet" is not set, then all constraints of i (except k)
1372 * are assumed to be valid for j.
1381 static enum isl_change
can_wrap_in_facet(int i
, int j
, int k
,
1382 struct isl_coalesce_info
*info
, int wrap_facet
)
1384 enum isl_change change
= isl_change_none
;
1385 struct isl_wraps wraps
;
1388 struct isl_set
*set_i
= NULL
;
1389 struct isl_set
*set_j
= NULL
;
1390 struct isl_vec
*bound
= NULL
;
1391 unsigned total
= isl_basic_map_total_dim(info
[i
].bmap
);
1393 set_i
= set_from_updated_bmap(info
[i
].bmap
, info
[i
].tab
);
1394 set_j
= set_from_updated_bmap(info
[j
].bmap
, info
[j
].tab
);
1395 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
1396 mat
= isl_mat_alloc(ctx
, 2 * (info
[i
].bmap
->n_eq
+ info
[j
].bmap
->n_eq
) +
1397 info
[i
].bmap
->n_ineq
+ info
[j
].bmap
->n_ineq
,
1399 wraps_init(&wraps
, mat
, info
, i
, j
);
1400 bound
= isl_vec_alloc(ctx
, 1 + total
);
1401 if (!set_i
|| !set_j
|| !wraps
.mat
|| !bound
)
1404 isl_seq_cpy(bound
->el
, info
[i
].bmap
->ineq
[k
], 1 + total
);
1405 isl_int_add_ui(bound
->el
[0], bound
->el
[0], 1);
1407 isl_seq_cpy(wraps
.mat
->row
[0], bound
->el
, 1 + total
);
1408 wraps
.mat
->n_row
= 1;
1410 if (add_wraps(&wraps
, &info
[j
], bound
->el
, set_i
) < 0)
1412 if (!wraps
.mat
->n_row
)
1416 if (add_wraps_around_facet(&wraps
, &info
[i
], k
,
1417 bound
->el
, set_j
) < 0)
1419 if (!wraps
.mat
->n_row
)
1423 change
= fuse(i
, j
, info
, wraps
.mat
, 0, 0);
1428 isl_set_free(set_i
);
1429 isl_set_free(set_j
);
1431 isl_vec_free(bound
);
1436 isl_vec_free(bound
);
1437 isl_set_free(set_i
);
1438 isl_set_free(set_j
);
1439 return isl_change_error
;
1442 /* Given a cut constraint t(x) >= 0 of basic map i, stored in row "w"
1443 * of wrap.mat, replace it by its relaxed version t(x) + 1 >= 0, and
1444 * add wrapping constraints to wrap.mat for all constraints
1445 * of basic map j that bound the part of basic map j that sticks out
1446 * of the cut constraint.
1447 * "set_i" is the underlying set of basic map i.
1448 * If any wrapping fails, then wraps->mat.n_row is reset to zero.
1450 * In particular, we first intersect basic map j with t(x) + 1 = 0.
1451 * If the result is empty, then t(x) >= 0 was actually a valid constraint
1452 * (with respect to the integer points), so we add t(x) >= 0 instead.
1453 * Otherwise, we wrap the constraints of basic map j that are not
1454 * redundant in this intersection and that are not already valid
1455 * for basic map i over basic map i.
1456 * Note that it is sufficient to wrap the constraints to include
1457 * basic map i, because we will only wrap the constraints that do
1458 * not include basic map i already. The wrapped constraint will
1459 * therefore be more relaxed compared to the original constraint.
1460 * Since the original constraint is valid for basic map j, so is
1461 * the wrapped constraint.
1463 static isl_stat
wrap_in_facet(struct isl_wraps
*wraps
, int w
,
1464 struct isl_coalesce_info
*info_j
, __isl_keep isl_set
*set_i
,
1465 struct isl_tab_undo
*snap
)
1467 isl_int_add_ui(wraps
->mat
->row
[w
][0], wraps
->mat
->row
[w
][0], 1);
1468 if (isl_tab_add_eq(info_j
->tab
, wraps
->mat
->row
[w
]) < 0)
1469 return isl_stat_error
;
1470 if (isl_tab_detect_redundant(info_j
->tab
) < 0)
1471 return isl_stat_error
;
1473 if (info_j
->tab
->empty
)
1474 isl_int_sub_ui(wraps
->mat
->row
[w
][0], wraps
->mat
->row
[w
][0], 1);
1475 else if (add_wraps(wraps
, info_j
, wraps
->mat
->row
[w
], set_i
) < 0)
1476 return isl_stat_error
;
1478 if (isl_tab_rollback(info_j
->tab
, snap
) < 0)
1479 return isl_stat_error
;
1484 /* Given a pair of basic maps i and j such that j sticks out
1485 * of i at n cut constraints, each time by at most one,
1486 * try to compute wrapping constraints and replace the two
1487 * basic maps by a single basic map.
1488 * The other constraints of i are assumed to be valid for j.
1489 * "set_i" is the underlying set of basic map i.
1490 * "wraps" has been initialized to be of the right size.
1492 * For each cut constraint t(x) >= 0 of i, we add the relaxed version
1493 * t(x) + 1 >= 0, along with wrapping constraints for all constraints
1494 * of basic map j that bound the part of basic map j that sticks out
1495 * of the cut constraint.
1497 * If any wrapping fails, i.e., if we cannot wrap to touch
1498 * the union, then we give up.
1499 * Otherwise, the pair of basic maps is replaced by their union.
1501 static enum isl_change
try_wrap_in_facets(int i
, int j
,
1502 struct isl_coalesce_info
*info
, struct isl_wraps
*wraps
,
1503 __isl_keep isl_set
*set_i
)
1507 struct isl_tab_undo
*snap
;
1509 total
= isl_basic_map_total_dim(info
[i
].bmap
);
1511 snap
= isl_tab_snap(info
[j
].tab
);
1513 wraps
->mat
->n_row
= 0;
1515 for (k
= 0; k
< info
[i
].bmap
->n_eq
; ++k
) {
1516 for (l
= 0; l
< 2; ++l
) {
1517 if (info
[i
].eq
[2 * k
+ l
] != STATUS_CUT
)
1519 w
= wraps
->mat
->n_row
++;
1521 isl_seq_neg(wraps
->mat
->row
[w
],
1522 info
[i
].bmap
->eq
[k
], 1 + total
);
1524 isl_seq_cpy(wraps
->mat
->row
[w
],
1525 info
[i
].bmap
->eq
[k
], 1 + total
);
1526 if (wrap_in_facet(wraps
, w
, &info
[j
], set_i
, snap
) < 0)
1527 return isl_change_error
;
1529 if (!wraps
->mat
->n_row
)
1530 return isl_change_none
;
1534 for (k
= 0; k
< info
[i
].bmap
->n_ineq
; ++k
) {
1535 if (info
[i
].ineq
[k
] != STATUS_CUT
)
1537 w
= wraps
->mat
->n_row
++;
1538 isl_seq_cpy(wraps
->mat
->row
[w
],
1539 info
[i
].bmap
->ineq
[k
], 1 + total
);
1540 if (wrap_in_facet(wraps
, w
, &info
[j
], set_i
, snap
) < 0)
1541 return isl_change_error
;
1543 if (!wraps
->mat
->n_row
)
1544 return isl_change_none
;
1547 return fuse(i
, j
, info
, wraps
->mat
, 0, 1);
1550 /* Given a pair of basic maps i and j such that j sticks out
1551 * of i at n cut constraints, each time by at most one,
1552 * try to compute wrapping constraints and replace the two
1553 * basic maps by a single basic map.
1554 * The other constraints of i are assumed to be valid for j.
1556 * The core computation is performed by try_wrap_in_facets.
1557 * This function simply extracts an underlying set representation
1558 * of basic map i and initializes the data structure for keeping
1559 * track of wrapping constraints.
1561 static enum isl_change
wrap_in_facets(int i
, int j
, int n
,
1562 struct isl_coalesce_info
*info
)
1564 enum isl_change change
= isl_change_none
;
1565 struct isl_wraps wraps
;
1568 isl_set
*set_i
= NULL
;
1569 unsigned total
= isl_basic_map_total_dim(info
[i
].bmap
);
1572 if (isl_tab_extend_cons(info
[j
].tab
, 1) < 0)
1573 return isl_change_error
;
1575 max_wrap
= 1 + 2 * info
[j
].bmap
->n_eq
+ info
[j
].bmap
->n_ineq
;
1578 set_i
= set_from_updated_bmap(info
[i
].bmap
, info
[i
].tab
);
1579 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
1580 mat
= isl_mat_alloc(ctx
, max_wrap
, 1 + total
);
1581 wraps_init(&wraps
, mat
, info
, i
, j
);
1582 if (!set_i
|| !wraps
.mat
)
1585 change
= try_wrap_in_facets(i
, j
, info
, &wraps
, set_i
);
1588 isl_set_free(set_i
);
1593 isl_set_free(set_i
);
1594 return isl_change_error
;
1597 /* Return the effect of inequality "ineq" on the tableau "tab",
1598 * after relaxing the constant term of "ineq" by one.
1600 static enum isl_ineq_type
type_of_relaxed(struct isl_tab
*tab
, isl_int
*ineq
)
1602 enum isl_ineq_type type
;
1604 isl_int_add_ui(ineq
[0], ineq
[0], 1);
1605 type
= isl_tab_ineq_type(tab
, ineq
);
1606 isl_int_sub_ui(ineq
[0], ineq
[0], 1);
1611 /* Given two basic sets i and j,
1612 * check if relaxing all the cut constraints of i by one turns
1613 * them into valid constraint for j and check if we can wrap in
1614 * the bits that are sticking out.
1615 * If so, replace the pair by their union.
1617 * We first check if all relaxed cut inequalities of i are valid for j
1618 * and then try to wrap in the intersections of the relaxed cut inequalities
1621 * During this wrapping, we consider the points of j that lie at a distance
1622 * of exactly 1 from i. In particular, we ignore the points that lie in
1623 * between this lower-dimensional space and the basic map i.
1624 * We can therefore only apply this to integer maps.
1650 * Wrapping can fail if the result of wrapping one of the facets
1651 * around its edges does not produce any new facet constraint.
1652 * In particular, this happens when we try to wrap in unbounded sets.
1654 * _______________________________________________________________________
1658 * |_| |_________________________________________________________________
1661 * The following is not an acceptable result of coalescing the above two
1662 * sets as it includes extra integer points.
1663 * _______________________________________________________________________
1668 * \______________________________________________________________________
1670 static enum isl_change
can_wrap_in_set(int i
, int j
,
1671 struct isl_coalesce_info
*info
)
1677 if (ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_RATIONAL
) ||
1678 ISL_F_ISSET(info
[j
].bmap
, ISL_BASIC_MAP_RATIONAL
))
1679 return isl_change_none
;
1681 n
= count(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_CUT
);
1682 n
+= count(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_CUT
);
1684 return isl_change_none
;
1686 total
= isl_basic_map_total_dim(info
[i
].bmap
);
1687 for (k
= 0; k
< info
[i
].bmap
->n_eq
; ++k
) {
1688 for (l
= 0; l
< 2; ++l
) {
1689 enum isl_ineq_type type
;
1691 if (info
[i
].eq
[2 * k
+ l
] != STATUS_CUT
)
1695 isl_seq_neg(info
[i
].bmap
->eq
[k
],
1696 info
[i
].bmap
->eq
[k
], 1 + total
);
1697 type
= type_of_relaxed(info
[j
].tab
,
1698 info
[i
].bmap
->eq
[k
]);
1700 isl_seq_neg(info
[i
].bmap
->eq
[k
],
1701 info
[i
].bmap
->eq
[k
], 1 + total
);
1702 if (type
== isl_ineq_error
)
1703 return isl_change_error
;
1704 if (type
!= isl_ineq_redundant
)
1705 return isl_change_none
;
1709 for (k
= 0; k
< info
[i
].bmap
->n_ineq
; ++k
) {
1710 enum isl_ineq_type type
;
1712 if (info
[i
].ineq
[k
] != STATUS_CUT
)
1715 type
= type_of_relaxed(info
[j
].tab
, info
[i
].bmap
->ineq
[k
]);
1716 if (type
== isl_ineq_error
)
1717 return isl_change_error
;
1718 if (type
!= isl_ineq_redundant
)
1719 return isl_change_none
;
1722 return wrap_in_facets(i
, j
, n
, info
);
1725 /* Check if either i or j has only cut constraints that can
1726 * be used to wrap in (a facet of) the other basic set.
1727 * if so, replace the pair by their union.
1729 static enum isl_change
check_wrap(int i
, int j
, struct isl_coalesce_info
*info
)
1731 enum isl_change change
= isl_change_none
;
1733 change
= can_wrap_in_set(i
, j
, info
);
1734 if (change
!= isl_change_none
)
1737 change
= can_wrap_in_set(j
, i
, info
);
1741 /* Check if all inequality constraints of "i" that cut "j" cease
1742 * to be cut constraints if they are relaxed by one.
1743 * If so, collect the cut constraints in "list".
1744 * The caller is responsible for allocating "list".
1746 static isl_bool
all_cut_by_one(int i
, int j
, struct isl_coalesce_info
*info
,
1752 for (l
= 0; l
< info
[i
].bmap
->n_ineq
; ++l
) {
1753 enum isl_ineq_type type
;
1755 if (info
[i
].ineq
[l
] != STATUS_CUT
)
1757 type
= type_of_relaxed(info
[j
].tab
, info
[i
].bmap
->ineq
[l
]);
1758 if (type
== isl_ineq_error
)
1759 return isl_bool_error
;
1760 if (type
!= isl_ineq_redundant
)
1761 return isl_bool_false
;
1765 return isl_bool_true
;
1768 /* Given two basic maps such that "j" has at least one equality constraint
1769 * that is adjacent to an inequality constraint of "i" and such that "i" has
1770 * exactly one inequality constraint that is adjacent to an equality
1771 * constraint of "j", check whether "i" can be extended to include "j" or
1772 * whether "j" can be wrapped into "i".
1773 * All remaining constraints of "i" and "j" are assumed to be valid
1774 * or cut constraints of the other basic map.
1775 * However, none of the equality constraints of "i" are cut constraints.
1777 * If "i" has any "cut" inequality constraints, then check if relaxing
1778 * each of them by one is sufficient for them to become valid.
1779 * If so, check if the inequality constraint adjacent to an equality
1780 * constraint of "j" along with all these cut constraints
1781 * can be relaxed by one to contain exactly "j".
1782 * Otherwise, or if this fails, check if "j" can be wrapped into "i".
1784 static enum isl_change
check_single_adj_eq(int i
, int j
,
1785 struct isl_coalesce_info
*info
)
1787 enum isl_change change
= isl_change_none
;
1794 n_cut
= count(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_CUT
);
1796 k
= find(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ADJ_EQ
);
1799 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
1800 relax
= isl_calloc_array(ctx
, int, 1 + n_cut
);
1802 return isl_change_error
;
1804 try_relax
= all_cut_by_one(i
, j
, info
, relax
+ 1);
1806 change
= isl_change_error
;
1808 try_relax
= isl_bool_true
;
1811 if (try_relax
&& change
== isl_change_none
)
1812 change
= is_relaxed_extension(i
, j
, 1 + n_cut
, relax
, info
);
1815 if (change
!= isl_change_none
)
1818 change
= can_wrap_in_facet(i
, j
, k
, info
, n_cut
> 0);
1823 /* At least one of the basic maps has an equality that is adjacent
1824 * to inequality. Make sure that only one of the basic maps has
1825 * such an equality and that the other basic map has exactly one
1826 * inequality adjacent to an equality.
1827 * If the other basic map does not have such an inequality, then
1828 * check if all its constraints are either valid or cut constraints
1829 * and, if so, try wrapping in the first map into the second.
1830 * Otherwise, try to extend one basic map with the other or
1831 * wrap one basic map in the other.
1833 static enum isl_change
check_adj_eq(int i
, int j
,
1834 struct isl_coalesce_info
*info
)
1836 if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_ADJ_INEQ
) &&
1837 any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_ADJ_INEQ
))
1838 /* ADJ EQ TOO MANY */
1839 return isl_change_none
;
1841 if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_ADJ_INEQ
))
1842 return check_adj_eq(j
, i
, info
);
1844 /* j has an equality adjacent to an inequality in i */
1846 if (count(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ADJ_EQ
) != 1) {
1847 if (all_valid_or_cut(&info
[i
]))
1848 return can_wrap_in_set(i
, j
, info
);
1849 return isl_change_none
;
1851 if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_CUT
))
1852 return isl_change_none
;
1853 if (any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_ADJ_EQ
) ||
1854 any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ADJ_INEQ
) ||
1855 any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_ADJ_INEQ
))
1856 /* ADJ EQ TOO MANY */
1857 return isl_change_none
;
1859 return check_single_adj_eq(i
, j
, info
);
1862 /* The two basic maps lie on adjacent hyperplanes. In particular,
1863 * basic map "i" has an equality that lies parallel to basic map "j".
1864 * Check if we can wrap the facets around the parallel hyperplanes
1865 * to include the other set.
1867 * We perform basically the same operations as can_wrap_in_facet,
1868 * except that we don't need to select a facet of one of the sets.
1874 * If there is more than one equality of "i" adjacent to an equality of "j",
1875 * then the result will satisfy one or more equalities that are a linear
1876 * combination of these equalities. These will be encoded as pairs
1877 * of inequalities in the wrapping constraints and need to be made
1880 static enum isl_change
check_eq_adj_eq(int i
, int j
,
1881 struct isl_coalesce_info
*info
)
1884 enum isl_change change
= isl_change_none
;
1885 int detect_equalities
= 0;
1886 struct isl_wraps wraps
;
1889 struct isl_set
*set_i
= NULL
;
1890 struct isl_set
*set_j
= NULL
;
1891 struct isl_vec
*bound
= NULL
;
1892 unsigned total
= isl_basic_map_total_dim(info
[i
].bmap
);
1894 if (count(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_ADJ_EQ
) != 1)
1895 detect_equalities
= 1;
1897 k
= find(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_ADJ_EQ
);
1899 set_i
= set_from_updated_bmap(info
[i
].bmap
, info
[i
].tab
);
1900 set_j
= set_from_updated_bmap(info
[j
].bmap
, info
[j
].tab
);
1901 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
1902 mat
= isl_mat_alloc(ctx
, 2 * (info
[i
].bmap
->n_eq
+ info
[j
].bmap
->n_eq
) +
1903 info
[i
].bmap
->n_ineq
+ info
[j
].bmap
->n_ineq
,
1905 wraps_init(&wraps
, mat
, info
, i
, j
);
1906 bound
= isl_vec_alloc(ctx
, 1 + total
);
1907 if (!set_i
|| !set_j
|| !wraps
.mat
|| !bound
)
1911 isl_seq_neg(bound
->el
, info
[i
].bmap
->eq
[k
/ 2], 1 + total
);
1913 isl_seq_cpy(bound
->el
, info
[i
].bmap
->eq
[k
/ 2], 1 + total
);
1914 isl_int_add_ui(bound
->el
[0], bound
->el
[0], 1);
1916 isl_seq_cpy(wraps
.mat
->row
[0], bound
->el
, 1 + total
);
1917 wraps
.mat
->n_row
= 1;
1919 if (add_wraps(&wraps
, &info
[j
], bound
->el
, set_i
) < 0)
1921 if (!wraps
.mat
->n_row
)
1924 isl_int_sub_ui(bound
->el
[0], bound
->el
[0], 1);
1925 isl_seq_neg(bound
->el
, bound
->el
, 1 + total
);
1927 isl_seq_cpy(wraps
.mat
->row
[wraps
.mat
->n_row
], bound
->el
, 1 + total
);
1930 if (add_wraps(&wraps
, &info
[i
], bound
->el
, set_j
) < 0)
1932 if (!wraps
.mat
->n_row
)
1935 change
= fuse(i
, j
, info
, wraps
.mat
, detect_equalities
, 0);
1938 error
: change
= isl_change_error
;
1943 isl_set_free(set_i
);
1944 isl_set_free(set_j
);
1945 isl_vec_free(bound
);
1950 /* Initialize the "eq" and "ineq" fields of "info".
1952 static void init_status(struct isl_coalesce_info
*info
)
1954 info
->eq
= info
->ineq
= NULL
;
1957 /* Set info->eq to the positions of the equalities of info->bmap
1958 * with respect to the basic map represented by "tab".
1959 * If info->eq has already been computed, then do not compute it again.
1961 static void set_eq_status_in(struct isl_coalesce_info
*info
,
1962 struct isl_tab
*tab
)
1966 info
->eq
= eq_status_in(info
->bmap
, tab
);
1969 /* Set info->ineq to the positions of the inequalities of info->bmap
1970 * with respect to the basic map represented by "tab".
1971 * If info->ineq has already been computed, then do not compute it again.
1973 static void set_ineq_status_in(struct isl_coalesce_info
*info
,
1974 struct isl_tab
*tab
)
1978 info
->ineq
= ineq_status_in(info
->bmap
, info
->tab
, tab
);
1981 /* Free the memory allocated by the "eq" and "ineq" fields of "info".
1982 * This function assumes that init_status has been called on "info" first,
1983 * after which the "eq" and "ineq" fields may or may not have been
1984 * assigned a newly allocated array.
1986 static void clear_status(struct isl_coalesce_info
*info
)
1992 /* Check if the union of the given pair of basic maps
1993 * can be represented by a single basic map.
1994 * If so, replace the pair by the single basic map and return
1995 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
1996 * Otherwise, return isl_change_none.
1997 * The two basic maps are assumed to live in the same local space.
1998 * The "eq" and "ineq" fields of info[i] and info[j] are assumed
1999 * to have been initialized by the caller, either to NULL or
2000 * to valid information.
2002 * We first check the effect of each constraint of one basic map
2003 * on the other basic map.
2004 * The constraint may be
2005 * redundant the constraint is redundant in its own
2006 * basic map and should be ignore and removed
2008 * valid all (integer) points of the other basic map
2009 * satisfy the constraint
2010 * separate no (integer) point of the other basic map
2011 * satisfies the constraint
2012 * cut some but not all points of the other basic map
2013 * satisfy the constraint
2014 * adj_eq the given constraint is adjacent (on the outside)
2015 * to an equality of the other basic map
2016 * adj_ineq the given constraint is adjacent (on the outside)
2017 * to an inequality of the other basic map
2019 * We consider seven cases in which we can replace the pair by a single
2020 * basic map. We ignore all "redundant" constraints.
2022 * 1. all constraints of one basic map are valid
2023 * => the other basic map is a subset and can be removed
2025 * 2. all constraints of both basic maps are either "valid" or "cut"
2026 * and the facets corresponding to the "cut" constraints
2027 * of one of the basic maps lies entirely inside the other basic map
2028 * => the pair can be replaced by a basic map consisting
2029 * of the valid constraints in both basic maps
2031 * 3. there is a single pair of adjacent inequalities
2032 * (all other constraints are "valid")
2033 * => the pair can be replaced by a basic map consisting
2034 * of the valid constraints in both basic maps
2036 * 4. one basic map has a single adjacent inequality, while the other
2037 * constraints are "valid". The other basic map has some
2038 * "cut" constraints, but replacing the adjacent inequality by
2039 * its opposite and adding the valid constraints of the other
2040 * basic map results in a subset of the other basic map
2041 * => the pair can be replaced by a basic map consisting
2042 * of the valid constraints in both basic maps
2044 * 5. there is a single adjacent pair of an inequality and an equality,
2045 * the other constraints of the basic map containing the inequality are
2046 * "valid". Moreover, if the inequality the basic map is relaxed
2047 * and then turned into an equality, then resulting facet lies
2048 * entirely inside the other basic map
2049 * => the pair can be replaced by the basic map containing
2050 * the inequality, with the inequality relaxed.
2052 * 6. there is a single adjacent pair of an inequality and an equality,
2053 * the other constraints of the basic map containing the inequality are
2054 * "valid". Moreover, the facets corresponding to both
2055 * the inequality and the equality can be wrapped around their
2056 * ridges to include the other basic map
2057 * => the pair can be replaced by a basic map consisting
2058 * of the valid constraints in both basic maps together
2059 * with all wrapping constraints
2061 * 7. one of the basic maps extends beyond the other by at most one.
2062 * Moreover, the facets corresponding to the cut constraints and
2063 * the pieces of the other basic map at offset one from these cut
2064 * constraints can be wrapped around their ridges to include
2065 * the union of the two basic maps
2066 * => the pair can be replaced by a basic map consisting
2067 * of the valid constraints in both basic maps together
2068 * with all wrapping constraints
2070 * 8. the two basic maps live in adjacent hyperplanes. In principle
2071 * such sets can always be combined through wrapping, but we impose
2072 * that there is only one such pair, to avoid overeager coalescing.
2074 * Throughout the computation, we maintain a collection of tableaus
2075 * corresponding to the basic maps. When the basic maps are dropped
2076 * or combined, the tableaus are modified accordingly.
2078 static enum isl_change
coalesce_local_pair_reuse(int i
, int j
,
2079 struct isl_coalesce_info
*info
)
2081 enum isl_change change
= isl_change_none
;
2083 set_eq_status_in(&info
[i
], info
[j
].tab
);
2084 if (info
[i
].bmap
->n_eq
&& !info
[i
].eq
)
2086 if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_ERROR
))
2088 if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_SEPARATE
))
2091 set_eq_status_in(&info
[j
], info
[i
].tab
);
2092 if (info
[j
].bmap
->n_eq
&& !info
[j
].eq
)
2094 if (any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_ERROR
))
2096 if (any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_SEPARATE
))
2099 set_ineq_status_in(&info
[i
], info
[j
].tab
);
2100 if (info
[i
].bmap
->n_ineq
&& !info
[i
].ineq
)
2102 if (any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ERROR
))
2104 if (any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_SEPARATE
))
2107 set_ineq_status_in(&info
[j
], info
[i
].tab
);
2108 if (info
[j
].bmap
->n_ineq
&& !info
[j
].ineq
)
2110 if (any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_ERROR
))
2112 if (any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_SEPARATE
))
2115 if (all(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_VALID
) &&
2116 all(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_VALID
)) {
2118 change
= isl_change_drop_second
;
2119 } else if (all(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_VALID
) &&
2120 all(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_VALID
)) {
2122 change
= isl_change_drop_first
;
2123 } else if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_ADJ_EQ
)) {
2124 change
= check_eq_adj_eq(i
, j
, info
);
2125 } else if (any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_ADJ_EQ
)) {
2126 change
= check_eq_adj_eq(j
, i
, info
);
2127 } else if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_ADJ_INEQ
) ||
2128 any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_ADJ_INEQ
)) {
2129 change
= check_adj_eq(i
, j
, info
);
2130 } else if (any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ADJ_EQ
) ||
2131 any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_ADJ_EQ
)) {
2134 } else if (any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ADJ_INEQ
) ||
2135 any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_ADJ_INEQ
)) {
2136 change
= check_adj_ineq(i
, j
, info
);
2138 if (!any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_CUT
) &&
2139 !any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_CUT
))
2140 change
= check_facets(i
, j
, info
);
2141 if (change
== isl_change_none
)
2142 change
= check_wrap(i
, j
, info
);
2146 clear_status(&info
[i
]);
2147 clear_status(&info
[j
]);
2150 clear_status(&info
[i
]);
2151 clear_status(&info
[j
]);
2152 return isl_change_error
;
2155 /* Check if the union of the given pair of basic maps
2156 * can be represented by a single basic map.
2157 * If so, replace the pair by the single basic map and return
2158 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
2159 * Otherwise, return isl_change_none.
2160 * The two basic maps are assumed to live in the same local space.
2162 static enum isl_change
coalesce_local_pair(int i
, int j
,
2163 struct isl_coalesce_info
*info
)
2165 init_status(&info
[i
]);
2166 init_status(&info
[j
]);
2167 return coalesce_local_pair_reuse(i
, j
, info
);
2170 /* Shift the integer division at position "div" of the basic map
2171 * represented by "info" by "shift".
2173 * That is, if the integer division has the form
2177 * then replace it by
2179 * floor((f(x) + shift * d)/d) - shift
2181 static int shift_div(struct isl_coalesce_info
*info
, int div
, isl_int shift
)
2185 info
->bmap
= isl_basic_map_shift_div(info
->bmap
, div
, 0, shift
);
2189 total
= isl_basic_map_dim(info
->bmap
, isl_dim_all
);
2190 total
-= isl_basic_map_dim(info
->bmap
, isl_dim_div
);
2191 if (isl_tab_shift_var(info
->tab
, total
+ div
, shift
) < 0)
2197 /* Check if some of the divs in the basic map represented by "info1"
2198 * are shifts of the corresponding divs in the basic map represented
2199 * by "info2". If so, align them with those of "info2".
2200 * Only do this if "info1" and "info2" have the same number
2201 * of integer divisions.
2203 * An integer division is considered to be a shift of another integer
2204 * division if one is equal to the other plus a constant.
2206 * In particular, for each pair of integer divisions, if both are known,
2207 * have identical coefficients (apart from the constant term) and
2208 * if the difference between the constant terms (taking into account
2209 * the denominator) is an integer, then move the difference outside.
2210 * That is, if one integer division is of the form
2212 * floor((f(x) + c_1)/d)
2214 * while the other is of the form
2216 * floor((f(x) + c_2)/d)
2218 * and n = (c_2 - c_1)/d is an integer, then replace the first
2219 * integer division by
2221 * floor((f(x) + c_1 + n * d)/d) - n = floor((f(x) + c_2)/d) - n
2223 static int harmonize_divs(struct isl_coalesce_info
*info1
,
2224 struct isl_coalesce_info
*info2
)
2229 if (!info1
->bmap
|| !info2
->bmap
)
2232 if (info1
->bmap
->n_div
!= info2
->bmap
->n_div
)
2234 if (info1
->bmap
->n_div
== 0)
2237 total
= isl_basic_map_total_dim(info1
->bmap
);
2238 for (i
= 0; i
< info1
->bmap
->n_div
; ++i
) {
2242 if (isl_int_is_zero(info1
->bmap
->div
[i
][0]) ||
2243 isl_int_is_zero(info2
->bmap
->div
[i
][0]))
2245 if (isl_int_ne(info1
->bmap
->div
[i
][0], info2
->bmap
->div
[i
][0]))
2247 if (isl_int_eq(info1
->bmap
->div
[i
][1], info2
->bmap
->div
[i
][1]))
2249 if (!isl_seq_eq(info1
->bmap
->div
[i
] + 2,
2250 info2
->bmap
->div
[i
] + 2, total
))
2253 isl_int_sub(d
, info2
->bmap
->div
[i
][1], info1
->bmap
->div
[i
][1]);
2254 if (isl_int_is_divisible_by(d
, info1
->bmap
->div
[i
][0])) {
2255 isl_int_divexact(d
, d
, info1
->bmap
->div
[i
][0]);
2256 r
= shift_div(info1
, i
, d
);
2266 /* Do the two basic maps live in the same local space, i.e.,
2267 * do they have the same (known) divs?
2268 * If either basic map has any unknown divs, then we can only assume
2269 * that they do not live in the same local space.
2271 static int same_divs(__isl_keep isl_basic_map
*bmap1
,
2272 __isl_keep isl_basic_map
*bmap2
)
2278 if (!bmap1
|| !bmap2
)
2280 if (bmap1
->n_div
!= bmap2
->n_div
)
2283 if (bmap1
->n_div
== 0)
2286 known
= isl_basic_map_divs_known(bmap1
);
2287 if (known
< 0 || !known
)
2289 known
= isl_basic_map_divs_known(bmap2
);
2290 if (known
< 0 || !known
)
2293 total
= isl_basic_map_total_dim(bmap1
);
2294 for (i
= 0; i
< bmap1
->n_div
; ++i
)
2295 if (!isl_seq_eq(bmap1
->div
[i
], bmap2
->div
[i
], 2 + total
))
2301 /* Assuming that "tab" contains the equality constraints and
2302 * the initial inequality constraints of "bmap", copy the remaining
2303 * inequality constraints of "bmap" to "Tab".
2305 static isl_stat
copy_ineq(struct isl_tab
*tab
, __isl_keep isl_basic_map
*bmap
)
2310 return isl_stat_error
;
2312 n_ineq
= tab
->n_con
- tab
->n_eq
;
2313 for (i
= n_ineq
; i
< bmap
->n_ineq
; ++i
)
2314 if (isl_tab_add_ineq(tab
, bmap
->ineq
[i
]) < 0)
2315 return isl_stat_error
;
2320 /* Description of an integer division that is added
2321 * during an expansion.
2322 * "pos" is the position of the corresponding variable.
2323 * "cst" indicates whether this integer division has a fixed value.
2324 * "val" contains the fixed value, if the value is fixed.
2326 struct isl_expanded
{
2332 /* For each of the "n" integer division variables "expanded",
2333 * if the variable has a fixed value, then add two inequality
2334 * constraints expressing the fixed value.
2335 * Otherwise, add the corresponding div constraints.
2336 * The caller is responsible for removing the div constraints
2337 * that it added for all these "n" integer divisions.
2339 * The div constraints and the pair of inequality constraints
2340 * forcing the fixed value cannot both be added for a given variable
2341 * as the combination may render some of the original constraints redundant.
2342 * These would then be ignored during the coalescing detection,
2343 * while they could remain in the fused result.
2345 * The two added inequality constraints are
2350 * with "a" the variable and "v" its fixed value.
2351 * The facet corresponding to one of these two constraints is selected
2352 * in the tableau to ensure that the pair of inequality constraints
2353 * is treated as an equality constraint.
2355 * The information in info->ineq is thrown away because it was
2356 * computed in terms of div constraints, while some of those
2357 * have now been replaced by these pairs of inequality constraints.
2359 static isl_stat
fix_constant_divs(struct isl_coalesce_info
*info
,
2360 int n
, struct isl_expanded
*expanded
)
2366 o_div
= isl_basic_map_offset(info
->bmap
, isl_dim_div
) - 1;
2367 ineq
= isl_vec_alloc(isl_tab_get_ctx(info
->tab
), 1 + info
->tab
->n_var
);
2369 return isl_stat_error
;
2370 isl_seq_clr(ineq
->el
+ 1, info
->tab
->n_var
);
2372 for (i
= 0; i
< n
; ++i
) {
2373 if (!expanded
[i
].cst
) {
2374 info
->bmap
= isl_basic_map_extend_constraints(
2376 if (isl_basic_map_add_div_constraints(info
->bmap
,
2377 expanded
[i
].pos
- o_div
) < 0)
2380 isl_int_set_si(ineq
->el
[1 + expanded
[i
].pos
], -1);
2381 isl_int_set(ineq
->el
[0], expanded
[i
].val
);
2382 info
->bmap
= isl_basic_map_add_ineq(info
->bmap
,
2384 isl_int_set_si(ineq
->el
[1 + expanded
[i
].pos
], 1);
2385 isl_int_neg(ineq
->el
[0], expanded
[i
].val
);
2386 info
->bmap
= isl_basic_map_add_ineq(info
->bmap
,
2388 isl_int_set_si(ineq
->el
[1 + expanded
[i
].pos
], 0);
2390 if (copy_ineq(info
->tab
, info
->bmap
) < 0)
2392 if (expanded
[i
].cst
&&
2393 isl_tab_select_facet(info
->tab
, info
->tab
->n_con
- 1) < 0)
2402 return i
< n
? isl_stat_error
: isl_stat_ok
;
2405 /* Insert the "n" integer division variables "expanded"
2406 * into info->tab and info->bmap and
2407 * update info->ineq with respect to the redundant constraints
2408 * in the resulting tableau.
2409 * "bmap" contains the result of this insertion in info->bmap,
2410 * while info->bmap is the original version
2411 * of "bmap", i.e., the one that corresponds to the current
2412 * state of info->tab. The number of constraints in info->bmap
2413 * is assumed to be the same as the number of constraints
2414 * in info->tab. This is required to be able to detect
2415 * the extra constraints in "bmap".
2417 * In particular, introduce extra variables corresponding
2418 * to the extra integer divisions and add the div constraints
2419 * that were added to "bmap" after info->tab was created
2421 * Furthermore, check if these extra integer divisions happen
2422 * to attain a fixed integer value in info->tab.
2423 * If so, replace the corresponding div constraints by pairs
2424 * of inequality constraints that fix these
2425 * integer divisions to their single integer values.
2426 * Replace info->bmap by "bmap" to match the changes to info->tab.
2427 * info->ineq was computed without a tableau and therefore
2428 * does not take into account the redundant constraints
2429 * in the tableau. Mark them here.
2430 * There is no need to check the newly added div constraints
2431 * since they cannot be redundant.
2432 * The redundancy check is not performed when constants have been discovered
2433 * since info->ineq is completely thrown away in this case.
2435 static isl_stat
tab_insert_divs(struct isl_coalesce_info
*info
,
2436 int n
, struct isl_expanded
*expanded
, __isl_take isl_basic_map
*bmap
)
2440 struct isl_tab_undo
*snap
;
2444 return isl_stat_error
;
2445 if (info
->bmap
->n_eq
+ info
->bmap
->n_ineq
!= info
->tab
->n_con
)
2446 isl_die(isl_basic_map_get_ctx(bmap
), isl_error_internal
,
2447 "original tableau does not correspond "
2448 "to original basic map", goto error
);
2450 if (isl_tab_extend_vars(info
->tab
, n
) < 0)
2452 if (isl_tab_extend_cons(info
->tab
, 2 * n
) < 0)
2455 for (i
= 0; i
< n
; ++i
) {
2456 if (isl_tab_insert_var(info
->tab
, expanded
[i
].pos
) < 0)
2460 snap
= isl_tab_snap(info
->tab
);
2462 n_ineq
= info
->tab
->n_con
- info
->tab
->n_eq
;
2463 if (copy_ineq(info
->tab
, bmap
) < 0)
2466 isl_basic_map_free(info
->bmap
);
2470 for (i
= 0; i
< n
; ++i
) {
2471 expanded
[i
].cst
= isl_tab_is_constant(info
->tab
,
2472 expanded
[i
].pos
, &expanded
[i
].val
);
2473 if (expanded
[i
].cst
< 0)
2474 return isl_stat_error
;
2475 if (expanded
[i
].cst
)
2480 if (isl_tab_rollback(info
->tab
, snap
) < 0)
2481 return isl_stat_error
;
2482 info
->bmap
= isl_basic_map_cow(info
->bmap
);
2483 if (isl_basic_map_free_inequality(info
->bmap
, 2 * n
) < 0)
2484 return isl_stat_error
;
2486 return fix_constant_divs(info
, n
, expanded
);
2489 n_eq
= info
->bmap
->n_eq
;
2490 for (i
= 0; i
< n_ineq
; ++i
) {
2491 if (isl_tab_is_redundant(info
->tab
, n_eq
+ i
))
2492 info
->ineq
[i
] = STATUS_REDUNDANT
;
2497 isl_basic_map_free(bmap
);
2498 return isl_stat_error
;
2501 /* Expand info->tab and info->bmap in the same way "bmap" was expanded
2502 * in isl_basic_map_expand_divs using the expansion "exp" and
2503 * update info->ineq with respect to the redundant constraints
2504 * in the resulting tableau. info->bmap is the original version
2505 * of "bmap", i.e., the one that corresponds to the current
2506 * state of info->tab. The number of constraints in info->bmap
2507 * is assumed to be the same as the number of constraints
2508 * in info->tab. This is required to be able to detect
2509 * the extra constraints in "bmap".
2511 * Extract the positions where extra local variables are introduced
2512 * from "exp" and call tab_insert_divs.
2514 static isl_stat
expand_tab(struct isl_coalesce_info
*info
, int *exp
,
2515 __isl_take isl_basic_map
*bmap
)
2518 struct isl_expanded
*expanded
;
2521 unsigned total
, pos
, n_div
;
2524 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
2525 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
2526 pos
= total
- n_div
;
2527 extra_var
= total
- info
->tab
->n_var
;
2528 n
= n_div
- extra_var
;
2530 ctx
= isl_basic_map_get_ctx(bmap
);
2531 expanded
= isl_calloc_array(ctx
, struct isl_expanded
, extra_var
);
2532 if (extra_var
&& !expanded
)
2537 for (j
= 0; j
< n_div
; ++j
) {
2538 if (i
< n
&& exp
[i
] == j
) {
2542 expanded
[k
++].pos
= pos
+ j
;
2545 for (k
= 0; k
< extra_var
; ++k
)
2546 isl_int_init(expanded
[k
].val
);
2548 r
= tab_insert_divs(info
, extra_var
, expanded
, bmap
);
2550 for (k
= 0; k
< extra_var
; ++k
)
2551 isl_int_clear(expanded
[k
].val
);
2556 isl_basic_map_free(bmap
);
2557 return isl_stat_error
;
2560 /* Check if the union of the basic maps represented by info[i] and info[j]
2561 * can be represented by a single basic map,
2562 * after expanding the divs of info[i] to match those of info[j].
2563 * If so, replace the pair by the single basic map and return
2564 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
2565 * Otherwise, return isl_change_none.
2567 * The caller has already checked for info[j] being a subset of info[i].
2568 * If some of the divs of info[j] are unknown, then the expanded info[i]
2569 * will not have the corresponding div constraints. The other patterns
2570 * therefore cannot apply. Skip the computation in this case.
2572 * The expansion is performed using the divs "div" and expansion "exp"
2573 * computed by the caller.
2574 * info[i].bmap has already been expanded and the result is passed in
2576 * The "eq" and "ineq" fields of info[i] reflect the status of
2577 * the constraints of the expanded "bmap" with respect to info[j].tab.
2578 * However, inequality constraints that are redundant in info[i].tab
2579 * have not yet been marked as such because no tableau was available.
2581 * Replace info[i].bmap by "bmap" and expand info[i].tab as well,
2582 * updating info[i].ineq with respect to the redundant constraints.
2583 * Then try and coalesce the expanded info[i] with info[j],
2584 * reusing the information in info[i].eq and info[i].ineq.
2585 * If this does not result in any coalescing or if it results in info[j]
2586 * getting dropped (which should not happen in practice, since the case
2587 * of info[j] being a subset of info[i] has already been checked by
2588 * the caller), then revert info[i] to its original state.
2590 static enum isl_change
coalesce_expand_tab_divs(__isl_take isl_basic_map
*bmap
,
2591 int i
, int j
, struct isl_coalesce_info
*info
, __isl_keep isl_mat
*div
,
2595 isl_basic_map
*bmap_i
;
2596 struct isl_tab_undo
*snap
;
2597 enum isl_change change
= isl_change_none
;
2599 known
= isl_basic_map_divs_known(info
[j
].bmap
);
2600 if (known
< 0 || !known
) {
2601 clear_status(&info
[i
]);
2602 isl_basic_map_free(bmap
);
2603 return known
< 0 ? isl_change_error
: isl_change_none
;
2606 bmap_i
= isl_basic_map_copy(info
[i
].bmap
);
2607 snap
= isl_tab_snap(info
[i
].tab
);
2608 if (expand_tab(&info
[i
], exp
, bmap
) < 0)
2609 change
= isl_change_error
;
2611 init_status(&info
[j
]);
2612 if (change
== isl_change_none
)
2613 change
= coalesce_local_pair_reuse(i
, j
, info
);
2615 clear_status(&info
[i
]);
2616 if (change
!= isl_change_none
&& change
!= isl_change_drop_second
) {
2617 isl_basic_map_free(bmap_i
);
2619 isl_basic_map_free(info
[i
].bmap
);
2620 info
[i
].bmap
= bmap_i
;
2622 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
2623 change
= isl_change_error
;
2629 /* Check if the union of "bmap" and the basic map represented by info[j]
2630 * can be represented by a single basic map,
2631 * after expanding the divs of "bmap" to match those of info[j].
2632 * If so, replace the pair by the single basic map and return
2633 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
2634 * Otherwise, return isl_change_none.
2636 * In particular, check if the expanded "bmap" contains the basic map
2637 * represented by the tableau info[j].tab.
2638 * The expansion is performed using the divs "div" and expansion "exp"
2639 * computed by the caller.
2640 * Then we check if all constraints of the expanded "bmap" are valid for
2643 * If "i" is not equal to -1, then "bmap" is equal to info[i].bmap.
2644 * In this case, the positions of the constraints of info[i].bmap
2645 * with respect to the basic map represented by info[j] are stored
2648 * If the expanded "bmap" does not contain the basic map
2649 * represented by the tableau info[j].tab and if "i" is not -1,
2650 * i.e., if the original "bmap" is info[i].bmap, then expand info[i].tab
2651 * as well and check if that results in coalescing.
2653 static enum isl_change
coalesce_with_expanded_divs(
2654 __isl_keep isl_basic_map
*bmap
, int i
, int j
,
2655 struct isl_coalesce_info
*info
, __isl_keep isl_mat
*div
, int *exp
)
2657 enum isl_change change
= isl_change_none
;
2658 struct isl_coalesce_info info_local
, *info_i
;
2660 info_i
= i
>= 0 ? &info
[i
] : &info_local
;
2661 init_status(info_i
);
2662 bmap
= isl_basic_map_copy(bmap
);
2663 bmap
= isl_basic_map_expand_divs(bmap
, isl_mat_copy(div
), exp
);
2664 bmap
= isl_basic_map_mark_final(bmap
);
2669 info_i
->eq
= eq_status_in(bmap
, info
[j
].tab
);
2670 if (bmap
->n_eq
&& !info_i
->eq
)
2672 if (any(info_i
->eq
, 2 * bmap
->n_eq
, STATUS_ERROR
))
2674 if (any(info_i
->eq
, 2 * bmap
->n_eq
, STATUS_SEPARATE
))
2677 info_i
->ineq
= ineq_status_in(bmap
, NULL
, info
[j
].tab
);
2678 if (bmap
->n_ineq
&& !info_i
->ineq
)
2680 if (any(info_i
->ineq
, bmap
->n_ineq
, STATUS_ERROR
))
2682 if (any(info_i
->ineq
, bmap
->n_ineq
, STATUS_SEPARATE
))
2685 if (all(info_i
->eq
, 2 * bmap
->n_eq
, STATUS_VALID
) &&
2686 all(info_i
->ineq
, bmap
->n_ineq
, STATUS_VALID
)) {
2688 change
= isl_change_drop_second
;
2691 if (change
== isl_change_none
&& i
!= -1)
2692 return coalesce_expand_tab_divs(bmap
, i
, j
, info
, div
, exp
);
2695 isl_basic_map_free(bmap
);
2696 clear_status(info_i
);
2699 isl_basic_map_free(bmap
);
2700 clear_status(info_i
);
2701 return isl_change_error
;
2704 /* Check if the union of "bmap_i" and the basic map represented by info[j]
2705 * can be represented by a single basic map,
2706 * after aligning the divs of "bmap_i" to match those of info[j].
2707 * If so, replace the pair by the single basic map and return
2708 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
2709 * Otherwise, return isl_change_none.
2711 * In particular, check if "bmap_i" contains the basic map represented by
2712 * info[j] after aligning the divs of "bmap_i" to those of info[j].
2713 * Note that this can only succeed if the number of divs of "bmap_i"
2714 * is smaller than (or equal to) the number of divs of info[j].
2716 * We first check if the divs of "bmap_i" are all known and form a subset
2717 * of those of info[j].bmap. If so, we pass control over to
2718 * coalesce_with_expanded_divs.
2720 * If "i" is not equal to -1, then "bmap" is equal to info[i].bmap.
2722 static enum isl_change
coalesce_after_aligning_divs(
2723 __isl_keep isl_basic_map
*bmap_i
, int i
, int j
,
2724 struct isl_coalesce_info
*info
)
2727 isl_mat
*div_i
, *div_j
, *div
;
2731 enum isl_change change
;
2733 known
= isl_basic_map_divs_known(bmap_i
);
2734 if (known
< 0 || !known
)
2737 ctx
= isl_basic_map_get_ctx(bmap_i
);
2739 div_i
= isl_basic_map_get_divs(bmap_i
);
2740 div_j
= isl_basic_map_get_divs(info
[j
].bmap
);
2742 if (!div_i
|| !div_j
)
2745 exp1
= isl_alloc_array(ctx
, int, div_i
->n_row
);
2746 exp2
= isl_alloc_array(ctx
, int, div_j
->n_row
);
2747 if ((div_i
->n_row
&& !exp1
) || (div_j
->n_row
&& !exp2
))
2750 div
= isl_merge_divs(div_i
, div_j
, exp1
, exp2
);
2754 if (div
->n_row
== div_j
->n_row
)
2755 change
= coalesce_with_expanded_divs(bmap_i
,
2756 i
, j
, info
, div
, exp1
);
2758 change
= isl_change_none
;
2762 isl_mat_free(div_i
);
2763 isl_mat_free(div_j
);
2770 isl_mat_free(div_i
);
2771 isl_mat_free(div_j
);
2774 return isl_change_error
;
2777 /* Check if basic map "j" is a subset of basic map "i" after
2778 * exploiting the extra equalities of "j" to simplify the divs of "i".
2779 * If so, remove basic map "j" and return isl_change_drop_second.
2781 * If "j" does not have any equalities or if they are the same
2782 * as those of "i", then we cannot exploit them to simplify the divs.
2783 * Similarly, if there are no divs in "i", then they cannot be simplified.
2784 * If, on the other hand, the affine hulls of "i" and "j" do not intersect,
2785 * then "j" cannot be a subset of "i".
2787 * Otherwise, we intersect "i" with the affine hull of "j" and then
2788 * check if "j" is a subset of the result after aligning the divs.
2789 * If so, then "j" is definitely a subset of "i" and can be removed.
2790 * Note that if after intersection with the affine hull of "j".
2791 * "i" still has more divs than "j", then there is no way we can
2792 * align the divs of "i" to those of "j".
2794 static enum isl_change
coalesce_subset_with_equalities(int i
, int j
,
2795 struct isl_coalesce_info
*info
)
2797 isl_basic_map
*hull_i
, *hull_j
, *bmap_i
;
2799 enum isl_change change
;
2801 if (info
[j
].bmap
->n_eq
== 0)
2802 return isl_change_none
;
2803 if (info
[i
].bmap
->n_div
== 0)
2804 return isl_change_none
;
2806 hull_i
= isl_basic_map_copy(info
[i
].bmap
);
2807 hull_i
= isl_basic_map_plain_affine_hull(hull_i
);
2808 hull_j
= isl_basic_map_copy(info
[j
].bmap
);
2809 hull_j
= isl_basic_map_plain_affine_hull(hull_j
);
2811 hull_j
= isl_basic_map_intersect(hull_j
, isl_basic_map_copy(hull_i
));
2812 equal
= isl_basic_map_plain_is_equal(hull_i
, hull_j
);
2813 empty
= isl_basic_map_plain_is_empty(hull_j
);
2814 isl_basic_map_free(hull_i
);
2816 if (equal
< 0 || equal
|| empty
< 0 || empty
) {
2817 isl_basic_map_free(hull_j
);
2818 if (equal
< 0 || empty
< 0)
2819 return isl_change_error
;
2820 return isl_change_none
;
2823 bmap_i
= isl_basic_map_copy(info
[i
].bmap
);
2824 bmap_i
= isl_basic_map_intersect(bmap_i
, hull_j
);
2826 return isl_change_error
;
2828 if (bmap_i
->n_div
> info
[j
].bmap
->n_div
) {
2829 isl_basic_map_free(bmap_i
);
2830 return isl_change_none
;
2833 change
= coalesce_after_aligning_divs(bmap_i
, -1, j
, info
);
2835 isl_basic_map_free(bmap_i
);
2840 /* Check if the union of and the basic maps represented by info[i] and info[j]
2841 * can be represented by a single basic map, by aligning or equating
2842 * their integer divisions.
2843 * If so, replace the pair by the single basic map and return
2844 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
2845 * Otherwise, return isl_change_none.
2847 * Note that we only perform any test if the number of divs is different
2848 * in the two basic maps. In case the number of divs is the same,
2849 * we have already established that the divs are different
2850 * in the two basic maps.
2851 * In particular, if the number of divs of basic map i is smaller than
2852 * the number of divs of basic map j, then we check if j is a subset of i
2855 static enum isl_change
coalesce_divs(int i
, int j
,
2856 struct isl_coalesce_info
*info
)
2858 enum isl_change change
= isl_change_none
;
2860 if (info
[i
].bmap
->n_div
< info
[j
].bmap
->n_div
)
2861 change
= coalesce_after_aligning_divs(info
[i
].bmap
, i
, j
, info
);
2862 if (change
!= isl_change_none
)
2865 if (info
[j
].bmap
->n_div
< info
[i
].bmap
->n_div
)
2866 change
= coalesce_after_aligning_divs(info
[j
].bmap
, j
, i
, info
);
2867 if (change
!= isl_change_none
)
2868 return invert_change(change
);
2870 change
= coalesce_subset_with_equalities(i
, j
, info
);
2871 if (change
!= isl_change_none
)
2874 change
= coalesce_subset_with_equalities(j
, i
, info
);
2875 if (change
!= isl_change_none
)
2876 return invert_change(change
);
2878 return isl_change_none
;
2881 /* Does "bmap" involve any divs that themselves refer to divs?
2883 static int has_nested_div(__isl_keep isl_basic_map
*bmap
)
2889 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
2890 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
2893 for (i
= 0; i
< n_div
; ++i
)
2894 if (isl_seq_first_non_zero(bmap
->div
[i
] + 2 + total
,
2901 /* Return a list of affine expressions, one for each integer division
2902 * in "bmap_i". For each integer division that also appears in "bmap_j",
2903 * the affine expression is set to NaN. The number of NaNs in the list
2904 * is equal to the number of integer divisions in "bmap_j".
2905 * For the other integer divisions of "bmap_i", the corresponding
2906 * element in the list is a purely affine expression equal to the integer
2907 * division in "hull".
2908 * If no such list can be constructed, then the number of elements
2909 * in the returned list is smaller than the number of integer divisions
2912 static __isl_give isl_aff_list
*set_up_substitutions(
2913 __isl_keep isl_basic_map
*bmap_i
, __isl_keep isl_basic_map
*bmap_j
,
2914 __isl_take isl_basic_map
*hull
)
2916 unsigned n_div_i
, n_div_j
, total
;
2918 isl_local_space
*ls
;
2919 isl_basic_set
*wrap_hull
;
2927 ctx
= isl_basic_map_get_ctx(hull
);
2929 n_div_i
= isl_basic_map_dim(bmap_i
, isl_dim_div
);
2930 n_div_j
= isl_basic_map_dim(bmap_j
, isl_dim_div
);
2931 total
= isl_basic_map_total_dim(bmap_i
) - n_div_i
;
2933 ls
= isl_basic_map_get_local_space(bmap_i
);
2934 ls
= isl_local_space_wrap(ls
);
2935 wrap_hull
= isl_basic_map_wrap(hull
);
2937 aff_nan
= isl_aff_nan_on_domain(isl_local_space_copy(ls
));
2938 list
= isl_aff_list_alloc(ctx
, n_div_i
);
2941 for (i
= 0; i
< n_div_i
; ++i
) {
2945 isl_seq_eq(bmap_i
->div
[i
], bmap_j
->div
[j
], 2 + total
)) {
2947 list
= isl_aff_list_add(list
, isl_aff_copy(aff_nan
));
2950 if (n_div_i
- i
<= n_div_j
- j
)
2953 aff
= isl_local_space_get_div(ls
, i
);
2954 aff
= isl_aff_substitute_equalities(aff
,
2955 isl_basic_set_copy(wrap_hull
));
2956 aff
= isl_aff_floor(aff
);
2959 if (isl_aff_dim(aff
, isl_dim_div
) != 0) {
2964 list
= isl_aff_list_add(list
, aff
);
2967 isl_aff_free(aff_nan
);
2968 isl_local_space_free(ls
);
2969 isl_basic_set_free(wrap_hull
);
2973 isl_aff_free(aff_nan
);
2974 isl_local_space_free(ls
);
2975 isl_basic_set_free(wrap_hull
);
2976 isl_aff_list_free(list
);
2980 /* Add variables to info->bmap and info->tab corresponding to the elements
2981 * in "list" that are not set to NaN.
2982 * "extra_var" is the number of these elements.
2983 * "dim" is the offset in the variables of "tab" where we should
2984 * start considering the elements in "list".
2985 * When this function returns, the total number of variables in "tab"
2986 * is equal to "dim" plus the number of elements in "list".
2988 * The newly added existentially quantified variables are not given
2989 * an explicit representation because the corresponding div constraints
2990 * do not appear in info->bmap. These constraints are not added
2991 * to info->bmap because for internal consistency, they would need to
2992 * be added to info->tab as well, where they could combine with the equality
2993 * that is added later to result in constraints that do not hold
2994 * in the original input.
2996 static int add_sub_vars(struct isl_coalesce_info
*info
,
2997 __isl_keep isl_aff_list
*list
, int dim
, int extra_var
)
3002 space
= isl_basic_map_get_space(info
->bmap
);
3003 info
->bmap
= isl_basic_map_cow(info
->bmap
);
3004 info
->bmap
= isl_basic_map_extend_space(info
->bmap
, space
,
3008 n
= isl_aff_list_n_aff(list
);
3009 for (i
= 0; i
< n
; ++i
) {
3013 aff
= isl_aff_list_get_aff(list
, i
);
3014 is_nan
= isl_aff_is_nan(aff
);
3021 if (isl_tab_insert_var(info
->tab
, dim
+ i
) < 0)
3023 d
= isl_basic_map_alloc_div(info
->bmap
);
3026 info
->bmap
= isl_basic_map_mark_div_unknown(info
->bmap
, d
);
3029 for (j
= d
; j
> i
; --j
)
3030 isl_basic_map_swap_div(info
->bmap
, j
- 1, j
);
3036 /* For each element in "list" that is not set to NaN, fix the corresponding
3037 * variable in "tab" to the purely affine expression defined by the element.
3038 * "dim" is the offset in the variables of "tab" where we should
3039 * start considering the elements in "list".
3041 * This function assumes that a sufficient number of rows and
3042 * elements in the constraint array are available in the tableau.
3044 static int add_sub_equalities(struct isl_tab
*tab
,
3045 __isl_keep isl_aff_list
*list
, int dim
)
3052 n
= isl_aff_list_n_aff(list
);
3054 ctx
= isl_tab_get_ctx(tab
);
3055 sub
= isl_vec_alloc(ctx
, 1 + dim
+ n
);
3058 isl_seq_clr(sub
->el
+ 1 + dim
, n
);
3060 for (i
= 0; i
< n
; ++i
) {
3061 aff
= isl_aff_list_get_aff(list
, i
);
3064 if (isl_aff_is_nan(aff
)) {
3068 isl_seq_cpy(sub
->el
, aff
->v
->el
+ 1, 1 + dim
);
3069 isl_int_neg(sub
->el
[1 + dim
+ i
], aff
->v
->el
[0]);
3070 if (isl_tab_add_eq(tab
, sub
->el
) < 0)
3072 isl_int_set_si(sub
->el
[1 + dim
+ i
], 0);
3084 /* Add variables to info->tab and info->bmap corresponding to the elements
3085 * in "list" that are not set to NaN. The value of the added variable
3086 * in info->tab is fixed to the purely affine expression defined by the element.
3087 * "dim" is the offset in the variables of info->tab where we should
3088 * start considering the elements in "list".
3089 * When this function returns, the total number of variables in info->tab
3090 * is equal to "dim" plus the number of elements in "list".
3092 static int add_subs(struct isl_coalesce_info
*info
,
3093 __isl_keep isl_aff_list
*list
, int dim
)
3101 n
= isl_aff_list_n_aff(list
);
3102 extra_var
= n
- (info
->tab
->n_var
- dim
);
3104 if (isl_tab_extend_vars(info
->tab
, extra_var
) < 0)
3106 if (isl_tab_extend_cons(info
->tab
, 2 * extra_var
) < 0)
3108 if (add_sub_vars(info
, list
, dim
, extra_var
) < 0)
3111 return add_sub_equalities(info
->tab
, list
, dim
);
3114 /* Coalesce basic map "j" into basic map "i" after adding the extra integer
3115 * divisions in "i" but not in "j" to basic map "j", with values
3116 * specified by "list". The total number of elements in "list"
3117 * is equal to the number of integer divisions in "i", while the number
3118 * of NaN elements in the list is equal to the number of integer divisions
3121 * If no coalescing can be performed, then we need to revert basic map "j"
3122 * to its original state. We do the same if basic map "i" gets dropped
3123 * during the coalescing, even though this should not happen in practice
3124 * since we have already checked for "j" being a subset of "i"
3125 * before we reach this stage.
3127 static enum isl_change
coalesce_with_subs(int i
, int j
,
3128 struct isl_coalesce_info
*info
, __isl_keep isl_aff_list
*list
)
3130 isl_basic_map
*bmap_j
;
3131 struct isl_tab_undo
*snap
;
3133 enum isl_change change
;
3135 bmap_j
= isl_basic_map_copy(info
[j
].bmap
);
3136 snap
= isl_tab_snap(info
[j
].tab
);
3138 dim
= isl_basic_map_dim(bmap_j
, isl_dim_all
);
3139 dim
-= isl_basic_map_dim(bmap_j
, isl_dim_div
);
3140 if (add_subs(&info
[j
], list
, dim
) < 0)
3143 change
= coalesce_local_pair(i
, j
, info
);
3144 if (change
!= isl_change_none
&& change
!= isl_change_drop_first
) {
3145 isl_basic_map_free(bmap_j
);
3147 isl_basic_map_free(info
[j
].bmap
);
3148 info
[j
].bmap
= bmap_j
;
3150 if (isl_tab_rollback(info
[j
].tab
, snap
) < 0)
3151 return isl_change_error
;
3156 isl_basic_map_free(bmap_j
);
3157 return isl_change_error
;
3160 /* Check if we can coalesce basic map "j" into basic map "i" after copying
3161 * those extra integer divisions in "i" that can be simplified away
3162 * using the extra equalities in "j".
3163 * All divs are assumed to be known and not contain any nested divs.
3165 * We first check if there are any extra equalities in "j" that we
3166 * can exploit. Then we check if every integer division in "i"
3167 * either already appears in "j" or can be simplified using the
3168 * extra equalities to a purely affine expression.
3169 * If these tests succeed, then we try to coalesce the two basic maps
3170 * by introducing extra dimensions in "j" corresponding to
3171 * the extra integer divsisions "i" fixed to the corresponding
3172 * purely affine expression.
3174 static enum isl_change
check_coalesce_into_eq(int i
, int j
,
3175 struct isl_coalesce_info
*info
)
3177 unsigned n_div_i
, n_div_j
;
3178 isl_basic_map
*hull_i
, *hull_j
;
3181 enum isl_change change
;
3183 n_div_i
= isl_basic_map_dim(info
[i
].bmap
, isl_dim_div
);
3184 n_div_j
= isl_basic_map_dim(info
[j
].bmap
, isl_dim_div
);
3185 if (n_div_i
<= n_div_j
)
3186 return isl_change_none
;
3187 if (info
[j
].bmap
->n_eq
== 0)
3188 return isl_change_none
;
3190 hull_i
= isl_basic_map_copy(info
[i
].bmap
);
3191 hull_i
= isl_basic_map_plain_affine_hull(hull_i
);
3192 hull_j
= isl_basic_map_copy(info
[j
].bmap
);
3193 hull_j
= isl_basic_map_plain_affine_hull(hull_j
);
3195 hull_j
= isl_basic_map_intersect(hull_j
, isl_basic_map_copy(hull_i
));
3196 equal
= isl_basic_map_plain_is_equal(hull_i
, hull_j
);
3197 empty
= isl_basic_map_plain_is_empty(hull_j
);
3198 isl_basic_map_free(hull_i
);
3200 if (equal
< 0 || empty
< 0)
3202 if (equal
|| empty
) {
3203 isl_basic_map_free(hull_j
);
3204 return isl_change_none
;
3207 list
= set_up_substitutions(info
[i
].bmap
, info
[j
].bmap
, hull_j
);
3209 return isl_change_error
;
3210 if (isl_aff_list_n_aff(list
) < n_div_i
)
3211 change
= isl_change_none
;
3213 change
= coalesce_with_subs(i
, j
, info
, list
);
3215 isl_aff_list_free(list
);
3219 isl_basic_map_free(hull_j
);
3220 return isl_change_error
;
3223 /* Check if we can coalesce basic maps "i" and "j" after copying
3224 * those extra integer divisions in one of the basic maps that can
3225 * be simplified away using the extra equalities in the other basic map.
3226 * We require all divs to be known in both basic maps.
3227 * Furthermore, to simplify the comparison of div expressions,
3228 * we do not allow any nested integer divisions.
3230 static enum isl_change
check_coalesce_eq(int i
, int j
,
3231 struct isl_coalesce_info
*info
)
3234 enum isl_change change
;
3236 known
= isl_basic_map_divs_known(info
[i
].bmap
);
3237 if (known
< 0 || !known
)
3238 return known
< 0 ? isl_change_error
: isl_change_none
;
3239 known
= isl_basic_map_divs_known(info
[j
].bmap
);
3240 if (known
< 0 || !known
)
3241 return known
< 0 ? isl_change_error
: isl_change_none
;
3242 nested
= has_nested_div(info
[i
].bmap
);
3243 if (nested
< 0 || nested
)
3244 return nested
< 0 ? isl_change_error
: isl_change_none
;
3245 nested
= has_nested_div(info
[j
].bmap
);
3246 if (nested
< 0 || nested
)
3247 return nested
< 0 ? isl_change_error
: isl_change_none
;
3249 change
= check_coalesce_into_eq(i
, j
, info
);
3250 if (change
!= isl_change_none
)
3252 change
= check_coalesce_into_eq(j
, i
, info
);
3253 if (change
!= isl_change_none
)
3254 return invert_change(change
);
3256 return isl_change_none
;
3259 /* Check if the union of the given pair of basic maps
3260 * can be represented by a single basic map.
3261 * If so, replace the pair by the single basic map and return
3262 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
3263 * Otherwise, return isl_change_none.
3265 * We first check if the two basic maps live in the same local space,
3266 * after aligning the divs that differ by only an integer constant.
3267 * If so, we do the complete check. Otherwise, we check if they have
3268 * the same number of integer divisions and can be coalesced, if one is
3269 * an obvious subset of the other or if the extra integer divisions
3270 * of one basic map can be simplified away using the extra equalities
3271 * of the other basic map.
3273 static enum isl_change
coalesce_pair(int i
, int j
,
3274 struct isl_coalesce_info
*info
)
3277 enum isl_change change
;
3279 if (harmonize_divs(&info
[i
], &info
[j
]) < 0)
3280 return isl_change_error
;
3281 same
= same_divs(info
[i
].bmap
, info
[j
].bmap
);
3283 return isl_change_error
;
3285 return coalesce_local_pair(i
, j
, info
);
3287 if (info
[i
].bmap
->n_div
== info
[j
].bmap
->n_div
) {
3288 change
= coalesce_local_pair(i
, j
, info
);
3289 if (change
!= isl_change_none
)
3293 change
= coalesce_divs(i
, j
, info
);
3294 if (change
!= isl_change_none
)
3297 return check_coalesce_eq(i
, j
, info
);
3300 /* Return the maximum of "a" and "b".
3302 static int isl_max(int a
, int b
)
3304 return a
> b
? a
: b
;
3307 /* Pairwise coalesce the basic maps in the range [start1, end1[ of "info"
3308 * with those in the range [start2, end2[, skipping basic maps
3309 * that have been removed (either before or within this function).
3311 * For each basic map i in the first range, we check if it can be coalesced
3312 * with respect to any previously considered basic map j in the second range.
3313 * If i gets dropped (because it was a subset of some j), then
3314 * we can move on to the next basic map.
3315 * If j gets dropped, we need to continue checking against the other
3316 * previously considered basic maps.
3317 * If the two basic maps got fused, then we recheck the fused basic map
3318 * against the previously considered basic maps, starting at i + 1
3319 * (even if start2 is greater than i + 1).
3321 static int coalesce_range(isl_ctx
*ctx
, struct isl_coalesce_info
*info
,
3322 int start1
, int end1
, int start2
, int end2
)
3326 for (i
= end1
- 1; i
>= start1
; --i
) {
3327 if (info
[i
].removed
)
3329 for (j
= isl_max(i
+ 1, start2
); j
< end2
; ++j
) {
3330 enum isl_change changed
;
3332 if (info
[j
].removed
)
3334 if (info
[i
].removed
)
3335 isl_die(ctx
, isl_error_internal
,
3336 "basic map unexpectedly removed",
3338 changed
= coalesce_pair(i
, j
, info
);
3340 case isl_change_error
:
3342 case isl_change_none
:
3343 case isl_change_drop_second
:
3345 case isl_change_drop_first
:
3348 case isl_change_fuse
:
3358 /* Pairwise coalesce the basic maps described by the "n" elements of "info".
3360 * We consider groups of basic maps that live in the same apparent
3361 * affine hull and we first coalesce within such a group before we
3362 * coalesce the elements in the group with elements of previously
3363 * considered groups. If a fuse happens during the second phase,
3364 * then we also reconsider the elements within the group.
3366 static int coalesce(isl_ctx
*ctx
, int n
, struct isl_coalesce_info
*info
)
3370 for (end
= n
; end
> 0; end
= start
) {
3372 while (start
>= 1 &&
3373 info
[start
- 1].hull_hash
== info
[start
].hull_hash
)
3375 if (coalesce_range(ctx
, info
, start
, end
, start
, end
) < 0)
3377 if (coalesce_range(ctx
, info
, start
, end
, end
, n
) < 0)
3384 /* Update the basic maps in "map" based on the information in "info".
3385 * In particular, remove the basic maps that have been marked removed and
3386 * update the others based on the information in the corresponding tableau.
3387 * Since we detected implicit equalities without calling
3388 * isl_basic_map_gauss, we need to do it now.
3389 * Also call isl_basic_map_simplify if we may have lost the definition
3390 * of one or more integer divisions.
3392 static __isl_give isl_map
*update_basic_maps(__isl_take isl_map
*map
,
3393 int n
, struct isl_coalesce_info
*info
)
3400 for (i
= n
- 1; i
>= 0; --i
) {
3401 if (info
[i
].removed
) {
3402 isl_basic_map_free(map
->p
[i
]);
3403 if (i
!= map
->n
- 1)
3404 map
->p
[i
] = map
->p
[map
->n
- 1];
3409 info
[i
].bmap
= isl_basic_map_update_from_tab(info
[i
].bmap
,
3411 info
[i
].bmap
= isl_basic_map_gauss(info
[i
].bmap
, NULL
);
3412 if (info
[i
].simplify
)
3413 info
[i
].bmap
= isl_basic_map_simplify(info
[i
].bmap
);
3414 info
[i
].bmap
= isl_basic_map_finalize(info
[i
].bmap
);
3416 return isl_map_free(map
);
3417 ISL_F_SET(info
[i
].bmap
, ISL_BASIC_MAP_NO_IMPLICIT
);
3418 ISL_F_SET(info
[i
].bmap
, ISL_BASIC_MAP_NO_REDUNDANT
);
3419 isl_basic_map_free(map
->p
[i
]);
3420 map
->p
[i
] = info
[i
].bmap
;
3421 info
[i
].bmap
= NULL
;
3427 /* For each pair of basic maps in the map, check if the union of the two
3428 * can be represented by a single basic map.
3429 * If so, replace the pair by the single basic map and start over.
3431 * We factor out any (hidden) common factor from the constraint
3432 * coefficients to improve the detection of adjacent constraints.
3434 * Since we are constructing the tableaus of the basic maps anyway,
3435 * we exploit them to detect implicit equalities and redundant constraints.
3436 * This also helps the coalescing as it can ignore the redundant constraints.
3437 * In order to avoid confusion, we make all implicit equalities explicit
3438 * in the basic maps. We don't call isl_basic_map_gauss, though,
3439 * as that may affect the number of constraints.
3440 * This means that we have to call isl_basic_map_gauss at the end
3441 * of the computation (in update_basic_maps) to ensure that
3442 * the basic maps are not left in an unexpected state.
3443 * For each basic map, we also compute the hash of the apparent affine hull
3444 * for use in coalesce.
3446 struct isl_map
*isl_map_coalesce(struct isl_map
*map
)
3451 struct isl_coalesce_info
*info
= NULL
;
3453 map
= isl_map_remove_empty_parts(map
);
3460 ctx
= isl_map_get_ctx(map
);
3461 map
= isl_map_sort_divs(map
);
3462 map
= isl_map_cow(map
);
3469 info
= isl_calloc_array(map
->ctx
, struct isl_coalesce_info
, n
);
3473 for (i
= 0; i
< map
->n
; ++i
) {
3474 map
->p
[i
] = isl_basic_map_reduce_coefficients(map
->p
[i
]);
3477 info
[i
].bmap
= isl_basic_map_copy(map
->p
[i
]);
3478 info
[i
].tab
= isl_tab_from_basic_map(info
[i
].bmap
, 0);
3481 if (!ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_NO_IMPLICIT
))
3482 if (isl_tab_detect_implicit_equalities(info
[i
].tab
) < 0)
3484 info
[i
].bmap
= isl_tab_make_equalities_explicit(info
[i
].tab
,
3488 if (!ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_NO_REDUNDANT
))
3489 if (isl_tab_detect_redundant(info
[i
].tab
) < 0)
3491 if (coalesce_info_set_hull_hash(&info
[i
]) < 0)
3494 for (i
= map
->n
- 1; i
>= 0; --i
)
3495 if (info
[i
].tab
->empty
)
3498 if (coalesce(ctx
, n
, info
) < 0)
3501 map
= update_basic_maps(map
, n
, info
);
3503 clear_coalesce_info(n
, info
);
3507 clear_coalesce_info(n
, info
);
3512 /* For each pair of basic sets in the set, check if the union of the two
3513 * can be represented by a single basic set.
3514 * If so, replace the pair by the single basic set and start over.
3516 struct isl_set
*isl_set_coalesce(struct isl_set
*set
)
3518 return set_from_map(isl_map_coalesce(set_to_map(set
)));