2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2010 INRIA Saclay
4 * Copyright 2012-2013 Ecole Normale Superieure
5 * Copyright 2014 INRIA Rocquencourt
7 * Use of this software is governed by the MIT license
9 * Written by Sven Verdoolaege, K.U.Leuven, Departement
10 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
11 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
12 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
13 * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
14 * and Inria Paris - Rocquencourt, Domaine de Voluceau - Rocquencourt,
15 * B.P. 105 - 78153 Le Chesnay, France
18 #include "isl_map_private.h"
20 #include <isl/options.h>
22 #include <isl_mat_private.h>
23 #include <isl_local_space_private.h>
24 #include <isl_vec_private.h>
26 #define STATUS_ERROR -1
27 #define STATUS_REDUNDANT 1
28 #define STATUS_VALID 2
29 #define STATUS_SEPARATE 3
31 #define STATUS_ADJ_EQ 5
32 #define STATUS_ADJ_INEQ 6
34 static int status_in(isl_int
*ineq
, struct isl_tab
*tab
)
36 enum isl_ineq_type type
= isl_tab_ineq_type(tab
, ineq
);
39 case isl_ineq_error
: return STATUS_ERROR
;
40 case isl_ineq_redundant
: return STATUS_VALID
;
41 case isl_ineq_separate
: return STATUS_SEPARATE
;
42 case isl_ineq_cut
: return STATUS_CUT
;
43 case isl_ineq_adj_eq
: return STATUS_ADJ_EQ
;
44 case isl_ineq_adj_ineq
: return STATUS_ADJ_INEQ
;
48 /* Compute the position of the equalities of basic map "bmap_i"
49 * with respect to the basic map represented by "tab_j".
50 * The resulting array has twice as many entries as the number
51 * of equalities corresponding to the two inequalties to which
52 * each equality corresponds.
54 static int *eq_status_in(__isl_keep isl_basic_map
*bmap_i
,
55 struct isl_tab
*tab_j
)
58 int *eq
= isl_calloc_array(bmap_i
->ctx
, int, 2 * bmap_i
->n_eq
);
64 dim
= isl_basic_map_total_dim(bmap_i
);
65 for (k
= 0; k
< bmap_i
->n_eq
; ++k
) {
66 for (l
= 0; l
< 2; ++l
) {
67 isl_seq_neg(bmap_i
->eq
[k
], bmap_i
->eq
[k
], 1+dim
);
68 eq
[2 * k
+ l
] = status_in(bmap_i
->eq
[k
], tab_j
);
69 if (eq
[2 * k
+ l
] == STATUS_ERROR
)
72 if (eq
[2 * k
] == STATUS_SEPARATE
||
73 eq
[2 * k
+ 1] == STATUS_SEPARATE
)
83 /* Compute the position of the inequalities of basic map "bmap_i"
84 * (also represented by "tab_i", if not NULL) with respect to the basic map
85 * represented by "tab_j".
87 static int *ineq_status_in(__isl_keep isl_basic_map
*bmap_i
,
88 struct isl_tab
*tab_i
, struct isl_tab
*tab_j
)
91 unsigned n_eq
= bmap_i
->n_eq
;
92 int *ineq
= isl_calloc_array(bmap_i
->ctx
, int, bmap_i
->n_ineq
);
97 for (k
= 0; k
< bmap_i
->n_ineq
; ++k
) {
98 if (tab_i
&& isl_tab_is_redundant(tab_i
, n_eq
+ k
)) {
99 ineq
[k
] = STATUS_REDUNDANT
;
102 ineq
[k
] = status_in(bmap_i
->ineq
[k
], tab_j
);
103 if (ineq
[k
] == STATUS_ERROR
)
105 if (ineq
[k
] == STATUS_SEPARATE
)
115 static int any(int *con
, unsigned len
, int status
)
119 for (i
= 0; i
< len
; ++i
)
120 if (con
[i
] == status
)
125 static int count(int *con
, unsigned len
, int status
)
130 for (i
= 0; i
< len
; ++i
)
131 if (con
[i
] == status
)
136 static int all(int *con
, unsigned len
, int status
)
140 for (i
= 0; i
< len
; ++i
) {
141 if (con
[i
] == STATUS_REDUNDANT
)
143 if (con
[i
] != status
)
149 /* Internal information associated to a basic map in a map
150 * that is to be coalesced by isl_map_coalesce.
152 * "bmap" is the basic map itself (or NULL if "removed" is set)
153 * "tab" is the corresponding tableau (or NULL if "removed" is set)
154 * "removed" is set if this basic map has been removed from the map
156 * "eq" and "ineq" are only set if we are currently trying to coalesce
157 * this basic map with another basic map, in which case they represent
158 * the position of the inequalities of this basic map with respect to
159 * the other basic map. The number of elements in the "eq" array
160 * is twice the number of equalities in the "bmap", corresponding
161 * to the two inequalities that make up each equality.
163 struct isl_coalesce_info
{
171 /* Free all the allocated memory in an array
172 * of "n" isl_coalesce_info elements.
174 static void clear_coalesce_info(int n
, struct isl_coalesce_info
*info
)
181 for (i
= 0; i
< n
; ++i
) {
182 isl_basic_map_free(info
[i
].bmap
);
183 isl_tab_free(info
[i
].tab
);
189 /* Drop the basic map represented by "info".
190 * That is, clear the memory associated to the entry and
191 * mark it as having been removed.
193 static void drop(struct isl_coalesce_info
*info
)
195 info
->bmap
= isl_basic_map_free(info
->bmap
);
196 isl_tab_free(info
->tab
);
201 /* Exchange the information in "info1" with that in "info2".
203 static void exchange(struct isl_coalesce_info
*info1
,
204 struct isl_coalesce_info
*info2
)
206 struct isl_coalesce_info info
;
213 /* This type represents the kind of change that has been performed
214 * while trying to coalesce two basic maps.
216 * isl_change_none: nothing was changed
217 * isl_change_drop_first: the first basic map was removed
218 * isl_change_drop_second: the second basic map was removed
219 * isl_change_fuse: the two basic maps were replaced by a new basic map.
222 isl_change_error
= -1,
224 isl_change_drop_first
,
225 isl_change_drop_second
,
229 /* Add the valid constraints of the basic map represented by "info"
230 * to "bmap". "len" is the size of the constraints.
231 * If only one of the pair of inequalities that make up an equality
232 * is valid, then add that inequality.
234 static __isl_give isl_basic_map
*add_valid_constraints(
235 __isl_take isl_basic_map
*bmap
, struct isl_coalesce_info
*info
,
243 for (k
= 0; k
< info
->bmap
->n_eq
; ++k
) {
244 if (info
->eq
[2 * k
] == STATUS_VALID
&&
245 info
->eq
[2 * k
+ 1] == STATUS_VALID
) {
246 l
= isl_basic_map_alloc_equality(bmap
);
248 return isl_basic_map_free(bmap
);
249 isl_seq_cpy(bmap
->eq
[l
], info
->bmap
->eq
[k
], len
);
250 } else if (info
->eq
[2 * k
] == STATUS_VALID
) {
251 l
= isl_basic_map_alloc_inequality(bmap
);
253 return isl_basic_map_free(bmap
);
254 isl_seq_neg(bmap
->ineq
[l
], info
->bmap
->eq
[k
], len
);
255 } else if (info
->eq
[2 * k
+ 1] == STATUS_VALID
) {
256 l
= isl_basic_map_alloc_inequality(bmap
);
258 return isl_basic_map_free(bmap
);
259 isl_seq_cpy(bmap
->ineq
[l
], info
->bmap
->eq
[k
], len
);
263 for (k
= 0; k
< info
->bmap
->n_ineq
; ++k
) {
264 if (info
->ineq
[k
] != STATUS_VALID
)
266 l
= isl_basic_map_alloc_inequality(bmap
);
268 return isl_basic_map_free(bmap
);
269 isl_seq_cpy(bmap
->ineq
[l
], info
->bmap
->ineq
[k
], len
);
275 /* Replace the pair of basic maps i and j by the basic map bounded
276 * by the valid constraints in both basic maps and the constraints
277 * in extra (if not NULL).
278 * Place the fused basic map in the position that is the smallest of i and j.
280 * If "detect_equalities" is set, then look for equalities encoded
281 * as pairs of inequalities.
283 static enum isl_change
fuse(int i
, int j
, struct isl_coalesce_info
*info
,
284 __isl_keep isl_mat
*extra
, int detect_equalities
)
287 struct isl_basic_map
*fused
= NULL
;
288 struct isl_tab
*fused_tab
= NULL
;
289 unsigned total
= isl_basic_map_total_dim(info
[i
].bmap
);
290 unsigned extra_rows
= extra
? extra
->n_row
: 0;
291 unsigned n_eq
, n_ineq
;
294 return fuse(j
, i
, info
, extra
, detect_equalities
);
296 n_eq
= info
[i
].bmap
->n_eq
+ info
[j
].bmap
->n_eq
;
297 n_ineq
= info
[i
].bmap
->n_ineq
+ info
[j
].bmap
->n_ineq
;
298 fused
= isl_basic_map_alloc_space(isl_space_copy(info
[i
].bmap
->dim
),
299 info
[i
].bmap
->n_div
, n_eq
, n_eq
+ n_ineq
+ extra_rows
);
300 fused
= add_valid_constraints(fused
, &info
[i
], 1 + total
);
301 fused
= add_valid_constraints(fused
, &info
[j
], 1 + total
);
305 for (k
= 0; k
< info
[i
].bmap
->n_div
; ++k
) {
306 int l
= isl_basic_map_alloc_div(fused
);
309 isl_seq_cpy(fused
->div
[l
], info
[i
].bmap
->div
[k
], 1 + 1 + total
);
312 for (k
= 0; k
< extra_rows
; ++k
) {
313 l
= isl_basic_map_alloc_inequality(fused
);
316 isl_seq_cpy(fused
->ineq
[l
], extra
->row
[k
], 1 + total
);
319 if (detect_equalities
)
320 fused
= isl_basic_map_detect_inequality_pairs(fused
, NULL
);
321 fused
= isl_basic_map_gauss(fused
, NULL
);
322 ISL_F_SET(fused
, ISL_BASIC_MAP_FINAL
);
323 if (ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_RATIONAL
) &&
324 ISL_F_ISSET(info
[j
].bmap
, ISL_BASIC_MAP_RATIONAL
))
325 ISL_F_SET(fused
, ISL_BASIC_MAP_RATIONAL
);
327 fused_tab
= isl_tab_from_basic_map(fused
, 0);
328 if (isl_tab_detect_redundant(fused_tab
) < 0)
331 isl_basic_map_free(info
[i
].bmap
);
332 info
[i
].bmap
= fused
;
333 isl_tab_free(info
[i
].tab
);
334 info
[i
].tab
= fused_tab
;
337 return isl_change_fuse
;
339 isl_tab_free(fused_tab
);
340 isl_basic_map_free(fused
);
341 return isl_change_error
;
344 /* Given a pair of basic maps i and j such that all constraints are either
345 * "valid" or "cut", check if the facets corresponding to the "cut"
346 * constraints of i lie entirely within basic map j.
347 * If so, replace the pair by the basic map consisting of the valid
348 * constraints in both basic maps.
349 * Checking whether the facet lies entirely within basic map j
350 * is performed by checking whether the constraints of basic map j
351 * are valid for the facet. These tests are performed on a rational
352 * tableau to avoid the theoretical possibility that a constraint
353 * that was considered to be a cut constraint for the entire basic map i
354 * happens to be considered to be a valid constraint for the facet,
355 * even though it cuts off the same rational points.
357 * To see that we are not introducing any extra points, call the
358 * two basic maps A and B and the resulting map U and let x
359 * be an element of U \setminus ( A \cup B ).
360 * A line connecting x with an element of A \cup B meets a facet F
361 * of either A or B. Assume it is a facet of B and let c_1 be
362 * the corresponding facet constraint. We have c_1(x) < 0 and
363 * so c_1 is a cut constraint. This implies that there is some
364 * (possibly rational) point x' satisfying the constraints of A
365 * and the opposite of c_1 as otherwise c_1 would have been marked
366 * valid for A. The line connecting x and x' meets a facet of A
367 * in a (possibly rational) point that also violates c_1, but this
368 * is impossible since all cut constraints of B are valid for all
370 * In case F is a facet of A rather than B, then we can apply the
371 * above reasoning to find a facet of B separating x from A \cup B first.
373 static enum isl_change
check_facets(int i
, int j
,
374 struct isl_coalesce_info
*info
)
377 struct isl_tab_undo
*snap
, *snap2
;
378 unsigned n_eq
= info
[i
].bmap
->n_eq
;
380 snap
= isl_tab_snap(info
[i
].tab
);
381 if (isl_tab_mark_rational(info
[i
].tab
) < 0)
382 return isl_change_error
;
383 snap2
= isl_tab_snap(info
[i
].tab
);
385 for (k
= 0; k
< info
[i
].bmap
->n_ineq
; ++k
) {
386 if (info
[i
].ineq
[k
] != STATUS_CUT
)
388 if (isl_tab_select_facet(info
[i
].tab
, n_eq
+ k
) < 0)
389 return isl_change_error
;
390 for (l
= 0; l
< info
[j
].bmap
->n_ineq
; ++l
) {
392 if (info
[j
].ineq
[l
] != STATUS_CUT
)
394 stat
= status_in(info
[j
].bmap
->ineq
[l
], info
[i
].tab
);
395 if (stat
!= STATUS_VALID
)
398 if (isl_tab_rollback(info
[i
].tab
, snap2
) < 0)
399 return isl_change_error
;
400 if (l
< info
[j
].bmap
->n_ineq
)
404 if (k
< info
[i
].bmap
->n_ineq
) {
405 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
406 return isl_change_error
;
407 return isl_change_none
;
409 return fuse(i
, j
, info
, NULL
, 0);
412 /* Check if info->bmap contains the basic map represented
413 * by the tableau "tab".
414 * For each equality, we check both the constraint itself
415 * (as an inequality) and its negation. Make sure the
416 * equality is returned to its original state before returning.
418 static int contains(struct isl_coalesce_info
*info
, struct isl_tab
*tab
)
422 isl_basic_map
*bmap
= info
->bmap
;
424 dim
= isl_basic_map_total_dim(bmap
);
425 for (k
= 0; k
< bmap
->n_eq
; ++k
) {
427 isl_seq_neg(bmap
->eq
[k
], bmap
->eq
[k
], 1 + dim
);
428 stat
= status_in(bmap
->eq
[k
], tab
);
429 isl_seq_neg(bmap
->eq
[k
], bmap
->eq
[k
], 1 + dim
);
430 if (stat
!= STATUS_VALID
)
432 stat
= status_in(bmap
->eq
[k
], tab
);
433 if (stat
!= STATUS_VALID
)
437 for (k
= 0; k
< bmap
->n_ineq
; ++k
) {
439 if (info
->ineq
[k
] == STATUS_REDUNDANT
)
441 stat
= status_in(bmap
->ineq
[k
], tab
);
442 if (stat
!= STATUS_VALID
)
448 /* Basic map "i" has an inequality (say "k") that is adjacent
449 * to some inequality of basic map "j". All the other inequalities
451 * Check if basic map "j" forms an extension of basic map "i".
453 * Note that this function is only called if some of the equalities or
454 * inequalities of basic map "j" do cut basic map "i". The function is
455 * correct even if there are no such cut constraints, but in that case
456 * the additional checks performed by this function are overkill.
458 * In particular, we replace constraint k, say f >= 0, by constraint
459 * f <= -1, add the inequalities of "j" that are valid for "i"
460 * and check if the result is a subset of basic map "j".
461 * If so, then we know that this result is exactly equal to basic map "j"
462 * since all its constraints are valid for basic map "j".
463 * By combining the valid constraints of "i" (all equalities and all
464 * inequalities except "k") and the valid constraints of "j" we therefore
465 * obtain a basic map that is equal to their union.
466 * In this case, there is no need to perform a rollback of the tableau
467 * since it is going to be destroyed in fuse().
473 * |_______| _ |_________\
485 static enum isl_change
is_adj_ineq_extension(int i
, int j
,
486 struct isl_coalesce_info
*info
)
489 struct isl_tab_undo
*snap
;
490 unsigned n_eq
= info
[i
].bmap
->n_eq
;
491 unsigned total
= isl_basic_map_total_dim(info
[i
].bmap
);
494 if (isl_tab_extend_cons(info
[i
].tab
, 1 + info
[j
].bmap
->n_ineq
) < 0)
495 return isl_change_error
;
497 for (k
= 0; k
< info
[i
].bmap
->n_ineq
; ++k
)
498 if (info
[i
].ineq
[k
] == STATUS_ADJ_INEQ
)
500 if (k
>= info
[i
].bmap
->n_ineq
)
501 isl_die(isl_basic_map_get_ctx(info
[i
].bmap
), isl_error_internal
,
502 "info[i].ineq should have exactly one STATUS_ADJ_INEQ",
503 return isl_change_error
);
505 snap
= isl_tab_snap(info
[i
].tab
);
507 if (isl_tab_unrestrict(info
[i
].tab
, n_eq
+ k
) < 0)
508 return isl_change_error
;
510 isl_seq_neg(info
[i
].bmap
->ineq
[k
], info
[i
].bmap
->ineq
[k
], 1 + total
);
511 isl_int_sub_ui(info
[i
].bmap
->ineq
[k
][0], info
[i
].bmap
->ineq
[k
][0], 1);
512 r
= isl_tab_add_ineq(info
[i
].tab
, info
[i
].bmap
->ineq
[k
]);
513 isl_seq_neg(info
[i
].bmap
->ineq
[k
], info
[i
].bmap
->ineq
[k
], 1 + total
);
514 isl_int_sub_ui(info
[i
].bmap
->ineq
[k
][0], info
[i
].bmap
->ineq
[k
][0], 1);
516 return isl_change_error
;
518 for (k
= 0; k
< info
[j
].bmap
->n_ineq
; ++k
) {
519 if (info
[j
].ineq
[k
] != STATUS_VALID
)
521 if (isl_tab_add_ineq(info
[i
].tab
, info
[j
].bmap
->ineq
[k
]) < 0)
522 return isl_change_error
;
525 if (contains(&info
[j
], info
[i
].tab
))
526 return fuse(i
, j
, info
, NULL
, 0);
528 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
529 return isl_change_error
;
531 return isl_change_none
;
535 /* Both basic maps have at least one inequality with and adjacent
536 * (but opposite) inequality in the other basic map.
537 * Check that there are no cut constraints and that there is only
538 * a single pair of adjacent inequalities.
539 * If so, we can replace the pair by a single basic map described
540 * by all but the pair of adjacent inequalities.
541 * Any additional points introduced lie strictly between the two
542 * adjacent hyperplanes and can therefore be integral.
551 * The test for a single pair of adjancent inequalities is important
552 * for avoiding the combination of two basic maps like the following
562 * If there are some cut constraints on one side, then we may
563 * still be able to fuse the two basic maps, but we need to perform
564 * some additional checks in is_adj_ineq_extension.
566 static enum isl_change
check_adj_ineq(int i
, int j
,
567 struct isl_coalesce_info
*info
)
569 int count_i
, count_j
;
572 count_i
= count(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ADJ_INEQ
);
573 count_j
= count(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_ADJ_INEQ
);
575 if (count_i
!= 1 && count_j
!= 1)
576 return isl_change_none
;
578 cut_i
= any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_CUT
) ||
579 any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_CUT
);
580 cut_j
= any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_CUT
) ||
581 any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_CUT
);
583 if (!cut_i
&& !cut_j
&& count_i
== 1 && count_j
== 1)
584 return fuse(i
, j
, info
, NULL
, 0);
586 if (count_i
== 1 && !cut_i
)
587 return is_adj_ineq_extension(i
, j
, info
);
589 if (count_j
== 1 && !cut_j
)
590 return is_adj_ineq_extension(j
, i
, info
);
592 return isl_change_none
;
595 /* Basic map "i" has an inequality "k" that is adjacent to some equality
596 * of basic map "j". All the other inequalities are valid for "j".
597 * Check if basic map "j" forms an extension of basic map "i".
599 * In particular, we relax constraint "k", compute the corresponding
600 * facet and check whether it is included in the other basic map.
601 * If so, we know that relaxing the constraint extends the basic
602 * map with exactly the other basic map (we already know that this
603 * other basic map is included in the extension, because there
604 * were no "cut" inequalities in "i") and we can replace the
605 * two basic maps by this extension.
606 * Place this extension in the position that is the smallest of i and j.
614 static enum isl_change
is_adj_eq_extension(int i
, int j
, int k
,
615 struct isl_coalesce_info
*info
)
617 int change
= isl_change_none
;
619 struct isl_tab_undo
*snap
, *snap2
;
620 unsigned n_eq
= info
[i
].bmap
->n_eq
;
622 if (isl_tab_is_equality(info
[i
].tab
, n_eq
+ k
))
623 return isl_change_none
;
625 snap
= isl_tab_snap(info
[i
].tab
);
626 if (isl_tab_relax(info
[i
].tab
, n_eq
+ k
) < 0)
627 return isl_change_error
;
628 snap2
= isl_tab_snap(info
[i
].tab
);
629 if (isl_tab_select_facet(info
[i
].tab
, n_eq
+ k
) < 0)
630 return isl_change_error
;
631 super
= contains(&info
[j
], info
[i
].tab
);
633 if (isl_tab_rollback(info
[i
].tab
, snap2
) < 0)
634 return isl_change_error
;
635 info
[i
].bmap
= isl_basic_map_cow(info
[i
].bmap
);
637 return isl_change_error
;
638 isl_int_add_ui(info
[i
].bmap
->ineq
[k
][0],
639 info
[i
].bmap
->ineq
[k
][0], 1);
640 ISL_F_SET(info
[i
].bmap
, ISL_BASIC_MAP_FINAL
);
643 exchange(&info
[i
], &info
[j
]);
644 change
= isl_change_fuse
;
646 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
647 return isl_change_error
;
652 /* Data structure that keeps track of the wrapping constraints
653 * and of information to bound the coefficients of those constraints.
655 * bound is set if we want to apply a bound on the coefficients
656 * mat contains the wrapping constraints
657 * max is the bound on the coefficients (if bound is set)
665 /* Update wraps->max to be greater than or equal to the coefficients
666 * in the equalities and inequalities of info->bmap that can be removed
667 * if we end up applying wrapping.
669 static void wraps_update_max(struct isl_wraps
*wraps
,
670 struct isl_coalesce_info
*info
)
674 unsigned total
= isl_basic_map_total_dim(info
->bmap
);
678 for (k
= 0; k
< info
->bmap
->n_eq
; ++k
) {
679 if (info
->eq
[2 * k
] == STATUS_VALID
&&
680 info
->eq
[2 * k
+ 1] == STATUS_VALID
)
682 isl_seq_abs_max(info
->bmap
->eq
[k
] + 1, total
, &max_k
);
683 if (isl_int_abs_gt(max_k
, wraps
->max
))
684 isl_int_set(wraps
->max
, max_k
);
687 for (k
= 0; k
< info
->bmap
->n_ineq
; ++k
) {
688 if (info
->ineq
[k
] == STATUS_VALID
||
689 info
->ineq
[k
] == STATUS_REDUNDANT
)
691 isl_seq_abs_max(info
->bmap
->ineq
[k
] + 1, total
, &max_k
);
692 if (isl_int_abs_gt(max_k
, wraps
->max
))
693 isl_int_set(wraps
->max
, max_k
);
696 isl_int_clear(max_k
);
699 /* Initialize the isl_wraps data structure.
700 * If we want to bound the coefficients of the wrapping constraints,
701 * we set wraps->max to the largest coefficient
702 * in the equalities and inequalities that can be removed if we end up
705 static void wraps_init(struct isl_wraps
*wraps
, __isl_take isl_mat
*mat
,
706 struct isl_coalesce_info
*info
, int i
, int j
)
714 ctx
= isl_mat_get_ctx(mat
);
715 wraps
->bound
= isl_options_get_coalesce_bounded_wrapping(ctx
);
718 isl_int_init(wraps
->max
);
719 isl_int_set_si(wraps
->max
, 0);
720 wraps_update_max(wraps
, &info
[i
]);
721 wraps_update_max(wraps
, &info
[j
]);
724 /* Free the contents of the isl_wraps data structure.
726 static void wraps_free(struct isl_wraps
*wraps
)
728 isl_mat_free(wraps
->mat
);
730 isl_int_clear(wraps
->max
);
733 /* Is the wrapping constraint in row "row" allowed?
735 * If wraps->bound is set, we check that none of the coefficients
736 * is greater than wraps->max.
738 static int allow_wrap(struct isl_wraps
*wraps
, int row
)
745 for (i
= 1; i
< wraps
->mat
->n_col
; ++i
)
746 if (isl_int_abs_gt(wraps
->mat
->row
[row
][i
], wraps
->max
))
752 /* For each non-redundant constraint in info->bmap (as determined by info->tab),
753 * wrap the constraint around "bound" such that it includes the whole
754 * set "set" and append the resulting constraint to "wraps".
755 * "wraps" is assumed to have been pre-allocated to the appropriate size.
756 * wraps->n_row is the number of actual wrapped constraints that have
758 * If any of the wrapping problems results in a constraint that is
759 * identical to "bound", then this means that "set" is unbounded in such
760 * way that no wrapping is possible. If this happens then wraps->n_row
762 * Similarly, if we want to bound the coefficients of the wrapping
763 * constraints and a newly added wrapping constraint does not
764 * satisfy the bound, then wraps->n_row is also reset to zero.
766 static int add_wraps(struct isl_wraps
*wraps
, struct isl_coalesce_info
*info
,
767 isl_int
*bound
, __isl_keep isl_set
*set
)
771 isl_basic_map
*bmap
= info
->bmap
;
772 unsigned total
= isl_basic_map_total_dim(bmap
);
774 w
= wraps
->mat
->n_row
;
776 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
777 if (isl_seq_is_neg(bound
, bmap
->ineq
[l
], 1 + total
))
779 if (isl_seq_eq(bound
, bmap
->ineq
[l
], 1 + total
))
781 if (isl_tab_is_redundant(info
->tab
, bmap
->n_eq
+ l
))
784 isl_seq_cpy(wraps
->mat
->row
[w
], bound
, 1 + total
);
785 if (!isl_set_wrap_facet(set
, wraps
->mat
->row
[w
], bmap
->ineq
[l
]))
787 if (isl_seq_eq(wraps
->mat
->row
[w
], bound
, 1 + total
))
789 if (!allow_wrap(wraps
, w
))
793 for (l
= 0; l
< bmap
->n_eq
; ++l
) {
794 if (isl_seq_is_neg(bound
, bmap
->eq
[l
], 1 + total
))
796 if (isl_seq_eq(bound
, bmap
->eq
[l
], 1 + total
))
799 isl_seq_cpy(wraps
->mat
->row
[w
], bound
, 1 + total
);
800 isl_seq_neg(wraps
->mat
->row
[w
+ 1], bmap
->eq
[l
], 1 + total
);
801 if (!isl_set_wrap_facet(set
, wraps
->mat
->row
[w
],
802 wraps
->mat
->row
[w
+ 1]))
804 if (isl_seq_eq(wraps
->mat
->row
[w
], bound
, 1 + total
))
806 if (!allow_wrap(wraps
, w
))
810 isl_seq_cpy(wraps
->mat
->row
[w
], bound
, 1 + total
);
811 if (!isl_set_wrap_facet(set
, wraps
->mat
->row
[w
], bmap
->eq
[l
]))
813 if (isl_seq_eq(wraps
->mat
->row
[w
], bound
, 1 + total
))
815 if (!allow_wrap(wraps
, w
))
820 wraps
->mat
->n_row
= w
;
823 wraps
->mat
->n_row
= 0;
827 /* Check if the constraints in "wraps" from "first" until the last
828 * are all valid for the basic set represented by "tab".
829 * If not, wraps->n_row is set to zero.
831 static int check_wraps(__isl_keep isl_mat
*wraps
, int first
,
836 for (i
= first
; i
< wraps
->n_row
; ++i
) {
837 enum isl_ineq_type type
;
838 type
= isl_tab_ineq_type(tab
, wraps
->row
[i
]);
839 if (type
== isl_ineq_error
)
841 if (type
== isl_ineq_redundant
)
850 /* Return a set that corresponds to the non-redundant constraints
851 * (as recorded in tab) of bmap.
853 * It's important to remove the redundant constraints as some
854 * of the other constraints may have been modified after the
855 * constraints were marked redundant.
856 * In particular, a constraint may have been relaxed.
857 * Redundant constraints are ignored when a constraint is relaxed
858 * and should therefore continue to be ignored ever after.
859 * Otherwise, the relaxation might be thwarted by some of
862 * Update the underlying set to ensure that the dimension doesn't change.
863 * Otherwise the integer divisions could get dropped if the tab
864 * turns out to be empty.
866 static __isl_give isl_set
*set_from_updated_bmap(__isl_keep isl_basic_map
*bmap
,
871 bmap
= isl_basic_map_copy(bmap
);
872 bset
= isl_basic_map_underlying_set(bmap
);
873 bset
= isl_basic_set_cow(bset
);
874 bset
= isl_basic_set_update_from_tab(bset
, tab
);
875 return isl_set_from_basic_set(bset
);
878 /* Given a basic set i with a constraint k that is adjacent to
879 * basic set j, check if we can wrap
880 * both the facet corresponding to k and basic map j
881 * around their ridges to include the other set.
882 * If so, replace the pair of basic sets by their union.
884 * All constraints of i (except k) are assumed to be valid for j.
885 * This means that there is no real need to wrap the ridges of
886 * the faces of basic map i around basic map j but since we do,
887 * we have to check that the resulting wrapping constraints are valid for i.
896 static enum isl_change
can_wrap_in_facet(int i
, int j
, int k
,
897 struct isl_coalesce_info
*info
)
899 enum isl_change change
= isl_change_none
;
900 struct isl_wraps wraps
;
903 struct isl_set
*set_i
= NULL
;
904 struct isl_set
*set_j
= NULL
;
905 struct isl_vec
*bound
= NULL
;
906 unsigned total
= isl_basic_map_total_dim(info
[i
].bmap
);
907 struct isl_tab_undo
*snap
;
910 set_i
= set_from_updated_bmap(info
[i
].bmap
, info
[i
].tab
);
911 set_j
= set_from_updated_bmap(info
[j
].bmap
, info
[j
].tab
);
912 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
913 mat
= isl_mat_alloc(ctx
, 2 * (info
[i
].bmap
->n_eq
+ info
[j
].bmap
->n_eq
) +
914 info
[i
].bmap
->n_ineq
+ info
[j
].bmap
->n_ineq
,
916 wraps_init(&wraps
, mat
, info
, i
, j
);
917 bound
= isl_vec_alloc(ctx
, 1 + total
);
918 if (!set_i
|| !set_j
|| !wraps
.mat
|| !bound
)
921 isl_seq_cpy(bound
->el
, info
[i
].bmap
->ineq
[k
], 1 + total
);
922 isl_int_add_ui(bound
->el
[0], bound
->el
[0], 1);
924 isl_seq_cpy(wraps
.mat
->row
[0], bound
->el
, 1 + total
);
925 wraps
.mat
->n_row
= 1;
927 if (add_wraps(&wraps
, &info
[j
], bound
->el
, set_i
) < 0)
929 if (!wraps
.mat
->n_row
)
932 snap
= isl_tab_snap(info
[i
].tab
);
934 if (isl_tab_select_facet(info
[i
].tab
, info
[i
].bmap
->n_eq
+ k
) < 0)
936 if (isl_tab_detect_redundant(info
[i
].tab
) < 0)
939 isl_seq_neg(bound
->el
, info
[i
].bmap
->ineq
[k
], 1 + total
);
941 n
= wraps
.mat
->n_row
;
942 if (add_wraps(&wraps
, &info
[i
], bound
->el
, set_j
) < 0)
945 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
947 if (check_wraps(wraps
.mat
, n
, info
[i
].tab
) < 0)
949 if (!wraps
.mat
->n_row
)
952 change
= fuse(i
, j
, info
, wraps
.mat
, 0);
968 return isl_change_error
;
971 /* Given a pair of basic maps i and j such that j sticks out
972 * of i at n cut constraints, each time by at most one,
973 * try to compute wrapping constraints and replace the two
974 * basic maps by a single basic map.
975 * The other constraints of i are assumed to be valid for j.
977 * For each cut constraint t(x) >= 0 of i, we add the relaxed version
978 * t(x) + 1 >= 0, along with wrapping constraints for all constraints
979 * of basic map j that bound the part of basic map j that sticks out
980 * of the cut constraint.
981 * In particular, we first intersect basic map j with t(x) + 1 = 0.
982 * If the result is empty, then t(x) >= 0 was actually a valid constraint
983 * (with respect to the integer points), so we add t(x) >= 0 instead.
984 * Otherwise, we wrap the constraints of basic map j that are not
985 * redundant in this intersection over the union of the two basic maps.
987 * If any wrapping fails, i.e., if we cannot wrap to touch
988 * the union, then we give up.
989 * Otherwise, the pair of basic maps is replaced by their union.
991 static enum isl_change
wrap_in_facets(int i
, int j
, int *cuts
, int n
,
992 struct isl_coalesce_info
*info
)
994 enum isl_change change
= isl_change_none
;
995 struct isl_wraps wraps
;
999 unsigned total
= isl_basic_map_total_dim(info
[i
].bmap
);
1002 struct isl_tab_undo
*snap
;
1004 if (isl_tab_extend_cons(info
[j
].tab
, 1) < 0)
1007 max_wrap
= 1 + 2 * info
[j
].bmap
->n_eq
+ info
[j
].bmap
->n_ineq
;
1010 set
= isl_set_union(set_from_updated_bmap(info
[i
].bmap
, info
[i
].tab
),
1011 set_from_updated_bmap(info
[j
].bmap
, info
[j
].tab
));
1012 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
1013 mat
= isl_mat_alloc(ctx
, max_wrap
, 1 + total
);
1014 wraps_init(&wraps
, mat
, info
, i
, j
);
1015 if (!set
|| !wraps
.mat
)
1018 snap
= isl_tab_snap(info
[j
].tab
);
1020 wraps
.mat
->n_row
= 0;
1022 for (k
= 0; k
< n
; ++k
) {
1023 w
= wraps
.mat
->n_row
++;
1024 isl_seq_cpy(wraps
.mat
->row
[w
],
1025 info
[i
].bmap
->ineq
[cuts
[k
]], 1 + total
);
1026 isl_int_add_ui(wraps
.mat
->row
[w
][0], wraps
.mat
->row
[w
][0], 1);
1027 if (isl_tab_add_eq(info
[j
].tab
, wraps
.mat
->row
[w
]) < 0)
1029 if (isl_tab_detect_redundant(info
[j
].tab
) < 0)
1032 if (info
[j
].tab
->empty
)
1033 isl_int_sub_ui(wraps
.mat
->row
[w
][0],
1034 wraps
.mat
->row
[w
][0], 1);
1035 else if (add_wraps(&wraps
, &info
[j
],
1036 wraps
.mat
->row
[w
], set
) < 0)
1039 if (isl_tab_rollback(info
[j
].tab
, snap
) < 0)
1042 if (!wraps
.mat
->n_row
)
1047 change
= fuse(i
, j
, info
, wraps
.mat
, 0);
1056 return isl_change_error
;
1059 /* Given two basic sets i and j such that i has no cut equalities,
1060 * check if relaxing all the cut inequalities of i by one turns
1061 * them into valid constraint for j and check if we can wrap in
1062 * the bits that are sticking out.
1063 * If so, replace the pair by their union.
1065 * We first check if all relaxed cut inequalities of i are valid for j
1066 * and then try to wrap in the intersections of the relaxed cut inequalities
1069 * During this wrapping, we consider the points of j that lie at a distance
1070 * of exactly 1 from i. In particular, we ignore the points that lie in
1071 * between this lower-dimensional space and the basic map i.
1072 * We can therefore only apply this to integer maps.
1098 * Wrapping can fail if the result of wrapping one of the facets
1099 * around its edges does not produce any new facet constraint.
1100 * In particular, this happens when we try to wrap in unbounded sets.
1102 * _______________________________________________________________________
1106 * |_| |_________________________________________________________________
1109 * The following is not an acceptable result of coalescing the above two
1110 * sets as it includes extra integer points.
1111 * _______________________________________________________________________
1116 * \______________________________________________________________________
1118 static enum isl_change
can_wrap_in_set(int i
, int j
,
1119 struct isl_coalesce_info
*info
)
1121 enum isl_change change
= isl_change_none
;
1127 if (ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_RATIONAL
) ||
1128 ISL_F_ISSET(info
[j
].bmap
, ISL_BASIC_MAP_RATIONAL
))
1129 return isl_change_none
;
1131 n
= count(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_CUT
);
1133 return isl_change_none
;
1135 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
1136 cuts
= isl_alloc_array(ctx
, int, n
);
1138 return isl_change_error
;
1140 for (k
= 0, m
= 0; m
< n
; ++k
) {
1141 enum isl_ineq_type type
;
1143 if (info
[i
].ineq
[k
] != STATUS_CUT
)
1146 isl_int_add_ui(info
[i
].bmap
->ineq
[k
][0],
1147 info
[i
].bmap
->ineq
[k
][0], 1);
1148 type
= isl_tab_ineq_type(info
[j
].tab
, info
[i
].bmap
->ineq
[k
]);
1149 isl_int_sub_ui(info
[i
].bmap
->ineq
[k
][0],
1150 info
[i
].bmap
->ineq
[k
][0], 1);
1151 if (type
== isl_ineq_error
)
1153 if (type
!= isl_ineq_redundant
)
1160 change
= wrap_in_facets(i
, j
, cuts
, n
, info
);
1167 return isl_change_error
;
1170 /* Check if either i or j has only cut inequalities that can
1171 * be used to wrap in (a facet of) the other basic set.
1172 * if so, replace the pair by their union.
1174 static enum isl_change
check_wrap(int i
, int j
, struct isl_coalesce_info
*info
)
1176 enum isl_change change
= isl_change_none
;
1178 if (!any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_CUT
))
1179 change
= can_wrap_in_set(i
, j
, info
);
1180 if (change
!= isl_change_none
)
1183 if (!any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_CUT
))
1184 change
= can_wrap_in_set(j
, i
, info
);
1188 /* At least one of the basic maps has an equality that is adjacent
1189 * to inequality. Make sure that only one of the basic maps has
1190 * such an equality and that the other basic map has exactly one
1191 * inequality adjacent to an equality.
1192 * We call the basic map that has the inequality "i" and the basic
1193 * map that has the equality "j".
1194 * If "i" has any "cut" (in)equality, then relaxing the inequality
1195 * by one would not result in a basic map that contains the other
1198 static enum isl_change
check_adj_eq(int i
, int j
,
1199 struct isl_coalesce_info
*info
)
1201 enum isl_change change
= isl_change_none
;
1204 if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_ADJ_INEQ
) &&
1205 any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_ADJ_INEQ
))
1206 /* ADJ EQ TOO MANY */
1207 return isl_change_none
;
1209 if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_ADJ_INEQ
))
1210 return check_adj_eq(j
, i
, info
);
1212 /* j has an equality adjacent to an inequality in i */
1214 if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_CUT
))
1215 return isl_change_none
;
1216 if (any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_CUT
))
1218 return isl_change_none
;
1219 if (count(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ADJ_EQ
) != 1 ||
1220 any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_ADJ_EQ
) ||
1221 any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ADJ_INEQ
) ||
1222 any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_ADJ_INEQ
))
1223 /* ADJ EQ TOO MANY */
1224 return isl_change_none
;
1226 for (k
= 0; k
< info
[i
].bmap
->n_ineq
; ++k
)
1227 if (info
[i
].ineq
[k
] == STATUS_ADJ_EQ
)
1230 change
= is_adj_eq_extension(i
, j
, k
, info
);
1231 if (change
!= isl_change_none
)
1234 if (count(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_ADJ_INEQ
) != 1)
1235 return isl_change_none
;
1237 change
= can_wrap_in_facet(i
, j
, k
, info
);
1242 /* The two basic maps lie on adjacent hyperplanes. In particular,
1243 * basic map "i" has an equality that lies parallel to basic map "j".
1244 * Check if we can wrap the facets around the parallel hyperplanes
1245 * to include the other set.
1247 * We perform basically the same operations as can_wrap_in_facet,
1248 * except that we don't need to select a facet of one of the sets.
1254 * If there is more than one equality of "i" adjacent to an equality of "j",
1255 * then the result will satisfy one or more equalities that are a linear
1256 * combination of these equalities. These will be encoded as pairs
1257 * of inequalities in the wrapping constraints and need to be made
1260 static enum isl_change
check_eq_adj_eq(int i
, int j
,
1261 struct isl_coalesce_info
*info
)
1264 enum isl_change change
= isl_change_none
;
1265 int detect_equalities
= 0;
1266 struct isl_wraps wraps
;
1269 struct isl_set
*set_i
= NULL
;
1270 struct isl_set
*set_j
= NULL
;
1271 struct isl_vec
*bound
= NULL
;
1272 unsigned total
= isl_basic_map_total_dim(info
[i
].bmap
);
1274 if (count(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_ADJ_EQ
) != 1)
1275 detect_equalities
= 1;
1277 for (k
= 0; k
< 2 * info
[i
].bmap
->n_eq
; ++k
)
1278 if (info
[i
].eq
[k
] == STATUS_ADJ_EQ
)
1281 set_i
= set_from_updated_bmap(info
[i
].bmap
, info
[i
].tab
);
1282 set_j
= set_from_updated_bmap(info
[j
].bmap
, info
[j
].tab
);
1283 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
1284 mat
= isl_mat_alloc(ctx
, 2 * (info
[i
].bmap
->n_eq
+ info
[j
].bmap
->n_eq
) +
1285 info
[i
].bmap
->n_ineq
+ info
[j
].bmap
->n_ineq
,
1287 wraps_init(&wraps
, mat
, info
, i
, j
);
1288 bound
= isl_vec_alloc(ctx
, 1 + total
);
1289 if (!set_i
|| !set_j
|| !wraps
.mat
|| !bound
)
1293 isl_seq_neg(bound
->el
, info
[i
].bmap
->eq
[k
/ 2], 1 + total
);
1295 isl_seq_cpy(bound
->el
, info
[i
].bmap
->eq
[k
/ 2], 1 + total
);
1296 isl_int_add_ui(bound
->el
[0], bound
->el
[0], 1);
1298 isl_seq_cpy(wraps
.mat
->row
[0], bound
->el
, 1 + total
);
1299 wraps
.mat
->n_row
= 1;
1301 if (add_wraps(&wraps
, &info
[j
], bound
->el
, set_i
) < 0)
1303 if (!wraps
.mat
->n_row
)
1306 isl_int_sub_ui(bound
->el
[0], bound
->el
[0], 1);
1307 isl_seq_neg(bound
->el
, bound
->el
, 1 + total
);
1309 isl_seq_cpy(wraps
.mat
->row
[wraps
.mat
->n_row
], bound
->el
, 1 + total
);
1312 if (add_wraps(&wraps
, &info
[i
], bound
->el
, set_j
) < 0)
1314 if (!wraps
.mat
->n_row
)
1317 change
= fuse(i
, j
, info
, wraps
.mat
, detect_equalities
);
1320 error
: change
= isl_change_error
;
1325 isl_set_free(set_i
);
1326 isl_set_free(set_j
);
1327 isl_vec_free(bound
);
1332 /* Check if the union of the given pair of basic maps
1333 * can be represented by a single basic map.
1334 * If so, replace the pair by the single basic map and return
1335 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
1336 * Otherwise, return isl_change_none.
1337 * The two basic maps are assumed to live in the same local space.
1339 * We first check the effect of each constraint of one basic map
1340 * on the other basic map.
1341 * The constraint may be
1342 * redundant the constraint is redundant in its own
1343 * basic map and should be ignore and removed
1345 * valid all (integer) points of the other basic map
1346 * satisfy the constraint
1347 * separate no (integer) point of the other basic map
1348 * satisfies the constraint
1349 * cut some but not all points of the other basic map
1350 * satisfy the constraint
1351 * adj_eq the given constraint is adjacent (on the outside)
1352 * to an equality of the other basic map
1353 * adj_ineq the given constraint is adjacent (on the outside)
1354 * to an inequality of the other basic map
1356 * We consider seven cases in which we can replace the pair by a single
1357 * basic map. We ignore all "redundant" constraints.
1359 * 1. all constraints of one basic map are valid
1360 * => the other basic map is a subset and can be removed
1362 * 2. all constraints of both basic maps are either "valid" or "cut"
1363 * and the facets corresponding to the "cut" constraints
1364 * of one of the basic maps lies entirely inside the other basic map
1365 * => the pair can be replaced by a basic map consisting
1366 * of the valid constraints in both basic maps
1368 * 3. there is a single pair of adjacent inequalities
1369 * (all other constraints are "valid")
1370 * => the pair can be replaced by a basic map consisting
1371 * of the valid constraints in both basic maps
1373 * 4. one basic map has a single adjacent inequality, while the other
1374 * constraints are "valid". The other basic map has some
1375 * "cut" constraints, but replacing the adjacent inequality by
1376 * its opposite and adding the valid constraints of the other
1377 * basic map results in a subset of the other basic map
1378 * => the pair can be replaced by a basic map consisting
1379 * of the valid constraints in both basic maps
1381 * 5. there is a single adjacent pair of an inequality and an equality,
1382 * the other constraints of the basic map containing the inequality are
1383 * "valid". Moreover, if the inequality the basic map is relaxed
1384 * and then turned into an equality, then resulting facet lies
1385 * entirely inside the other basic map
1386 * => the pair can be replaced by the basic map containing
1387 * the inequality, with the inequality relaxed.
1389 * 6. there is a single adjacent pair of an inequality and an equality,
1390 * the other constraints of the basic map containing the inequality are
1391 * "valid". Moreover, the facets corresponding to both
1392 * the inequality and the equality can be wrapped around their
1393 * ridges to include the other basic map
1394 * => the pair can be replaced by a basic map consisting
1395 * of the valid constraints in both basic maps together
1396 * with all wrapping constraints
1398 * 7. one of the basic maps extends beyond the other by at most one.
1399 * Moreover, the facets corresponding to the cut constraints and
1400 * the pieces of the other basic map at offset one from these cut
1401 * constraints can be wrapped around their ridges to include
1402 * the union of the two basic maps
1403 * => the pair can be replaced by a basic map consisting
1404 * of the valid constraints in both basic maps together
1405 * with all wrapping constraints
1407 * 8. the two basic maps live in adjacent hyperplanes. In principle
1408 * such sets can always be combined through wrapping, but we impose
1409 * that there is only one such pair, to avoid overeager coalescing.
1411 * Throughout the computation, we maintain a collection of tableaus
1412 * corresponding to the basic maps. When the basic maps are dropped
1413 * or combined, the tableaus are modified accordingly.
1415 static enum isl_change
coalesce_local_pair(int i
, int j
,
1416 struct isl_coalesce_info
*info
)
1418 enum isl_change change
= isl_change_none
;
1420 info
[i
].eq
= info
[i
].ineq
= NULL
;
1421 info
[j
].eq
= info
[j
].ineq
= NULL
;
1423 info
[i
].eq
= eq_status_in(info
[i
].bmap
, info
[j
].tab
);
1424 if (info
[i
].bmap
->n_eq
&& !info
[i
].eq
)
1426 if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_ERROR
))
1428 if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_SEPARATE
))
1431 info
[j
].eq
= eq_status_in(info
[j
].bmap
, info
[i
].tab
);
1432 if (info
[j
].bmap
->n_eq
&& !info
[j
].eq
)
1434 if (any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_ERROR
))
1436 if (any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_SEPARATE
))
1439 info
[i
].ineq
= ineq_status_in(info
[i
].bmap
, info
[i
].tab
, info
[j
].tab
);
1440 if (info
[i
].bmap
->n_ineq
&& !info
[i
].ineq
)
1442 if (any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ERROR
))
1444 if (any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_SEPARATE
))
1447 info
[j
].ineq
= ineq_status_in(info
[j
].bmap
, info
[j
].tab
, info
[i
].tab
);
1448 if (info
[j
].bmap
->n_ineq
&& !info
[j
].ineq
)
1450 if (any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_ERROR
))
1452 if (any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_SEPARATE
))
1455 if (all(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_VALID
) &&
1456 all(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_VALID
)) {
1458 change
= isl_change_drop_second
;
1459 } else if (all(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_VALID
) &&
1460 all(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_VALID
)) {
1462 change
= isl_change_drop_first
;
1463 } else if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_ADJ_EQ
)) {
1464 change
= check_eq_adj_eq(i
, j
, info
);
1465 } else if (any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_ADJ_EQ
)) {
1466 change
= check_eq_adj_eq(j
, i
, info
);
1467 } else if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_ADJ_INEQ
) ||
1468 any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_ADJ_INEQ
)) {
1469 change
= check_adj_eq(i
, j
, info
);
1470 } else if (any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ADJ_EQ
) ||
1471 any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_ADJ_EQ
)) {
1474 } else if (any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ADJ_INEQ
) ||
1475 any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_ADJ_INEQ
)) {
1476 change
= check_adj_ineq(i
, j
, info
);
1478 if (!any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_CUT
) &&
1479 !any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_CUT
))
1480 change
= check_facets(i
, j
, info
);
1481 if (change
== isl_change_none
)
1482 change
= check_wrap(i
, j
, info
);
1496 return isl_change_error
;
1499 /* Do the two basic maps live in the same local space, i.e.,
1500 * do they have the same (known) divs?
1501 * If either basic map has any unknown divs, then we can only assume
1502 * that they do not live in the same local space.
1504 static int same_divs(__isl_keep isl_basic_map
*bmap1
,
1505 __isl_keep isl_basic_map
*bmap2
)
1511 if (!bmap1
|| !bmap2
)
1513 if (bmap1
->n_div
!= bmap2
->n_div
)
1516 if (bmap1
->n_div
== 0)
1519 known
= isl_basic_map_divs_known(bmap1
);
1520 if (known
< 0 || !known
)
1522 known
= isl_basic_map_divs_known(bmap2
);
1523 if (known
< 0 || !known
)
1526 total
= isl_basic_map_total_dim(bmap1
);
1527 for (i
= 0; i
< bmap1
->n_div
; ++i
)
1528 if (!isl_seq_eq(bmap1
->div
[i
], bmap2
->div
[i
], 2 + total
))
1534 /* Does "bmap" contain the basic map represented by the tableau "tab"
1535 * after expanding the divs of "bmap" to match those of "tab"?
1536 * The expansion is performed using the divs "div" and expansion "exp"
1537 * computed by the caller.
1538 * Then we check if all constraints of the expanded "bmap" are valid for "tab".
1540 static int contains_with_expanded_divs(__isl_keep isl_basic_map
*bmap
,
1541 struct isl_tab
*tab
, __isl_keep isl_mat
*div
, int *exp
)
1547 bmap
= isl_basic_map_copy(bmap
);
1548 bmap
= isl_basic_set_expand_divs(bmap
, isl_mat_copy(div
), exp
);
1553 eq_i
= eq_status_in(bmap
, tab
);
1554 if (bmap
->n_eq
&& !eq_i
)
1556 if (any(eq_i
, 2 * bmap
->n_eq
, STATUS_ERROR
))
1558 if (any(eq_i
, 2 * bmap
->n_eq
, STATUS_SEPARATE
))
1561 ineq_i
= ineq_status_in(bmap
, NULL
, tab
);
1562 if (bmap
->n_ineq
&& !ineq_i
)
1564 if (any(ineq_i
, bmap
->n_ineq
, STATUS_ERROR
))
1566 if (any(ineq_i
, bmap
->n_ineq
, STATUS_SEPARATE
))
1569 if (all(eq_i
, 2 * bmap
->n_eq
, STATUS_VALID
) &&
1570 all(ineq_i
, bmap
->n_ineq
, STATUS_VALID
))
1574 isl_basic_map_free(bmap
);
1579 isl_basic_map_free(bmap
);
1585 /* Does "bmap_i" contain the basic map represented by "info_j"
1586 * after aligning the divs of "bmap_i" to those of "info_j".
1587 * Note that this can only succeed if the number of divs of "bmap_i"
1588 * is smaller than (or equal to) the number of divs of "info_j".
1590 * We first check if the divs of "bmap_i" are all known and form a subset
1591 * of those of "bmap_j". If so, we pass control over to
1592 * contains_with_expanded_divs.
1594 static int contains_after_aligning_divs(__isl_keep isl_basic_map
*bmap_i
,
1595 struct isl_coalesce_info
*info_j
)
1598 isl_mat
*div_i
, *div_j
, *div
;
1604 known
= isl_basic_map_divs_known(bmap_i
);
1605 if (known
< 0 || !known
)
1608 ctx
= isl_basic_map_get_ctx(bmap_i
);
1610 div_i
= isl_basic_map_get_divs(bmap_i
);
1611 div_j
= isl_basic_map_get_divs(info_j
->bmap
);
1613 if (!div_i
|| !div_j
)
1616 exp1
= isl_alloc_array(ctx
, int, div_i
->n_row
);
1617 exp2
= isl_alloc_array(ctx
, int, div_j
->n_row
);
1618 if ((div_i
->n_row
&& !exp1
) || (div_j
->n_row
&& !exp2
))
1621 div
= isl_merge_divs(div_i
, div_j
, exp1
, exp2
);
1625 if (div
->n_row
== div_j
->n_row
)
1626 subset
= contains_with_expanded_divs(bmap_i
,
1627 info_j
->tab
, div
, exp1
);
1633 isl_mat_free(div_i
);
1634 isl_mat_free(div_j
);
1641 isl_mat_free(div_i
);
1642 isl_mat_free(div_j
);
1648 /* Check if the basic map "j" is a subset of basic map "i",
1649 * if "i" has fewer divs that "j".
1650 * If so, remove basic map "j".
1652 * If the two basic maps have the same number of divs, then
1653 * they must necessarily be different. Otherwise, we would have
1654 * called coalesce_local_pair. We therefore don't try anything
1657 static int coalesced_subset(int i
, int j
, struct isl_coalesce_info
*info
)
1661 if (info
[i
].bmap
->n_div
>= info
[j
].bmap
->n_div
)
1664 superset
= contains_after_aligning_divs(info
[i
].bmap
, &info
[j
]);
1673 /* Check if one of the basic maps is a subset of the other and, if so,
1675 * Note that we only perform any test if the number of divs is different
1676 * in the two basic maps. In case the number of divs is the same,
1677 * we have already established that the divs are different
1678 * in the two basic maps.
1679 * In particular, if the number of divs of basic map i is smaller than
1680 * the number of divs of basic map j, then we check if j is a subset of i
1683 static enum isl_change
check_coalesce_subset(int i
, int j
,
1684 struct isl_coalesce_info
*info
)
1688 changed
= coalesced_subset(i
, j
, info
);
1689 if (changed
< 0 || changed
)
1690 return changed
< 0 ? isl_change_error
: isl_change_drop_second
;
1692 changed
= coalesced_subset(j
, i
, info
);
1693 if (changed
< 0 || changed
)
1694 return changed
< 0 ? isl_change_error
: isl_change_drop_first
;
1696 return isl_change_none
;
1699 /* Check if the union of the given pair of basic maps
1700 * can be represented by a single basic map.
1701 * If so, replace the pair by the single basic map and return
1702 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
1703 * Otherwise, return isl_change_none.
1705 * We first check if the two basic maps live in the same local space.
1706 * If so, we do the complete check. Otherwise, we check if one is
1707 * an obvious subset of the other.
1709 static enum isl_change
coalesce_pair(int i
, int j
,
1710 struct isl_coalesce_info
*info
)
1714 same
= same_divs(info
[i
].bmap
, info
[j
].bmap
);
1716 return isl_change_error
;
1718 return coalesce_local_pair(i
, j
, info
);
1720 return check_coalesce_subset(i
, j
, info
);
1723 /* Pairwise coalesce the basic maps described by the "n" elements of "info",
1724 * skipping basic maps that have been removed (either before or within
1727 * For each basic map i, we check if it can be coalesced with respect
1728 * to any previously considered basic map j.
1729 * If i gets dropped (because it was a subset of some j), then
1730 * we can move on to the next basic map.
1731 * If j gets dropped, we need to continue checking against the other
1732 * previously considered basic maps.
1733 * If the two basic maps got fused, then we recheck the fused basic map
1734 * against the previously considered basic maps.
1736 static int coalesce(isl_ctx
*ctx
, int n
, struct isl_coalesce_info
*info
)
1740 for (i
= n
- 2; i
>= 0; --i
) {
1741 if (info
[i
].removed
)
1743 for (j
= i
+ 1; j
< n
; ++j
) {
1744 enum isl_change changed
;
1746 if (info
[j
].removed
)
1748 if (info
[i
].removed
)
1749 isl_die(ctx
, isl_error_internal
,
1750 "basic map unexpectedly removed",
1752 changed
= coalesce_pair(i
, j
, info
);
1754 case isl_change_error
:
1756 case isl_change_none
:
1757 case isl_change_drop_second
:
1759 case isl_change_drop_first
:
1762 case isl_change_fuse
:
1772 /* Update the basic maps in "map" based on the information in "info".
1773 * In particular, remove the basic maps that have been marked removed and
1774 * update the others based on the information in the corresponding tableau.
1775 * Since we detected implicit equalities without calling
1776 * isl_basic_map_gauss, we need to do it now.
1778 static __isl_give isl_map
*update_basic_maps(__isl_take isl_map
*map
,
1779 int n
, struct isl_coalesce_info
*info
)
1786 for (i
= n
- 1; i
>= 0; --i
) {
1787 if (info
[i
].removed
) {
1788 isl_basic_map_free(map
->p
[i
]);
1789 if (i
!= map
->n
- 1)
1790 map
->p
[i
] = map
->p
[map
->n
- 1];
1795 info
[i
].bmap
= isl_basic_map_update_from_tab(info
[i
].bmap
,
1797 info
[i
].bmap
= isl_basic_map_gauss(info
[i
].bmap
, NULL
);
1798 info
[i
].bmap
= isl_basic_map_finalize(info
[i
].bmap
);
1800 return isl_map_free(map
);
1801 ISL_F_SET(info
[i
].bmap
, ISL_BASIC_MAP_NO_IMPLICIT
);
1802 ISL_F_SET(info
[i
].bmap
, ISL_BASIC_MAP_NO_REDUNDANT
);
1803 isl_basic_map_free(map
->p
[i
]);
1804 map
->p
[i
] = info
[i
].bmap
;
1805 info
[i
].bmap
= NULL
;
1811 /* For each pair of basic maps in the map, check if the union of the two
1812 * can be represented by a single basic map.
1813 * If so, replace the pair by the single basic map and start over.
1815 * Since we are constructing the tableaus of the basic maps anyway,
1816 * we exploit them to detect implicit equalities and redundant constraints.
1817 * This also helps the coalescing as it can ignore the redundant constraints.
1818 * In order to avoid confusion, we make all implicit equalities explicit
1819 * in the basic maps. We don't call isl_basic_map_gauss, though,
1820 * as that may affect the number of constraints.
1821 * This means that we have to call isl_basic_map_gauss at the end
1822 * of the computation (in update_basic_maps) to ensure that
1823 * the basic maps are not left in an unexpected state.
1825 struct isl_map
*isl_map_coalesce(struct isl_map
*map
)
1830 struct isl_coalesce_info
*info
= NULL
;
1832 map
= isl_map_remove_empty_parts(map
);
1839 ctx
= isl_map_get_ctx(map
);
1840 map
= isl_map_sort_divs(map
);
1841 map
= isl_map_cow(map
);
1848 info
= isl_calloc_array(map
->ctx
, struct isl_coalesce_info
, n
);
1852 for (i
= 0; i
< map
->n
; ++i
) {
1853 info
[i
].bmap
= isl_basic_map_copy(map
->p
[i
]);
1854 info
[i
].tab
= isl_tab_from_basic_map(info
[i
].bmap
, 0);
1857 if (!ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_NO_IMPLICIT
))
1858 if (isl_tab_detect_implicit_equalities(info
[i
].tab
) < 0)
1860 info
[i
].bmap
= isl_tab_make_equalities_explicit(info
[i
].tab
,
1864 if (!ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_NO_REDUNDANT
))
1865 if (isl_tab_detect_redundant(info
[i
].tab
) < 0)
1868 for (i
= map
->n
- 1; i
>= 0; --i
)
1869 if (info
[i
].tab
->empty
)
1872 if (coalesce(ctx
, n
, info
) < 0)
1875 map
= update_basic_maps(map
, n
, info
);
1877 clear_coalesce_info(n
, info
);
1881 clear_coalesce_info(n
, info
);
1886 /* For each pair of basic sets in the set, check if the union of the two
1887 * can be represented by a single basic set.
1888 * If so, replace the pair by the single basic set and start over.
1890 struct isl_set
*isl_set_coalesce(struct isl_set
*set
)
1892 return (struct isl_set
*)isl_map_coalesce((struct isl_map
*)set
);