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>
25 #include <isl_aff_private.h>
27 #define STATUS_ERROR -1
28 #define STATUS_REDUNDANT 1
29 #define STATUS_VALID 2
30 #define STATUS_SEPARATE 3
32 #define STATUS_ADJ_EQ 5
33 #define STATUS_ADJ_INEQ 6
35 static int status_in(isl_int
*ineq
, struct isl_tab
*tab
)
37 enum isl_ineq_type type
= isl_tab_ineq_type(tab
, ineq
);
40 case isl_ineq_error
: return STATUS_ERROR
;
41 case isl_ineq_redundant
: return STATUS_VALID
;
42 case isl_ineq_separate
: return STATUS_SEPARATE
;
43 case isl_ineq_cut
: return STATUS_CUT
;
44 case isl_ineq_adj_eq
: return STATUS_ADJ_EQ
;
45 case isl_ineq_adj_ineq
: return STATUS_ADJ_INEQ
;
49 /* Compute the position of the equalities of basic map "bmap_i"
50 * with respect to the basic map represented by "tab_j".
51 * The resulting array has twice as many entries as the number
52 * of equalities corresponding to the two inequalties to which
53 * each equality corresponds.
55 static int *eq_status_in(__isl_keep isl_basic_map
*bmap_i
,
56 struct isl_tab
*tab_j
)
59 int *eq
= isl_calloc_array(bmap_i
->ctx
, int, 2 * bmap_i
->n_eq
);
65 dim
= isl_basic_map_total_dim(bmap_i
);
66 for (k
= 0; k
< bmap_i
->n_eq
; ++k
) {
67 for (l
= 0; l
< 2; ++l
) {
68 isl_seq_neg(bmap_i
->eq
[k
], bmap_i
->eq
[k
], 1+dim
);
69 eq
[2 * k
+ l
] = status_in(bmap_i
->eq
[k
], tab_j
);
70 if (eq
[2 * k
+ l
] == STATUS_ERROR
)
73 if (eq
[2 * k
] == STATUS_SEPARATE
||
74 eq
[2 * k
+ 1] == STATUS_SEPARATE
)
84 /* Compute the position of the inequalities of basic map "bmap_i"
85 * (also represented by "tab_i", if not NULL) with respect to the basic map
86 * represented by "tab_j".
88 static int *ineq_status_in(__isl_keep isl_basic_map
*bmap_i
,
89 struct isl_tab
*tab_i
, struct isl_tab
*tab_j
)
92 unsigned n_eq
= bmap_i
->n_eq
;
93 int *ineq
= isl_calloc_array(bmap_i
->ctx
, int, bmap_i
->n_ineq
);
98 for (k
= 0; k
< bmap_i
->n_ineq
; ++k
) {
99 if (tab_i
&& isl_tab_is_redundant(tab_i
, n_eq
+ k
)) {
100 ineq
[k
] = STATUS_REDUNDANT
;
103 ineq
[k
] = status_in(bmap_i
->ineq
[k
], tab_j
);
104 if (ineq
[k
] == STATUS_ERROR
)
106 if (ineq
[k
] == STATUS_SEPARATE
)
116 static int any(int *con
, unsigned len
, int status
)
120 for (i
= 0; i
< len
; ++i
)
121 if (con
[i
] == status
)
126 static int count(int *con
, unsigned len
, int status
)
131 for (i
= 0; i
< len
; ++i
)
132 if (con
[i
] == status
)
137 static int all(int *con
, unsigned len
, int status
)
141 for (i
= 0; i
< len
; ++i
) {
142 if (con
[i
] == STATUS_REDUNDANT
)
144 if (con
[i
] != status
)
150 /* Internal information associated to a basic map in a map
151 * that is to be coalesced by isl_map_coalesce.
153 * "bmap" is the basic map itself (or NULL if "removed" is set)
154 * "tab" is the corresponding tableau (or NULL if "removed" is set)
155 * "removed" is set if this basic map has been removed from the map
156 * "simplify" is set if this basic map may have some unknown integer
157 * divisions that were not present in the input basic maps. The basic
158 * map should then be simplified such that we may be able to find
159 * a definition among the constraints.
161 * "eq" and "ineq" are only set if we are currently trying to coalesce
162 * this basic map with another basic map, in which case they represent
163 * the position of the inequalities of this basic map with respect to
164 * the other basic map. The number of elements in the "eq" array
165 * is twice the number of equalities in the "bmap", corresponding
166 * to the two inequalities that make up each equality.
168 struct isl_coalesce_info
{
177 /* Free all the allocated memory in an array
178 * of "n" isl_coalesce_info elements.
180 static void clear_coalesce_info(int n
, struct isl_coalesce_info
*info
)
187 for (i
= 0; i
< n
; ++i
) {
188 isl_basic_map_free(info
[i
].bmap
);
189 isl_tab_free(info
[i
].tab
);
195 /* Drop the basic map represented by "info".
196 * That is, clear the memory associated to the entry and
197 * mark it as having been removed.
199 static void drop(struct isl_coalesce_info
*info
)
201 info
->bmap
= isl_basic_map_free(info
->bmap
);
202 isl_tab_free(info
->tab
);
207 /* Exchange the information in "info1" with that in "info2".
209 static void exchange(struct isl_coalesce_info
*info1
,
210 struct isl_coalesce_info
*info2
)
212 struct isl_coalesce_info info
;
219 /* This type represents the kind of change that has been performed
220 * while trying to coalesce two basic maps.
222 * isl_change_none: nothing was changed
223 * isl_change_drop_first: the first basic map was removed
224 * isl_change_drop_second: the second basic map was removed
225 * isl_change_fuse: the two basic maps were replaced by a new basic map.
228 isl_change_error
= -1,
230 isl_change_drop_first
,
231 isl_change_drop_second
,
235 /* Update "change" based on an interchange of the first and the second
236 * basic map. That is, interchange isl_change_drop_first and
237 * isl_change_drop_second.
239 static enum isl_change
invert_change(enum isl_change change
)
242 case isl_change_error
:
243 return isl_change_error
;
244 case isl_change_none
:
245 return isl_change_none
;
246 case isl_change_drop_first
:
247 return isl_change_drop_second
;
248 case isl_change_drop_second
:
249 return isl_change_drop_first
;
250 case isl_change_fuse
:
251 return isl_change_fuse
;
255 /* Add the valid constraints of the basic map represented by "info"
256 * to "bmap". "len" is the size of the constraints.
257 * If only one of the pair of inequalities that make up an equality
258 * is valid, then add that inequality.
260 static __isl_give isl_basic_map
*add_valid_constraints(
261 __isl_take isl_basic_map
*bmap
, struct isl_coalesce_info
*info
,
269 for (k
= 0; k
< info
->bmap
->n_eq
; ++k
) {
270 if (info
->eq
[2 * k
] == STATUS_VALID
&&
271 info
->eq
[2 * k
+ 1] == STATUS_VALID
) {
272 l
= isl_basic_map_alloc_equality(bmap
);
274 return isl_basic_map_free(bmap
);
275 isl_seq_cpy(bmap
->eq
[l
], info
->bmap
->eq
[k
], len
);
276 } else if (info
->eq
[2 * k
] == STATUS_VALID
) {
277 l
= isl_basic_map_alloc_inequality(bmap
);
279 return isl_basic_map_free(bmap
);
280 isl_seq_neg(bmap
->ineq
[l
], info
->bmap
->eq
[k
], len
);
281 } else if (info
->eq
[2 * k
+ 1] == STATUS_VALID
) {
282 l
= isl_basic_map_alloc_inequality(bmap
);
284 return isl_basic_map_free(bmap
);
285 isl_seq_cpy(bmap
->ineq
[l
], info
->bmap
->eq
[k
], len
);
289 for (k
= 0; k
< info
->bmap
->n_ineq
; ++k
) {
290 if (info
->ineq
[k
] != STATUS_VALID
)
292 l
= isl_basic_map_alloc_inequality(bmap
);
294 return isl_basic_map_free(bmap
);
295 isl_seq_cpy(bmap
->ineq
[l
], info
->bmap
->ineq
[k
], len
);
301 /* Is "bmap" defined by a number of (non-redundant) constraints that
302 * is greater than the number of constraints of basic maps i and j combined?
303 * Equalities are counted as two inequalities.
305 static int number_of_constraints_increases(int i
, int j
,
306 struct isl_coalesce_info
*info
,
307 __isl_keep isl_basic_map
*bmap
, struct isl_tab
*tab
)
311 n_old
= 2 * info
[i
].bmap
->n_eq
+ info
[i
].bmap
->n_ineq
;
312 n_old
+= 2 * info
[j
].bmap
->n_eq
+ info
[j
].bmap
->n_ineq
;
314 n_new
= 2 * bmap
->n_eq
;
315 for (k
= 0; k
< bmap
->n_ineq
; ++k
)
316 if (!isl_tab_is_redundant(tab
, bmap
->n_eq
+ k
))
319 return n_new
> n_old
;
322 /* Replace the pair of basic maps i and j by the basic map bounded
323 * by the valid constraints in both basic maps and the constraints
324 * in extra (if not NULL).
325 * Place the fused basic map in the position that is the smallest of i and j.
327 * If "detect_equalities" is set, then look for equalities encoded
328 * as pairs of inequalities.
329 * If "check_number" is set, then the original basic maps are only
330 * replaced if the total number of constraints does not increase.
331 * While the number of integer divisions in the two basic maps
332 * is assumed to be the same, the actual definitions may be different.
333 * We only copy the definition from one of the basic map if it is
334 * the same as that of the other basic map. Otherwise, we mark
335 * the integer division as unknown and schedule for the basic map
336 * to be simplified in an attempt to recover the integer division definition.
338 static enum isl_change
fuse(int i
, int j
, struct isl_coalesce_info
*info
,
339 __isl_keep isl_mat
*extra
, int detect_equalities
, int check_number
)
342 struct isl_basic_map
*fused
= NULL
;
343 struct isl_tab
*fused_tab
= NULL
;
344 unsigned total
= isl_basic_map_total_dim(info
[i
].bmap
);
345 unsigned extra_rows
= extra
? extra
->n_row
: 0;
346 unsigned n_eq
, n_ineq
;
349 return fuse(j
, i
, info
, extra
, detect_equalities
, check_number
);
351 n_eq
= info
[i
].bmap
->n_eq
+ info
[j
].bmap
->n_eq
;
352 n_ineq
= info
[i
].bmap
->n_ineq
+ info
[j
].bmap
->n_ineq
;
353 fused
= isl_basic_map_alloc_space(isl_space_copy(info
[i
].bmap
->dim
),
354 info
[i
].bmap
->n_div
, n_eq
, n_eq
+ n_ineq
+ extra_rows
);
355 fused
= add_valid_constraints(fused
, &info
[i
], 1 + total
);
356 fused
= add_valid_constraints(fused
, &info
[j
], 1 + total
);
360 for (k
= 0; k
< info
[i
].bmap
->n_div
; ++k
) {
361 int l
= isl_basic_map_alloc_div(fused
);
364 if (isl_seq_eq(info
[i
].bmap
->div
[k
], info
[j
].bmap
->div
[k
],
366 isl_seq_cpy(fused
->div
[l
], info
[i
].bmap
->div
[k
],
369 isl_int_set_si(fused
->div
[l
][0], 0);
370 info
[i
].simplify
= 1;
374 for (k
= 0; k
< extra_rows
; ++k
) {
375 l
= isl_basic_map_alloc_inequality(fused
);
378 isl_seq_cpy(fused
->ineq
[l
], extra
->row
[k
], 1 + total
);
381 if (detect_equalities
)
382 fused
= isl_basic_map_detect_inequality_pairs(fused
, NULL
);
383 fused
= isl_basic_map_gauss(fused
, NULL
);
384 ISL_F_SET(fused
, ISL_BASIC_MAP_FINAL
);
385 if (ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_RATIONAL
) &&
386 ISL_F_ISSET(info
[j
].bmap
, ISL_BASIC_MAP_RATIONAL
))
387 ISL_F_SET(fused
, ISL_BASIC_MAP_RATIONAL
);
389 fused_tab
= isl_tab_from_basic_map(fused
, 0);
390 if (isl_tab_detect_redundant(fused_tab
) < 0)
394 number_of_constraints_increases(i
, j
, info
, fused
, fused_tab
)) {
395 isl_tab_free(fused_tab
);
396 isl_basic_map_free(fused
);
397 return isl_change_none
;
400 info
[i
].simplify
|= info
[j
].simplify
;
401 isl_basic_map_free(info
[i
].bmap
);
402 info
[i
].bmap
= fused
;
403 isl_tab_free(info
[i
].tab
);
404 info
[i
].tab
= fused_tab
;
407 return isl_change_fuse
;
409 isl_tab_free(fused_tab
);
410 isl_basic_map_free(fused
);
411 return isl_change_error
;
414 /* Given a pair of basic maps i and j such that all constraints are either
415 * "valid" or "cut", check if the facets corresponding to the "cut"
416 * constraints of i lie entirely within basic map j.
417 * If so, replace the pair by the basic map consisting of the valid
418 * constraints in both basic maps.
419 * Checking whether the facet lies entirely within basic map j
420 * is performed by checking whether the constraints of basic map j
421 * are valid for the facet. These tests are performed on a rational
422 * tableau to avoid the theoretical possibility that a constraint
423 * that was considered to be a cut constraint for the entire basic map i
424 * happens to be considered to be a valid constraint for the facet,
425 * even though it cuts off the same rational points.
427 * To see that we are not introducing any extra points, call the
428 * two basic maps A and B and the resulting map U and let x
429 * be an element of U \setminus ( A \cup B ).
430 * A line connecting x with an element of A \cup B meets a facet F
431 * of either A or B. Assume it is a facet of B and let c_1 be
432 * the corresponding facet constraint. We have c_1(x) < 0 and
433 * so c_1 is a cut constraint. This implies that there is some
434 * (possibly rational) point x' satisfying the constraints of A
435 * and the opposite of c_1 as otherwise c_1 would have been marked
436 * valid for A. The line connecting x and x' meets a facet of A
437 * in a (possibly rational) point that also violates c_1, but this
438 * is impossible since all cut constraints of B are valid for all
440 * In case F is a facet of A rather than B, then we can apply the
441 * above reasoning to find a facet of B separating x from A \cup B first.
443 static enum isl_change
check_facets(int i
, int j
,
444 struct isl_coalesce_info
*info
)
447 struct isl_tab_undo
*snap
, *snap2
;
448 unsigned n_eq
= info
[i
].bmap
->n_eq
;
450 snap
= isl_tab_snap(info
[i
].tab
);
451 if (isl_tab_mark_rational(info
[i
].tab
) < 0)
452 return isl_change_error
;
453 snap2
= isl_tab_snap(info
[i
].tab
);
455 for (k
= 0; k
< info
[i
].bmap
->n_ineq
; ++k
) {
456 if (info
[i
].ineq
[k
] != STATUS_CUT
)
458 if (isl_tab_select_facet(info
[i
].tab
, n_eq
+ k
) < 0)
459 return isl_change_error
;
460 for (l
= 0; l
< info
[j
].bmap
->n_ineq
; ++l
) {
462 if (info
[j
].ineq
[l
] != STATUS_CUT
)
464 stat
= status_in(info
[j
].bmap
->ineq
[l
], info
[i
].tab
);
465 if (stat
!= STATUS_VALID
)
468 if (isl_tab_rollback(info
[i
].tab
, snap2
) < 0)
469 return isl_change_error
;
470 if (l
< info
[j
].bmap
->n_ineq
)
474 if (k
< info
[i
].bmap
->n_ineq
) {
475 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
476 return isl_change_error
;
477 return isl_change_none
;
479 return fuse(i
, j
, info
, NULL
, 0, 0);
482 /* Check if info->bmap contains the basic map represented
483 * by the tableau "tab".
484 * For each equality, we check both the constraint itself
485 * (as an inequality) and its negation. Make sure the
486 * equality is returned to its original state before returning.
488 static int contains(struct isl_coalesce_info
*info
, struct isl_tab
*tab
)
492 isl_basic_map
*bmap
= info
->bmap
;
494 dim
= isl_basic_map_total_dim(bmap
);
495 for (k
= 0; k
< bmap
->n_eq
; ++k
) {
497 isl_seq_neg(bmap
->eq
[k
], bmap
->eq
[k
], 1 + dim
);
498 stat
= status_in(bmap
->eq
[k
], tab
);
499 isl_seq_neg(bmap
->eq
[k
], bmap
->eq
[k
], 1 + dim
);
500 if (stat
!= STATUS_VALID
)
502 stat
= status_in(bmap
->eq
[k
], tab
);
503 if (stat
!= STATUS_VALID
)
507 for (k
= 0; k
< bmap
->n_ineq
; ++k
) {
509 if (info
->ineq
[k
] == STATUS_REDUNDANT
)
511 stat
= status_in(bmap
->ineq
[k
], tab
);
512 if (stat
!= STATUS_VALID
)
518 /* Basic map "i" has an inequality (say "k") that is adjacent
519 * to some inequality of basic map "j". All the other inequalities
521 * Check if basic map "j" forms an extension of basic map "i".
523 * Note that this function is only called if some of the equalities or
524 * inequalities of basic map "j" do cut basic map "i". The function is
525 * correct even if there are no such cut constraints, but in that case
526 * the additional checks performed by this function are overkill.
528 * In particular, we replace constraint k, say f >= 0, by constraint
529 * f <= -1, add the inequalities of "j" that are valid for "i"
530 * and check if the result is a subset of basic map "j".
531 * If so, then we know that this result is exactly equal to basic map "j"
532 * since all its constraints are valid for basic map "j".
533 * By combining the valid constraints of "i" (all equalities and all
534 * inequalities except "k") and the valid constraints of "j" we therefore
535 * obtain a basic map that is equal to their union.
536 * In this case, there is no need to perform a rollback of the tableau
537 * since it is going to be destroyed in fuse().
543 * |_______| _ |_________\
555 static enum isl_change
is_adj_ineq_extension(int i
, int j
,
556 struct isl_coalesce_info
*info
)
559 struct isl_tab_undo
*snap
;
560 unsigned n_eq
= info
[i
].bmap
->n_eq
;
561 unsigned total
= isl_basic_map_total_dim(info
[i
].bmap
);
564 if (isl_tab_extend_cons(info
[i
].tab
, 1 + info
[j
].bmap
->n_ineq
) < 0)
565 return isl_change_error
;
567 for (k
= 0; k
< info
[i
].bmap
->n_ineq
; ++k
)
568 if (info
[i
].ineq
[k
] == STATUS_ADJ_INEQ
)
570 if (k
>= info
[i
].bmap
->n_ineq
)
571 isl_die(isl_basic_map_get_ctx(info
[i
].bmap
), isl_error_internal
,
572 "info[i].ineq should have exactly one STATUS_ADJ_INEQ",
573 return isl_change_error
);
575 snap
= isl_tab_snap(info
[i
].tab
);
577 if (isl_tab_unrestrict(info
[i
].tab
, n_eq
+ k
) < 0)
578 return isl_change_error
;
580 isl_seq_neg(info
[i
].bmap
->ineq
[k
], info
[i
].bmap
->ineq
[k
], 1 + total
);
581 isl_int_sub_ui(info
[i
].bmap
->ineq
[k
][0], info
[i
].bmap
->ineq
[k
][0], 1);
582 r
= isl_tab_add_ineq(info
[i
].tab
, info
[i
].bmap
->ineq
[k
]);
583 isl_seq_neg(info
[i
].bmap
->ineq
[k
], info
[i
].bmap
->ineq
[k
], 1 + total
);
584 isl_int_sub_ui(info
[i
].bmap
->ineq
[k
][0], info
[i
].bmap
->ineq
[k
][0], 1);
586 return isl_change_error
;
588 for (k
= 0; k
< info
[j
].bmap
->n_ineq
; ++k
) {
589 if (info
[j
].ineq
[k
] != STATUS_VALID
)
591 if (isl_tab_add_ineq(info
[i
].tab
, info
[j
].bmap
->ineq
[k
]) < 0)
592 return isl_change_error
;
595 if (contains(&info
[j
], info
[i
].tab
))
596 return fuse(i
, j
, info
, NULL
, 0, 0);
598 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
599 return isl_change_error
;
601 return isl_change_none
;
605 /* Both basic maps have at least one inequality with and adjacent
606 * (but opposite) inequality in the other basic map.
607 * Check that there are no cut constraints and that there is only
608 * a single pair of adjacent inequalities.
609 * If so, we can replace the pair by a single basic map described
610 * by all but the pair of adjacent inequalities.
611 * Any additional points introduced lie strictly between the two
612 * adjacent hyperplanes and can therefore be integral.
621 * The test for a single pair of adjancent inequalities is important
622 * for avoiding the combination of two basic maps like the following
632 * If there are some cut constraints on one side, then we may
633 * still be able to fuse the two basic maps, but we need to perform
634 * some additional checks in is_adj_ineq_extension.
636 static enum isl_change
check_adj_ineq(int i
, int j
,
637 struct isl_coalesce_info
*info
)
639 int count_i
, count_j
;
642 count_i
= count(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ADJ_INEQ
);
643 count_j
= count(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_ADJ_INEQ
);
645 if (count_i
!= 1 && count_j
!= 1)
646 return isl_change_none
;
648 cut_i
= any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_CUT
) ||
649 any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_CUT
);
650 cut_j
= any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_CUT
) ||
651 any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_CUT
);
653 if (!cut_i
&& !cut_j
&& count_i
== 1 && count_j
== 1)
654 return fuse(i
, j
, info
, NULL
, 0, 0);
656 if (count_i
== 1 && !cut_i
)
657 return is_adj_ineq_extension(i
, j
, info
);
659 if (count_j
== 1 && !cut_j
)
660 return is_adj_ineq_extension(j
, i
, info
);
662 return isl_change_none
;
665 /* Basic map "i" has an inequality "k" that is adjacent to some equality
666 * of basic map "j". All the other inequalities are valid for "j".
667 * Check if basic map "j" forms an extension of basic map "i".
669 * In particular, we relax constraint "k", compute the corresponding
670 * facet and check whether it is included in the other basic map.
671 * If so, we know that relaxing the constraint extends the basic
672 * map with exactly the other basic map (we already know that this
673 * other basic map is included in the extension, because there
674 * were no "cut" inequalities in "i") and we can replace the
675 * two basic maps by this extension.
676 * Each integer division that does not have exactly the same
677 * definition in "i" and "j" is marked unknown and the basic map
678 * is scheduled to be simplified in an attempt to recover
679 * the integer division definition.
680 * Place this extension in the position that is the smallest of i and j.
688 static enum isl_change
is_adj_eq_extension(int i
, int j
, int k
,
689 struct isl_coalesce_info
*info
)
691 int change
= isl_change_none
;
693 struct isl_tab_undo
*snap
, *snap2
;
694 unsigned n_eq
= info
[i
].bmap
->n_eq
;
696 if (isl_tab_is_equality(info
[i
].tab
, n_eq
+ k
))
697 return isl_change_none
;
699 snap
= isl_tab_snap(info
[i
].tab
);
700 if (isl_tab_relax(info
[i
].tab
, n_eq
+ k
) < 0)
701 return isl_change_error
;
702 snap2
= isl_tab_snap(info
[i
].tab
);
703 if (isl_tab_select_facet(info
[i
].tab
, n_eq
+ k
) < 0)
704 return isl_change_error
;
705 super
= contains(&info
[j
], info
[i
].tab
);
710 if (isl_tab_rollback(info
[i
].tab
, snap2
) < 0)
711 return isl_change_error
;
712 info
[i
].bmap
= isl_basic_map_cow(info
[i
].bmap
);
714 return isl_change_error
;
715 total
= isl_basic_map_total_dim(info
[i
].bmap
);
716 for (l
= 0; l
< info
[i
].bmap
->n_div
; ++l
)
717 if (!isl_seq_eq(info
[i
].bmap
->div
[l
],
718 info
[j
].bmap
->div
[l
], 1 + 1 + total
)) {
719 isl_int_set_si(info
[i
].bmap
->div
[l
][0], 0);
720 info
[i
].simplify
= 1;
722 isl_int_add_ui(info
[i
].bmap
->ineq
[k
][0],
723 info
[i
].bmap
->ineq
[k
][0], 1);
724 ISL_F_SET(info
[i
].bmap
, ISL_BASIC_MAP_FINAL
);
727 exchange(&info
[i
], &info
[j
]);
728 change
= isl_change_fuse
;
730 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
731 return isl_change_error
;
736 /* Data structure that keeps track of the wrapping constraints
737 * and of information to bound the coefficients of those constraints.
739 * bound is set if we want to apply a bound on the coefficients
740 * mat contains the wrapping constraints
741 * max is the bound on the coefficients (if bound is set)
749 /* Update wraps->max to be greater than or equal to the coefficients
750 * in the equalities and inequalities of info->bmap that can be removed
751 * if we end up applying wrapping.
753 static void wraps_update_max(struct isl_wraps
*wraps
,
754 struct isl_coalesce_info
*info
)
758 unsigned total
= isl_basic_map_total_dim(info
->bmap
);
762 for (k
= 0; k
< info
->bmap
->n_eq
; ++k
) {
763 if (info
->eq
[2 * k
] == STATUS_VALID
&&
764 info
->eq
[2 * k
+ 1] == STATUS_VALID
)
766 isl_seq_abs_max(info
->bmap
->eq
[k
] + 1, total
, &max_k
);
767 if (isl_int_abs_gt(max_k
, wraps
->max
))
768 isl_int_set(wraps
->max
, max_k
);
771 for (k
= 0; k
< info
->bmap
->n_ineq
; ++k
) {
772 if (info
->ineq
[k
] == STATUS_VALID
||
773 info
->ineq
[k
] == STATUS_REDUNDANT
)
775 isl_seq_abs_max(info
->bmap
->ineq
[k
] + 1, total
, &max_k
);
776 if (isl_int_abs_gt(max_k
, wraps
->max
))
777 isl_int_set(wraps
->max
, max_k
);
780 isl_int_clear(max_k
);
783 /* Initialize the isl_wraps data structure.
784 * If we want to bound the coefficients of the wrapping constraints,
785 * we set wraps->max to the largest coefficient
786 * in the equalities and inequalities that can be removed if we end up
789 static void wraps_init(struct isl_wraps
*wraps
, __isl_take isl_mat
*mat
,
790 struct isl_coalesce_info
*info
, int i
, int j
)
798 ctx
= isl_mat_get_ctx(mat
);
799 wraps
->bound
= isl_options_get_coalesce_bounded_wrapping(ctx
);
802 isl_int_init(wraps
->max
);
803 isl_int_set_si(wraps
->max
, 0);
804 wraps_update_max(wraps
, &info
[i
]);
805 wraps_update_max(wraps
, &info
[j
]);
808 /* Free the contents of the isl_wraps data structure.
810 static void wraps_free(struct isl_wraps
*wraps
)
812 isl_mat_free(wraps
->mat
);
814 isl_int_clear(wraps
->max
);
817 /* Is the wrapping constraint in row "row" allowed?
819 * If wraps->bound is set, we check that none of the coefficients
820 * is greater than wraps->max.
822 static int allow_wrap(struct isl_wraps
*wraps
, int row
)
829 for (i
= 1; i
< wraps
->mat
->n_col
; ++i
)
830 if (isl_int_abs_gt(wraps
->mat
->row
[row
][i
], wraps
->max
))
836 /* Wrap "ineq" (or its opposite if "negate" is set) around "bound"
837 * to include "set" and add the result in position "w" of "wraps".
838 * "len" is the total number of coefficients in "bound" and "ineq".
839 * Return 1 on success, 0 on failure and -1 on error.
840 * Wrapping can fail if the result of wrapping is equal to "bound"
841 * or if we want to bound the sizes of the coefficients and
842 * the wrapped constraint does not satisfy this bound.
844 static int add_wrap(struct isl_wraps
*wraps
, int w
, isl_int
*bound
,
845 isl_int
*ineq
, unsigned len
, __isl_keep isl_set
*set
, int negate
)
847 isl_seq_cpy(wraps
->mat
->row
[w
], bound
, len
);
849 isl_seq_neg(wraps
->mat
->row
[w
+ 1], ineq
, len
);
850 ineq
= wraps
->mat
->row
[w
+ 1];
852 if (!isl_set_wrap_facet(set
, wraps
->mat
->row
[w
], ineq
))
854 if (isl_seq_eq(wraps
->mat
->row
[w
], bound
, len
))
856 if (!allow_wrap(wraps
, w
))
861 /* For each constraint in info->bmap that is not redundant (as determined
862 * by info->tab) and that is not a valid constraint for the other basic map,
863 * wrap the constraint around "bound" such that it includes the whole
864 * set "set" and append the resulting constraint to "wraps".
865 * Note that the constraints that are valid for the other basic map
866 * will be added to the combined basic map by default, so there is
867 * no need to wrap them.
868 * The caller wrap_in_facets even relies on this function not wrapping
869 * any constraints that are already valid.
870 * "wraps" is assumed to have been pre-allocated to the appropriate size.
871 * wraps->n_row is the number of actual wrapped constraints that have
873 * If any of the wrapping problems results in a constraint that is
874 * identical to "bound", then this means that "set" is unbounded in such
875 * way that no wrapping is possible. If this happens then wraps->n_row
877 * Similarly, if we want to bound the coefficients of the wrapping
878 * constraints and a newly added wrapping constraint does not
879 * satisfy the bound, then wraps->n_row is also reset to zero.
881 static int add_wraps(struct isl_wraps
*wraps
, struct isl_coalesce_info
*info
,
882 isl_int
*bound
, __isl_keep isl_set
*set
)
887 isl_basic_map
*bmap
= info
->bmap
;
888 unsigned len
= 1 + isl_basic_map_total_dim(bmap
);
890 w
= wraps
->mat
->n_row
;
892 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
893 if (info
->ineq
[l
] == STATUS_VALID
||
894 info
->ineq
[l
] == STATUS_REDUNDANT
)
896 if (isl_seq_is_neg(bound
, bmap
->ineq
[l
], len
))
898 if (isl_seq_eq(bound
, bmap
->ineq
[l
], len
))
900 if (isl_tab_is_redundant(info
->tab
, bmap
->n_eq
+ l
))
903 added
= add_wrap(wraps
, w
, bound
, bmap
->ineq
[l
], len
, set
, 0);
910 for (l
= 0; l
< bmap
->n_eq
; ++l
) {
911 if (isl_seq_is_neg(bound
, bmap
->eq
[l
], len
))
913 if (isl_seq_eq(bound
, bmap
->eq
[l
], len
))
916 for (m
= 0; m
< 2; ++m
) {
917 if (info
->eq
[2 * l
+ m
] == STATUS_VALID
)
919 added
= add_wrap(wraps
, w
, bound
, bmap
->eq
[l
], len
,
929 wraps
->mat
->n_row
= w
;
932 wraps
->mat
->n_row
= 0;
936 /* Check if the constraints in "wraps" from "first" until the last
937 * are all valid for the basic set represented by "tab".
938 * If not, wraps->n_row is set to zero.
940 static int check_wraps(__isl_keep isl_mat
*wraps
, int first
,
945 for (i
= first
; i
< wraps
->n_row
; ++i
) {
946 enum isl_ineq_type type
;
947 type
= isl_tab_ineq_type(tab
, wraps
->row
[i
]);
948 if (type
== isl_ineq_error
)
950 if (type
== isl_ineq_redundant
)
959 /* Return a set that corresponds to the non-redundant constraints
960 * (as recorded in tab) of bmap.
962 * It's important to remove the redundant constraints as some
963 * of the other constraints may have been modified after the
964 * constraints were marked redundant.
965 * In particular, a constraint may have been relaxed.
966 * Redundant constraints are ignored when a constraint is relaxed
967 * and should therefore continue to be ignored ever after.
968 * Otherwise, the relaxation might be thwarted by some of
971 * Update the underlying set to ensure that the dimension doesn't change.
972 * Otherwise the integer divisions could get dropped if the tab
973 * turns out to be empty.
975 static __isl_give isl_set
*set_from_updated_bmap(__isl_keep isl_basic_map
*bmap
,
980 bmap
= isl_basic_map_copy(bmap
);
981 bset
= isl_basic_map_underlying_set(bmap
);
982 bset
= isl_basic_set_cow(bset
);
983 bset
= isl_basic_set_update_from_tab(bset
, tab
);
984 return isl_set_from_basic_set(bset
);
987 /* Wrap the constraints of info->bmap that bound the facet defined
988 * by inequality "k" around (the opposite of) this inequality to
989 * include "set". "bound" may be used to store the negated inequality.
990 * Since the wrapped constraints are not guaranteed to contain the whole
991 * of info->bmap, we check them in check_wraps.
992 * If any of the wrapped constraints turn out to be invalid, then
993 * check_wraps will reset wrap->n_row to zero.
995 static int add_wraps_around_facet(struct isl_wraps
*wraps
,
996 struct isl_coalesce_info
*info
, int k
, isl_int
*bound
,
997 __isl_keep isl_set
*set
)
999 struct isl_tab_undo
*snap
;
1001 unsigned total
= isl_basic_map_total_dim(info
->bmap
);
1003 snap
= isl_tab_snap(info
->tab
);
1005 if (isl_tab_select_facet(info
->tab
, info
->bmap
->n_eq
+ k
) < 0)
1007 if (isl_tab_detect_redundant(info
->tab
) < 0)
1010 isl_seq_neg(bound
, info
->bmap
->ineq
[k
], 1 + total
);
1012 n
= wraps
->mat
->n_row
;
1013 if (add_wraps(wraps
, info
, bound
, set
) < 0)
1016 if (isl_tab_rollback(info
->tab
, snap
) < 0)
1018 if (check_wraps(wraps
->mat
, n
, info
->tab
) < 0)
1024 /* Given a basic set i with a constraint k that is adjacent to
1025 * basic set j, check if we can wrap
1026 * both the facet corresponding to k (if "wrap_facet" is set) and basic map j
1027 * (always) around their ridges to include the other set.
1028 * If so, replace the pair of basic sets by their union.
1030 * All constraints of i (except k) are assumed to be valid or
1031 * cut constraints for j.
1032 * Wrapping the cut constraints to include basic map j may result
1033 * in constraints that are no longer valid of basic map i
1034 * we have to check that the resulting wrapping constraints are valid for i.
1035 * If "wrap_facet" is not set, then all constraints of i (except k)
1036 * are assumed to be valid for j.
1045 static enum isl_change
can_wrap_in_facet(int i
, int j
, int k
,
1046 struct isl_coalesce_info
*info
, int wrap_facet
)
1048 enum isl_change change
= isl_change_none
;
1049 struct isl_wraps wraps
;
1052 struct isl_set
*set_i
= NULL
;
1053 struct isl_set
*set_j
= NULL
;
1054 struct isl_vec
*bound
= NULL
;
1055 unsigned total
= isl_basic_map_total_dim(info
[i
].bmap
);
1057 set_i
= set_from_updated_bmap(info
[i
].bmap
, info
[i
].tab
);
1058 set_j
= set_from_updated_bmap(info
[j
].bmap
, info
[j
].tab
);
1059 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
1060 mat
= isl_mat_alloc(ctx
, 2 * (info
[i
].bmap
->n_eq
+ info
[j
].bmap
->n_eq
) +
1061 info
[i
].bmap
->n_ineq
+ info
[j
].bmap
->n_ineq
,
1063 wraps_init(&wraps
, mat
, info
, i
, j
);
1064 bound
= isl_vec_alloc(ctx
, 1 + total
);
1065 if (!set_i
|| !set_j
|| !wraps
.mat
|| !bound
)
1068 isl_seq_cpy(bound
->el
, info
[i
].bmap
->ineq
[k
], 1 + total
);
1069 isl_int_add_ui(bound
->el
[0], bound
->el
[0], 1);
1071 isl_seq_cpy(wraps
.mat
->row
[0], bound
->el
, 1 + total
);
1072 wraps
.mat
->n_row
= 1;
1074 if (add_wraps(&wraps
, &info
[j
], bound
->el
, set_i
) < 0)
1076 if (!wraps
.mat
->n_row
)
1080 if (add_wraps_around_facet(&wraps
, &info
[i
], k
,
1081 bound
->el
, set_j
) < 0)
1083 if (!wraps
.mat
->n_row
)
1087 change
= fuse(i
, j
, info
, wraps
.mat
, 0, 0);
1092 isl_set_free(set_i
);
1093 isl_set_free(set_j
);
1095 isl_vec_free(bound
);
1100 isl_vec_free(bound
);
1101 isl_set_free(set_i
);
1102 isl_set_free(set_j
);
1103 return isl_change_error
;
1106 /* Given a pair of basic maps i and j such that j sticks out
1107 * of i at n cut constraints, each time by at most one,
1108 * try to compute wrapping constraints and replace the two
1109 * basic maps by a single basic map.
1110 * The other constraints of i are assumed to be valid for j.
1112 * For each cut constraint t(x) >= 0 of i, we add the relaxed version
1113 * t(x) + 1 >= 0, along with wrapping constraints for all constraints
1114 * of basic map j that bound the part of basic map j that sticks out
1115 * of the cut constraint.
1116 * In particular, we first intersect basic map j with t(x) + 1 = 0.
1117 * If the result is empty, then t(x) >= 0 was actually a valid constraint
1118 * (with respect to the integer points), so we add t(x) >= 0 instead.
1119 * Otherwise, we wrap the constraints of basic map j that are not
1120 * redundant in this intersection and that are not already valid
1121 * for basic map i over basic map i.
1122 * Note that it is sufficient to wrap the constraints to include
1123 * basic map i, because we will only wrap the constraints that do
1124 * not include basic map i already. The wrapped constraint will
1125 * therefore be more relaxed compared to the original constraint.
1126 * Since the original constraint is valid for basic map j, so is
1127 * the wrapped constraint.
1129 * If any wrapping fails, i.e., if we cannot wrap to touch
1130 * the union, then we give up.
1131 * Otherwise, the pair of basic maps is replaced by their union.
1133 static enum isl_change
wrap_in_facets(int i
, int j
, int *cuts
, int n
,
1134 struct isl_coalesce_info
*info
)
1136 enum isl_change change
= isl_change_none
;
1137 struct isl_wraps wraps
;
1140 isl_set
*set_i
= NULL
;
1141 unsigned total
= isl_basic_map_total_dim(info
[i
].bmap
);
1144 struct isl_tab_undo
*snap
;
1146 if (isl_tab_extend_cons(info
[j
].tab
, 1) < 0)
1149 max_wrap
= 1 + 2 * info
[j
].bmap
->n_eq
+ info
[j
].bmap
->n_ineq
;
1152 set_i
= set_from_updated_bmap(info
[i
].bmap
, info
[i
].tab
);
1153 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
1154 mat
= isl_mat_alloc(ctx
, max_wrap
, 1 + total
);
1155 wraps_init(&wraps
, mat
, info
, i
, j
);
1156 if (!set_i
|| !wraps
.mat
)
1159 snap
= isl_tab_snap(info
[j
].tab
);
1161 wraps
.mat
->n_row
= 0;
1163 for (k
= 0; k
< n
; ++k
) {
1164 w
= wraps
.mat
->n_row
++;
1165 isl_seq_cpy(wraps
.mat
->row
[w
],
1166 info
[i
].bmap
->ineq
[cuts
[k
]], 1 + total
);
1167 isl_int_add_ui(wraps
.mat
->row
[w
][0], wraps
.mat
->row
[w
][0], 1);
1168 if (isl_tab_add_eq(info
[j
].tab
, wraps
.mat
->row
[w
]) < 0)
1170 if (isl_tab_detect_redundant(info
[j
].tab
) < 0)
1173 if (info
[j
].tab
->empty
)
1174 isl_int_sub_ui(wraps
.mat
->row
[w
][0],
1175 wraps
.mat
->row
[w
][0], 1);
1176 else if (add_wraps(&wraps
, &info
[j
],
1177 wraps
.mat
->row
[w
], set_i
) < 0)
1180 if (isl_tab_rollback(info
[j
].tab
, snap
) < 0)
1183 if (!wraps
.mat
->n_row
)
1188 change
= fuse(i
, j
, info
, wraps
.mat
, 0, 1);
1191 isl_set_free(set_i
);
1196 isl_set_free(set_i
);
1197 return isl_change_error
;
1200 /* Given two basic sets i and j such that i has no cut equalities,
1201 * check if relaxing all the cut inequalities of i by one turns
1202 * them into valid constraint for j and check if we can wrap in
1203 * the bits that are sticking out.
1204 * If so, replace the pair by their union.
1206 * We first check if all relaxed cut inequalities of i are valid for j
1207 * and then try to wrap in the intersections of the relaxed cut inequalities
1210 * During this wrapping, we consider the points of j that lie at a distance
1211 * of exactly 1 from i. In particular, we ignore the points that lie in
1212 * between this lower-dimensional space and the basic map i.
1213 * We can therefore only apply this to integer maps.
1239 * Wrapping can fail if the result of wrapping one of the facets
1240 * around its edges does not produce any new facet constraint.
1241 * In particular, this happens when we try to wrap in unbounded sets.
1243 * _______________________________________________________________________
1247 * |_| |_________________________________________________________________
1250 * The following is not an acceptable result of coalescing the above two
1251 * sets as it includes extra integer points.
1252 * _______________________________________________________________________
1257 * \______________________________________________________________________
1259 static enum isl_change
can_wrap_in_set(int i
, int j
,
1260 struct isl_coalesce_info
*info
)
1262 enum isl_change change
= isl_change_none
;
1268 if (ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_RATIONAL
) ||
1269 ISL_F_ISSET(info
[j
].bmap
, ISL_BASIC_MAP_RATIONAL
))
1270 return isl_change_none
;
1272 n
= count(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_CUT
);
1274 return isl_change_none
;
1276 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
1277 cuts
= isl_alloc_array(ctx
, int, n
);
1279 return isl_change_error
;
1281 for (k
= 0, m
= 0; m
< n
; ++k
) {
1282 enum isl_ineq_type type
;
1284 if (info
[i
].ineq
[k
] != STATUS_CUT
)
1287 isl_int_add_ui(info
[i
].bmap
->ineq
[k
][0],
1288 info
[i
].bmap
->ineq
[k
][0], 1);
1289 type
= isl_tab_ineq_type(info
[j
].tab
, info
[i
].bmap
->ineq
[k
]);
1290 isl_int_sub_ui(info
[i
].bmap
->ineq
[k
][0],
1291 info
[i
].bmap
->ineq
[k
][0], 1);
1292 if (type
== isl_ineq_error
)
1294 if (type
!= isl_ineq_redundant
)
1301 change
= wrap_in_facets(i
, j
, cuts
, n
, info
);
1308 return isl_change_error
;
1311 /* Check if either i or j has only cut inequalities that can
1312 * be used to wrap in (a facet of) the other basic set.
1313 * if so, replace the pair by their union.
1315 static enum isl_change
check_wrap(int i
, int j
, struct isl_coalesce_info
*info
)
1317 enum isl_change change
= isl_change_none
;
1319 if (!any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_CUT
))
1320 change
= can_wrap_in_set(i
, j
, info
);
1321 if (change
!= isl_change_none
)
1324 if (!any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_CUT
))
1325 change
= can_wrap_in_set(j
, i
, info
);
1329 /* At least one of the basic maps has an equality that is adjacent
1330 * to inequality. Make sure that only one of the basic maps has
1331 * such an equality and that the other basic map has exactly one
1332 * inequality adjacent to an equality.
1333 * We call the basic map that has the inequality "i" and the basic
1334 * map that has the equality "j".
1335 * If "i" has any "cut" (in)equality, then relaxing the inequality
1336 * by one would not result in a basic map that contains the other
1337 * basic map. However, it may still be possible to wrap in the other
1340 static enum isl_change
check_adj_eq(int i
, int j
,
1341 struct isl_coalesce_info
*info
)
1343 enum isl_change change
= isl_change_none
;
1347 if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_ADJ_INEQ
) &&
1348 any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_ADJ_INEQ
))
1349 /* ADJ EQ TOO MANY */
1350 return isl_change_none
;
1352 if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_ADJ_INEQ
))
1353 return check_adj_eq(j
, i
, info
);
1355 /* j has an equality adjacent to an inequality in i */
1357 if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_CUT
))
1358 return isl_change_none
;
1359 any_cut
= any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_CUT
);
1360 if (count(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ADJ_EQ
) != 1 ||
1361 any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_ADJ_EQ
) ||
1362 any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ADJ_INEQ
) ||
1363 any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_ADJ_INEQ
))
1364 /* ADJ EQ TOO MANY */
1365 return isl_change_none
;
1367 for (k
= 0; k
< info
[i
].bmap
->n_ineq
; ++k
)
1368 if (info
[i
].ineq
[k
] == STATUS_ADJ_EQ
)
1372 change
= is_adj_eq_extension(i
, j
, k
, info
);
1373 if (change
!= isl_change_none
)
1377 change
= can_wrap_in_facet(i
, j
, k
, info
, any_cut
);
1382 /* The two basic maps lie on adjacent hyperplanes. In particular,
1383 * basic map "i" has an equality that lies parallel to basic map "j".
1384 * Check if we can wrap the facets around the parallel hyperplanes
1385 * to include the other set.
1387 * We perform basically the same operations as can_wrap_in_facet,
1388 * except that we don't need to select a facet of one of the sets.
1394 * If there is more than one equality of "i" adjacent to an equality of "j",
1395 * then the result will satisfy one or more equalities that are a linear
1396 * combination of these equalities. These will be encoded as pairs
1397 * of inequalities in the wrapping constraints and need to be made
1400 static enum isl_change
check_eq_adj_eq(int i
, int j
,
1401 struct isl_coalesce_info
*info
)
1404 enum isl_change change
= isl_change_none
;
1405 int detect_equalities
= 0;
1406 struct isl_wraps wraps
;
1409 struct isl_set
*set_i
= NULL
;
1410 struct isl_set
*set_j
= NULL
;
1411 struct isl_vec
*bound
= NULL
;
1412 unsigned total
= isl_basic_map_total_dim(info
[i
].bmap
);
1414 if (count(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_ADJ_EQ
) != 1)
1415 detect_equalities
= 1;
1417 for (k
= 0; k
< 2 * info
[i
].bmap
->n_eq
; ++k
)
1418 if (info
[i
].eq
[k
] == STATUS_ADJ_EQ
)
1421 set_i
= set_from_updated_bmap(info
[i
].bmap
, info
[i
].tab
);
1422 set_j
= set_from_updated_bmap(info
[j
].bmap
, info
[j
].tab
);
1423 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
1424 mat
= isl_mat_alloc(ctx
, 2 * (info
[i
].bmap
->n_eq
+ info
[j
].bmap
->n_eq
) +
1425 info
[i
].bmap
->n_ineq
+ info
[j
].bmap
->n_ineq
,
1427 wraps_init(&wraps
, mat
, info
, i
, j
);
1428 bound
= isl_vec_alloc(ctx
, 1 + total
);
1429 if (!set_i
|| !set_j
|| !wraps
.mat
|| !bound
)
1433 isl_seq_neg(bound
->el
, info
[i
].bmap
->eq
[k
/ 2], 1 + total
);
1435 isl_seq_cpy(bound
->el
, info
[i
].bmap
->eq
[k
/ 2], 1 + total
);
1436 isl_int_add_ui(bound
->el
[0], bound
->el
[0], 1);
1438 isl_seq_cpy(wraps
.mat
->row
[0], bound
->el
, 1 + total
);
1439 wraps
.mat
->n_row
= 1;
1441 if (add_wraps(&wraps
, &info
[j
], bound
->el
, set_i
) < 0)
1443 if (!wraps
.mat
->n_row
)
1446 isl_int_sub_ui(bound
->el
[0], bound
->el
[0], 1);
1447 isl_seq_neg(bound
->el
, bound
->el
, 1 + total
);
1449 isl_seq_cpy(wraps
.mat
->row
[wraps
.mat
->n_row
], bound
->el
, 1 + total
);
1452 if (add_wraps(&wraps
, &info
[i
], bound
->el
, set_j
) < 0)
1454 if (!wraps
.mat
->n_row
)
1457 change
= fuse(i
, j
, info
, wraps
.mat
, detect_equalities
, 0);
1460 error
: change
= isl_change_error
;
1465 isl_set_free(set_i
);
1466 isl_set_free(set_j
);
1467 isl_vec_free(bound
);
1472 /* Check if the union of the given pair of basic maps
1473 * can be represented by a single basic map.
1474 * If so, replace the pair by the single basic map and return
1475 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
1476 * Otherwise, return isl_change_none.
1477 * The two basic maps are assumed to live in the same local space.
1479 * We first check the effect of each constraint of one basic map
1480 * on the other basic map.
1481 * The constraint may be
1482 * redundant the constraint is redundant in its own
1483 * basic map and should be ignore and removed
1485 * valid all (integer) points of the other basic map
1486 * satisfy the constraint
1487 * separate no (integer) point of the other basic map
1488 * satisfies the constraint
1489 * cut some but not all points of the other basic map
1490 * satisfy the constraint
1491 * adj_eq the given constraint is adjacent (on the outside)
1492 * to an equality of the other basic map
1493 * adj_ineq the given constraint is adjacent (on the outside)
1494 * to an inequality of the other basic map
1496 * We consider seven cases in which we can replace the pair by a single
1497 * basic map. We ignore all "redundant" constraints.
1499 * 1. all constraints of one basic map are valid
1500 * => the other basic map is a subset and can be removed
1502 * 2. all constraints of both basic maps are either "valid" or "cut"
1503 * and the facets corresponding to the "cut" constraints
1504 * of one of the basic maps lies entirely inside the other basic map
1505 * => the pair can be replaced by a basic map consisting
1506 * of the valid constraints in both basic maps
1508 * 3. there is a single pair of adjacent inequalities
1509 * (all other constraints are "valid")
1510 * => the pair can be replaced by a basic map consisting
1511 * of the valid constraints in both basic maps
1513 * 4. one basic map has a single adjacent inequality, while the other
1514 * constraints are "valid". The other basic map has some
1515 * "cut" constraints, but replacing the adjacent inequality by
1516 * its opposite and adding the valid constraints of the other
1517 * basic map results in a subset of the other basic map
1518 * => the pair can be replaced by a basic map consisting
1519 * of the valid constraints in both basic maps
1521 * 5. there is a single adjacent pair of an inequality and an equality,
1522 * the other constraints of the basic map containing the inequality are
1523 * "valid". Moreover, if the inequality the basic map is relaxed
1524 * and then turned into an equality, then resulting facet lies
1525 * entirely inside the other basic map
1526 * => the pair can be replaced by the basic map containing
1527 * the inequality, with the inequality relaxed.
1529 * 6. there is a single adjacent pair of an inequality and an equality,
1530 * the other constraints of the basic map containing the inequality are
1531 * "valid". Moreover, the facets corresponding to both
1532 * the inequality and the equality can be wrapped around their
1533 * ridges to include the other basic map
1534 * => the pair can be replaced by a basic map consisting
1535 * of the valid constraints in both basic maps together
1536 * with all wrapping constraints
1538 * 7. one of the basic maps extends beyond the other by at most one.
1539 * Moreover, the facets corresponding to the cut constraints and
1540 * the pieces of the other basic map at offset one from these cut
1541 * constraints can be wrapped around their ridges to include
1542 * the union of the two basic maps
1543 * => the pair can be replaced by a basic map consisting
1544 * of the valid constraints in both basic maps together
1545 * with all wrapping constraints
1547 * 8. the two basic maps live in adjacent hyperplanes. In principle
1548 * such sets can always be combined through wrapping, but we impose
1549 * that there is only one such pair, to avoid overeager coalescing.
1551 * Throughout the computation, we maintain a collection of tableaus
1552 * corresponding to the basic maps. When the basic maps are dropped
1553 * or combined, the tableaus are modified accordingly.
1555 static enum isl_change
coalesce_local_pair(int i
, int j
,
1556 struct isl_coalesce_info
*info
)
1558 enum isl_change change
= isl_change_none
;
1560 info
[i
].eq
= info
[i
].ineq
= NULL
;
1561 info
[j
].eq
= info
[j
].ineq
= NULL
;
1563 info
[i
].eq
= eq_status_in(info
[i
].bmap
, info
[j
].tab
);
1564 if (info
[i
].bmap
->n_eq
&& !info
[i
].eq
)
1566 if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_ERROR
))
1568 if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_SEPARATE
))
1571 info
[j
].eq
= eq_status_in(info
[j
].bmap
, info
[i
].tab
);
1572 if (info
[j
].bmap
->n_eq
&& !info
[j
].eq
)
1574 if (any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_ERROR
))
1576 if (any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_SEPARATE
))
1579 info
[i
].ineq
= ineq_status_in(info
[i
].bmap
, info
[i
].tab
, info
[j
].tab
);
1580 if (info
[i
].bmap
->n_ineq
&& !info
[i
].ineq
)
1582 if (any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ERROR
))
1584 if (any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_SEPARATE
))
1587 info
[j
].ineq
= ineq_status_in(info
[j
].bmap
, info
[j
].tab
, info
[i
].tab
);
1588 if (info
[j
].bmap
->n_ineq
&& !info
[j
].ineq
)
1590 if (any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_ERROR
))
1592 if (any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_SEPARATE
))
1595 if (all(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_VALID
) &&
1596 all(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_VALID
)) {
1598 change
= isl_change_drop_second
;
1599 } else if (all(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_VALID
) &&
1600 all(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_VALID
)) {
1602 change
= isl_change_drop_first
;
1603 } else if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_ADJ_EQ
)) {
1604 change
= check_eq_adj_eq(i
, j
, info
);
1605 } else if (any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_ADJ_EQ
)) {
1606 change
= check_eq_adj_eq(j
, i
, info
);
1607 } else if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_ADJ_INEQ
) ||
1608 any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_ADJ_INEQ
)) {
1609 change
= check_adj_eq(i
, j
, info
);
1610 } else if (any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ADJ_EQ
) ||
1611 any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_ADJ_EQ
)) {
1614 } else if (any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ADJ_INEQ
) ||
1615 any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_ADJ_INEQ
)) {
1616 change
= check_adj_ineq(i
, j
, info
);
1618 if (!any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_CUT
) &&
1619 !any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_CUT
))
1620 change
= check_facets(i
, j
, info
);
1621 if (change
== isl_change_none
)
1622 change
= check_wrap(i
, j
, info
);
1636 return isl_change_error
;
1639 /* Do the two basic maps live in the same local space, i.e.,
1640 * do they have the same (known) divs?
1641 * If either basic map has any unknown divs, then we can only assume
1642 * that they do not live in the same local space.
1644 static int same_divs(__isl_keep isl_basic_map
*bmap1
,
1645 __isl_keep isl_basic_map
*bmap2
)
1651 if (!bmap1
|| !bmap2
)
1653 if (bmap1
->n_div
!= bmap2
->n_div
)
1656 if (bmap1
->n_div
== 0)
1659 known
= isl_basic_map_divs_known(bmap1
);
1660 if (known
< 0 || !known
)
1662 known
= isl_basic_map_divs_known(bmap2
);
1663 if (known
< 0 || !known
)
1666 total
= isl_basic_map_total_dim(bmap1
);
1667 for (i
= 0; i
< bmap1
->n_div
; ++i
)
1668 if (!isl_seq_eq(bmap1
->div
[i
], bmap2
->div
[i
], 2 + total
))
1674 /* Does "bmap" contain the basic map represented by the tableau "tab"
1675 * after expanding the divs of "bmap" to match those of "tab"?
1676 * The expansion is performed using the divs "div" and expansion "exp"
1677 * computed by the caller.
1678 * Then we check if all constraints of the expanded "bmap" are valid for "tab".
1680 static int contains_with_expanded_divs(__isl_keep isl_basic_map
*bmap
,
1681 struct isl_tab
*tab
, __isl_keep isl_mat
*div
, int *exp
)
1687 bmap
= isl_basic_map_copy(bmap
);
1688 bmap
= isl_basic_set_expand_divs(bmap
, isl_mat_copy(div
), exp
);
1693 eq_i
= eq_status_in(bmap
, tab
);
1694 if (bmap
->n_eq
&& !eq_i
)
1696 if (any(eq_i
, 2 * bmap
->n_eq
, STATUS_ERROR
))
1698 if (any(eq_i
, 2 * bmap
->n_eq
, STATUS_SEPARATE
))
1701 ineq_i
= ineq_status_in(bmap
, NULL
, tab
);
1702 if (bmap
->n_ineq
&& !ineq_i
)
1704 if (any(ineq_i
, bmap
->n_ineq
, STATUS_ERROR
))
1706 if (any(ineq_i
, bmap
->n_ineq
, STATUS_SEPARATE
))
1709 if (all(eq_i
, 2 * bmap
->n_eq
, STATUS_VALID
) &&
1710 all(ineq_i
, bmap
->n_ineq
, STATUS_VALID
))
1714 isl_basic_map_free(bmap
);
1719 isl_basic_map_free(bmap
);
1725 /* Does "bmap_i" contain the basic map represented by "info_j"
1726 * after aligning the divs of "bmap_i" to those of "info_j".
1727 * Note that this can only succeed if the number of divs of "bmap_i"
1728 * is smaller than (or equal to) the number of divs of "info_j".
1730 * We first check if the divs of "bmap_i" are all known and form a subset
1731 * of those of "bmap_j". If so, we pass control over to
1732 * contains_with_expanded_divs.
1734 static int contains_after_aligning_divs(__isl_keep isl_basic_map
*bmap_i
,
1735 struct isl_coalesce_info
*info_j
)
1738 isl_mat
*div_i
, *div_j
, *div
;
1744 known
= isl_basic_map_divs_known(bmap_i
);
1745 if (known
< 0 || !known
)
1748 ctx
= isl_basic_map_get_ctx(bmap_i
);
1750 div_i
= isl_basic_map_get_divs(bmap_i
);
1751 div_j
= isl_basic_map_get_divs(info_j
->bmap
);
1753 if (!div_i
|| !div_j
)
1756 exp1
= isl_alloc_array(ctx
, int, div_i
->n_row
);
1757 exp2
= isl_alloc_array(ctx
, int, div_j
->n_row
);
1758 if ((div_i
->n_row
&& !exp1
) || (div_j
->n_row
&& !exp2
))
1761 div
= isl_merge_divs(div_i
, div_j
, exp1
, exp2
);
1765 if (div
->n_row
== div_j
->n_row
)
1766 subset
= contains_with_expanded_divs(bmap_i
,
1767 info_j
->tab
, div
, exp1
);
1773 isl_mat_free(div_i
);
1774 isl_mat_free(div_j
);
1781 isl_mat_free(div_i
);
1782 isl_mat_free(div_j
);
1788 /* Check if the basic map "j" is a subset of basic map "i",
1789 * if "i" has fewer divs that "j".
1790 * If so, remove basic map "j".
1792 * If the two basic maps have the same number of divs, then
1793 * they must necessarily be different. Otherwise, we would have
1794 * called coalesce_local_pair. We therefore don't try anything
1797 static int coalesced_subset(int i
, int j
, struct isl_coalesce_info
*info
)
1801 if (info
[i
].bmap
->n_div
>= info
[j
].bmap
->n_div
)
1804 superset
= contains_after_aligning_divs(info
[i
].bmap
, &info
[j
]);
1813 /* Check if basic map "j" is a subset of basic map "i" after
1814 * exploiting the extra equalities of "j" to simplify the divs of "i".
1815 * If so, remove basic map "j".
1817 * If "j" does not have any equalities or if they are the same
1818 * as those of "i", then we cannot exploit them to simplify the divs.
1819 * Similarly, if there are no divs in "i", then they cannot be simplified.
1820 * If, on the other hand, the affine hulls of "i" and "j" do not intersect,
1821 * then "j" cannot be a subset of "i".
1823 * Otherwise, we intersect "i" with the affine hull of "j" and then
1824 * check if "j" is a subset of the result after aligning the divs.
1825 * If so, then "j" is definitely a subset of "i" and can be removed.
1826 * Note that if after intersection with the affine hull of "j".
1827 * "i" still has more divs than "j", then there is no way we can
1828 * align the divs of "i" to those of "j".
1830 static int coalesced_subset_with_equalities(int i
, int j
,
1831 struct isl_coalesce_info
*info
)
1833 isl_basic_map
*hull_i
, *hull_j
, *bmap_i
;
1834 int equal
, empty
, subset
;
1836 if (info
[j
].bmap
->n_eq
== 0)
1838 if (info
[i
].bmap
->n_div
== 0)
1841 hull_i
= isl_basic_map_copy(info
[i
].bmap
);
1842 hull_i
= isl_basic_map_plain_affine_hull(hull_i
);
1843 hull_j
= isl_basic_map_copy(info
[j
].bmap
);
1844 hull_j
= isl_basic_map_plain_affine_hull(hull_j
);
1846 hull_j
= isl_basic_map_intersect(hull_j
, isl_basic_map_copy(hull_i
));
1847 equal
= isl_basic_map_plain_is_equal(hull_i
, hull_j
);
1848 empty
= isl_basic_map_plain_is_empty(hull_j
);
1849 isl_basic_map_free(hull_i
);
1851 if (equal
< 0 || equal
|| empty
< 0 || empty
) {
1852 isl_basic_map_free(hull_j
);
1853 return equal
< 0 || empty
< 0 ? -1 : 0;
1856 bmap_i
= isl_basic_map_copy(info
[i
].bmap
);
1857 bmap_i
= isl_basic_map_intersect(bmap_i
, hull_j
);
1861 if (bmap_i
->n_div
> info
[j
].bmap
->n_div
) {
1862 isl_basic_map_free(bmap_i
);
1866 subset
= contains_after_aligning_divs(bmap_i
, &info
[j
]);
1868 isl_basic_map_free(bmap_i
);
1878 /* Check if one of the basic maps is a subset of the other and, if so,
1880 * Note that we only perform any test if the number of divs is different
1881 * in the two basic maps. In case the number of divs is the same,
1882 * we have already established that the divs are different
1883 * in the two basic maps.
1884 * In particular, if the number of divs of basic map i is smaller than
1885 * the number of divs of basic map j, then we check if j is a subset of i
1888 static enum isl_change
check_coalesce_subset(int i
, int j
,
1889 struct isl_coalesce_info
*info
)
1893 changed
= coalesced_subset(i
, j
, info
);
1894 if (changed
< 0 || changed
)
1895 return changed
< 0 ? isl_change_error
: isl_change_drop_second
;
1897 changed
= coalesced_subset(j
, i
, info
);
1898 if (changed
< 0 || changed
)
1899 return changed
< 0 ? isl_change_error
: isl_change_drop_first
;
1901 changed
= coalesced_subset_with_equalities(i
, j
, info
);
1902 if (changed
< 0 || changed
)
1903 return changed
< 0 ? isl_change_error
: isl_change_drop_second
;
1905 changed
= coalesced_subset_with_equalities(j
, i
, info
);
1906 if (changed
< 0 || changed
)
1907 return changed
< 0 ? isl_change_error
: isl_change_drop_first
;
1909 return isl_change_none
;
1912 /* Does "bmap" involve any divs that themselves refer to divs?
1914 static int has_nested_div(__isl_keep isl_basic_map
*bmap
)
1920 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
1921 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
1924 for (i
= 0; i
< n_div
; ++i
)
1925 if (isl_seq_first_non_zero(bmap
->div
[i
] + 2 + total
,
1932 /* Return a list of affine expressions, one for each integer division
1933 * in "bmap_i". For each integer division that also appears in "bmap_j",
1934 * the affine expression is set to NaN. The number of NaNs in the list
1935 * is equal to the number of integer divisions in "bmap_j".
1936 * For the other integer divisions of "bmap_i", the corresponding
1937 * element in the list is a purely affine expression equal to the integer
1938 * division in "hull".
1939 * If no such list can be constructed, then the number of elements
1940 * in the returned list is smaller than the number of integer divisions
1943 static __isl_give isl_aff_list
*set_up_substitutions(
1944 __isl_keep isl_basic_map
*bmap_i
, __isl_keep isl_basic_map
*bmap_j
,
1945 __isl_take isl_basic_map
*hull
)
1947 unsigned n_div_i
, n_div_j
, total
;
1949 isl_local_space
*ls
;
1950 isl_basic_set
*wrap_hull
;
1958 ctx
= isl_basic_map_get_ctx(hull
);
1960 n_div_i
= isl_basic_map_dim(bmap_i
, isl_dim_div
);
1961 n_div_j
= isl_basic_map_dim(bmap_j
, isl_dim_div
);
1962 total
= isl_basic_map_total_dim(bmap_i
) - n_div_i
;
1964 ls
= isl_basic_map_get_local_space(bmap_i
);
1965 ls
= isl_local_space_wrap(ls
);
1966 wrap_hull
= isl_basic_map_wrap(hull
);
1968 aff_nan
= isl_aff_nan_on_domain(isl_local_space_copy(ls
));
1969 list
= isl_aff_list_alloc(ctx
, n_div_i
);
1972 for (i
= 0; i
< n_div_i
; ++i
) {
1976 isl_seq_eq(bmap_i
->div
[i
], bmap_j
->div
[j
], 2 + total
)) {
1978 list
= isl_aff_list_add(list
, isl_aff_copy(aff_nan
));
1981 if (n_div_i
- i
<= n_div_j
- j
)
1984 aff
= isl_local_space_get_div(ls
, i
);
1985 aff
= isl_aff_substitute_equalities(aff
,
1986 isl_basic_set_copy(wrap_hull
));
1987 aff
= isl_aff_floor(aff
);
1990 if (isl_aff_dim(aff
, isl_dim_div
) != 0) {
1995 list
= isl_aff_list_add(list
, aff
);
1998 isl_aff_free(aff_nan
);
1999 isl_local_space_free(ls
);
2000 isl_basic_set_free(wrap_hull
);
2004 isl_local_space_free(ls
);
2005 isl_basic_set_free(wrap_hull
);
2006 isl_aff_list_free(list
);
2010 /* Add variables to "tab" corresponding to the elements in "list"
2011 * that are not set to NaN. The value of the added variable
2012 * is fixed to the purely affine expression defined by the element.
2013 * "dim" is the offset in the variables of "tab" where we should
2014 * start considering the elements in "list".
2015 * When this function returns, the total number of variables in "tab"
2016 * is equal to "dim" plus the number of elements in "list".
2018 static int add_subs(struct isl_tab
*tab
, __isl_keep isl_aff_list
*list
, int dim
)
2029 n
= isl_aff_list_n_aff(list
);
2030 extra
= n
- (tab
->n_var
- dim
);
2032 if (isl_tab_extend_vars(tab
, extra
) < 0)
2034 if (isl_tab_extend_cons(tab
, 2 * extra
) < 0)
2037 ctx
= isl_tab_get_ctx(tab
);
2038 sub
= isl_vec_alloc(ctx
, 1 + dim
+ n
);
2041 isl_seq_clr(sub
->el
+ 1 + dim
, n
);
2043 for (i
= 0; i
< n
; ++i
) {
2044 aff
= isl_aff_list_get_aff(list
, i
);
2047 if (isl_aff_is_nan(aff
)) {
2051 if (isl_tab_insert_var(tab
, dim
+ i
) < 0)
2053 isl_seq_cpy(sub
->el
, aff
->v
->el
+ 1, 1 + dim
);
2054 isl_int_neg(sub
->el
[1 + dim
+ i
], aff
->v
->el
[0]);
2055 if (isl_tab_add_eq(tab
, sub
->el
) < 0)
2057 isl_int_set_si(sub
->el
[1 + dim
+ i
], 0);
2069 /* Coalesce basic map "j" into basic map "i" after adding the extra integer
2070 * divisions in "i" but not in "j" to basic map "j", with values
2071 * specified by "list". The total number of elements in "list"
2072 * is equal to the number of integer divisions in "i", while the number
2073 * of NaN elements in the list is equal to the number of integer divisions
2075 * If no coalescing can be performed, then we need to revert basic map "j"
2076 * to its original state. We do the same if basic map "i" gets dropped
2077 * during the coalescing, even though this should not happen in practice
2078 * since we have already checked for "j" being a subset of "i"
2079 * before we reach this stage.
2081 static enum isl_change
coalesce_with_subs(int i
, int j
,
2082 struct isl_coalesce_info
*info
, __isl_keep isl_aff_list
*list
)
2084 isl_basic_map
*bmap_j
;
2085 struct isl_tab_undo
*snap
;
2087 enum isl_change change
;
2089 bmap_j
= isl_basic_map_copy(info
[j
].bmap
);
2090 info
[j
].bmap
= isl_basic_map_align_divs(info
[j
].bmap
, info
[i
].bmap
);
2094 snap
= isl_tab_snap(info
[j
].tab
);
2096 dim
= isl_basic_map_dim(bmap_j
, isl_dim_all
);
2097 dim
-= isl_basic_map_dim(bmap_j
, isl_dim_div
);
2098 if (add_subs(info
[j
].tab
, list
, dim
) < 0)
2101 change
= coalesce_local_pair(i
, j
, info
);
2102 if (change
!= isl_change_none
&& change
!= isl_change_drop_first
) {
2103 isl_basic_map_free(bmap_j
);
2105 isl_basic_map_free(info
[j
].bmap
);
2106 info
[j
].bmap
= bmap_j
;
2108 if (isl_tab_rollback(info
[j
].tab
, snap
) < 0)
2109 return isl_change_error
;
2114 isl_basic_map_free(bmap_j
);
2115 return isl_change_error
;
2118 /* Check if we can coalesce basic map "j" into basic map "i" after copying
2119 * those extra integer divisions in "i" that can be simplified away
2120 * using the extra equalities in "j".
2121 * All divs are assumed to be known and not contain any nested divs.
2123 * We first check if there are any extra equalities in "j" that we
2124 * can exploit. Then we check if every integer division in "i"
2125 * either already appears in "j" or can be simplified using the
2126 * extra equalities to a purely affine expression.
2127 * If these tests succeed, then we try to coalesce the two basic maps
2128 * by introducing extra dimensions in "j" corresponding to
2129 * the extra integer divsisions "i" fixed to the corresponding
2130 * purely affine expression.
2132 static enum isl_change
check_coalesce_into_eq(int i
, int j
,
2133 struct isl_coalesce_info
*info
)
2135 unsigned n_div_i
, n_div_j
;
2136 isl_basic_map
*hull_i
, *hull_j
;
2139 enum isl_change change
;
2141 n_div_i
= isl_basic_map_dim(info
[i
].bmap
, isl_dim_div
);
2142 n_div_j
= isl_basic_map_dim(info
[j
].bmap
, isl_dim_div
);
2143 if (n_div_i
<= n_div_j
)
2144 return isl_change_none
;
2145 if (info
[j
].bmap
->n_eq
== 0)
2146 return isl_change_none
;
2148 hull_i
= isl_basic_map_copy(info
[i
].bmap
);
2149 hull_i
= isl_basic_map_plain_affine_hull(hull_i
);
2150 hull_j
= isl_basic_map_copy(info
[j
].bmap
);
2151 hull_j
= isl_basic_map_plain_affine_hull(hull_j
);
2153 hull_j
= isl_basic_map_intersect(hull_j
, isl_basic_map_copy(hull_i
));
2154 equal
= isl_basic_map_plain_is_equal(hull_i
, hull_j
);
2155 empty
= isl_basic_map_plain_is_empty(hull_j
);
2156 isl_basic_map_free(hull_i
);
2158 if (equal
< 0 || empty
< 0)
2160 if (equal
|| empty
) {
2161 isl_basic_map_free(hull_j
);
2162 return isl_change_none
;
2165 list
= set_up_substitutions(info
[i
].bmap
, info
[j
].bmap
, hull_j
);
2168 if (isl_aff_list_n_aff(list
) < n_div_i
)
2169 change
= isl_change_none
;
2171 change
= coalesce_with_subs(i
, j
, info
, list
);
2173 isl_aff_list_free(list
);
2177 isl_basic_map_free(hull_j
);
2178 return isl_change_error
;
2181 /* Check if we can coalesce basic maps "i" and "j" after copying
2182 * those extra integer divisions in one of the basic maps that can
2183 * be simplified away using the extra equalities in the other basic map.
2184 * We require all divs to be known in both basic maps.
2185 * Furthermore, to simplify the comparison of div expressions,
2186 * we do not allow any nested integer divisions.
2188 static enum isl_change
check_coalesce_eq(int i
, int j
,
2189 struct isl_coalesce_info
*info
)
2192 enum isl_change change
;
2194 known
= isl_basic_map_divs_known(info
[i
].bmap
);
2195 if (known
< 0 || !known
)
2196 return known
< 0 ? isl_change_error
: isl_change_none
;
2197 known
= isl_basic_map_divs_known(info
[j
].bmap
);
2198 if (known
< 0 || !known
)
2199 return known
< 0 ? isl_change_error
: isl_change_none
;
2200 nested
= has_nested_div(info
[i
].bmap
);
2201 if (nested
< 0 || nested
)
2202 return nested
< 0 ? isl_change_error
: isl_change_none
;
2203 nested
= has_nested_div(info
[j
].bmap
);
2204 if (nested
< 0 || nested
)
2205 return nested
< 0 ? isl_change_error
: isl_change_none
;
2207 change
= check_coalesce_into_eq(i
, j
, info
);
2208 if (change
!= isl_change_none
)
2210 change
= check_coalesce_into_eq(j
, i
, info
);
2211 if (change
!= isl_change_none
)
2212 return invert_change(change
);
2214 return isl_change_none
;
2217 /* Check if the union of the given pair of basic maps
2218 * can be represented by a single basic map.
2219 * If so, replace the pair by the single basic map and return
2220 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
2221 * Otherwise, return isl_change_none.
2223 * We first check if the two basic maps live in the same local space.
2224 * If so, we do the complete check. Otherwise, we check if one is
2225 * an obvious subset of the other or if the extra integer divisions
2226 * of one basic map can be simplified away using the extra equalities
2227 * of the other basic map.
2229 static enum isl_change
coalesce_pair(int i
, int j
,
2230 struct isl_coalesce_info
*info
)
2233 enum isl_change change
;
2235 same
= same_divs(info
[i
].bmap
, info
[j
].bmap
);
2237 return isl_change_error
;
2239 return coalesce_local_pair(i
, j
, info
);
2241 change
= check_coalesce_subset(i
, j
, info
);
2242 if (change
!= isl_change_none
)
2245 return check_coalesce_eq(i
, j
, info
);
2248 /* Pairwise coalesce the basic maps described by the "n" elements of "info",
2249 * skipping basic maps that have been removed (either before or within
2252 * For each basic map i, we check if it can be coalesced with respect
2253 * to any previously considered basic map j.
2254 * If i gets dropped (because it was a subset of some j), then
2255 * we can move on to the next basic map.
2256 * If j gets dropped, we need to continue checking against the other
2257 * previously considered basic maps.
2258 * If the two basic maps got fused, then we recheck the fused basic map
2259 * against the previously considered basic maps.
2261 static int coalesce(isl_ctx
*ctx
, int n
, struct isl_coalesce_info
*info
)
2265 for (i
= n
- 2; i
>= 0; --i
) {
2266 if (info
[i
].removed
)
2268 for (j
= i
+ 1; j
< n
; ++j
) {
2269 enum isl_change changed
;
2271 if (info
[j
].removed
)
2273 if (info
[i
].removed
)
2274 isl_die(ctx
, isl_error_internal
,
2275 "basic map unexpectedly removed",
2277 changed
= coalesce_pair(i
, j
, info
);
2279 case isl_change_error
:
2281 case isl_change_none
:
2282 case isl_change_drop_second
:
2284 case isl_change_drop_first
:
2287 case isl_change_fuse
:
2297 /* Update the basic maps in "map" based on the information in "info".
2298 * In particular, remove the basic maps that have been marked removed and
2299 * update the others based on the information in the corresponding tableau.
2300 * Since we detected implicit equalities without calling
2301 * isl_basic_map_gauss, we need to do it now.
2302 * Also call isl_basic_map_simplify if we may have lost the definition
2303 * of one or more integer divisions.
2305 static __isl_give isl_map
*update_basic_maps(__isl_take isl_map
*map
,
2306 int n
, struct isl_coalesce_info
*info
)
2313 for (i
= n
- 1; i
>= 0; --i
) {
2314 if (info
[i
].removed
) {
2315 isl_basic_map_free(map
->p
[i
]);
2316 if (i
!= map
->n
- 1)
2317 map
->p
[i
] = map
->p
[map
->n
- 1];
2322 info
[i
].bmap
= isl_basic_map_update_from_tab(info
[i
].bmap
,
2324 info
[i
].bmap
= isl_basic_map_gauss(info
[i
].bmap
, NULL
);
2325 if (info
[i
].simplify
)
2326 info
[i
].bmap
= isl_basic_map_simplify(info
[i
].bmap
);
2327 info
[i
].bmap
= isl_basic_map_finalize(info
[i
].bmap
);
2329 return isl_map_free(map
);
2330 ISL_F_SET(info
[i
].bmap
, ISL_BASIC_MAP_NO_IMPLICIT
);
2331 ISL_F_SET(info
[i
].bmap
, ISL_BASIC_MAP_NO_REDUNDANT
);
2332 isl_basic_map_free(map
->p
[i
]);
2333 map
->p
[i
] = info
[i
].bmap
;
2334 info
[i
].bmap
= NULL
;
2340 /* For each pair of basic maps in the map, check if the union of the two
2341 * can be represented by a single basic map.
2342 * If so, replace the pair by the single basic map and start over.
2344 * We factor out any (hidden) common factor from the constraint
2345 * coefficients to improve the detection of adjacent constraints.
2347 * Since we are constructing the tableaus of the basic maps anyway,
2348 * we exploit them to detect implicit equalities and redundant constraints.
2349 * This also helps the coalescing as it can ignore the redundant constraints.
2350 * In order to avoid confusion, we make all implicit equalities explicit
2351 * in the basic maps. We don't call isl_basic_map_gauss, though,
2352 * as that may affect the number of constraints.
2353 * This means that we have to call isl_basic_map_gauss at the end
2354 * of the computation (in update_basic_maps) to ensure that
2355 * the basic maps are not left in an unexpected state.
2357 struct isl_map
*isl_map_coalesce(struct isl_map
*map
)
2362 struct isl_coalesce_info
*info
= NULL
;
2364 map
= isl_map_remove_empty_parts(map
);
2371 ctx
= isl_map_get_ctx(map
);
2372 map
= isl_map_sort_divs(map
);
2373 map
= isl_map_cow(map
);
2380 info
= isl_calloc_array(map
->ctx
, struct isl_coalesce_info
, n
);
2384 for (i
= 0; i
< map
->n
; ++i
) {
2385 map
->p
[i
] = isl_basic_map_reduce_coefficients(map
->p
[i
]);
2388 info
[i
].bmap
= isl_basic_map_copy(map
->p
[i
]);
2389 info
[i
].tab
= isl_tab_from_basic_map(info
[i
].bmap
, 0);
2392 if (!ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_NO_IMPLICIT
))
2393 if (isl_tab_detect_implicit_equalities(info
[i
].tab
) < 0)
2395 info
[i
].bmap
= isl_tab_make_equalities_explicit(info
[i
].tab
,
2399 if (!ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_NO_REDUNDANT
))
2400 if (isl_tab_detect_redundant(info
[i
].tab
) < 0)
2403 for (i
= map
->n
- 1; i
>= 0; --i
)
2404 if (info
[i
].tab
->empty
)
2407 if (coalesce(ctx
, n
, info
) < 0)
2410 map
= update_basic_maps(map
, n
, info
);
2412 clear_coalesce_info(n
, info
);
2416 clear_coalesce_info(n
, info
);
2421 /* For each pair of basic sets in the set, check if the union of the two
2422 * can be represented by a single basic set.
2423 * If so, replace the pair by the single basic set and start over.
2425 struct isl_set
*isl_set_coalesce(struct isl_set
*set
)
2427 return (struct isl_set
*)isl_map_coalesce((struct isl_map
*)set
);