2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2010 INRIA Saclay
4 * Copyright 2012-2013 Ecole Normale Superieure
5 * Copyright 2014 INRIA Rocquencourt
6 * Copyright 2016 Sven Verdoolaege
8 * Use of this software is governed by the MIT license
10 * Written by Sven Verdoolaege, K.U.Leuven, Departement
11 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
12 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
13 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
14 * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
15 * and Inria Paris - Rocquencourt, Domaine de Voluceau - Rocquencourt,
16 * B.P. 105 - 78153 Le Chesnay, France
19 #include <isl_ctx_private.h>
20 #include "isl_map_private.h"
22 #include <isl/options.h>
24 #include <isl_mat_private.h>
25 #include <isl_local_space_private.h>
26 #include <isl_vec_private.h>
27 #include <isl_aff_private.h>
28 #include <isl_equalities.h>
30 #include <set_to_map.c>
31 #include <set_from_map.c>
33 #define STATUS_ERROR -1
34 #define STATUS_REDUNDANT 1
35 #define STATUS_VALID 2
36 #define STATUS_SEPARATE 3
38 #define STATUS_ADJ_EQ 5
39 #define STATUS_ADJ_INEQ 6
41 static int status_in(isl_int
*ineq
, struct isl_tab
*tab
)
43 enum isl_ineq_type type
= isl_tab_ineq_type(tab
, ineq
);
46 case isl_ineq_error
: return STATUS_ERROR
;
47 case isl_ineq_redundant
: return STATUS_VALID
;
48 case isl_ineq_separate
: return STATUS_SEPARATE
;
49 case isl_ineq_cut
: return STATUS_CUT
;
50 case isl_ineq_adj_eq
: return STATUS_ADJ_EQ
;
51 case isl_ineq_adj_ineq
: return STATUS_ADJ_INEQ
;
55 /* Compute the position of the equalities of basic map "bmap_i"
56 * with respect to the basic map represented by "tab_j".
57 * The resulting array has twice as many entries as the number
58 * of equalities corresponding to the two inequalties to which
59 * each equality corresponds.
61 static int *eq_status_in(__isl_keep isl_basic_map
*bmap_i
,
62 struct isl_tab
*tab_j
)
65 int *eq
= isl_calloc_array(bmap_i
->ctx
, int, 2 * bmap_i
->n_eq
);
71 dim
= isl_basic_map_total_dim(bmap_i
);
72 for (k
= 0; k
< bmap_i
->n_eq
; ++k
) {
73 for (l
= 0; l
< 2; ++l
) {
74 isl_seq_neg(bmap_i
->eq
[k
], bmap_i
->eq
[k
], 1+dim
);
75 eq
[2 * k
+ l
] = status_in(bmap_i
->eq
[k
], tab_j
);
76 if (eq
[2 * k
+ l
] == STATUS_ERROR
)
79 if (eq
[2 * k
] == STATUS_SEPARATE
||
80 eq
[2 * k
+ 1] == STATUS_SEPARATE
)
90 /* Compute the position of the inequalities of basic map "bmap_i"
91 * (also represented by "tab_i", if not NULL) with respect to the basic map
92 * represented by "tab_j".
94 static int *ineq_status_in(__isl_keep isl_basic_map
*bmap_i
,
95 struct isl_tab
*tab_i
, struct isl_tab
*tab_j
)
98 unsigned n_eq
= bmap_i
->n_eq
;
99 int *ineq
= isl_calloc_array(bmap_i
->ctx
, int, bmap_i
->n_ineq
);
104 for (k
= 0; k
< bmap_i
->n_ineq
; ++k
) {
105 if (tab_i
&& isl_tab_is_redundant(tab_i
, n_eq
+ k
)) {
106 ineq
[k
] = STATUS_REDUNDANT
;
109 ineq
[k
] = status_in(bmap_i
->ineq
[k
], tab_j
);
110 if (ineq
[k
] == STATUS_ERROR
)
112 if (ineq
[k
] == STATUS_SEPARATE
)
122 static int any(int *con
, unsigned len
, int status
)
126 for (i
= 0; i
< len
; ++i
)
127 if (con
[i
] == status
)
132 static int count(int *con
, unsigned len
, int status
)
137 for (i
= 0; i
< len
; ++i
)
138 if (con
[i
] == status
)
143 static int all(int *con
, unsigned len
, int status
)
147 for (i
= 0; i
< len
; ++i
) {
148 if (con
[i
] == STATUS_REDUNDANT
)
150 if (con
[i
] != status
)
156 /* Internal information associated to a basic map in a map
157 * that is to be coalesced by isl_map_coalesce.
159 * "bmap" is the basic map itself (or NULL if "removed" is set)
160 * "tab" is the corresponding tableau (or NULL if "removed" is set)
161 * "hull_hash" identifies the affine space in which "bmap" lives.
162 * "removed" is set if this basic map has been removed from the map
163 * "simplify" is set if this basic map may have some unknown integer
164 * divisions that were not present in the input basic maps. The basic
165 * map should then be simplified such that we may be able to find
166 * a definition among the constraints.
168 * "eq" and "ineq" are only set if we are currently trying to coalesce
169 * this basic map with another basic map, in which case they represent
170 * the position of the inequalities of this basic map with respect to
171 * the other basic map. The number of elements in the "eq" array
172 * is twice the number of equalities in the "bmap", corresponding
173 * to the two inequalities that make up each equality.
175 struct isl_coalesce_info
{
185 /* Are all non-redundant constraints of the basic map represented by "info"
186 * either valid or cut constraints with respect to the other basic map?
188 static int all_valid_or_cut(struct isl_coalesce_info
*info
)
192 for (i
= 0; i
< 2 * info
->bmap
->n_eq
; ++i
) {
193 if (info
->eq
[i
] == STATUS_REDUNDANT
)
195 if (info
->eq
[i
] == STATUS_VALID
)
197 if (info
->eq
[i
] == STATUS_CUT
)
202 for (i
= 0; i
< info
->bmap
->n_ineq
; ++i
) {
203 if (info
->ineq
[i
] == STATUS_REDUNDANT
)
205 if (info
->ineq
[i
] == STATUS_VALID
)
207 if (info
->ineq
[i
] == STATUS_CUT
)
215 /* Compute the hash of the (apparent) affine hull of info->bmap (with
216 * the existentially quantified variables removed) and store it
219 static int coalesce_info_set_hull_hash(struct isl_coalesce_info
*info
)
224 hull
= isl_basic_map_copy(info
->bmap
);
225 hull
= isl_basic_map_plain_affine_hull(hull
);
226 n_div
= isl_basic_map_dim(hull
, isl_dim_div
);
227 hull
= isl_basic_map_drop_constraints_involving_dims(hull
,
228 isl_dim_div
, 0, n_div
);
229 info
->hull_hash
= isl_basic_map_get_hash(hull
);
230 isl_basic_map_free(hull
);
232 return hull
? 0 : -1;
235 /* Free all the allocated memory in an array
236 * of "n" isl_coalesce_info elements.
238 static void clear_coalesce_info(int n
, struct isl_coalesce_info
*info
)
245 for (i
= 0; i
< n
; ++i
) {
246 isl_basic_map_free(info
[i
].bmap
);
247 isl_tab_free(info
[i
].tab
);
253 /* Drop the basic map represented by "info".
254 * That is, clear the memory associated to the entry and
255 * mark it as having been removed.
257 static void drop(struct isl_coalesce_info
*info
)
259 info
->bmap
= isl_basic_map_free(info
->bmap
);
260 isl_tab_free(info
->tab
);
265 /* Exchange the information in "info1" with that in "info2".
267 static void exchange(struct isl_coalesce_info
*info1
,
268 struct isl_coalesce_info
*info2
)
270 struct isl_coalesce_info info
;
277 /* This type represents the kind of change that has been performed
278 * while trying to coalesce two basic maps.
280 * isl_change_none: nothing was changed
281 * isl_change_drop_first: the first basic map was removed
282 * isl_change_drop_second: the second basic map was removed
283 * isl_change_fuse: the two basic maps were replaced by a new basic map.
286 isl_change_error
= -1,
288 isl_change_drop_first
,
289 isl_change_drop_second
,
293 /* Update "change" based on an interchange of the first and the second
294 * basic map. That is, interchange isl_change_drop_first and
295 * isl_change_drop_second.
297 static enum isl_change
invert_change(enum isl_change change
)
300 case isl_change_error
:
301 return isl_change_error
;
302 case isl_change_none
:
303 return isl_change_none
;
304 case isl_change_drop_first
:
305 return isl_change_drop_second
;
306 case isl_change_drop_second
:
307 return isl_change_drop_first
;
308 case isl_change_fuse
:
309 return isl_change_fuse
;
312 return isl_change_error
;
315 /* Add the valid constraints of the basic map represented by "info"
316 * to "bmap". "len" is the size of the constraints.
317 * If only one of the pair of inequalities that make up an equality
318 * is valid, then add that inequality.
320 static __isl_give isl_basic_map
*add_valid_constraints(
321 __isl_take isl_basic_map
*bmap
, struct isl_coalesce_info
*info
,
329 for (k
= 0; k
< info
->bmap
->n_eq
; ++k
) {
330 if (info
->eq
[2 * k
] == STATUS_VALID
&&
331 info
->eq
[2 * k
+ 1] == STATUS_VALID
) {
332 l
= isl_basic_map_alloc_equality(bmap
);
334 return isl_basic_map_free(bmap
);
335 isl_seq_cpy(bmap
->eq
[l
], info
->bmap
->eq
[k
], len
);
336 } else if (info
->eq
[2 * k
] == STATUS_VALID
) {
337 l
= isl_basic_map_alloc_inequality(bmap
);
339 return isl_basic_map_free(bmap
);
340 isl_seq_neg(bmap
->ineq
[l
], info
->bmap
->eq
[k
], len
);
341 } else if (info
->eq
[2 * k
+ 1] == STATUS_VALID
) {
342 l
= isl_basic_map_alloc_inequality(bmap
);
344 return isl_basic_map_free(bmap
);
345 isl_seq_cpy(bmap
->ineq
[l
], info
->bmap
->eq
[k
], len
);
349 for (k
= 0; k
< info
->bmap
->n_ineq
; ++k
) {
350 if (info
->ineq
[k
] != STATUS_VALID
)
352 l
= isl_basic_map_alloc_inequality(bmap
);
354 return isl_basic_map_free(bmap
);
355 isl_seq_cpy(bmap
->ineq
[l
], info
->bmap
->ineq
[k
], len
);
361 /* Is "bmap" defined by a number of (non-redundant) constraints that
362 * is greater than the number of constraints of basic maps i and j combined?
363 * Equalities are counted as two inequalities.
365 static int number_of_constraints_increases(int i
, int j
,
366 struct isl_coalesce_info
*info
,
367 __isl_keep isl_basic_map
*bmap
, struct isl_tab
*tab
)
371 n_old
= 2 * info
[i
].bmap
->n_eq
+ info
[i
].bmap
->n_ineq
;
372 n_old
+= 2 * info
[j
].bmap
->n_eq
+ info
[j
].bmap
->n_ineq
;
374 n_new
= 2 * bmap
->n_eq
;
375 for (k
= 0; k
< bmap
->n_ineq
; ++k
)
376 if (!isl_tab_is_redundant(tab
, bmap
->n_eq
+ k
))
379 return n_new
> n_old
;
382 /* Replace the pair of basic maps i and j by the basic map bounded
383 * by the valid constraints in both basic maps and the constraints
384 * in extra (if not NULL).
385 * Place the fused basic map in the position that is the smallest of i and j.
387 * If "detect_equalities" is set, then look for equalities encoded
388 * as pairs of inequalities.
389 * If "check_number" is set, then the original basic maps are only
390 * replaced if the total number of constraints does not increase.
391 * While the number of integer divisions in the two basic maps
392 * is assumed to be the same, the actual definitions may be different.
393 * We only copy the definition from one of the basic map if it is
394 * the same as that of the other basic map. Otherwise, we mark
395 * the integer division as unknown and simplify the basic map
396 * in an attempt to recover the integer division definition.
398 static enum isl_change
fuse(int i
, int j
, struct isl_coalesce_info
*info
,
399 __isl_keep isl_mat
*extra
, int detect_equalities
, int check_number
)
402 struct isl_basic_map
*fused
= NULL
;
403 struct isl_tab
*fused_tab
= NULL
;
404 unsigned total
= isl_basic_map_total_dim(info
[i
].bmap
);
405 unsigned extra_rows
= extra
? extra
->n_row
: 0;
406 unsigned n_eq
, n_ineq
;
410 return fuse(j
, i
, info
, extra
, detect_equalities
, check_number
);
412 n_eq
= info
[i
].bmap
->n_eq
+ info
[j
].bmap
->n_eq
;
413 n_ineq
= info
[i
].bmap
->n_ineq
+ info
[j
].bmap
->n_ineq
;
414 fused
= isl_basic_map_alloc_space(isl_space_copy(info
[i
].bmap
->dim
),
415 info
[i
].bmap
->n_div
, n_eq
, n_eq
+ n_ineq
+ extra_rows
);
416 fused
= add_valid_constraints(fused
, &info
[i
], 1 + total
);
417 fused
= add_valid_constraints(fused
, &info
[j
], 1 + total
);
420 if (ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_RATIONAL
) &&
421 ISL_F_ISSET(info
[j
].bmap
, ISL_BASIC_MAP_RATIONAL
))
422 ISL_F_SET(fused
, ISL_BASIC_MAP_RATIONAL
);
424 for (k
= 0; k
< info
[i
].bmap
->n_div
; ++k
) {
425 int l
= isl_basic_map_alloc_div(fused
);
428 if (isl_seq_eq(info
[i
].bmap
->div
[k
], info
[j
].bmap
->div
[k
],
430 isl_seq_cpy(fused
->div
[l
], info
[i
].bmap
->div
[k
],
433 isl_int_set_si(fused
->div
[l
][0], 0);
438 for (k
= 0; k
< extra_rows
; ++k
) {
439 l
= isl_basic_map_alloc_inequality(fused
);
442 isl_seq_cpy(fused
->ineq
[l
], extra
->row
[k
], 1 + total
);
445 if (detect_equalities
)
446 fused
= isl_basic_map_detect_inequality_pairs(fused
, NULL
);
447 fused
= isl_basic_map_gauss(fused
, NULL
);
448 if (simplify
|| info
[j
].simplify
) {
449 fused
= isl_basic_map_simplify(fused
);
450 info
[i
].simplify
= 0;
452 fused
= isl_basic_map_finalize(fused
);
454 fused_tab
= isl_tab_from_basic_map(fused
, 0);
455 if (isl_tab_detect_redundant(fused_tab
) < 0)
459 number_of_constraints_increases(i
, j
, info
, fused
, fused_tab
)) {
460 isl_tab_free(fused_tab
);
461 isl_basic_map_free(fused
);
462 return isl_change_none
;
465 isl_basic_map_free(info
[i
].bmap
);
466 info
[i
].bmap
= fused
;
467 isl_tab_free(info
[i
].tab
);
468 info
[i
].tab
= fused_tab
;
471 return isl_change_fuse
;
473 isl_tab_free(fused_tab
);
474 isl_basic_map_free(fused
);
475 return isl_change_error
;
478 /* Given a pair of basic maps i and j such that all constraints are either
479 * "valid" or "cut", check if the facets corresponding to the "cut"
480 * constraints of i lie entirely within basic map j.
481 * If so, replace the pair by the basic map consisting of the valid
482 * constraints in both basic maps.
483 * Checking whether the facet lies entirely within basic map j
484 * is performed by checking whether the constraints of basic map j
485 * are valid for the facet. These tests are performed on a rational
486 * tableau to avoid the theoretical possibility that a constraint
487 * that was considered to be a cut constraint for the entire basic map i
488 * happens to be considered to be a valid constraint for the facet,
489 * even though it cuts off the same rational points.
491 * To see that we are not introducing any extra points, call the
492 * two basic maps A and B and the resulting map U and let x
493 * be an element of U \setminus ( A \cup B ).
494 * A line connecting x with an element of A \cup B meets a facet F
495 * of either A or B. Assume it is a facet of B and let c_1 be
496 * the corresponding facet constraint. We have c_1(x) < 0 and
497 * so c_1 is a cut constraint. This implies that there is some
498 * (possibly rational) point x' satisfying the constraints of A
499 * and the opposite of c_1 as otherwise c_1 would have been marked
500 * valid for A. The line connecting x and x' meets a facet of A
501 * in a (possibly rational) point that also violates c_1, but this
502 * is impossible since all cut constraints of B are valid for all
504 * In case F is a facet of A rather than B, then we can apply the
505 * above reasoning to find a facet of B separating x from A \cup B first.
507 static enum isl_change
check_facets(int i
, int j
,
508 struct isl_coalesce_info
*info
)
511 struct isl_tab_undo
*snap
, *snap2
;
512 unsigned n_eq
= info
[i
].bmap
->n_eq
;
514 snap
= isl_tab_snap(info
[i
].tab
);
515 if (isl_tab_mark_rational(info
[i
].tab
) < 0)
516 return isl_change_error
;
517 snap2
= isl_tab_snap(info
[i
].tab
);
519 for (k
= 0; k
< info
[i
].bmap
->n_ineq
; ++k
) {
520 if (info
[i
].ineq
[k
] != STATUS_CUT
)
522 if (isl_tab_select_facet(info
[i
].tab
, n_eq
+ k
) < 0)
523 return isl_change_error
;
524 for (l
= 0; l
< info
[j
].bmap
->n_ineq
; ++l
) {
526 if (info
[j
].ineq
[l
] != STATUS_CUT
)
528 stat
= status_in(info
[j
].bmap
->ineq
[l
], info
[i
].tab
);
530 return isl_change_error
;
531 if (stat
!= STATUS_VALID
)
534 if (isl_tab_rollback(info
[i
].tab
, snap2
) < 0)
535 return isl_change_error
;
536 if (l
< info
[j
].bmap
->n_ineq
)
540 if (k
< info
[i
].bmap
->n_ineq
) {
541 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
542 return isl_change_error
;
543 return isl_change_none
;
545 return fuse(i
, j
, info
, NULL
, 0, 0);
548 /* Check if info->bmap contains the basic map represented
549 * by the tableau "tab".
550 * For each equality, we check both the constraint itself
551 * (as an inequality) and its negation. Make sure the
552 * equality is returned to its original state before returning.
554 static int contains(struct isl_coalesce_info
*info
, struct isl_tab
*tab
)
558 isl_basic_map
*bmap
= info
->bmap
;
560 dim
= isl_basic_map_total_dim(bmap
);
561 for (k
= 0; k
< bmap
->n_eq
; ++k
) {
563 isl_seq_neg(bmap
->eq
[k
], bmap
->eq
[k
], 1 + dim
);
564 stat
= status_in(bmap
->eq
[k
], tab
);
565 isl_seq_neg(bmap
->eq
[k
], bmap
->eq
[k
], 1 + dim
);
568 if (stat
!= STATUS_VALID
)
570 stat
= status_in(bmap
->eq
[k
], tab
);
573 if (stat
!= STATUS_VALID
)
577 for (k
= 0; k
< bmap
->n_ineq
; ++k
) {
579 if (info
->ineq
[k
] == STATUS_REDUNDANT
)
581 stat
= status_in(bmap
->ineq
[k
], tab
);
584 if (stat
!= STATUS_VALID
)
590 /* Basic map "i" has an inequality (say "k") that is adjacent
591 * to some inequality of basic map "j". All the other inequalities
593 * Check if basic map "j" forms an extension of basic map "i".
595 * Note that this function is only called if some of the equalities or
596 * inequalities of basic map "j" do cut basic map "i". The function is
597 * correct even if there are no such cut constraints, but in that case
598 * the additional checks performed by this function are overkill.
600 * In particular, we replace constraint k, say f >= 0, by constraint
601 * f <= -1, add the inequalities of "j" that are valid for "i"
602 * and check if the result is a subset of basic map "j".
603 * If so, then we know that this result is exactly equal to basic map "j"
604 * since all its constraints are valid for basic map "j".
605 * By combining the valid constraints of "i" (all equalities and all
606 * inequalities except "k") and the valid constraints of "j" we therefore
607 * obtain a basic map that is equal to their union.
608 * In this case, there is no need to perform a rollback of the tableau
609 * since it is going to be destroyed in fuse().
615 * |_______| _ |_________\
627 static enum isl_change
is_adj_ineq_extension(int i
, int j
,
628 struct isl_coalesce_info
*info
)
631 struct isl_tab_undo
*snap
;
632 unsigned n_eq
= info
[i
].bmap
->n_eq
;
633 unsigned total
= isl_basic_map_total_dim(info
[i
].bmap
);
637 if (isl_tab_extend_cons(info
[i
].tab
, 1 + info
[j
].bmap
->n_ineq
) < 0)
638 return isl_change_error
;
640 for (k
= 0; k
< info
[i
].bmap
->n_ineq
; ++k
)
641 if (info
[i
].ineq
[k
] == STATUS_ADJ_INEQ
)
643 if (k
>= info
[i
].bmap
->n_ineq
)
644 isl_die(isl_basic_map_get_ctx(info
[i
].bmap
), isl_error_internal
,
645 "info[i].ineq should have exactly one STATUS_ADJ_INEQ",
646 return isl_change_error
);
648 snap
= isl_tab_snap(info
[i
].tab
);
650 if (isl_tab_unrestrict(info
[i
].tab
, n_eq
+ k
) < 0)
651 return isl_change_error
;
653 isl_seq_neg(info
[i
].bmap
->ineq
[k
], info
[i
].bmap
->ineq
[k
], 1 + total
);
654 isl_int_sub_ui(info
[i
].bmap
->ineq
[k
][0], info
[i
].bmap
->ineq
[k
][0], 1);
655 r
= isl_tab_add_ineq(info
[i
].tab
, info
[i
].bmap
->ineq
[k
]);
656 isl_seq_neg(info
[i
].bmap
->ineq
[k
], info
[i
].bmap
->ineq
[k
], 1 + total
);
657 isl_int_sub_ui(info
[i
].bmap
->ineq
[k
][0], info
[i
].bmap
->ineq
[k
][0], 1);
659 return isl_change_error
;
661 for (k
= 0; k
< info
[j
].bmap
->n_ineq
; ++k
) {
662 if (info
[j
].ineq
[k
] != STATUS_VALID
)
664 if (isl_tab_add_ineq(info
[i
].tab
, info
[j
].bmap
->ineq
[k
]) < 0)
665 return isl_change_error
;
668 super
= contains(&info
[j
], info
[i
].tab
);
670 return isl_change_error
;
672 return fuse(i
, j
, info
, NULL
, 0, 0);
674 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
675 return isl_change_error
;
677 return isl_change_none
;
681 /* Both basic maps have at least one inequality with and adjacent
682 * (but opposite) inequality in the other basic map.
683 * Check that there are no cut constraints and that there is only
684 * a single pair of adjacent inequalities.
685 * If so, we can replace the pair by a single basic map described
686 * by all but the pair of adjacent inequalities.
687 * Any additional points introduced lie strictly between the two
688 * adjacent hyperplanes and can therefore be integral.
697 * The test for a single pair of adjancent inequalities is important
698 * for avoiding the combination of two basic maps like the following
708 * If there are some cut constraints on one side, then we may
709 * still be able to fuse the two basic maps, but we need to perform
710 * some additional checks in is_adj_ineq_extension.
712 static enum isl_change
check_adj_ineq(int i
, int j
,
713 struct isl_coalesce_info
*info
)
715 int count_i
, count_j
;
718 count_i
= count(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ADJ_INEQ
);
719 count_j
= count(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_ADJ_INEQ
);
721 if (count_i
!= 1 && count_j
!= 1)
722 return isl_change_none
;
724 cut_i
= any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_CUT
) ||
725 any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_CUT
);
726 cut_j
= any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_CUT
) ||
727 any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_CUT
);
729 if (!cut_i
&& !cut_j
&& count_i
== 1 && count_j
== 1)
730 return fuse(i
, j
, info
, NULL
, 0, 0);
732 if (count_i
== 1 && !cut_i
)
733 return is_adj_ineq_extension(i
, j
, info
);
735 if (count_j
== 1 && !cut_j
)
736 return is_adj_ineq_extension(j
, i
, info
);
738 return isl_change_none
;
741 /* Given an affine transformation matrix "T", does row "row" represent
742 * anything other than a unit vector (possibly shifted by a constant)
743 * that is not involved in any of the other rows?
745 * That is, if a constraint involves the variable corresponding to
746 * the row, then could its preimage by "T" have any coefficients
747 * that are different from those in the original constraint?
749 static int not_unique_unit_row(__isl_keep isl_mat
*T
, int row
)
752 int len
= T
->n_col
- 1;
754 i
= isl_seq_first_non_zero(T
->row
[row
] + 1, len
);
757 if (!isl_int_is_one(T
->row
[row
][1 + i
]) &&
758 !isl_int_is_negone(T
->row
[row
][1 + i
]))
761 j
= isl_seq_first_non_zero(T
->row
[row
] + 1 + i
+ 1, len
- (i
+ 1));
765 for (j
= 1; j
< T
->n_row
; ++j
) {
768 if (!isl_int_is_zero(T
->row
[j
][1 + i
]))
775 /* Does inequality constraint "ineq" of "bmap" involve any of
776 * the variables marked in "affected"?
777 * "total" is the total number of variables, i.e., the number
778 * of entries in "affected".
780 static int is_affected(__isl_keep isl_basic_map
*bmap
, int ineq
, int *affected
,
785 for (i
= 0; i
< total
; ++i
) {
788 if (!isl_int_is_zero(bmap
->ineq
[ineq
][1 + i
]))
795 /* Given the compressed version of inequality constraint "ineq"
796 * of info->bmap in "v", check if the constraint can be tightened,
797 * where the compression is based on an equality constraint valid
799 * If so, add the tightened version of the inequality constraint
800 * to info->tab. "v" may be modified by this function.
802 * That is, if the compressed constraint is of the form
806 * with 0 < c < m, then it is equivalent to
810 * This means that c can also be subtracted from the original,
811 * uncompressed constraint without affecting the integer points
812 * in info->tab. Add this tightened constraint as an extra row
813 * to info->tab to make this information explicitly available.
815 static __isl_give isl_vec
*try_tightening(struct isl_coalesce_info
*info
,
816 int ineq
, __isl_take isl_vec
*v
)
824 ctx
= isl_vec_get_ctx(v
);
825 isl_seq_gcd(v
->el
+ 1, v
->size
- 1, &ctx
->normalize_gcd
);
826 if (isl_int_is_zero(ctx
->normalize_gcd
) ||
827 isl_int_is_one(ctx
->normalize_gcd
)) {
835 isl_int_fdiv_r(v
->el
[0], v
->el
[0], ctx
->normalize_gcd
);
836 if (isl_int_is_zero(v
->el
[0]))
839 if (isl_tab_extend_cons(info
->tab
, 1) < 0)
840 return isl_vec_free(v
);
842 isl_int_sub(info
->bmap
->ineq
[ineq
][0],
843 info
->bmap
->ineq
[ineq
][0], v
->el
[0]);
844 r
= isl_tab_add_ineq(info
->tab
, info
->bmap
->ineq
[ineq
]);
845 isl_int_add(info
->bmap
->ineq
[ineq
][0],
846 info
->bmap
->ineq
[ineq
][0], v
->el
[0]);
849 return isl_vec_free(v
);
854 /* Tighten the (non-redundant) constraints on the facet represented
856 * In particular, on input, info->tab represents the result
857 * of replacing constraint k of info->bmap, i.e., f_k >= 0,
858 * by the adjacent equality, i.e., f_k + 1 = 0.
860 * Compute a variable compression from the equality constraint f_k + 1 = 0
861 * and use it to tighten the other constraints of info->bmap,
862 * updating info->tab (and leaving info->bmap untouched).
863 * The compression handles essentially two cases, one where a variable
864 * is assigned a fixed value and can therefore be eliminated, and one
865 * where one variable is a shifted multiple of some other variable and
866 * can therefore be replaced by that multiple.
867 * Gaussian elimination would also work for the first case, but for
868 * the second case, the effectiveness would depend on the order
870 * After compression, some of the constraints may have coefficients
871 * with a common divisor. If this divisor does not divide the constant
872 * term, then the constraint can be tightened.
873 * The tightening is performed on the tableau info->tab by introducing
874 * extra (temporary) constraints.
876 * Only constraints that are possibly affected by the compression are
877 * considered. In particular, if the constraint only involves variables
878 * that are directly mapped to a distinct set of other variables, then
879 * no common divisor can be introduced and no tightening can occur.
881 * It is important to only consider the non-redundant constraints
882 * since the facet constraint has been relaxed prior to the call
883 * to this function, meaning that the constraints that were redundant
884 * prior to the relaxation may no longer be redundant.
885 * These constraints will be ignored in the fused result, so
886 * the fusion detection should not exploit them.
888 static isl_stat
tighten_on_relaxed_facet(struct isl_coalesce_info
*info
,
898 ctx
= isl_basic_map_get_ctx(info
->bmap
);
899 total
= isl_basic_map_total_dim(info
->bmap
);
900 isl_int_add_ui(info
->bmap
->ineq
[k
][0], info
->bmap
->ineq
[k
][0], 1);
901 T
= isl_mat_sub_alloc6(ctx
, info
->bmap
->ineq
, k
, 1, 0, 1 + total
);
902 T
= isl_mat_variable_compression(T
, NULL
);
903 isl_int_sub_ui(info
->bmap
->ineq
[k
][0], info
->bmap
->ineq
[k
][0], 1);
905 return isl_stat_error
;
911 affected
= isl_alloc_array(ctx
, int, total
);
915 for (i
= 0; i
< total
; ++i
)
916 affected
[i
] = not_unique_unit_row(T
, 1 + i
);
918 for (i
= 0; i
< info
->bmap
->n_ineq
; ++i
) {
921 if (info
->ineq
[i
] == STATUS_REDUNDANT
)
923 if (!is_affected(info
->bmap
, i
, affected
, total
))
925 v
= isl_vec_alloc(ctx
, 1 + total
);
928 isl_seq_cpy(v
->el
, info
->bmap
->ineq
[i
], 1 + total
);
929 v
= isl_vec_mat_product(v
, isl_mat_copy(T
));
930 v
= try_tightening(info
, i
, v
);
942 return isl_stat_error
;
945 /* Basic map "i" has an inequality "k" that is adjacent to some equality
946 * of basic map "j". All the other inequalities are valid for "j".
947 * Check if basic map "j" forms an extension of basic map "i".
949 * In particular, we relax constraint "k", compute the corresponding
950 * facet and check whether it is included in the other basic map.
951 * Before testing for inclusion, the constraints on the facet
952 * are tightened to increase the chance of an inclusion being detected.
953 * If the facet is included, we know that relaxing the constraint extends
954 * the basic map with exactly the other basic map (we already know that this
955 * other basic map is included in the extension, because there
956 * were no "cut" inequalities in "i") and we can replace the
957 * two basic maps by this extension.
958 * Each integer division that does not have exactly the same
959 * definition in "i" and "j" is marked unknown and the basic map
960 * is scheduled to be simplified in an attempt to recover
961 * the integer division definition.
962 * Place this extension in the position that is the smallest of i and j.
970 static enum isl_change
is_adj_eq_extension(int i
, int j
, int k
,
971 struct isl_coalesce_info
*info
)
973 int change
= isl_change_none
;
975 struct isl_tab_undo
*snap
, *snap2
;
976 unsigned n_eq
= info
[i
].bmap
->n_eq
;
978 if (isl_tab_is_equality(info
[i
].tab
, n_eq
+ k
))
979 return isl_change_none
;
981 snap
= isl_tab_snap(info
[i
].tab
);
982 if (isl_tab_relax(info
[i
].tab
, n_eq
+ k
) < 0)
983 return isl_change_error
;
984 snap2
= isl_tab_snap(info
[i
].tab
);
985 if (isl_tab_select_facet(info
[i
].tab
, n_eq
+ k
) < 0)
986 return isl_change_error
;
987 if (tighten_on_relaxed_facet(&info
[i
], k
) < 0)
988 return isl_change_error
;
989 super
= contains(&info
[j
], info
[i
].tab
);
991 return isl_change_error
;
996 if (isl_tab_rollback(info
[i
].tab
, snap2
) < 0)
997 return isl_change_error
;
998 info
[i
].bmap
= isl_basic_map_cow(info
[i
].bmap
);
1000 return isl_change_error
;
1001 total
= isl_basic_map_total_dim(info
[i
].bmap
);
1002 for (l
= 0; l
< info
[i
].bmap
->n_div
; ++l
)
1003 if (!isl_seq_eq(info
[i
].bmap
->div
[l
],
1004 info
[j
].bmap
->div
[l
], 1 + 1 + total
)) {
1005 isl_int_set_si(info
[i
].bmap
->div
[l
][0], 0);
1006 info
[i
].simplify
= 1;
1008 isl_int_add_ui(info
[i
].bmap
->ineq
[k
][0],
1009 info
[i
].bmap
->ineq
[k
][0], 1);
1010 ISL_F_SET(info
[i
].bmap
, ISL_BASIC_MAP_FINAL
);
1013 exchange(&info
[i
], &info
[j
]);
1014 change
= isl_change_fuse
;
1016 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
1017 return isl_change_error
;
1022 /* Data structure that keeps track of the wrapping constraints
1023 * and of information to bound the coefficients of those constraints.
1025 * bound is set if we want to apply a bound on the coefficients
1026 * mat contains the wrapping constraints
1027 * max is the bound on the coefficients (if bound is set)
1035 /* Update wraps->max to be greater than or equal to the coefficients
1036 * in the equalities and inequalities of info->bmap that can be removed
1037 * if we end up applying wrapping.
1039 static void wraps_update_max(struct isl_wraps
*wraps
,
1040 struct isl_coalesce_info
*info
)
1044 unsigned total
= isl_basic_map_total_dim(info
->bmap
);
1046 isl_int_init(max_k
);
1048 for (k
= 0; k
< info
->bmap
->n_eq
; ++k
) {
1049 if (info
->eq
[2 * k
] == STATUS_VALID
&&
1050 info
->eq
[2 * k
+ 1] == STATUS_VALID
)
1052 isl_seq_abs_max(info
->bmap
->eq
[k
] + 1, total
, &max_k
);
1053 if (isl_int_abs_gt(max_k
, wraps
->max
))
1054 isl_int_set(wraps
->max
, max_k
);
1057 for (k
= 0; k
< info
->bmap
->n_ineq
; ++k
) {
1058 if (info
->ineq
[k
] == STATUS_VALID
||
1059 info
->ineq
[k
] == STATUS_REDUNDANT
)
1061 isl_seq_abs_max(info
->bmap
->ineq
[k
] + 1, total
, &max_k
);
1062 if (isl_int_abs_gt(max_k
, wraps
->max
))
1063 isl_int_set(wraps
->max
, max_k
);
1066 isl_int_clear(max_k
);
1069 /* Initialize the isl_wraps data structure.
1070 * If we want to bound the coefficients of the wrapping constraints,
1071 * we set wraps->max to the largest coefficient
1072 * in the equalities and inequalities that can be removed if we end up
1073 * applying wrapping.
1075 static void wraps_init(struct isl_wraps
*wraps
, __isl_take isl_mat
*mat
,
1076 struct isl_coalesce_info
*info
, int i
, int j
)
1084 ctx
= isl_mat_get_ctx(mat
);
1085 wraps
->bound
= isl_options_get_coalesce_bounded_wrapping(ctx
);
1088 isl_int_init(wraps
->max
);
1089 isl_int_set_si(wraps
->max
, 0);
1090 wraps_update_max(wraps
, &info
[i
]);
1091 wraps_update_max(wraps
, &info
[j
]);
1094 /* Free the contents of the isl_wraps data structure.
1096 static void wraps_free(struct isl_wraps
*wraps
)
1098 isl_mat_free(wraps
->mat
);
1100 isl_int_clear(wraps
->max
);
1103 /* Is the wrapping constraint in row "row" allowed?
1105 * If wraps->bound is set, we check that none of the coefficients
1106 * is greater than wraps->max.
1108 static int allow_wrap(struct isl_wraps
*wraps
, int row
)
1115 for (i
= 1; i
< wraps
->mat
->n_col
; ++i
)
1116 if (isl_int_abs_gt(wraps
->mat
->row
[row
][i
], wraps
->max
))
1122 /* Wrap "ineq" (or its opposite if "negate" is set) around "bound"
1123 * to include "set" and add the result in position "w" of "wraps".
1124 * "len" is the total number of coefficients in "bound" and "ineq".
1125 * Return 1 on success, 0 on failure and -1 on error.
1126 * Wrapping can fail if the result of wrapping is equal to "bound"
1127 * or if we want to bound the sizes of the coefficients and
1128 * the wrapped constraint does not satisfy this bound.
1130 static int add_wrap(struct isl_wraps
*wraps
, int w
, isl_int
*bound
,
1131 isl_int
*ineq
, unsigned len
, __isl_keep isl_set
*set
, int negate
)
1133 isl_seq_cpy(wraps
->mat
->row
[w
], bound
, len
);
1135 isl_seq_neg(wraps
->mat
->row
[w
+ 1], ineq
, len
);
1136 ineq
= wraps
->mat
->row
[w
+ 1];
1138 if (!isl_set_wrap_facet(set
, wraps
->mat
->row
[w
], ineq
))
1140 if (isl_seq_eq(wraps
->mat
->row
[w
], bound
, len
))
1142 if (!allow_wrap(wraps
, w
))
1147 /* For each constraint in info->bmap that is not redundant (as determined
1148 * by info->tab) and that is not a valid constraint for the other basic map,
1149 * wrap the constraint around "bound" such that it includes the whole
1150 * set "set" and append the resulting constraint to "wraps".
1151 * Note that the constraints that are valid for the other basic map
1152 * will be added to the combined basic map by default, so there is
1153 * no need to wrap them.
1154 * The caller wrap_in_facets even relies on this function not wrapping
1155 * any constraints that are already valid.
1156 * "wraps" is assumed to have been pre-allocated to the appropriate size.
1157 * wraps->n_row is the number of actual wrapped constraints that have
1159 * If any of the wrapping problems results in a constraint that is
1160 * identical to "bound", then this means that "set" is unbounded in such
1161 * way that no wrapping is possible. If this happens then wraps->n_row
1163 * Similarly, if we want to bound the coefficients of the wrapping
1164 * constraints and a newly added wrapping constraint does not
1165 * satisfy the bound, then wraps->n_row is also reset to zero.
1167 static int add_wraps(struct isl_wraps
*wraps
, struct isl_coalesce_info
*info
,
1168 isl_int
*bound
, __isl_keep isl_set
*set
)
1173 isl_basic_map
*bmap
= info
->bmap
;
1174 unsigned len
= 1 + isl_basic_map_total_dim(bmap
);
1176 w
= wraps
->mat
->n_row
;
1178 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
1179 if (info
->ineq
[l
] == STATUS_VALID
||
1180 info
->ineq
[l
] == STATUS_REDUNDANT
)
1182 if (isl_seq_is_neg(bound
, bmap
->ineq
[l
], len
))
1184 if (isl_seq_eq(bound
, bmap
->ineq
[l
], len
))
1186 if (isl_tab_is_redundant(info
->tab
, bmap
->n_eq
+ l
))
1189 added
= add_wrap(wraps
, w
, bound
, bmap
->ineq
[l
], len
, set
, 0);
1196 for (l
= 0; l
< bmap
->n_eq
; ++l
) {
1197 if (isl_seq_is_neg(bound
, bmap
->eq
[l
], len
))
1199 if (isl_seq_eq(bound
, bmap
->eq
[l
], len
))
1202 for (m
= 0; m
< 2; ++m
) {
1203 if (info
->eq
[2 * l
+ m
] == STATUS_VALID
)
1205 added
= add_wrap(wraps
, w
, bound
, bmap
->eq
[l
], len
,
1215 wraps
->mat
->n_row
= w
;
1218 wraps
->mat
->n_row
= 0;
1222 /* Check if the constraints in "wraps" from "first" until the last
1223 * are all valid for the basic set represented by "tab".
1224 * If not, wraps->n_row is set to zero.
1226 static int check_wraps(__isl_keep isl_mat
*wraps
, int first
,
1227 struct isl_tab
*tab
)
1231 for (i
= first
; i
< wraps
->n_row
; ++i
) {
1232 enum isl_ineq_type type
;
1233 type
= isl_tab_ineq_type(tab
, wraps
->row
[i
]);
1234 if (type
== isl_ineq_error
)
1236 if (type
== isl_ineq_redundant
)
1245 /* Return a set that corresponds to the non-redundant constraints
1246 * (as recorded in tab) of bmap.
1248 * It's important to remove the redundant constraints as some
1249 * of the other constraints may have been modified after the
1250 * constraints were marked redundant.
1251 * In particular, a constraint may have been relaxed.
1252 * Redundant constraints are ignored when a constraint is relaxed
1253 * and should therefore continue to be ignored ever after.
1254 * Otherwise, the relaxation might be thwarted by some of
1255 * these constraints.
1257 * Update the underlying set to ensure that the dimension doesn't change.
1258 * Otherwise the integer divisions could get dropped if the tab
1259 * turns out to be empty.
1261 static __isl_give isl_set
*set_from_updated_bmap(__isl_keep isl_basic_map
*bmap
,
1262 struct isl_tab
*tab
)
1264 isl_basic_set
*bset
;
1266 bmap
= isl_basic_map_copy(bmap
);
1267 bset
= isl_basic_map_underlying_set(bmap
);
1268 bset
= isl_basic_set_cow(bset
);
1269 bset
= isl_basic_set_update_from_tab(bset
, tab
);
1270 return isl_set_from_basic_set(bset
);
1273 /* Wrap the constraints of info->bmap that bound the facet defined
1274 * by inequality "k" around (the opposite of) this inequality to
1275 * include "set". "bound" may be used to store the negated inequality.
1276 * Since the wrapped constraints are not guaranteed to contain the whole
1277 * of info->bmap, we check them in check_wraps.
1278 * If any of the wrapped constraints turn out to be invalid, then
1279 * check_wraps will reset wrap->n_row to zero.
1281 static int add_wraps_around_facet(struct isl_wraps
*wraps
,
1282 struct isl_coalesce_info
*info
, int k
, isl_int
*bound
,
1283 __isl_keep isl_set
*set
)
1285 struct isl_tab_undo
*snap
;
1287 unsigned total
= isl_basic_map_total_dim(info
->bmap
);
1289 snap
= isl_tab_snap(info
->tab
);
1291 if (isl_tab_select_facet(info
->tab
, info
->bmap
->n_eq
+ k
) < 0)
1293 if (isl_tab_detect_redundant(info
->tab
) < 0)
1296 isl_seq_neg(bound
, info
->bmap
->ineq
[k
], 1 + total
);
1298 n
= wraps
->mat
->n_row
;
1299 if (add_wraps(wraps
, info
, bound
, set
) < 0)
1302 if (isl_tab_rollback(info
->tab
, snap
) < 0)
1304 if (check_wraps(wraps
->mat
, n
, info
->tab
) < 0)
1310 /* Given a basic set i with a constraint k that is adjacent to
1311 * basic set j, check if we can wrap
1312 * both the facet corresponding to k (if "wrap_facet" is set) and basic map j
1313 * (always) around their ridges to include the other set.
1314 * If so, replace the pair of basic sets by their union.
1316 * All constraints of i (except k) are assumed to be valid or
1317 * cut constraints for j.
1318 * Wrapping the cut constraints to include basic map j may result
1319 * in constraints that are no longer valid of basic map i
1320 * we have to check that the resulting wrapping constraints are valid for i.
1321 * If "wrap_facet" is not set, then all constraints of i (except k)
1322 * are assumed to be valid for j.
1331 static enum isl_change
can_wrap_in_facet(int i
, int j
, int k
,
1332 struct isl_coalesce_info
*info
, int wrap_facet
)
1334 enum isl_change change
= isl_change_none
;
1335 struct isl_wraps wraps
;
1338 struct isl_set
*set_i
= NULL
;
1339 struct isl_set
*set_j
= NULL
;
1340 struct isl_vec
*bound
= NULL
;
1341 unsigned total
= isl_basic_map_total_dim(info
[i
].bmap
);
1343 set_i
= set_from_updated_bmap(info
[i
].bmap
, info
[i
].tab
);
1344 set_j
= set_from_updated_bmap(info
[j
].bmap
, info
[j
].tab
);
1345 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
1346 mat
= isl_mat_alloc(ctx
, 2 * (info
[i
].bmap
->n_eq
+ info
[j
].bmap
->n_eq
) +
1347 info
[i
].bmap
->n_ineq
+ info
[j
].bmap
->n_ineq
,
1349 wraps_init(&wraps
, mat
, info
, i
, j
);
1350 bound
= isl_vec_alloc(ctx
, 1 + total
);
1351 if (!set_i
|| !set_j
|| !wraps
.mat
|| !bound
)
1354 isl_seq_cpy(bound
->el
, info
[i
].bmap
->ineq
[k
], 1 + total
);
1355 isl_int_add_ui(bound
->el
[0], bound
->el
[0], 1);
1357 isl_seq_cpy(wraps
.mat
->row
[0], bound
->el
, 1 + total
);
1358 wraps
.mat
->n_row
= 1;
1360 if (add_wraps(&wraps
, &info
[j
], bound
->el
, set_i
) < 0)
1362 if (!wraps
.mat
->n_row
)
1366 if (add_wraps_around_facet(&wraps
, &info
[i
], k
,
1367 bound
->el
, set_j
) < 0)
1369 if (!wraps
.mat
->n_row
)
1373 change
= fuse(i
, j
, info
, wraps
.mat
, 0, 0);
1378 isl_set_free(set_i
);
1379 isl_set_free(set_j
);
1381 isl_vec_free(bound
);
1386 isl_vec_free(bound
);
1387 isl_set_free(set_i
);
1388 isl_set_free(set_j
);
1389 return isl_change_error
;
1392 /* Given a cut constraint t(x) >= 0 of basic map i, stored in row "w"
1393 * of wrap.mat, replace it by its relaxed version t(x) + 1 >= 0, and
1394 * add wrapping constraints to wrap.mat for all constraints
1395 * of basic map j that bound the part of basic map j that sticks out
1396 * of the cut constraint.
1397 * "set_i" is the underlying set of basic map i.
1398 * If any wrapping fails, then wraps->mat.n_row is reset to zero.
1400 * In particular, we first intersect basic map j with t(x) + 1 = 0.
1401 * If the result is empty, then t(x) >= 0 was actually a valid constraint
1402 * (with respect to the integer points), so we add t(x) >= 0 instead.
1403 * Otherwise, we wrap the constraints of basic map j that are not
1404 * redundant in this intersection and that are not already valid
1405 * for basic map i over basic map i.
1406 * Note that it is sufficient to wrap the constraints to include
1407 * basic map i, because we will only wrap the constraints that do
1408 * not include basic map i already. The wrapped constraint will
1409 * therefore be more relaxed compared to the original constraint.
1410 * Since the original constraint is valid for basic map j, so is
1411 * the wrapped constraint.
1413 static isl_stat
wrap_in_facet(struct isl_wraps
*wraps
, int w
,
1414 struct isl_coalesce_info
*info_j
, __isl_keep isl_set
*set_i
,
1415 struct isl_tab_undo
*snap
)
1417 isl_int_add_ui(wraps
->mat
->row
[w
][0], wraps
->mat
->row
[w
][0], 1);
1418 if (isl_tab_add_eq(info_j
->tab
, wraps
->mat
->row
[w
]) < 0)
1419 return isl_stat_error
;
1420 if (isl_tab_detect_redundant(info_j
->tab
) < 0)
1421 return isl_stat_error
;
1423 if (info_j
->tab
->empty
)
1424 isl_int_sub_ui(wraps
->mat
->row
[w
][0], wraps
->mat
->row
[w
][0], 1);
1425 else if (add_wraps(wraps
, info_j
, wraps
->mat
->row
[w
], set_i
) < 0)
1426 return isl_stat_error
;
1428 if (isl_tab_rollback(info_j
->tab
, snap
) < 0)
1429 return isl_stat_error
;
1434 /* Given a pair of basic maps i and j such that j sticks out
1435 * of i at n cut constraints, each time by at most one,
1436 * try to compute wrapping constraints and replace the two
1437 * basic maps by a single basic map.
1438 * The other constraints of i are assumed to be valid for j.
1439 * "set_i" is the underlying set of basic map i.
1440 * "wraps" has been initialized to be of the right size.
1442 * For each cut constraint t(x) >= 0 of i, we add the relaxed version
1443 * t(x) + 1 >= 0, along with wrapping constraints for all constraints
1444 * of basic map j that bound the part of basic map j that sticks out
1445 * of the cut constraint.
1447 * If any wrapping fails, i.e., if we cannot wrap to touch
1448 * the union, then we give up.
1449 * Otherwise, the pair of basic maps is replaced by their union.
1451 static enum isl_change
try_wrap_in_facets(int i
, int j
,
1452 struct isl_coalesce_info
*info
, struct isl_wraps
*wraps
,
1453 __isl_keep isl_set
*set_i
)
1457 struct isl_tab_undo
*snap
;
1459 total
= isl_basic_map_total_dim(info
[i
].bmap
);
1461 snap
= isl_tab_snap(info
[j
].tab
);
1463 wraps
->mat
->n_row
= 0;
1465 for (k
= 0; k
< info
[i
].bmap
->n_eq
; ++k
) {
1466 for (l
= 0; l
< 2; ++l
) {
1467 if (info
[i
].eq
[2 * k
+ l
] != STATUS_CUT
)
1469 w
= wraps
->mat
->n_row
++;
1471 isl_seq_neg(wraps
->mat
->row
[w
],
1472 info
[i
].bmap
->eq
[k
], 1 + total
);
1474 isl_seq_cpy(wraps
->mat
->row
[w
],
1475 info
[i
].bmap
->eq
[k
], 1 + total
);
1476 if (wrap_in_facet(wraps
, w
, &info
[j
], set_i
, snap
) < 0)
1477 return isl_change_error
;
1479 if (!wraps
->mat
->n_row
)
1480 return isl_change_none
;
1484 for (k
= 0; k
< info
[i
].bmap
->n_ineq
; ++k
) {
1485 if (info
[i
].ineq
[k
] != STATUS_CUT
)
1487 w
= wraps
->mat
->n_row
++;
1488 isl_seq_cpy(wraps
->mat
->row
[w
],
1489 info
[i
].bmap
->ineq
[k
], 1 + total
);
1490 if (wrap_in_facet(wraps
, w
, &info
[j
], set_i
, snap
) < 0)
1491 return isl_change_error
;
1493 if (!wraps
->mat
->n_row
)
1494 return isl_change_none
;
1497 return fuse(i
, j
, info
, wraps
->mat
, 0, 1);
1500 /* Given a pair of basic maps i and j such that j sticks out
1501 * of i at n cut constraints, each time by at most one,
1502 * try to compute wrapping constraints and replace the two
1503 * basic maps by a single basic map.
1504 * The other constraints of i are assumed to be valid for j.
1506 * The core computation is performed by try_wrap_in_facets.
1507 * This function simply extracts an underlying set representation
1508 * of basic map i and initializes the data structure for keeping
1509 * track of wrapping constraints.
1511 static enum isl_change
wrap_in_facets(int i
, int j
, int n
,
1512 struct isl_coalesce_info
*info
)
1514 enum isl_change change
= isl_change_none
;
1515 struct isl_wraps wraps
;
1518 isl_set
*set_i
= NULL
;
1519 unsigned total
= isl_basic_map_total_dim(info
[i
].bmap
);
1522 if (isl_tab_extend_cons(info
[j
].tab
, 1) < 0)
1523 return isl_change_error
;
1525 max_wrap
= 1 + 2 * info
[j
].bmap
->n_eq
+ info
[j
].bmap
->n_ineq
;
1528 set_i
= set_from_updated_bmap(info
[i
].bmap
, info
[i
].tab
);
1529 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
1530 mat
= isl_mat_alloc(ctx
, max_wrap
, 1 + total
);
1531 wraps_init(&wraps
, mat
, info
, i
, j
);
1532 if (!set_i
|| !wraps
.mat
)
1535 change
= try_wrap_in_facets(i
, j
, info
, &wraps
, set_i
);
1538 isl_set_free(set_i
);
1543 isl_set_free(set_i
);
1544 return isl_change_error
;
1547 /* Return the effect of inequality "ineq" on the tableau "tab",
1548 * after relaxing the constant term of "ineq" by one.
1550 static enum isl_ineq_type
type_of_relaxed(struct isl_tab
*tab
, isl_int
*ineq
)
1552 enum isl_ineq_type type
;
1554 isl_int_add_ui(ineq
[0], ineq
[0], 1);
1555 type
= isl_tab_ineq_type(tab
, ineq
);
1556 isl_int_sub_ui(ineq
[0], ineq
[0], 1);
1561 /* Given two basic sets i and j,
1562 * check if relaxing all the cut constraints of i by one turns
1563 * them into valid constraint for j and check if we can wrap in
1564 * the bits that are sticking out.
1565 * If so, replace the pair by their union.
1567 * We first check if all relaxed cut inequalities of i are valid for j
1568 * and then try to wrap in the intersections of the relaxed cut inequalities
1571 * During this wrapping, we consider the points of j that lie at a distance
1572 * of exactly 1 from i. In particular, we ignore the points that lie in
1573 * between this lower-dimensional space and the basic map i.
1574 * We can therefore only apply this to integer maps.
1600 * Wrapping can fail if the result of wrapping one of the facets
1601 * around its edges does not produce any new facet constraint.
1602 * In particular, this happens when we try to wrap in unbounded sets.
1604 * _______________________________________________________________________
1608 * |_| |_________________________________________________________________
1611 * The following is not an acceptable result of coalescing the above two
1612 * sets as it includes extra integer points.
1613 * _______________________________________________________________________
1618 * \______________________________________________________________________
1620 static enum isl_change
can_wrap_in_set(int i
, int j
,
1621 struct isl_coalesce_info
*info
)
1627 if (ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_RATIONAL
) ||
1628 ISL_F_ISSET(info
[j
].bmap
, ISL_BASIC_MAP_RATIONAL
))
1629 return isl_change_none
;
1631 n
= count(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_CUT
);
1632 n
+= count(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_CUT
);
1634 return isl_change_none
;
1636 total
= isl_basic_map_total_dim(info
[i
].bmap
);
1637 for (k
= 0; k
< info
[i
].bmap
->n_eq
; ++k
) {
1638 for (l
= 0; l
< 2; ++l
) {
1639 enum isl_ineq_type type
;
1641 if (info
[i
].eq
[2 * k
+ l
] != STATUS_CUT
)
1645 isl_seq_neg(info
[i
].bmap
->eq
[k
],
1646 info
[i
].bmap
->eq
[k
], 1 + total
);
1647 type
= type_of_relaxed(info
[j
].tab
,
1648 info
[i
].bmap
->eq
[k
]);
1650 isl_seq_neg(info
[i
].bmap
->eq
[k
],
1651 info
[i
].bmap
->eq
[k
], 1 + total
);
1652 if (type
== isl_ineq_error
)
1653 return isl_change_error
;
1654 if (type
!= isl_ineq_redundant
)
1655 return isl_change_none
;
1659 for (k
= 0; k
< info
[i
].bmap
->n_ineq
; ++k
) {
1660 enum isl_ineq_type type
;
1662 if (info
[i
].ineq
[k
] != STATUS_CUT
)
1665 type
= type_of_relaxed(info
[j
].tab
, info
[i
].bmap
->ineq
[k
]);
1666 if (type
== isl_ineq_error
)
1667 return isl_change_error
;
1668 if (type
!= isl_ineq_redundant
)
1669 return isl_change_none
;
1672 return wrap_in_facets(i
, j
, n
, info
);
1675 /* Check if either i or j has only cut constraints that can
1676 * be used to wrap in (a facet of) the other basic set.
1677 * if so, replace the pair by their union.
1679 static enum isl_change
check_wrap(int i
, int j
, struct isl_coalesce_info
*info
)
1681 enum isl_change change
= isl_change_none
;
1683 change
= can_wrap_in_set(i
, j
, info
);
1684 if (change
!= isl_change_none
)
1687 change
= can_wrap_in_set(j
, i
, info
);
1691 /* At least one of the basic maps has an equality that is adjacent
1692 * to inequality. Make sure that only one of the basic maps has
1693 * such an equality and that the other basic map has exactly one
1694 * inequality adjacent to an equality.
1695 * If the other basic map does not have such an inequality, then
1696 * check if all its constraints are either valid or cut constraints
1697 * and, if so, try wrapping in the first map into the second.
1699 * We call the basic map that has the inequality "i" and the basic
1700 * map that has the equality "j".
1701 * If "i" has any "cut" (in)equality, then relaxing the inequality
1702 * by one would not result in a basic map that contains the other
1703 * basic map. However, it may still be possible to wrap in the other
1706 static enum isl_change
check_adj_eq(int i
, int j
,
1707 struct isl_coalesce_info
*info
)
1709 enum isl_change change
= isl_change_none
;
1713 if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_ADJ_INEQ
) &&
1714 any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_ADJ_INEQ
))
1715 /* ADJ EQ TOO MANY */
1716 return isl_change_none
;
1718 if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_ADJ_INEQ
))
1719 return check_adj_eq(j
, i
, info
);
1721 /* j has an equality adjacent to an inequality in i */
1723 if (count(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ADJ_EQ
) != 1) {
1724 if (all_valid_or_cut(&info
[i
]))
1725 return can_wrap_in_set(i
, j
, info
);
1726 return isl_change_none
;
1728 if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_CUT
))
1729 return isl_change_none
;
1730 any_cut
= any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_CUT
);
1731 if (any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_ADJ_EQ
) ||
1732 any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ADJ_INEQ
) ||
1733 any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_ADJ_INEQ
))
1734 /* ADJ EQ TOO MANY */
1735 return isl_change_none
;
1737 for (k
= 0; k
< info
[i
].bmap
->n_ineq
; ++k
)
1738 if (info
[i
].ineq
[k
] == STATUS_ADJ_EQ
)
1742 change
= is_adj_eq_extension(i
, j
, k
, info
);
1743 if (change
!= isl_change_none
)
1747 change
= can_wrap_in_facet(i
, j
, k
, info
, any_cut
);
1752 /* The two basic maps lie on adjacent hyperplanes. In particular,
1753 * basic map "i" has an equality that lies parallel to basic map "j".
1754 * Check if we can wrap the facets around the parallel hyperplanes
1755 * to include the other set.
1757 * We perform basically the same operations as can_wrap_in_facet,
1758 * except that we don't need to select a facet of one of the sets.
1764 * If there is more than one equality of "i" adjacent to an equality of "j",
1765 * then the result will satisfy one or more equalities that are a linear
1766 * combination of these equalities. These will be encoded as pairs
1767 * of inequalities in the wrapping constraints and need to be made
1770 static enum isl_change
check_eq_adj_eq(int i
, int j
,
1771 struct isl_coalesce_info
*info
)
1774 enum isl_change change
= isl_change_none
;
1775 int detect_equalities
= 0;
1776 struct isl_wraps wraps
;
1779 struct isl_set
*set_i
= NULL
;
1780 struct isl_set
*set_j
= NULL
;
1781 struct isl_vec
*bound
= NULL
;
1782 unsigned total
= isl_basic_map_total_dim(info
[i
].bmap
);
1784 if (count(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_ADJ_EQ
) != 1)
1785 detect_equalities
= 1;
1787 for (k
= 0; k
< 2 * info
[i
].bmap
->n_eq
; ++k
)
1788 if (info
[i
].eq
[k
] == STATUS_ADJ_EQ
)
1791 set_i
= set_from_updated_bmap(info
[i
].bmap
, info
[i
].tab
);
1792 set_j
= set_from_updated_bmap(info
[j
].bmap
, info
[j
].tab
);
1793 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
1794 mat
= isl_mat_alloc(ctx
, 2 * (info
[i
].bmap
->n_eq
+ info
[j
].bmap
->n_eq
) +
1795 info
[i
].bmap
->n_ineq
+ info
[j
].bmap
->n_ineq
,
1797 wraps_init(&wraps
, mat
, info
, i
, j
);
1798 bound
= isl_vec_alloc(ctx
, 1 + total
);
1799 if (!set_i
|| !set_j
|| !wraps
.mat
|| !bound
)
1803 isl_seq_neg(bound
->el
, info
[i
].bmap
->eq
[k
/ 2], 1 + total
);
1805 isl_seq_cpy(bound
->el
, info
[i
].bmap
->eq
[k
/ 2], 1 + total
);
1806 isl_int_add_ui(bound
->el
[0], bound
->el
[0], 1);
1808 isl_seq_cpy(wraps
.mat
->row
[0], bound
->el
, 1 + total
);
1809 wraps
.mat
->n_row
= 1;
1811 if (add_wraps(&wraps
, &info
[j
], bound
->el
, set_i
) < 0)
1813 if (!wraps
.mat
->n_row
)
1816 isl_int_sub_ui(bound
->el
[0], bound
->el
[0], 1);
1817 isl_seq_neg(bound
->el
, bound
->el
, 1 + total
);
1819 isl_seq_cpy(wraps
.mat
->row
[wraps
.mat
->n_row
], bound
->el
, 1 + total
);
1822 if (add_wraps(&wraps
, &info
[i
], bound
->el
, set_j
) < 0)
1824 if (!wraps
.mat
->n_row
)
1827 change
= fuse(i
, j
, info
, wraps
.mat
, detect_equalities
, 0);
1830 error
: change
= isl_change_error
;
1835 isl_set_free(set_i
);
1836 isl_set_free(set_j
);
1837 isl_vec_free(bound
);
1842 /* Initialize the "eq" and "ineq" fields of "info".
1844 static void init_status(struct isl_coalesce_info
*info
)
1846 info
->eq
= info
->ineq
= NULL
;
1849 /* Set info->eq to the positions of the equalities of info->bmap
1850 * with respect to the basic map represented by "tab".
1851 * If info->eq has already been computed, then do not compute it again.
1853 static void set_eq_status_in(struct isl_coalesce_info
*info
,
1854 struct isl_tab
*tab
)
1858 info
->eq
= eq_status_in(info
->bmap
, tab
);
1861 /* Set info->ineq to the positions of the inequalities of info->bmap
1862 * with respect to the basic map represented by "tab".
1863 * If info->ineq has already been computed, then do not compute it again.
1865 static void set_ineq_status_in(struct isl_coalesce_info
*info
,
1866 struct isl_tab
*tab
)
1870 info
->ineq
= ineq_status_in(info
->bmap
, info
->tab
, tab
);
1873 /* Free the memory allocated by the "eq" and "ineq" fields of "info".
1874 * This function assumes that init_status has been called on "info" first,
1875 * after which the "eq" and "ineq" fields may or may not have been
1876 * assigned a newly allocated array.
1878 static void clear_status(struct isl_coalesce_info
*info
)
1884 /* Check if the union of the given pair of basic maps
1885 * can be represented by a single basic map.
1886 * If so, replace the pair by the single basic map and return
1887 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
1888 * Otherwise, return isl_change_none.
1889 * The two basic maps are assumed to live in the same local space.
1890 * The "eq" and "ineq" fields of info[i] and info[j] are assumed
1891 * to have been initialized by the caller, either to NULL or
1892 * to valid information.
1894 * We first check the effect of each constraint of one basic map
1895 * on the other basic map.
1896 * The constraint may be
1897 * redundant the constraint is redundant in its own
1898 * basic map and should be ignore and removed
1900 * valid all (integer) points of the other basic map
1901 * satisfy the constraint
1902 * separate no (integer) point of the other basic map
1903 * satisfies the constraint
1904 * cut some but not all points of the other basic map
1905 * satisfy the constraint
1906 * adj_eq the given constraint is adjacent (on the outside)
1907 * to an equality of the other basic map
1908 * adj_ineq the given constraint is adjacent (on the outside)
1909 * to an inequality of the other basic map
1911 * We consider seven cases in which we can replace the pair by a single
1912 * basic map. We ignore all "redundant" constraints.
1914 * 1. all constraints of one basic map are valid
1915 * => the other basic map is a subset and can be removed
1917 * 2. all constraints of both basic maps are either "valid" or "cut"
1918 * and the facets corresponding to the "cut" constraints
1919 * of one of the basic maps lies entirely inside the other basic map
1920 * => the pair can be replaced by a basic map consisting
1921 * of the valid constraints in both basic maps
1923 * 3. there is a single pair of adjacent inequalities
1924 * (all other constraints are "valid")
1925 * => the pair can be replaced by a basic map consisting
1926 * of the valid constraints in both basic maps
1928 * 4. one basic map has a single adjacent inequality, while the other
1929 * constraints are "valid". The other basic map has some
1930 * "cut" constraints, but replacing the adjacent inequality by
1931 * its opposite and adding the valid constraints of the other
1932 * basic map results in a subset of the other basic map
1933 * => the pair can be replaced by a basic map consisting
1934 * of the valid constraints in both basic maps
1936 * 5. there is a single adjacent pair of an inequality and an equality,
1937 * the other constraints of the basic map containing the inequality are
1938 * "valid". Moreover, if the inequality the basic map is relaxed
1939 * and then turned into an equality, then resulting facet lies
1940 * entirely inside the other basic map
1941 * => the pair can be replaced by the basic map containing
1942 * the inequality, with the inequality relaxed.
1944 * 6. there is a single adjacent pair of an inequality and an equality,
1945 * the other constraints of the basic map containing the inequality are
1946 * "valid". Moreover, the facets corresponding to both
1947 * the inequality and the equality can be wrapped around their
1948 * ridges to include the other basic map
1949 * => the pair can be replaced by a basic map consisting
1950 * of the valid constraints in both basic maps together
1951 * with all wrapping constraints
1953 * 7. one of the basic maps extends beyond the other by at most one.
1954 * Moreover, the facets corresponding to the cut constraints and
1955 * the pieces of the other basic map at offset one from these cut
1956 * constraints can be wrapped around their ridges to include
1957 * the union of the two basic maps
1958 * => the pair can be replaced by a basic map consisting
1959 * of the valid constraints in both basic maps together
1960 * with all wrapping constraints
1962 * 8. the two basic maps live in adjacent hyperplanes. In principle
1963 * such sets can always be combined through wrapping, but we impose
1964 * that there is only one such pair, to avoid overeager coalescing.
1966 * Throughout the computation, we maintain a collection of tableaus
1967 * corresponding to the basic maps. When the basic maps are dropped
1968 * or combined, the tableaus are modified accordingly.
1970 static enum isl_change
coalesce_local_pair_reuse(int i
, int j
,
1971 struct isl_coalesce_info
*info
)
1973 enum isl_change change
= isl_change_none
;
1975 set_eq_status_in(&info
[i
], info
[j
].tab
);
1976 if (info
[i
].bmap
->n_eq
&& !info
[i
].eq
)
1978 if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_ERROR
))
1980 if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_SEPARATE
))
1983 set_eq_status_in(&info
[j
], info
[i
].tab
);
1984 if (info
[j
].bmap
->n_eq
&& !info
[j
].eq
)
1986 if (any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_ERROR
))
1988 if (any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_SEPARATE
))
1991 set_ineq_status_in(&info
[i
], info
[j
].tab
);
1992 if (info
[i
].bmap
->n_ineq
&& !info
[i
].ineq
)
1994 if (any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ERROR
))
1996 if (any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_SEPARATE
))
1999 set_ineq_status_in(&info
[j
], info
[i
].tab
);
2000 if (info
[j
].bmap
->n_ineq
&& !info
[j
].ineq
)
2002 if (any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_ERROR
))
2004 if (any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_SEPARATE
))
2007 if (all(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_VALID
) &&
2008 all(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_VALID
)) {
2010 change
= isl_change_drop_second
;
2011 } else if (all(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_VALID
) &&
2012 all(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_VALID
)) {
2014 change
= isl_change_drop_first
;
2015 } else if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_ADJ_EQ
)) {
2016 change
= check_eq_adj_eq(i
, j
, info
);
2017 } else if (any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_ADJ_EQ
)) {
2018 change
= check_eq_adj_eq(j
, i
, info
);
2019 } else if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_ADJ_INEQ
) ||
2020 any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_ADJ_INEQ
)) {
2021 change
= check_adj_eq(i
, j
, info
);
2022 } else if (any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ADJ_EQ
) ||
2023 any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_ADJ_EQ
)) {
2026 } else if (any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ADJ_INEQ
) ||
2027 any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_ADJ_INEQ
)) {
2028 change
= check_adj_ineq(i
, j
, info
);
2030 if (!any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_CUT
) &&
2031 !any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_CUT
))
2032 change
= check_facets(i
, j
, info
);
2033 if (change
== isl_change_none
)
2034 change
= check_wrap(i
, j
, info
);
2038 clear_status(&info
[i
]);
2039 clear_status(&info
[j
]);
2042 clear_status(&info
[i
]);
2043 clear_status(&info
[j
]);
2044 return isl_change_error
;
2047 /* Check if the union of the given pair of basic maps
2048 * can be represented by a single basic map.
2049 * If so, replace the pair by the single basic map and return
2050 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
2051 * Otherwise, return isl_change_none.
2052 * The two basic maps are assumed to live in the same local space.
2054 static enum isl_change
coalesce_local_pair(int i
, int j
,
2055 struct isl_coalesce_info
*info
)
2057 init_status(&info
[i
]);
2058 init_status(&info
[j
]);
2059 return coalesce_local_pair_reuse(i
, j
, info
);
2062 /* Shift the integer division at position "div" of the basic map
2063 * represented by "info" by "shift".
2065 * That is, if the integer division has the form
2069 * then replace it by
2071 * floor((f(x) + shift * d)/d) - shift
2073 static int shift_div(struct isl_coalesce_info
*info
, int div
, isl_int shift
)
2077 info
->bmap
= isl_basic_map_shift_div(info
->bmap
, div
, 0, shift
);
2081 total
= isl_basic_map_dim(info
->bmap
, isl_dim_all
);
2082 total
-= isl_basic_map_dim(info
->bmap
, isl_dim_div
);
2083 if (isl_tab_shift_var(info
->tab
, total
+ div
, shift
) < 0)
2089 /* Check if some of the divs in the basic map represented by "info1"
2090 * are shifts of the corresponding divs in the basic map represented
2091 * by "info2". If so, align them with those of "info2".
2092 * Only do this if "info1" and "info2" have the same number
2093 * of integer divisions.
2095 * An integer division is considered to be a shift of another integer
2096 * division if one is equal to the other plus a constant.
2098 * In particular, for each pair of integer divisions, if both are known,
2099 * have identical coefficients (apart from the constant term) and
2100 * if the difference between the constant terms (taking into account
2101 * the denominator) is an integer, then move the difference outside.
2102 * That is, if one integer division is of the form
2104 * floor((f(x) + c_1)/d)
2106 * while the other is of the form
2108 * floor((f(x) + c_2)/d)
2110 * and n = (c_2 - c_1)/d is an integer, then replace the first
2111 * integer division by
2113 * floor((f(x) + c_1 + n * d)/d) - n = floor((f(x) + c_2)/d) - n
2115 static int harmonize_divs(struct isl_coalesce_info
*info1
,
2116 struct isl_coalesce_info
*info2
)
2121 if (!info1
->bmap
|| !info2
->bmap
)
2124 if (info1
->bmap
->n_div
!= info2
->bmap
->n_div
)
2126 if (info1
->bmap
->n_div
== 0)
2129 total
= isl_basic_map_total_dim(info1
->bmap
);
2130 for (i
= 0; i
< info1
->bmap
->n_div
; ++i
) {
2134 if (isl_int_is_zero(info1
->bmap
->div
[i
][0]) ||
2135 isl_int_is_zero(info2
->bmap
->div
[i
][0]))
2137 if (isl_int_ne(info1
->bmap
->div
[i
][0], info2
->bmap
->div
[i
][0]))
2139 if (isl_int_eq(info1
->bmap
->div
[i
][1], info2
->bmap
->div
[i
][1]))
2141 if (!isl_seq_eq(info1
->bmap
->div
[i
] + 2,
2142 info2
->bmap
->div
[i
] + 2, total
))
2145 isl_int_sub(d
, info2
->bmap
->div
[i
][1], info1
->bmap
->div
[i
][1]);
2146 if (isl_int_is_divisible_by(d
, info1
->bmap
->div
[i
][0])) {
2147 isl_int_divexact(d
, d
, info1
->bmap
->div
[i
][0]);
2148 r
= shift_div(info1
, i
, d
);
2158 /* Do the two basic maps live in the same local space, i.e.,
2159 * do they have the same (known) divs?
2160 * If either basic map has any unknown divs, then we can only assume
2161 * that they do not live in the same local space.
2163 static int same_divs(__isl_keep isl_basic_map
*bmap1
,
2164 __isl_keep isl_basic_map
*bmap2
)
2170 if (!bmap1
|| !bmap2
)
2172 if (bmap1
->n_div
!= bmap2
->n_div
)
2175 if (bmap1
->n_div
== 0)
2178 known
= isl_basic_map_divs_known(bmap1
);
2179 if (known
< 0 || !known
)
2181 known
= isl_basic_map_divs_known(bmap2
);
2182 if (known
< 0 || !known
)
2185 total
= isl_basic_map_total_dim(bmap1
);
2186 for (i
= 0; i
< bmap1
->n_div
; ++i
)
2187 if (!isl_seq_eq(bmap1
->div
[i
], bmap2
->div
[i
], 2 + total
))
2193 /* Expand info->tab in the same way info->bmap was expanded in
2194 * isl_basic_map_expand_divs using the expansion "exp" and
2195 * update info->ineq with respect to the redundant constraints
2196 * in the resulting tableau. "bmap" is the original version
2197 * of info->bmap, i.e., the one that corresponds to the current
2198 * state of info->tab. The number of constraints in "bmap"
2199 * is assumed to be the same as the number of constraints
2200 * in info->tab. This is required to be able to detect
2201 * the extra constraints in info->bmap.
2203 * In particular, introduce extra variables corresponding
2204 * to the extra integer divisions and add the div constraints
2205 * that were added to info->bmap after info->tab was created
2206 * from the original info->bmap.
2207 * info->ineq was computed without a tableau and therefore
2208 * does not take into account the redundant constraints
2209 * in the tableau. Mark them here.
2211 static isl_stat
expand_tab(struct isl_coalesce_info
*info
, int *exp
,
2212 __isl_keep isl_basic_map
*bmap
)
2214 unsigned total
, pos
, n_div
;
2216 int i
, n
, j
, n_ineq
;
2220 return isl_stat_error
;
2221 if (bmap
->n_eq
+ bmap
->n_ineq
!= info
->tab
->n_con
)
2222 isl_die(isl_basic_map_get_ctx(bmap
), isl_error_internal
,
2223 "original tableau does not correspond "
2224 "to original basic map", return isl_stat_error
);
2226 total
= isl_basic_map_dim(info
->bmap
, isl_dim_all
);
2227 n_div
= isl_basic_map_dim(info
->bmap
, isl_dim_div
);
2228 pos
= total
- n_div
;
2229 extra_var
= total
- info
->tab
->n_var
;
2230 n
= n_div
- extra_var
;
2232 if (isl_tab_extend_vars(info
->tab
, extra_var
) < 0)
2233 return isl_stat_error
;
2234 if (isl_tab_extend_cons(info
->tab
, 2 * extra_var
) < 0)
2235 return isl_stat_error
;
2238 for (j
= 0; j
< n_div
; ++j
) {
2239 if (i
< n
&& exp
[i
] == j
) {
2243 if (isl_tab_insert_var(info
->tab
, pos
+ j
) < 0)
2244 return isl_stat_error
;
2247 n_ineq
= info
->tab
->n_con
- info
->tab
->n_eq
;
2248 for (i
= n_ineq
; i
< info
->bmap
->n_ineq
; ++i
)
2249 if (isl_tab_add_ineq(info
->tab
, info
->bmap
->ineq
[i
]) < 0)
2250 return isl_stat_error
;
2252 n_eq
= info
->bmap
->n_eq
;
2253 for (i
= 0; i
< info
->bmap
->n_ineq
; ++i
) {
2254 if (isl_tab_is_redundant(info
->tab
, n_eq
+ i
))
2255 info
->ineq
[i
] = STATUS_REDUNDANT
;
2261 /* Check if the union of the basic maps represented by info[i] and info[j]
2262 * can be represented by a single basic map,
2263 * after expanding the divs of info[i] to match those of info[j].
2264 * If so, replace the pair by the single basic map and return
2265 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
2266 * Otherwise, return isl_change_none.
2268 * The caller has already checked for info[j] being a subset of info[i].
2269 * If some of the divs of info[j] are unknown, then the expanded info[i]
2270 * will not have the corresponding div constraints. The other patterns
2271 * therefore cannot apply. Skip the computation in this case.
2273 * The expansion is performed using the divs "div" and expansion "exp"
2274 * computed by the caller.
2275 * info[i].bmap has already been expanded and the result is passed in
2277 * The "eq" and "ineq" fields of info[i] reflect the status of
2278 * the constraints of the expanded "bmap" with respect to info[j].tab.
2279 * However, inequality constraints that are redundant in info[i].tab
2280 * have not yet been marked as such because no tableau was available.
2282 * Replace info[i].bmap by "bmap" and expand info[i].tab as well,
2283 * updating info[i].ineq with respect to the redundant constraints.
2284 * Then try and coalesce the expanded info[i] with info[j],
2285 * reusing the information in info[i].eq and info[i].ineq.
2286 * If this does not result in any coalescing or if it results in info[j]
2287 * getting dropped (which should not happen in practice, since the case
2288 * of info[j] being a subset of info[i] has already been checked by
2289 * the caller), then revert info[i] to its original state.
2291 static enum isl_change
coalesce_expand_tab_divs(__isl_take isl_basic_map
*bmap
,
2292 int i
, int j
, struct isl_coalesce_info
*info
, __isl_keep isl_mat
*div
,
2296 isl_basic_map
*bmap_i
;
2297 struct isl_tab_undo
*snap
;
2298 enum isl_change change
= isl_change_none
;
2300 known
= isl_basic_map_divs_known(info
[j
].bmap
);
2301 if (known
< 0 || !known
) {
2302 clear_status(&info
[i
]);
2303 isl_basic_map_free(bmap
);
2304 return known
< 0 ? isl_change_error
: isl_change_none
;
2307 bmap_i
= info
[i
].bmap
;
2308 info
[i
].bmap
= isl_basic_map_copy(bmap
);
2309 snap
= isl_tab_snap(info
[i
].tab
);
2310 if (!info
[i
].bmap
|| expand_tab(&info
[i
], exp
, bmap_i
) < 0)
2311 change
= isl_change_error
;
2313 init_status(&info
[j
]);
2314 if (change
== isl_change_none
)
2315 change
= coalesce_local_pair_reuse(i
, j
, info
);
2317 clear_status(&info
[i
]);
2318 if (change
!= isl_change_none
&& change
!= isl_change_drop_second
) {
2319 isl_basic_map_free(bmap_i
);
2321 isl_basic_map_free(info
[i
].bmap
);
2322 info
[i
].bmap
= bmap_i
;
2324 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
2325 change
= isl_change_error
;
2328 isl_basic_map_free(bmap
);
2332 /* Check if the union of "bmap" and the basic map represented by info[j]
2333 * can be represented by a single basic map,
2334 * after expanding the divs of "bmap" to match those of info[j].
2335 * If so, replace the pair by the single basic map and return
2336 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
2337 * Otherwise, return isl_change_none.
2339 * In particular, check if the expanded "bmap" contains the basic map
2340 * represented by the tableau info[j].tab.
2341 * The expansion is performed using the divs "div" and expansion "exp"
2342 * computed by the caller.
2343 * Then we check if all constraints of the expanded "bmap" are valid for
2346 * If "i" is not equal to -1, then "bmap" is equal to info[i].bmap.
2347 * In this case, the positions of the constraints of info[i].bmap
2348 * with respect to the basic map represented by info[j] are stored
2351 * If the expanded "bmap" does not contain the basic map
2352 * represented by the tableau info[j].tab and if "i" is not -1,
2353 * i.e., if the original "bmap" is info[i].bmap, then expand info[i].tab
2354 * as well and check if that results in coalescing.
2356 static enum isl_change
coalesce_with_expanded_divs(
2357 __isl_keep isl_basic_map
*bmap
, int i
, int j
,
2358 struct isl_coalesce_info
*info
, __isl_keep isl_mat
*div
, int *exp
)
2360 enum isl_change change
= isl_change_none
;
2361 struct isl_coalesce_info info_local
, *info_i
;
2363 info_i
= i
>= 0 ? &info
[i
] : &info_local
;
2364 init_status(info_i
);
2365 bmap
= isl_basic_map_copy(bmap
);
2366 bmap
= isl_basic_map_expand_divs(bmap
, isl_mat_copy(div
), exp
);
2371 info_i
->eq
= eq_status_in(bmap
, info
[j
].tab
);
2372 if (bmap
->n_eq
&& !info_i
->eq
)
2374 if (any(info_i
->eq
, 2 * bmap
->n_eq
, STATUS_ERROR
))
2376 if (any(info_i
->eq
, 2 * bmap
->n_eq
, STATUS_SEPARATE
))
2379 info_i
->ineq
= ineq_status_in(bmap
, NULL
, info
[j
].tab
);
2380 if (bmap
->n_ineq
&& !info_i
->ineq
)
2382 if (any(info_i
->ineq
, bmap
->n_ineq
, STATUS_ERROR
))
2384 if (any(info_i
->ineq
, bmap
->n_ineq
, STATUS_SEPARATE
))
2387 if (all(info_i
->eq
, 2 * bmap
->n_eq
, STATUS_VALID
) &&
2388 all(info_i
->ineq
, bmap
->n_ineq
, STATUS_VALID
)) {
2390 change
= isl_change_drop_second
;
2393 if (change
== isl_change_none
&& i
!= -1)
2394 return coalesce_expand_tab_divs(bmap
, i
, j
, info
, div
, exp
);
2397 isl_basic_map_free(bmap
);
2398 clear_status(info_i
);
2401 isl_basic_map_free(bmap
);
2402 clear_status(info_i
);
2403 return isl_change_error
;
2406 /* Check if the union of "bmap_i" and the basic map represented by info[j]
2407 * can be represented by a single basic map,
2408 * after aligning the divs of "bmap_i" to match those of info[j].
2409 * If so, replace the pair by the single basic map and return
2410 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
2411 * Otherwise, return isl_change_none.
2413 * In particular, check if "bmap_i" contains the basic map represented by
2414 * info[j] after aligning the divs of "bmap_i" to those of info[j].
2415 * Note that this can only succeed if the number of divs of "bmap_i"
2416 * is smaller than (or equal to) the number of divs of info[j].
2418 * We first check if the divs of "bmap_i" are all known and form a subset
2419 * of those of info[j].bmap. If so, we pass control over to
2420 * coalesce_with_expanded_divs.
2422 * If "i" is not equal to -1, then "bmap" is equal to info[i].bmap.
2424 static enum isl_change
coalesce_after_aligning_divs(
2425 __isl_keep isl_basic_map
*bmap_i
, int i
, int j
,
2426 struct isl_coalesce_info
*info
)
2429 isl_mat
*div_i
, *div_j
, *div
;
2433 enum isl_change change
;
2435 known
= isl_basic_map_divs_known(bmap_i
);
2436 if (known
< 0 || !known
)
2439 ctx
= isl_basic_map_get_ctx(bmap_i
);
2441 div_i
= isl_basic_map_get_divs(bmap_i
);
2442 div_j
= isl_basic_map_get_divs(info
[j
].bmap
);
2444 if (!div_i
|| !div_j
)
2447 exp1
= isl_alloc_array(ctx
, int, div_i
->n_row
);
2448 exp2
= isl_alloc_array(ctx
, int, div_j
->n_row
);
2449 if ((div_i
->n_row
&& !exp1
) || (div_j
->n_row
&& !exp2
))
2452 div
= isl_merge_divs(div_i
, div_j
, exp1
, exp2
);
2456 if (div
->n_row
== div_j
->n_row
)
2457 change
= coalesce_with_expanded_divs(bmap_i
,
2458 i
, j
, info
, div
, exp1
);
2460 change
= isl_change_none
;
2464 isl_mat_free(div_i
);
2465 isl_mat_free(div_j
);
2472 isl_mat_free(div_i
);
2473 isl_mat_free(div_j
);
2476 return isl_change_error
;
2479 /* Check if basic map "j" is a subset of basic map "i" after
2480 * exploiting the extra equalities of "j" to simplify the divs of "i".
2481 * If so, remove basic map "j" and return isl_change_drop_second.
2483 * If "j" does not have any equalities or if they are the same
2484 * as those of "i", then we cannot exploit them to simplify the divs.
2485 * Similarly, if there are no divs in "i", then they cannot be simplified.
2486 * If, on the other hand, the affine hulls of "i" and "j" do not intersect,
2487 * then "j" cannot be a subset of "i".
2489 * Otherwise, we intersect "i" with the affine hull of "j" and then
2490 * check if "j" is a subset of the result after aligning the divs.
2491 * If so, then "j" is definitely a subset of "i" and can be removed.
2492 * Note that if after intersection with the affine hull of "j".
2493 * "i" still has more divs than "j", then there is no way we can
2494 * align the divs of "i" to those of "j".
2496 static enum isl_change
coalesce_subset_with_equalities(int i
, int j
,
2497 struct isl_coalesce_info
*info
)
2499 isl_basic_map
*hull_i
, *hull_j
, *bmap_i
;
2501 enum isl_change change
;
2503 if (info
[j
].bmap
->n_eq
== 0)
2504 return isl_change_none
;
2505 if (info
[i
].bmap
->n_div
== 0)
2506 return isl_change_none
;
2508 hull_i
= isl_basic_map_copy(info
[i
].bmap
);
2509 hull_i
= isl_basic_map_plain_affine_hull(hull_i
);
2510 hull_j
= isl_basic_map_copy(info
[j
].bmap
);
2511 hull_j
= isl_basic_map_plain_affine_hull(hull_j
);
2513 hull_j
= isl_basic_map_intersect(hull_j
, isl_basic_map_copy(hull_i
));
2514 equal
= isl_basic_map_plain_is_equal(hull_i
, hull_j
);
2515 empty
= isl_basic_map_plain_is_empty(hull_j
);
2516 isl_basic_map_free(hull_i
);
2518 if (equal
< 0 || equal
|| empty
< 0 || empty
) {
2519 isl_basic_map_free(hull_j
);
2520 if (equal
< 0 || empty
< 0)
2521 return isl_change_error
;
2522 return isl_change_none
;
2525 bmap_i
= isl_basic_map_copy(info
[i
].bmap
);
2526 bmap_i
= isl_basic_map_intersect(bmap_i
, hull_j
);
2528 return isl_change_error
;
2530 if (bmap_i
->n_div
> info
[j
].bmap
->n_div
) {
2531 isl_basic_map_free(bmap_i
);
2532 return isl_change_none
;
2535 change
= coalesce_after_aligning_divs(bmap_i
, -1, j
, info
);
2537 isl_basic_map_free(bmap_i
);
2542 /* Check if the union of and the basic maps represented by info[i] and info[j]
2543 * can be represented by a single basic map, by aligning or equating
2544 * their integer divisions.
2545 * If so, replace the pair by the single basic map and return
2546 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
2547 * Otherwise, return isl_change_none.
2549 * Note that we only perform any test if the number of divs is different
2550 * in the two basic maps. In case the number of divs is the same,
2551 * we have already established that the divs are different
2552 * in the two basic maps.
2553 * In particular, if the number of divs of basic map i is smaller than
2554 * the number of divs of basic map j, then we check if j is a subset of i
2557 static enum isl_change
coalesce_divs(int i
, int j
,
2558 struct isl_coalesce_info
*info
)
2560 enum isl_change change
= isl_change_none
;
2562 if (info
[i
].bmap
->n_div
< info
[j
].bmap
->n_div
)
2563 change
= coalesce_after_aligning_divs(info
[i
].bmap
, i
, j
, info
);
2564 if (change
!= isl_change_none
)
2567 if (info
[j
].bmap
->n_div
< info
[i
].bmap
->n_div
)
2568 change
= coalesce_after_aligning_divs(info
[j
].bmap
, j
, i
, info
);
2569 if (change
!= isl_change_none
)
2570 return invert_change(change
);
2572 change
= coalesce_subset_with_equalities(i
, j
, info
);
2573 if (change
!= isl_change_none
)
2576 change
= coalesce_subset_with_equalities(j
, i
, info
);
2577 if (change
!= isl_change_none
)
2578 return invert_change(change
);
2580 return isl_change_none
;
2583 /* Does "bmap" involve any divs that themselves refer to divs?
2585 static int has_nested_div(__isl_keep isl_basic_map
*bmap
)
2591 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
2592 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
2595 for (i
= 0; i
< n_div
; ++i
)
2596 if (isl_seq_first_non_zero(bmap
->div
[i
] + 2 + total
,
2603 /* Return a list of affine expressions, one for each integer division
2604 * in "bmap_i". For each integer division that also appears in "bmap_j",
2605 * the affine expression is set to NaN. The number of NaNs in the list
2606 * is equal to the number of integer divisions in "bmap_j".
2607 * For the other integer divisions of "bmap_i", the corresponding
2608 * element in the list is a purely affine expression equal to the integer
2609 * division in "hull".
2610 * If no such list can be constructed, then the number of elements
2611 * in the returned list is smaller than the number of integer divisions
2614 static __isl_give isl_aff_list
*set_up_substitutions(
2615 __isl_keep isl_basic_map
*bmap_i
, __isl_keep isl_basic_map
*bmap_j
,
2616 __isl_take isl_basic_map
*hull
)
2618 unsigned n_div_i
, n_div_j
, total
;
2620 isl_local_space
*ls
;
2621 isl_basic_set
*wrap_hull
;
2629 ctx
= isl_basic_map_get_ctx(hull
);
2631 n_div_i
= isl_basic_map_dim(bmap_i
, isl_dim_div
);
2632 n_div_j
= isl_basic_map_dim(bmap_j
, isl_dim_div
);
2633 total
= isl_basic_map_total_dim(bmap_i
) - n_div_i
;
2635 ls
= isl_basic_map_get_local_space(bmap_i
);
2636 ls
= isl_local_space_wrap(ls
);
2637 wrap_hull
= isl_basic_map_wrap(hull
);
2639 aff_nan
= isl_aff_nan_on_domain(isl_local_space_copy(ls
));
2640 list
= isl_aff_list_alloc(ctx
, n_div_i
);
2643 for (i
= 0; i
< n_div_i
; ++i
) {
2647 isl_seq_eq(bmap_i
->div
[i
], bmap_j
->div
[j
], 2 + total
)) {
2649 list
= isl_aff_list_add(list
, isl_aff_copy(aff_nan
));
2652 if (n_div_i
- i
<= n_div_j
- j
)
2655 aff
= isl_local_space_get_div(ls
, i
);
2656 aff
= isl_aff_substitute_equalities(aff
,
2657 isl_basic_set_copy(wrap_hull
));
2658 aff
= isl_aff_floor(aff
);
2661 if (isl_aff_dim(aff
, isl_dim_div
) != 0) {
2666 list
= isl_aff_list_add(list
, aff
);
2669 isl_aff_free(aff_nan
);
2670 isl_local_space_free(ls
);
2671 isl_basic_set_free(wrap_hull
);
2675 isl_aff_free(aff_nan
);
2676 isl_local_space_free(ls
);
2677 isl_basic_set_free(wrap_hull
);
2678 isl_aff_list_free(list
);
2682 /* Add variables to info->bmap and info->tab corresponding to the elements
2683 * in "list" that are not set to NaN.
2684 * "extra_var" is the number of these elements.
2685 * "dim" is the offset in the variables of "tab" where we should
2686 * start considering the elements in "list".
2687 * When this function returns, the total number of variables in "tab"
2688 * is equal to "dim" plus the number of elements in "list".
2690 * The newly added existentially quantified variables are not given
2691 * an explicit representation because the corresponding div constraints
2692 * do not appear in info->bmap. These constraints are not added
2693 * to info->bmap because for internal consistency, they would need to
2694 * be added to info->tab as well, where they could combine with the equality
2695 * that is added later to result in constraints that do not hold
2696 * in the original input.
2698 static int add_sub_vars(struct isl_coalesce_info
*info
,
2699 __isl_keep isl_aff_list
*list
, int dim
, int extra_var
)
2704 space
= isl_basic_map_get_space(info
->bmap
);
2705 info
->bmap
= isl_basic_map_cow(info
->bmap
);
2706 info
->bmap
= isl_basic_map_extend_space(info
->bmap
, space
,
2710 n
= isl_aff_list_n_aff(list
);
2711 for (i
= 0; i
< n
; ++i
) {
2715 aff
= isl_aff_list_get_aff(list
, i
);
2716 is_nan
= isl_aff_is_nan(aff
);
2723 if (isl_tab_insert_var(info
->tab
, dim
+ i
) < 0)
2725 d
= isl_basic_map_alloc_div(info
->bmap
);
2728 info
->bmap
= isl_basic_map_mark_div_unknown(info
->bmap
, d
);
2731 for (j
= d
; j
> i
; --j
)
2732 isl_basic_map_swap_div(info
->bmap
, j
- 1, j
);
2738 /* For each element in "list" that is not set to NaN, fix the corresponding
2739 * variable in "tab" to the purely affine expression defined by the element.
2740 * "dim" is the offset in the variables of "tab" where we should
2741 * start considering the elements in "list".
2743 * This function assumes that a sufficient number of rows and
2744 * elements in the constraint array are available in the tableau.
2746 static int add_sub_equalities(struct isl_tab
*tab
,
2747 __isl_keep isl_aff_list
*list
, int dim
)
2754 n
= isl_aff_list_n_aff(list
);
2756 ctx
= isl_tab_get_ctx(tab
);
2757 sub
= isl_vec_alloc(ctx
, 1 + dim
+ n
);
2760 isl_seq_clr(sub
->el
+ 1 + dim
, n
);
2762 for (i
= 0; i
< n
; ++i
) {
2763 aff
= isl_aff_list_get_aff(list
, i
);
2766 if (isl_aff_is_nan(aff
)) {
2770 isl_seq_cpy(sub
->el
, aff
->v
->el
+ 1, 1 + dim
);
2771 isl_int_neg(sub
->el
[1 + dim
+ i
], aff
->v
->el
[0]);
2772 if (isl_tab_add_eq(tab
, sub
->el
) < 0)
2774 isl_int_set_si(sub
->el
[1 + dim
+ i
], 0);
2786 /* Add variables to info->tab and info->bmap corresponding to the elements
2787 * in "list" that are not set to NaN. The value of the added variable
2788 * in info->tab is fixed to the purely affine expression defined by the element.
2789 * "dim" is the offset in the variables of info->tab where we should
2790 * start considering the elements in "list".
2791 * When this function returns, the total number of variables in info->tab
2792 * is equal to "dim" plus the number of elements in "list".
2794 static int add_subs(struct isl_coalesce_info
*info
,
2795 __isl_keep isl_aff_list
*list
, int dim
)
2803 n
= isl_aff_list_n_aff(list
);
2804 extra_var
= n
- (info
->tab
->n_var
- dim
);
2806 if (isl_tab_extend_vars(info
->tab
, extra_var
) < 0)
2808 if (isl_tab_extend_cons(info
->tab
, 2 * extra_var
) < 0)
2810 if (add_sub_vars(info
, list
, dim
, extra_var
) < 0)
2813 return add_sub_equalities(info
->tab
, list
, dim
);
2816 /* Coalesce basic map "j" into basic map "i" after adding the extra integer
2817 * divisions in "i" but not in "j" to basic map "j", with values
2818 * specified by "list". The total number of elements in "list"
2819 * is equal to the number of integer divisions in "i", while the number
2820 * of NaN elements in the list is equal to the number of integer divisions
2823 * If no coalescing can be performed, then we need to revert basic map "j"
2824 * to its original state. We do the same if basic map "i" gets dropped
2825 * during the coalescing, even though this should not happen in practice
2826 * since we have already checked for "j" being a subset of "i"
2827 * before we reach this stage.
2829 static enum isl_change
coalesce_with_subs(int i
, int j
,
2830 struct isl_coalesce_info
*info
, __isl_keep isl_aff_list
*list
)
2832 isl_basic_map
*bmap_j
;
2833 struct isl_tab_undo
*snap
;
2835 enum isl_change change
;
2837 bmap_j
= isl_basic_map_copy(info
[j
].bmap
);
2838 snap
= isl_tab_snap(info
[j
].tab
);
2840 dim
= isl_basic_map_dim(bmap_j
, isl_dim_all
);
2841 dim
-= isl_basic_map_dim(bmap_j
, isl_dim_div
);
2842 if (add_subs(&info
[j
], list
, dim
) < 0)
2845 change
= coalesce_local_pair(i
, j
, info
);
2846 if (change
!= isl_change_none
&& change
!= isl_change_drop_first
) {
2847 isl_basic_map_free(bmap_j
);
2849 isl_basic_map_free(info
[j
].bmap
);
2850 info
[j
].bmap
= bmap_j
;
2852 if (isl_tab_rollback(info
[j
].tab
, snap
) < 0)
2853 return isl_change_error
;
2858 isl_basic_map_free(bmap_j
);
2859 return isl_change_error
;
2862 /* Check if we can coalesce basic map "j" into basic map "i" after copying
2863 * those extra integer divisions in "i" that can be simplified away
2864 * using the extra equalities in "j".
2865 * All divs are assumed to be known and not contain any nested divs.
2867 * We first check if there are any extra equalities in "j" that we
2868 * can exploit. Then we check if every integer division in "i"
2869 * either already appears in "j" or can be simplified using the
2870 * extra equalities to a purely affine expression.
2871 * If these tests succeed, then we try to coalesce the two basic maps
2872 * by introducing extra dimensions in "j" corresponding to
2873 * the extra integer divsisions "i" fixed to the corresponding
2874 * purely affine expression.
2876 static enum isl_change
check_coalesce_into_eq(int i
, int j
,
2877 struct isl_coalesce_info
*info
)
2879 unsigned n_div_i
, n_div_j
;
2880 isl_basic_map
*hull_i
, *hull_j
;
2883 enum isl_change change
;
2885 n_div_i
= isl_basic_map_dim(info
[i
].bmap
, isl_dim_div
);
2886 n_div_j
= isl_basic_map_dim(info
[j
].bmap
, isl_dim_div
);
2887 if (n_div_i
<= n_div_j
)
2888 return isl_change_none
;
2889 if (info
[j
].bmap
->n_eq
== 0)
2890 return isl_change_none
;
2892 hull_i
= isl_basic_map_copy(info
[i
].bmap
);
2893 hull_i
= isl_basic_map_plain_affine_hull(hull_i
);
2894 hull_j
= isl_basic_map_copy(info
[j
].bmap
);
2895 hull_j
= isl_basic_map_plain_affine_hull(hull_j
);
2897 hull_j
= isl_basic_map_intersect(hull_j
, isl_basic_map_copy(hull_i
));
2898 equal
= isl_basic_map_plain_is_equal(hull_i
, hull_j
);
2899 empty
= isl_basic_map_plain_is_empty(hull_j
);
2900 isl_basic_map_free(hull_i
);
2902 if (equal
< 0 || empty
< 0)
2904 if (equal
|| empty
) {
2905 isl_basic_map_free(hull_j
);
2906 return isl_change_none
;
2909 list
= set_up_substitutions(info
[i
].bmap
, info
[j
].bmap
, hull_j
);
2911 return isl_change_error
;
2912 if (isl_aff_list_n_aff(list
) < n_div_i
)
2913 change
= isl_change_none
;
2915 change
= coalesce_with_subs(i
, j
, info
, list
);
2917 isl_aff_list_free(list
);
2921 isl_basic_map_free(hull_j
);
2922 return isl_change_error
;
2925 /* Check if we can coalesce basic maps "i" and "j" after copying
2926 * those extra integer divisions in one of the basic maps that can
2927 * be simplified away using the extra equalities in the other basic map.
2928 * We require all divs to be known in both basic maps.
2929 * Furthermore, to simplify the comparison of div expressions,
2930 * we do not allow any nested integer divisions.
2932 static enum isl_change
check_coalesce_eq(int i
, int j
,
2933 struct isl_coalesce_info
*info
)
2936 enum isl_change change
;
2938 known
= isl_basic_map_divs_known(info
[i
].bmap
);
2939 if (known
< 0 || !known
)
2940 return known
< 0 ? isl_change_error
: isl_change_none
;
2941 known
= isl_basic_map_divs_known(info
[j
].bmap
);
2942 if (known
< 0 || !known
)
2943 return known
< 0 ? isl_change_error
: isl_change_none
;
2944 nested
= has_nested_div(info
[i
].bmap
);
2945 if (nested
< 0 || nested
)
2946 return nested
< 0 ? isl_change_error
: isl_change_none
;
2947 nested
= has_nested_div(info
[j
].bmap
);
2948 if (nested
< 0 || nested
)
2949 return nested
< 0 ? isl_change_error
: isl_change_none
;
2951 change
= check_coalesce_into_eq(i
, j
, info
);
2952 if (change
!= isl_change_none
)
2954 change
= check_coalesce_into_eq(j
, i
, info
);
2955 if (change
!= isl_change_none
)
2956 return invert_change(change
);
2958 return isl_change_none
;
2961 /* Check if the union of the given pair of basic maps
2962 * can be represented by a single basic map.
2963 * If so, replace the pair by the single basic map and return
2964 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
2965 * Otherwise, return isl_change_none.
2967 * We first check if the two basic maps live in the same local space,
2968 * after aligning the divs that differ by only an integer constant.
2969 * If so, we do the complete check. Otherwise, we check if they have
2970 * the same number of integer divisions and can be coalesced, if one is
2971 * an obvious subset of the other or if the extra integer divisions
2972 * of one basic map can be simplified away using the extra equalities
2973 * of the other basic map.
2975 static enum isl_change
coalesce_pair(int i
, int j
,
2976 struct isl_coalesce_info
*info
)
2979 enum isl_change change
;
2981 if (harmonize_divs(&info
[i
], &info
[j
]) < 0)
2982 return isl_change_error
;
2983 same
= same_divs(info
[i
].bmap
, info
[j
].bmap
);
2985 return isl_change_error
;
2987 return coalesce_local_pair(i
, j
, info
);
2989 if (info
[i
].bmap
->n_div
== info
[j
].bmap
->n_div
) {
2990 change
= coalesce_local_pair(i
, j
, info
);
2991 if (change
!= isl_change_none
)
2995 change
= coalesce_divs(i
, j
, info
);
2996 if (change
!= isl_change_none
)
2999 return check_coalesce_eq(i
, j
, info
);
3002 /* Return the maximum of "a" and "b".
3004 static int isl_max(int a
, int b
)
3006 return a
> b
? a
: b
;
3009 /* Pairwise coalesce the basic maps in the range [start1, end1[ of "info"
3010 * with those in the range [start2, end2[, skipping basic maps
3011 * that have been removed (either before or within this function).
3013 * For each basic map i in the first range, we check if it can be coalesced
3014 * with respect to any previously considered basic map j in the second range.
3015 * If i gets dropped (because it was a subset of some j), then
3016 * we can move on to the next basic map.
3017 * If j gets dropped, we need to continue checking against the other
3018 * previously considered basic maps.
3019 * If the two basic maps got fused, then we recheck the fused basic map
3020 * against the previously considered basic maps, starting at i + 1
3021 * (even if start2 is greater than i + 1).
3023 static int coalesce_range(isl_ctx
*ctx
, struct isl_coalesce_info
*info
,
3024 int start1
, int end1
, int start2
, int end2
)
3028 for (i
= end1
- 1; i
>= start1
; --i
) {
3029 if (info
[i
].removed
)
3031 for (j
= isl_max(i
+ 1, start2
); j
< end2
; ++j
) {
3032 enum isl_change changed
;
3034 if (info
[j
].removed
)
3036 if (info
[i
].removed
)
3037 isl_die(ctx
, isl_error_internal
,
3038 "basic map unexpectedly removed",
3040 changed
= coalesce_pair(i
, j
, info
);
3042 case isl_change_error
:
3044 case isl_change_none
:
3045 case isl_change_drop_second
:
3047 case isl_change_drop_first
:
3050 case isl_change_fuse
:
3060 /* Pairwise coalesce the basic maps described by the "n" elements of "info".
3062 * We consider groups of basic maps that live in the same apparent
3063 * affine hull and we first coalesce within such a group before we
3064 * coalesce the elements in the group with elements of previously
3065 * considered groups. If a fuse happens during the second phase,
3066 * then we also reconsider the elements within the group.
3068 static int coalesce(isl_ctx
*ctx
, int n
, struct isl_coalesce_info
*info
)
3072 for (end
= n
; end
> 0; end
= start
) {
3074 while (start
>= 1 &&
3075 info
[start
- 1].hull_hash
== info
[start
].hull_hash
)
3077 if (coalesce_range(ctx
, info
, start
, end
, start
, end
) < 0)
3079 if (coalesce_range(ctx
, info
, start
, end
, end
, n
) < 0)
3086 /* Update the basic maps in "map" based on the information in "info".
3087 * In particular, remove the basic maps that have been marked removed and
3088 * update the others based on the information in the corresponding tableau.
3089 * Since we detected implicit equalities without calling
3090 * isl_basic_map_gauss, we need to do it now.
3091 * Also call isl_basic_map_simplify if we may have lost the definition
3092 * of one or more integer divisions.
3094 static __isl_give isl_map
*update_basic_maps(__isl_take isl_map
*map
,
3095 int n
, struct isl_coalesce_info
*info
)
3102 for (i
= n
- 1; i
>= 0; --i
) {
3103 if (info
[i
].removed
) {
3104 isl_basic_map_free(map
->p
[i
]);
3105 if (i
!= map
->n
- 1)
3106 map
->p
[i
] = map
->p
[map
->n
- 1];
3111 info
[i
].bmap
= isl_basic_map_update_from_tab(info
[i
].bmap
,
3113 info
[i
].bmap
= isl_basic_map_gauss(info
[i
].bmap
, NULL
);
3114 if (info
[i
].simplify
)
3115 info
[i
].bmap
= isl_basic_map_simplify(info
[i
].bmap
);
3116 info
[i
].bmap
= isl_basic_map_finalize(info
[i
].bmap
);
3118 return isl_map_free(map
);
3119 ISL_F_SET(info
[i
].bmap
, ISL_BASIC_MAP_NO_IMPLICIT
);
3120 ISL_F_SET(info
[i
].bmap
, ISL_BASIC_MAP_NO_REDUNDANT
);
3121 isl_basic_map_free(map
->p
[i
]);
3122 map
->p
[i
] = info
[i
].bmap
;
3123 info
[i
].bmap
= NULL
;
3129 /* For each pair of basic maps in the map, check if the union of the two
3130 * can be represented by a single basic map.
3131 * If so, replace the pair by the single basic map and start over.
3133 * We factor out any (hidden) common factor from the constraint
3134 * coefficients to improve the detection of adjacent constraints.
3136 * Since we are constructing the tableaus of the basic maps anyway,
3137 * we exploit them to detect implicit equalities and redundant constraints.
3138 * This also helps the coalescing as it can ignore the redundant constraints.
3139 * In order to avoid confusion, we make all implicit equalities explicit
3140 * in the basic maps. We don't call isl_basic_map_gauss, though,
3141 * as that may affect the number of constraints.
3142 * This means that we have to call isl_basic_map_gauss at the end
3143 * of the computation (in update_basic_maps) to ensure that
3144 * the basic maps are not left in an unexpected state.
3145 * For each basic map, we also compute the hash of the apparent affine hull
3146 * for use in coalesce.
3148 struct isl_map
*isl_map_coalesce(struct isl_map
*map
)
3153 struct isl_coalesce_info
*info
= NULL
;
3155 map
= isl_map_remove_empty_parts(map
);
3162 ctx
= isl_map_get_ctx(map
);
3163 map
= isl_map_sort_divs(map
);
3164 map
= isl_map_cow(map
);
3171 info
= isl_calloc_array(map
->ctx
, struct isl_coalesce_info
, n
);
3175 for (i
= 0; i
< map
->n
; ++i
) {
3176 map
->p
[i
] = isl_basic_map_reduce_coefficients(map
->p
[i
]);
3179 info
[i
].bmap
= isl_basic_map_copy(map
->p
[i
]);
3180 info
[i
].tab
= isl_tab_from_basic_map(info
[i
].bmap
, 0);
3183 if (!ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_NO_IMPLICIT
))
3184 if (isl_tab_detect_implicit_equalities(info
[i
].tab
) < 0)
3186 info
[i
].bmap
= isl_tab_make_equalities_explicit(info
[i
].tab
,
3190 if (!ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_NO_REDUNDANT
))
3191 if (isl_tab_detect_redundant(info
[i
].tab
) < 0)
3193 if (coalesce_info_set_hull_hash(&info
[i
]) < 0)
3196 for (i
= map
->n
- 1; i
>= 0; --i
)
3197 if (info
[i
].tab
->empty
)
3200 if (coalesce(ctx
, n
, info
) < 0)
3203 map
= update_basic_maps(map
, n
, info
);
3205 clear_coalesce_info(n
, info
);
3209 clear_coalesce_info(n
, info
);
3214 /* For each pair of basic sets in the set, check if the union of the two
3215 * can be represented by a single basic set.
3216 * If so, replace the pair by the single basic set and start over.
3218 struct isl_set
*isl_set_coalesce(struct isl_set
*set
)
3220 return set_from_map(isl_map_coalesce(set_to_map(set
)));