2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2010 INRIA Saclay
4 * Copyright 2012-2013 Ecole Normale Superieure
5 * Copyright 2014 INRIA Rocquencourt
6 * Copyright 2016 INRIA Paris
8 * Use of this software is governed by the MIT license
10 * Written by Sven Verdoolaege, K.U.Leuven, Departement
11 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
12 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
13 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
14 * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
15 * and Inria Paris - Rocquencourt, Domaine de Voluceau - Rocquencourt,
16 * B.P. 105 - 78153 Le Chesnay, France
17 * and Centre de Recherche Inria de Paris, 2 rue Simone Iff - Voie DQ12,
18 * CS 42112, 75589 Paris Cedex 12, France
21 #include <isl_ctx_private.h>
22 #include "isl_map_private.h"
24 #include <isl/options.h>
26 #include <isl_mat_private.h>
27 #include <isl_local_space_private.h>
28 #include <isl_val_private.h>
29 #include <isl_vec_private.h>
30 #include <isl_aff_private.h>
31 #include <isl_equalities.h>
32 #include <isl_constraint_private.h>
34 #include <set_to_map.c>
35 #include <set_from_map.c>
37 #define STATUS_ERROR -1
38 #define STATUS_REDUNDANT 1
39 #define STATUS_VALID 2
40 #define STATUS_SEPARATE 3
42 #define STATUS_ADJ_EQ 5
43 #define STATUS_ADJ_INEQ 6
45 static int status_in(isl_int
*ineq
, struct isl_tab
*tab
)
47 enum isl_ineq_type type
= isl_tab_ineq_type(tab
, ineq
);
50 case isl_ineq_error
: return STATUS_ERROR
;
51 case isl_ineq_redundant
: return STATUS_VALID
;
52 case isl_ineq_separate
: return STATUS_SEPARATE
;
53 case isl_ineq_cut
: return STATUS_CUT
;
54 case isl_ineq_adj_eq
: return STATUS_ADJ_EQ
;
55 case isl_ineq_adj_ineq
: return STATUS_ADJ_INEQ
;
59 /* Compute the position of the equalities of basic map "bmap_i"
60 * with respect to the basic map represented by "tab_j".
61 * The resulting array has twice as many entries as the number
62 * of equalities corresponding to the two inequalties to which
63 * each equality corresponds.
65 static int *eq_status_in(__isl_keep isl_basic_map
*bmap_i
,
66 struct isl_tab
*tab_j
)
69 int *eq
= isl_calloc_array(bmap_i
->ctx
, int, 2 * bmap_i
->n_eq
);
75 dim
= isl_basic_map_total_dim(bmap_i
);
76 for (k
= 0; k
< bmap_i
->n_eq
; ++k
) {
77 for (l
= 0; l
< 2; ++l
) {
78 isl_seq_neg(bmap_i
->eq
[k
], bmap_i
->eq
[k
], 1+dim
);
79 eq
[2 * k
+ l
] = status_in(bmap_i
->eq
[k
], tab_j
);
80 if (eq
[2 * k
+ l
] == STATUS_ERROR
)
91 /* Compute the position of the inequalities of basic map "bmap_i"
92 * (also represented by "tab_i", if not NULL) with respect to the basic map
93 * represented by "tab_j".
95 static int *ineq_status_in(__isl_keep isl_basic_map
*bmap_i
,
96 struct isl_tab
*tab_i
, struct isl_tab
*tab_j
)
99 unsigned n_eq
= bmap_i
->n_eq
;
100 int *ineq
= isl_calloc_array(bmap_i
->ctx
, int, bmap_i
->n_ineq
);
105 for (k
= 0; k
< bmap_i
->n_ineq
; ++k
) {
106 if (tab_i
&& isl_tab_is_redundant(tab_i
, n_eq
+ k
)) {
107 ineq
[k
] = STATUS_REDUNDANT
;
110 ineq
[k
] = status_in(bmap_i
->ineq
[k
], tab_j
);
111 if (ineq
[k
] == STATUS_ERROR
)
113 if (ineq
[k
] == STATUS_SEPARATE
)
123 static int any(int *con
, unsigned len
, int status
)
127 for (i
= 0; i
< len
; ++i
)
128 if (con
[i
] == status
)
133 /* Return the first position of "status" in the list "con" of length "len".
134 * Return -1 if there is no such entry.
136 static int find(int *con
, unsigned len
, int status
)
140 for (i
= 0; i
< len
; ++i
)
141 if (con
[i
] == status
)
146 static int count(int *con
, unsigned len
, int status
)
151 for (i
= 0; i
< len
; ++i
)
152 if (con
[i
] == status
)
157 static int all(int *con
, unsigned len
, int status
)
161 for (i
= 0; i
< len
; ++i
) {
162 if (con
[i
] == STATUS_REDUNDANT
)
164 if (con
[i
] != status
)
170 /* Internal information associated to a basic map in a map
171 * that is to be coalesced by isl_map_coalesce.
173 * "bmap" is the basic map itself (or NULL if "removed" is set)
174 * "tab" is the corresponding tableau (or NULL if "removed" is set)
175 * "hull_hash" identifies the affine space in which "bmap" lives.
176 * "removed" is set if this basic map has been removed from the map
177 * "simplify" is set if this basic map may have some unknown integer
178 * divisions that were not present in the input basic maps. The basic
179 * map should then be simplified such that we may be able to find
180 * a definition among the constraints.
182 * "eq" and "ineq" are only set if we are currently trying to coalesce
183 * this basic map with another basic map, in which case they represent
184 * the position of the inequalities of this basic map with respect to
185 * the other basic map. The number of elements in the "eq" array
186 * is twice the number of equalities in the "bmap", corresponding
187 * to the two inequalities that make up each equality.
189 struct isl_coalesce_info
{
199 /* Are all non-redundant constraints of the basic map represented by "info"
200 * either valid or cut constraints with respect to the other basic map?
202 static int all_valid_or_cut(struct isl_coalesce_info
*info
)
206 for (i
= 0; i
< 2 * info
->bmap
->n_eq
; ++i
) {
207 if (info
->eq
[i
] == STATUS_REDUNDANT
)
209 if (info
->eq
[i
] == STATUS_VALID
)
211 if (info
->eq
[i
] == STATUS_CUT
)
216 for (i
= 0; i
< info
->bmap
->n_ineq
; ++i
) {
217 if (info
->ineq
[i
] == STATUS_REDUNDANT
)
219 if (info
->ineq
[i
] == STATUS_VALID
)
221 if (info
->ineq
[i
] == STATUS_CUT
)
229 /* Compute the hash of the (apparent) affine hull of info->bmap (with
230 * the existentially quantified variables removed) and store it
233 static int coalesce_info_set_hull_hash(struct isl_coalesce_info
*info
)
238 hull
= isl_basic_map_copy(info
->bmap
);
239 hull
= isl_basic_map_plain_affine_hull(hull
);
240 n_div
= isl_basic_map_dim(hull
, isl_dim_div
);
241 hull
= isl_basic_map_drop_constraints_involving_dims(hull
,
242 isl_dim_div
, 0, n_div
);
243 info
->hull_hash
= isl_basic_map_get_hash(hull
);
244 isl_basic_map_free(hull
);
246 return hull
? 0 : -1;
249 /* Free all the allocated memory in an array
250 * of "n" isl_coalesce_info elements.
252 static void clear_coalesce_info(int n
, struct isl_coalesce_info
*info
)
259 for (i
= 0; i
< n
; ++i
) {
260 isl_basic_map_free(info
[i
].bmap
);
261 isl_tab_free(info
[i
].tab
);
267 /* Drop the basic map represented by "info".
268 * That is, clear the memory associated to the entry and
269 * mark it as having been removed.
271 static void drop(struct isl_coalesce_info
*info
)
273 info
->bmap
= isl_basic_map_free(info
->bmap
);
274 isl_tab_free(info
->tab
);
279 /* Exchange the information in "info1" with that in "info2".
281 static void exchange(struct isl_coalesce_info
*info1
,
282 struct isl_coalesce_info
*info2
)
284 struct isl_coalesce_info info
;
291 /* This type represents the kind of change that has been performed
292 * while trying to coalesce two basic maps.
294 * isl_change_none: nothing was changed
295 * isl_change_drop_first: the first basic map was removed
296 * isl_change_drop_second: the second basic map was removed
297 * isl_change_fuse: the two basic maps were replaced by a new basic map.
300 isl_change_error
= -1,
302 isl_change_drop_first
,
303 isl_change_drop_second
,
307 /* Update "change" based on an interchange of the first and the second
308 * basic map. That is, interchange isl_change_drop_first and
309 * isl_change_drop_second.
311 static enum isl_change
invert_change(enum isl_change change
)
314 case isl_change_error
:
315 return isl_change_error
;
316 case isl_change_none
:
317 return isl_change_none
;
318 case isl_change_drop_first
:
319 return isl_change_drop_second
;
320 case isl_change_drop_second
:
321 return isl_change_drop_first
;
322 case isl_change_fuse
:
323 return isl_change_fuse
;
326 return isl_change_error
;
329 /* Add the valid constraints of the basic map represented by "info"
330 * to "bmap". "len" is the size of the constraints.
331 * If only one of the pair of inequalities that make up an equality
332 * is valid, then add that inequality.
334 static __isl_give isl_basic_map
*add_valid_constraints(
335 __isl_take isl_basic_map
*bmap
, struct isl_coalesce_info
*info
,
343 for (k
= 0; k
< info
->bmap
->n_eq
; ++k
) {
344 if (info
->eq
[2 * k
] == STATUS_VALID
&&
345 info
->eq
[2 * k
+ 1] == STATUS_VALID
) {
346 l
= isl_basic_map_alloc_equality(bmap
);
348 return isl_basic_map_free(bmap
);
349 isl_seq_cpy(bmap
->eq
[l
], info
->bmap
->eq
[k
], len
);
350 } else if (info
->eq
[2 * k
] == STATUS_VALID
) {
351 l
= isl_basic_map_alloc_inequality(bmap
);
353 return isl_basic_map_free(bmap
);
354 isl_seq_neg(bmap
->ineq
[l
], info
->bmap
->eq
[k
], len
);
355 } else if (info
->eq
[2 * k
+ 1] == STATUS_VALID
) {
356 l
= isl_basic_map_alloc_inequality(bmap
);
358 return isl_basic_map_free(bmap
);
359 isl_seq_cpy(bmap
->ineq
[l
], info
->bmap
->eq
[k
], len
);
363 for (k
= 0; k
< info
->bmap
->n_ineq
; ++k
) {
364 if (info
->ineq
[k
] != STATUS_VALID
)
366 l
= isl_basic_map_alloc_inequality(bmap
);
368 return isl_basic_map_free(bmap
);
369 isl_seq_cpy(bmap
->ineq
[l
], info
->bmap
->ineq
[k
], len
);
375 /* Is "bmap" defined by a number of (non-redundant) constraints that
376 * is greater than the number of constraints of basic maps i and j combined?
377 * Equalities are counted as two inequalities.
379 static int number_of_constraints_increases(int i
, int j
,
380 struct isl_coalesce_info
*info
,
381 __isl_keep isl_basic_map
*bmap
, struct isl_tab
*tab
)
385 n_old
= 2 * info
[i
].bmap
->n_eq
+ info
[i
].bmap
->n_ineq
;
386 n_old
+= 2 * info
[j
].bmap
->n_eq
+ info
[j
].bmap
->n_ineq
;
388 n_new
= 2 * bmap
->n_eq
;
389 for (k
= 0; k
< bmap
->n_ineq
; ++k
)
390 if (!isl_tab_is_redundant(tab
, bmap
->n_eq
+ k
))
393 return n_new
> n_old
;
396 /* Replace the pair of basic maps i and j by the basic map bounded
397 * by the valid constraints in both basic maps and the constraints
398 * in extra (if not NULL).
399 * Place the fused basic map in the position that is the smallest of i and j.
401 * If "detect_equalities" is set, then look for equalities encoded
402 * as pairs of inequalities.
403 * If "check_number" is set, then the original basic maps are only
404 * replaced if the total number of constraints does not increase.
405 * While the number of integer divisions in the two basic maps
406 * is assumed to be the same, the actual definitions may be different.
407 * We only copy the definition from one of the basic map if it is
408 * the same as that of the other basic map. Otherwise, we mark
409 * the integer division as unknown and simplify the basic map
410 * in an attempt to recover the integer division definition.
412 static enum isl_change
fuse(int i
, int j
, struct isl_coalesce_info
*info
,
413 __isl_keep isl_mat
*extra
, int detect_equalities
, int check_number
)
416 struct isl_basic_map
*fused
= NULL
;
417 struct isl_tab
*fused_tab
= NULL
;
418 unsigned total
= isl_basic_map_total_dim(info
[i
].bmap
);
419 unsigned extra_rows
= extra
? extra
->n_row
: 0;
420 unsigned n_eq
, n_ineq
;
424 return fuse(j
, i
, info
, extra
, detect_equalities
, check_number
);
426 n_eq
= info
[i
].bmap
->n_eq
+ info
[j
].bmap
->n_eq
;
427 n_ineq
= info
[i
].bmap
->n_ineq
+ info
[j
].bmap
->n_ineq
;
428 fused
= isl_basic_map_alloc_space(isl_space_copy(info
[i
].bmap
->dim
),
429 info
[i
].bmap
->n_div
, n_eq
, n_eq
+ n_ineq
+ extra_rows
);
430 fused
= add_valid_constraints(fused
, &info
[i
], 1 + total
);
431 fused
= add_valid_constraints(fused
, &info
[j
], 1 + total
);
434 if (ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_RATIONAL
) &&
435 ISL_F_ISSET(info
[j
].bmap
, ISL_BASIC_MAP_RATIONAL
))
436 ISL_F_SET(fused
, ISL_BASIC_MAP_RATIONAL
);
438 for (k
= 0; k
< info
[i
].bmap
->n_div
; ++k
) {
439 int l
= isl_basic_map_alloc_div(fused
);
442 if (isl_seq_eq(info
[i
].bmap
->div
[k
], info
[j
].bmap
->div
[k
],
444 isl_seq_cpy(fused
->div
[l
], info
[i
].bmap
->div
[k
],
447 isl_int_set_si(fused
->div
[l
][0], 0);
452 for (k
= 0; k
< extra_rows
; ++k
) {
453 l
= isl_basic_map_alloc_inequality(fused
);
456 isl_seq_cpy(fused
->ineq
[l
], extra
->row
[k
], 1 + total
);
459 if (detect_equalities
)
460 fused
= isl_basic_map_detect_inequality_pairs(fused
, NULL
);
461 fused
= isl_basic_map_gauss(fused
, NULL
);
462 if (simplify
|| info
[j
].simplify
) {
463 fused
= isl_basic_map_simplify(fused
);
464 info
[i
].simplify
= 0;
466 fused
= isl_basic_map_finalize(fused
);
468 fused_tab
= isl_tab_from_basic_map(fused
, 0);
469 if (isl_tab_detect_redundant(fused_tab
) < 0)
473 number_of_constraints_increases(i
, j
, info
, fused
, fused_tab
)) {
474 isl_tab_free(fused_tab
);
475 isl_basic_map_free(fused
);
476 return isl_change_none
;
479 isl_basic_map_free(info
[i
].bmap
);
480 info
[i
].bmap
= fused
;
481 isl_tab_free(info
[i
].tab
);
482 info
[i
].tab
= fused_tab
;
485 return isl_change_fuse
;
487 isl_tab_free(fused_tab
);
488 isl_basic_map_free(fused
);
489 return isl_change_error
;
492 /* Given a pair of basic maps i and j such that all constraints are either
493 * "valid" or "cut", check if the facets corresponding to the "cut"
494 * constraints of i lie entirely within basic map j.
495 * If so, replace the pair by the basic map consisting of the valid
496 * constraints in both basic maps.
497 * Checking whether the facet lies entirely within basic map j
498 * is performed by checking whether the constraints of basic map j
499 * are valid for the facet. These tests are performed on a rational
500 * tableau to avoid the theoretical possibility that a constraint
501 * that was considered to be a cut constraint for the entire basic map i
502 * happens to be considered to be a valid constraint for the facet,
503 * even though it cuts off the same rational points.
505 * To see that we are not introducing any extra points, call the
506 * two basic maps A and B and the resulting map U and let x
507 * be an element of U \setminus ( A \cup B ).
508 * A line connecting x with an element of A \cup B meets a facet F
509 * of either A or B. Assume it is a facet of B and let c_1 be
510 * the corresponding facet constraint. We have c_1(x) < 0 and
511 * so c_1 is a cut constraint. This implies that there is some
512 * (possibly rational) point x' satisfying the constraints of A
513 * and the opposite of c_1 as otherwise c_1 would have been marked
514 * valid for A. The line connecting x and x' meets a facet of A
515 * in a (possibly rational) point that also violates c_1, but this
516 * is impossible since all cut constraints of B are valid for all
518 * In case F is a facet of A rather than B, then we can apply the
519 * above reasoning to find a facet of B separating x from A \cup B first.
521 static enum isl_change
check_facets(int i
, int j
,
522 struct isl_coalesce_info
*info
)
525 struct isl_tab_undo
*snap
, *snap2
;
526 unsigned n_eq
= info
[i
].bmap
->n_eq
;
528 snap
= isl_tab_snap(info
[i
].tab
);
529 if (isl_tab_mark_rational(info
[i
].tab
) < 0)
530 return isl_change_error
;
531 snap2
= isl_tab_snap(info
[i
].tab
);
533 for (k
= 0; k
< info
[i
].bmap
->n_ineq
; ++k
) {
534 if (info
[i
].ineq
[k
] != STATUS_CUT
)
536 if (isl_tab_select_facet(info
[i
].tab
, n_eq
+ k
) < 0)
537 return isl_change_error
;
538 for (l
= 0; l
< info
[j
].bmap
->n_ineq
; ++l
) {
540 if (info
[j
].ineq
[l
] != STATUS_CUT
)
542 stat
= status_in(info
[j
].bmap
->ineq
[l
], info
[i
].tab
);
544 return isl_change_error
;
545 if (stat
!= STATUS_VALID
)
548 if (isl_tab_rollback(info
[i
].tab
, snap2
) < 0)
549 return isl_change_error
;
550 if (l
< info
[j
].bmap
->n_ineq
)
554 if (k
< info
[i
].bmap
->n_ineq
) {
555 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
556 return isl_change_error
;
557 return isl_change_none
;
559 return fuse(i
, j
, info
, NULL
, 0, 0);
562 /* Check if info->bmap contains the basic map represented
563 * by the tableau "tab".
564 * For each equality, we check both the constraint itself
565 * (as an inequality) and its negation. Make sure the
566 * equality is returned to its original state before returning.
568 static int contains(struct isl_coalesce_info
*info
, struct isl_tab
*tab
)
572 isl_basic_map
*bmap
= info
->bmap
;
574 dim
= isl_basic_map_total_dim(bmap
);
575 for (k
= 0; k
< bmap
->n_eq
; ++k
) {
577 isl_seq_neg(bmap
->eq
[k
], bmap
->eq
[k
], 1 + dim
);
578 stat
= status_in(bmap
->eq
[k
], tab
);
579 isl_seq_neg(bmap
->eq
[k
], bmap
->eq
[k
], 1 + dim
);
582 if (stat
!= STATUS_VALID
)
584 stat
= status_in(bmap
->eq
[k
], tab
);
587 if (stat
!= STATUS_VALID
)
591 for (k
= 0; k
< bmap
->n_ineq
; ++k
) {
593 if (info
->ineq
[k
] == STATUS_REDUNDANT
)
595 stat
= status_in(bmap
->ineq
[k
], tab
);
598 if (stat
!= STATUS_VALID
)
604 /* Basic map "i" has an inequality (say "k") that is adjacent
605 * to some inequality of basic map "j". All the other inequalities
607 * Check if basic map "j" forms an extension of basic map "i".
609 * Note that this function is only called if some of the equalities or
610 * inequalities of basic map "j" do cut basic map "i". The function is
611 * correct even if there are no such cut constraints, but in that case
612 * the additional checks performed by this function are overkill.
614 * In particular, we replace constraint k, say f >= 0, by constraint
615 * f <= -1, add the inequalities of "j" that are valid for "i"
616 * and check if the result is a subset of basic map "j".
617 * To improve the chances of the subset relation being detected,
618 * any variable that only attains a single integer value
619 * in the tableau of "i" is first fixed to that value.
620 * If the result is a subset, then we know that this result is exactly equal
621 * to basic map "j" since all its constraints are valid for basic map "j".
622 * By combining the valid constraints of "i" (all equalities and all
623 * inequalities except "k") and the valid constraints of "j" we therefore
624 * obtain a basic map that is equal to their union.
625 * In this case, there is no need to perform a rollback of the tableau
626 * since it is going to be destroyed in fuse().
632 * |_______| _ |_________\
644 static enum isl_change
is_adj_ineq_extension(int i
, int j
,
645 struct isl_coalesce_info
*info
)
648 struct isl_tab_undo
*snap
;
649 unsigned n_eq
= info
[i
].bmap
->n_eq
;
650 unsigned total
= isl_basic_map_total_dim(info
[i
].bmap
);
654 if (isl_tab_extend_cons(info
[i
].tab
, 1 + info
[j
].bmap
->n_ineq
) < 0)
655 return isl_change_error
;
657 k
= find(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ADJ_INEQ
);
659 isl_die(isl_basic_map_get_ctx(info
[i
].bmap
), isl_error_internal
,
660 "info[i].ineq should have exactly one STATUS_ADJ_INEQ",
661 return isl_change_error
);
663 snap
= isl_tab_snap(info
[i
].tab
);
665 if (isl_tab_unrestrict(info
[i
].tab
, n_eq
+ k
) < 0)
666 return isl_change_error
;
668 isl_seq_neg(info
[i
].bmap
->ineq
[k
], info
[i
].bmap
->ineq
[k
], 1 + total
);
669 isl_int_sub_ui(info
[i
].bmap
->ineq
[k
][0], info
[i
].bmap
->ineq
[k
][0], 1);
670 r
= isl_tab_add_ineq(info
[i
].tab
, info
[i
].bmap
->ineq
[k
]);
671 isl_seq_neg(info
[i
].bmap
->ineq
[k
], info
[i
].bmap
->ineq
[k
], 1 + total
);
672 isl_int_sub_ui(info
[i
].bmap
->ineq
[k
][0], info
[i
].bmap
->ineq
[k
][0], 1);
674 return isl_change_error
;
676 for (k
= 0; k
< info
[j
].bmap
->n_ineq
; ++k
) {
677 if (info
[j
].ineq
[k
] != STATUS_VALID
)
679 if (isl_tab_add_ineq(info
[i
].tab
, info
[j
].bmap
->ineq
[k
]) < 0)
680 return isl_change_error
;
682 if (isl_tab_detect_constants(info
[i
].tab
) < 0)
683 return isl_change_error
;
685 super
= contains(&info
[j
], info
[i
].tab
);
687 return isl_change_error
;
689 return fuse(i
, j
, info
, NULL
, 0, 0);
691 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
692 return isl_change_error
;
694 return isl_change_none
;
698 /* Both basic maps have at least one inequality with and adjacent
699 * (but opposite) inequality in the other basic map.
700 * Check that there are no cut constraints and that there is only
701 * a single pair of adjacent inequalities.
702 * If so, we can replace the pair by a single basic map described
703 * by all but the pair of adjacent inequalities.
704 * Any additional points introduced lie strictly between the two
705 * adjacent hyperplanes and can therefore be integral.
714 * The test for a single pair of adjancent inequalities is important
715 * for avoiding the combination of two basic maps like the following
725 * If there are some cut constraints on one side, then we may
726 * still be able to fuse the two basic maps, but we need to perform
727 * some additional checks in is_adj_ineq_extension.
729 static enum isl_change
check_adj_ineq(int i
, int j
,
730 struct isl_coalesce_info
*info
)
732 int count_i
, count_j
;
735 count_i
= count(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ADJ_INEQ
);
736 count_j
= count(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_ADJ_INEQ
);
738 if (count_i
!= 1 && count_j
!= 1)
739 return isl_change_none
;
741 cut_i
= any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_CUT
) ||
742 any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_CUT
);
743 cut_j
= any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_CUT
) ||
744 any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_CUT
);
746 if (!cut_i
&& !cut_j
&& count_i
== 1 && count_j
== 1)
747 return fuse(i
, j
, info
, NULL
, 0, 0);
749 if (count_i
== 1 && !cut_i
)
750 return is_adj_ineq_extension(i
, j
, info
);
752 if (count_j
== 1 && !cut_j
)
753 return is_adj_ineq_extension(j
, i
, info
);
755 return isl_change_none
;
758 /* Given an affine transformation matrix "T", does row "row" represent
759 * anything other than a unit vector (possibly shifted by a constant)
760 * that is not involved in any of the other rows?
762 * That is, if a constraint involves the variable corresponding to
763 * the row, then could its preimage by "T" have any coefficients
764 * that are different from those in the original constraint?
766 static int not_unique_unit_row(__isl_keep isl_mat
*T
, int row
)
769 int len
= T
->n_col
- 1;
771 i
= isl_seq_first_non_zero(T
->row
[row
] + 1, len
);
774 if (!isl_int_is_one(T
->row
[row
][1 + i
]) &&
775 !isl_int_is_negone(T
->row
[row
][1 + i
]))
778 j
= isl_seq_first_non_zero(T
->row
[row
] + 1 + i
+ 1, len
- (i
+ 1));
782 for (j
= 1; j
< T
->n_row
; ++j
) {
785 if (!isl_int_is_zero(T
->row
[j
][1 + i
]))
792 /* Does inequality constraint "ineq" of "bmap" involve any of
793 * the variables marked in "affected"?
794 * "total" is the total number of variables, i.e., the number
795 * of entries in "affected".
797 static int is_affected(__isl_keep isl_basic_map
*bmap
, int ineq
, int *affected
,
802 for (i
= 0; i
< total
; ++i
) {
805 if (!isl_int_is_zero(bmap
->ineq
[ineq
][1 + i
]))
812 /* Given the compressed version of inequality constraint "ineq"
813 * of info->bmap in "v", check if the constraint can be tightened,
814 * where the compression is based on an equality constraint valid
816 * If so, add the tightened version of the inequality constraint
817 * to info->tab. "v" may be modified by this function.
819 * That is, if the compressed constraint is of the form
823 * with 0 < c < m, then it is equivalent to
827 * This means that c can also be subtracted from the original,
828 * uncompressed constraint without affecting the integer points
829 * in info->tab. Add this tightened constraint as an extra row
830 * to info->tab to make this information explicitly available.
832 static __isl_give isl_vec
*try_tightening(struct isl_coalesce_info
*info
,
833 int ineq
, __isl_take isl_vec
*v
)
841 ctx
= isl_vec_get_ctx(v
);
842 isl_seq_gcd(v
->el
+ 1, v
->size
- 1, &ctx
->normalize_gcd
);
843 if (isl_int_is_zero(ctx
->normalize_gcd
) ||
844 isl_int_is_one(ctx
->normalize_gcd
)) {
852 isl_int_fdiv_r(v
->el
[0], v
->el
[0], ctx
->normalize_gcd
);
853 if (isl_int_is_zero(v
->el
[0]))
856 if (isl_tab_extend_cons(info
->tab
, 1) < 0)
857 return isl_vec_free(v
);
859 isl_int_sub(info
->bmap
->ineq
[ineq
][0],
860 info
->bmap
->ineq
[ineq
][0], v
->el
[0]);
861 r
= isl_tab_add_ineq(info
->tab
, info
->bmap
->ineq
[ineq
]);
862 isl_int_add(info
->bmap
->ineq
[ineq
][0],
863 info
->bmap
->ineq
[ineq
][0], v
->el
[0]);
866 return isl_vec_free(v
);
871 /* Tighten the (non-redundant) constraints on the facet represented
873 * In particular, on input, info->tab represents the result
874 * of relaxing the "n" inequality constraints of info->bmap in "relaxed"
875 * by one, i.e., replacing f_i >= 0 by f_i + 1 >= 0, and then
876 * replacing the one at index "l" by the corresponding equality,
877 * i.e., f_k + 1 = 0, with k = relaxed[l].
879 * Compute a variable compression from the equality constraint f_k + 1 = 0
880 * and use it to tighten the other constraints of info->bmap
881 * (that is, all constraints that have not been relaxed),
882 * updating info->tab (and leaving info->bmap untouched).
883 * The compression handles essentially two cases, one where a variable
884 * is assigned a fixed value and can therefore be eliminated, and one
885 * where one variable is a shifted multiple of some other variable and
886 * can therefore be replaced by that multiple.
887 * Gaussian elimination would also work for the first case, but for
888 * the second case, the effectiveness would depend on the order
890 * After compression, some of the constraints may have coefficients
891 * with a common divisor. If this divisor does not divide the constant
892 * term, then the constraint can be tightened.
893 * The tightening is performed on the tableau info->tab by introducing
894 * extra (temporary) constraints.
896 * Only constraints that are possibly affected by the compression are
897 * considered. In particular, if the constraint only involves variables
898 * that are directly mapped to a distinct set of other variables, then
899 * no common divisor can be introduced and no tightening can occur.
901 * It is important to only consider the non-redundant constraints
902 * since the facet constraint has been relaxed prior to the call
903 * to this function, meaning that the constraints that were redundant
904 * prior to the relaxation may no longer be redundant.
905 * These constraints will be ignored in the fused result, so
906 * the fusion detection should not exploit them.
908 static isl_stat
tighten_on_relaxed_facet(struct isl_coalesce_info
*info
,
909 int n
, int *relaxed
, int l
)
920 ctx
= isl_basic_map_get_ctx(info
->bmap
);
921 total
= isl_basic_map_total_dim(info
->bmap
);
922 isl_int_add_ui(info
->bmap
->ineq
[k
][0], info
->bmap
->ineq
[k
][0], 1);
923 T
= isl_mat_sub_alloc6(ctx
, info
->bmap
->ineq
, k
, 1, 0, 1 + total
);
924 T
= isl_mat_variable_compression(T
, NULL
);
925 isl_int_sub_ui(info
->bmap
->ineq
[k
][0], info
->bmap
->ineq
[k
][0], 1);
927 return isl_stat_error
;
933 affected
= isl_alloc_array(ctx
, int, total
);
937 for (i
= 0; i
< total
; ++i
)
938 affected
[i
] = not_unique_unit_row(T
, 1 + i
);
940 for (i
= 0; i
< info
->bmap
->n_ineq
; ++i
) {
941 if (any(relaxed
, n
, i
))
943 if (info
->ineq
[i
] == STATUS_REDUNDANT
)
945 if (!is_affected(info
->bmap
, i
, affected
, total
))
947 v
= isl_vec_alloc(ctx
, 1 + total
);
950 isl_seq_cpy(v
->el
, info
->bmap
->ineq
[i
], 1 + total
);
951 v
= isl_vec_mat_product(v
, isl_mat_copy(T
));
952 v
= try_tightening(info
, i
, v
);
964 return isl_stat_error
;
967 /* Replace the basic maps "i" and "j" by an extension of "i"
968 * along the "n" inequality constraints in "relax" by one.
969 * The tableau info[i].tab has already been extended.
970 * Extend info[i].bmap accordingly by relaxing all constraints in "relax"
972 * Each integer division that does not have exactly the same
973 * definition in "i" and "j" is marked unknown and the basic map
974 * is scheduled to be simplified in an attempt to recover
975 * the integer division definition.
976 * Place the extension in the position that is the smallest of i and j.
978 static enum isl_change
extend(int i
, int j
, int n
, int *relax
,
979 struct isl_coalesce_info
*info
)
984 info
[i
].bmap
= isl_basic_map_cow(info
[i
].bmap
);
986 return isl_change_error
;
987 total
= isl_basic_map_total_dim(info
[i
].bmap
);
988 for (l
= 0; l
< info
[i
].bmap
->n_div
; ++l
)
989 if (!isl_seq_eq(info
[i
].bmap
->div
[l
],
990 info
[j
].bmap
->div
[l
], 1 + 1 + total
)) {
991 isl_int_set_si(info
[i
].bmap
->div
[l
][0], 0);
992 info
[i
].simplify
= 1;
994 for (l
= 0; l
< n
; ++l
)
995 isl_int_add_ui(info
[i
].bmap
->ineq
[relax
[l
]][0],
996 info
[i
].bmap
->ineq
[relax
[l
]][0], 1);
997 ISL_F_SET(info
[i
].bmap
, ISL_BASIC_MAP_FINAL
);
1000 exchange(&info
[i
], &info
[j
]);
1001 return isl_change_fuse
;
1004 /* Basic map "i" has "n" inequality constraints (collected in "relax")
1005 * that are such that they include basic map "j" if they are relaxed
1006 * by one. All the other inequalities are valid for "j".
1007 * Check if basic map "j" forms an extension of basic map "i".
1009 * In particular, relax the constraints in "relax", compute the corresponding
1010 * facets one by one and check whether each of these is included
1011 * in the other basic map.
1012 * Before testing for inclusion, the constraints on each facet
1013 * are tightened to increase the chance of an inclusion being detected.
1014 * (Adding the valid constraints of "j" to the tableau of "i", as is done
1015 * in is_adj_ineq_extension, may further increase those chances, but this
1016 * is not currently done.)
1017 * If each facet is included, we know that relaxing the constraints extends
1018 * the basic map with exactly the other basic map (we already know that this
1019 * other basic map is included in the extension, because all other
1020 * inequality constraints are valid of "j") and we can replace the
1021 * two basic maps by this extension.
1037 static enum isl_change
is_relaxed_extension(int i
, int j
, int n
, int *relax
,
1038 struct isl_coalesce_info
*info
)
1042 struct isl_tab_undo
*snap
, *snap2
;
1043 unsigned n_eq
= info
[i
].bmap
->n_eq
;
1045 for (l
= 0; l
< n
; ++l
)
1046 if (isl_tab_is_equality(info
[i
].tab
, n_eq
+ relax
[l
]))
1047 return isl_change_none
;
1049 snap
= isl_tab_snap(info
[i
].tab
);
1050 for (l
= 0; l
< n
; ++l
)
1051 if (isl_tab_relax(info
[i
].tab
, n_eq
+ relax
[l
]) < 0)
1052 return isl_change_error
;
1053 snap2
= isl_tab_snap(info
[i
].tab
);
1054 for (l
= 0; l
< n
; ++l
) {
1055 if (isl_tab_rollback(info
[i
].tab
, snap2
) < 0)
1056 return isl_change_error
;
1057 if (isl_tab_select_facet(info
[i
].tab
, n_eq
+ relax
[l
]) < 0)
1058 return isl_change_error
;
1059 if (tighten_on_relaxed_facet(&info
[i
], n
, relax
, l
) < 0)
1060 return isl_change_error
;
1061 super
= contains(&info
[j
], info
[i
].tab
);
1063 return isl_change_error
;
1066 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
1067 return isl_change_error
;
1068 return isl_change_none
;
1071 if (isl_tab_rollback(info
[i
].tab
, snap2
) < 0)
1072 return isl_change_error
;
1073 return extend(i
, j
, n
, relax
, info
);
1076 /* Data structure that keeps track of the wrapping constraints
1077 * and of information to bound the coefficients of those constraints.
1079 * bound is set if we want to apply a bound on the coefficients
1080 * mat contains the wrapping constraints
1081 * max is the bound on the coefficients (if bound is set)
1089 /* Update wraps->max to be greater than or equal to the coefficients
1090 * in the equalities and inequalities of info->bmap that can be removed
1091 * if we end up applying wrapping.
1093 static void wraps_update_max(struct isl_wraps
*wraps
,
1094 struct isl_coalesce_info
*info
)
1098 unsigned total
= isl_basic_map_total_dim(info
->bmap
);
1100 isl_int_init(max_k
);
1102 for (k
= 0; k
< info
->bmap
->n_eq
; ++k
) {
1103 if (info
->eq
[2 * k
] == STATUS_VALID
&&
1104 info
->eq
[2 * k
+ 1] == STATUS_VALID
)
1106 isl_seq_abs_max(info
->bmap
->eq
[k
] + 1, total
, &max_k
);
1107 if (isl_int_abs_gt(max_k
, wraps
->max
))
1108 isl_int_set(wraps
->max
, max_k
);
1111 for (k
= 0; k
< info
->bmap
->n_ineq
; ++k
) {
1112 if (info
->ineq
[k
] == STATUS_VALID
||
1113 info
->ineq
[k
] == STATUS_REDUNDANT
)
1115 isl_seq_abs_max(info
->bmap
->ineq
[k
] + 1, total
, &max_k
);
1116 if (isl_int_abs_gt(max_k
, wraps
->max
))
1117 isl_int_set(wraps
->max
, max_k
);
1120 isl_int_clear(max_k
);
1123 /* Initialize the isl_wraps data structure.
1124 * If we want to bound the coefficients of the wrapping constraints,
1125 * we set wraps->max to the largest coefficient
1126 * in the equalities and inequalities that can be removed if we end up
1127 * applying wrapping.
1129 static void wraps_init(struct isl_wraps
*wraps
, __isl_take isl_mat
*mat
,
1130 struct isl_coalesce_info
*info
, int i
, int j
)
1138 ctx
= isl_mat_get_ctx(mat
);
1139 wraps
->bound
= isl_options_get_coalesce_bounded_wrapping(ctx
);
1142 isl_int_init(wraps
->max
);
1143 isl_int_set_si(wraps
->max
, 0);
1144 wraps_update_max(wraps
, &info
[i
]);
1145 wraps_update_max(wraps
, &info
[j
]);
1148 /* Free the contents of the isl_wraps data structure.
1150 static void wraps_free(struct isl_wraps
*wraps
)
1152 isl_mat_free(wraps
->mat
);
1154 isl_int_clear(wraps
->max
);
1157 /* Is the wrapping constraint in row "row" allowed?
1159 * If wraps->bound is set, we check that none of the coefficients
1160 * is greater than wraps->max.
1162 static int allow_wrap(struct isl_wraps
*wraps
, int row
)
1169 for (i
= 1; i
< wraps
->mat
->n_col
; ++i
)
1170 if (isl_int_abs_gt(wraps
->mat
->row
[row
][i
], wraps
->max
))
1176 /* Wrap "ineq" (or its opposite if "negate" is set) around "bound"
1177 * to include "set" and add the result in position "w" of "wraps".
1178 * "len" is the total number of coefficients in "bound" and "ineq".
1179 * Return 1 on success, 0 on failure and -1 on error.
1180 * Wrapping can fail if the result of wrapping is equal to "bound"
1181 * or if we want to bound the sizes of the coefficients and
1182 * the wrapped constraint does not satisfy this bound.
1184 static int add_wrap(struct isl_wraps
*wraps
, int w
, isl_int
*bound
,
1185 isl_int
*ineq
, unsigned len
, __isl_keep isl_set
*set
, int negate
)
1187 isl_seq_cpy(wraps
->mat
->row
[w
], bound
, len
);
1189 isl_seq_neg(wraps
->mat
->row
[w
+ 1], ineq
, len
);
1190 ineq
= wraps
->mat
->row
[w
+ 1];
1192 if (!isl_set_wrap_facet(set
, wraps
->mat
->row
[w
], ineq
))
1194 if (isl_seq_eq(wraps
->mat
->row
[w
], bound
, len
))
1196 if (!allow_wrap(wraps
, w
))
1201 /* For each constraint in info->bmap that is not redundant (as determined
1202 * by info->tab) and that is not a valid constraint for the other basic map,
1203 * wrap the constraint around "bound" such that it includes the whole
1204 * set "set" and append the resulting constraint to "wraps".
1205 * Note that the constraints that are valid for the other basic map
1206 * will be added to the combined basic map by default, so there is
1207 * no need to wrap them.
1208 * The caller wrap_in_facets even relies on this function not wrapping
1209 * any constraints that are already valid.
1210 * "wraps" is assumed to have been pre-allocated to the appropriate size.
1211 * wraps->n_row is the number of actual wrapped constraints that have
1213 * If any of the wrapping problems results in a constraint that is
1214 * identical to "bound", then this means that "set" is unbounded in such
1215 * way that no wrapping is possible. If this happens then wraps->n_row
1217 * Similarly, if we want to bound the coefficients of the wrapping
1218 * constraints and a newly added wrapping constraint does not
1219 * satisfy the bound, then wraps->n_row is also reset to zero.
1221 static int add_wraps(struct isl_wraps
*wraps
, struct isl_coalesce_info
*info
,
1222 isl_int
*bound
, __isl_keep isl_set
*set
)
1227 isl_basic_map
*bmap
= info
->bmap
;
1228 unsigned len
= 1 + isl_basic_map_total_dim(bmap
);
1230 w
= wraps
->mat
->n_row
;
1232 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
1233 if (info
->ineq
[l
] == STATUS_VALID
||
1234 info
->ineq
[l
] == STATUS_REDUNDANT
)
1236 if (isl_seq_is_neg(bound
, bmap
->ineq
[l
], len
))
1238 if (isl_seq_eq(bound
, bmap
->ineq
[l
], len
))
1240 if (isl_tab_is_redundant(info
->tab
, bmap
->n_eq
+ l
))
1243 added
= add_wrap(wraps
, w
, bound
, bmap
->ineq
[l
], len
, set
, 0);
1250 for (l
= 0; l
< bmap
->n_eq
; ++l
) {
1251 if (isl_seq_is_neg(bound
, bmap
->eq
[l
], len
))
1253 if (isl_seq_eq(bound
, bmap
->eq
[l
], len
))
1256 for (m
= 0; m
< 2; ++m
) {
1257 if (info
->eq
[2 * l
+ m
] == STATUS_VALID
)
1259 added
= add_wrap(wraps
, w
, bound
, bmap
->eq
[l
], len
,
1269 wraps
->mat
->n_row
= w
;
1272 wraps
->mat
->n_row
= 0;
1276 /* Check if the constraints in "wraps" from "first" until the last
1277 * are all valid for the basic set represented by "tab".
1278 * If not, wraps->n_row is set to zero.
1280 static int check_wraps(__isl_keep isl_mat
*wraps
, int first
,
1281 struct isl_tab
*tab
)
1285 for (i
= first
; i
< wraps
->n_row
; ++i
) {
1286 enum isl_ineq_type type
;
1287 type
= isl_tab_ineq_type(tab
, wraps
->row
[i
]);
1288 if (type
== isl_ineq_error
)
1290 if (type
== isl_ineq_redundant
)
1299 /* Return a set that corresponds to the non-redundant constraints
1300 * (as recorded in tab) of bmap.
1302 * It's important to remove the redundant constraints as some
1303 * of the other constraints may have been modified after the
1304 * constraints were marked redundant.
1305 * In particular, a constraint may have been relaxed.
1306 * Redundant constraints are ignored when a constraint is relaxed
1307 * and should therefore continue to be ignored ever after.
1308 * Otherwise, the relaxation might be thwarted by some of
1309 * these constraints.
1311 * Update the underlying set to ensure that the dimension doesn't change.
1312 * Otherwise the integer divisions could get dropped if the tab
1313 * turns out to be empty.
1315 static __isl_give isl_set
*set_from_updated_bmap(__isl_keep isl_basic_map
*bmap
,
1316 struct isl_tab
*tab
)
1318 isl_basic_set
*bset
;
1320 bmap
= isl_basic_map_copy(bmap
);
1321 bset
= isl_basic_map_underlying_set(bmap
);
1322 bset
= isl_basic_set_cow(bset
);
1323 bset
= isl_basic_set_update_from_tab(bset
, tab
);
1324 return isl_set_from_basic_set(bset
);
1327 /* Wrap the constraints of info->bmap that bound the facet defined
1328 * by inequality "k" around (the opposite of) this inequality to
1329 * include "set". "bound" may be used to store the negated inequality.
1330 * Since the wrapped constraints are not guaranteed to contain the whole
1331 * of info->bmap, we check them in check_wraps.
1332 * If any of the wrapped constraints turn out to be invalid, then
1333 * check_wraps will reset wrap->n_row to zero.
1335 static int add_wraps_around_facet(struct isl_wraps
*wraps
,
1336 struct isl_coalesce_info
*info
, int k
, isl_int
*bound
,
1337 __isl_keep isl_set
*set
)
1339 struct isl_tab_undo
*snap
;
1341 unsigned total
= isl_basic_map_total_dim(info
->bmap
);
1343 snap
= isl_tab_snap(info
->tab
);
1345 if (isl_tab_select_facet(info
->tab
, info
->bmap
->n_eq
+ k
) < 0)
1347 if (isl_tab_detect_redundant(info
->tab
) < 0)
1350 isl_seq_neg(bound
, info
->bmap
->ineq
[k
], 1 + total
);
1352 n
= wraps
->mat
->n_row
;
1353 if (add_wraps(wraps
, info
, bound
, set
) < 0)
1356 if (isl_tab_rollback(info
->tab
, snap
) < 0)
1358 if (check_wraps(wraps
->mat
, n
, info
->tab
) < 0)
1364 /* Given a basic set i with a constraint k that is adjacent to
1365 * basic set j, check if we can wrap
1366 * both the facet corresponding to k (if "wrap_facet" is set) and basic map j
1367 * (always) around their ridges to include the other set.
1368 * If so, replace the pair of basic sets by their union.
1370 * All constraints of i (except k) are assumed to be valid or
1371 * cut constraints for j.
1372 * Wrapping the cut constraints to include basic map j may result
1373 * in constraints that are no longer valid of basic map i
1374 * we have to check that the resulting wrapping constraints are valid for i.
1375 * If "wrap_facet" is not set, then all constraints of i (except k)
1376 * are assumed to be valid for j.
1385 static enum isl_change
can_wrap_in_facet(int i
, int j
, int k
,
1386 struct isl_coalesce_info
*info
, int wrap_facet
)
1388 enum isl_change change
= isl_change_none
;
1389 struct isl_wraps wraps
;
1392 struct isl_set
*set_i
= NULL
;
1393 struct isl_set
*set_j
= NULL
;
1394 struct isl_vec
*bound
= NULL
;
1395 unsigned total
= isl_basic_map_total_dim(info
[i
].bmap
);
1397 set_i
= set_from_updated_bmap(info
[i
].bmap
, info
[i
].tab
);
1398 set_j
= set_from_updated_bmap(info
[j
].bmap
, info
[j
].tab
);
1399 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
1400 mat
= isl_mat_alloc(ctx
, 2 * (info
[i
].bmap
->n_eq
+ info
[j
].bmap
->n_eq
) +
1401 info
[i
].bmap
->n_ineq
+ info
[j
].bmap
->n_ineq
,
1403 wraps_init(&wraps
, mat
, info
, i
, j
);
1404 bound
= isl_vec_alloc(ctx
, 1 + total
);
1405 if (!set_i
|| !set_j
|| !wraps
.mat
|| !bound
)
1408 isl_seq_cpy(bound
->el
, info
[i
].bmap
->ineq
[k
], 1 + total
);
1409 isl_int_add_ui(bound
->el
[0], bound
->el
[0], 1);
1411 isl_seq_cpy(wraps
.mat
->row
[0], bound
->el
, 1 + total
);
1412 wraps
.mat
->n_row
= 1;
1414 if (add_wraps(&wraps
, &info
[j
], bound
->el
, set_i
) < 0)
1416 if (!wraps
.mat
->n_row
)
1420 if (add_wraps_around_facet(&wraps
, &info
[i
], k
,
1421 bound
->el
, set_j
) < 0)
1423 if (!wraps
.mat
->n_row
)
1427 change
= fuse(i
, j
, info
, wraps
.mat
, 0, 0);
1432 isl_set_free(set_i
);
1433 isl_set_free(set_j
);
1435 isl_vec_free(bound
);
1440 isl_vec_free(bound
);
1441 isl_set_free(set_i
);
1442 isl_set_free(set_j
);
1443 return isl_change_error
;
1446 /* Given a cut constraint t(x) >= 0 of basic map i, stored in row "w"
1447 * of wrap.mat, replace it by its relaxed version t(x) + 1 >= 0, and
1448 * add wrapping constraints to wrap.mat for all constraints
1449 * of basic map j that bound the part of basic map j that sticks out
1450 * of the cut constraint.
1451 * "set_i" is the underlying set of basic map i.
1452 * If any wrapping fails, then wraps->mat.n_row is reset to zero.
1454 * In particular, we first intersect basic map j with t(x) + 1 = 0.
1455 * If the result is empty, then t(x) >= 0 was actually a valid constraint
1456 * (with respect to the integer points), so we add t(x) >= 0 instead.
1457 * Otherwise, we wrap the constraints of basic map j that are not
1458 * redundant in this intersection and that are not already valid
1459 * for basic map i over basic map i.
1460 * Note that it is sufficient to wrap the constraints to include
1461 * basic map i, because we will only wrap the constraints that do
1462 * not include basic map i already. The wrapped constraint will
1463 * therefore be more relaxed compared to the original constraint.
1464 * Since the original constraint is valid for basic map j, so is
1465 * the wrapped constraint.
1467 static isl_stat
wrap_in_facet(struct isl_wraps
*wraps
, int w
,
1468 struct isl_coalesce_info
*info_j
, __isl_keep isl_set
*set_i
,
1469 struct isl_tab_undo
*snap
)
1471 isl_int_add_ui(wraps
->mat
->row
[w
][0], wraps
->mat
->row
[w
][0], 1);
1472 if (isl_tab_add_eq(info_j
->tab
, wraps
->mat
->row
[w
]) < 0)
1473 return isl_stat_error
;
1474 if (isl_tab_detect_redundant(info_j
->tab
) < 0)
1475 return isl_stat_error
;
1477 if (info_j
->tab
->empty
)
1478 isl_int_sub_ui(wraps
->mat
->row
[w
][0], wraps
->mat
->row
[w
][0], 1);
1479 else if (add_wraps(wraps
, info_j
, wraps
->mat
->row
[w
], set_i
) < 0)
1480 return isl_stat_error
;
1482 if (isl_tab_rollback(info_j
->tab
, snap
) < 0)
1483 return isl_stat_error
;
1488 /* Given a pair of basic maps i and j such that j sticks out
1489 * of i at n cut constraints, each time by at most one,
1490 * try to compute wrapping constraints and replace the two
1491 * basic maps by a single basic map.
1492 * The other constraints of i are assumed to be valid for j.
1493 * "set_i" is the underlying set of basic map i.
1494 * "wraps" has been initialized to be of the right size.
1496 * For each cut constraint t(x) >= 0 of i, we add the relaxed version
1497 * t(x) + 1 >= 0, along with wrapping constraints for all constraints
1498 * of basic map j that bound the part of basic map j that sticks out
1499 * of the cut constraint.
1501 * If any wrapping fails, i.e., if we cannot wrap to touch
1502 * the union, then we give up.
1503 * Otherwise, the pair of basic maps is replaced by their union.
1505 static enum isl_change
try_wrap_in_facets(int i
, int j
,
1506 struct isl_coalesce_info
*info
, struct isl_wraps
*wraps
,
1507 __isl_keep isl_set
*set_i
)
1511 struct isl_tab_undo
*snap
;
1513 total
= isl_basic_map_total_dim(info
[i
].bmap
);
1515 snap
= isl_tab_snap(info
[j
].tab
);
1517 wraps
->mat
->n_row
= 0;
1519 for (k
= 0; k
< info
[i
].bmap
->n_eq
; ++k
) {
1520 for (l
= 0; l
< 2; ++l
) {
1521 if (info
[i
].eq
[2 * k
+ l
] != STATUS_CUT
)
1523 w
= wraps
->mat
->n_row
++;
1525 isl_seq_neg(wraps
->mat
->row
[w
],
1526 info
[i
].bmap
->eq
[k
], 1 + total
);
1528 isl_seq_cpy(wraps
->mat
->row
[w
],
1529 info
[i
].bmap
->eq
[k
], 1 + total
);
1530 if (wrap_in_facet(wraps
, w
, &info
[j
], set_i
, snap
) < 0)
1531 return isl_change_error
;
1533 if (!wraps
->mat
->n_row
)
1534 return isl_change_none
;
1538 for (k
= 0; k
< info
[i
].bmap
->n_ineq
; ++k
) {
1539 if (info
[i
].ineq
[k
] != STATUS_CUT
)
1541 w
= wraps
->mat
->n_row
++;
1542 isl_seq_cpy(wraps
->mat
->row
[w
],
1543 info
[i
].bmap
->ineq
[k
], 1 + total
);
1544 if (wrap_in_facet(wraps
, w
, &info
[j
], set_i
, snap
) < 0)
1545 return isl_change_error
;
1547 if (!wraps
->mat
->n_row
)
1548 return isl_change_none
;
1551 return fuse(i
, j
, info
, wraps
->mat
, 0, 1);
1554 /* Given a pair of basic maps i and j such that j sticks out
1555 * of i at n cut constraints, each time by at most one,
1556 * try to compute wrapping constraints and replace the two
1557 * basic maps by a single basic map.
1558 * The other constraints of i are assumed to be valid for j.
1560 * The core computation is performed by try_wrap_in_facets.
1561 * This function simply extracts an underlying set representation
1562 * of basic map i and initializes the data structure for keeping
1563 * track of wrapping constraints.
1565 static enum isl_change
wrap_in_facets(int i
, int j
, int n
,
1566 struct isl_coalesce_info
*info
)
1568 enum isl_change change
= isl_change_none
;
1569 struct isl_wraps wraps
;
1572 isl_set
*set_i
= NULL
;
1573 unsigned total
= isl_basic_map_total_dim(info
[i
].bmap
);
1576 if (isl_tab_extend_cons(info
[j
].tab
, 1) < 0)
1577 return isl_change_error
;
1579 max_wrap
= 1 + 2 * info
[j
].bmap
->n_eq
+ info
[j
].bmap
->n_ineq
;
1582 set_i
= set_from_updated_bmap(info
[i
].bmap
, info
[i
].tab
);
1583 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
1584 mat
= isl_mat_alloc(ctx
, max_wrap
, 1 + total
);
1585 wraps_init(&wraps
, mat
, info
, i
, j
);
1586 if (!set_i
|| !wraps
.mat
)
1589 change
= try_wrap_in_facets(i
, j
, info
, &wraps
, set_i
);
1592 isl_set_free(set_i
);
1597 isl_set_free(set_i
);
1598 return isl_change_error
;
1601 /* Return the effect of inequality "ineq" on the tableau "tab",
1602 * after relaxing the constant term of "ineq" by one.
1604 static enum isl_ineq_type
type_of_relaxed(struct isl_tab
*tab
, isl_int
*ineq
)
1606 enum isl_ineq_type type
;
1608 isl_int_add_ui(ineq
[0], ineq
[0], 1);
1609 type
= isl_tab_ineq_type(tab
, ineq
);
1610 isl_int_sub_ui(ineq
[0], ineq
[0], 1);
1615 /* Given two basic sets i and j,
1616 * check if relaxing all the cut constraints of i by one turns
1617 * them into valid constraint for j and check if we can wrap in
1618 * the bits that are sticking out.
1619 * If so, replace the pair by their union.
1621 * We first check if all relaxed cut inequalities of i are valid for j
1622 * and then try to wrap in the intersections of the relaxed cut inequalities
1625 * During this wrapping, we consider the points of j that lie at a distance
1626 * of exactly 1 from i. In particular, we ignore the points that lie in
1627 * between this lower-dimensional space and the basic map i.
1628 * We can therefore only apply this to integer maps.
1654 * Wrapping can fail if the result of wrapping one of the facets
1655 * around its edges does not produce any new facet constraint.
1656 * In particular, this happens when we try to wrap in unbounded sets.
1658 * _______________________________________________________________________
1662 * |_| |_________________________________________________________________
1665 * The following is not an acceptable result of coalescing the above two
1666 * sets as it includes extra integer points.
1667 * _______________________________________________________________________
1672 * \______________________________________________________________________
1674 static enum isl_change
can_wrap_in_set(int i
, int j
,
1675 struct isl_coalesce_info
*info
)
1681 if (ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_RATIONAL
) ||
1682 ISL_F_ISSET(info
[j
].bmap
, ISL_BASIC_MAP_RATIONAL
))
1683 return isl_change_none
;
1685 n
= count(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_CUT
);
1686 n
+= count(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_CUT
);
1688 return isl_change_none
;
1690 total
= isl_basic_map_total_dim(info
[i
].bmap
);
1691 for (k
= 0; k
< info
[i
].bmap
->n_eq
; ++k
) {
1692 for (l
= 0; l
< 2; ++l
) {
1693 enum isl_ineq_type type
;
1695 if (info
[i
].eq
[2 * k
+ l
] != STATUS_CUT
)
1699 isl_seq_neg(info
[i
].bmap
->eq
[k
],
1700 info
[i
].bmap
->eq
[k
], 1 + total
);
1701 type
= type_of_relaxed(info
[j
].tab
,
1702 info
[i
].bmap
->eq
[k
]);
1704 isl_seq_neg(info
[i
].bmap
->eq
[k
],
1705 info
[i
].bmap
->eq
[k
], 1 + total
);
1706 if (type
== isl_ineq_error
)
1707 return isl_change_error
;
1708 if (type
!= isl_ineq_redundant
)
1709 return isl_change_none
;
1713 for (k
= 0; k
< info
[i
].bmap
->n_ineq
; ++k
) {
1714 enum isl_ineq_type type
;
1716 if (info
[i
].ineq
[k
] != STATUS_CUT
)
1719 type
= type_of_relaxed(info
[j
].tab
, info
[i
].bmap
->ineq
[k
]);
1720 if (type
== isl_ineq_error
)
1721 return isl_change_error
;
1722 if (type
!= isl_ineq_redundant
)
1723 return isl_change_none
;
1726 return wrap_in_facets(i
, j
, n
, info
);
1729 /* Check if either i or j has only cut constraints that can
1730 * be used to wrap in (a facet of) the other basic set.
1731 * if so, replace the pair by their union.
1733 static enum isl_change
check_wrap(int i
, int j
, struct isl_coalesce_info
*info
)
1735 enum isl_change change
= isl_change_none
;
1737 change
= can_wrap_in_set(i
, j
, info
);
1738 if (change
!= isl_change_none
)
1741 change
= can_wrap_in_set(j
, i
, info
);
1745 /* Check if all inequality constraints of "i" that cut "j" cease
1746 * to be cut constraints if they are relaxed by one.
1747 * If so, collect the cut constraints in "list".
1748 * The caller is responsible for allocating "list".
1750 static isl_bool
all_cut_by_one(int i
, int j
, struct isl_coalesce_info
*info
,
1756 for (l
= 0; l
< info
[i
].bmap
->n_ineq
; ++l
) {
1757 enum isl_ineq_type type
;
1759 if (info
[i
].ineq
[l
] != STATUS_CUT
)
1761 type
= type_of_relaxed(info
[j
].tab
, info
[i
].bmap
->ineq
[l
]);
1762 if (type
== isl_ineq_error
)
1763 return isl_bool_error
;
1764 if (type
!= isl_ineq_redundant
)
1765 return isl_bool_false
;
1769 return isl_bool_true
;
1772 /* Given two basic maps such that "j" has at least one equality constraint
1773 * that is adjacent to an inequality constraint of "i" and such that "i" has
1774 * exactly one inequality constraint that is adjacent to an equality
1775 * constraint of "j", check whether "i" can be extended to include "j" or
1776 * whether "j" can be wrapped into "i".
1777 * All remaining constraints of "i" and "j" are assumed to be valid
1778 * or cut constraints of the other basic map.
1779 * However, none of the equality constraints of "i" are cut constraints.
1781 * If "i" has any "cut" inequality constraints, then check if relaxing
1782 * each of them by one is sufficient for them to become valid.
1783 * If so, check if the inequality constraint adjacent to an equality
1784 * constraint of "j" along with all these cut constraints
1785 * can be relaxed by one to contain exactly "j".
1786 * Otherwise, or if this fails, check if "j" can be wrapped into "i".
1788 static enum isl_change
check_single_adj_eq(int i
, int j
,
1789 struct isl_coalesce_info
*info
)
1791 enum isl_change change
= isl_change_none
;
1798 n_cut
= count(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_CUT
);
1800 k
= find(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ADJ_EQ
);
1803 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
1804 relax
= isl_calloc_array(ctx
, int, 1 + n_cut
);
1806 return isl_change_error
;
1808 try_relax
= all_cut_by_one(i
, j
, info
, relax
+ 1);
1810 change
= isl_change_error
;
1812 try_relax
= isl_bool_true
;
1815 if (try_relax
&& change
== isl_change_none
)
1816 change
= is_relaxed_extension(i
, j
, 1 + n_cut
, relax
, info
);
1819 if (change
!= isl_change_none
)
1822 change
= can_wrap_in_facet(i
, j
, k
, info
, n_cut
> 0);
1827 /* At least one of the basic maps has an equality that is adjacent
1828 * to inequality. Make sure that only one of the basic maps has
1829 * such an equality and that the other basic map has exactly one
1830 * inequality adjacent to an equality.
1831 * If the other basic map does not have such an inequality, then
1832 * check if all its constraints are either valid or cut constraints
1833 * and, if so, try wrapping in the first map into the second.
1834 * Otherwise, try to extend one basic map with the other or
1835 * wrap one basic map in the other.
1837 static enum isl_change
check_adj_eq(int i
, int j
,
1838 struct isl_coalesce_info
*info
)
1840 if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_ADJ_INEQ
) &&
1841 any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_ADJ_INEQ
))
1842 /* ADJ EQ TOO MANY */
1843 return isl_change_none
;
1845 if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_ADJ_INEQ
))
1846 return check_adj_eq(j
, i
, info
);
1848 /* j has an equality adjacent to an inequality in i */
1850 if (count(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ADJ_EQ
) != 1) {
1851 if (all_valid_or_cut(&info
[i
]))
1852 return can_wrap_in_set(i
, j
, info
);
1853 return isl_change_none
;
1855 if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_CUT
))
1856 return isl_change_none
;
1857 if (any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_ADJ_EQ
) ||
1858 any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ADJ_INEQ
) ||
1859 any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_ADJ_INEQ
))
1860 /* ADJ EQ TOO MANY */
1861 return isl_change_none
;
1863 return check_single_adj_eq(i
, j
, info
);
1866 /* The two basic maps lie on adjacent hyperplanes. In particular,
1867 * basic map "i" has an equality that lies parallel to basic map "j".
1868 * Check if we can wrap the facets around the parallel hyperplanes
1869 * to include the other set.
1871 * We perform basically the same operations as can_wrap_in_facet,
1872 * except that we don't need to select a facet of one of the sets.
1878 * If there is more than one equality of "i" adjacent to an equality of "j",
1879 * then the result will satisfy one or more equalities that are a linear
1880 * combination of these equalities. These will be encoded as pairs
1881 * of inequalities in the wrapping constraints and need to be made
1884 static enum isl_change
check_eq_adj_eq(int i
, int j
,
1885 struct isl_coalesce_info
*info
)
1888 enum isl_change change
= isl_change_none
;
1889 int detect_equalities
= 0;
1890 struct isl_wraps wraps
;
1893 struct isl_set
*set_i
= NULL
;
1894 struct isl_set
*set_j
= NULL
;
1895 struct isl_vec
*bound
= NULL
;
1896 unsigned total
= isl_basic_map_total_dim(info
[i
].bmap
);
1898 if (count(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_ADJ_EQ
) != 1)
1899 detect_equalities
= 1;
1901 k
= find(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_ADJ_EQ
);
1903 set_i
= set_from_updated_bmap(info
[i
].bmap
, info
[i
].tab
);
1904 set_j
= set_from_updated_bmap(info
[j
].bmap
, info
[j
].tab
);
1905 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
1906 mat
= isl_mat_alloc(ctx
, 2 * (info
[i
].bmap
->n_eq
+ info
[j
].bmap
->n_eq
) +
1907 info
[i
].bmap
->n_ineq
+ info
[j
].bmap
->n_ineq
,
1909 wraps_init(&wraps
, mat
, info
, i
, j
);
1910 bound
= isl_vec_alloc(ctx
, 1 + total
);
1911 if (!set_i
|| !set_j
|| !wraps
.mat
|| !bound
)
1915 isl_seq_neg(bound
->el
, info
[i
].bmap
->eq
[k
/ 2], 1 + total
);
1917 isl_seq_cpy(bound
->el
, info
[i
].bmap
->eq
[k
/ 2], 1 + total
);
1918 isl_int_add_ui(bound
->el
[0], bound
->el
[0], 1);
1920 isl_seq_cpy(wraps
.mat
->row
[0], bound
->el
, 1 + total
);
1921 wraps
.mat
->n_row
= 1;
1923 if (add_wraps(&wraps
, &info
[j
], bound
->el
, set_i
) < 0)
1925 if (!wraps
.mat
->n_row
)
1928 isl_int_sub_ui(bound
->el
[0], bound
->el
[0], 1);
1929 isl_seq_neg(bound
->el
, bound
->el
, 1 + total
);
1931 isl_seq_cpy(wraps
.mat
->row
[wraps
.mat
->n_row
], bound
->el
, 1 + total
);
1934 if (add_wraps(&wraps
, &info
[i
], bound
->el
, set_j
) < 0)
1936 if (!wraps
.mat
->n_row
)
1939 change
= fuse(i
, j
, info
, wraps
.mat
, detect_equalities
, 0);
1942 error
: change
= isl_change_error
;
1947 isl_set_free(set_i
);
1948 isl_set_free(set_j
);
1949 isl_vec_free(bound
);
1954 /* Initialize the "eq" and "ineq" fields of "info".
1956 static void init_status(struct isl_coalesce_info
*info
)
1958 info
->eq
= info
->ineq
= NULL
;
1961 /* Set info->eq to the positions of the equalities of info->bmap
1962 * with respect to the basic map represented by "tab".
1963 * If info->eq has already been computed, then do not compute it again.
1965 static void set_eq_status_in(struct isl_coalesce_info
*info
,
1966 struct isl_tab
*tab
)
1970 info
->eq
= eq_status_in(info
->bmap
, tab
);
1973 /* Set info->ineq to the positions of the inequalities of info->bmap
1974 * with respect to the basic map represented by "tab".
1975 * If info->ineq has already been computed, then do not compute it again.
1977 static void set_ineq_status_in(struct isl_coalesce_info
*info
,
1978 struct isl_tab
*tab
)
1982 info
->ineq
= ineq_status_in(info
->bmap
, info
->tab
, tab
);
1985 /* Free the memory allocated by the "eq" and "ineq" fields of "info".
1986 * This function assumes that init_status has been called on "info" first,
1987 * after which the "eq" and "ineq" fields may or may not have been
1988 * assigned a newly allocated array.
1990 static void clear_status(struct isl_coalesce_info
*info
)
1996 /* Are all inequality constraints of the basic map represented by "info"
1997 * valid for the other basic map, except for a single constraint
1998 * that is adjacent to an inequality constraint of the other basic map?
2000 static int all_ineq_valid_or_single_adj_ineq(struct isl_coalesce_info
*info
)
2005 for (i
= 0; i
< info
->bmap
->n_ineq
; ++i
) {
2006 if (info
->ineq
[i
] == STATUS_REDUNDANT
)
2008 if (info
->ineq
[i
] == STATUS_VALID
)
2010 if (info
->ineq
[i
] != STATUS_ADJ_INEQ
)
2020 /* Basic map "i" has one or more equality constraints that separate it
2021 * from basic map "j". Check if it happens to be an extension
2023 * In particular, check that all constraints of "j" are valid for "i",
2024 * except for one inequality constraint that is adjacent
2025 * to an inequality constraints of "i".
2026 * If so, check for "i" being an extension of "j" by calling
2027 * is_adj_ineq_extension.
2029 * Clean up the memory allocated for keeping track of the status
2030 * of the constraints before returning.
2032 static enum isl_change
separating_equality(int i
, int j
,
2033 struct isl_coalesce_info
*info
)
2035 enum isl_change change
= isl_change_none
;
2037 if (all(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_VALID
) &&
2038 all_ineq_valid_or_single_adj_ineq(&info
[j
]))
2039 change
= is_adj_ineq_extension(j
, i
, info
);
2041 clear_status(&info
[i
]);
2042 clear_status(&info
[j
]);
2046 /* Check if the union of the given pair of basic maps
2047 * can be represented by a single basic map.
2048 * If so, replace the pair by the single basic map and return
2049 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
2050 * Otherwise, return isl_change_none.
2051 * The two basic maps are assumed to live in the same local space.
2052 * The "eq" and "ineq" fields of info[i] and info[j] are assumed
2053 * to have been initialized by the caller, either to NULL or
2054 * to valid information.
2056 * We first check the effect of each constraint of one basic map
2057 * on the other basic map.
2058 * The constraint may be
2059 * redundant the constraint is redundant in its own
2060 * basic map and should be ignore and removed
2062 * valid all (integer) points of the other basic map
2063 * satisfy the constraint
2064 * separate no (integer) point of the other basic map
2065 * satisfies the constraint
2066 * cut some but not all points of the other basic map
2067 * satisfy the constraint
2068 * adj_eq the given constraint is adjacent (on the outside)
2069 * to an equality of the other basic map
2070 * adj_ineq the given constraint is adjacent (on the outside)
2071 * to an inequality of the other basic map
2073 * We consider seven cases in which we can replace the pair by a single
2074 * basic map. We ignore all "redundant" constraints.
2076 * 1. all constraints of one basic map are valid
2077 * => the other basic map is a subset and can be removed
2079 * 2. all constraints of both basic maps are either "valid" or "cut"
2080 * and the facets corresponding to the "cut" constraints
2081 * of one of the basic maps lies entirely inside the other basic map
2082 * => the pair can be replaced by a basic map consisting
2083 * of the valid constraints in both basic maps
2085 * 3. there is a single pair of adjacent inequalities
2086 * (all other constraints are "valid")
2087 * => the pair can be replaced by a basic map consisting
2088 * of the valid constraints in both basic maps
2090 * 4. one basic map has a single adjacent inequality, while the other
2091 * constraints are "valid". The other basic map has some
2092 * "cut" constraints, but replacing the adjacent inequality by
2093 * its opposite and adding the valid constraints of the other
2094 * basic map results in a subset of the other basic map
2095 * => the pair can be replaced by a basic map consisting
2096 * of the valid constraints in both basic maps
2098 * 5. there is a single adjacent pair of an inequality and an equality,
2099 * the other constraints of the basic map containing the inequality are
2100 * "valid". Moreover, if the inequality the basic map is relaxed
2101 * and then turned into an equality, then resulting facet lies
2102 * entirely inside the other basic map
2103 * => the pair can be replaced by the basic map containing
2104 * the inequality, with the inequality relaxed.
2106 * 6. there is a single adjacent pair of an inequality and an equality,
2107 * the other constraints of the basic map containing the inequality are
2108 * "valid". Moreover, the facets corresponding to both
2109 * the inequality and the equality can be wrapped around their
2110 * ridges to include the other basic map
2111 * => the pair can be replaced by a basic map consisting
2112 * of the valid constraints in both basic maps together
2113 * with all wrapping constraints
2115 * 7. one of the basic maps extends beyond the other by at most one.
2116 * Moreover, the facets corresponding to the cut constraints and
2117 * the pieces of the other basic map at offset one from these cut
2118 * constraints can be wrapped around their ridges to include
2119 * the union of the two basic maps
2120 * => the pair can be replaced by a basic map consisting
2121 * of the valid constraints in both basic maps together
2122 * with all wrapping constraints
2124 * 8. the two basic maps live in adjacent hyperplanes. In principle
2125 * such sets can always be combined through wrapping, but we impose
2126 * that there is only one such pair, to avoid overeager coalescing.
2128 * Throughout the computation, we maintain a collection of tableaus
2129 * corresponding to the basic maps. When the basic maps are dropped
2130 * or combined, the tableaus are modified accordingly.
2132 static enum isl_change
coalesce_local_pair_reuse(int i
, int j
,
2133 struct isl_coalesce_info
*info
)
2135 enum isl_change change
= isl_change_none
;
2137 set_ineq_status_in(&info
[i
], info
[j
].tab
);
2138 if (info
[i
].bmap
->n_ineq
&& !info
[i
].ineq
)
2140 if (any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ERROR
))
2142 if (any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_SEPARATE
))
2145 set_ineq_status_in(&info
[j
], info
[i
].tab
);
2146 if (info
[j
].bmap
->n_ineq
&& !info
[j
].ineq
)
2148 if (any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_ERROR
))
2150 if (any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_SEPARATE
))
2153 set_eq_status_in(&info
[i
], info
[j
].tab
);
2154 if (info
[i
].bmap
->n_eq
&& !info
[i
].eq
)
2156 if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_ERROR
))
2159 set_eq_status_in(&info
[j
], info
[i
].tab
);
2160 if (info
[j
].bmap
->n_eq
&& !info
[j
].eq
)
2162 if (any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_ERROR
))
2165 if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_SEPARATE
))
2166 return separating_equality(i
, j
, info
);
2167 if (any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_SEPARATE
))
2168 return separating_equality(j
, i
, info
);
2170 if (all(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_VALID
) &&
2171 all(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_VALID
)) {
2173 change
= isl_change_drop_second
;
2174 } else if (all(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_VALID
) &&
2175 all(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_VALID
)) {
2177 change
= isl_change_drop_first
;
2178 } else if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_ADJ_EQ
)) {
2179 change
= check_eq_adj_eq(i
, j
, info
);
2180 } else if (any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_ADJ_EQ
)) {
2181 change
= check_eq_adj_eq(j
, i
, info
);
2182 } else if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_ADJ_INEQ
) ||
2183 any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_ADJ_INEQ
)) {
2184 change
= check_adj_eq(i
, j
, info
);
2185 } else if (any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ADJ_EQ
) ||
2186 any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_ADJ_EQ
)) {
2189 } else if (any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ADJ_INEQ
) ||
2190 any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_ADJ_INEQ
)) {
2191 change
= check_adj_ineq(i
, j
, info
);
2193 if (!any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_CUT
) &&
2194 !any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_CUT
))
2195 change
= check_facets(i
, j
, info
);
2196 if (change
== isl_change_none
)
2197 change
= check_wrap(i
, j
, info
);
2201 clear_status(&info
[i
]);
2202 clear_status(&info
[j
]);
2205 clear_status(&info
[i
]);
2206 clear_status(&info
[j
]);
2207 return isl_change_error
;
2210 /* Check if the union of the given pair of basic maps
2211 * can be represented by a single basic map.
2212 * If so, replace the pair by the single basic map and return
2213 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
2214 * Otherwise, return isl_change_none.
2215 * The two basic maps are assumed to live in the same local space.
2217 static enum isl_change
coalesce_local_pair(int i
, int j
,
2218 struct isl_coalesce_info
*info
)
2220 init_status(&info
[i
]);
2221 init_status(&info
[j
]);
2222 return coalesce_local_pair_reuse(i
, j
, info
);
2225 /* Shift the integer division at position "div" of the basic map
2226 * represented by "info" by "shift".
2228 * That is, if the integer division has the form
2232 * then replace it by
2234 * floor((f(x) + shift * d)/d) - shift
2236 static isl_stat
shift_div(struct isl_coalesce_info
*info
, int div
,
2241 info
->bmap
= isl_basic_map_shift_div(info
->bmap
, div
, 0, shift
);
2243 return isl_stat_error
;
2245 total
= isl_basic_map_dim(info
->bmap
, isl_dim_all
);
2246 total
-= isl_basic_map_dim(info
->bmap
, isl_dim_div
);
2247 if (isl_tab_shift_var(info
->tab
, total
+ div
, shift
) < 0)
2248 return isl_stat_error
;
2253 /* If the integer division at position "div" is defined by an equality,
2254 * i.e., a stride constraint, then change the integer division expression
2255 * to have a constant term equal to zero.
2257 * Let the equality constraint be
2261 * The integer division expression is then of the form
2263 * a = floor((-f - c')/m)
2265 * The integer division is first shifted by t = floor(c/m),
2266 * turning the equality constraint into
2268 * c - m floor(c/m) + f + m a' = 0
2272 * (c mod m) + f + m a' = 0
2276 * a' = (-f - (c mod m))/m = floor((-f)/m)
2278 * because a' is an integer and 0 <= (c mod m) < m.
2279 * The constant term of a' can therefore be zeroed out.
2281 static isl_stat
normalize_stride_div(struct isl_coalesce_info
*info
, int div
)
2286 isl_int shift
, stride
;
2288 defined
= isl_basic_map_has_defining_equality(info
->bmap
, isl_dim_div
,
2291 return isl_stat_error
;
2295 return isl_stat_error
;
2296 isl_int_init(shift
);
2297 isl_int_init(stride
);
2298 isl_constraint_get_constant(c
, &shift
);
2299 isl_constraint_get_coefficient(c
, isl_dim_div
, div
, &stride
);
2300 isl_int_fdiv_q(shift
, shift
, stride
);
2301 r
= shift_div(info
, div
, shift
);
2302 isl_int_clear(stride
);
2303 isl_int_clear(shift
);
2304 isl_constraint_free(c
);
2306 return isl_stat_error
;
2307 info
->bmap
= isl_basic_map_set_div_expr_constant_num_si_inplace(
2308 info
->bmap
, div
, 0);
2310 return isl_stat_error
;
2314 /* The basic maps represented by "info1" and "info2" are known
2315 * to have the same number of integer divisions.
2316 * Check if pairs of integer divisions are equal to each other
2317 * despite the fact that they differ by a rational constant.
2319 * In particular, look for any pair of integer divisions that
2320 * only differ in their constant terms.
2321 * If either of these integer divisions is defined
2322 * by stride constraints, then modify it to have a zero constant term.
2323 * If both are defined by stride constraints then in the end they will have
2324 * the same (zero) constant term.
2326 static isl_stat
harmonize_stride_divs(struct isl_coalesce_info
*info1
,
2327 struct isl_coalesce_info
*info2
)
2332 total
= isl_basic_map_total_dim(info1
->bmap
);
2333 n
= isl_basic_map_dim(info1
->bmap
, isl_dim_div
);
2334 for (i
= 0; i
< n
; ++i
) {
2335 isl_bool known
, harmonize
;
2337 known
= isl_basic_map_div_is_known(info1
->bmap
, i
);
2338 if (known
>= 0 && known
)
2339 known
= isl_basic_map_div_is_known(info2
->bmap
, i
);
2341 return isl_stat_error
;
2344 harmonize
= isl_basic_map_equal_div_expr_except_constant(
2345 info1
->bmap
, i
, info2
->bmap
, i
);
2347 return isl_stat_error
;
2350 if (normalize_stride_div(info1
, i
) < 0)
2351 return isl_stat_error
;
2352 if (normalize_stride_div(info2
, i
) < 0)
2353 return isl_stat_error
;
2359 /* If "shift" is an integer constant, then shift the integer division
2360 * at position "div" of the basic map represented by "info" by "shift".
2361 * If "shift" is not an integer constant, then do nothing.
2362 * If "shift" is equal to zero, then no shift needs to be performed either.
2364 * That is, if the integer division has the form
2368 * then replace it by
2370 * floor((f(x) + shift * d)/d) - shift
2372 static isl_stat
shift_if_cst_int(struct isl_coalesce_info
*info
, int div
,
2373 __isl_keep isl_aff
*shift
)
2380 cst
= isl_aff_is_cst(shift
);
2381 if (cst
< 0 || !cst
)
2382 return cst
< 0 ? isl_stat_error
: isl_stat_ok
;
2384 c
= isl_aff_get_constant_val(shift
);
2385 cst
= isl_val_is_int(c
);
2386 if (cst
>= 0 && cst
)
2387 cst
= isl_bool_not(isl_val_is_zero(c
));
2388 if (cst
< 0 || !cst
) {
2390 return cst
< 0 ? isl_stat_error
: isl_stat_ok
;
2394 r
= isl_val_get_num_isl_int(c
, &d
);
2396 r
= shift_div(info
, div
, d
);
2404 /* Check if some of the divs in the basic map represented by "info1"
2405 * are shifts of the corresponding divs in the basic map represented
2406 * by "info2", taking into account the equality constraints "eq1" of "info1"
2407 * and "eq2" of "info2". If so, align them with those of "info2".
2408 * "info1" and "info2" are assumed to have the same number
2409 * of integer divisions.
2411 * An integer division is considered to be a shift of another integer
2412 * division if, after simplification with respect to the equality
2413 * constraints of the other basic map, one is equal to the other
2416 * In particular, for each pair of integer divisions, if both are known,
2417 * have the same denominator and are not already equal to each other,
2418 * simplify each with respect to the equality constraints
2419 * of the other basic map. If the difference is an integer constant,
2420 * then move this difference outside.
2421 * That is, if, after simplification, one integer division is of the form
2423 * floor((f(x) + c_1)/d)
2425 * while the other is of the form
2427 * floor((f(x) + c_2)/d)
2429 * and n = (c_2 - c_1)/d is an integer, then replace the first
2430 * integer division by
2432 * floor((f_1(x) + c_1 + n * d)/d) - n,
2434 * where floor((f_1(x) + c_1 + n * d)/d) = floor((f2(x) + c_2)/d)
2435 * after simplification with respect to the equality constraints.
2437 static isl_stat
harmonize_divs_with_hulls(struct isl_coalesce_info
*info1
,
2438 struct isl_coalesce_info
*info2
, __isl_keep isl_basic_set
*eq1
,
2439 __isl_keep isl_basic_set
*eq2
)
2443 isl_local_space
*ls1
, *ls2
;
2445 total
= isl_basic_map_total_dim(info1
->bmap
);
2446 ls1
= isl_local_space_wrap(isl_basic_map_get_local_space(info1
->bmap
));
2447 ls2
= isl_local_space_wrap(isl_basic_map_get_local_space(info2
->bmap
));
2448 for (i
= 0; i
< info1
->bmap
->n_div
; ++i
) {
2450 isl_aff
*div1
, *div2
;
2452 if (!isl_local_space_div_is_known(ls1
, i
) ||
2453 !isl_local_space_div_is_known(ls2
, i
))
2455 if (isl_int_ne(info1
->bmap
->div
[i
][0], info2
->bmap
->div
[i
][0]))
2457 if (isl_seq_eq(info1
->bmap
->div
[i
] + 1,
2458 info2
->bmap
->div
[i
] + 1, 1 + total
))
2460 div1
= isl_local_space_get_div(ls1
, i
);
2461 div2
= isl_local_space_get_div(ls2
, i
);
2462 div1
= isl_aff_substitute_equalities(div1
,
2463 isl_basic_set_copy(eq2
));
2464 div2
= isl_aff_substitute_equalities(div2
,
2465 isl_basic_set_copy(eq1
));
2466 div2
= isl_aff_sub(div2
, div1
);
2467 r
= shift_if_cst_int(info1
, i
, div2
);
2472 isl_local_space_free(ls1
);
2473 isl_local_space_free(ls2
);
2475 if (i
< info1
->bmap
->n_div
)
2476 return isl_stat_error
;
2480 /* Check if some of the divs in the basic map represented by "info1"
2481 * are shifts of the corresponding divs in the basic map represented
2482 * by "info2". If so, align them with those of "info2".
2483 * Only do this if "info1" and "info2" have the same number
2484 * of integer divisions.
2486 * An integer division is considered to be a shift of another integer
2487 * division if, after simplification with respect to the equality
2488 * constraints of the other basic map, one is equal to the other
2491 * First check if pairs of integer divisions are equal to each other
2492 * despite the fact that they differ by a rational constant.
2493 * If so, try and arrange for them to have the same constant term.
2495 * Then, extract the equality constraints and continue with
2496 * harmonize_divs_with_hulls.
2498 * If the equality constraints of both basic maps are the same,
2499 * then there is no need to perform any shifting since
2500 * the coefficients of the integer divisions should have been
2501 * reduced in the same way.
2503 static isl_stat
harmonize_divs(struct isl_coalesce_info
*info1
,
2504 struct isl_coalesce_info
*info2
)
2507 isl_basic_map
*bmap1
, *bmap2
;
2508 isl_basic_set
*eq1
, *eq2
;
2511 if (!info1
->bmap
|| !info2
->bmap
)
2512 return isl_stat_error
;
2514 if (info1
->bmap
->n_div
!= info2
->bmap
->n_div
)
2516 if (info1
->bmap
->n_div
== 0)
2519 if (harmonize_stride_divs(info1
, info2
) < 0)
2520 return isl_stat_error
;
2522 bmap1
= isl_basic_map_copy(info1
->bmap
);
2523 bmap2
= isl_basic_map_copy(info2
->bmap
);
2524 eq1
= isl_basic_map_wrap(isl_basic_map_plain_affine_hull(bmap1
));
2525 eq2
= isl_basic_map_wrap(isl_basic_map_plain_affine_hull(bmap2
));
2526 equal
= isl_basic_set_plain_is_equal(eq1
, eq2
);
2532 r
= harmonize_divs_with_hulls(info1
, info2
, eq1
, eq2
);
2533 isl_basic_set_free(eq1
);
2534 isl_basic_set_free(eq2
);
2539 /* Do the two basic maps live in the same local space, i.e.,
2540 * do they have the same (known) divs?
2541 * If either basic map has any unknown divs, then we can only assume
2542 * that they do not live in the same local space.
2544 static int same_divs(__isl_keep isl_basic_map
*bmap1
,
2545 __isl_keep isl_basic_map
*bmap2
)
2551 if (!bmap1
|| !bmap2
)
2553 if (bmap1
->n_div
!= bmap2
->n_div
)
2556 if (bmap1
->n_div
== 0)
2559 known
= isl_basic_map_divs_known(bmap1
);
2560 if (known
< 0 || !known
)
2562 known
= isl_basic_map_divs_known(bmap2
);
2563 if (known
< 0 || !known
)
2566 total
= isl_basic_map_total_dim(bmap1
);
2567 for (i
= 0; i
< bmap1
->n_div
; ++i
)
2568 if (!isl_seq_eq(bmap1
->div
[i
], bmap2
->div
[i
], 2 + total
))
2574 /* Assuming that "tab" contains the equality constraints and
2575 * the initial inequality constraints of "bmap", copy the remaining
2576 * inequality constraints of "bmap" to "Tab".
2578 static isl_stat
copy_ineq(struct isl_tab
*tab
, __isl_keep isl_basic_map
*bmap
)
2583 return isl_stat_error
;
2585 n_ineq
= tab
->n_con
- tab
->n_eq
;
2586 for (i
= n_ineq
; i
< bmap
->n_ineq
; ++i
)
2587 if (isl_tab_add_ineq(tab
, bmap
->ineq
[i
]) < 0)
2588 return isl_stat_error
;
2593 /* Description of an integer division that is added
2594 * during an expansion.
2595 * "pos" is the position of the corresponding variable.
2596 * "cst" indicates whether this integer division has a fixed value.
2597 * "val" contains the fixed value, if the value is fixed.
2599 struct isl_expanded
{
2605 /* For each of the "n" integer division variables "expanded",
2606 * if the variable has a fixed value, then add two inequality
2607 * constraints expressing the fixed value.
2608 * Otherwise, add the corresponding div constraints.
2609 * The caller is responsible for removing the div constraints
2610 * that it added for all these "n" integer divisions.
2612 * The div constraints and the pair of inequality constraints
2613 * forcing the fixed value cannot both be added for a given variable
2614 * as the combination may render some of the original constraints redundant.
2615 * These would then be ignored during the coalescing detection,
2616 * while they could remain in the fused result.
2618 * The two added inequality constraints are
2623 * with "a" the variable and "v" its fixed value.
2624 * The facet corresponding to one of these two constraints is selected
2625 * in the tableau to ensure that the pair of inequality constraints
2626 * is treated as an equality constraint.
2628 * The information in info->ineq is thrown away because it was
2629 * computed in terms of div constraints, while some of those
2630 * have now been replaced by these pairs of inequality constraints.
2632 static isl_stat
fix_constant_divs(struct isl_coalesce_info
*info
,
2633 int n
, struct isl_expanded
*expanded
)
2639 o_div
= isl_basic_map_offset(info
->bmap
, isl_dim_div
) - 1;
2640 ineq
= isl_vec_alloc(isl_tab_get_ctx(info
->tab
), 1 + info
->tab
->n_var
);
2642 return isl_stat_error
;
2643 isl_seq_clr(ineq
->el
+ 1, info
->tab
->n_var
);
2645 for (i
= 0; i
< n
; ++i
) {
2646 if (!expanded
[i
].cst
) {
2647 info
->bmap
= isl_basic_map_extend_constraints(
2649 if (isl_basic_map_add_div_constraints(info
->bmap
,
2650 expanded
[i
].pos
- o_div
) < 0)
2653 isl_int_set_si(ineq
->el
[1 + expanded
[i
].pos
], -1);
2654 isl_int_set(ineq
->el
[0], expanded
[i
].val
);
2655 info
->bmap
= isl_basic_map_add_ineq(info
->bmap
,
2657 isl_int_set_si(ineq
->el
[1 + expanded
[i
].pos
], 1);
2658 isl_int_neg(ineq
->el
[0], expanded
[i
].val
);
2659 info
->bmap
= isl_basic_map_add_ineq(info
->bmap
,
2661 isl_int_set_si(ineq
->el
[1 + expanded
[i
].pos
], 0);
2663 if (copy_ineq(info
->tab
, info
->bmap
) < 0)
2665 if (expanded
[i
].cst
&&
2666 isl_tab_select_facet(info
->tab
, info
->tab
->n_con
- 1) < 0)
2675 return i
< n
? isl_stat_error
: isl_stat_ok
;
2678 /* Insert the "n" integer division variables "expanded"
2679 * into info->tab and info->bmap and
2680 * update info->ineq with respect to the redundant constraints
2681 * in the resulting tableau.
2682 * "bmap" contains the result of this insertion in info->bmap,
2683 * while info->bmap is the original version
2684 * of "bmap", i.e., the one that corresponds to the current
2685 * state of info->tab. The number of constraints in info->bmap
2686 * is assumed to be the same as the number of constraints
2687 * in info->tab. This is required to be able to detect
2688 * the extra constraints in "bmap".
2690 * In particular, introduce extra variables corresponding
2691 * to the extra integer divisions and add the div constraints
2692 * that were added to "bmap" after info->tab was created
2694 * Furthermore, check if these extra integer divisions happen
2695 * to attain a fixed integer value in info->tab.
2696 * If so, replace the corresponding div constraints by pairs
2697 * of inequality constraints that fix these
2698 * integer divisions to their single integer values.
2699 * Replace info->bmap by "bmap" to match the changes to info->tab.
2700 * info->ineq was computed without a tableau and therefore
2701 * does not take into account the redundant constraints
2702 * in the tableau. Mark them here.
2703 * There is no need to check the newly added div constraints
2704 * since they cannot be redundant.
2705 * The redundancy check is not performed when constants have been discovered
2706 * since info->ineq is completely thrown away in this case.
2708 static isl_stat
tab_insert_divs(struct isl_coalesce_info
*info
,
2709 int n
, struct isl_expanded
*expanded
, __isl_take isl_basic_map
*bmap
)
2713 struct isl_tab_undo
*snap
;
2717 return isl_stat_error
;
2718 if (info
->bmap
->n_eq
+ info
->bmap
->n_ineq
!= info
->tab
->n_con
)
2719 isl_die(isl_basic_map_get_ctx(bmap
), isl_error_internal
,
2720 "original tableau does not correspond "
2721 "to original basic map", goto error
);
2723 if (isl_tab_extend_vars(info
->tab
, n
) < 0)
2725 if (isl_tab_extend_cons(info
->tab
, 2 * n
) < 0)
2728 for (i
= 0; i
< n
; ++i
) {
2729 if (isl_tab_insert_var(info
->tab
, expanded
[i
].pos
) < 0)
2733 snap
= isl_tab_snap(info
->tab
);
2735 n_ineq
= info
->tab
->n_con
- info
->tab
->n_eq
;
2736 if (copy_ineq(info
->tab
, bmap
) < 0)
2739 isl_basic_map_free(info
->bmap
);
2743 for (i
= 0; i
< n
; ++i
) {
2744 expanded
[i
].cst
= isl_tab_is_constant(info
->tab
,
2745 expanded
[i
].pos
, &expanded
[i
].val
);
2746 if (expanded
[i
].cst
< 0)
2747 return isl_stat_error
;
2748 if (expanded
[i
].cst
)
2753 if (isl_tab_rollback(info
->tab
, snap
) < 0)
2754 return isl_stat_error
;
2755 info
->bmap
= isl_basic_map_cow(info
->bmap
);
2756 if (isl_basic_map_free_inequality(info
->bmap
, 2 * n
) < 0)
2757 return isl_stat_error
;
2759 return fix_constant_divs(info
, n
, expanded
);
2762 n_eq
= info
->bmap
->n_eq
;
2763 for (i
= 0; i
< n_ineq
; ++i
) {
2764 if (isl_tab_is_redundant(info
->tab
, n_eq
+ i
))
2765 info
->ineq
[i
] = STATUS_REDUNDANT
;
2770 isl_basic_map_free(bmap
);
2771 return isl_stat_error
;
2774 /* Expand info->tab and info->bmap in the same way "bmap" was expanded
2775 * in isl_basic_map_expand_divs using the expansion "exp" and
2776 * update info->ineq with respect to the redundant constraints
2777 * in the resulting tableau. info->bmap is the original version
2778 * of "bmap", i.e., the one that corresponds to the current
2779 * state of info->tab. The number of constraints in info->bmap
2780 * is assumed to be the same as the number of constraints
2781 * in info->tab. This is required to be able to detect
2782 * the extra constraints in "bmap".
2784 * Extract the positions where extra local variables are introduced
2785 * from "exp" and call tab_insert_divs.
2787 static isl_stat
expand_tab(struct isl_coalesce_info
*info
, int *exp
,
2788 __isl_take isl_basic_map
*bmap
)
2791 struct isl_expanded
*expanded
;
2794 unsigned total
, pos
, n_div
;
2797 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
2798 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
2799 pos
= total
- n_div
;
2800 extra_var
= total
- info
->tab
->n_var
;
2801 n
= n_div
- extra_var
;
2803 ctx
= isl_basic_map_get_ctx(bmap
);
2804 expanded
= isl_calloc_array(ctx
, struct isl_expanded
, extra_var
);
2805 if (extra_var
&& !expanded
)
2810 for (j
= 0; j
< n_div
; ++j
) {
2811 if (i
< n
&& exp
[i
] == j
) {
2815 expanded
[k
++].pos
= pos
+ j
;
2818 for (k
= 0; k
< extra_var
; ++k
)
2819 isl_int_init(expanded
[k
].val
);
2821 r
= tab_insert_divs(info
, extra_var
, expanded
, bmap
);
2823 for (k
= 0; k
< extra_var
; ++k
)
2824 isl_int_clear(expanded
[k
].val
);
2829 isl_basic_map_free(bmap
);
2830 return isl_stat_error
;
2833 /* Check if the union of the basic maps represented by info[i] and info[j]
2834 * can be represented by a single basic map,
2835 * after expanding the divs of info[i] to match those of info[j].
2836 * If so, replace the pair by the single basic map and return
2837 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
2838 * Otherwise, return isl_change_none.
2840 * The caller has already checked for info[j] being a subset of info[i].
2841 * If some of the divs of info[j] are unknown, then the expanded info[i]
2842 * will not have the corresponding div constraints. The other patterns
2843 * therefore cannot apply. Skip the computation in this case.
2845 * The expansion is performed using the divs "div" and expansion "exp"
2846 * computed by the caller.
2847 * info[i].bmap has already been expanded and the result is passed in
2849 * The "eq" and "ineq" fields of info[i] reflect the status of
2850 * the constraints of the expanded "bmap" with respect to info[j].tab.
2851 * However, inequality constraints that are redundant in info[i].tab
2852 * have not yet been marked as such because no tableau was available.
2854 * Replace info[i].bmap by "bmap" and expand info[i].tab as well,
2855 * updating info[i].ineq with respect to the redundant constraints.
2856 * Then try and coalesce the expanded info[i] with info[j],
2857 * reusing the information in info[i].eq and info[i].ineq.
2858 * If this does not result in any coalescing or if it results in info[j]
2859 * getting dropped (which should not happen in practice, since the case
2860 * of info[j] being a subset of info[i] has already been checked by
2861 * the caller), then revert info[i] to its original state.
2863 static enum isl_change
coalesce_expand_tab_divs(__isl_take isl_basic_map
*bmap
,
2864 int i
, int j
, struct isl_coalesce_info
*info
, __isl_keep isl_mat
*div
,
2868 isl_basic_map
*bmap_i
;
2869 struct isl_tab_undo
*snap
;
2870 enum isl_change change
= isl_change_none
;
2872 known
= isl_basic_map_divs_known(info
[j
].bmap
);
2873 if (known
< 0 || !known
) {
2874 clear_status(&info
[i
]);
2875 isl_basic_map_free(bmap
);
2876 return known
< 0 ? isl_change_error
: isl_change_none
;
2879 bmap_i
= isl_basic_map_copy(info
[i
].bmap
);
2880 snap
= isl_tab_snap(info
[i
].tab
);
2881 if (expand_tab(&info
[i
], exp
, bmap
) < 0)
2882 change
= isl_change_error
;
2884 init_status(&info
[j
]);
2885 if (change
== isl_change_none
)
2886 change
= coalesce_local_pair_reuse(i
, j
, info
);
2888 clear_status(&info
[i
]);
2889 if (change
!= isl_change_none
&& change
!= isl_change_drop_second
) {
2890 isl_basic_map_free(bmap_i
);
2892 isl_basic_map_free(info
[i
].bmap
);
2893 info
[i
].bmap
= bmap_i
;
2895 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
2896 change
= isl_change_error
;
2902 /* Check if the union of "bmap" and the basic map represented by info[j]
2903 * can be represented by a single basic map,
2904 * after expanding the divs of "bmap" to match those of info[j].
2905 * If so, replace the pair by the single basic map and return
2906 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
2907 * Otherwise, return isl_change_none.
2909 * In particular, check if the expanded "bmap" contains the basic map
2910 * represented by the tableau info[j].tab.
2911 * The expansion is performed using the divs "div" and expansion "exp"
2912 * computed by the caller.
2913 * Then we check if all constraints of the expanded "bmap" are valid for
2916 * If "i" is not equal to -1, then "bmap" is equal to info[i].bmap.
2917 * In this case, the positions of the constraints of info[i].bmap
2918 * with respect to the basic map represented by info[j] are stored
2921 * If the expanded "bmap" does not contain the basic map
2922 * represented by the tableau info[j].tab and if "i" is not -1,
2923 * i.e., if the original "bmap" is info[i].bmap, then expand info[i].tab
2924 * as well and check if that results in coalescing.
2926 static enum isl_change
coalesce_with_expanded_divs(
2927 __isl_keep isl_basic_map
*bmap
, int i
, int j
,
2928 struct isl_coalesce_info
*info
, __isl_keep isl_mat
*div
, int *exp
)
2930 enum isl_change change
= isl_change_none
;
2931 struct isl_coalesce_info info_local
, *info_i
;
2933 info_i
= i
>= 0 ? &info
[i
] : &info_local
;
2934 init_status(info_i
);
2935 bmap
= isl_basic_map_copy(bmap
);
2936 bmap
= isl_basic_map_expand_divs(bmap
, isl_mat_copy(div
), exp
);
2937 bmap
= isl_basic_map_mark_final(bmap
);
2942 info_i
->eq
= eq_status_in(bmap
, info
[j
].tab
);
2943 if (bmap
->n_eq
&& !info_i
->eq
)
2945 if (any(info_i
->eq
, 2 * bmap
->n_eq
, STATUS_ERROR
))
2947 if (any(info_i
->eq
, 2 * bmap
->n_eq
, STATUS_SEPARATE
))
2950 info_i
->ineq
= ineq_status_in(bmap
, NULL
, info
[j
].tab
);
2951 if (bmap
->n_ineq
&& !info_i
->ineq
)
2953 if (any(info_i
->ineq
, bmap
->n_ineq
, STATUS_ERROR
))
2955 if (any(info_i
->ineq
, bmap
->n_ineq
, STATUS_SEPARATE
))
2958 if (all(info_i
->eq
, 2 * bmap
->n_eq
, STATUS_VALID
) &&
2959 all(info_i
->ineq
, bmap
->n_ineq
, STATUS_VALID
)) {
2961 change
= isl_change_drop_second
;
2964 if (change
== isl_change_none
&& i
!= -1)
2965 return coalesce_expand_tab_divs(bmap
, i
, j
, info
, div
, exp
);
2968 isl_basic_map_free(bmap
);
2969 clear_status(info_i
);
2972 isl_basic_map_free(bmap
);
2973 clear_status(info_i
);
2974 return isl_change_error
;
2977 /* Check if the union of "bmap_i" and the basic map represented by info[j]
2978 * can be represented by a single basic map,
2979 * after aligning the divs of "bmap_i" to match those of info[j].
2980 * If so, replace the pair by the single basic map and return
2981 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
2982 * Otherwise, return isl_change_none.
2984 * In particular, check if "bmap_i" contains the basic map represented by
2985 * info[j] after aligning the divs of "bmap_i" to those of info[j].
2986 * Note that this can only succeed if the number of divs of "bmap_i"
2987 * is smaller than (or equal to) the number of divs of info[j].
2989 * We first check if the divs of "bmap_i" are all known and form a subset
2990 * of those of info[j].bmap. If so, we pass control over to
2991 * coalesce_with_expanded_divs.
2993 * If "i" is not equal to -1, then "bmap" is equal to info[i].bmap.
2995 static enum isl_change
coalesce_after_aligning_divs(
2996 __isl_keep isl_basic_map
*bmap_i
, int i
, int j
,
2997 struct isl_coalesce_info
*info
)
3000 isl_mat
*div_i
, *div_j
, *div
;
3004 enum isl_change change
;
3006 known
= isl_basic_map_divs_known(bmap_i
);
3007 if (known
< 0 || !known
)
3010 ctx
= isl_basic_map_get_ctx(bmap_i
);
3012 div_i
= isl_basic_map_get_divs(bmap_i
);
3013 div_j
= isl_basic_map_get_divs(info
[j
].bmap
);
3015 if (!div_i
|| !div_j
)
3018 exp1
= isl_alloc_array(ctx
, int, div_i
->n_row
);
3019 exp2
= isl_alloc_array(ctx
, int, div_j
->n_row
);
3020 if ((div_i
->n_row
&& !exp1
) || (div_j
->n_row
&& !exp2
))
3023 div
= isl_merge_divs(div_i
, div_j
, exp1
, exp2
);
3027 if (div
->n_row
== div_j
->n_row
)
3028 change
= coalesce_with_expanded_divs(bmap_i
,
3029 i
, j
, info
, div
, exp1
);
3031 change
= isl_change_none
;
3035 isl_mat_free(div_i
);
3036 isl_mat_free(div_j
);
3043 isl_mat_free(div_i
);
3044 isl_mat_free(div_j
);
3047 return isl_change_error
;
3050 /* Check if basic map "j" is a subset of basic map "i" after
3051 * exploiting the extra equalities of "j" to simplify the divs of "i".
3052 * If so, remove basic map "j" and return isl_change_drop_second.
3054 * If "j" does not have any equalities or if they are the same
3055 * as those of "i", then we cannot exploit them to simplify the divs.
3056 * Similarly, if there are no divs in "i", then they cannot be simplified.
3057 * If, on the other hand, the affine hulls of "i" and "j" do not intersect,
3058 * then "j" cannot be a subset of "i".
3060 * Otherwise, we intersect "i" with the affine hull of "j" and then
3061 * check if "j" is a subset of the result after aligning the divs.
3062 * If so, then "j" is definitely a subset of "i" and can be removed.
3063 * Note that if after intersection with the affine hull of "j".
3064 * "i" still has more divs than "j", then there is no way we can
3065 * align the divs of "i" to those of "j".
3067 static enum isl_change
coalesce_subset_with_equalities(int i
, int j
,
3068 struct isl_coalesce_info
*info
)
3070 isl_basic_map
*hull_i
, *hull_j
, *bmap_i
;
3072 enum isl_change change
;
3074 if (info
[j
].bmap
->n_eq
== 0)
3075 return isl_change_none
;
3076 if (info
[i
].bmap
->n_div
== 0)
3077 return isl_change_none
;
3079 hull_i
= isl_basic_map_copy(info
[i
].bmap
);
3080 hull_i
= isl_basic_map_plain_affine_hull(hull_i
);
3081 hull_j
= isl_basic_map_copy(info
[j
].bmap
);
3082 hull_j
= isl_basic_map_plain_affine_hull(hull_j
);
3084 hull_j
= isl_basic_map_intersect(hull_j
, isl_basic_map_copy(hull_i
));
3085 equal
= isl_basic_map_plain_is_equal(hull_i
, hull_j
);
3086 empty
= isl_basic_map_plain_is_empty(hull_j
);
3087 isl_basic_map_free(hull_i
);
3089 if (equal
< 0 || equal
|| empty
< 0 || empty
) {
3090 isl_basic_map_free(hull_j
);
3091 if (equal
< 0 || empty
< 0)
3092 return isl_change_error
;
3093 return isl_change_none
;
3096 bmap_i
= isl_basic_map_copy(info
[i
].bmap
);
3097 bmap_i
= isl_basic_map_intersect(bmap_i
, hull_j
);
3099 return isl_change_error
;
3101 if (bmap_i
->n_div
> info
[j
].bmap
->n_div
) {
3102 isl_basic_map_free(bmap_i
);
3103 return isl_change_none
;
3106 change
= coalesce_after_aligning_divs(bmap_i
, -1, j
, info
);
3108 isl_basic_map_free(bmap_i
);
3113 /* Check if the union of and the basic maps represented by info[i] and info[j]
3114 * can be represented by a single basic map, by aligning or equating
3115 * their integer divisions.
3116 * If so, replace the pair by the single basic map and return
3117 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
3118 * Otherwise, return isl_change_none.
3120 * Note that we only perform any test if the number of divs is different
3121 * in the two basic maps. In case the number of divs is the same,
3122 * we have already established that the divs are different
3123 * in the two basic maps.
3124 * In particular, if the number of divs of basic map i is smaller than
3125 * the number of divs of basic map j, then we check if j is a subset of i
3128 static enum isl_change
coalesce_divs(int i
, int j
,
3129 struct isl_coalesce_info
*info
)
3131 enum isl_change change
= isl_change_none
;
3133 if (info
[i
].bmap
->n_div
< info
[j
].bmap
->n_div
)
3134 change
= coalesce_after_aligning_divs(info
[i
].bmap
, i
, j
, info
);
3135 if (change
!= isl_change_none
)
3138 if (info
[j
].bmap
->n_div
< info
[i
].bmap
->n_div
)
3139 change
= coalesce_after_aligning_divs(info
[j
].bmap
, j
, i
, info
);
3140 if (change
!= isl_change_none
)
3141 return invert_change(change
);
3143 change
= coalesce_subset_with_equalities(i
, j
, info
);
3144 if (change
!= isl_change_none
)
3147 change
= coalesce_subset_with_equalities(j
, i
, info
);
3148 if (change
!= isl_change_none
)
3149 return invert_change(change
);
3151 return isl_change_none
;
3154 /* Does "bmap" involve any divs that themselves refer to divs?
3156 static int has_nested_div(__isl_keep isl_basic_map
*bmap
)
3162 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
3163 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
3166 for (i
= 0; i
< n_div
; ++i
)
3167 if (isl_seq_first_non_zero(bmap
->div
[i
] + 2 + total
,
3174 /* Return a list of affine expressions, one for each integer division
3175 * in "bmap_i". For each integer division that also appears in "bmap_j",
3176 * the affine expression is set to NaN. The number of NaNs in the list
3177 * is equal to the number of integer divisions in "bmap_j".
3178 * For the other integer divisions of "bmap_i", the corresponding
3179 * element in the list is a purely affine expression equal to the integer
3180 * division in "hull".
3181 * If no such list can be constructed, then the number of elements
3182 * in the returned list is smaller than the number of integer divisions
3185 static __isl_give isl_aff_list
*set_up_substitutions(
3186 __isl_keep isl_basic_map
*bmap_i
, __isl_keep isl_basic_map
*bmap_j
,
3187 __isl_take isl_basic_map
*hull
)
3189 unsigned n_div_i
, n_div_j
, total
;
3191 isl_local_space
*ls
;
3192 isl_basic_set
*wrap_hull
;
3200 ctx
= isl_basic_map_get_ctx(hull
);
3202 n_div_i
= isl_basic_map_dim(bmap_i
, isl_dim_div
);
3203 n_div_j
= isl_basic_map_dim(bmap_j
, isl_dim_div
);
3204 total
= isl_basic_map_total_dim(bmap_i
) - n_div_i
;
3206 ls
= isl_basic_map_get_local_space(bmap_i
);
3207 ls
= isl_local_space_wrap(ls
);
3208 wrap_hull
= isl_basic_map_wrap(hull
);
3210 aff_nan
= isl_aff_nan_on_domain(isl_local_space_copy(ls
));
3211 list
= isl_aff_list_alloc(ctx
, n_div_i
);
3214 for (i
= 0; i
< n_div_i
; ++i
) {
3218 isl_basic_map_equal_div_expr_part(bmap_i
, i
, bmap_j
, j
,
3221 list
= isl_aff_list_add(list
, isl_aff_copy(aff_nan
));
3224 if (n_div_i
- i
<= n_div_j
- j
)
3227 aff
= isl_local_space_get_div(ls
, i
);
3228 aff
= isl_aff_substitute_equalities(aff
,
3229 isl_basic_set_copy(wrap_hull
));
3230 aff
= isl_aff_floor(aff
);
3233 if (isl_aff_dim(aff
, isl_dim_div
) != 0) {
3238 list
= isl_aff_list_add(list
, aff
);
3241 isl_aff_free(aff_nan
);
3242 isl_local_space_free(ls
);
3243 isl_basic_set_free(wrap_hull
);
3247 isl_aff_free(aff_nan
);
3248 isl_local_space_free(ls
);
3249 isl_basic_set_free(wrap_hull
);
3250 isl_aff_list_free(list
);
3254 /* Add variables to info->bmap and info->tab corresponding to the elements
3255 * in "list" that are not set to NaN.
3256 * "extra_var" is the number of these elements.
3257 * "dim" is the offset in the variables of "tab" where we should
3258 * start considering the elements in "list".
3259 * When this function returns, the total number of variables in "tab"
3260 * is equal to "dim" plus the number of elements in "list".
3262 * The newly added existentially quantified variables are not given
3263 * an explicit representation because the corresponding div constraints
3264 * do not appear in info->bmap. These constraints are not added
3265 * to info->bmap because for internal consistency, they would need to
3266 * be added to info->tab as well, where they could combine with the equality
3267 * that is added later to result in constraints that do not hold
3268 * in the original input.
3270 static int add_sub_vars(struct isl_coalesce_info
*info
,
3271 __isl_keep isl_aff_list
*list
, int dim
, int extra_var
)
3276 space
= isl_basic_map_get_space(info
->bmap
);
3277 info
->bmap
= isl_basic_map_cow(info
->bmap
);
3278 info
->bmap
= isl_basic_map_extend_space(info
->bmap
, space
,
3282 n
= isl_aff_list_n_aff(list
);
3283 for (i
= 0; i
< n
; ++i
) {
3287 aff
= isl_aff_list_get_aff(list
, i
);
3288 is_nan
= isl_aff_is_nan(aff
);
3295 if (isl_tab_insert_var(info
->tab
, dim
+ i
) < 0)
3297 d
= isl_basic_map_alloc_div(info
->bmap
);
3300 info
->bmap
= isl_basic_map_mark_div_unknown(info
->bmap
, d
);
3303 for (j
= d
; j
> i
; --j
)
3304 isl_basic_map_swap_div(info
->bmap
, j
- 1, j
);
3310 /* For each element in "list" that is not set to NaN, fix the corresponding
3311 * variable in "tab" to the purely affine expression defined by the element.
3312 * "dim" is the offset in the variables of "tab" where we should
3313 * start considering the elements in "list".
3315 * This function assumes that a sufficient number of rows and
3316 * elements in the constraint array are available in the tableau.
3318 static int add_sub_equalities(struct isl_tab
*tab
,
3319 __isl_keep isl_aff_list
*list
, int dim
)
3326 n
= isl_aff_list_n_aff(list
);
3328 ctx
= isl_tab_get_ctx(tab
);
3329 sub
= isl_vec_alloc(ctx
, 1 + dim
+ n
);
3332 isl_seq_clr(sub
->el
+ 1 + dim
, n
);
3334 for (i
= 0; i
< n
; ++i
) {
3335 aff
= isl_aff_list_get_aff(list
, i
);
3338 if (isl_aff_is_nan(aff
)) {
3342 isl_seq_cpy(sub
->el
, aff
->v
->el
+ 1, 1 + dim
);
3343 isl_int_neg(sub
->el
[1 + dim
+ i
], aff
->v
->el
[0]);
3344 if (isl_tab_add_eq(tab
, sub
->el
) < 0)
3346 isl_int_set_si(sub
->el
[1 + dim
+ i
], 0);
3358 /* Add variables to info->tab and info->bmap corresponding to the elements
3359 * in "list" that are not set to NaN. The value of the added variable
3360 * in info->tab is fixed to the purely affine expression defined by the element.
3361 * "dim" is the offset in the variables of info->tab where we should
3362 * start considering the elements in "list".
3363 * When this function returns, the total number of variables in info->tab
3364 * is equal to "dim" plus the number of elements in "list".
3366 static int add_subs(struct isl_coalesce_info
*info
,
3367 __isl_keep isl_aff_list
*list
, int dim
)
3375 n
= isl_aff_list_n_aff(list
);
3376 extra_var
= n
- (info
->tab
->n_var
- dim
);
3378 if (isl_tab_extend_vars(info
->tab
, extra_var
) < 0)
3380 if (isl_tab_extend_cons(info
->tab
, 2 * extra_var
) < 0)
3382 if (add_sub_vars(info
, list
, dim
, extra_var
) < 0)
3385 return add_sub_equalities(info
->tab
, list
, dim
);
3388 /* Coalesce basic map "j" into basic map "i" after adding the extra integer
3389 * divisions in "i" but not in "j" to basic map "j", with values
3390 * specified by "list". The total number of elements in "list"
3391 * is equal to the number of integer divisions in "i", while the number
3392 * of NaN elements in the list is equal to the number of integer divisions
3395 * If no coalescing can be performed, then we need to revert basic map "j"
3396 * to its original state. We do the same if basic map "i" gets dropped
3397 * during the coalescing, even though this should not happen in practice
3398 * since we have already checked for "j" being a subset of "i"
3399 * before we reach this stage.
3401 static enum isl_change
coalesce_with_subs(int i
, int j
,
3402 struct isl_coalesce_info
*info
, __isl_keep isl_aff_list
*list
)
3404 isl_basic_map
*bmap_j
;
3405 struct isl_tab_undo
*snap
;
3407 enum isl_change change
;
3409 bmap_j
= isl_basic_map_copy(info
[j
].bmap
);
3410 snap
= isl_tab_snap(info
[j
].tab
);
3412 dim
= isl_basic_map_dim(bmap_j
, isl_dim_all
);
3413 dim
-= isl_basic_map_dim(bmap_j
, isl_dim_div
);
3414 if (add_subs(&info
[j
], list
, dim
) < 0)
3417 change
= coalesce_local_pair(i
, j
, info
);
3418 if (change
!= isl_change_none
&& change
!= isl_change_drop_first
) {
3419 isl_basic_map_free(bmap_j
);
3421 isl_basic_map_free(info
[j
].bmap
);
3422 info
[j
].bmap
= bmap_j
;
3424 if (isl_tab_rollback(info
[j
].tab
, snap
) < 0)
3425 return isl_change_error
;
3430 isl_basic_map_free(bmap_j
);
3431 return isl_change_error
;
3434 /* Check if we can coalesce basic map "j" into basic map "i" after copying
3435 * those extra integer divisions in "i" that can be simplified away
3436 * using the extra equalities in "j".
3437 * All divs are assumed to be known and not contain any nested divs.
3439 * We first check if there are any extra equalities in "j" that we
3440 * can exploit. Then we check if every integer division in "i"
3441 * either already appears in "j" or can be simplified using the
3442 * extra equalities to a purely affine expression.
3443 * If these tests succeed, then we try to coalesce the two basic maps
3444 * by introducing extra dimensions in "j" corresponding to
3445 * the extra integer divsisions "i" fixed to the corresponding
3446 * purely affine expression.
3448 static enum isl_change
check_coalesce_into_eq(int i
, int j
,
3449 struct isl_coalesce_info
*info
)
3451 unsigned n_div_i
, n_div_j
;
3452 isl_basic_map
*hull_i
, *hull_j
;
3455 enum isl_change change
;
3457 n_div_i
= isl_basic_map_dim(info
[i
].bmap
, isl_dim_div
);
3458 n_div_j
= isl_basic_map_dim(info
[j
].bmap
, isl_dim_div
);
3459 if (n_div_i
<= n_div_j
)
3460 return isl_change_none
;
3461 if (info
[j
].bmap
->n_eq
== 0)
3462 return isl_change_none
;
3464 hull_i
= isl_basic_map_copy(info
[i
].bmap
);
3465 hull_i
= isl_basic_map_plain_affine_hull(hull_i
);
3466 hull_j
= isl_basic_map_copy(info
[j
].bmap
);
3467 hull_j
= isl_basic_map_plain_affine_hull(hull_j
);
3469 hull_j
= isl_basic_map_intersect(hull_j
, isl_basic_map_copy(hull_i
));
3470 equal
= isl_basic_map_plain_is_equal(hull_i
, hull_j
);
3471 empty
= isl_basic_map_plain_is_empty(hull_j
);
3472 isl_basic_map_free(hull_i
);
3474 if (equal
< 0 || empty
< 0)
3476 if (equal
|| empty
) {
3477 isl_basic_map_free(hull_j
);
3478 return isl_change_none
;
3481 list
= set_up_substitutions(info
[i
].bmap
, info
[j
].bmap
, hull_j
);
3483 return isl_change_error
;
3484 if (isl_aff_list_n_aff(list
) < n_div_i
)
3485 change
= isl_change_none
;
3487 change
= coalesce_with_subs(i
, j
, info
, list
);
3489 isl_aff_list_free(list
);
3493 isl_basic_map_free(hull_j
);
3494 return isl_change_error
;
3497 /* Check if we can coalesce basic maps "i" and "j" after copying
3498 * those extra integer divisions in one of the basic maps that can
3499 * be simplified away using the extra equalities in the other basic map.
3500 * We require all divs to be known in both basic maps.
3501 * Furthermore, to simplify the comparison of div expressions,
3502 * we do not allow any nested integer divisions.
3504 static enum isl_change
check_coalesce_eq(int i
, int j
,
3505 struct isl_coalesce_info
*info
)
3508 enum isl_change change
;
3510 known
= isl_basic_map_divs_known(info
[i
].bmap
);
3511 if (known
< 0 || !known
)
3512 return known
< 0 ? isl_change_error
: isl_change_none
;
3513 known
= isl_basic_map_divs_known(info
[j
].bmap
);
3514 if (known
< 0 || !known
)
3515 return known
< 0 ? isl_change_error
: isl_change_none
;
3516 nested
= has_nested_div(info
[i
].bmap
);
3517 if (nested
< 0 || nested
)
3518 return nested
< 0 ? isl_change_error
: isl_change_none
;
3519 nested
= has_nested_div(info
[j
].bmap
);
3520 if (nested
< 0 || nested
)
3521 return nested
< 0 ? isl_change_error
: isl_change_none
;
3523 change
= check_coalesce_into_eq(i
, j
, info
);
3524 if (change
!= isl_change_none
)
3526 change
= check_coalesce_into_eq(j
, i
, info
);
3527 if (change
!= isl_change_none
)
3528 return invert_change(change
);
3530 return isl_change_none
;
3533 /* Check if the union of the given pair of basic maps
3534 * can be represented by a single basic map.
3535 * If so, replace the pair by the single basic map and return
3536 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
3537 * Otherwise, return isl_change_none.
3539 * We first check if the two basic maps live in the same local space,
3540 * after aligning the divs that differ by only an integer constant.
3541 * If so, we do the complete check. Otherwise, we check if they have
3542 * the same number of integer divisions and can be coalesced, if one is
3543 * an obvious subset of the other or if the extra integer divisions
3544 * of one basic map can be simplified away using the extra equalities
3545 * of the other basic map.
3547 static enum isl_change
coalesce_pair(int i
, int j
,
3548 struct isl_coalesce_info
*info
)
3551 enum isl_change change
;
3553 if (harmonize_divs(&info
[i
], &info
[j
]) < 0)
3554 return isl_change_error
;
3555 same
= same_divs(info
[i
].bmap
, info
[j
].bmap
);
3557 return isl_change_error
;
3559 return coalesce_local_pair(i
, j
, info
);
3561 if (info
[i
].bmap
->n_div
== info
[j
].bmap
->n_div
) {
3562 change
= coalesce_local_pair(i
, j
, info
);
3563 if (change
!= isl_change_none
)
3567 change
= coalesce_divs(i
, j
, info
);
3568 if (change
!= isl_change_none
)
3571 return check_coalesce_eq(i
, j
, info
);
3574 /* Return the maximum of "a" and "b".
3576 static int isl_max(int a
, int b
)
3578 return a
> b
? a
: b
;
3581 /* Pairwise coalesce the basic maps in the range [start1, end1[ of "info"
3582 * with those in the range [start2, end2[, skipping basic maps
3583 * that have been removed (either before or within this function).
3585 * For each basic map i in the first range, we check if it can be coalesced
3586 * with respect to any previously considered basic map j in the second range.
3587 * If i gets dropped (because it was a subset of some j), then
3588 * we can move on to the next basic map.
3589 * If j gets dropped, we need to continue checking against the other
3590 * previously considered basic maps.
3591 * If the two basic maps got fused, then we recheck the fused basic map
3592 * against the previously considered basic maps, starting at i + 1
3593 * (even if start2 is greater than i + 1).
3595 static int coalesce_range(isl_ctx
*ctx
, struct isl_coalesce_info
*info
,
3596 int start1
, int end1
, int start2
, int end2
)
3600 for (i
= end1
- 1; i
>= start1
; --i
) {
3601 if (info
[i
].removed
)
3603 for (j
= isl_max(i
+ 1, start2
); j
< end2
; ++j
) {
3604 enum isl_change changed
;
3606 if (info
[j
].removed
)
3608 if (info
[i
].removed
)
3609 isl_die(ctx
, isl_error_internal
,
3610 "basic map unexpectedly removed",
3612 changed
= coalesce_pair(i
, j
, info
);
3614 case isl_change_error
:
3616 case isl_change_none
:
3617 case isl_change_drop_second
:
3619 case isl_change_drop_first
:
3622 case isl_change_fuse
:
3632 /* Pairwise coalesce the basic maps described by the "n" elements of "info".
3634 * We consider groups of basic maps that live in the same apparent
3635 * affine hull and we first coalesce within such a group before we
3636 * coalesce the elements in the group with elements of previously
3637 * considered groups. If a fuse happens during the second phase,
3638 * then we also reconsider the elements within the group.
3640 static int coalesce(isl_ctx
*ctx
, int n
, struct isl_coalesce_info
*info
)
3644 for (end
= n
; end
> 0; end
= start
) {
3646 while (start
>= 1 &&
3647 info
[start
- 1].hull_hash
== info
[start
].hull_hash
)
3649 if (coalesce_range(ctx
, info
, start
, end
, start
, end
) < 0)
3651 if (coalesce_range(ctx
, info
, start
, end
, end
, n
) < 0)
3658 /* Update the basic maps in "map" based on the information in "info".
3659 * In particular, remove the basic maps that have been marked removed and
3660 * update the others based on the information in the corresponding tableau.
3661 * Since we detected implicit equalities without calling
3662 * isl_basic_map_gauss, we need to do it now.
3663 * Also call isl_basic_map_simplify if we may have lost the definition
3664 * of one or more integer divisions.
3666 static __isl_give isl_map
*update_basic_maps(__isl_take isl_map
*map
,
3667 int n
, struct isl_coalesce_info
*info
)
3674 for (i
= n
- 1; i
>= 0; --i
) {
3675 if (info
[i
].removed
) {
3676 isl_basic_map_free(map
->p
[i
]);
3677 if (i
!= map
->n
- 1)
3678 map
->p
[i
] = map
->p
[map
->n
- 1];
3683 info
[i
].bmap
= isl_basic_map_update_from_tab(info
[i
].bmap
,
3685 info
[i
].bmap
= isl_basic_map_gauss(info
[i
].bmap
, NULL
);
3686 if (info
[i
].simplify
)
3687 info
[i
].bmap
= isl_basic_map_simplify(info
[i
].bmap
);
3688 info
[i
].bmap
= isl_basic_map_finalize(info
[i
].bmap
);
3690 return isl_map_free(map
);
3691 ISL_F_SET(info
[i
].bmap
, ISL_BASIC_MAP_NO_IMPLICIT
);
3692 ISL_F_SET(info
[i
].bmap
, ISL_BASIC_MAP_NO_REDUNDANT
);
3693 isl_basic_map_free(map
->p
[i
]);
3694 map
->p
[i
] = info
[i
].bmap
;
3695 info
[i
].bmap
= NULL
;
3701 /* For each pair of basic maps in the map, check if the union of the two
3702 * can be represented by a single basic map.
3703 * If so, replace the pair by the single basic map and start over.
3705 * We factor out any (hidden) common factor from the constraint
3706 * coefficients to improve the detection of adjacent constraints.
3708 * Since we are constructing the tableaus of the basic maps anyway,
3709 * we exploit them to detect implicit equalities and redundant constraints.
3710 * This also helps the coalescing as it can ignore the redundant constraints.
3711 * In order to avoid confusion, we make all implicit equalities explicit
3712 * in the basic maps. We don't call isl_basic_map_gauss, though,
3713 * as that may affect the number of constraints.
3714 * This means that we have to call isl_basic_map_gauss at the end
3715 * of the computation (in update_basic_maps) to ensure that
3716 * the basic maps are not left in an unexpected state.
3717 * For each basic map, we also compute the hash of the apparent affine hull
3718 * for use in coalesce.
3720 struct isl_map
*isl_map_coalesce(struct isl_map
*map
)
3725 struct isl_coalesce_info
*info
= NULL
;
3727 map
= isl_map_remove_empty_parts(map
);
3734 ctx
= isl_map_get_ctx(map
);
3735 map
= isl_map_sort_divs(map
);
3736 map
= isl_map_cow(map
);
3743 info
= isl_calloc_array(map
->ctx
, struct isl_coalesce_info
, n
);
3747 for (i
= 0; i
< map
->n
; ++i
) {
3748 map
->p
[i
] = isl_basic_map_reduce_coefficients(map
->p
[i
]);
3751 info
[i
].bmap
= isl_basic_map_copy(map
->p
[i
]);
3752 info
[i
].tab
= isl_tab_from_basic_map(info
[i
].bmap
, 0);
3755 if (!ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_NO_IMPLICIT
))
3756 if (isl_tab_detect_implicit_equalities(info
[i
].tab
) < 0)
3758 info
[i
].bmap
= isl_tab_make_equalities_explicit(info
[i
].tab
,
3762 if (!ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_NO_REDUNDANT
))
3763 if (isl_tab_detect_redundant(info
[i
].tab
) < 0)
3765 if (coalesce_info_set_hull_hash(&info
[i
]) < 0)
3768 for (i
= map
->n
- 1; i
>= 0; --i
)
3769 if (info
[i
].tab
->empty
)
3772 if (coalesce(ctx
, n
, info
) < 0)
3775 map
= update_basic_maps(map
, n
, info
);
3777 clear_coalesce_info(n
, info
);
3781 clear_coalesce_info(n
, info
);
3786 /* For each pair of basic sets in the set, check if the union of the two
3787 * can be represented by a single basic set.
3788 * If so, replace the pair by the single basic set and start over.
3790 struct isl_set
*isl_set_coalesce(struct isl_set
*set
)
3792 return set_from_map(isl_map_coalesce(set_to_map(set
)));