2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2010 INRIA Saclay
4 * Copyright 2012-2013 Ecole Normale Superieure
5 * Copyright 2014 INRIA Rocquencourt
6 * Copyright 2016 Sven Verdoolaege
8 * Use of this software is governed by the MIT license
10 * Written by Sven Verdoolaege, K.U.Leuven, Departement
11 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
12 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
13 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
14 * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
15 * and Inria Paris - Rocquencourt, Domaine de Voluceau - Rocquencourt,
16 * B.P. 105 - 78153 Le Chesnay, France
19 #include "isl_map_private.h"
21 #include <isl/options.h>
23 #include <isl_mat_private.h>
24 #include <isl_local_space_private.h>
25 #include <isl_vec_private.h>
26 #include <isl_aff_private.h>
28 #define STATUS_ERROR -1
29 #define STATUS_REDUNDANT 1
30 #define STATUS_VALID 2
31 #define STATUS_SEPARATE 3
33 #define STATUS_ADJ_EQ 5
34 #define STATUS_ADJ_INEQ 6
36 static int status_in(isl_int
*ineq
, struct isl_tab
*tab
)
38 enum isl_ineq_type type
= isl_tab_ineq_type(tab
, ineq
);
41 case isl_ineq_error
: return STATUS_ERROR
;
42 case isl_ineq_redundant
: return STATUS_VALID
;
43 case isl_ineq_separate
: return STATUS_SEPARATE
;
44 case isl_ineq_cut
: return STATUS_CUT
;
45 case isl_ineq_adj_eq
: return STATUS_ADJ_EQ
;
46 case isl_ineq_adj_ineq
: return STATUS_ADJ_INEQ
;
50 /* Compute the position of the equalities of basic map "bmap_i"
51 * with respect to the basic map represented by "tab_j".
52 * The resulting array has twice as many entries as the number
53 * of equalities corresponding to the two inequalties to which
54 * each equality corresponds.
56 static int *eq_status_in(__isl_keep isl_basic_map
*bmap_i
,
57 struct isl_tab
*tab_j
)
60 int *eq
= isl_calloc_array(bmap_i
->ctx
, int, 2 * bmap_i
->n_eq
);
66 dim
= isl_basic_map_total_dim(bmap_i
);
67 for (k
= 0; k
< bmap_i
->n_eq
; ++k
) {
68 for (l
= 0; l
< 2; ++l
) {
69 isl_seq_neg(bmap_i
->eq
[k
], bmap_i
->eq
[k
], 1+dim
);
70 eq
[2 * k
+ l
] = status_in(bmap_i
->eq
[k
], tab_j
);
71 if (eq
[2 * k
+ l
] == STATUS_ERROR
)
74 if (eq
[2 * k
] == STATUS_SEPARATE
||
75 eq
[2 * k
+ 1] == STATUS_SEPARATE
)
85 /* Compute the position of the inequalities of basic map "bmap_i"
86 * (also represented by "tab_i", if not NULL) with respect to the basic map
87 * represented by "tab_j".
89 static int *ineq_status_in(__isl_keep isl_basic_map
*bmap_i
,
90 struct isl_tab
*tab_i
, struct isl_tab
*tab_j
)
93 unsigned n_eq
= bmap_i
->n_eq
;
94 int *ineq
= isl_calloc_array(bmap_i
->ctx
, int, bmap_i
->n_ineq
);
99 for (k
= 0; k
< bmap_i
->n_ineq
; ++k
) {
100 if (tab_i
&& isl_tab_is_redundant(tab_i
, n_eq
+ k
)) {
101 ineq
[k
] = STATUS_REDUNDANT
;
104 ineq
[k
] = status_in(bmap_i
->ineq
[k
], tab_j
);
105 if (ineq
[k
] == STATUS_ERROR
)
107 if (ineq
[k
] == STATUS_SEPARATE
)
117 static int any(int *con
, unsigned len
, int status
)
121 for (i
= 0; i
< len
; ++i
)
122 if (con
[i
] == status
)
127 static int count(int *con
, unsigned len
, int status
)
132 for (i
= 0; i
< len
; ++i
)
133 if (con
[i
] == status
)
138 static int all(int *con
, unsigned len
, int status
)
142 for (i
= 0; i
< len
; ++i
) {
143 if (con
[i
] == STATUS_REDUNDANT
)
145 if (con
[i
] != status
)
151 /* Internal information associated to a basic map in a map
152 * that is to be coalesced by isl_map_coalesce.
154 * "bmap" is the basic map itself (or NULL if "removed" is set)
155 * "tab" is the corresponding tableau (or NULL if "removed" is set)
156 * "hull_hash" identifies the affine space in which "bmap" lives.
157 * "removed" is set if this basic map has been removed from the map
158 * "simplify" is set if this basic map may have some unknown integer
159 * divisions that were not present in the input basic maps. The basic
160 * map should then be simplified such that we may be able to find
161 * a definition among the constraints.
163 * "eq" and "ineq" are only set if we are currently trying to coalesce
164 * this basic map with another basic map, in which case they represent
165 * the position of the inequalities of this basic map with respect to
166 * the other basic map. The number of elements in the "eq" array
167 * is twice the number of equalities in the "bmap", corresponding
168 * to the two inequalities that make up each equality.
170 struct isl_coalesce_info
{
180 /* Compute the hash of the (apparent) affine hull of info->bmap (with
181 * the existentially quantified variables removed) and store it
184 static int coalesce_info_set_hull_hash(struct isl_coalesce_info
*info
)
189 hull
= isl_basic_map_copy(info
->bmap
);
190 hull
= isl_basic_map_plain_affine_hull(hull
);
191 n_div
= isl_basic_map_dim(hull
, isl_dim_div
);
192 hull
= isl_basic_map_drop_constraints_involving_dims(hull
,
193 isl_dim_div
, 0, n_div
);
194 info
->hull_hash
= isl_basic_map_get_hash(hull
);
195 isl_basic_map_free(hull
);
197 return hull
? 0 : -1;
200 /* Free all the allocated memory in an array
201 * of "n" isl_coalesce_info elements.
203 static void clear_coalesce_info(int n
, struct isl_coalesce_info
*info
)
210 for (i
= 0; i
< n
; ++i
) {
211 isl_basic_map_free(info
[i
].bmap
);
212 isl_tab_free(info
[i
].tab
);
218 /* Drop the basic map represented by "info".
219 * That is, clear the memory associated to the entry and
220 * mark it as having been removed.
222 static void drop(struct isl_coalesce_info
*info
)
224 info
->bmap
= isl_basic_map_free(info
->bmap
);
225 isl_tab_free(info
->tab
);
230 /* Exchange the information in "info1" with that in "info2".
232 static void exchange(struct isl_coalesce_info
*info1
,
233 struct isl_coalesce_info
*info2
)
235 struct isl_coalesce_info info
;
242 /* This type represents the kind of change that has been performed
243 * while trying to coalesce two basic maps.
245 * isl_change_none: nothing was changed
246 * isl_change_drop_first: the first basic map was removed
247 * isl_change_drop_second: the second basic map was removed
248 * isl_change_fuse: the two basic maps were replaced by a new basic map.
251 isl_change_error
= -1,
253 isl_change_drop_first
,
254 isl_change_drop_second
,
258 /* Update "change" based on an interchange of the first and the second
259 * basic map. That is, interchange isl_change_drop_first and
260 * isl_change_drop_second.
262 static enum isl_change
invert_change(enum isl_change change
)
265 case isl_change_error
:
266 return isl_change_error
;
267 case isl_change_none
:
268 return isl_change_none
;
269 case isl_change_drop_first
:
270 return isl_change_drop_second
;
271 case isl_change_drop_second
:
272 return isl_change_drop_first
;
273 case isl_change_fuse
:
274 return isl_change_fuse
;
277 return isl_change_error
;
280 /* Add the valid constraints of the basic map represented by "info"
281 * to "bmap". "len" is the size of the constraints.
282 * If only one of the pair of inequalities that make up an equality
283 * is valid, then add that inequality.
285 static __isl_give isl_basic_map
*add_valid_constraints(
286 __isl_take isl_basic_map
*bmap
, struct isl_coalesce_info
*info
,
294 for (k
= 0; k
< info
->bmap
->n_eq
; ++k
) {
295 if (info
->eq
[2 * k
] == STATUS_VALID
&&
296 info
->eq
[2 * k
+ 1] == STATUS_VALID
) {
297 l
= isl_basic_map_alloc_equality(bmap
);
299 return isl_basic_map_free(bmap
);
300 isl_seq_cpy(bmap
->eq
[l
], info
->bmap
->eq
[k
], len
);
301 } else if (info
->eq
[2 * k
] == STATUS_VALID
) {
302 l
= isl_basic_map_alloc_inequality(bmap
);
304 return isl_basic_map_free(bmap
);
305 isl_seq_neg(bmap
->ineq
[l
], info
->bmap
->eq
[k
], len
);
306 } else if (info
->eq
[2 * k
+ 1] == STATUS_VALID
) {
307 l
= isl_basic_map_alloc_inequality(bmap
);
309 return isl_basic_map_free(bmap
);
310 isl_seq_cpy(bmap
->ineq
[l
], info
->bmap
->eq
[k
], len
);
314 for (k
= 0; k
< info
->bmap
->n_ineq
; ++k
) {
315 if (info
->ineq
[k
] != STATUS_VALID
)
317 l
= isl_basic_map_alloc_inequality(bmap
);
319 return isl_basic_map_free(bmap
);
320 isl_seq_cpy(bmap
->ineq
[l
], info
->bmap
->ineq
[k
], len
);
326 /* Is "bmap" defined by a number of (non-redundant) constraints that
327 * is greater than the number of constraints of basic maps i and j combined?
328 * Equalities are counted as two inequalities.
330 static int number_of_constraints_increases(int i
, int j
,
331 struct isl_coalesce_info
*info
,
332 __isl_keep isl_basic_map
*bmap
, struct isl_tab
*tab
)
336 n_old
= 2 * info
[i
].bmap
->n_eq
+ info
[i
].bmap
->n_ineq
;
337 n_old
+= 2 * info
[j
].bmap
->n_eq
+ info
[j
].bmap
->n_ineq
;
339 n_new
= 2 * bmap
->n_eq
;
340 for (k
= 0; k
< bmap
->n_ineq
; ++k
)
341 if (!isl_tab_is_redundant(tab
, bmap
->n_eq
+ k
))
344 return n_new
> n_old
;
347 /* Replace the pair of basic maps i and j by the basic map bounded
348 * by the valid constraints in both basic maps and the constraints
349 * in extra (if not NULL).
350 * Place the fused basic map in the position that is the smallest of i and j.
352 * If "detect_equalities" is set, then look for equalities encoded
353 * as pairs of inequalities.
354 * If "check_number" is set, then the original basic maps are only
355 * replaced if the total number of constraints does not increase.
356 * While the number of integer divisions in the two basic maps
357 * is assumed to be the same, the actual definitions may be different.
358 * We only copy the definition from one of the basic map if it is
359 * the same as that of the other basic map. Otherwise, we mark
360 * the integer division as unknown and schedule for the basic map
361 * to be simplified in an attempt to recover the integer division definition.
363 static enum isl_change
fuse(int i
, int j
, struct isl_coalesce_info
*info
,
364 __isl_keep isl_mat
*extra
, int detect_equalities
, int check_number
)
367 struct isl_basic_map
*fused
= NULL
;
368 struct isl_tab
*fused_tab
= NULL
;
369 unsigned total
= isl_basic_map_total_dim(info
[i
].bmap
);
370 unsigned extra_rows
= extra
? extra
->n_row
: 0;
371 unsigned n_eq
, n_ineq
;
374 return fuse(j
, i
, info
, extra
, detect_equalities
, check_number
);
376 n_eq
= info
[i
].bmap
->n_eq
+ info
[j
].bmap
->n_eq
;
377 n_ineq
= info
[i
].bmap
->n_ineq
+ info
[j
].bmap
->n_ineq
;
378 fused
= isl_basic_map_alloc_space(isl_space_copy(info
[i
].bmap
->dim
),
379 info
[i
].bmap
->n_div
, n_eq
, n_eq
+ n_ineq
+ extra_rows
);
380 fused
= add_valid_constraints(fused
, &info
[i
], 1 + total
);
381 fused
= add_valid_constraints(fused
, &info
[j
], 1 + total
);
385 for (k
= 0; k
< info
[i
].bmap
->n_div
; ++k
) {
386 int l
= isl_basic_map_alloc_div(fused
);
389 if (isl_seq_eq(info
[i
].bmap
->div
[k
], info
[j
].bmap
->div
[k
],
391 isl_seq_cpy(fused
->div
[l
], info
[i
].bmap
->div
[k
],
394 isl_int_set_si(fused
->div
[l
][0], 0);
395 info
[i
].simplify
= 1;
399 for (k
= 0; k
< extra_rows
; ++k
) {
400 l
= isl_basic_map_alloc_inequality(fused
);
403 isl_seq_cpy(fused
->ineq
[l
], extra
->row
[k
], 1 + total
);
406 if (detect_equalities
)
407 fused
= isl_basic_map_detect_inequality_pairs(fused
, NULL
);
408 fused
= isl_basic_map_gauss(fused
, NULL
);
409 ISL_F_SET(fused
, ISL_BASIC_MAP_FINAL
);
410 if (ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_RATIONAL
) &&
411 ISL_F_ISSET(info
[j
].bmap
, ISL_BASIC_MAP_RATIONAL
))
412 ISL_F_SET(fused
, ISL_BASIC_MAP_RATIONAL
);
414 fused_tab
= isl_tab_from_basic_map(fused
, 0);
415 if (isl_tab_detect_redundant(fused_tab
) < 0)
419 number_of_constraints_increases(i
, j
, info
, fused
, fused_tab
)) {
420 isl_tab_free(fused_tab
);
421 isl_basic_map_free(fused
);
422 return isl_change_none
;
425 info
[i
].simplify
|= info
[j
].simplify
;
426 isl_basic_map_free(info
[i
].bmap
);
427 info
[i
].bmap
= fused
;
428 isl_tab_free(info
[i
].tab
);
429 info
[i
].tab
= fused_tab
;
432 return isl_change_fuse
;
434 isl_tab_free(fused_tab
);
435 isl_basic_map_free(fused
);
436 return isl_change_error
;
439 /* Given a pair of basic maps i and j such that all constraints are either
440 * "valid" or "cut", check if the facets corresponding to the "cut"
441 * constraints of i lie entirely within basic map j.
442 * If so, replace the pair by the basic map consisting of the valid
443 * constraints in both basic maps.
444 * Checking whether the facet lies entirely within basic map j
445 * is performed by checking whether the constraints of basic map j
446 * are valid for the facet. These tests are performed on a rational
447 * tableau to avoid the theoretical possibility that a constraint
448 * that was considered to be a cut constraint for the entire basic map i
449 * happens to be considered to be a valid constraint for the facet,
450 * even though it cuts off the same rational points.
452 * To see that we are not introducing any extra points, call the
453 * two basic maps A and B and the resulting map U and let x
454 * be an element of U \setminus ( A \cup B ).
455 * A line connecting x with an element of A \cup B meets a facet F
456 * of either A or B. Assume it is a facet of B and let c_1 be
457 * the corresponding facet constraint. We have c_1(x) < 0 and
458 * so c_1 is a cut constraint. This implies that there is some
459 * (possibly rational) point x' satisfying the constraints of A
460 * and the opposite of c_1 as otherwise c_1 would have been marked
461 * valid for A. The line connecting x and x' meets a facet of A
462 * in a (possibly rational) point that also violates c_1, but this
463 * is impossible since all cut constraints of B are valid for all
465 * In case F is a facet of A rather than B, then we can apply the
466 * above reasoning to find a facet of B separating x from A \cup B first.
468 static enum isl_change
check_facets(int i
, int j
,
469 struct isl_coalesce_info
*info
)
472 struct isl_tab_undo
*snap
, *snap2
;
473 unsigned n_eq
= info
[i
].bmap
->n_eq
;
475 snap
= isl_tab_snap(info
[i
].tab
);
476 if (isl_tab_mark_rational(info
[i
].tab
) < 0)
477 return isl_change_error
;
478 snap2
= isl_tab_snap(info
[i
].tab
);
480 for (k
= 0; k
< info
[i
].bmap
->n_ineq
; ++k
) {
481 if (info
[i
].ineq
[k
] != STATUS_CUT
)
483 if (isl_tab_select_facet(info
[i
].tab
, n_eq
+ k
) < 0)
484 return isl_change_error
;
485 for (l
= 0; l
< info
[j
].bmap
->n_ineq
; ++l
) {
487 if (info
[j
].ineq
[l
] != STATUS_CUT
)
489 stat
= status_in(info
[j
].bmap
->ineq
[l
], info
[i
].tab
);
491 return isl_change_error
;
492 if (stat
!= STATUS_VALID
)
495 if (isl_tab_rollback(info
[i
].tab
, snap2
) < 0)
496 return isl_change_error
;
497 if (l
< info
[j
].bmap
->n_ineq
)
501 if (k
< info
[i
].bmap
->n_ineq
) {
502 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
503 return isl_change_error
;
504 return isl_change_none
;
506 return fuse(i
, j
, info
, NULL
, 0, 0);
509 /* Check if info->bmap contains the basic map represented
510 * by the tableau "tab".
511 * For each equality, we check both the constraint itself
512 * (as an inequality) and its negation. Make sure the
513 * equality is returned to its original state before returning.
515 static int contains(struct isl_coalesce_info
*info
, struct isl_tab
*tab
)
519 isl_basic_map
*bmap
= info
->bmap
;
521 dim
= isl_basic_map_total_dim(bmap
);
522 for (k
= 0; k
< bmap
->n_eq
; ++k
) {
524 isl_seq_neg(bmap
->eq
[k
], bmap
->eq
[k
], 1 + dim
);
525 stat
= status_in(bmap
->eq
[k
], tab
);
526 isl_seq_neg(bmap
->eq
[k
], bmap
->eq
[k
], 1 + dim
);
529 if (stat
!= STATUS_VALID
)
531 stat
= status_in(bmap
->eq
[k
], tab
);
534 if (stat
!= STATUS_VALID
)
538 for (k
= 0; k
< bmap
->n_ineq
; ++k
) {
540 if (info
->ineq
[k
] == STATUS_REDUNDANT
)
542 stat
= status_in(bmap
->ineq
[k
], tab
);
545 if (stat
!= STATUS_VALID
)
551 /* Basic map "i" has an inequality (say "k") that is adjacent
552 * to some inequality of basic map "j". All the other inequalities
554 * Check if basic map "j" forms an extension of basic map "i".
556 * Note that this function is only called if some of the equalities or
557 * inequalities of basic map "j" do cut basic map "i". The function is
558 * correct even if there are no such cut constraints, but in that case
559 * the additional checks performed by this function are overkill.
561 * In particular, we replace constraint k, say f >= 0, by constraint
562 * f <= -1, add the inequalities of "j" that are valid for "i"
563 * and check if the result is a subset of basic map "j".
564 * If so, then we know that this result is exactly equal to basic map "j"
565 * since all its constraints are valid for basic map "j".
566 * By combining the valid constraints of "i" (all equalities and all
567 * inequalities except "k") and the valid constraints of "j" we therefore
568 * obtain a basic map that is equal to their union.
569 * In this case, there is no need to perform a rollback of the tableau
570 * since it is going to be destroyed in fuse().
576 * |_______| _ |_________\
588 static enum isl_change
is_adj_ineq_extension(int i
, int j
,
589 struct isl_coalesce_info
*info
)
592 struct isl_tab_undo
*snap
;
593 unsigned n_eq
= info
[i
].bmap
->n_eq
;
594 unsigned total
= isl_basic_map_total_dim(info
[i
].bmap
);
598 if (isl_tab_extend_cons(info
[i
].tab
, 1 + info
[j
].bmap
->n_ineq
) < 0)
599 return isl_change_error
;
601 for (k
= 0; k
< info
[i
].bmap
->n_ineq
; ++k
)
602 if (info
[i
].ineq
[k
] == STATUS_ADJ_INEQ
)
604 if (k
>= info
[i
].bmap
->n_ineq
)
605 isl_die(isl_basic_map_get_ctx(info
[i
].bmap
), isl_error_internal
,
606 "info[i].ineq should have exactly one STATUS_ADJ_INEQ",
607 return isl_change_error
);
609 snap
= isl_tab_snap(info
[i
].tab
);
611 if (isl_tab_unrestrict(info
[i
].tab
, n_eq
+ k
) < 0)
612 return isl_change_error
;
614 isl_seq_neg(info
[i
].bmap
->ineq
[k
], info
[i
].bmap
->ineq
[k
], 1 + total
);
615 isl_int_sub_ui(info
[i
].bmap
->ineq
[k
][0], info
[i
].bmap
->ineq
[k
][0], 1);
616 r
= isl_tab_add_ineq(info
[i
].tab
, info
[i
].bmap
->ineq
[k
]);
617 isl_seq_neg(info
[i
].bmap
->ineq
[k
], info
[i
].bmap
->ineq
[k
], 1 + total
);
618 isl_int_sub_ui(info
[i
].bmap
->ineq
[k
][0], info
[i
].bmap
->ineq
[k
][0], 1);
620 return isl_change_error
;
622 for (k
= 0; k
< info
[j
].bmap
->n_ineq
; ++k
) {
623 if (info
[j
].ineq
[k
] != STATUS_VALID
)
625 if (isl_tab_add_ineq(info
[i
].tab
, info
[j
].bmap
->ineq
[k
]) < 0)
626 return isl_change_error
;
629 super
= contains(&info
[j
], info
[i
].tab
);
631 return isl_change_error
;
633 return fuse(i
, j
, info
, NULL
, 0, 0);
635 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
636 return isl_change_error
;
638 return isl_change_none
;
642 /* Both basic maps have at least one inequality with and adjacent
643 * (but opposite) inequality in the other basic map.
644 * Check that there are no cut constraints and that there is only
645 * a single pair of adjacent inequalities.
646 * If so, we can replace the pair by a single basic map described
647 * by all but the pair of adjacent inequalities.
648 * Any additional points introduced lie strictly between the two
649 * adjacent hyperplanes and can therefore be integral.
658 * The test for a single pair of adjancent inequalities is important
659 * for avoiding the combination of two basic maps like the following
669 * If there are some cut constraints on one side, then we may
670 * still be able to fuse the two basic maps, but we need to perform
671 * some additional checks in is_adj_ineq_extension.
673 static enum isl_change
check_adj_ineq(int i
, int j
,
674 struct isl_coalesce_info
*info
)
676 int count_i
, count_j
;
679 count_i
= count(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ADJ_INEQ
);
680 count_j
= count(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_ADJ_INEQ
);
682 if (count_i
!= 1 && count_j
!= 1)
683 return isl_change_none
;
685 cut_i
= any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_CUT
) ||
686 any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_CUT
);
687 cut_j
= any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_CUT
) ||
688 any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_CUT
);
690 if (!cut_i
&& !cut_j
&& count_i
== 1 && count_j
== 1)
691 return fuse(i
, j
, info
, NULL
, 0, 0);
693 if (count_i
== 1 && !cut_i
)
694 return is_adj_ineq_extension(i
, j
, info
);
696 if (count_j
== 1 && !cut_j
)
697 return is_adj_ineq_extension(j
, i
, info
);
699 return isl_change_none
;
702 /* Basic map "i" has an inequality "k" that is adjacent to some equality
703 * of basic map "j". All the other inequalities are valid for "j".
704 * Check if basic map "j" forms an extension of basic map "i".
706 * In particular, we relax constraint "k", compute the corresponding
707 * facet and check whether it is included in the other basic map.
708 * If so, we know that relaxing the constraint extends the basic
709 * map with exactly the other basic map (we already know that this
710 * other basic map is included in the extension, because there
711 * were no "cut" inequalities in "i") and we can replace the
712 * two basic maps by this extension.
713 * Each integer division that does not have exactly the same
714 * definition in "i" and "j" is marked unknown and the basic map
715 * is scheduled to be simplified in an attempt to recover
716 * the integer division definition.
717 * Place this extension in the position that is the smallest of i and j.
725 static enum isl_change
is_adj_eq_extension(int i
, int j
, int k
,
726 struct isl_coalesce_info
*info
)
728 int change
= isl_change_none
;
730 struct isl_tab_undo
*snap
, *snap2
;
731 unsigned n_eq
= info
[i
].bmap
->n_eq
;
733 if (isl_tab_is_equality(info
[i
].tab
, n_eq
+ k
))
734 return isl_change_none
;
736 snap
= isl_tab_snap(info
[i
].tab
);
737 if (isl_tab_relax(info
[i
].tab
, n_eq
+ k
) < 0)
738 return isl_change_error
;
739 snap2
= isl_tab_snap(info
[i
].tab
);
740 if (isl_tab_select_facet(info
[i
].tab
, n_eq
+ k
) < 0)
741 return isl_change_error
;
742 super
= contains(&info
[j
], info
[i
].tab
);
744 return isl_change_error
;
749 if (isl_tab_rollback(info
[i
].tab
, snap2
) < 0)
750 return isl_change_error
;
751 info
[i
].bmap
= isl_basic_map_cow(info
[i
].bmap
);
753 return isl_change_error
;
754 total
= isl_basic_map_total_dim(info
[i
].bmap
);
755 for (l
= 0; l
< info
[i
].bmap
->n_div
; ++l
)
756 if (!isl_seq_eq(info
[i
].bmap
->div
[l
],
757 info
[j
].bmap
->div
[l
], 1 + 1 + total
)) {
758 isl_int_set_si(info
[i
].bmap
->div
[l
][0], 0);
759 info
[i
].simplify
= 1;
761 isl_int_add_ui(info
[i
].bmap
->ineq
[k
][0],
762 info
[i
].bmap
->ineq
[k
][0], 1);
763 ISL_F_SET(info
[i
].bmap
, ISL_BASIC_MAP_FINAL
);
766 exchange(&info
[i
], &info
[j
]);
767 change
= isl_change_fuse
;
769 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
770 return isl_change_error
;
775 /* Data structure that keeps track of the wrapping constraints
776 * and of information to bound the coefficients of those constraints.
778 * bound is set if we want to apply a bound on the coefficients
779 * mat contains the wrapping constraints
780 * max is the bound on the coefficients (if bound is set)
788 /* Update wraps->max to be greater than or equal to the coefficients
789 * in the equalities and inequalities of info->bmap that can be removed
790 * if we end up applying wrapping.
792 static void wraps_update_max(struct isl_wraps
*wraps
,
793 struct isl_coalesce_info
*info
)
797 unsigned total
= isl_basic_map_total_dim(info
->bmap
);
801 for (k
= 0; k
< info
->bmap
->n_eq
; ++k
) {
802 if (info
->eq
[2 * k
] == STATUS_VALID
&&
803 info
->eq
[2 * k
+ 1] == STATUS_VALID
)
805 isl_seq_abs_max(info
->bmap
->eq
[k
] + 1, total
, &max_k
);
806 if (isl_int_abs_gt(max_k
, wraps
->max
))
807 isl_int_set(wraps
->max
, max_k
);
810 for (k
= 0; k
< info
->bmap
->n_ineq
; ++k
) {
811 if (info
->ineq
[k
] == STATUS_VALID
||
812 info
->ineq
[k
] == STATUS_REDUNDANT
)
814 isl_seq_abs_max(info
->bmap
->ineq
[k
] + 1, total
, &max_k
);
815 if (isl_int_abs_gt(max_k
, wraps
->max
))
816 isl_int_set(wraps
->max
, max_k
);
819 isl_int_clear(max_k
);
822 /* Initialize the isl_wraps data structure.
823 * If we want to bound the coefficients of the wrapping constraints,
824 * we set wraps->max to the largest coefficient
825 * in the equalities and inequalities that can be removed if we end up
828 static void wraps_init(struct isl_wraps
*wraps
, __isl_take isl_mat
*mat
,
829 struct isl_coalesce_info
*info
, int i
, int j
)
837 ctx
= isl_mat_get_ctx(mat
);
838 wraps
->bound
= isl_options_get_coalesce_bounded_wrapping(ctx
);
841 isl_int_init(wraps
->max
);
842 isl_int_set_si(wraps
->max
, 0);
843 wraps_update_max(wraps
, &info
[i
]);
844 wraps_update_max(wraps
, &info
[j
]);
847 /* Free the contents of the isl_wraps data structure.
849 static void wraps_free(struct isl_wraps
*wraps
)
851 isl_mat_free(wraps
->mat
);
853 isl_int_clear(wraps
->max
);
856 /* Is the wrapping constraint in row "row" allowed?
858 * If wraps->bound is set, we check that none of the coefficients
859 * is greater than wraps->max.
861 static int allow_wrap(struct isl_wraps
*wraps
, int row
)
868 for (i
= 1; i
< wraps
->mat
->n_col
; ++i
)
869 if (isl_int_abs_gt(wraps
->mat
->row
[row
][i
], wraps
->max
))
875 /* Wrap "ineq" (or its opposite if "negate" is set) around "bound"
876 * to include "set" and add the result in position "w" of "wraps".
877 * "len" is the total number of coefficients in "bound" and "ineq".
878 * Return 1 on success, 0 on failure and -1 on error.
879 * Wrapping can fail if the result of wrapping is equal to "bound"
880 * or if we want to bound the sizes of the coefficients and
881 * the wrapped constraint does not satisfy this bound.
883 static int add_wrap(struct isl_wraps
*wraps
, int w
, isl_int
*bound
,
884 isl_int
*ineq
, unsigned len
, __isl_keep isl_set
*set
, int negate
)
886 isl_seq_cpy(wraps
->mat
->row
[w
], bound
, len
);
888 isl_seq_neg(wraps
->mat
->row
[w
+ 1], ineq
, len
);
889 ineq
= wraps
->mat
->row
[w
+ 1];
891 if (!isl_set_wrap_facet(set
, wraps
->mat
->row
[w
], ineq
))
893 if (isl_seq_eq(wraps
->mat
->row
[w
], bound
, len
))
895 if (!allow_wrap(wraps
, w
))
900 /* For each constraint in info->bmap that is not redundant (as determined
901 * by info->tab) and that is not a valid constraint for the other basic map,
902 * wrap the constraint around "bound" such that it includes the whole
903 * set "set" and append the resulting constraint to "wraps".
904 * Note that the constraints that are valid for the other basic map
905 * will be added to the combined basic map by default, so there is
906 * no need to wrap them.
907 * The caller wrap_in_facets even relies on this function not wrapping
908 * any constraints that are already valid.
909 * "wraps" is assumed to have been pre-allocated to the appropriate size.
910 * wraps->n_row is the number of actual wrapped constraints that have
912 * If any of the wrapping problems results in a constraint that is
913 * identical to "bound", then this means that "set" is unbounded in such
914 * way that no wrapping is possible. If this happens then wraps->n_row
916 * Similarly, if we want to bound the coefficients of the wrapping
917 * constraints and a newly added wrapping constraint does not
918 * satisfy the bound, then wraps->n_row is also reset to zero.
920 static int add_wraps(struct isl_wraps
*wraps
, struct isl_coalesce_info
*info
,
921 isl_int
*bound
, __isl_keep isl_set
*set
)
926 isl_basic_map
*bmap
= info
->bmap
;
927 unsigned len
= 1 + isl_basic_map_total_dim(bmap
);
929 w
= wraps
->mat
->n_row
;
931 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
932 if (info
->ineq
[l
] == STATUS_VALID
||
933 info
->ineq
[l
] == STATUS_REDUNDANT
)
935 if (isl_seq_is_neg(bound
, bmap
->ineq
[l
], len
))
937 if (isl_seq_eq(bound
, bmap
->ineq
[l
], len
))
939 if (isl_tab_is_redundant(info
->tab
, bmap
->n_eq
+ l
))
942 added
= add_wrap(wraps
, w
, bound
, bmap
->ineq
[l
], len
, set
, 0);
949 for (l
= 0; l
< bmap
->n_eq
; ++l
) {
950 if (isl_seq_is_neg(bound
, bmap
->eq
[l
], len
))
952 if (isl_seq_eq(bound
, bmap
->eq
[l
], len
))
955 for (m
= 0; m
< 2; ++m
) {
956 if (info
->eq
[2 * l
+ m
] == STATUS_VALID
)
958 added
= add_wrap(wraps
, w
, bound
, bmap
->eq
[l
], len
,
968 wraps
->mat
->n_row
= w
;
971 wraps
->mat
->n_row
= 0;
975 /* Check if the constraints in "wraps" from "first" until the last
976 * are all valid for the basic set represented by "tab".
977 * If not, wraps->n_row is set to zero.
979 static int check_wraps(__isl_keep isl_mat
*wraps
, int first
,
984 for (i
= first
; i
< wraps
->n_row
; ++i
) {
985 enum isl_ineq_type type
;
986 type
= isl_tab_ineq_type(tab
, wraps
->row
[i
]);
987 if (type
== isl_ineq_error
)
989 if (type
== isl_ineq_redundant
)
998 /* Return a set that corresponds to the non-redundant constraints
999 * (as recorded in tab) of bmap.
1001 * It's important to remove the redundant constraints as some
1002 * of the other constraints may have been modified after the
1003 * constraints were marked redundant.
1004 * In particular, a constraint may have been relaxed.
1005 * Redundant constraints are ignored when a constraint is relaxed
1006 * and should therefore continue to be ignored ever after.
1007 * Otherwise, the relaxation might be thwarted by some of
1008 * these constraints.
1010 * Update the underlying set to ensure that the dimension doesn't change.
1011 * Otherwise the integer divisions could get dropped if the tab
1012 * turns out to be empty.
1014 static __isl_give isl_set
*set_from_updated_bmap(__isl_keep isl_basic_map
*bmap
,
1015 struct isl_tab
*tab
)
1017 isl_basic_set
*bset
;
1019 bmap
= isl_basic_map_copy(bmap
);
1020 bset
= isl_basic_map_underlying_set(bmap
);
1021 bset
= isl_basic_set_cow(bset
);
1022 bset
= isl_basic_set_update_from_tab(bset
, tab
);
1023 return isl_set_from_basic_set(bset
);
1026 /* Wrap the constraints of info->bmap that bound the facet defined
1027 * by inequality "k" around (the opposite of) this inequality to
1028 * include "set". "bound" may be used to store the negated inequality.
1029 * Since the wrapped constraints are not guaranteed to contain the whole
1030 * of info->bmap, we check them in check_wraps.
1031 * If any of the wrapped constraints turn out to be invalid, then
1032 * check_wraps will reset wrap->n_row to zero.
1034 static int add_wraps_around_facet(struct isl_wraps
*wraps
,
1035 struct isl_coalesce_info
*info
, int k
, isl_int
*bound
,
1036 __isl_keep isl_set
*set
)
1038 struct isl_tab_undo
*snap
;
1040 unsigned total
= isl_basic_map_total_dim(info
->bmap
);
1042 snap
= isl_tab_snap(info
->tab
);
1044 if (isl_tab_select_facet(info
->tab
, info
->bmap
->n_eq
+ k
) < 0)
1046 if (isl_tab_detect_redundant(info
->tab
) < 0)
1049 isl_seq_neg(bound
, info
->bmap
->ineq
[k
], 1 + total
);
1051 n
= wraps
->mat
->n_row
;
1052 if (add_wraps(wraps
, info
, bound
, set
) < 0)
1055 if (isl_tab_rollback(info
->tab
, snap
) < 0)
1057 if (check_wraps(wraps
->mat
, n
, info
->tab
) < 0)
1063 /* Given a basic set i with a constraint k that is adjacent to
1064 * basic set j, check if we can wrap
1065 * both the facet corresponding to k (if "wrap_facet" is set) and basic map j
1066 * (always) around their ridges to include the other set.
1067 * If so, replace the pair of basic sets by their union.
1069 * All constraints of i (except k) are assumed to be valid or
1070 * cut constraints for j.
1071 * Wrapping the cut constraints to include basic map j may result
1072 * in constraints that are no longer valid of basic map i
1073 * we have to check that the resulting wrapping constraints are valid for i.
1074 * If "wrap_facet" is not set, then all constraints of i (except k)
1075 * are assumed to be valid for j.
1084 static enum isl_change
can_wrap_in_facet(int i
, int j
, int k
,
1085 struct isl_coalesce_info
*info
, int wrap_facet
)
1087 enum isl_change change
= isl_change_none
;
1088 struct isl_wraps wraps
;
1091 struct isl_set
*set_i
= NULL
;
1092 struct isl_set
*set_j
= NULL
;
1093 struct isl_vec
*bound
= NULL
;
1094 unsigned total
= isl_basic_map_total_dim(info
[i
].bmap
);
1096 set_i
= set_from_updated_bmap(info
[i
].bmap
, info
[i
].tab
);
1097 set_j
= set_from_updated_bmap(info
[j
].bmap
, info
[j
].tab
);
1098 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
1099 mat
= isl_mat_alloc(ctx
, 2 * (info
[i
].bmap
->n_eq
+ info
[j
].bmap
->n_eq
) +
1100 info
[i
].bmap
->n_ineq
+ info
[j
].bmap
->n_ineq
,
1102 wraps_init(&wraps
, mat
, info
, i
, j
);
1103 bound
= isl_vec_alloc(ctx
, 1 + total
);
1104 if (!set_i
|| !set_j
|| !wraps
.mat
|| !bound
)
1107 isl_seq_cpy(bound
->el
, info
[i
].bmap
->ineq
[k
], 1 + total
);
1108 isl_int_add_ui(bound
->el
[0], bound
->el
[0], 1);
1110 isl_seq_cpy(wraps
.mat
->row
[0], bound
->el
, 1 + total
);
1111 wraps
.mat
->n_row
= 1;
1113 if (add_wraps(&wraps
, &info
[j
], bound
->el
, set_i
) < 0)
1115 if (!wraps
.mat
->n_row
)
1119 if (add_wraps_around_facet(&wraps
, &info
[i
], k
,
1120 bound
->el
, set_j
) < 0)
1122 if (!wraps
.mat
->n_row
)
1126 change
= fuse(i
, j
, info
, wraps
.mat
, 0, 0);
1131 isl_set_free(set_i
);
1132 isl_set_free(set_j
);
1134 isl_vec_free(bound
);
1139 isl_vec_free(bound
);
1140 isl_set_free(set_i
);
1141 isl_set_free(set_j
);
1142 return isl_change_error
;
1145 /* Given a pair of basic maps i and j such that j sticks out
1146 * of i at n cut constraints, each time by at most one,
1147 * try to compute wrapping constraints and replace the two
1148 * basic maps by a single basic map.
1149 * The other constraints of i are assumed to be valid for j.
1151 * For each cut constraint t(x) >= 0 of i, we add the relaxed version
1152 * t(x) + 1 >= 0, along with wrapping constraints for all constraints
1153 * of basic map j that bound the part of basic map j that sticks out
1154 * of the cut constraint.
1155 * In particular, we first intersect basic map j with t(x) + 1 = 0.
1156 * If the result is empty, then t(x) >= 0 was actually a valid constraint
1157 * (with respect to the integer points), so we add t(x) >= 0 instead.
1158 * Otherwise, we wrap the constraints of basic map j that are not
1159 * redundant in this intersection and that are not already valid
1160 * for basic map i over basic map i.
1161 * Note that it is sufficient to wrap the constraints to include
1162 * basic map i, because we will only wrap the constraints that do
1163 * not include basic map i already. The wrapped constraint will
1164 * therefore be more relaxed compared to the original constraint.
1165 * Since the original constraint is valid for basic map j, so is
1166 * the wrapped constraint.
1168 * If any wrapping fails, i.e., if we cannot wrap to touch
1169 * the union, then we give up.
1170 * Otherwise, the pair of basic maps is replaced by their union.
1172 static enum isl_change
wrap_in_facets(int i
, int j
, int *cuts
, int n
,
1173 struct isl_coalesce_info
*info
)
1175 enum isl_change change
= isl_change_none
;
1176 struct isl_wraps wraps
;
1179 isl_set
*set_i
= NULL
;
1180 unsigned total
= isl_basic_map_total_dim(info
[i
].bmap
);
1183 struct isl_tab_undo
*snap
;
1185 if (isl_tab_extend_cons(info
[j
].tab
, 1) < 0)
1186 return isl_change_error
;
1188 max_wrap
= 1 + 2 * info
[j
].bmap
->n_eq
+ info
[j
].bmap
->n_ineq
;
1191 set_i
= set_from_updated_bmap(info
[i
].bmap
, info
[i
].tab
);
1192 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
1193 mat
= isl_mat_alloc(ctx
, max_wrap
, 1 + total
);
1194 wraps_init(&wraps
, mat
, info
, i
, j
);
1195 if (!set_i
|| !wraps
.mat
)
1198 snap
= isl_tab_snap(info
[j
].tab
);
1200 wraps
.mat
->n_row
= 0;
1202 for (k
= 0; k
< n
; ++k
) {
1203 w
= wraps
.mat
->n_row
++;
1204 isl_seq_cpy(wraps
.mat
->row
[w
],
1205 info
[i
].bmap
->ineq
[cuts
[k
]], 1 + total
);
1206 isl_int_add_ui(wraps
.mat
->row
[w
][0], wraps
.mat
->row
[w
][0], 1);
1207 if (isl_tab_add_eq(info
[j
].tab
, wraps
.mat
->row
[w
]) < 0)
1209 if (isl_tab_detect_redundant(info
[j
].tab
) < 0)
1212 if (info
[j
].tab
->empty
)
1213 isl_int_sub_ui(wraps
.mat
->row
[w
][0],
1214 wraps
.mat
->row
[w
][0], 1);
1215 else if (add_wraps(&wraps
, &info
[j
],
1216 wraps
.mat
->row
[w
], set_i
) < 0)
1219 if (isl_tab_rollback(info
[j
].tab
, snap
) < 0)
1222 if (!wraps
.mat
->n_row
)
1227 change
= fuse(i
, j
, info
, wraps
.mat
, 0, 1);
1230 isl_set_free(set_i
);
1235 isl_set_free(set_i
);
1236 return isl_change_error
;
1239 /* Given two basic sets i and j such that i has no cut equalities,
1240 * check if relaxing all the cut inequalities of i by one turns
1241 * them into valid constraint for j and check if we can wrap in
1242 * the bits that are sticking out.
1243 * If so, replace the pair by their union.
1245 * We first check if all relaxed cut inequalities of i are valid for j
1246 * and then try to wrap in the intersections of the relaxed cut inequalities
1249 * During this wrapping, we consider the points of j that lie at a distance
1250 * of exactly 1 from i. In particular, we ignore the points that lie in
1251 * between this lower-dimensional space and the basic map i.
1252 * We can therefore only apply this to integer maps.
1278 * Wrapping can fail if the result of wrapping one of the facets
1279 * around its edges does not produce any new facet constraint.
1280 * In particular, this happens when we try to wrap in unbounded sets.
1282 * _______________________________________________________________________
1286 * |_| |_________________________________________________________________
1289 * The following is not an acceptable result of coalescing the above two
1290 * sets as it includes extra integer points.
1291 * _______________________________________________________________________
1296 * \______________________________________________________________________
1298 static enum isl_change
can_wrap_in_set(int i
, int j
,
1299 struct isl_coalesce_info
*info
)
1301 enum isl_change change
= isl_change_none
;
1307 if (ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_RATIONAL
) ||
1308 ISL_F_ISSET(info
[j
].bmap
, ISL_BASIC_MAP_RATIONAL
))
1309 return isl_change_none
;
1311 n
= count(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_CUT
);
1313 return isl_change_none
;
1315 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
1316 cuts
= isl_alloc_array(ctx
, int, n
);
1318 return isl_change_error
;
1320 for (k
= 0, m
= 0; m
< n
; ++k
) {
1321 enum isl_ineq_type type
;
1323 if (info
[i
].ineq
[k
] != STATUS_CUT
)
1326 isl_int_add_ui(info
[i
].bmap
->ineq
[k
][0],
1327 info
[i
].bmap
->ineq
[k
][0], 1);
1328 type
= isl_tab_ineq_type(info
[j
].tab
, info
[i
].bmap
->ineq
[k
]);
1329 isl_int_sub_ui(info
[i
].bmap
->ineq
[k
][0],
1330 info
[i
].bmap
->ineq
[k
][0], 1);
1331 if (type
== isl_ineq_error
)
1333 if (type
!= isl_ineq_redundant
)
1340 change
= wrap_in_facets(i
, j
, cuts
, n
, info
);
1347 return isl_change_error
;
1350 /* Check if either i or j has only cut inequalities that can
1351 * be used to wrap in (a facet of) the other basic set.
1352 * if so, replace the pair by their union.
1354 static enum isl_change
check_wrap(int i
, int j
, struct isl_coalesce_info
*info
)
1356 enum isl_change change
= isl_change_none
;
1358 if (!any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_CUT
))
1359 change
= can_wrap_in_set(i
, j
, info
);
1360 if (change
!= isl_change_none
)
1363 if (!any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_CUT
))
1364 change
= can_wrap_in_set(j
, i
, info
);
1368 /* At least one of the basic maps has an equality that is adjacent
1369 * to inequality. Make sure that only one of the basic maps has
1370 * such an equality and that the other basic map has exactly one
1371 * inequality adjacent to an equality.
1372 * We call the basic map that has the inequality "i" and the basic
1373 * map that has the equality "j".
1374 * If "i" has any "cut" (in)equality, then relaxing the inequality
1375 * by one would not result in a basic map that contains the other
1376 * basic map. However, it may still be possible to wrap in the other
1379 static enum isl_change
check_adj_eq(int i
, int j
,
1380 struct isl_coalesce_info
*info
)
1382 enum isl_change change
= isl_change_none
;
1386 if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_ADJ_INEQ
) &&
1387 any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_ADJ_INEQ
))
1388 /* ADJ EQ TOO MANY */
1389 return isl_change_none
;
1391 if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_ADJ_INEQ
))
1392 return check_adj_eq(j
, i
, info
);
1394 /* j has an equality adjacent to an inequality in i */
1396 if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_CUT
))
1397 return isl_change_none
;
1398 any_cut
= any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_CUT
);
1399 if (count(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ADJ_EQ
) != 1 ||
1400 any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_ADJ_EQ
) ||
1401 any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ADJ_INEQ
) ||
1402 any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_ADJ_INEQ
))
1403 /* ADJ EQ TOO MANY */
1404 return isl_change_none
;
1406 for (k
= 0; k
< info
[i
].bmap
->n_ineq
; ++k
)
1407 if (info
[i
].ineq
[k
] == STATUS_ADJ_EQ
)
1411 change
= is_adj_eq_extension(i
, j
, k
, info
);
1412 if (change
!= isl_change_none
)
1416 change
= can_wrap_in_facet(i
, j
, k
, info
, any_cut
);
1421 /* The two basic maps lie on adjacent hyperplanes. In particular,
1422 * basic map "i" has an equality that lies parallel to basic map "j".
1423 * Check if we can wrap the facets around the parallel hyperplanes
1424 * to include the other set.
1426 * We perform basically the same operations as can_wrap_in_facet,
1427 * except that we don't need to select a facet of one of the sets.
1433 * If there is more than one equality of "i" adjacent to an equality of "j",
1434 * then the result will satisfy one or more equalities that are a linear
1435 * combination of these equalities. These will be encoded as pairs
1436 * of inequalities in the wrapping constraints and need to be made
1439 static enum isl_change
check_eq_adj_eq(int i
, int j
,
1440 struct isl_coalesce_info
*info
)
1443 enum isl_change change
= isl_change_none
;
1444 int detect_equalities
= 0;
1445 struct isl_wraps wraps
;
1448 struct isl_set
*set_i
= NULL
;
1449 struct isl_set
*set_j
= NULL
;
1450 struct isl_vec
*bound
= NULL
;
1451 unsigned total
= isl_basic_map_total_dim(info
[i
].bmap
);
1453 if (count(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_ADJ_EQ
) != 1)
1454 detect_equalities
= 1;
1456 for (k
= 0; k
< 2 * info
[i
].bmap
->n_eq
; ++k
)
1457 if (info
[i
].eq
[k
] == STATUS_ADJ_EQ
)
1460 set_i
= set_from_updated_bmap(info
[i
].bmap
, info
[i
].tab
);
1461 set_j
= set_from_updated_bmap(info
[j
].bmap
, info
[j
].tab
);
1462 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
1463 mat
= isl_mat_alloc(ctx
, 2 * (info
[i
].bmap
->n_eq
+ info
[j
].bmap
->n_eq
) +
1464 info
[i
].bmap
->n_ineq
+ info
[j
].bmap
->n_ineq
,
1466 wraps_init(&wraps
, mat
, info
, i
, j
);
1467 bound
= isl_vec_alloc(ctx
, 1 + total
);
1468 if (!set_i
|| !set_j
|| !wraps
.mat
|| !bound
)
1472 isl_seq_neg(bound
->el
, info
[i
].bmap
->eq
[k
/ 2], 1 + total
);
1474 isl_seq_cpy(bound
->el
, info
[i
].bmap
->eq
[k
/ 2], 1 + total
);
1475 isl_int_add_ui(bound
->el
[0], bound
->el
[0], 1);
1477 isl_seq_cpy(wraps
.mat
->row
[0], bound
->el
, 1 + total
);
1478 wraps
.mat
->n_row
= 1;
1480 if (add_wraps(&wraps
, &info
[j
], bound
->el
, set_i
) < 0)
1482 if (!wraps
.mat
->n_row
)
1485 isl_int_sub_ui(bound
->el
[0], bound
->el
[0], 1);
1486 isl_seq_neg(bound
->el
, bound
->el
, 1 + total
);
1488 isl_seq_cpy(wraps
.mat
->row
[wraps
.mat
->n_row
], bound
->el
, 1 + total
);
1491 if (add_wraps(&wraps
, &info
[i
], bound
->el
, set_j
) < 0)
1493 if (!wraps
.mat
->n_row
)
1496 change
= fuse(i
, j
, info
, wraps
.mat
, detect_equalities
, 0);
1499 error
: change
= isl_change_error
;
1504 isl_set_free(set_i
);
1505 isl_set_free(set_j
);
1506 isl_vec_free(bound
);
1511 /* Initialize the "eq" and "ineq" fields of "info".
1513 static void init_status(struct isl_coalesce_info
*info
)
1515 info
->eq
= info
->ineq
= NULL
;
1518 /* Set info->eq to the positions of the equalities of info->bmap
1519 * with respect to the basic map represented by "tab".
1520 * If info->eq has already been computed, then do not compute it again.
1522 static void set_eq_status_in(struct isl_coalesce_info
*info
,
1523 struct isl_tab
*tab
)
1527 info
->eq
= eq_status_in(info
->bmap
, tab
);
1530 /* Set info->ineq to the positions of the inequalities of info->bmap
1531 * with respect to the basic map represented by "tab".
1532 * If info->ineq has already been computed, then do not compute it again.
1534 static void set_ineq_status_in(struct isl_coalesce_info
*info
,
1535 struct isl_tab
*tab
)
1539 info
->ineq
= ineq_status_in(info
->bmap
, info
->tab
, tab
);
1542 /* Free the memory allocated by the "eq" and "ineq" fields of "info".
1543 * This function assumes that init_status has been called on "info" first,
1544 * after which the "eq" and "ineq" fields may or may not have been
1545 * assigned a newly allocated array.
1547 static void clear_status(struct isl_coalesce_info
*info
)
1553 /* Check if the union of the given pair of basic maps
1554 * can be represented by a single basic map.
1555 * If so, replace the pair by the single basic map and return
1556 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
1557 * Otherwise, return isl_change_none.
1558 * The two basic maps are assumed to live in the same local space.
1559 * The "eq" and "ineq" fields of info[i] and info[j] are assumed
1560 * to have been initialized by the caller, either to NULL or
1561 * to valid information.
1563 * We first check the effect of each constraint of one basic map
1564 * on the other basic map.
1565 * The constraint may be
1566 * redundant the constraint is redundant in its own
1567 * basic map and should be ignore and removed
1569 * valid all (integer) points of the other basic map
1570 * satisfy the constraint
1571 * separate no (integer) point of the other basic map
1572 * satisfies the constraint
1573 * cut some but not all points of the other basic map
1574 * satisfy the constraint
1575 * adj_eq the given constraint is adjacent (on the outside)
1576 * to an equality of the other basic map
1577 * adj_ineq the given constraint is adjacent (on the outside)
1578 * to an inequality of the other basic map
1580 * We consider seven cases in which we can replace the pair by a single
1581 * basic map. We ignore all "redundant" constraints.
1583 * 1. all constraints of one basic map are valid
1584 * => the other basic map is a subset and can be removed
1586 * 2. all constraints of both basic maps are either "valid" or "cut"
1587 * and the facets corresponding to the "cut" constraints
1588 * of one of the basic maps lies entirely inside the other basic map
1589 * => the pair can be replaced by a basic map consisting
1590 * of the valid constraints in both basic maps
1592 * 3. there is a single pair of adjacent inequalities
1593 * (all other constraints are "valid")
1594 * => the pair can be replaced by a basic map consisting
1595 * of the valid constraints in both basic maps
1597 * 4. one basic map has a single adjacent inequality, while the other
1598 * constraints are "valid". The other basic map has some
1599 * "cut" constraints, but replacing the adjacent inequality by
1600 * its opposite and adding the valid constraints of the other
1601 * basic map results in a subset of the other basic map
1602 * => the pair can be replaced by a basic map consisting
1603 * of the valid constraints in both basic maps
1605 * 5. there is a single adjacent pair of an inequality and an equality,
1606 * the other constraints of the basic map containing the inequality are
1607 * "valid". Moreover, if the inequality the basic map is relaxed
1608 * and then turned into an equality, then resulting facet lies
1609 * entirely inside the other basic map
1610 * => the pair can be replaced by the basic map containing
1611 * the inequality, with the inequality relaxed.
1613 * 6. there is a single adjacent pair of an inequality and an equality,
1614 * the other constraints of the basic map containing the inequality are
1615 * "valid". Moreover, the facets corresponding to both
1616 * the inequality and the equality can be wrapped around their
1617 * ridges to include the other basic map
1618 * => the pair can be replaced by a basic map consisting
1619 * of the valid constraints in both basic maps together
1620 * with all wrapping constraints
1622 * 7. one of the basic maps extends beyond the other by at most one.
1623 * Moreover, the facets corresponding to the cut constraints and
1624 * the pieces of the other basic map at offset one from these cut
1625 * constraints can be wrapped around their ridges to include
1626 * the union of the two basic maps
1627 * => the pair can be replaced by a basic map consisting
1628 * of the valid constraints in both basic maps together
1629 * with all wrapping constraints
1631 * 8. the two basic maps live in adjacent hyperplanes. In principle
1632 * such sets can always be combined through wrapping, but we impose
1633 * that there is only one such pair, to avoid overeager coalescing.
1635 * Throughout the computation, we maintain a collection of tableaus
1636 * corresponding to the basic maps. When the basic maps are dropped
1637 * or combined, the tableaus are modified accordingly.
1639 static enum isl_change
coalesce_local_pair_reuse(int i
, int j
,
1640 struct isl_coalesce_info
*info
)
1642 enum isl_change change
= isl_change_none
;
1644 set_eq_status_in(&info
[i
], info
[j
].tab
);
1645 if (info
[i
].bmap
->n_eq
&& !info
[i
].eq
)
1647 if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_ERROR
))
1649 if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_SEPARATE
))
1652 set_eq_status_in(&info
[j
], info
[i
].tab
);
1653 if (info
[j
].bmap
->n_eq
&& !info
[j
].eq
)
1655 if (any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_ERROR
))
1657 if (any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_SEPARATE
))
1660 set_ineq_status_in(&info
[i
], info
[j
].tab
);
1661 if (info
[i
].bmap
->n_ineq
&& !info
[i
].ineq
)
1663 if (any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ERROR
))
1665 if (any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_SEPARATE
))
1668 set_ineq_status_in(&info
[j
], info
[i
].tab
);
1669 if (info
[j
].bmap
->n_ineq
&& !info
[j
].ineq
)
1671 if (any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_ERROR
))
1673 if (any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_SEPARATE
))
1676 if (all(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_VALID
) &&
1677 all(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_VALID
)) {
1679 change
= isl_change_drop_second
;
1680 } else if (all(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_VALID
) &&
1681 all(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_VALID
)) {
1683 change
= isl_change_drop_first
;
1684 } else if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_ADJ_EQ
)) {
1685 change
= check_eq_adj_eq(i
, j
, info
);
1686 } else if (any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_ADJ_EQ
)) {
1687 change
= check_eq_adj_eq(j
, i
, info
);
1688 } else if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_ADJ_INEQ
) ||
1689 any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_ADJ_INEQ
)) {
1690 change
= check_adj_eq(i
, j
, info
);
1691 } else if (any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ADJ_EQ
) ||
1692 any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_ADJ_EQ
)) {
1695 } else if (any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ADJ_INEQ
) ||
1696 any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_ADJ_INEQ
)) {
1697 change
= check_adj_ineq(i
, j
, info
);
1699 if (!any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_CUT
) &&
1700 !any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_CUT
))
1701 change
= check_facets(i
, j
, info
);
1702 if (change
== isl_change_none
)
1703 change
= check_wrap(i
, j
, info
);
1707 clear_status(&info
[i
]);
1708 clear_status(&info
[j
]);
1711 clear_status(&info
[i
]);
1712 clear_status(&info
[j
]);
1713 return isl_change_error
;
1716 /* Check if the union of the given pair of basic maps
1717 * can be represented by a single basic map.
1718 * If so, replace the pair by the single basic map and return
1719 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
1720 * Otherwise, return isl_change_none.
1721 * The two basic maps are assumed to live in the same local space.
1723 static enum isl_change
coalesce_local_pair(int i
, int j
,
1724 struct isl_coalesce_info
*info
)
1726 init_status(&info
[i
]);
1727 init_status(&info
[j
]);
1728 return coalesce_local_pair_reuse(i
, j
, info
);
1731 /* Shift the integer division at position "div" of the basic map
1732 * represented by "info" by "shift".
1734 * That is, if the integer division has the form
1738 * then replace it by
1740 * floor((f(x) + shift * d)/d) - shift
1742 static int shift_div(struct isl_coalesce_info
*info
, int div
, isl_int shift
)
1746 info
->bmap
= isl_basic_map_shift_div(info
->bmap
, div
, 0, shift
);
1750 total
= isl_basic_map_dim(info
->bmap
, isl_dim_all
);
1751 total
-= isl_basic_map_dim(info
->bmap
, isl_dim_div
);
1752 if (isl_tab_shift_var(info
->tab
, total
+ div
, shift
) < 0)
1758 /* Check if some of the divs in the basic map represented by "info1"
1759 * are shifts of the corresponding divs in the basic map represented
1760 * by "info2". If so, align them with those of "info2".
1761 * Only do this if "info1" and "info2" have the same number
1762 * of integer divisions.
1764 * An integer division is considered to be a shift of another integer
1765 * division if one is equal to the other plus a constant.
1767 * In particular, for each pair of integer divisions, if both are known,
1768 * have identical coefficients (apart from the constant term) and
1769 * if the difference between the constant terms (taking into account
1770 * the denominator) is an integer, then move the difference outside.
1771 * That is, if one integer division is of the form
1773 * floor((f(x) + c_1)/d)
1775 * while the other is of the form
1777 * floor((f(x) + c_2)/d)
1779 * and n = (c_2 - c_1)/d is an integer, then replace the first
1780 * integer division by
1782 * floor((f(x) + c_1 + n * d)/d) - n = floor((f(x) + c_2)/d) - n
1784 static int harmonize_divs(struct isl_coalesce_info
*info1
,
1785 struct isl_coalesce_info
*info2
)
1790 if (!info1
->bmap
|| !info2
->bmap
)
1793 if (info1
->bmap
->n_div
!= info2
->bmap
->n_div
)
1795 if (info1
->bmap
->n_div
== 0)
1798 total
= isl_basic_map_total_dim(info1
->bmap
);
1799 for (i
= 0; i
< info1
->bmap
->n_div
; ++i
) {
1803 if (isl_int_is_zero(info1
->bmap
->div
[i
][0]) ||
1804 isl_int_is_zero(info2
->bmap
->div
[i
][0]))
1806 if (isl_int_ne(info1
->bmap
->div
[i
][0], info2
->bmap
->div
[i
][0]))
1808 if (isl_int_eq(info1
->bmap
->div
[i
][1], info2
->bmap
->div
[i
][1]))
1810 if (!isl_seq_eq(info1
->bmap
->div
[i
] + 2,
1811 info2
->bmap
->div
[i
] + 2, total
))
1814 isl_int_sub(d
, info2
->bmap
->div
[i
][1], info1
->bmap
->div
[i
][1]);
1815 if (isl_int_is_divisible_by(d
, info1
->bmap
->div
[i
][0])) {
1816 isl_int_divexact(d
, d
, info1
->bmap
->div
[i
][0]);
1817 r
= shift_div(info1
, i
, d
);
1827 /* Do the two basic maps live in the same local space, i.e.,
1828 * do they have the same (known) divs?
1829 * If either basic map has any unknown divs, then we can only assume
1830 * that they do not live in the same local space.
1832 static int same_divs(__isl_keep isl_basic_map
*bmap1
,
1833 __isl_keep isl_basic_map
*bmap2
)
1839 if (!bmap1
|| !bmap2
)
1841 if (bmap1
->n_div
!= bmap2
->n_div
)
1844 if (bmap1
->n_div
== 0)
1847 known
= isl_basic_map_divs_known(bmap1
);
1848 if (known
< 0 || !known
)
1850 known
= isl_basic_map_divs_known(bmap2
);
1851 if (known
< 0 || !known
)
1854 total
= isl_basic_map_total_dim(bmap1
);
1855 for (i
= 0; i
< bmap1
->n_div
; ++i
)
1856 if (!isl_seq_eq(bmap1
->div
[i
], bmap2
->div
[i
], 2 + total
))
1862 /* Expand info->tab in the same way info->bmap was expanded in
1863 * isl_basic_map_expand_divs using the expansion "exp" and
1864 * update info->ineq with respect to the redundant constraints
1865 * in the resulting tableau.
1866 * In particular, introduce extra variables corresponding
1867 * to the extra integer divisions and add the div constraints
1868 * that were added to info->bmap after info->tab was created
1869 * from the original info->bmap.
1870 * info->ineq was computed without a tableau and therefore
1871 * does not take into account the redundant constraints
1872 * in the tableau. Mark them here.
1874 static isl_stat
expand_tab(struct isl_coalesce_info
*info
, int *exp
)
1876 unsigned total
, pos
, n_div
;
1878 int i
, n
, j
, n_ineq
;
1881 total
= isl_basic_map_dim(info
->bmap
, isl_dim_all
);
1882 n_div
= isl_basic_map_dim(info
->bmap
, isl_dim_div
);
1883 pos
= total
- n_div
;
1884 extra_var
= total
- info
->tab
->n_var
;
1885 n
= n_div
- extra_var
;
1887 if (isl_tab_extend_vars(info
->tab
, extra_var
) < 0)
1888 return isl_stat_error
;
1889 if (isl_tab_extend_cons(info
->tab
, 2 * extra_var
) < 0)
1890 return isl_stat_error
;
1893 for (j
= 0; j
< n_div
; ++j
) {
1894 if (i
< n
&& exp
[i
] == j
) {
1898 if (isl_tab_insert_var(info
->tab
, pos
+ j
) < 0)
1899 return isl_stat_error
;
1902 n_ineq
= info
->tab
->n_con
- info
->tab
->n_eq
;
1903 for (i
= n_ineq
; i
< info
->bmap
->n_ineq
; ++i
)
1904 if (isl_tab_add_ineq(info
->tab
, info
->bmap
->ineq
[i
]) < 0)
1905 return isl_stat_error
;
1907 n_eq
= info
->bmap
->n_eq
;
1908 for (i
= 0; i
< info
->bmap
->n_ineq
; ++i
) {
1909 if (isl_tab_is_redundant(info
->tab
, n_eq
+ i
))
1910 info
->ineq
[i
] = STATUS_REDUNDANT
;
1916 /* Check if the union of the basic maps represented by info[i] and info[j]
1917 * can be represented by a single basic map,
1918 * after expanding the divs of info[i] to match those of info[j].
1919 * If so, replace the pair by the single basic map and return
1920 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
1921 * Otherwise, return isl_change_none.
1923 * The caller has already checked for info[j] being a subset of info[i].
1924 * If some of the divs of info[j] are unknown, then the expanded info[i]
1925 * will not have the corresponding div constraints. The other patterns
1926 * therefore cannot apply. Skip the computation in this case.
1928 * The expansion is performed using the divs "div" and expansion "exp"
1929 * computed by the caller.
1930 * info[i].bmap has already been expanded and the result is passed in
1932 * The "eq" and "ineq" fields of info[i] reflect the status of
1933 * the constraints of the expanded "bmap" with respect to info[j].tab.
1934 * However, inequality constraints that are redundant in info[i].tab
1935 * have not yet been marked as such because no tableau was available.
1937 * Replace info[i].bmap by "bmap" and expand info[i].tab as well,
1938 * updating info[i].ineq with respect to the redundant constraints.
1939 * Then try and coalesce the expanded info[i] with info[j],
1940 * reusing the information in info[i].eq and info[i].ineq.
1941 * If this does not result in any coalescing or if it results in info[j]
1942 * getting dropped (which should not happen in practice, since the case
1943 * of info[j] being a subset of info[i] has already been checked by
1944 * the caller), then revert info[i] to its original state.
1946 static enum isl_change
coalesce_expand_tab_divs(__isl_take isl_basic_map
*bmap
,
1947 int i
, int j
, struct isl_coalesce_info
*info
, __isl_keep isl_mat
*div
,
1951 isl_basic_map
*bmap_i
;
1952 struct isl_tab_undo
*snap
;
1953 enum isl_change change
= isl_change_none
;
1955 known
= isl_basic_map_divs_known(info
[j
].bmap
);
1956 if (known
< 0 || !known
) {
1957 clear_status(&info
[i
]);
1958 isl_basic_map_free(bmap
);
1959 return known
< 0 ? isl_change_error
: isl_change_none
;
1962 bmap_i
= info
[i
].bmap
;
1963 info
[i
].bmap
= isl_basic_map_copy(bmap
);
1964 snap
= isl_tab_snap(info
[i
].tab
);
1965 if (!info
[i
].bmap
|| expand_tab(&info
[i
], exp
) < 0)
1966 change
= isl_change_error
;
1968 init_status(&info
[j
]);
1969 if (change
== isl_change_none
)
1970 change
= coalesce_local_pair_reuse(i
, j
, info
);
1972 clear_status(&info
[i
]);
1973 if (change
!= isl_change_none
&& change
!= isl_change_drop_second
) {
1974 isl_basic_map_free(bmap_i
);
1976 isl_basic_map_free(info
[i
].bmap
);
1977 info
[i
].bmap
= bmap_i
;
1979 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
1980 change
= isl_change_error
;
1983 isl_basic_map_free(bmap
);
1987 /* Check if the union of "bmap" and the basic map represented by info[j]
1988 * can be represented by a single basic map,
1989 * after expanding the divs of "bmap" to match those of info[j].
1990 * If so, replace the pair by the single basic map and return
1991 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
1992 * Otherwise, return isl_change_none.
1994 * In particular, check if the expanded "bmap" contains the basic map
1995 * represented by the tableau info[j].tab.
1996 * The expansion is performed using the divs "div" and expansion "exp"
1997 * computed by the caller.
1998 * Then we check if all constraints of the expanded "bmap" are valid for
2001 * If "i" is not equal to -1, then "bmap" is equal to info[i].bmap.
2002 * In this case, the positions of the constraints of info[i].bmap
2003 * with respect to the basic map represented by info[j] are stored
2006 * If the expanded "bmap" does not contain the basic map
2007 * represented by the tableau info[j].tab and if "i" is not -1,
2008 * i.e., if the original "bmap" is info[i].bmap, then expand info[i].tab
2009 * as well and check if that results in coalescing.
2011 static enum isl_change
coalesce_with_expanded_divs(
2012 __isl_keep isl_basic_map
*bmap
, int i
, int j
,
2013 struct isl_coalesce_info
*info
, __isl_keep isl_mat
*div
, int *exp
)
2015 enum isl_change change
= isl_change_none
;
2016 struct isl_coalesce_info info_local
, *info_i
;
2018 info_i
= i
>= 0 ? &info
[i
] : &info_local
;
2019 init_status(info_i
);
2020 bmap
= isl_basic_map_copy(bmap
);
2021 bmap
= isl_basic_map_expand_divs(bmap
, isl_mat_copy(div
), exp
);
2026 info_i
->eq
= eq_status_in(bmap
, info
[j
].tab
);
2027 if (bmap
->n_eq
&& !info_i
->eq
)
2029 if (any(info_i
->eq
, 2 * bmap
->n_eq
, STATUS_ERROR
))
2031 if (any(info_i
->eq
, 2 * bmap
->n_eq
, STATUS_SEPARATE
))
2034 info_i
->ineq
= ineq_status_in(bmap
, NULL
, info
[j
].tab
);
2035 if (bmap
->n_ineq
&& !info_i
->ineq
)
2037 if (any(info_i
->ineq
, bmap
->n_ineq
, STATUS_ERROR
))
2039 if (any(info_i
->ineq
, bmap
->n_ineq
, STATUS_SEPARATE
))
2042 if (all(info_i
->eq
, 2 * bmap
->n_eq
, STATUS_VALID
) &&
2043 all(info_i
->ineq
, bmap
->n_ineq
, STATUS_VALID
)) {
2045 change
= isl_change_drop_second
;
2048 if (change
== isl_change_none
&& i
!= -1)
2049 return coalesce_expand_tab_divs(bmap
, i
, j
, info
, div
, exp
);
2052 isl_basic_map_free(bmap
);
2053 clear_status(info_i
);
2056 isl_basic_map_free(bmap
);
2057 clear_status(info_i
);
2058 return isl_change_error
;
2061 /* Check if the union of "bmap_i" and the basic map represented by info[j]
2062 * can be represented by a single basic map,
2063 * after aligning the divs of "bmap_i" to match those of info[j].
2064 * If so, replace the pair by the single basic map and return
2065 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
2066 * Otherwise, return isl_change_none.
2068 * In particular, check if "bmap_i" contains the basic map represented by
2069 * info[j] after aligning the divs of "bmap_i" to those of info[j].
2070 * Note that this can only succeed if the number of divs of "bmap_i"
2071 * is smaller than (or equal to) the number of divs of info[j].
2073 * We first check if the divs of "bmap_i" are all known and form a subset
2074 * of those of info[j].bmap. If so, we pass control over to
2075 * coalesce_with_expanded_divs.
2077 * If "i" is not equal to -1, then "bmap" is equal to info[i].bmap.
2079 static enum isl_change
coalesce_after_aligning_divs(
2080 __isl_keep isl_basic_map
*bmap_i
, int i
, int j
,
2081 struct isl_coalesce_info
*info
)
2084 isl_mat
*div_i
, *div_j
, *div
;
2088 enum isl_change change
;
2090 known
= isl_basic_map_divs_known(bmap_i
);
2091 if (known
< 0 || !known
)
2094 ctx
= isl_basic_map_get_ctx(bmap_i
);
2096 div_i
= isl_basic_map_get_divs(bmap_i
);
2097 div_j
= isl_basic_map_get_divs(info
[j
].bmap
);
2099 if (!div_i
|| !div_j
)
2102 exp1
= isl_alloc_array(ctx
, int, div_i
->n_row
);
2103 exp2
= isl_alloc_array(ctx
, int, div_j
->n_row
);
2104 if ((div_i
->n_row
&& !exp1
) || (div_j
->n_row
&& !exp2
))
2107 div
= isl_merge_divs(div_i
, div_j
, exp1
, exp2
);
2111 if (div
->n_row
== div_j
->n_row
)
2112 change
= coalesce_with_expanded_divs(bmap_i
,
2113 i
, j
, info
, div
, exp1
);
2115 change
= isl_change_none
;
2119 isl_mat_free(div_i
);
2120 isl_mat_free(div_j
);
2127 isl_mat_free(div_i
);
2128 isl_mat_free(div_j
);
2131 return isl_change_error
;
2134 /* Check if basic map "j" is a subset of basic map "i" after
2135 * exploiting the extra equalities of "j" to simplify the divs of "i".
2136 * If so, remove basic map "j" and return isl_change_drop_second.
2138 * If "j" does not have any equalities or if they are the same
2139 * as those of "i", then we cannot exploit them to simplify the divs.
2140 * Similarly, if there are no divs in "i", then they cannot be simplified.
2141 * If, on the other hand, the affine hulls of "i" and "j" do not intersect,
2142 * then "j" cannot be a subset of "i".
2144 * Otherwise, we intersect "i" with the affine hull of "j" and then
2145 * check if "j" is a subset of the result after aligning the divs.
2146 * If so, then "j" is definitely a subset of "i" and can be removed.
2147 * Note that if after intersection with the affine hull of "j".
2148 * "i" still has more divs than "j", then there is no way we can
2149 * align the divs of "i" to those of "j".
2151 static enum isl_change
coalesce_subset_with_equalities(int i
, int j
,
2152 struct isl_coalesce_info
*info
)
2154 isl_basic_map
*hull_i
, *hull_j
, *bmap_i
;
2156 enum isl_change change
;
2158 if (info
[j
].bmap
->n_eq
== 0)
2159 return isl_change_none
;
2160 if (info
[i
].bmap
->n_div
== 0)
2161 return isl_change_none
;
2163 hull_i
= isl_basic_map_copy(info
[i
].bmap
);
2164 hull_i
= isl_basic_map_plain_affine_hull(hull_i
);
2165 hull_j
= isl_basic_map_copy(info
[j
].bmap
);
2166 hull_j
= isl_basic_map_plain_affine_hull(hull_j
);
2168 hull_j
= isl_basic_map_intersect(hull_j
, isl_basic_map_copy(hull_i
));
2169 equal
= isl_basic_map_plain_is_equal(hull_i
, hull_j
);
2170 empty
= isl_basic_map_plain_is_empty(hull_j
);
2171 isl_basic_map_free(hull_i
);
2173 if (equal
< 0 || equal
|| empty
< 0 || empty
) {
2174 isl_basic_map_free(hull_j
);
2175 if (equal
< 0 || empty
< 0)
2176 return isl_change_error
;
2177 return isl_change_none
;
2180 bmap_i
= isl_basic_map_copy(info
[i
].bmap
);
2181 bmap_i
= isl_basic_map_intersect(bmap_i
, hull_j
);
2183 return isl_change_error
;
2185 if (bmap_i
->n_div
> info
[j
].bmap
->n_div
) {
2186 isl_basic_map_free(bmap_i
);
2187 return isl_change_none
;
2190 change
= coalesce_after_aligning_divs(bmap_i
, -1, j
, info
);
2192 isl_basic_map_free(bmap_i
);
2197 /* Check if the union of and the basic maps represented by info[i] and info[j]
2198 * can be represented by a single basic map, by aligning or equating
2199 * their integer divisions.
2200 * If so, replace the pair by the single basic map and return
2201 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
2202 * Otherwise, return isl_change_none.
2204 * Note that we only perform any test if the number of divs is different
2205 * in the two basic maps. In case the number of divs is the same,
2206 * we have already established that the divs are different
2207 * in the two basic maps.
2208 * In particular, if the number of divs of basic map i is smaller than
2209 * the number of divs of basic map j, then we check if j is a subset of i
2212 static enum isl_change
coalesce_divs(int i
, int j
,
2213 struct isl_coalesce_info
*info
)
2215 enum isl_change change
= isl_change_none
;
2217 if (info
[i
].bmap
->n_div
< info
[j
].bmap
->n_div
)
2218 change
= coalesce_after_aligning_divs(info
[i
].bmap
, i
, j
, info
);
2219 if (change
!= isl_change_none
)
2222 if (info
[j
].bmap
->n_div
< info
[i
].bmap
->n_div
)
2223 change
= coalesce_after_aligning_divs(info
[j
].bmap
, j
, i
, info
);
2224 if (change
!= isl_change_none
)
2225 return invert_change(change
);
2227 change
= coalesce_subset_with_equalities(i
, j
, info
);
2228 if (change
!= isl_change_none
)
2231 change
= coalesce_subset_with_equalities(j
, i
, info
);
2232 if (change
!= isl_change_none
)
2233 return invert_change(change
);
2235 return isl_change_none
;
2238 /* Does "bmap" involve any divs that themselves refer to divs?
2240 static int has_nested_div(__isl_keep isl_basic_map
*bmap
)
2246 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
2247 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
2250 for (i
= 0; i
< n_div
; ++i
)
2251 if (isl_seq_first_non_zero(bmap
->div
[i
] + 2 + total
,
2258 /* Return a list of affine expressions, one for each integer division
2259 * in "bmap_i". For each integer division that also appears in "bmap_j",
2260 * the affine expression is set to NaN. The number of NaNs in the list
2261 * is equal to the number of integer divisions in "bmap_j".
2262 * For the other integer divisions of "bmap_i", the corresponding
2263 * element in the list is a purely affine expression equal to the integer
2264 * division in "hull".
2265 * If no such list can be constructed, then the number of elements
2266 * in the returned list is smaller than the number of integer divisions
2269 static __isl_give isl_aff_list
*set_up_substitutions(
2270 __isl_keep isl_basic_map
*bmap_i
, __isl_keep isl_basic_map
*bmap_j
,
2271 __isl_take isl_basic_map
*hull
)
2273 unsigned n_div_i
, n_div_j
, total
;
2275 isl_local_space
*ls
;
2276 isl_basic_set
*wrap_hull
;
2284 ctx
= isl_basic_map_get_ctx(hull
);
2286 n_div_i
= isl_basic_map_dim(bmap_i
, isl_dim_div
);
2287 n_div_j
= isl_basic_map_dim(bmap_j
, isl_dim_div
);
2288 total
= isl_basic_map_total_dim(bmap_i
) - n_div_i
;
2290 ls
= isl_basic_map_get_local_space(bmap_i
);
2291 ls
= isl_local_space_wrap(ls
);
2292 wrap_hull
= isl_basic_map_wrap(hull
);
2294 aff_nan
= isl_aff_nan_on_domain(isl_local_space_copy(ls
));
2295 list
= isl_aff_list_alloc(ctx
, n_div_i
);
2298 for (i
= 0; i
< n_div_i
; ++i
) {
2302 isl_seq_eq(bmap_i
->div
[i
], bmap_j
->div
[j
], 2 + total
)) {
2304 list
= isl_aff_list_add(list
, isl_aff_copy(aff_nan
));
2307 if (n_div_i
- i
<= n_div_j
- j
)
2310 aff
= isl_local_space_get_div(ls
, i
);
2311 aff
= isl_aff_substitute_equalities(aff
,
2312 isl_basic_set_copy(wrap_hull
));
2313 aff
= isl_aff_floor(aff
);
2316 if (isl_aff_dim(aff
, isl_dim_div
) != 0) {
2321 list
= isl_aff_list_add(list
, aff
);
2324 isl_aff_free(aff_nan
);
2325 isl_local_space_free(ls
);
2326 isl_basic_set_free(wrap_hull
);
2330 isl_aff_free(aff_nan
);
2331 isl_local_space_free(ls
);
2332 isl_basic_set_free(wrap_hull
);
2333 isl_aff_list_free(list
);
2337 /* Add variables to info->bmap and info->tab corresponding to the elements
2338 * in "list" that are not set to NaN.
2339 * "extra_var" is the number of these elements.
2340 * "dim" is the offset in the variables of "tab" where we should
2341 * start considering the elements in "list".
2342 * When this function returns, the total number of variables in "tab"
2343 * is equal to "dim" plus the number of elements in "list".
2345 * The newly added existentially quantified variables are not given
2346 * an explicit representation because the corresponding div constraints
2347 * do not appear in info->bmap. These constraints are not added
2348 * to info->bmap because for internal consistency, they would need to
2349 * be added to info->tab as well, where they could combine with the equality
2350 * that is added later to result in constraints that do not hold
2351 * in the original input.
2353 static int add_sub_vars(struct isl_coalesce_info
*info
,
2354 __isl_keep isl_aff_list
*list
, int dim
, int extra_var
)
2359 space
= isl_basic_map_get_space(info
->bmap
);
2360 info
->bmap
= isl_basic_map_cow(info
->bmap
);
2361 info
->bmap
= isl_basic_map_extend_space(info
->bmap
, space
,
2365 n
= isl_aff_list_n_aff(list
);
2366 for (i
= 0; i
< n
; ++i
) {
2370 aff
= isl_aff_list_get_aff(list
, i
);
2371 is_nan
= isl_aff_is_nan(aff
);
2378 if (isl_tab_insert_var(info
->tab
, dim
+ i
) < 0)
2380 d
= isl_basic_map_alloc_div(info
->bmap
);
2383 info
->bmap
= isl_basic_map_mark_div_unknown(info
->bmap
, d
);
2386 for (j
= d
; j
> i
; --j
)
2387 isl_basic_map_swap_div(info
->bmap
, j
- 1, j
);
2393 /* For each element in "list" that is not set to NaN, fix the corresponding
2394 * variable in "tab" to the purely affine expression defined by the element.
2395 * "dim" is the offset in the variables of "tab" where we should
2396 * start considering the elements in "list".
2398 * This function assumes that a sufficient number of rows and
2399 * elements in the constraint array are available in the tableau.
2401 static int add_sub_equalities(struct isl_tab
*tab
,
2402 __isl_keep isl_aff_list
*list
, int dim
)
2409 n
= isl_aff_list_n_aff(list
);
2411 ctx
= isl_tab_get_ctx(tab
);
2412 sub
= isl_vec_alloc(ctx
, 1 + dim
+ n
);
2415 isl_seq_clr(sub
->el
+ 1 + dim
, n
);
2417 for (i
= 0; i
< n
; ++i
) {
2418 aff
= isl_aff_list_get_aff(list
, i
);
2421 if (isl_aff_is_nan(aff
)) {
2425 isl_seq_cpy(sub
->el
, aff
->v
->el
+ 1, 1 + dim
);
2426 isl_int_neg(sub
->el
[1 + dim
+ i
], aff
->v
->el
[0]);
2427 if (isl_tab_add_eq(tab
, sub
->el
) < 0)
2429 isl_int_set_si(sub
->el
[1 + dim
+ i
], 0);
2441 /* Add variables to info->tab and info->bmap corresponding to the elements
2442 * in "list" that are not set to NaN. The value of the added variable
2443 * in info->tab is fixed to the purely affine expression defined by the element.
2444 * "dim" is the offset in the variables of info->tab where we should
2445 * start considering the elements in "list".
2446 * When this function returns, the total number of variables in info->tab
2447 * is equal to "dim" plus the number of elements in "list".
2449 static int add_subs(struct isl_coalesce_info
*info
,
2450 __isl_keep isl_aff_list
*list
, int dim
)
2458 n
= isl_aff_list_n_aff(list
);
2459 extra_var
= n
- (info
->tab
->n_var
- dim
);
2461 if (isl_tab_extend_vars(info
->tab
, extra_var
) < 0)
2463 if (isl_tab_extend_cons(info
->tab
, 2 * extra_var
) < 0)
2465 if (add_sub_vars(info
, list
, dim
, extra_var
) < 0)
2468 return add_sub_equalities(info
->tab
, list
, dim
);
2471 /* Coalesce basic map "j" into basic map "i" after adding the extra integer
2472 * divisions in "i" but not in "j" to basic map "j", with values
2473 * specified by "list". The total number of elements in "list"
2474 * is equal to the number of integer divisions in "i", while the number
2475 * of NaN elements in the list is equal to the number of integer divisions
2478 * If no coalescing can be performed, then we need to revert basic map "j"
2479 * to its original state. We do the same if basic map "i" gets dropped
2480 * during the coalescing, even though this should not happen in practice
2481 * since we have already checked for "j" being a subset of "i"
2482 * before we reach this stage.
2484 static enum isl_change
coalesce_with_subs(int i
, int j
,
2485 struct isl_coalesce_info
*info
, __isl_keep isl_aff_list
*list
)
2487 isl_basic_map
*bmap_j
;
2488 struct isl_tab_undo
*snap
;
2490 enum isl_change change
;
2492 bmap_j
= isl_basic_map_copy(info
[j
].bmap
);
2493 snap
= isl_tab_snap(info
[j
].tab
);
2495 dim
= isl_basic_map_dim(bmap_j
, isl_dim_all
);
2496 dim
-= isl_basic_map_dim(bmap_j
, isl_dim_div
);
2497 if (add_subs(&info
[j
], list
, dim
) < 0)
2500 change
= coalesce_local_pair(i
, j
, info
);
2501 if (change
!= isl_change_none
&& change
!= isl_change_drop_first
) {
2502 isl_basic_map_free(bmap_j
);
2504 isl_basic_map_free(info
[j
].bmap
);
2505 info
[j
].bmap
= bmap_j
;
2507 if (isl_tab_rollback(info
[j
].tab
, snap
) < 0)
2508 return isl_change_error
;
2513 isl_basic_map_free(bmap_j
);
2514 return isl_change_error
;
2517 /* Check if we can coalesce basic map "j" into basic map "i" after copying
2518 * those extra integer divisions in "i" that can be simplified away
2519 * using the extra equalities in "j".
2520 * All divs are assumed to be known and not contain any nested divs.
2522 * We first check if there are any extra equalities in "j" that we
2523 * can exploit. Then we check if every integer division in "i"
2524 * either already appears in "j" or can be simplified using the
2525 * extra equalities to a purely affine expression.
2526 * If these tests succeed, then we try to coalesce the two basic maps
2527 * by introducing extra dimensions in "j" corresponding to
2528 * the extra integer divsisions "i" fixed to the corresponding
2529 * purely affine expression.
2531 static enum isl_change
check_coalesce_into_eq(int i
, int j
,
2532 struct isl_coalesce_info
*info
)
2534 unsigned n_div_i
, n_div_j
;
2535 isl_basic_map
*hull_i
, *hull_j
;
2538 enum isl_change change
;
2540 n_div_i
= isl_basic_map_dim(info
[i
].bmap
, isl_dim_div
);
2541 n_div_j
= isl_basic_map_dim(info
[j
].bmap
, isl_dim_div
);
2542 if (n_div_i
<= n_div_j
)
2543 return isl_change_none
;
2544 if (info
[j
].bmap
->n_eq
== 0)
2545 return isl_change_none
;
2547 hull_i
= isl_basic_map_copy(info
[i
].bmap
);
2548 hull_i
= isl_basic_map_plain_affine_hull(hull_i
);
2549 hull_j
= isl_basic_map_copy(info
[j
].bmap
);
2550 hull_j
= isl_basic_map_plain_affine_hull(hull_j
);
2552 hull_j
= isl_basic_map_intersect(hull_j
, isl_basic_map_copy(hull_i
));
2553 equal
= isl_basic_map_plain_is_equal(hull_i
, hull_j
);
2554 empty
= isl_basic_map_plain_is_empty(hull_j
);
2555 isl_basic_map_free(hull_i
);
2557 if (equal
< 0 || empty
< 0)
2559 if (equal
|| empty
) {
2560 isl_basic_map_free(hull_j
);
2561 return isl_change_none
;
2564 list
= set_up_substitutions(info
[i
].bmap
, info
[j
].bmap
, hull_j
);
2566 return isl_change_error
;
2567 if (isl_aff_list_n_aff(list
) < n_div_i
)
2568 change
= isl_change_none
;
2570 change
= coalesce_with_subs(i
, j
, info
, list
);
2572 isl_aff_list_free(list
);
2576 isl_basic_map_free(hull_j
);
2577 return isl_change_error
;
2580 /* Check if we can coalesce basic maps "i" and "j" after copying
2581 * those extra integer divisions in one of the basic maps that can
2582 * be simplified away using the extra equalities in the other basic map.
2583 * We require all divs to be known in both basic maps.
2584 * Furthermore, to simplify the comparison of div expressions,
2585 * we do not allow any nested integer divisions.
2587 static enum isl_change
check_coalesce_eq(int i
, int j
,
2588 struct isl_coalesce_info
*info
)
2591 enum isl_change change
;
2593 known
= isl_basic_map_divs_known(info
[i
].bmap
);
2594 if (known
< 0 || !known
)
2595 return known
< 0 ? isl_change_error
: isl_change_none
;
2596 known
= isl_basic_map_divs_known(info
[j
].bmap
);
2597 if (known
< 0 || !known
)
2598 return known
< 0 ? isl_change_error
: isl_change_none
;
2599 nested
= has_nested_div(info
[i
].bmap
);
2600 if (nested
< 0 || nested
)
2601 return nested
< 0 ? isl_change_error
: isl_change_none
;
2602 nested
= has_nested_div(info
[j
].bmap
);
2603 if (nested
< 0 || nested
)
2604 return nested
< 0 ? isl_change_error
: isl_change_none
;
2606 change
= check_coalesce_into_eq(i
, j
, info
);
2607 if (change
!= isl_change_none
)
2609 change
= check_coalesce_into_eq(j
, i
, info
);
2610 if (change
!= isl_change_none
)
2611 return invert_change(change
);
2613 return isl_change_none
;
2616 /* Check if the union of the given pair of basic maps
2617 * can be represented by a single basic map.
2618 * If so, replace the pair by the single basic map and return
2619 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
2620 * Otherwise, return isl_change_none.
2622 * We first check if the two basic maps live in the same local space,
2623 * after aligning the divs that differ by only an integer constant.
2624 * If so, we do the complete check. Otherwise, we check if they have
2625 * the same number of integer divisions and can be coalesced, if one is
2626 * an obvious subset of the other or if the extra integer divisions
2627 * of one basic map can be simplified away using the extra equalities
2628 * of the other basic map.
2630 static enum isl_change
coalesce_pair(int i
, int j
,
2631 struct isl_coalesce_info
*info
)
2634 enum isl_change change
;
2636 if (harmonize_divs(&info
[i
], &info
[j
]) < 0)
2637 return isl_change_error
;
2638 same
= same_divs(info
[i
].bmap
, info
[j
].bmap
);
2640 return isl_change_error
;
2642 return coalesce_local_pair(i
, j
, info
);
2644 if (info
[i
].bmap
->n_div
== info
[j
].bmap
->n_div
) {
2645 change
= coalesce_local_pair(i
, j
, info
);
2646 if (change
!= isl_change_none
)
2650 change
= coalesce_divs(i
, j
, info
);
2651 if (change
!= isl_change_none
)
2654 return check_coalesce_eq(i
, j
, info
);
2657 /* Return the maximum of "a" and "b".
2659 static int isl_max(int a
, int b
)
2661 return a
> b
? a
: b
;
2664 /* Pairwise coalesce the basic maps in the range [start1, end1[ of "info"
2665 * with those in the range [start2, end2[, skipping basic maps
2666 * that have been removed (either before or within this function).
2668 * For each basic map i in the first range, we check if it can be coalesced
2669 * with respect to any previously considered basic map j in the second range.
2670 * If i gets dropped (because it was a subset of some j), then
2671 * we can move on to the next basic map.
2672 * If j gets dropped, we need to continue checking against the other
2673 * previously considered basic maps.
2674 * If the two basic maps got fused, then we recheck the fused basic map
2675 * against the previously considered basic maps, starting at i + 1
2676 * (even if start2 is greater than i + 1).
2678 static int coalesce_range(isl_ctx
*ctx
, struct isl_coalesce_info
*info
,
2679 int start1
, int end1
, int start2
, int end2
)
2683 for (i
= end1
- 1; i
>= start1
; --i
) {
2684 if (info
[i
].removed
)
2686 for (j
= isl_max(i
+ 1, start2
); j
< end2
; ++j
) {
2687 enum isl_change changed
;
2689 if (info
[j
].removed
)
2691 if (info
[i
].removed
)
2692 isl_die(ctx
, isl_error_internal
,
2693 "basic map unexpectedly removed",
2695 changed
= coalesce_pair(i
, j
, info
);
2697 case isl_change_error
:
2699 case isl_change_none
:
2700 case isl_change_drop_second
:
2702 case isl_change_drop_first
:
2705 case isl_change_fuse
:
2715 /* Pairwise coalesce the basic maps described by the "n" elements of "info".
2717 * We consider groups of basic maps that live in the same apparent
2718 * affine hull and we first coalesce within such a group before we
2719 * coalesce the elements in the group with elements of previously
2720 * considered groups. If a fuse happens during the second phase,
2721 * then we also reconsider the elements within the group.
2723 static int coalesce(isl_ctx
*ctx
, int n
, struct isl_coalesce_info
*info
)
2727 for (end
= n
; end
> 0; end
= start
) {
2729 while (start
>= 1 &&
2730 info
[start
- 1].hull_hash
== info
[start
].hull_hash
)
2732 if (coalesce_range(ctx
, info
, start
, end
, start
, end
) < 0)
2734 if (coalesce_range(ctx
, info
, start
, end
, end
, n
) < 0)
2741 /* Update the basic maps in "map" based on the information in "info".
2742 * In particular, remove the basic maps that have been marked removed and
2743 * update the others based on the information in the corresponding tableau.
2744 * Since we detected implicit equalities without calling
2745 * isl_basic_map_gauss, we need to do it now.
2746 * Also call isl_basic_map_simplify if we may have lost the definition
2747 * of one or more integer divisions.
2749 static __isl_give isl_map
*update_basic_maps(__isl_take isl_map
*map
,
2750 int n
, struct isl_coalesce_info
*info
)
2757 for (i
= n
- 1; i
>= 0; --i
) {
2758 if (info
[i
].removed
) {
2759 isl_basic_map_free(map
->p
[i
]);
2760 if (i
!= map
->n
- 1)
2761 map
->p
[i
] = map
->p
[map
->n
- 1];
2766 info
[i
].bmap
= isl_basic_map_update_from_tab(info
[i
].bmap
,
2768 info
[i
].bmap
= isl_basic_map_gauss(info
[i
].bmap
, NULL
);
2769 if (info
[i
].simplify
)
2770 info
[i
].bmap
= isl_basic_map_simplify(info
[i
].bmap
);
2771 info
[i
].bmap
= isl_basic_map_finalize(info
[i
].bmap
);
2773 return isl_map_free(map
);
2774 ISL_F_SET(info
[i
].bmap
, ISL_BASIC_MAP_NO_IMPLICIT
);
2775 ISL_F_SET(info
[i
].bmap
, ISL_BASIC_MAP_NO_REDUNDANT
);
2776 isl_basic_map_free(map
->p
[i
]);
2777 map
->p
[i
] = info
[i
].bmap
;
2778 info
[i
].bmap
= NULL
;
2784 /* For each pair of basic maps in the map, check if the union of the two
2785 * can be represented by a single basic map.
2786 * If so, replace the pair by the single basic map and start over.
2788 * We factor out any (hidden) common factor from the constraint
2789 * coefficients to improve the detection of adjacent constraints.
2791 * Since we are constructing the tableaus of the basic maps anyway,
2792 * we exploit them to detect implicit equalities and redundant constraints.
2793 * This also helps the coalescing as it can ignore the redundant constraints.
2794 * In order to avoid confusion, we make all implicit equalities explicit
2795 * in the basic maps. We don't call isl_basic_map_gauss, though,
2796 * as that may affect the number of constraints.
2797 * This means that we have to call isl_basic_map_gauss at the end
2798 * of the computation (in update_basic_maps) to ensure that
2799 * the basic maps are not left in an unexpected state.
2800 * For each basic map, we also compute the hash of the apparent affine hull
2801 * for use in coalesce.
2803 struct isl_map
*isl_map_coalesce(struct isl_map
*map
)
2808 struct isl_coalesce_info
*info
= NULL
;
2810 map
= isl_map_remove_empty_parts(map
);
2817 ctx
= isl_map_get_ctx(map
);
2818 map
= isl_map_sort_divs(map
);
2819 map
= isl_map_cow(map
);
2826 info
= isl_calloc_array(map
->ctx
, struct isl_coalesce_info
, n
);
2830 for (i
= 0; i
< map
->n
; ++i
) {
2831 map
->p
[i
] = isl_basic_map_reduce_coefficients(map
->p
[i
]);
2834 info
[i
].bmap
= isl_basic_map_copy(map
->p
[i
]);
2835 info
[i
].tab
= isl_tab_from_basic_map(info
[i
].bmap
, 0);
2838 if (!ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_NO_IMPLICIT
))
2839 if (isl_tab_detect_implicit_equalities(info
[i
].tab
) < 0)
2841 info
[i
].bmap
= isl_tab_make_equalities_explicit(info
[i
].tab
,
2845 if (!ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_NO_REDUNDANT
))
2846 if (isl_tab_detect_redundant(info
[i
].tab
) < 0)
2848 if (coalesce_info_set_hull_hash(&info
[i
]) < 0)
2851 for (i
= map
->n
- 1; i
>= 0; --i
)
2852 if (info
[i
].tab
->empty
)
2855 if (coalesce(ctx
, n
, info
) < 0)
2858 map
= update_basic_maps(map
, n
, info
);
2860 clear_coalesce_info(n
, info
);
2864 clear_coalesce_info(n
, info
);
2869 /* For each pair of basic sets in the set, check if the union of the two
2870 * can be represented by a single basic set.
2871 * If so, replace the pair by the single basic set and start over.
2873 struct isl_set
*isl_set_coalesce(struct isl_set
*set
)
2875 return (struct isl_set
*)isl_map_coalesce((struct isl_map
*)set
);