2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2010 INRIA Saclay
4 * Copyright 2012-2013 Ecole Normale Superieure
5 * Copyright 2014 INRIA Rocquencourt
7 * Use of this software is governed by the MIT license
9 * Written by Sven Verdoolaege, K.U.Leuven, Departement
10 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
11 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
12 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
13 * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
14 * and Inria Paris - Rocquencourt, Domaine de Voluceau - Rocquencourt,
15 * B.P. 105 - 78153 Le Chesnay, France
18 #include "isl_map_private.h"
20 #include <isl/options.h>
22 #include <isl_mat_private.h>
23 #include <isl_local_space_private.h>
24 #include <isl_vec_private.h>
26 #define STATUS_ERROR -1
27 #define STATUS_REDUNDANT 1
28 #define STATUS_VALID 2
29 #define STATUS_SEPARATE 3
31 #define STATUS_ADJ_EQ 5
32 #define STATUS_ADJ_INEQ 6
34 static int status_in(isl_int
*ineq
, struct isl_tab
*tab
)
36 enum isl_ineq_type type
= isl_tab_ineq_type(tab
, ineq
);
39 case isl_ineq_error
: return STATUS_ERROR
;
40 case isl_ineq_redundant
: return STATUS_VALID
;
41 case isl_ineq_separate
: return STATUS_SEPARATE
;
42 case isl_ineq_cut
: return STATUS_CUT
;
43 case isl_ineq_adj_eq
: return STATUS_ADJ_EQ
;
44 case isl_ineq_adj_ineq
: return STATUS_ADJ_INEQ
;
48 /* Compute the position of the equalities of basic map "bmap_i"
49 * with respect to the basic map represented by "tab_j".
50 * The resulting array has twice as many entries as the number
51 * of equalities corresponding to the two inequalties to which
52 * each equality corresponds.
54 static int *eq_status_in(__isl_keep isl_basic_map
*bmap_i
,
55 struct isl_tab
*tab_j
)
58 int *eq
= isl_calloc_array(bmap_i
->ctx
, int, 2 * bmap_i
->n_eq
);
64 dim
= isl_basic_map_total_dim(bmap_i
);
65 for (k
= 0; k
< bmap_i
->n_eq
; ++k
) {
66 for (l
= 0; l
< 2; ++l
) {
67 isl_seq_neg(bmap_i
->eq
[k
], bmap_i
->eq
[k
], 1+dim
);
68 eq
[2 * k
+ l
] = status_in(bmap_i
->eq
[k
], tab_j
);
69 if (eq
[2 * k
+ l
] == STATUS_ERROR
)
72 if (eq
[2 * k
] == STATUS_SEPARATE
||
73 eq
[2 * k
+ 1] == STATUS_SEPARATE
)
83 /* Compute the position of the inequalities of basic map "bmap_i"
84 * (also represented by "tab_i", if not NULL) with respect to the basic map
85 * represented by "tab_j".
87 static int *ineq_status_in(__isl_keep isl_basic_map
*bmap_i
,
88 struct isl_tab
*tab_i
, struct isl_tab
*tab_j
)
91 unsigned n_eq
= bmap_i
->n_eq
;
92 int *ineq
= isl_calloc_array(bmap_i
->ctx
, int, bmap_i
->n_ineq
);
97 for (k
= 0; k
< bmap_i
->n_ineq
; ++k
) {
98 if (tab_i
&& isl_tab_is_redundant(tab_i
, n_eq
+ k
)) {
99 ineq
[k
] = STATUS_REDUNDANT
;
102 ineq
[k
] = status_in(bmap_i
->ineq
[k
], tab_j
);
103 if (ineq
[k
] == STATUS_ERROR
)
105 if (ineq
[k
] == STATUS_SEPARATE
)
115 static int any(int *con
, unsigned len
, int status
)
119 for (i
= 0; i
< len
; ++i
)
120 if (con
[i
] == status
)
125 static int count(int *con
, unsigned len
, int status
)
130 for (i
= 0; i
< len
; ++i
)
131 if (con
[i
] == status
)
136 static int all(int *con
, unsigned len
, int status
)
140 for (i
= 0; i
< len
; ++i
) {
141 if (con
[i
] == STATUS_REDUNDANT
)
143 if (con
[i
] != status
)
149 /* Internal information associated to a basic map in a map
150 * that is to be coalesced by isl_map_coalesce.
152 * "bmap" is the basic map itself (or NULL if "removed" is set)
153 * "tab" is the corresponding tableau (or NULL if "removed" is set)
154 * "removed" is set if this basic map has been removed from the map
156 * "eq" and "ineq" are only set if we are currently trying to coalesce
157 * this basic map with another basic map, in which case they represent
158 * the position of the inequalities of this basic map with respect to
159 * the other basic map. The number of elements in the "eq" array
160 * is twice the number of equalities in the "bmap", corresponding
161 * to the two inequalities that make up each equality.
163 struct isl_coalesce_info
{
171 /* Free all the allocated memory in an array
172 * of "n" isl_coalesce_info elements.
174 static void clear_coalesce_info(int n
, struct isl_coalesce_info
*info
)
181 for (i
= 0; i
< n
; ++i
) {
182 isl_basic_map_free(info
[i
].bmap
);
183 isl_tab_free(info
[i
].tab
);
189 /* Drop the basic map represented by "info".
190 * That is, clear the memory associated to the entry and
191 * mark it as having been removed.
193 static void drop(struct isl_coalesce_info
*info
)
195 info
->bmap
= isl_basic_map_free(info
->bmap
);
196 isl_tab_free(info
->tab
);
201 /* Exchange the information in "info1" with that in "info2".
203 static void exchange(struct isl_coalesce_info
*info1
,
204 struct isl_coalesce_info
*info2
)
206 struct isl_coalesce_info info
;
213 /* This type represents the kind of change that has been performed
214 * while trying to coalesce two basic maps.
216 * isl_change_none: nothing was changed
217 * isl_change_drop_first: the first basic map was removed
218 * isl_change_drop_second: the second basic map was removed
219 * isl_change_fuse: the two basic maps were replaced by a new basic map.
222 isl_change_error
= -1,
224 isl_change_drop_first
,
225 isl_change_drop_second
,
229 /* Replace the pair of basic maps i and j by the basic map bounded
230 * by the valid constraints in both basic maps and the constraints
231 * in extra (if not NULL).
232 * Place the fused basic map in the position that is the smallest of i and j.
234 * If "detect_equalities" is set, then look for equalities encoded
235 * as pairs of inequalities.
237 static enum isl_change
fuse(int i
, int j
, struct isl_coalesce_info
*info
,
238 __isl_keep isl_mat
*extra
, int detect_equalities
)
241 struct isl_basic_map
*fused
= NULL
;
242 struct isl_tab
*fused_tab
= NULL
;
243 unsigned total
= isl_basic_map_total_dim(info
[i
].bmap
);
244 unsigned extra_rows
= extra
? extra
->n_row
: 0;
247 return fuse(j
, i
, info
, extra
, detect_equalities
);
249 fused
= isl_basic_map_alloc_space(isl_space_copy(info
[i
].bmap
->dim
),
251 info
[i
].bmap
->n_eq
+ info
[j
].bmap
->n_eq
,
252 info
[i
].bmap
->n_ineq
+ info
[j
].bmap
->n_ineq
+ extra_rows
);
256 for (k
= 0; k
< info
[i
].bmap
->n_eq
; ++k
) {
257 if (info
[i
].eq
[2 * k
] != STATUS_VALID
||
258 info
[i
].eq
[2 * k
+ 1] != STATUS_VALID
)
260 l
= isl_basic_map_alloc_equality(fused
);
263 isl_seq_cpy(fused
->eq
[l
], info
[i
].bmap
->eq
[k
], 1 + total
);
266 for (k
= 0; k
< info
[j
].bmap
->n_eq
; ++k
) {
267 if (info
[j
].eq
[2 * k
] != STATUS_VALID
||
268 info
[j
].eq
[2 * k
+ 1] != STATUS_VALID
)
270 l
= isl_basic_map_alloc_equality(fused
);
273 isl_seq_cpy(fused
->eq
[l
], info
[j
].bmap
->eq
[k
], 1 + total
);
276 for (k
= 0; k
< info
[i
].bmap
->n_ineq
; ++k
) {
277 if (info
[i
].ineq
[k
] != STATUS_VALID
)
279 l
= isl_basic_map_alloc_inequality(fused
);
282 isl_seq_cpy(fused
->ineq
[l
], info
[i
].bmap
->ineq
[k
], 1 + total
);
285 for (k
= 0; k
< info
[j
].bmap
->n_ineq
; ++k
) {
286 if (info
[j
].ineq
[k
] != STATUS_VALID
)
288 l
= isl_basic_map_alloc_inequality(fused
);
291 isl_seq_cpy(fused
->ineq
[l
], info
[j
].bmap
->ineq
[k
], 1 + total
);
294 for (k
= 0; k
< info
[i
].bmap
->n_div
; ++k
) {
295 int l
= isl_basic_map_alloc_div(fused
);
298 isl_seq_cpy(fused
->div
[l
], info
[i
].bmap
->div
[k
], 1 + 1 + total
);
301 for (k
= 0; k
< extra_rows
; ++k
) {
302 l
= isl_basic_map_alloc_inequality(fused
);
305 isl_seq_cpy(fused
->ineq
[l
], extra
->row
[k
], 1 + total
);
308 if (detect_equalities
)
309 fused
= isl_basic_map_detect_inequality_pairs(fused
, NULL
);
310 fused
= isl_basic_map_gauss(fused
, NULL
);
311 ISL_F_SET(fused
, ISL_BASIC_MAP_FINAL
);
312 if (ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_RATIONAL
) &&
313 ISL_F_ISSET(info
[j
].bmap
, ISL_BASIC_MAP_RATIONAL
))
314 ISL_F_SET(fused
, ISL_BASIC_MAP_RATIONAL
);
316 fused_tab
= isl_tab_from_basic_map(fused
, 0);
317 if (isl_tab_detect_redundant(fused_tab
) < 0)
320 isl_basic_map_free(info
[i
].bmap
);
321 info
[i
].bmap
= fused
;
322 isl_tab_free(info
[i
].tab
);
323 info
[i
].tab
= fused_tab
;
326 return isl_change_fuse
;
328 isl_tab_free(fused_tab
);
329 isl_basic_map_free(fused
);
330 return isl_change_error
;
333 /* Given a pair of basic maps i and j such that all constraints are either
334 * "valid" or "cut", check if the facets corresponding to the "cut"
335 * constraints of i lie entirely within basic map j.
336 * If so, replace the pair by the basic map consisting of the valid
337 * constraints in both basic maps.
338 * Checking whether the facet lies entirely within basic map j
339 * is performed by checking whether the constraints of basic map j
340 * are valid for the facet. These tests are performed on a rational
341 * tableau to avoid the theoretical possibility that a constraint
342 * that was considered to be a cut constraint for the entire basic map i
343 * happens to be considered to be a valid constraint for the facet,
344 * even though it cuts off the same rational points.
346 * To see that we are not introducing any extra points, call the
347 * two basic maps A and B and the resulting map U and let x
348 * be an element of U \setminus ( A \cup B ).
349 * A line connecting x with an element of A \cup B meets a facet F
350 * of either A or B. Assume it is a facet of B and let c_1 be
351 * the corresponding facet constraint. We have c_1(x) < 0 and
352 * so c_1 is a cut constraint. This implies that there is some
353 * (possibly rational) point x' satisfying the constraints of A
354 * and the opposite of c_1 as otherwise c_1 would have been marked
355 * valid for A. The line connecting x and x' meets a facet of A
356 * in a (possibly rational) point that also violates c_1, but this
357 * is impossible since all cut constraints of B are valid for all
359 * In case F is a facet of A rather than B, then we can apply the
360 * above reasoning to find a facet of B separating x from A \cup B first.
362 static enum isl_change
check_facets(int i
, int j
,
363 struct isl_coalesce_info
*info
)
366 struct isl_tab_undo
*snap
, *snap2
;
367 unsigned n_eq
= info
[i
].bmap
->n_eq
;
369 snap
= isl_tab_snap(info
[i
].tab
);
370 if (isl_tab_mark_rational(info
[i
].tab
) < 0)
371 return isl_change_error
;
372 snap2
= isl_tab_snap(info
[i
].tab
);
374 for (k
= 0; k
< info
[i
].bmap
->n_ineq
; ++k
) {
375 if (info
[i
].ineq
[k
] != STATUS_CUT
)
377 if (isl_tab_select_facet(info
[i
].tab
, n_eq
+ k
) < 0)
378 return isl_change_error
;
379 for (l
= 0; l
< info
[j
].bmap
->n_ineq
; ++l
) {
381 if (info
[j
].ineq
[l
] != STATUS_CUT
)
383 stat
= status_in(info
[j
].bmap
->ineq
[l
], info
[i
].tab
);
384 if (stat
!= STATUS_VALID
)
387 if (isl_tab_rollback(info
[i
].tab
, snap2
) < 0)
388 return isl_change_error
;
389 if (l
< info
[j
].bmap
->n_ineq
)
393 if (k
< info
[i
].bmap
->n_ineq
) {
394 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
395 return isl_change_error
;
396 return isl_change_none
;
398 return fuse(i
, j
, info
, NULL
, 0);
401 /* Check if info->bmap contains the basic map represented
402 * by the tableau "tab".
403 * For each equality, we check both the constraint itself
404 * (as an inequality) and its negation. Make sure the
405 * equality is returned to its original state before returning.
407 static int contains(struct isl_coalesce_info
*info
, struct isl_tab
*tab
)
411 isl_basic_map
*bmap
= info
->bmap
;
413 dim
= isl_basic_map_total_dim(bmap
);
414 for (k
= 0; k
< bmap
->n_eq
; ++k
) {
416 isl_seq_neg(bmap
->eq
[k
], bmap
->eq
[k
], 1 + dim
);
417 stat
= status_in(bmap
->eq
[k
], tab
);
418 isl_seq_neg(bmap
->eq
[k
], bmap
->eq
[k
], 1 + dim
);
419 if (stat
!= STATUS_VALID
)
421 stat
= status_in(bmap
->eq
[k
], tab
);
422 if (stat
!= STATUS_VALID
)
426 for (k
= 0; k
< bmap
->n_ineq
; ++k
) {
428 if (info
->ineq
[k
] == STATUS_REDUNDANT
)
430 stat
= status_in(bmap
->ineq
[k
], tab
);
431 if (stat
!= STATUS_VALID
)
437 /* Basic map "i" has an inequality (say "k") that is adjacent
438 * to some inequality of basic map "j". All the other inequalities
440 * Check if basic map "j" forms an extension of basic map "i".
442 * Note that this function is only called if some of the equalities or
443 * inequalities of basic map "j" do cut basic map "i". The function is
444 * correct even if there are no such cut constraints, but in that case
445 * the additional checks performed by this function are overkill.
447 * In particular, we replace constraint k, say f >= 0, by constraint
448 * f <= -1, add the inequalities of "j" that are valid for "i"
449 * and check if the result is a subset of basic map "j".
450 * If so, then we know that this result is exactly equal to basic map "j"
451 * since all its constraints are valid for basic map "j".
452 * By combining the valid constraints of "i" (all equalities and all
453 * inequalities except "k") and the valid constraints of "j" we therefore
454 * obtain a basic map that is equal to their union.
455 * In this case, there is no need to perform a rollback of the tableau
456 * since it is going to be destroyed in fuse().
462 * |_______| _ |_________\
474 static enum isl_change
is_adj_ineq_extension(int i
, int j
,
475 struct isl_coalesce_info
*info
)
478 struct isl_tab_undo
*snap
;
479 unsigned n_eq
= info
[i
].bmap
->n_eq
;
480 unsigned total
= isl_basic_map_total_dim(info
[i
].bmap
);
483 if (isl_tab_extend_cons(info
[i
].tab
, 1 + info
[j
].bmap
->n_ineq
) < 0)
484 return isl_change_error
;
486 for (k
= 0; k
< info
[i
].bmap
->n_ineq
; ++k
)
487 if (info
[i
].ineq
[k
] == STATUS_ADJ_INEQ
)
489 if (k
>= info
[i
].bmap
->n_ineq
)
490 isl_die(isl_basic_map_get_ctx(info
[i
].bmap
), isl_error_internal
,
491 "info[i].ineq should have exactly one STATUS_ADJ_INEQ",
492 return isl_change_error
);
494 snap
= isl_tab_snap(info
[i
].tab
);
496 if (isl_tab_unrestrict(info
[i
].tab
, n_eq
+ k
) < 0)
497 return isl_change_error
;
499 isl_seq_neg(info
[i
].bmap
->ineq
[k
], info
[i
].bmap
->ineq
[k
], 1 + total
);
500 isl_int_sub_ui(info
[i
].bmap
->ineq
[k
][0], info
[i
].bmap
->ineq
[k
][0], 1);
501 r
= isl_tab_add_ineq(info
[i
].tab
, info
[i
].bmap
->ineq
[k
]);
502 isl_seq_neg(info
[i
].bmap
->ineq
[k
], info
[i
].bmap
->ineq
[k
], 1 + total
);
503 isl_int_sub_ui(info
[i
].bmap
->ineq
[k
][0], info
[i
].bmap
->ineq
[k
][0], 1);
505 return isl_change_error
;
507 for (k
= 0; k
< info
[j
].bmap
->n_ineq
; ++k
) {
508 if (info
[j
].ineq
[k
] != STATUS_VALID
)
510 if (isl_tab_add_ineq(info
[i
].tab
, info
[j
].bmap
->ineq
[k
]) < 0)
511 return isl_change_error
;
514 if (contains(&info
[j
], info
[i
].tab
))
515 return fuse(i
, j
, info
, NULL
, 0);
517 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
518 return isl_change_error
;
520 return isl_change_none
;
524 /* Both basic maps have at least one inequality with and adjacent
525 * (but opposite) inequality in the other basic map.
526 * Check that there are no cut constraints and that there is only
527 * a single pair of adjacent inequalities.
528 * If so, we can replace the pair by a single basic map described
529 * by all but the pair of adjacent inequalities.
530 * Any additional points introduced lie strictly between the two
531 * adjacent hyperplanes and can therefore be integral.
540 * The test for a single pair of adjancent inequalities is important
541 * for avoiding the combination of two basic maps like the following
551 * If there are some cut constraints on one side, then we may
552 * still be able to fuse the two basic maps, but we need to perform
553 * some additional checks in is_adj_ineq_extension.
555 static enum isl_change
check_adj_ineq(int i
, int j
,
556 struct isl_coalesce_info
*info
)
558 int count_i
, count_j
;
561 count_i
= count(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ADJ_INEQ
);
562 count_j
= count(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_ADJ_INEQ
);
564 if (count_i
!= 1 && count_j
!= 1)
565 return isl_change_none
;
567 cut_i
= any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_CUT
) ||
568 any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_CUT
);
569 cut_j
= any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_CUT
) ||
570 any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_CUT
);
572 if (!cut_i
&& !cut_j
&& count_i
== 1 && count_j
== 1)
573 return fuse(i
, j
, info
, NULL
, 0);
575 if (count_i
== 1 && !cut_i
)
576 return is_adj_ineq_extension(i
, j
, info
);
578 if (count_j
== 1 && !cut_j
)
579 return is_adj_ineq_extension(j
, i
, info
);
581 return isl_change_none
;
584 /* Basic map "i" has an inequality "k" that is adjacent to some equality
585 * of basic map "j". All the other inequalities are valid for "j".
586 * Check if basic map "j" forms an extension of basic map "i".
588 * In particular, we relax constraint "k", compute the corresponding
589 * facet and check whether it is included in the other basic map.
590 * If so, we know that relaxing the constraint extends the basic
591 * map with exactly the other basic map (we already know that this
592 * other basic map is included in the extension, because there
593 * were no "cut" inequalities in "i") and we can replace the
594 * two basic maps by this extension.
595 * Place this extension in the position that is the smallest of i and j.
603 static enum isl_change
is_adj_eq_extension(int i
, int j
, int k
,
604 struct isl_coalesce_info
*info
)
606 int change
= isl_change_none
;
608 struct isl_tab_undo
*snap
, *snap2
;
609 unsigned n_eq
= info
[i
].bmap
->n_eq
;
611 if (isl_tab_is_equality(info
[i
].tab
, n_eq
+ k
))
612 return isl_change_none
;
614 snap
= isl_tab_snap(info
[i
].tab
);
615 if (isl_tab_relax(info
[i
].tab
, n_eq
+ k
) < 0)
616 return isl_change_error
;
617 snap2
= isl_tab_snap(info
[i
].tab
);
618 if (isl_tab_select_facet(info
[i
].tab
, n_eq
+ k
) < 0)
619 return isl_change_error
;
620 super
= contains(&info
[j
], info
[i
].tab
);
622 if (isl_tab_rollback(info
[i
].tab
, snap2
) < 0)
623 return isl_change_error
;
624 info
[i
].bmap
= isl_basic_map_cow(info
[i
].bmap
);
626 return isl_change_error
;
627 isl_int_add_ui(info
[i
].bmap
->ineq
[k
][0],
628 info
[i
].bmap
->ineq
[k
][0], 1);
629 ISL_F_SET(info
[i
].bmap
, ISL_BASIC_MAP_FINAL
);
632 exchange(&info
[i
], &info
[j
]);
633 change
= isl_change_fuse
;
635 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
636 return isl_change_error
;
641 /* Data structure that keeps track of the wrapping constraints
642 * and of information to bound the coefficients of those constraints.
644 * bound is set if we want to apply a bound on the coefficients
645 * mat contains the wrapping constraints
646 * max is the bound on the coefficients (if bound is set)
654 /* Update wraps->max to be greater than or equal to the coefficients
655 * in the equalities and inequalities of info->bmap that can be removed
656 * if we end up applying wrapping.
658 static void wraps_update_max(struct isl_wraps
*wraps
,
659 struct isl_coalesce_info
*info
)
663 unsigned total
= isl_basic_map_total_dim(info
->bmap
);
667 for (k
= 0; k
< info
->bmap
->n_eq
; ++k
) {
668 if (info
->eq
[2 * k
] == STATUS_VALID
&&
669 info
->eq
[2 * k
+ 1] == STATUS_VALID
)
671 isl_seq_abs_max(info
->bmap
->eq
[k
] + 1, total
, &max_k
);
672 if (isl_int_abs_gt(max_k
, wraps
->max
))
673 isl_int_set(wraps
->max
, max_k
);
676 for (k
= 0; k
< info
->bmap
->n_ineq
; ++k
) {
677 if (info
->ineq
[k
] == STATUS_VALID
||
678 info
->ineq
[k
] == STATUS_REDUNDANT
)
680 isl_seq_abs_max(info
->bmap
->ineq
[k
] + 1, total
, &max_k
);
681 if (isl_int_abs_gt(max_k
, wraps
->max
))
682 isl_int_set(wraps
->max
, max_k
);
685 isl_int_clear(max_k
);
688 /* Initialize the isl_wraps data structure.
689 * If we want to bound the coefficients of the wrapping constraints,
690 * we set wraps->max to the largest coefficient
691 * in the equalities and inequalities that can be removed if we end up
694 static void wraps_init(struct isl_wraps
*wraps
, __isl_take isl_mat
*mat
,
695 struct isl_coalesce_info
*info
, int i
, int j
)
703 ctx
= isl_mat_get_ctx(mat
);
704 wraps
->bound
= isl_options_get_coalesce_bounded_wrapping(ctx
);
707 isl_int_init(wraps
->max
);
708 isl_int_set_si(wraps
->max
, 0);
709 wraps_update_max(wraps
, &info
[i
]);
710 wraps_update_max(wraps
, &info
[j
]);
713 /* Free the contents of the isl_wraps data structure.
715 static void wraps_free(struct isl_wraps
*wraps
)
717 isl_mat_free(wraps
->mat
);
719 isl_int_clear(wraps
->max
);
722 /* Is the wrapping constraint in row "row" allowed?
724 * If wraps->bound is set, we check that none of the coefficients
725 * is greater than wraps->max.
727 static int allow_wrap(struct isl_wraps
*wraps
, int row
)
734 for (i
= 1; i
< wraps
->mat
->n_col
; ++i
)
735 if (isl_int_abs_gt(wraps
->mat
->row
[row
][i
], wraps
->max
))
741 /* For each non-redundant constraint in info->bmap (as determined by info->tab),
742 * wrap the constraint around "bound" such that it includes the whole
743 * set "set" and append the resulting constraint to "wraps".
744 * "wraps" is assumed to have been pre-allocated to the appropriate size.
745 * wraps->n_row is the number of actual wrapped constraints that have
747 * If any of the wrapping problems results in a constraint that is
748 * identical to "bound", then this means that "set" is unbounded in such
749 * way that no wrapping is possible. If this happens then wraps->n_row
751 * Similarly, if we want to bound the coefficients of the wrapping
752 * constraints and a newly added wrapping constraint does not
753 * satisfy the bound, then wraps->n_row is also reset to zero.
755 static int add_wraps(struct isl_wraps
*wraps
, struct isl_coalesce_info
*info
,
756 isl_int
*bound
, __isl_keep isl_set
*set
)
760 isl_basic_map
*bmap
= info
->bmap
;
761 unsigned total
= isl_basic_map_total_dim(bmap
);
763 w
= wraps
->mat
->n_row
;
765 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
766 if (isl_seq_is_neg(bound
, bmap
->ineq
[l
], 1 + total
))
768 if (isl_seq_eq(bound
, bmap
->ineq
[l
], 1 + total
))
770 if (isl_tab_is_redundant(info
->tab
, bmap
->n_eq
+ l
))
773 isl_seq_cpy(wraps
->mat
->row
[w
], bound
, 1 + total
);
774 if (!isl_set_wrap_facet(set
, wraps
->mat
->row
[w
], bmap
->ineq
[l
]))
776 if (isl_seq_eq(wraps
->mat
->row
[w
], bound
, 1 + total
))
778 if (!allow_wrap(wraps
, w
))
782 for (l
= 0; l
< bmap
->n_eq
; ++l
) {
783 if (isl_seq_is_neg(bound
, bmap
->eq
[l
], 1 + total
))
785 if (isl_seq_eq(bound
, bmap
->eq
[l
], 1 + total
))
788 isl_seq_cpy(wraps
->mat
->row
[w
], bound
, 1 + total
);
789 isl_seq_neg(wraps
->mat
->row
[w
+ 1], bmap
->eq
[l
], 1 + total
);
790 if (!isl_set_wrap_facet(set
, wraps
->mat
->row
[w
],
791 wraps
->mat
->row
[w
+ 1]))
793 if (isl_seq_eq(wraps
->mat
->row
[w
], bound
, 1 + total
))
795 if (!allow_wrap(wraps
, w
))
799 isl_seq_cpy(wraps
->mat
->row
[w
], bound
, 1 + total
);
800 if (!isl_set_wrap_facet(set
, wraps
->mat
->row
[w
], bmap
->eq
[l
]))
802 if (isl_seq_eq(wraps
->mat
->row
[w
], bound
, 1 + total
))
804 if (!allow_wrap(wraps
, w
))
809 wraps
->mat
->n_row
= w
;
812 wraps
->mat
->n_row
= 0;
816 /* Check if the constraints in "wraps" from "first" until the last
817 * are all valid for the basic set represented by "tab".
818 * If not, wraps->n_row is set to zero.
820 static int check_wraps(__isl_keep isl_mat
*wraps
, int first
,
825 for (i
= first
; i
< wraps
->n_row
; ++i
) {
826 enum isl_ineq_type type
;
827 type
= isl_tab_ineq_type(tab
, wraps
->row
[i
]);
828 if (type
== isl_ineq_error
)
830 if (type
== isl_ineq_redundant
)
839 /* Return a set that corresponds to the non-redundant constraints
840 * (as recorded in tab) of bmap.
842 * It's important to remove the redundant constraints as some
843 * of the other constraints may have been modified after the
844 * constraints were marked redundant.
845 * In particular, a constraint may have been relaxed.
846 * Redundant constraints are ignored when a constraint is relaxed
847 * and should therefore continue to be ignored ever after.
848 * Otherwise, the relaxation might be thwarted by some of
851 * Update the underlying set to ensure that the dimension doesn't change.
852 * Otherwise the integer divisions could get dropped if the tab
853 * turns out to be empty.
855 static __isl_give isl_set
*set_from_updated_bmap(__isl_keep isl_basic_map
*bmap
,
860 bmap
= isl_basic_map_copy(bmap
);
861 bset
= isl_basic_map_underlying_set(bmap
);
862 bset
= isl_basic_set_cow(bset
);
863 bset
= isl_basic_set_update_from_tab(bset
, tab
);
864 return isl_set_from_basic_set(bset
);
867 /* Given a basic set i with a constraint k that is adjacent to
868 * basic set j, check if we can wrap
869 * both the facet corresponding to k and basic map j
870 * around their ridges to include the other set.
871 * If so, replace the pair of basic sets by their union.
873 * All constraints of i (except k) are assumed to be valid for j.
874 * This means that there is no real need to wrap the ridges of
875 * the faces of basic map i around basic map j but since we do,
876 * we have to check that the resulting wrapping constraints are valid for i.
885 static enum isl_change
can_wrap_in_facet(int i
, int j
, int k
,
886 struct isl_coalesce_info
*info
)
888 enum isl_change change
= isl_change_none
;
889 struct isl_wraps wraps
;
892 struct isl_set
*set_i
= NULL
;
893 struct isl_set
*set_j
= NULL
;
894 struct isl_vec
*bound
= NULL
;
895 unsigned total
= isl_basic_map_total_dim(info
[i
].bmap
);
896 struct isl_tab_undo
*snap
;
899 set_i
= set_from_updated_bmap(info
[i
].bmap
, info
[i
].tab
);
900 set_j
= set_from_updated_bmap(info
[j
].bmap
, info
[j
].tab
);
901 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
902 mat
= isl_mat_alloc(ctx
, 2 * (info
[i
].bmap
->n_eq
+ info
[j
].bmap
->n_eq
) +
903 info
[i
].bmap
->n_ineq
+ info
[j
].bmap
->n_ineq
,
905 wraps_init(&wraps
, mat
, info
, i
, j
);
906 bound
= isl_vec_alloc(ctx
, 1 + total
);
907 if (!set_i
|| !set_j
|| !wraps
.mat
|| !bound
)
910 isl_seq_cpy(bound
->el
, info
[i
].bmap
->ineq
[k
], 1 + total
);
911 isl_int_add_ui(bound
->el
[0], bound
->el
[0], 1);
913 isl_seq_cpy(wraps
.mat
->row
[0], bound
->el
, 1 + total
);
914 wraps
.mat
->n_row
= 1;
916 if (add_wraps(&wraps
, &info
[j
], bound
->el
, set_i
) < 0)
918 if (!wraps
.mat
->n_row
)
921 snap
= isl_tab_snap(info
[i
].tab
);
923 if (isl_tab_select_facet(info
[i
].tab
, info
[i
].bmap
->n_eq
+ k
) < 0)
925 if (isl_tab_detect_redundant(info
[i
].tab
) < 0)
928 isl_seq_neg(bound
->el
, info
[i
].bmap
->ineq
[k
], 1 + total
);
930 n
= wraps
.mat
->n_row
;
931 if (add_wraps(&wraps
, &info
[i
], bound
->el
, set_j
) < 0)
934 if (isl_tab_rollback(info
[i
].tab
, snap
) < 0)
936 if (check_wraps(wraps
.mat
, n
, info
[i
].tab
) < 0)
938 if (!wraps
.mat
->n_row
)
941 change
= fuse(i
, j
, info
, wraps
.mat
, 0);
957 return isl_change_error
;
960 /* Given a pair of basic maps i and j such that j sticks out
961 * of i at n cut constraints, each time by at most one,
962 * try to compute wrapping constraints and replace the two
963 * basic maps by a single basic map.
964 * The other constraints of i are assumed to be valid for j.
966 * For each cut constraint t(x) >= 0 of i, we add the relaxed version
967 * t(x) + 1 >= 0, along with wrapping constraints for all constraints
968 * of basic map j that bound the part of basic map j that sticks out
969 * of the cut constraint.
970 * In particular, we first intersect basic map j with t(x) + 1 = 0.
971 * If the result is empty, then t(x) >= 0 was actually a valid constraint
972 * (with respect to the integer points), so we add t(x) >= 0 instead.
973 * Otherwise, we wrap the constraints of basic map j that are not
974 * redundant in this intersection over the union of the two basic maps.
976 * If any wrapping fails, i.e., if we cannot wrap to touch
977 * the union, then we give up.
978 * Otherwise, the pair of basic maps is replaced by their union.
980 static enum isl_change
wrap_in_facets(int i
, int j
, int *cuts
, int n
,
981 struct isl_coalesce_info
*info
)
983 enum isl_change change
= isl_change_none
;
984 struct isl_wraps wraps
;
988 unsigned total
= isl_basic_map_total_dim(info
[i
].bmap
);
991 struct isl_tab_undo
*snap
;
993 if (isl_tab_extend_cons(info
[j
].tab
, 1) < 0)
996 max_wrap
= 1 + 2 * info
[j
].bmap
->n_eq
+ info
[j
].bmap
->n_ineq
;
999 set
= isl_set_union(set_from_updated_bmap(info
[i
].bmap
, info
[i
].tab
),
1000 set_from_updated_bmap(info
[j
].bmap
, info
[j
].tab
));
1001 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
1002 mat
= isl_mat_alloc(ctx
, max_wrap
, 1 + total
);
1003 wraps_init(&wraps
, mat
, info
, i
, j
);
1004 if (!set
|| !wraps
.mat
)
1007 snap
= isl_tab_snap(info
[j
].tab
);
1009 wraps
.mat
->n_row
= 0;
1011 for (k
= 0; k
< n
; ++k
) {
1012 w
= wraps
.mat
->n_row
++;
1013 isl_seq_cpy(wraps
.mat
->row
[w
],
1014 info
[i
].bmap
->ineq
[cuts
[k
]], 1 + total
);
1015 isl_int_add_ui(wraps
.mat
->row
[w
][0], wraps
.mat
->row
[w
][0], 1);
1016 if (isl_tab_add_eq(info
[j
].tab
, wraps
.mat
->row
[w
]) < 0)
1018 if (isl_tab_detect_redundant(info
[j
].tab
) < 0)
1021 if (info
[j
].tab
->empty
)
1022 isl_int_sub_ui(wraps
.mat
->row
[w
][0],
1023 wraps
.mat
->row
[w
][0], 1);
1024 else if (add_wraps(&wraps
, &info
[j
],
1025 wraps
.mat
->row
[w
], set
) < 0)
1028 if (isl_tab_rollback(info
[j
].tab
, snap
) < 0)
1031 if (!wraps
.mat
->n_row
)
1036 change
= fuse(i
, j
, info
, wraps
.mat
, 0);
1045 return isl_change_error
;
1048 /* Given two basic sets i and j such that i has no cut equalities,
1049 * check if relaxing all the cut inequalities of i by one turns
1050 * them into valid constraint for j and check if we can wrap in
1051 * the bits that are sticking out.
1052 * If so, replace the pair by their union.
1054 * We first check if all relaxed cut inequalities of i are valid for j
1055 * and then try to wrap in the intersections of the relaxed cut inequalities
1058 * During this wrapping, we consider the points of j that lie at a distance
1059 * of exactly 1 from i. In particular, we ignore the points that lie in
1060 * between this lower-dimensional space and the basic map i.
1061 * We can therefore only apply this to integer maps.
1087 * Wrapping can fail if the result of wrapping one of the facets
1088 * around its edges does not produce any new facet constraint.
1089 * In particular, this happens when we try to wrap in unbounded sets.
1091 * _______________________________________________________________________
1095 * |_| |_________________________________________________________________
1098 * The following is not an acceptable result of coalescing the above two
1099 * sets as it includes extra integer points.
1100 * _______________________________________________________________________
1105 * \______________________________________________________________________
1107 static enum isl_change
can_wrap_in_set(int i
, int j
,
1108 struct isl_coalesce_info
*info
)
1110 enum isl_change change
= isl_change_none
;
1116 if (ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_RATIONAL
) ||
1117 ISL_F_ISSET(info
[j
].bmap
, ISL_BASIC_MAP_RATIONAL
))
1118 return isl_change_none
;
1120 n
= count(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_CUT
);
1122 return isl_change_none
;
1124 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
1125 cuts
= isl_alloc_array(ctx
, int, n
);
1127 return isl_change_error
;
1129 for (k
= 0, m
= 0; m
< n
; ++k
) {
1130 enum isl_ineq_type type
;
1132 if (info
[i
].ineq
[k
] != STATUS_CUT
)
1135 isl_int_add_ui(info
[i
].bmap
->ineq
[k
][0],
1136 info
[i
].bmap
->ineq
[k
][0], 1);
1137 type
= isl_tab_ineq_type(info
[j
].tab
, info
[i
].bmap
->ineq
[k
]);
1138 isl_int_sub_ui(info
[i
].bmap
->ineq
[k
][0],
1139 info
[i
].bmap
->ineq
[k
][0], 1);
1140 if (type
== isl_ineq_error
)
1142 if (type
!= isl_ineq_redundant
)
1149 change
= wrap_in_facets(i
, j
, cuts
, n
, info
);
1156 return isl_change_error
;
1159 /* Check if either i or j has only cut inequalities that can
1160 * be used to wrap in (a facet of) the other basic set.
1161 * if so, replace the pair by their union.
1163 static enum isl_change
check_wrap(int i
, int j
, struct isl_coalesce_info
*info
)
1165 enum isl_change change
= isl_change_none
;
1167 if (!any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_CUT
))
1168 change
= can_wrap_in_set(i
, j
, info
);
1169 if (change
!= isl_change_none
)
1172 if (!any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_CUT
))
1173 change
= can_wrap_in_set(j
, i
, info
);
1177 /* At least one of the basic maps has an equality that is adjacent
1178 * to inequality. Make sure that only one of the basic maps has
1179 * such an equality and that the other basic map has exactly one
1180 * inequality adjacent to an equality.
1181 * We call the basic map that has the inequality "i" and the basic
1182 * map that has the equality "j".
1183 * If "i" has any "cut" (in)equality, then relaxing the inequality
1184 * by one would not result in a basic map that contains the other
1187 static enum isl_change
check_adj_eq(int i
, int j
,
1188 struct isl_coalesce_info
*info
)
1190 enum isl_change change
= isl_change_none
;
1193 if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_ADJ_INEQ
) &&
1194 any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_ADJ_INEQ
))
1195 /* ADJ EQ TOO MANY */
1196 return isl_change_none
;
1198 if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_ADJ_INEQ
))
1199 return check_adj_eq(j
, i
, info
);
1201 /* j has an equality adjacent to an inequality in i */
1203 if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_CUT
))
1204 return isl_change_none
;
1205 if (any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_CUT
))
1207 return isl_change_none
;
1208 if (count(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ADJ_EQ
) != 1 ||
1209 any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_ADJ_EQ
) ||
1210 any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ADJ_INEQ
) ||
1211 any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_ADJ_INEQ
))
1212 /* ADJ EQ TOO MANY */
1213 return isl_change_none
;
1215 for (k
= 0; k
< info
[i
].bmap
->n_ineq
; ++k
)
1216 if (info
[i
].ineq
[k
] == STATUS_ADJ_EQ
)
1219 change
= is_adj_eq_extension(i
, j
, k
, info
);
1220 if (change
!= isl_change_none
)
1223 if (count(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_ADJ_INEQ
) != 1)
1224 return isl_change_none
;
1226 change
= can_wrap_in_facet(i
, j
, k
, info
);
1231 /* The two basic maps lie on adjacent hyperplanes. In particular,
1232 * basic map "i" has an equality that lies parallel to basic map "j".
1233 * Check if we can wrap the facets around the parallel hyperplanes
1234 * to include the other set.
1236 * We perform basically the same operations as can_wrap_in_facet,
1237 * except that we don't need to select a facet of one of the sets.
1243 * If there is more than one equality of "i" adjacent to an equality of "j",
1244 * then the result will satisfy one or more equalities that are a linear
1245 * combination of these equalities. These will be encoded as pairs
1246 * of inequalities in the wrapping constraints and need to be made
1249 static enum isl_change
check_eq_adj_eq(int i
, int j
,
1250 struct isl_coalesce_info
*info
)
1253 enum isl_change change
= isl_change_none
;
1254 int detect_equalities
= 0;
1255 struct isl_wraps wraps
;
1258 struct isl_set
*set_i
= NULL
;
1259 struct isl_set
*set_j
= NULL
;
1260 struct isl_vec
*bound
= NULL
;
1261 unsigned total
= isl_basic_map_total_dim(info
[i
].bmap
);
1263 if (count(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_ADJ_EQ
) != 1)
1264 detect_equalities
= 1;
1266 for (k
= 0; k
< 2 * info
[i
].bmap
->n_eq
; ++k
)
1267 if (info
[i
].eq
[k
] == STATUS_ADJ_EQ
)
1270 set_i
= set_from_updated_bmap(info
[i
].bmap
, info
[i
].tab
);
1271 set_j
= set_from_updated_bmap(info
[j
].bmap
, info
[j
].tab
);
1272 ctx
= isl_basic_map_get_ctx(info
[i
].bmap
);
1273 mat
= isl_mat_alloc(ctx
, 2 * (info
[i
].bmap
->n_eq
+ info
[j
].bmap
->n_eq
) +
1274 info
[i
].bmap
->n_ineq
+ info
[j
].bmap
->n_ineq
,
1276 wraps_init(&wraps
, mat
, info
, i
, j
);
1277 bound
= isl_vec_alloc(ctx
, 1 + total
);
1278 if (!set_i
|| !set_j
|| !wraps
.mat
|| !bound
)
1282 isl_seq_neg(bound
->el
, info
[i
].bmap
->eq
[k
/ 2], 1 + total
);
1284 isl_seq_cpy(bound
->el
, info
[i
].bmap
->eq
[k
/ 2], 1 + total
);
1285 isl_int_add_ui(bound
->el
[0], bound
->el
[0], 1);
1287 isl_seq_cpy(wraps
.mat
->row
[0], bound
->el
, 1 + total
);
1288 wraps
.mat
->n_row
= 1;
1290 if (add_wraps(&wraps
, &info
[j
], bound
->el
, set_i
) < 0)
1292 if (!wraps
.mat
->n_row
)
1295 isl_int_sub_ui(bound
->el
[0], bound
->el
[0], 1);
1296 isl_seq_neg(bound
->el
, bound
->el
, 1 + total
);
1298 isl_seq_cpy(wraps
.mat
->row
[wraps
.mat
->n_row
], bound
->el
, 1 + total
);
1301 if (add_wraps(&wraps
, &info
[i
], bound
->el
, set_j
) < 0)
1303 if (!wraps
.mat
->n_row
)
1306 change
= fuse(i
, j
, info
, wraps
.mat
, detect_equalities
);
1309 error
: change
= isl_change_error
;
1314 isl_set_free(set_i
);
1315 isl_set_free(set_j
);
1316 isl_vec_free(bound
);
1321 /* Check if the union of the given pair of basic maps
1322 * can be represented by a single basic map.
1323 * If so, replace the pair by the single basic map and return
1324 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
1325 * Otherwise, return isl_change_none.
1326 * The two basic maps are assumed to live in the same local space.
1328 * We first check the effect of each constraint of one basic map
1329 * on the other basic map.
1330 * The constraint may be
1331 * redundant the constraint is redundant in its own
1332 * basic map and should be ignore and removed
1334 * valid all (integer) points of the other basic map
1335 * satisfy the constraint
1336 * separate no (integer) point of the other basic map
1337 * satisfies the constraint
1338 * cut some but not all points of the other basic map
1339 * satisfy the constraint
1340 * adj_eq the given constraint is adjacent (on the outside)
1341 * to an equality of the other basic map
1342 * adj_ineq the given constraint is adjacent (on the outside)
1343 * to an inequality of the other basic map
1345 * We consider seven cases in which we can replace the pair by a single
1346 * basic map. We ignore all "redundant" constraints.
1348 * 1. all constraints of one basic map are valid
1349 * => the other basic map is a subset and can be removed
1351 * 2. all constraints of both basic maps are either "valid" or "cut"
1352 * and the facets corresponding to the "cut" constraints
1353 * of one of the basic maps lies entirely inside the other basic map
1354 * => the pair can be replaced by a basic map consisting
1355 * of the valid constraints in both basic maps
1357 * 3. there is a single pair of adjacent inequalities
1358 * (all other constraints are "valid")
1359 * => the pair can be replaced by a basic map consisting
1360 * of the valid constraints in both basic maps
1362 * 4. one basic map has a single adjacent inequality, while the other
1363 * constraints are "valid". The other basic map has some
1364 * "cut" constraints, but replacing the adjacent inequality by
1365 * its opposite and adding the valid constraints of the other
1366 * basic map results in a subset of the other basic map
1367 * => the pair can be replaced by a basic map consisting
1368 * of the valid constraints in both basic maps
1370 * 5. there is a single adjacent pair of an inequality and an equality,
1371 * the other constraints of the basic map containing the inequality are
1372 * "valid". Moreover, if the inequality the basic map is relaxed
1373 * and then turned into an equality, then resulting facet lies
1374 * entirely inside the other basic map
1375 * => the pair can be replaced by the basic map containing
1376 * the inequality, with the inequality relaxed.
1378 * 6. there is a single adjacent pair of an inequality and an equality,
1379 * the other constraints of the basic map containing the inequality are
1380 * "valid". Moreover, the facets corresponding to both
1381 * the inequality and the equality can be wrapped around their
1382 * ridges to include the other basic map
1383 * => the pair can be replaced by a basic map consisting
1384 * of the valid constraints in both basic maps together
1385 * with all wrapping constraints
1387 * 7. one of the basic maps extends beyond the other by at most one.
1388 * Moreover, the facets corresponding to the cut constraints and
1389 * the pieces of the other basic map at offset one from these cut
1390 * constraints can be wrapped around their ridges to include
1391 * the union of the two basic maps
1392 * => the pair can be replaced by a basic map consisting
1393 * of the valid constraints in both basic maps together
1394 * with all wrapping constraints
1396 * 8. the two basic maps live in adjacent hyperplanes. In principle
1397 * such sets can always be combined through wrapping, but we impose
1398 * that there is only one such pair, to avoid overeager coalescing.
1400 * Throughout the computation, we maintain a collection of tableaus
1401 * corresponding to the basic maps. When the basic maps are dropped
1402 * or combined, the tableaus are modified accordingly.
1404 static enum isl_change
coalesce_local_pair(int i
, int j
,
1405 struct isl_coalesce_info
*info
)
1407 enum isl_change change
= isl_change_none
;
1409 info
[i
].eq
= info
[i
].ineq
= NULL
;
1410 info
[j
].eq
= info
[j
].ineq
= NULL
;
1412 info
[i
].eq
= eq_status_in(info
[i
].bmap
, info
[j
].tab
);
1413 if (info
[i
].bmap
->n_eq
&& !info
[i
].eq
)
1415 if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_ERROR
))
1417 if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_SEPARATE
))
1420 info
[j
].eq
= eq_status_in(info
[j
].bmap
, info
[i
].tab
);
1421 if (info
[j
].bmap
->n_eq
&& !info
[j
].eq
)
1423 if (any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_ERROR
))
1425 if (any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_SEPARATE
))
1428 info
[i
].ineq
= ineq_status_in(info
[i
].bmap
, info
[i
].tab
, info
[j
].tab
);
1429 if (info
[i
].bmap
->n_ineq
&& !info
[i
].ineq
)
1431 if (any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ERROR
))
1433 if (any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_SEPARATE
))
1436 info
[j
].ineq
= ineq_status_in(info
[j
].bmap
, info
[j
].tab
, info
[i
].tab
);
1437 if (info
[j
].bmap
->n_ineq
&& !info
[j
].ineq
)
1439 if (any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_ERROR
))
1441 if (any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_SEPARATE
))
1444 if (all(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_VALID
) &&
1445 all(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_VALID
)) {
1447 change
= isl_change_drop_second
;
1448 } else if (all(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_VALID
) &&
1449 all(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_VALID
)) {
1451 change
= isl_change_drop_first
;
1452 } else if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_ADJ_EQ
)) {
1453 change
= check_eq_adj_eq(i
, j
, info
);
1454 } else if (any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_ADJ_EQ
)) {
1455 change
= check_eq_adj_eq(j
, i
, info
);
1456 } else if (any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_ADJ_INEQ
) ||
1457 any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_ADJ_INEQ
)) {
1458 change
= check_adj_eq(i
, j
, info
);
1459 } else if (any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ADJ_EQ
) ||
1460 any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_ADJ_EQ
)) {
1463 } else if (any(info
[i
].ineq
, info
[i
].bmap
->n_ineq
, STATUS_ADJ_INEQ
) ||
1464 any(info
[j
].ineq
, info
[j
].bmap
->n_ineq
, STATUS_ADJ_INEQ
)) {
1465 change
= check_adj_ineq(i
, j
, info
);
1467 if (!any(info
[i
].eq
, 2 * info
[i
].bmap
->n_eq
, STATUS_CUT
) &&
1468 !any(info
[j
].eq
, 2 * info
[j
].bmap
->n_eq
, STATUS_CUT
))
1469 change
= check_facets(i
, j
, info
);
1470 if (change
== isl_change_none
)
1471 change
= check_wrap(i
, j
, info
);
1485 return isl_change_error
;
1488 /* Do the two basic maps live in the same local space, i.e.,
1489 * do they have the same (known) divs?
1490 * If either basic map has any unknown divs, then we can only assume
1491 * that they do not live in the same local space.
1493 static int same_divs(__isl_keep isl_basic_map
*bmap1
,
1494 __isl_keep isl_basic_map
*bmap2
)
1500 if (!bmap1
|| !bmap2
)
1502 if (bmap1
->n_div
!= bmap2
->n_div
)
1505 if (bmap1
->n_div
== 0)
1508 known
= isl_basic_map_divs_known(bmap1
);
1509 if (known
< 0 || !known
)
1511 known
= isl_basic_map_divs_known(bmap2
);
1512 if (known
< 0 || !known
)
1515 total
= isl_basic_map_total_dim(bmap1
);
1516 for (i
= 0; i
< bmap1
->n_div
; ++i
)
1517 if (!isl_seq_eq(bmap1
->div
[i
], bmap2
->div
[i
], 2 + total
))
1523 /* Does "bmap" contain the basic map represented by the tableau "tab"
1524 * after expanding the divs of "bmap" to match those of "tab"?
1525 * The expansion is performed using the divs "div" and expansion "exp"
1526 * computed by the caller.
1527 * Then we check if all constraints of the expanded "bmap" are valid for "tab".
1529 static int contains_with_expanded_divs(__isl_keep isl_basic_map
*bmap
,
1530 struct isl_tab
*tab
, __isl_keep isl_mat
*div
, int *exp
)
1536 bmap
= isl_basic_map_copy(bmap
);
1537 bmap
= isl_basic_set_expand_divs(bmap
, isl_mat_copy(div
), exp
);
1542 eq_i
= eq_status_in(bmap
, tab
);
1543 if (bmap
->n_eq
&& !eq_i
)
1545 if (any(eq_i
, 2 * bmap
->n_eq
, STATUS_ERROR
))
1547 if (any(eq_i
, 2 * bmap
->n_eq
, STATUS_SEPARATE
))
1550 ineq_i
= ineq_status_in(bmap
, NULL
, tab
);
1551 if (bmap
->n_ineq
&& !ineq_i
)
1553 if (any(ineq_i
, bmap
->n_ineq
, STATUS_ERROR
))
1555 if (any(ineq_i
, bmap
->n_ineq
, STATUS_SEPARATE
))
1558 if (all(eq_i
, 2 * bmap
->n_eq
, STATUS_VALID
) &&
1559 all(ineq_i
, bmap
->n_ineq
, STATUS_VALID
))
1563 isl_basic_map_free(bmap
);
1568 isl_basic_map_free(bmap
);
1574 /* Does "bmap_i" contain the basic map represented by "info_j"
1575 * after aligning the divs of "bmap_i" to those of "info_j".
1576 * Note that this can only succeed if the number of divs of "bmap_i"
1577 * is smaller than (or equal to) the number of divs of "info_j".
1579 * We first check if the divs of "bmap_i" are all known and form a subset
1580 * of those of "bmap_j". If so, we pass control over to
1581 * contains_with_expanded_divs.
1583 static int contains_after_aligning_divs(__isl_keep isl_basic_map
*bmap_i
,
1584 struct isl_coalesce_info
*info_j
)
1587 isl_mat
*div_i
, *div_j
, *div
;
1593 known
= isl_basic_map_divs_known(bmap_i
);
1594 if (known
< 0 || !known
)
1597 ctx
= isl_basic_map_get_ctx(bmap_i
);
1599 div_i
= isl_basic_map_get_divs(bmap_i
);
1600 div_j
= isl_basic_map_get_divs(info_j
->bmap
);
1602 if (!div_i
|| !div_j
)
1605 exp1
= isl_alloc_array(ctx
, int, div_i
->n_row
);
1606 exp2
= isl_alloc_array(ctx
, int, div_j
->n_row
);
1607 if ((div_i
->n_row
&& !exp1
) || (div_j
->n_row
&& !exp2
))
1610 div
= isl_merge_divs(div_i
, div_j
, exp1
, exp2
);
1614 if (div
->n_row
== div_j
->n_row
)
1615 subset
= contains_with_expanded_divs(bmap_i
,
1616 info_j
->tab
, div
, exp1
);
1622 isl_mat_free(div_i
);
1623 isl_mat_free(div_j
);
1630 isl_mat_free(div_i
);
1631 isl_mat_free(div_j
);
1637 /* Check if the basic map "j" is a subset of basic map "i",
1638 * if "i" has fewer divs that "j".
1639 * If so, remove basic map "j".
1641 * If the two basic maps have the same number of divs, then
1642 * they must necessarily be different. Otherwise, we would have
1643 * called coalesce_local_pair. We therefore don't try anything
1646 static int coalesced_subset(int i
, int j
, struct isl_coalesce_info
*info
)
1650 if (info
[i
].bmap
->n_div
>= info
[j
].bmap
->n_div
)
1653 superset
= contains_after_aligning_divs(info
[i
].bmap
, &info
[j
]);
1662 /* Check if one of the basic maps is a subset of the other and, if so,
1664 * Note that we only perform any test if the number of divs is different
1665 * in the two basic maps. In case the number of divs is the same,
1666 * we have already established that the divs are different
1667 * in the two basic maps.
1668 * In particular, if the number of divs of basic map i is smaller than
1669 * the number of divs of basic map j, then we check if j is a subset of i
1672 static enum isl_change
check_coalesce_subset(int i
, int j
,
1673 struct isl_coalesce_info
*info
)
1677 changed
= coalesced_subset(i
, j
, info
);
1678 if (changed
< 0 || changed
)
1679 return changed
< 0 ? isl_change_error
: isl_change_drop_second
;
1681 changed
= coalesced_subset(j
, i
, info
);
1682 if (changed
< 0 || changed
)
1683 return changed
< 0 ? isl_change_error
: isl_change_drop_first
;
1685 return isl_change_none
;
1688 /* Check if the union of the given pair of basic maps
1689 * can be represented by a single basic map.
1690 * If so, replace the pair by the single basic map and return
1691 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
1692 * Otherwise, return isl_change_none.
1694 * We first check if the two basic maps live in the same local space.
1695 * If so, we do the complete check. Otherwise, we check if one is
1696 * an obvious subset of the other.
1698 static enum isl_change
coalesce_pair(int i
, int j
,
1699 struct isl_coalesce_info
*info
)
1703 same
= same_divs(info
[i
].bmap
, info
[j
].bmap
);
1705 return isl_change_error
;
1707 return coalesce_local_pair(i
, j
, info
);
1709 return check_coalesce_subset(i
, j
, info
);
1712 /* Pairwise coalesce the basic maps described by the "n" elements of "info",
1713 * skipping basic maps that have been removed (either before or within
1716 * For each basic map i, we check if it can be coalesced with respect
1717 * to any previously considered basic map j.
1718 * If i gets dropped (because it was a subset of some j), then
1719 * we can move on to the next basic map.
1720 * If j gets dropped, we need to continue checking against the other
1721 * previously considered basic maps.
1722 * If the two basic maps got fused, then we recheck the fused basic map
1723 * against the previously considered basic maps.
1725 static int coalesce(isl_ctx
*ctx
, int n
, struct isl_coalesce_info
*info
)
1729 for (i
= n
- 2; i
>= 0; --i
) {
1730 if (info
[i
].removed
)
1732 for (j
= i
+ 1; j
< n
; ++j
) {
1733 enum isl_change changed
;
1735 if (info
[j
].removed
)
1737 if (info
[i
].removed
)
1738 isl_die(ctx
, isl_error_internal
,
1739 "basic map unexpectedly removed",
1741 changed
= coalesce_pair(i
, j
, info
);
1743 case isl_change_error
:
1745 case isl_change_none
:
1746 case isl_change_drop_second
:
1748 case isl_change_drop_first
:
1751 case isl_change_fuse
:
1761 /* Update the basic maps in "map" based on the information in "info".
1762 * In particular, remove the basic maps that have been marked removed and
1763 * update the others based on the information in the corresponding tableau.
1764 * Since we detected implicit equalities without calling
1765 * isl_basic_map_gauss, we need to do it now.
1767 static __isl_give isl_map
*update_basic_maps(__isl_take isl_map
*map
,
1768 int n
, struct isl_coalesce_info
*info
)
1775 for (i
= n
- 1; i
>= 0; --i
) {
1776 if (info
[i
].removed
) {
1777 isl_basic_map_free(map
->p
[i
]);
1778 if (i
!= map
->n
- 1)
1779 map
->p
[i
] = map
->p
[map
->n
- 1];
1784 info
[i
].bmap
= isl_basic_map_update_from_tab(info
[i
].bmap
,
1786 info
[i
].bmap
= isl_basic_map_gauss(info
[i
].bmap
, NULL
);
1787 info
[i
].bmap
= isl_basic_map_finalize(info
[i
].bmap
);
1789 return isl_map_free(map
);
1790 ISL_F_SET(info
[i
].bmap
, ISL_BASIC_MAP_NO_IMPLICIT
);
1791 ISL_F_SET(info
[i
].bmap
, ISL_BASIC_MAP_NO_REDUNDANT
);
1792 isl_basic_map_free(map
->p
[i
]);
1793 map
->p
[i
] = info
[i
].bmap
;
1794 info
[i
].bmap
= NULL
;
1800 /* For each pair of basic maps in the map, check if the union of the two
1801 * can be represented by a single basic map.
1802 * If so, replace the pair by the single basic map and start over.
1804 * Since we are constructing the tableaus of the basic maps anyway,
1805 * we exploit them to detect implicit equalities and redundant constraints.
1806 * This also helps the coalescing as it can ignore the redundant constraints.
1807 * In order to avoid confusion, we make all implicit equalities explicit
1808 * in the basic maps. We don't call isl_basic_map_gauss, though,
1809 * as that may affect the number of constraints.
1810 * This means that we have to call isl_basic_map_gauss at the end
1811 * of the computation (in update_basic_maps) to ensure that
1812 * the basic maps are not left in an unexpected state.
1814 struct isl_map
*isl_map_coalesce(struct isl_map
*map
)
1819 struct isl_coalesce_info
*info
= NULL
;
1821 map
= isl_map_remove_empty_parts(map
);
1828 ctx
= isl_map_get_ctx(map
);
1829 map
= isl_map_sort_divs(map
);
1830 map
= isl_map_cow(map
);
1837 info
= isl_calloc_array(map
->ctx
, struct isl_coalesce_info
, n
);
1841 for (i
= 0; i
< map
->n
; ++i
) {
1842 info
[i
].bmap
= isl_basic_map_copy(map
->p
[i
]);
1843 info
[i
].tab
= isl_tab_from_basic_map(info
[i
].bmap
, 0);
1846 if (!ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_NO_IMPLICIT
))
1847 if (isl_tab_detect_implicit_equalities(info
[i
].tab
) < 0)
1849 info
[i
].bmap
= isl_tab_make_equalities_explicit(info
[i
].tab
,
1853 if (!ISL_F_ISSET(info
[i
].bmap
, ISL_BASIC_MAP_NO_REDUNDANT
))
1854 if (isl_tab_detect_redundant(info
[i
].tab
) < 0)
1857 for (i
= map
->n
- 1; i
>= 0; --i
)
1858 if (info
[i
].tab
->empty
)
1861 if (coalesce(ctx
, n
, info
) < 0)
1864 map
= update_basic_maps(map
, n
, info
);
1866 clear_coalesce_info(n
, info
);
1870 clear_coalesce_info(n
, info
);
1875 /* For each pair of basic sets in the set, check if the union of the two
1876 * can be represented by a single basic set.
1877 * If so, replace the pair by the single basic set and start over.
1879 struct isl_set
*isl_set_coalesce(struct isl_set
*set
)
1881 return (struct isl_set
*)isl_map_coalesce((struct isl_map
*)set
);