2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2010 INRIA Saclay
5 * Use of this software is governed by the GNU LGPLv2.1 license
7 * Written by Sven Verdoolaege, K.U.Leuven, Departement
8 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
9 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
10 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
13 #include "isl_map_private.h"
17 #define STATUS_ERROR -1
18 #define STATUS_REDUNDANT 1
19 #define STATUS_VALID 2
20 #define STATUS_SEPARATE 3
22 #define STATUS_ADJ_EQ 5
23 #define STATUS_ADJ_INEQ 6
25 static int status_in(isl_int
*ineq
, struct isl_tab
*tab
)
27 enum isl_ineq_type type
= isl_tab_ineq_type(tab
, ineq
);
29 case isl_ineq_error
: return STATUS_ERROR
;
30 case isl_ineq_redundant
: return STATUS_VALID
;
31 case isl_ineq_separate
: return STATUS_SEPARATE
;
32 case isl_ineq_cut
: return STATUS_CUT
;
33 case isl_ineq_adj_eq
: return STATUS_ADJ_EQ
;
34 case isl_ineq_adj_ineq
: return STATUS_ADJ_INEQ
;
38 /* Compute the position of the equalities of basic map "i"
39 * with respect to basic map "j".
40 * The resulting array has twice as many entries as the number
41 * of equalities corresponding to the two inequalties to which
42 * each equality corresponds.
44 static int *eq_status_in(struct isl_map
*map
, int i
, int j
,
45 struct isl_tab
**tabs
)
48 int *eq
= isl_calloc_array(map
->ctx
, int, 2 * map
->p
[i
]->n_eq
);
51 dim
= isl_basic_map_total_dim(map
->p
[i
]);
52 for (k
= 0; k
< map
->p
[i
]->n_eq
; ++k
) {
53 for (l
= 0; l
< 2; ++l
) {
54 isl_seq_neg(map
->p
[i
]->eq
[k
], map
->p
[i
]->eq
[k
], 1+dim
);
55 eq
[2 * k
+ l
] = status_in(map
->p
[i
]->eq
[k
], tabs
[j
]);
56 if (eq
[2 * k
+ l
] == STATUS_ERROR
)
59 if (eq
[2 * k
] == STATUS_SEPARATE
||
60 eq
[2 * k
+ 1] == STATUS_SEPARATE
)
70 /* Compute the position of the inequalities of basic map "i"
71 * with respect to basic map "j".
73 static int *ineq_status_in(struct isl_map
*map
, int i
, int j
,
74 struct isl_tab
**tabs
)
77 unsigned n_eq
= map
->p
[i
]->n_eq
;
78 int *ineq
= isl_calloc_array(map
->ctx
, int, map
->p
[i
]->n_ineq
);
80 for (k
= 0; k
< map
->p
[i
]->n_ineq
; ++k
) {
81 if (isl_tab_is_redundant(tabs
[i
], n_eq
+ k
)) {
82 ineq
[k
] = STATUS_REDUNDANT
;
85 ineq
[k
] = status_in(map
->p
[i
]->ineq
[k
], tabs
[j
]);
86 if (ineq
[k
] == STATUS_ERROR
)
88 if (ineq
[k
] == STATUS_SEPARATE
)
98 static int any(int *con
, unsigned len
, int status
)
102 for (i
= 0; i
< len
; ++i
)
103 if (con
[i
] == status
)
108 static int count(int *con
, unsigned len
, int status
)
113 for (i
= 0; i
< len
; ++i
)
114 if (con
[i
] == status
)
119 static int all(int *con
, unsigned len
, int status
)
123 for (i
= 0; i
< len
; ++i
) {
124 if (con
[i
] == STATUS_REDUNDANT
)
126 if (con
[i
] != status
)
132 static void drop(struct isl_map
*map
, int i
, struct isl_tab
**tabs
)
134 isl_basic_map_free(map
->p
[i
]);
135 isl_tab_free(tabs
[i
]);
137 if (i
!= map
->n
- 1) {
138 map
->p
[i
] = map
->p
[map
->n
- 1];
139 tabs
[i
] = tabs
[map
->n
- 1];
141 tabs
[map
->n
- 1] = NULL
;
145 /* Replace the pair of basic maps i and j by the basic map bounded
146 * by the valid constraints in both basic maps and the constraint
147 * in extra (if not NULL).
149 static int fuse(struct isl_map
*map
, int i
, int j
,
150 struct isl_tab
**tabs
, int *eq_i
, int *ineq_i
, int *eq_j
, int *ineq_j
,
151 __isl_keep isl_mat
*extra
)
154 struct isl_basic_map
*fused
= NULL
;
155 struct isl_tab
*fused_tab
= NULL
;
156 unsigned total
= isl_basic_map_total_dim(map
->p
[i
]);
157 unsigned extra_rows
= extra
? extra
->n_row
: 0;
159 fused
= isl_basic_map_alloc_dim(isl_dim_copy(map
->p
[i
]->dim
),
161 map
->p
[i
]->n_eq
+ map
->p
[j
]->n_eq
,
162 map
->p
[i
]->n_ineq
+ map
->p
[j
]->n_ineq
+ extra_rows
);
166 for (k
= 0; k
< map
->p
[i
]->n_eq
; ++k
) {
167 if (eq_i
&& (eq_i
[2 * k
] != STATUS_VALID
||
168 eq_i
[2 * k
+ 1] != STATUS_VALID
))
170 l
= isl_basic_map_alloc_equality(fused
);
173 isl_seq_cpy(fused
->eq
[l
], map
->p
[i
]->eq
[k
], 1 + total
);
176 for (k
= 0; k
< map
->p
[j
]->n_eq
; ++k
) {
177 if (eq_j
&& (eq_j
[2 * k
] != STATUS_VALID
||
178 eq_j
[2 * k
+ 1] != STATUS_VALID
))
180 l
= isl_basic_map_alloc_equality(fused
);
183 isl_seq_cpy(fused
->eq
[l
], map
->p
[j
]->eq
[k
], 1 + total
);
186 for (k
= 0; k
< map
->p
[i
]->n_ineq
; ++k
) {
187 if (ineq_i
[k
] != STATUS_VALID
)
189 l
= isl_basic_map_alloc_inequality(fused
);
192 isl_seq_cpy(fused
->ineq
[l
], map
->p
[i
]->ineq
[k
], 1 + total
);
195 for (k
= 0; k
< map
->p
[j
]->n_ineq
; ++k
) {
196 if (ineq_j
[k
] != STATUS_VALID
)
198 l
= isl_basic_map_alloc_inequality(fused
);
201 isl_seq_cpy(fused
->ineq
[l
], map
->p
[j
]->ineq
[k
], 1 + total
);
204 for (k
= 0; k
< map
->p
[i
]->n_div
; ++k
) {
205 int l
= isl_basic_map_alloc_div(fused
);
208 isl_seq_cpy(fused
->div
[l
], map
->p
[i
]->div
[k
], 1 + 1 + total
);
211 for (k
= 0; k
< extra_rows
; ++k
) {
212 l
= isl_basic_map_alloc_inequality(fused
);
215 isl_seq_cpy(fused
->ineq
[l
], extra
->row
[k
], 1 + total
);
218 fused
= isl_basic_map_gauss(fused
, NULL
);
219 ISL_F_SET(fused
, ISL_BASIC_MAP_FINAL
);
220 if (ISL_F_ISSET(map
->p
[i
], ISL_BASIC_MAP_RATIONAL
) &&
221 ISL_F_ISSET(map
->p
[j
], ISL_BASIC_MAP_RATIONAL
))
222 ISL_F_SET(fused
, ISL_BASIC_MAP_RATIONAL
);
224 fused_tab
= isl_tab_from_basic_map(fused
);
225 if (isl_tab_detect_redundant(fused_tab
) < 0)
228 isl_basic_map_free(map
->p
[i
]);
230 isl_tab_free(tabs
[i
]);
236 isl_tab_free(fused_tab
);
237 isl_basic_map_free(fused
);
241 /* Given a pair of basic maps i and j such that all constraints are either
242 * "valid" or "cut", check if the facets corresponding to the "cut"
243 * constraints of i lie entirely within basic map j.
244 * If so, replace the pair by the basic map consisting of the valid
245 * constraints in both basic maps.
247 * To see that we are not introducing any extra points, call the
248 * two basic maps A and B and the resulting map U and let x
249 * be an element of U \setminus ( A \cup B ).
250 * Then there is a pair of cut constraints c_1 and c_2 in A and B such that x
251 * violates them. Let X be the intersection of U with the opposites
252 * of these constraints. Then x \in X.
253 * The facet corresponding to c_1 contains the corresponding facet of A.
254 * This facet is entirely contained in B, so c_2 is valid on the facet.
255 * However, since it is also (part of) a facet of X, -c_2 is also valid
256 * on the facet. This means c_2 is saturated on the facet, so c_1 and
257 * c_2 must be opposites of each other, but then x could not violate
260 static int check_facets(struct isl_map
*map
, int i
, int j
,
261 struct isl_tab
**tabs
, int *ineq_i
, int *ineq_j
)
264 struct isl_tab_undo
*snap
;
265 unsigned n_eq
= map
->p
[i
]->n_eq
;
267 snap
= isl_tab_snap(tabs
[i
]);
269 for (k
= 0; k
< map
->p
[i
]->n_ineq
; ++k
) {
270 if (ineq_i
[k
] != STATUS_CUT
)
272 tabs
[i
] = isl_tab_select_facet(tabs
[i
], n_eq
+ k
);
273 for (l
= 0; l
< map
->p
[j
]->n_ineq
; ++l
) {
275 if (ineq_j
[l
] != STATUS_CUT
)
277 stat
= status_in(map
->p
[j
]->ineq
[l
], tabs
[i
]);
278 if (stat
!= STATUS_VALID
)
281 if (isl_tab_rollback(tabs
[i
], snap
) < 0)
283 if (l
< map
->p
[j
]->n_ineq
)
287 if (k
< map
->p
[i
]->n_ineq
)
290 return fuse(map
, i
, j
, tabs
, NULL
, ineq_i
, NULL
, ineq_j
, NULL
);
293 /* Both basic maps have at least one inequality with and adjacent
294 * (but opposite) inequality in the other basic map.
295 * Check that there are no cut constraints and that there is only
296 * a single pair of adjacent inequalities.
297 * If so, we can replace the pair by a single basic map described
298 * by all but the pair of adjacent inequalities.
299 * Any additional points introduced lie strictly between the two
300 * adjacent hyperplanes and can therefore be integral.
309 * The test for a single pair of adjancent inequalities is important
310 * for avoiding the combination of two basic maps like the following
320 static int check_adj_ineq(struct isl_map
*map
, int i
, int j
,
321 struct isl_tab
**tabs
, int *ineq_i
, int *ineq_j
)
325 if (any(ineq_i
, map
->p
[i
]->n_ineq
, STATUS_CUT
) ||
326 any(ineq_j
, map
->p
[j
]->n_ineq
, STATUS_CUT
))
329 else if (count(ineq_i
, map
->p
[i
]->n_ineq
, STATUS_ADJ_INEQ
) == 1 &&
330 count(ineq_j
, map
->p
[j
]->n_ineq
, STATUS_ADJ_INEQ
) == 1)
331 changed
= fuse(map
, i
, j
, tabs
, NULL
, ineq_i
, NULL
, ineq_j
, NULL
);
332 /* else ADJ INEQ TOO MANY */
337 /* Check if basic map "i" contains the basic map represented
338 * by the tableau "tab".
340 static int contains(struct isl_map
*map
, int i
, int *ineq_i
,
346 dim
= isl_basic_map_total_dim(map
->p
[i
]);
347 for (k
= 0; k
< map
->p
[i
]->n_eq
; ++k
) {
348 for (l
= 0; l
< 2; ++l
) {
350 isl_seq_neg(map
->p
[i
]->eq
[k
], map
->p
[i
]->eq
[k
], 1+dim
);
351 stat
= status_in(map
->p
[i
]->eq
[k
], tab
);
352 if (stat
!= STATUS_VALID
)
357 for (k
= 0; k
< map
->p
[i
]->n_ineq
; ++k
) {
359 if (ineq_i
[k
] == STATUS_REDUNDANT
)
361 stat
= status_in(map
->p
[i
]->ineq
[k
], tab
);
362 if (stat
!= STATUS_VALID
)
368 /* Basic map "i" has an inequality "k" that is adjacent to some equality
369 * of basic map "j". All the other inequalities are valid for "j".
370 * Check if basic map "j" forms an extension of basic map "i".
372 * In particular, we relax constraint "k", compute the corresponding
373 * facet and check whether it is included in the other basic map.
374 * If so, we know that relaxing the constraint extends the basic
375 * map with exactly the other basic map (we already know that this
376 * other basic map is included in the extension, because there
377 * were no "cut" inequalities in "i") and we can replace the
378 * two basic maps by thie extension.
386 static int is_extension(struct isl_map
*map
, int i
, int j
, int k
,
387 struct isl_tab
**tabs
, int *eq_i
, int *ineq_i
, int *eq_j
, int *ineq_j
)
391 struct isl_tab_undo
*snap
, *snap2
;
392 unsigned n_eq
= map
->p
[i
]->n_eq
;
394 snap
= isl_tab_snap(tabs
[i
]);
395 tabs
[i
] = isl_tab_relax(tabs
[i
], n_eq
+ k
);
396 snap2
= isl_tab_snap(tabs
[i
]);
397 tabs
[i
] = isl_tab_select_facet(tabs
[i
], n_eq
+ k
);
398 super
= contains(map
, j
, ineq_j
, tabs
[i
]);
400 if (isl_tab_rollback(tabs
[i
], snap2
) < 0)
402 map
->p
[i
] = isl_basic_map_cow(map
->p
[i
]);
405 isl_int_add_ui(map
->p
[i
]->ineq
[k
][0], map
->p
[i
]->ineq
[k
][0], 1);
406 ISL_F_SET(map
->p
[i
], ISL_BASIC_MAP_FINAL
);
410 if (isl_tab_rollback(tabs
[i
], snap
) < 0)
416 /* For each non-redundant constraint in "bmap" (as determined by "tab"),
417 * wrap the constraint around "bound" such that it includes the whole
418 * set "set" and append the resulting constraint to "wraps".
419 * "wraps" is assumed to have been pre-allocated to the appropriate size.
420 * wraps->n_row is the number of actual wrapped constraints that have
422 * If any of the wrapping problems results in a constraint that is
423 * identical to "bound", then this means that "set" is unbounded in such
424 * way that no wrapping is possible. If this happens then wraps->n_row
427 static int add_wraps(__isl_keep isl_mat
*wraps
, __isl_keep isl_basic_map
*bmap
,
428 struct isl_tab
*tab
, isl_int
*bound
, __isl_keep isl_set
*set
)
432 unsigned total
= isl_basic_map_total_dim(bmap
);
436 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
437 if (isl_seq_is_neg(bound
, bmap
->ineq
[l
], 1 + total
))
439 if (isl_seq_eq(bound
, bmap
->ineq
[l
], 1 + total
))
441 if (isl_tab_is_redundant(tab
, bmap
->n_eq
+ l
))
444 isl_seq_cpy(wraps
->row
[w
], bound
, 1 + total
);
445 if (!isl_set_wrap_facet(set
, wraps
->row
[w
], bmap
->ineq
[l
]))
447 if (isl_seq_eq(wraps
->row
[w
], bound
, 1 + total
))
451 for (l
= 0; l
< bmap
->n_eq
; ++l
) {
452 if (isl_seq_is_neg(bound
, bmap
->eq
[l
], 1 + total
))
454 if (isl_seq_eq(bound
, bmap
->eq
[l
], 1 + total
))
457 isl_seq_cpy(wraps
->row
[w
], bound
, 1 + total
);
458 isl_seq_neg(wraps
->row
[w
+ 1], bmap
->eq
[l
], 1 + total
);
459 if (!isl_set_wrap_facet(set
, wraps
->row
[w
], wraps
->row
[w
+ 1]))
461 if (isl_seq_eq(wraps
->row
[w
], bound
, 1 + total
))
465 isl_seq_cpy(wraps
->row
[w
], bound
, 1 + total
);
466 if (!isl_set_wrap_facet(set
, wraps
->row
[w
], bmap
->eq
[l
]))
468 if (isl_seq_eq(wraps
->row
[w
], bound
, 1 + total
))
480 /* Check if the constraints in "wraps" from "first" until the last
481 * are all valid for the basic set represented by "tab".
482 * If not, wraps->n_row is set to zero.
484 static int check_wraps(__isl_keep isl_mat
*wraps
, int first
,
489 for (i
= first
; i
< wraps
->n_row
; ++i
) {
490 enum isl_ineq_type type
;
491 type
= isl_tab_ineq_type(tab
, wraps
->row
[i
]);
492 if (type
== isl_ineq_error
)
494 if (type
== isl_ineq_redundant
)
503 /* Return a set that corresponds to the non-redudant constraints
504 * (as recorded in tab) of bmap.
506 * It's important to remove the redundant constraints as some
507 * of the other constraints may have been modified after the
508 * constraints were marked redundant.
509 * In particular, a constraint may have been relaxed.
510 * Redundant constraints are ignored when a constraint is relaxed
511 * and should therefore continue to be ignored ever after.
512 * Otherwise, the relaxation might be thwarted by some of
515 static __isl_give isl_set
*set_from_updated_bmap(__isl_keep isl_basic_map
*bmap
,
518 bmap
= isl_basic_map_copy(bmap
);
519 bmap
= isl_basic_map_cow(bmap
);
520 bmap
= isl_basic_map_update_from_tab(bmap
, tab
);
521 return isl_set_from_basic_set(isl_basic_map_underlying_set(bmap
));
524 /* Given a basic set i with a constraint k that is adjacent to either the
525 * whole of basic set j or a facet of basic set j, check if we can wrap
526 * both the facet corresponding to k and the facet of j (or the whole of j)
527 * around their ridges to include the other set.
528 * If so, replace the pair of basic sets by their union.
530 * All constraints of i (except k) are assumed to be valid for j.
532 * However, the constraints of j may not be valid for i and so
533 * we have to check that the wrapping constraints for j are valid for i.
535 * In the case where j has a facet adjacent to i, tab[j] is assumed
536 * to have been restricted to this facet, so that the non-redundant
537 * constraints in tab[j] are the ridges of the facet.
538 * Note that for the purpose of wrapping, it does not matter whether
539 * we wrap the ridges of i around the whole of j or just around
540 * the facet since all the other constraints are assumed to be valid for j.
541 * In practice, we wrap to include the whole of j.
550 static int can_wrap_in_facet(struct isl_map
*map
, int i
, int j
, int k
,
551 struct isl_tab
**tabs
, int *eq_i
, int *ineq_i
, int *eq_j
, int *ineq_j
)
554 struct isl_mat
*wraps
= NULL
;
555 struct isl_set
*set_i
= NULL
;
556 struct isl_set
*set_j
= NULL
;
557 struct isl_vec
*bound
= NULL
;
558 unsigned total
= isl_basic_map_total_dim(map
->p
[i
]);
559 struct isl_tab_undo
*snap
;
562 set_i
= set_from_updated_bmap(map
->p
[i
], tabs
[i
]);
563 set_j
= set_from_updated_bmap(map
->p
[j
], tabs
[j
]);
564 wraps
= isl_mat_alloc(map
->ctx
, 2 * (map
->p
[i
]->n_eq
+ map
->p
[j
]->n_eq
) +
565 map
->p
[i
]->n_ineq
+ map
->p
[j
]->n_ineq
,
567 bound
= isl_vec_alloc(map
->ctx
, 1 + total
);
568 if (!set_i
|| !set_j
|| !wraps
|| !bound
)
571 isl_seq_cpy(bound
->el
, map
->p
[i
]->ineq
[k
], 1 + total
);
572 isl_int_add_ui(bound
->el
[0], bound
->el
[0], 1);
574 isl_seq_cpy(wraps
->row
[0], bound
->el
, 1 + total
);
577 if (add_wraps(wraps
, map
->p
[j
], tabs
[j
], bound
->el
, set_i
) < 0)
582 snap
= isl_tab_snap(tabs
[i
]);
584 tabs
[i
] = isl_tab_select_facet(tabs
[i
], map
->p
[i
]->n_eq
+ k
);
585 if (isl_tab_detect_redundant(tabs
[i
]) < 0)
588 isl_seq_neg(bound
->el
, map
->p
[i
]->ineq
[k
], 1 + total
);
591 if (add_wraps(wraps
, map
->p
[i
], tabs
[i
], bound
->el
, set_j
) < 0)
594 if (isl_tab_rollback(tabs
[i
], snap
) < 0)
596 if (check_wraps(wraps
, n
, tabs
[i
]) < 0)
601 changed
= fuse(map
, i
, j
, tabs
, eq_i
, ineq_i
, eq_j
, ineq_j
, wraps
);
620 /* Set the is_redundant property of the "n" constraints in "cuts",
622 * This is a fairly tricky operation as it bypasses isl_tab.c.
623 * The reason we want to temporarily mark some constraints redundant
624 * is that we want to ignore them in add_wraps.
626 * Initially all cut constraints are non-redundant, but the
627 * selection of a facet right before the call to this function
628 * may have made some of them redundant.
629 * Likewise, the same constraints are marked non-redundant
630 * in the second call to this function, before they are officially
631 * made non-redundant again in the subsequent rollback.
633 static void set_is_redundant(struct isl_tab
*tab
, unsigned n_eq
,
634 int *cuts
, int n
, int k
, int v
)
638 for (l
= 0; l
< n
; ++l
) {
641 tab
->con
[n_eq
+ cuts
[l
]].is_redundant
= v
;
645 /* Given a pair of basic maps i and j such that j stick out
646 * of i at n cut constraints, each time by at most one,
647 * try to compute wrapping constraints and replace the two
648 * basic maps by a single basic map.
649 * The other constraints of i are assumed to be valid for j.
651 * The facets of i corresponding to the cut constraints are
652 * wrapped around their ridges, except those ridges determined
653 * by any of the other cut constraints.
654 * The intersections of cut constraints need to be ignored
655 * as the result of wrapping on cur constraint around another
656 * would result in a constraint cutting the union.
657 * In each case, the facets are wrapped to include the union
658 * of the two basic maps.
660 * The pieces of j that lie at an offset of exactly one from
661 * one of the cut constraints of i are wrapped around their edges.
662 * Here, there is no need to ignore intersections because we
663 * are wrapping around the union of the two basic maps.
665 * If any wrapping fails, i.e., if we cannot wrap to touch
666 * the union, then we give up.
667 * Otherwise, the pair of basic maps is replaced by their union.
669 static int wrap_in_facets(struct isl_map
*map
, int i
, int j
,
670 int *cuts
, int n
, struct isl_tab
**tabs
,
671 int *eq_i
, int *ineq_i
, int *eq_j
, int *ineq_j
)
674 isl_mat
*wraps
= NULL
;
676 isl_vec
*bound
= NULL
;
677 unsigned total
= isl_basic_map_total_dim(map
->p
[i
]);
680 struct isl_tab_undo
*snap_i
, *snap_j
;
682 if (isl_tab_extend_cons(tabs
[j
], 1) < 0)
685 max_wrap
= 2 * (map
->p
[i
]->n_eq
+ map
->p
[j
]->n_eq
) +
686 map
->p
[i
]->n_ineq
+ map
->p
[j
]->n_ineq
;
689 set
= isl_set_union(set_from_updated_bmap(map
->p
[i
], tabs
[i
]),
690 set_from_updated_bmap(map
->p
[j
], tabs
[j
]));
691 wraps
= isl_mat_alloc(map
->ctx
, max_wrap
, 1 + total
);
692 bound
= isl_vec_alloc(map
->ctx
, 1 + total
);
693 if (!set
|| !wraps
|| !bound
)
696 snap_i
= isl_tab_snap(tabs
[i
]);
697 snap_j
= isl_tab_snap(tabs
[j
]);
701 for (k
= 0; k
< n
; ++k
) {
702 tabs
[i
] = isl_tab_select_facet(tabs
[i
],
703 map
->p
[i
]->n_eq
+ cuts
[k
]);
704 if (isl_tab_detect_redundant(tabs
[i
]) < 0)
706 set_is_redundant(tabs
[i
], map
->p
[i
]->n_eq
, cuts
, n
, k
, 1);
708 isl_seq_neg(bound
->el
, map
->p
[i
]->ineq
[cuts
[k
]], 1 + total
);
709 if (add_wraps(wraps
, map
->p
[i
], tabs
[i
], bound
->el
, set
) < 0)
712 set_is_redundant(tabs
[i
], map
->p
[i
]->n_eq
, cuts
, n
, k
, 0);
713 if (isl_tab_rollback(tabs
[i
], snap_i
) < 0)
719 isl_seq_cpy(bound
->el
, map
->p
[i
]->ineq
[cuts
[k
]], 1 + total
);
720 isl_int_add_ui(bound
->el
[0], bound
->el
[0], 1);
721 tabs
[j
] = isl_tab_add_eq(tabs
[j
], bound
->el
);
722 if (isl_tab_detect_redundant(tabs
[j
]) < 0)
725 if (!tabs
[j
]->empty
&&
726 add_wraps(wraps
, map
->p
[j
], tabs
[j
], bound
->el
, set
) < 0)
729 if (isl_tab_rollback(tabs
[j
], snap_j
) < 0)
737 changed
= fuse(map
, i
, j
, tabs
,
738 eq_i
, ineq_i
, eq_j
, ineq_j
, wraps
);
752 /* Given two basic sets i and j such that i has not cut equalities,
753 * check if relaxing all the cut inequalities of i by one turns
754 * them into valid constraint for j and check if we can wrap in
755 * the bits that are sticking out.
756 * If so, replace the pair by their union.
758 * We first check if all relaxed cut inequalities of i are valid for j
759 * and then try to wrap in the intersections of the relaxed cut inequalities
762 * During this wrapping, we consider the points of j that lie at a distance
763 * of exactly 1 from i. In particular, we ignore the points that lie in
764 * between this lower-dimensional space and the basic map i.
765 * We can therefore only apply this to integer maps.
791 * Wrapping can fail if the result of wrapping one of the facets
792 * around its edges does not produce any new facet constraint.
793 * In particular, this happens when we try to wrap in unbounded sets.
795 * _______________________________________________________________________
799 * |_| |_________________________________________________________________
802 * The following is not an acceptable result of coalescing the above two
803 * sets as it includes extra integer points.
804 * _______________________________________________________________________
809 * \______________________________________________________________________
811 static int can_wrap_in_set(struct isl_map
*map
, int i
, int j
,
812 struct isl_tab
**tabs
, int *eq_i
, int *ineq_i
, int *eq_j
, int *ineq_j
)
816 unsigned total
= isl_basic_map_total_dim(map
->p
[i
]);
817 struct isl_tab_undo
*snap
;
821 if (ISL_F_ISSET(map
->p
[i
], ISL_BASIC_MAP_RATIONAL
) ||
822 ISL_F_ISSET(map
->p
[j
], ISL_BASIC_MAP_RATIONAL
))
825 n
= count(ineq_i
, map
->p
[i
]->n_ineq
, STATUS_CUT
);
829 cuts
= isl_alloc_array(map
->ctx
, int, n
);
833 for (k
= 0, m
= 0; m
< n
; ++k
) {
834 enum isl_ineq_type type
;
836 if (ineq_i
[k
] != STATUS_CUT
)
839 isl_int_add_ui(map
->p
[i
]->ineq
[k
][0], map
->p
[i
]->ineq
[k
][0], 1);
840 type
= isl_tab_ineq_type(tabs
[j
], map
->p
[i
]->ineq
[k
]);
841 isl_int_sub_ui(map
->p
[i
]->ineq
[k
][0], map
->p
[i
]->ineq
[k
][0], 1);
842 if (type
== isl_ineq_error
)
844 if (type
!= isl_ineq_redundant
)
851 changed
= wrap_in_facets(map
, i
, j
, cuts
, n
, tabs
,
852 eq_i
, ineq_i
, eq_j
, ineq_j
);
862 /* Check if either i or j has a single cut constraint that can
863 * be used to wrap in (a facet of) the other basic set.
864 * if so, replace the pair by their union.
866 static int check_wrap(struct isl_map
*map
, int i
, int j
,
867 struct isl_tab
**tabs
, int *eq_i
, int *ineq_i
, int *eq_j
, int *ineq_j
)
871 if (!any(eq_i
, 2 * map
->p
[i
]->n_eq
, STATUS_CUT
))
872 changed
= can_wrap_in_set(map
, i
, j
, tabs
,
873 eq_i
, ineq_i
, eq_j
, ineq_j
);
877 if (!any(eq_j
, 2 * map
->p
[j
]->n_eq
, STATUS_CUT
))
878 changed
= can_wrap_in_set(map
, j
, i
, tabs
,
879 eq_j
, ineq_j
, eq_i
, ineq_i
);
883 /* At least one of the basic maps has an equality that is adjacent
884 * to inequality. Make sure that only one of the basic maps has
885 * such an equality and that the other basic map has exactly one
886 * inequality adjacent to an equality.
887 * We call the basic map that has the inequality "i" and the basic
888 * map that has the equality "j".
889 * If "i" has any "cut" (in)equality, then relaxing the inequality
890 * by one would not result in a basic map that contains the other
893 static int check_adj_eq(struct isl_map
*map
, int i
, int j
,
894 struct isl_tab
**tabs
, int *eq_i
, int *ineq_i
, int *eq_j
, int *ineq_j
)
899 if (any(eq_i
, 2 * map
->p
[i
]->n_eq
, STATUS_ADJ_INEQ
) &&
900 any(eq_j
, 2 * map
->p
[j
]->n_eq
, STATUS_ADJ_INEQ
))
901 /* ADJ EQ TOO MANY */
904 if (any(eq_i
, 2 * map
->p
[i
]->n_eq
, STATUS_ADJ_INEQ
))
905 return check_adj_eq(map
, j
, i
, tabs
,
906 eq_j
, ineq_j
, eq_i
, ineq_i
);
908 /* j has an equality adjacent to an inequality in i */
910 if (any(eq_i
, 2 * map
->p
[i
]->n_eq
, STATUS_CUT
))
912 if (any(ineq_i
, map
->p
[i
]->n_ineq
, STATUS_CUT
))
915 if (count(eq_j
, 2 * map
->p
[j
]->n_eq
, STATUS_ADJ_INEQ
) != 1 ||
916 count(ineq_i
, map
->p
[i
]->n_ineq
, STATUS_ADJ_EQ
) != 1 ||
917 any(ineq_j
, map
->p
[j
]->n_ineq
, STATUS_ADJ_EQ
) ||
918 any(ineq_i
, map
->p
[i
]->n_ineq
, STATUS_ADJ_INEQ
) ||
919 any(ineq_j
, map
->p
[j
]->n_ineq
, STATUS_ADJ_INEQ
))
920 /* ADJ EQ TOO MANY */
923 for (k
= 0; k
< map
->p
[i
]->n_ineq
; ++k
)
924 if (ineq_i
[k
] == STATUS_ADJ_EQ
)
927 changed
= is_extension(map
, i
, j
, k
, tabs
, eq_i
, ineq_i
, eq_j
, ineq_j
);
931 changed
= can_wrap_in_facet(map
, i
, j
, k
, tabs
, eq_i
, ineq_i
, eq_j
, ineq_j
);
936 /* Check if the union of the given pair of basic maps
937 * can be represented by a single basic map.
938 * If so, replace the pair by the single basic map and return 1.
939 * Otherwise, return 0;
941 * We first check the effect of each constraint of one basic map
942 * on the other basic map.
943 * The constraint may be
944 * redundant the constraint is redundant in its own
945 * basic map and should be ignore and removed
947 * valid all (integer) points of the other basic map
948 * satisfy the constraint
949 * separate no (integer) point of the other basic map
950 * satisfies the constraint
951 * cut some but not all points of the other basic map
952 * satisfy the constraint
953 * adj_eq the given constraint is adjacent (on the outside)
954 * to an equality of the other basic map
955 * adj_ineq the given constraint is adjacent (on the outside)
956 * to an inequality of the other basic map
958 * We consider six cases in which we can replace the pair by a single
959 * basic map. We ignore all "redundant" constraints.
961 * 1. all constraints of one basic map are valid
962 * => the other basic map is a subset and can be removed
964 * 2. all constraints of both basic maps are either "valid" or "cut"
965 * and the facets corresponding to the "cut" constraints
966 * of one of the basic maps lies entirely inside the other basic map
967 * => the pair can be replaced by a basic map consisting
968 * of the valid constraints in both basic maps
970 * 3. there is a single pair of adjacent inequalities
971 * (all other constraints are "valid")
972 * => the pair can be replaced by a basic map consisting
973 * of the valid constraints in both basic maps
975 * 4. there is a single adjacent pair of an inequality and an equality,
976 * the other constraints of the basic map containing the inequality are
977 * "valid". Moreover, if the inequality the basic map is relaxed
978 * and then turned into an equality, then resulting facet lies
979 * entirely inside the other basic map
980 * => the pair can be replaced by the basic map containing
981 * the inequality, with the inequality relaxed.
983 * 5. there is a single adjacent pair of an inequality and an equality,
984 * the other constraints of the basic map containing the inequality are
985 * "valid". Moreover, the facets corresponding to both
986 * the inequality and the equality can be wrapped around their
987 * ridges to include the other basic map
988 * => the pair can be replaced by a basic map consisting
989 * of the valid constraints in both basic maps together
990 * with all wrapping constraints
992 * 6. one of the basic maps extends beyond the other by at most one.
993 * Moreover, the facets corresponding to the cut constraints and
994 * the pieces of the other basic map at offset one from these cut
995 * constraints can be wrapped around their ridges to include
996 * the unione of the two basic maps
997 * => the pair can be replaced by a basic map consisting
998 * of the valid constraints in both basic maps together
999 * with all wrapping constraints
1001 * Throughout the computation, we maintain a collection of tableaus
1002 * corresponding to the basic maps. When the basic maps are dropped
1003 * or combined, the tableaus are modified accordingly.
1005 static int coalesce_pair(struct isl_map
*map
, int i
, int j
,
1006 struct isl_tab
**tabs
)
1014 eq_i
= eq_status_in(map
, i
, j
, tabs
);
1015 if (any(eq_i
, 2 * map
->p
[i
]->n_eq
, STATUS_ERROR
))
1017 if (any(eq_i
, 2 * map
->p
[i
]->n_eq
, STATUS_SEPARATE
))
1020 eq_j
= eq_status_in(map
, j
, i
, tabs
);
1021 if (any(eq_j
, 2 * map
->p
[j
]->n_eq
, STATUS_ERROR
))
1023 if (any(eq_j
, 2 * map
->p
[j
]->n_eq
, STATUS_SEPARATE
))
1026 ineq_i
= ineq_status_in(map
, i
, j
, tabs
);
1027 if (any(ineq_i
, map
->p
[i
]->n_ineq
, STATUS_ERROR
))
1029 if (any(ineq_i
, map
->p
[i
]->n_ineq
, STATUS_SEPARATE
))
1032 ineq_j
= ineq_status_in(map
, j
, i
, tabs
);
1033 if (any(ineq_j
, map
->p
[j
]->n_ineq
, STATUS_ERROR
))
1035 if (any(ineq_j
, map
->p
[j
]->n_ineq
, STATUS_SEPARATE
))
1038 if (all(eq_i
, 2 * map
->p
[i
]->n_eq
, STATUS_VALID
) &&
1039 all(ineq_i
, map
->p
[i
]->n_ineq
, STATUS_VALID
)) {
1042 } else if (all(eq_j
, 2 * map
->p
[j
]->n_eq
, STATUS_VALID
) &&
1043 all(ineq_j
, map
->p
[j
]->n_ineq
, STATUS_VALID
)) {
1046 } else if (any(eq_i
, 2 * map
->p
[i
]->n_eq
, STATUS_ADJ_EQ
) ||
1047 any(eq_j
, 2 * map
->p
[j
]->n_eq
, STATUS_ADJ_EQ
)) {
1049 } else if (any(eq_i
, 2 * map
->p
[i
]->n_eq
, STATUS_ADJ_INEQ
) ||
1050 any(eq_j
, 2 * map
->p
[j
]->n_eq
, STATUS_ADJ_INEQ
)) {
1051 changed
= check_adj_eq(map
, i
, j
, tabs
,
1052 eq_i
, ineq_i
, eq_j
, ineq_j
);
1053 } else if (any(ineq_i
, map
->p
[i
]->n_ineq
, STATUS_ADJ_EQ
) ||
1054 any(ineq_j
, map
->p
[j
]->n_ineq
, STATUS_ADJ_EQ
)) {
1057 } else if (any(ineq_i
, map
->p
[i
]->n_ineq
, STATUS_ADJ_INEQ
) ||
1058 any(ineq_j
, map
->p
[j
]->n_ineq
, STATUS_ADJ_INEQ
)) {
1059 if (!any(eq_i
, 2 * map
->p
[i
]->n_eq
, STATUS_CUT
) &&
1060 !any(eq_j
, 2 * map
->p
[j
]->n_eq
, STATUS_CUT
))
1061 changed
= check_adj_ineq(map
, i
, j
, tabs
,
1064 if (!any(eq_i
, 2 * map
->p
[i
]->n_eq
, STATUS_CUT
) &&
1065 !any(eq_j
, 2 * map
->p
[j
]->n_eq
, STATUS_CUT
))
1066 changed
= check_facets(map
, i
, j
, tabs
, ineq_i
, ineq_j
);
1068 changed
= check_wrap(map
, i
, j
, tabs
,
1069 eq_i
, ineq_i
, eq_j
, ineq_j
);
1086 static struct isl_map
*coalesce(struct isl_map
*map
, struct isl_tab
**tabs
)
1090 for (i
= map
->n
- 2; i
>= 0; --i
)
1092 for (j
= i
+ 1; j
< map
->n
; ++j
) {
1094 changed
= coalesce_pair(map
, i
, j
, tabs
);
1106 /* For each pair of basic maps in the map, check if the union of the two
1107 * can be represented by a single basic map.
1108 * If so, replace the pair by the single basic map and start over.
1110 struct isl_map
*isl_map_coalesce(struct isl_map
*map
)
1114 struct isl_tab
**tabs
= NULL
;
1122 map
= isl_map_align_divs(map
);
1124 tabs
= isl_calloc_array(map
->ctx
, struct isl_tab
*, map
->n
);
1129 for (i
= 0; i
< map
->n
; ++i
) {
1130 tabs
[i
] = isl_tab_from_basic_map(map
->p
[i
]);
1133 if (!ISL_F_ISSET(map
->p
[i
], ISL_BASIC_MAP_NO_IMPLICIT
))
1134 tabs
[i
] = isl_tab_detect_implicit_equalities(tabs
[i
]);
1135 if (!ISL_F_ISSET(map
->p
[i
], ISL_BASIC_MAP_NO_REDUNDANT
))
1136 if (isl_tab_detect_redundant(tabs
[i
]) < 0)
1139 for (i
= map
->n
- 1; i
>= 0; --i
)
1143 map
= coalesce(map
, tabs
);
1146 for (i
= 0; i
< map
->n
; ++i
) {
1147 map
->p
[i
] = isl_basic_map_update_from_tab(map
->p
[i
],
1149 map
->p
[i
] = isl_basic_map_finalize(map
->p
[i
]);
1152 ISL_F_SET(map
->p
[i
], ISL_BASIC_MAP_NO_IMPLICIT
);
1153 ISL_F_SET(map
->p
[i
], ISL_BASIC_MAP_NO_REDUNDANT
);
1156 for (i
= 0; i
< n
; ++i
)
1157 isl_tab_free(tabs
[i
]);
1164 for (i
= 0; i
< n
; ++i
)
1165 isl_tab_free(tabs
[i
]);
1170 /* For each pair of basic sets in the set, check if the union of the two
1171 * can be represented by a single basic set.
1172 * If so, replace the pair by the single basic set and start over.
1174 struct isl_set
*isl_set_coalesce(struct isl_set
*set
)
1176 return (struct isl_set
*)isl_map_coalesce((struct isl_map
*)set
);