2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2010 INRIA Saclay
4 * Copyright 2012-2013 Ecole Normale Superieure
6 * Use of this software is governed by the MIT license
8 * Written by Sven Verdoolaege, K.U.Leuven, Departement
9 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
10 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
11 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
12 * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
15 #include "isl_map_private.h"
17 #include <isl/options.h>
19 #include <isl_mat_private.h>
20 #include <isl_local_space_private.h>
21 #include <isl_vec_private.h>
23 #define STATUS_ERROR -1
24 #define STATUS_REDUNDANT 1
25 #define STATUS_VALID 2
26 #define STATUS_SEPARATE 3
28 #define STATUS_ADJ_EQ 5
29 #define STATUS_ADJ_INEQ 6
31 static int status_in(isl_int
*ineq
, struct isl_tab
*tab
)
33 enum isl_ineq_type type
= isl_tab_ineq_type(tab
, ineq
);
36 case isl_ineq_error
: return STATUS_ERROR
;
37 case isl_ineq_redundant
: return STATUS_VALID
;
38 case isl_ineq_separate
: return STATUS_SEPARATE
;
39 case isl_ineq_cut
: return STATUS_CUT
;
40 case isl_ineq_adj_eq
: return STATUS_ADJ_EQ
;
41 case isl_ineq_adj_ineq
: return STATUS_ADJ_INEQ
;
45 /* Compute the position of the equalities of basic map "bmap_i"
46 * with respect to the basic map represented by "tab_j".
47 * The resulting array has twice as many entries as the number
48 * of equalities corresponding to the two inequalties to which
49 * each equality corresponds.
51 static int *eq_status_in(__isl_keep isl_basic_map
*bmap_i
,
52 struct isl_tab
*tab_j
)
55 int *eq
= isl_calloc_array(bmap_i
->ctx
, int, 2 * bmap_i
->n_eq
);
61 dim
= isl_basic_map_total_dim(bmap_i
);
62 for (k
= 0; k
< bmap_i
->n_eq
; ++k
) {
63 for (l
= 0; l
< 2; ++l
) {
64 isl_seq_neg(bmap_i
->eq
[k
], bmap_i
->eq
[k
], 1+dim
);
65 eq
[2 * k
+ l
] = status_in(bmap_i
->eq
[k
], tab_j
);
66 if (eq
[2 * k
+ l
] == STATUS_ERROR
)
69 if (eq
[2 * k
] == STATUS_SEPARATE
||
70 eq
[2 * k
+ 1] == STATUS_SEPARATE
)
80 /* Compute the position of the inequalities of basic map "bmap_i"
81 * (also represented by "tab_i", if not NULL) with respect to the basic map
82 * represented by "tab_j".
84 static int *ineq_status_in(__isl_keep isl_basic_map
*bmap_i
,
85 struct isl_tab
*tab_i
, struct isl_tab
*tab_j
)
88 unsigned n_eq
= bmap_i
->n_eq
;
89 int *ineq
= isl_calloc_array(bmap_i
->ctx
, int, bmap_i
->n_ineq
);
94 for (k
= 0; k
< bmap_i
->n_ineq
; ++k
) {
95 if (tab_i
&& isl_tab_is_redundant(tab_i
, n_eq
+ k
)) {
96 ineq
[k
] = STATUS_REDUNDANT
;
99 ineq
[k
] = status_in(bmap_i
->ineq
[k
], tab_j
);
100 if (ineq
[k
] == STATUS_ERROR
)
102 if (ineq
[k
] == STATUS_SEPARATE
)
112 static int any(int *con
, unsigned len
, int status
)
116 for (i
= 0; i
< len
; ++i
)
117 if (con
[i
] == status
)
122 static int count(int *con
, unsigned len
, int status
)
127 for (i
= 0; i
< len
; ++i
)
128 if (con
[i
] == status
)
133 static int all(int *con
, unsigned len
, int status
)
137 for (i
= 0; i
< len
; ++i
) {
138 if (con
[i
] == STATUS_REDUNDANT
)
140 if (con
[i
] != status
)
146 static void drop(struct isl_map
*map
, int i
, struct isl_tab
**tabs
)
148 isl_basic_map_free(map
->p
[i
]);
149 isl_tab_free(tabs
[i
]);
151 if (i
!= map
->n
- 1) {
152 map
->p
[i
] = map
->p
[map
->n
- 1];
153 tabs
[i
] = tabs
[map
->n
- 1];
155 tabs
[map
->n
- 1] = NULL
;
159 /* Replace the pair of basic maps i and j by the basic map bounded
160 * by the valid constraints in both basic maps and the constraint
161 * in extra (if not NULL).
163 static int fuse(struct isl_map
*map
, int i
, int j
,
164 struct isl_tab
**tabs
, int *eq_i
, int *ineq_i
, int *eq_j
, int *ineq_j
,
165 __isl_keep isl_mat
*extra
)
168 struct isl_basic_map
*fused
= NULL
;
169 struct isl_tab
*fused_tab
= NULL
;
170 unsigned total
= isl_basic_map_total_dim(map
->p
[i
]);
171 unsigned extra_rows
= extra
? extra
->n_row
: 0;
173 fused
= isl_basic_map_alloc_space(isl_space_copy(map
->p
[i
]->dim
),
175 map
->p
[i
]->n_eq
+ map
->p
[j
]->n_eq
,
176 map
->p
[i
]->n_ineq
+ map
->p
[j
]->n_ineq
+ extra_rows
);
180 for (k
= 0; k
< map
->p
[i
]->n_eq
; ++k
) {
181 if (eq_i
&& (eq_i
[2 * k
] != STATUS_VALID
||
182 eq_i
[2 * k
+ 1] != STATUS_VALID
))
184 l
= isl_basic_map_alloc_equality(fused
);
187 isl_seq_cpy(fused
->eq
[l
], map
->p
[i
]->eq
[k
], 1 + total
);
190 for (k
= 0; k
< map
->p
[j
]->n_eq
; ++k
) {
191 if (eq_j
&& (eq_j
[2 * k
] != STATUS_VALID
||
192 eq_j
[2 * k
+ 1] != STATUS_VALID
))
194 l
= isl_basic_map_alloc_equality(fused
);
197 isl_seq_cpy(fused
->eq
[l
], map
->p
[j
]->eq
[k
], 1 + total
);
200 for (k
= 0; k
< map
->p
[i
]->n_ineq
; ++k
) {
201 if (ineq_i
[k
] != STATUS_VALID
)
203 l
= isl_basic_map_alloc_inequality(fused
);
206 isl_seq_cpy(fused
->ineq
[l
], map
->p
[i
]->ineq
[k
], 1 + total
);
209 for (k
= 0; k
< map
->p
[j
]->n_ineq
; ++k
) {
210 if (ineq_j
[k
] != STATUS_VALID
)
212 l
= isl_basic_map_alloc_inequality(fused
);
215 isl_seq_cpy(fused
->ineq
[l
], map
->p
[j
]->ineq
[k
], 1 + total
);
218 for (k
= 0; k
< map
->p
[i
]->n_div
; ++k
) {
219 int l
= isl_basic_map_alloc_div(fused
);
222 isl_seq_cpy(fused
->div
[l
], map
->p
[i
]->div
[k
], 1 + 1 + total
);
225 for (k
= 0; k
< extra_rows
; ++k
) {
226 l
= isl_basic_map_alloc_inequality(fused
);
229 isl_seq_cpy(fused
->ineq
[l
], extra
->row
[k
], 1 + total
);
232 fused
= isl_basic_map_gauss(fused
, NULL
);
233 ISL_F_SET(fused
, ISL_BASIC_MAP_FINAL
);
234 if (ISL_F_ISSET(map
->p
[i
], ISL_BASIC_MAP_RATIONAL
) &&
235 ISL_F_ISSET(map
->p
[j
], ISL_BASIC_MAP_RATIONAL
))
236 ISL_F_SET(fused
, ISL_BASIC_MAP_RATIONAL
);
238 fused_tab
= isl_tab_from_basic_map(fused
, 0);
239 if (isl_tab_detect_redundant(fused_tab
) < 0)
242 isl_basic_map_free(map
->p
[i
]);
244 isl_tab_free(tabs
[i
]);
250 isl_tab_free(fused_tab
);
251 isl_basic_map_free(fused
);
255 /* Given a pair of basic maps i and j such that all constraints are either
256 * "valid" or "cut", check if the facets corresponding to the "cut"
257 * constraints of i lie entirely within basic map j.
258 * If so, replace the pair by the basic map consisting of the valid
259 * constraints in both basic maps.
261 * To see that we are not introducing any extra points, call the
262 * two basic maps A and B and the resulting map U and let x
263 * be an element of U \setminus ( A \cup B ).
264 * Then there is a pair of cut constraints c_1 and c_2 in A and B such that x
265 * violates them. Let X be the intersection of U with the opposites
266 * of these constraints. Then x \in X.
267 * The facet corresponding to c_1 contains the corresponding facet of A.
268 * This facet is entirely contained in B, so c_2 is valid on the facet.
269 * However, since it is also (part of) a facet of X, -c_2 is also valid
270 * on the facet. This means c_2 is saturated on the facet, so c_1 and
271 * c_2 must be opposites of each other, but then x could not violate
274 static int check_facets(struct isl_map
*map
, int i
, int j
,
275 struct isl_tab
**tabs
, int *ineq_i
, int *ineq_j
)
278 struct isl_tab_undo
*snap
;
279 unsigned n_eq
= map
->p
[i
]->n_eq
;
281 snap
= isl_tab_snap(tabs
[i
]);
283 for (k
= 0; k
< map
->p
[i
]->n_ineq
; ++k
) {
284 if (ineq_i
[k
] != STATUS_CUT
)
286 if (isl_tab_select_facet(tabs
[i
], n_eq
+ k
) < 0)
288 for (l
= 0; l
< map
->p
[j
]->n_ineq
; ++l
) {
290 if (ineq_j
[l
] != STATUS_CUT
)
292 stat
= status_in(map
->p
[j
]->ineq
[l
], tabs
[i
]);
295 if (stat
!= STATUS_VALID
)
298 if (isl_tab_rollback(tabs
[i
], snap
) < 0)
300 if (l
< map
->p
[j
]->n_ineq
)
304 if (k
< map
->p
[i
]->n_ineq
)
307 return fuse(map
, i
, j
, tabs
, NULL
, ineq_i
, NULL
, ineq_j
, NULL
);
310 /* Check if basic map "i" contains the basic map represented
311 * by the tableau "tab".
313 static int contains(struct isl_map
*map
, int i
, int *ineq_i
,
319 dim
= isl_basic_map_total_dim(map
->p
[i
]);
320 for (k
= 0; k
< map
->p
[i
]->n_eq
; ++k
) {
321 for (l
= 0; l
< 2; ++l
) {
323 isl_seq_neg(map
->p
[i
]->eq
[k
], map
->p
[i
]->eq
[k
], 1+dim
);
324 stat
= status_in(map
->p
[i
]->eq
[k
], tab
);
327 if (stat
!= STATUS_VALID
)
332 for (k
= 0; k
< map
->p
[i
]->n_ineq
; ++k
) {
334 if (ineq_i
[k
] == STATUS_REDUNDANT
)
336 stat
= status_in(map
->p
[i
]->ineq
[k
], tab
);
339 if (stat
!= STATUS_VALID
)
345 /* Basic map "i" has an inequality (say "k") that is adjacent
346 * to some inequality of basic map "j". All the other inequalities
348 * Check if basic map "j" forms an extension of basic map "i".
350 * Note that this function is only called if some of the equalities or
351 * inequalities of basic map "j" do cut basic map "i". The function is
352 * correct even if there are no such cut constraints, but in that case
353 * the additional checks performed by this function are overkill.
355 * In particular, we replace constraint k, say f >= 0, by constraint
356 * f <= -1, add the inequalities of "j" that are valid for "i"
357 * and check if the result is a subset of basic map "j".
358 * If so, then we know that this result is exactly equal to basic map "j"
359 * since all its constraints are valid for basic map "j".
360 * By combining the valid constraints of "i" (all equalities and all
361 * inequalities except "k") and the valid constraints of "j" we therefore
362 * obtain a basic map that is equal to their union.
363 * In this case, there is no need to perform a rollback of the tableau
364 * since it is going to be destroyed in fuse().
370 * |_______| _ |_________\
382 static int is_adj_ineq_extension(__isl_keep isl_map
*map
, int i
, int j
,
383 struct isl_tab
**tabs
, int *eq_i
, int *ineq_i
, int *eq_j
, int *ineq_j
)
386 struct isl_tab_undo
*snap
;
387 unsigned n_eq
= map
->p
[i
]->n_eq
;
388 unsigned total
= isl_basic_map_total_dim(map
->p
[i
]);
392 if (isl_tab_extend_cons(tabs
[i
], 1 + map
->p
[j
]->n_ineq
) < 0)
395 for (k
= 0; k
< map
->p
[i
]->n_ineq
; ++k
)
396 if (ineq_i
[k
] == STATUS_ADJ_INEQ
)
398 if (k
>= map
->p
[i
]->n_ineq
)
399 isl_die(isl_map_get_ctx(map
), isl_error_internal
,
400 "ineq_i should have exactly one STATUS_ADJ_INEQ",
403 snap
= isl_tab_snap(tabs
[i
]);
405 if (isl_tab_unrestrict(tabs
[i
], n_eq
+ k
) < 0)
408 isl_seq_neg(map
->p
[i
]->ineq
[k
], map
->p
[i
]->ineq
[k
], 1 + total
);
409 isl_int_sub_ui(map
->p
[i
]->ineq
[k
][0], map
->p
[i
]->ineq
[k
][0], 1);
410 r
= isl_tab_add_ineq(tabs
[i
], map
->p
[i
]->ineq
[k
]);
411 isl_seq_neg(map
->p
[i
]->ineq
[k
], map
->p
[i
]->ineq
[k
], 1 + total
);
412 isl_int_sub_ui(map
->p
[i
]->ineq
[k
][0], map
->p
[i
]->ineq
[k
][0], 1);
416 for (k
= 0; k
< map
->p
[j
]->n_ineq
; ++k
) {
417 if (ineq_j
[k
] != STATUS_VALID
)
419 if (isl_tab_add_ineq(tabs
[i
], map
->p
[j
]->ineq
[k
]) < 0)
423 super
= contains(map
, j
, ineq_j
, tabs
[i
]);
427 return fuse(map
, i
, j
, tabs
, eq_i
, ineq_i
, eq_j
, ineq_j
, NULL
);
429 if (isl_tab_rollback(tabs
[i
], snap
) < 0)
436 /* Both basic maps have at least one inequality with and adjacent
437 * (but opposite) inequality in the other basic map.
438 * Check that there are no cut constraints and that there is only
439 * a single pair of adjacent inequalities.
440 * If so, we can replace the pair by a single basic map described
441 * by all but the pair of adjacent inequalities.
442 * Any additional points introduced lie strictly between the two
443 * adjacent hyperplanes and can therefore be integral.
452 * The test for a single pair of adjancent inequalities is important
453 * for avoiding the combination of two basic maps like the following
463 * If there are some cut constraints on one side, then we may
464 * still be able to fuse the two basic maps, but we need to perform
465 * some additional checks in is_adj_ineq_extension.
467 static int check_adj_ineq(struct isl_map
*map
, int i
, int j
,
468 struct isl_tab
**tabs
, int *eq_i
, int *ineq_i
, int *eq_j
, int *ineq_j
)
470 int count_i
, count_j
;
473 count_i
= count(ineq_i
, map
->p
[i
]->n_ineq
, STATUS_ADJ_INEQ
);
474 count_j
= count(ineq_j
, map
->p
[j
]->n_ineq
, STATUS_ADJ_INEQ
);
476 if (count_i
!= 1 && count_j
!= 1)
479 cut_i
= any(eq_i
, 2 * map
->p
[i
]->n_eq
, STATUS_CUT
) ||
480 any(ineq_i
, map
->p
[i
]->n_ineq
, STATUS_CUT
);
481 cut_j
= any(eq_j
, 2 * map
->p
[j
]->n_eq
, STATUS_CUT
) ||
482 any(ineq_j
, map
->p
[j
]->n_ineq
, STATUS_CUT
);
484 if (!cut_i
&& !cut_j
&& count_i
== 1 && count_j
== 1)
485 return fuse(map
, i
, j
, tabs
, NULL
, ineq_i
, NULL
, ineq_j
, NULL
);
487 if (count_i
== 1 && !cut_i
)
488 return is_adj_ineq_extension(map
, i
, j
, tabs
,
489 eq_i
, ineq_i
, eq_j
, ineq_j
);
491 if (count_j
== 1 && !cut_j
)
492 return is_adj_ineq_extension(map
, j
, i
, tabs
,
493 eq_j
, ineq_j
, eq_i
, ineq_i
);
498 /* Basic map "i" has an inequality "k" that is adjacent to some equality
499 * of basic map "j". All the other inequalities are valid for "j".
500 * Check if basic map "j" forms an extension of basic map "i".
502 * In particular, we relax constraint "k", compute the corresponding
503 * facet and check whether it is included in the other basic map.
504 * If so, we know that relaxing the constraint extends the basic
505 * map with exactly the other basic map (we already know that this
506 * other basic map is included in the extension, because there
507 * were no "cut" inequalities in "i") and we can replace the
508 * two basic maps by this extension.
516 static int is_adj_eq_extension(struct isl_map
*map
, int i
, int j
, int k
,
517 struct isl_tab
**tabs
, int *eq_i
, int *ineq_i
, int *eq_j
, int *ineq_j
)
521 struct isl_tab_undo
*snap
, *snap2
;
522 unsigned n_eq
= map
->p
[i
]->n_eq
;
524 if (isl_tab_is_equality(tabs
[i
], n_eq
+ k
))
527 snap
= isl_tab_snap(tabs
[i
]);
528 tabs
[i
] = isl_tab_relax(tabs
[i
], n_eq
+ k
);
529 snap2
= isl_tab_snap(tabs
[i
]);
530 if (isl_tab_select_facet(tabs
[i
], n_eq
+ k
) < 0)
532 super
= contains(map
, j
, ineq_j
, tabs
[i
]);
536 if (isl_tab_rollback(tabs
[i
], snap2
) < 0)
538 map
->p
[i
] = isl_basic_map_cow(map
->p
[i
]);
541 isl_int_add_ui(map
->p
[i
]->ineq
[k
][0], map
->p
[i
]->ineq
[k
][0], 1);
542 ISL_F_SET(map
->p
[i
], ISL_BASIC_MAP_FINAL
);
546 if (isl_tab_rollback(tabs
[i
], snap
) < 0)
552 /* Data structure that keeps track of the wrapping constraints
553 * and of information to bound the coefficients of those constraints.
555 * bound is set if we want to apply a bound on the coefficients
556 * mat contains the wrapping constraints
557 * max is the bound on the coefficients (if bound is set)
565 /* Update wraps->max to be greater than or equal to the coefficients
566 * in the equalities and inequalities of bmap that can be removed if we end up
569 static void wraps_update_max(struct isl_wraps
*wraps
,
570 __isl_keep isl_basic_map
*bmap
, int *eq
, int *ineq
)
574 unsigned total
= isl_basic_map_total_dim(bmap
);
578 for (k
= 0; k
< bmap
->n_eq
; ++k
) {
579 if (eq
[2 * k
] == STATUS_VALID
&&
580 eq
[2 * k
+ 1] == STATUS_VALID
)
582 isl_seq_abs_max(bmap
->eq
[k
] + 1, total
, &max_k
);
583 if (isl_int_abs_gt(max_k
, wraps
->max
))
584 isl_int_set(wraps
->max
, max_k
);
587 for (k
= 0; k
< bmap
->n_ineq
; ++k
) {
588 if (ineq
[k
] == STATUS_VALID
|| ineq
[k
] == STATUS_REDUNDANT
)
590 isl_seq_abs_max(bmap
->ineq
[k
] + 1, total
, &max_k
);
591 if (isl_int_abs_gt(max_k
, wraps
->max
))
592 isl_int_set(wraps
->max
, max_k
);
595 isl_int_clear(max_k
);
598 /* Initialize the isl_wraps data structure.
599 * If we want to bound the coefficients of the wrapping constraints,
600 * we set wraps->max to the largest coefficient
601 * in the equalities and inequalities that can be removed if we end up
604 static void wraps_init(struct isl_wraps
*wraps
, __isl_take isl_mat
*mat
,
605 __isl_keep isl_map
*map
, int i
, int j
,
606 int *eq_i
, int *ineq_i
, int *eq_j
, int *ineq_j
)
614 ctx
= isl_mat_get_ctx(mat
);
615 wraps
->bound
= isl_options_get_coalesce_bounded_wrapping(ctx
);
618 isl_int_init(wraps
->max
);
619 isl_int_set_si(wraps
->max
, 0);
620 wraps_update_max(wraps
, map
->p
[i
], eq_i
, ineq_i
);
621 wraps_update_max(wraps
, map
->p
[j
], eq_j
, ineq_j
);
624 /* Free the contents of the isl_wraps data structure.
626 static void wraps_free(struct isl_wraps
*wraps
)
628 isl_mat_free(wraps
->mat
);
630 isl_int_clear(wraps
->max
);
633 /* Is the wrapping constraint in row "row" allowed?
635 * If wraps->bound is set, we check that none of the coefficients
636 * is greater than wraps->max.
638 static int allow_wrap(struct isl_wraps
*wraps
, int row
)
645 for (i
= 1; i
< wraps
->mat
->n_col
; ++i
)
646 if (isl_int_abs_gt(wraps
->mat
->row
[row
][i
], wraps
->max
))
652 /* For each non-redundant constraint in "bmap" (as determined by "tab"),
653 * wrap the constraint around "bound" such that it includes the whole
654 * set "set" and append the resulting constraint to "wraps".
655 * "wraps" is assumed to have been pre-allocated to the appropriate size.
656 * wraps->n_row is the number of actual wrapped constraints that have
658 * If any of the wrapping problems results in a constraint that is
659 * identical to "bound", then this means that "set" is unbounded in such
660 * way that no wrapping is possible. If this happens then wraps->n_row
662 * Similarly, if we want to bound the coefficients of the wrapping
663 * constraints and a newly added wrapping constraint does not
664 * satisfy the bound, then wraps->n_row is also reset to zero.
666 static int add_wraps(struct isl_wraps
*wraps
, __isl_keep isl_basic_map
*bmap
,
667 struct isl_tab
*tab
, isl_int
*bound
, __isl_keep isl_set
*set
)
671 unsigned total
= isl_basic_map_total_dim(bmap
);
673 w
= wraps
->mat
->n_row
;
675 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
676 if (isl_seq_is_neg(bound
, bmap
->ineq
[l
], 1 + total
))
678 if (isl_seq_eq(bound
, bmap
->ineq
[l
], 1 + total
))
680 if (isl_tab_is_redundant(tab
, bmap
->n_eq
+ l
))
683 isl_seq_cpy(wraps
->mat
->row
[w
], bound
, 1 + total
);
684 if (!isl_set_wrap_facet(set
, wraps
->mat
->row
[w
], bmap
->ineq
[l
]))
686 if (isl_seq_eq(wraps
->mat
->row
[w
], bound
, 1 + total
))
688 if (!allow_wrap(wraps
, w
))
692 for (l
= 0; l
< bmap
->n_eq
; ++l
) {
693 if (isl_seq_is_neg(bound
, bmap
->eq
[l
], 1 + total
))
695 if (isl_seq_eq(bound
, bmap
->eq
[l
], 1 + total
))
698 isl_seq_cpy(wraps
->mat
->row
[w
], bound
, 1 + total
);
699 isl_seq_neg(wraps
->mat
->row
[w
+ 1], bmap
->eq
[l
], 1 + total
);
700 if (!isl_set_wrap_facet(set
, wraps
->mat
->row
[w
],
701 wraps
->mat
->row
[w
+ 1]))
703 if (isl_seq_eq(wraps
->mat
->row
[w
], bound
, 1 + total
))
705 if (!allow_wrap(wraps
, w
))
709 isl_seq_cpy(wraps
->mat
->row
[w
], bound
, 1 + total
);
710 if (!isl_set_wrap_facet(set
, wraps
->mat
->row
[w
], bmap
->eq
[l
]))
712 if (isl_seq_eq(wraps
->mat
->row
[w
], bound
, 1 + total
))
714 if (!allow_wrap(wraps
, w
))
719 wraps
->mat
->n_row
= w
;
722 wraps
->mat
->n_row
= 0;
726 /* Check if the constraints in "wraps" from "first" until the last
727 * are all valid for the basic set represented by "tab".
728 * If not, wraps->n_row is set to zero.
730 static int check_wraps(__isl_keep isl_mat
*wraps
, int first
,
735 for (i
= first
; i
< wraps
->n_row
; ++i
) {
736 enum isl_ineq_type type
;
737 type
= isl_tab_ineq_type(tab
, wraps
->row
[i
]);
738 if (type
== isl_ineq_error
)
740 if (type
== isl_ineq_redundant
)
749 /* Return a set that corresponds to the non-redudant constraints
750 * (as recorded in tab) of bmap.
752 * It's important to remove the redundant constraints as some
753 * of the other constraints may have been modified after the
754 * constraints were marked redundant.
755 * In particular, a constraint may have been relaxed.
756 * Redundant constraints are ignored when a constraint is relaxed
757 * and should therefore continue to be ignored ever after.
758 * Otherwise, the relaxation might be thwarted by some of
761 static __isl_give isl_set
*set_from_updated_bmap(__isl_keep isl_basic_map
*bmap
,
764 bmap
= isl_basic_map_copy(bmap
);
765 bmap
= isl_basic_map_cow(bmap
);
766 bmap
= isl_basic_map_update_from_tab(bmap
, tab
);
767 return isl_set_from_basic_set(isl_basic_map_underlying_set(bmap
));
770 /* Given a basic set i with a constraint k that is adjacent to either the
771 * whole of basic set j or a facet of basic set j, check if we can wrap
772 * both the facet corresponding to k and the facet of j (or the whole of j)
773 * around their ridges to include the other set.
774 * If so, replace the pair of basic sets by their union.
776 * All constraints of i (except k) are assumed to be valid for j.
778 * However, the constraints of j may not be valid for i and so
779 * we have to check that the wrapping constraints for j are valid for i.
781 * In the case where j has a facet adjacent to i, tab[j] is assumed
782 * to have been restricted to this facet, so that the non-redundant
783 * constraints in tab[j] are the ridges of the facet.
784 * Note that for the purpose of wrapping, it does not matter whether
785 * we wrap the ridges of i around the whole of j or just around
786 * the facet since all the other constraints are assumed to be valid for j.
787 * In practice, we wrap to include the whole of j.
796 static int can_wrap_in_facet(struct isl_map
*map
, int i
, int j
, int k
,
797 struct isl_tab
**tabs
, int *eq_i
, int *ineq_i
, int *eq_j
, int *ineq_j
)
800 struct isl_wraps wraps
;
802 struct isl_set
*set_i
= NULL
;
803 struct isl_set
*set_j
= NULL
;
804 struct isl_vec
*bound
= NULL
;
805 unsigned total
= isl_basic_map_total_dim(map
->p
[i
]);
806 struct isl_tab_undo
*snap
;
809 set_i
= set_from_updated_bmap(map
->p
[i
], tabs
[i
]);
810 set_j
= set_from_updated_bmap(map
->p
[j
], tabs
[j
]);
811 mat
= isl_mat_alloc(map
->ctx
, 2 * (map
->p
[i
]->n_eq
+ map
->p
[j
]->n_eq
) +
812 map
->p
[i
]->n_ineq
+ map
->p
[j
]->n_ineq
,
814 wraps_init(&wraps
, mat
, map
, i
, j
, eq_i
, ineq_i
, eq_j
, ineq_j
);
815 bound
= isl_vec_alloc(map
->ctx
, 1 + total
);
816 if (!set_i
|| !set_j
|| !wraps
.mat
|| !bound
)
819 isl_seq_cpy(bound
->el
, map
->p
[i
]->ineq
[k
], 1 + total
);
820 isl_int_add_ui(bound
->el
[0], bound
->el
[0], 1);
822 isl_seq_cpy(wraps
.mat
->row
[0], bound
->el
, 1 + total
);
823 wraps
.mat
->n_row
= 1;
825 if (add_wraps(&wraps
, map
->p
[j
], tabs
[j
], bound
->el
, set_i
) < 0)
827 if (!wraps
.mat
->n_row
)
830 snap
= isl_tab_snap(tabs
[i
]);
832 if (isl_tab_select_facet(tabs
[i
], map
->p
[i
]->n_eq
+ k
) < 0)
834 if (isl_tab_detect_redundant(tabs
[i
]) < 0)
837 isl_seq_neg(bound
->el
, map
->p
[i
]->ineq
[k
], 1 + total
);
839 n
= wraps
.mat
->n_row
;
840 if (add_wraps(&wraps
, map
->p
[i
], tabs
[i
], bound
->el
, set_j
) < 0)
843 if (isl_tab_rollback(tabs
[i
], snap
) < 0)
845 if (check_wraps(wraps
.mat
, n
, tabs
[i
]) < 0)
847 if (!wraps
.mat
->n_row
)
850 changed
= fuse(map
, i
, j
, tabs
, eq_i
, ineq_i
, eq_j
, ineq_j
, wraps
.mat
);
869 /* Set the is_redundant property of the "n" constraints in "cuts",
871 * This is a fairly tricky operation as it bypasses isl_tab.c.
872 * The reason we want to temporarily mark some constraints redundant
873 * is that we want to ignore them in add_wraps.
875 * Initially all cut constraints are non-redundant, but the
876 * selection of a facet right before the call to this function
877 * may have made some of them redundant.
878 * Likewise, the same constraints are marked non-redundant
879 * in the second call to this function, before they are officially
880 * made non-redundant again in the subsequent rollback.
882 static void set_is_redundant(struct isl_tab
*tab
, unsigned n_eq
,
883 int *cuts
, int n
, int k
, int v
)
887 for (l
= 0; l
< n
; ++l
) {
890 tab
->con
[n_eq
+ cuts
[l
]].is_redundant
= v
;
894 /* Given a pair of basic maps i and j such that j sticks out
895 * of i at n cut constraints, each time by at most one,
896 * try to compute wrapping constraints and replace the two
897 * basic maps by a single basic map.
898 * The other constraints of i are assumed to be valid for j.
900 * The facets of i corresponding to the cut constraints are
901 * wrapped around their ridges, except those ridges determined
902 * by any of the other cut constraints.
903 * The intersections of cut constraints need to be ignored
904 * as the result of wrapping one cut constraint around another
905 * would result in a constraint cutting the union.
906 * In each case, the facets are wrapped to include the union
907 * of the two basic maps.
909 * The pieces of j that lie at an offset of exactly one from
910 * one of the cut constraints of i are wrapped around their edges.
911 * Here, there is no need to ignore intersections because we
912 * are wrapping around the union of the two basic maps.
914 * If any wrapping fails, i.e., if we cannot wrap to touch
915 * the union, then we give up.
916 * Otherwise, the pair of basic maps is replaced by their union.
918 static int wrap_in_facets(struct isl_map
*map
, int i
, int j
,
919 int *cuts
, int n
, struct isl_tab
**tabs
,
920 int *eq_i
, int *ineq_i
, int *eq_j
, int *ineq_j
)
923 struct isl_wraps wraps
;
926 isl_vec
*bound
= NULL
;
927 unsigned total
= isl_basic_map_total_dim(map
->p
[i
]);
930 struct isl_tab_undo
*snap_i
, *snap_j
;
932 if (isl_tab_extend_cons(tabs
[j
], 1) < 0)
935 max_wrap
= 2 * (map
->p
[i
]->n_eq
+ map
->p
[j
]->n_eq
) +
936 map
->p
[i
]->n_ineq
+ map
->p
[j
]->n_ineq
;
939 set
= isl_set_union(set_from_updated_bmap(map
->p
[i
], tabs
[i
]),
940 set_from_updated_bmap(map
->p
[j
], tabs
[j
]));
941 mat
= isl_mat_alloc(map
->ctx
, max_wrap
, 1 + total
);
942 wraps_init(&wraps
, mat
, map
, i
, j
, eq_i
, ineq_i
, eq_j
, ineq_j
);
943 bound
= isl_vec_alloc(map
->ctx
, 1 + total
);
944 if (!set
|| !wraps
.mat
|| !bound
)
947 snap_i
= isl_tab_snap(tabs
[i
]);
948 snap_j
= isl_tab_snap(tabs
[j
]);
950 wraps
.mat
->n_row
= 0;
952 for (k
= 0; k
< n
; ++k
) {
953 if (isl_tab_select_facet(tabs
[i
], map
->p
[i
]->n_eq
+ cuts
[k
]) < 0)
955 if (isl_tab_detect_redundant(tabs
[i
]) < 0)
957 set_is_redundant(tabs
[i
], map
->p
[i
]->n_eq
, cuts
, n
, k
, 1);
959 isl_seq_neg(bound
->el
, map
->p
[i
]->ineq
[cuts
[k
]], 1 + total
);
960 if (!tabs
[i
]->empty
&&
961 add_wraps(&wraps
, map
->p
[i
], tabs
[i
], bound
->el
, set
) < 0)
964 set_is_redundant(tabs
[i
], map
->p
[i
]->n_eq
, cuts
, n
, k
, 0);
965 if (isl_tab_rollback(tabs
[i
], snap_i
) < 0)
970 if (!wraps
.mat
->n_row
)
973 isl_seq_cpy(bound
->el
, map
->p
[i
]->ineq
[cuts
[k
]], 1 + total
);
974 isl_int_add_ui(bound
->el
[0], bound
->el
[0], 1);
975 if (isl_tab_add_eq(tabs
[j
], bound
->el
) < 0)
977 if (isl_tab_detect_redundant(tabs
[j
]) < 0)
980 if (!tabs
[j
]->empty
&&
981 add_wraps(&wraps
, map
->p
[j
], tabs
[j
], bound
->el
, set
) < 0)
984 if (isl_tab_rollback(tabs
[j
], snap_j
) < 0)
987 if (!wraps
.mat
->n_row
)
992 changed
= fuse(map
, i
, j
, tabs
,
993 eq_i
, ineq_i
, eq_j
, ineq_j
, wraps
.mat
);
1001 isl_vec_free(bound
);
1007 /* Given two basic sets i and j such that i has no cut equalities,
1008 * check if relaxing all the cut inequalities of i by one turns
1009 * them into valid constraint for j and check if we can wrap in
1010 * the bits that are sticking out.
1011 * If so, replace the pair by their union.
1013 * We first check if all relaxed cut inequalities of i are valid for j
1014 * and then try to wrap in the intersections of the relaxed cut inequalities
1017 * During this wrapping, we consider the points of j that lie at a distance
1018 * of exactly 1 from i. In particular, we ignore the points that lie in
1019 * between this lower-dimensional space and the basic map i.
1020 * We can therefore only apply this to integer maps.
1046 * Wrapping can fail if the result of wrapping one of the facets
1047 * around its edges does not produce any new facet constraint.
1048 * In particular, this happens when we try to wrap in unbounded sets.
1050 * _______________________________________________________________________
1054 * |_| |_________________________________________________________________
1057 * The following is not an acceptable result of coalescing the above two
1058 * sets as it includes extra integer points.
1059 * _______________________________________________________________________
1064 * \______________________________________________________________________
1066 static int can_wrap_in_set(struct isl_map
*map
, int i
, int j
,
1067 struct isl_tab
**tabs
, int *eq_i
, int *ineq_i
, int *eq_j
, int *ineq_j
)
1074 if (ISL_F_ISSET(map
->p
[i
], ISL_BASIC_MAP_RATIONAL
) ||
1075 ISL_F_ISSET(map
->p
[j
], ISL_BASIC_MAP_RATIONAL
))
1078 n
= count(ineq_i
, map
->p
[i
]->n_ineq
, STATUS_CUT
);
1082 cuts
= isl_alloc_array(map
->ctx
, int, n
);
1086 for (k
= 0, m
= 0; m
< n
; ++k
) {
1087 enum isl_ineq_type type
;
1089 if (ineq_i
[k
] != STATUS_CUT
)
1092 isl_int_add_ui(map
->p
[i
]->ineq
[k
][0], map
->p
[i
]->ineq
[k
][0], 1);
1093 type
= isl_tab_ineq_type(tabs
[j
], map
->p
[i
]->ineq
[k
]);
1094 isl_int_sub_ui(map
->p
[i
]->ineq
[k
][0], map
->p
[i
]->ineq
[k
][0], 1);
1095 if (type
== isl_ineq_error
)
1097 if (type
!= isl_ineq_redundant
)
1104 changed
= wrap_in_facets(map
, i
, j
, cuts
, n
, tabs
,
1105 eq_i
, ineq_i
, eq_j
, ineq_j
);
1115 /* Check if either i or j has a single cut constraint that can
1116 * be used to wrap in (a facet of) the other basic set.
1117 * if so, replace the pair by their union.
1119 static int check_wrap(struct isl_map
*map
, int i
, int j
,
1120 struct isl_tab
**tabs
, int *eq_i
, int *ineq_i
, int *eq_j
, int *ineq_j
)
1124 if (!any(eq_i
, 2 * map
->p
[i
]->n_eq
, STATUS_CUT
))
1125 changed
= can_wrap_in_set(map
, i
, j
, tabs
,
1126 eq_i
, ineq_i
, eq_j
, ineq_j
);
1130 if (!any(eq_j
, 2 * map
->p
[j
]->n_eq
, STATUS_CUT
))
1131 changed
= can_wrap_in_set(map
, j
, i
, tabs
,
1132 eq_j
, ineq_j
, eq_i
, ineq_i
);
1136 /* At least one of the basic maps has an equality that is adjacent
1137 * to inequality. Make sure that only one of the basic maps has
1138 * such an equality and that the other basic map has exactly one
1139 * inequality adjacent to an equality.
1140 * We call the basic map that has the inequality "i" and the basic
1141 * map that has the equality "j".
1142 * If "i" has any "cut" (in)equality, then relaxing the inequality
1143 * by one would not result in a basic map that contains the other
1146 static int check_adj_eq(struct isl_map
*map
, int i
, int j
,
1147 struct isl_tab
**tabs
, int *eq_i
, int *ineq_i
, int *eq_j
, int *ineq_j
)
1152 if (any(eq_i
, 2 * map
->p
[i
]->n_eq
, STATUS_ADJ_INEQ
) &&
1153 any(eq_j
, 2 * map
->p
[j
]->n_eq
, STATUS_ADJ_INEQ
))
1154 /* ADJ EQ TOO MANY */
1157 if (any(eq_i
, 2 * map
->p
[i
]->n_eq
, STATUS_ADJ_INEQ
))
1158 return check_adj_eq(map
, j
, i
, tabs
,
1159 eq_j
, ineq_j
, eq_i
, ineq_i
);
1161 /* j has an equality adjacent to an inequality in i */
1163 if (any(eq_i
, 2 * map
->p
[i
]->n_eq
, STATUS_CUT
))
1165 if (any(ineq_i
, map
->p
[i
]->n_ineq
, STATUS_CUT
))
1168 if (count(ineq_i
, map
->p
[i
]->n_ineq
, STATUS_ADJ_EQ
) != 1 ||
1169 any(ineq_j
, map
->p
[j
]->n_ineq
, STATUS_ADJ_EQ
) ||
1170 any(ineq_i
, map
->p
[i
]->n_ineq
, STATUS_ADJ_INEQ
) ||
1171 any(ineq_j
, map
->p
[j
]->n_ineq
, STATUS_ADJ_INEQ
))
1172 /* ADJ EQ TOO MANY */
1175 for (k
= 0; k
< map
->p
[i
]->n_ineq
; ++k
)
1176 if (ineq_i
[k
] == STATUS_ADJ_EQ
)
1179 changed
= is_adj_eq_extension(map
, i
, j
, k
, tabs
,
1180 eq_i
, ineq_i
, eq_j
, ineq_j
);
1184 if (count(eq_j
, 2 * map
->p
[j
]->n_eq
, STATUS_ADJ_INEQ
) != 1)
1187 changed
= can_wrap_in_facet(map
, i
, j
, k
, tabs
, eq_i
, ineq_i
, eq_j
, ineq_j
);
1192 /* The two basic maps lie on adjacent hyperplanes. In particular,
1193 * basic map "i" has an equality that lies parallel to basic map "j".
1194 * Check if we can wrap the facets around the parallel hyperplanes
1195 * to include the other set.
1197 * We perform basically the same operations as can_wrap_in_facet,
1198 * except that we don't need to select a facet of one of the sets.
1204 * We only allow one equality of "i" to be adjacent to an equality of "j"
1205 * to avoid coalescing
1207 * [m, n] -> { [x, y] -> [x, 1 + y] : x >= 1 and y >= 1 and
1208 * x <= 10 and y <= 10;
1209 * [x, y] -> [1 + x, y] : x >= 1 and x <= 20 and
1210 * y >= 5 and y <= 15 }
1214 * [m, n] -> { [x, y] -> [x2, y2] : x >= 1 and 10y2 <= 20 - x + 10y and
1215 * 4y2 >= 5 + 3y and 5y2 <= 15 + 4y and
1216 * y2 <= 1 + x + y - x2 and y2 >= y and
1217 * y2 >= 1 + x + y - x2 }
1219 static int check_eq_adj_eq(struct isl_map
*map
, int i
, int j
,
1220 struct isl_tab
**tabs
, int *eq_i
, int *ineq_i
, int *eq_j
, int *ineq_j
)
1224 struct isl_wraps wraps
;
1226 struct isl_set
*set_i
= NULL
;
1227 struct isl_set
*set_j
= NULL
;
1228 struct isl_vec
*bound
= NULL
;
1229 unsigned total
= isl_basic_map_total_dim(map
->p
[i
]);
1231 if (count(eq_i
, 2 * map
->p
[i
]->n_eq
, STATUS_ADJ_EQ
) != 1)
1234 for (k
= 0; k
< 2 * map
->p
[i
]->n_eq
; ++k
)
1235 if (eq_i
[k
] == STATUS_ADJ_EQ
)
1238 set_i
= set_from_updated_bmap(map
->p
[i
], tabs
[i
]);
1239 set_j
= set_from_updated_bmap(map
->p
[j
], tabs
[j
]);
1240 mat
= isl_mat_alloc(map
->ctx
, 2 * (map
->p
[i
]->n_eq
+ map
->p
[j
]->n_eq
) +
1241 map
->p
[i
]->n_ineq
+ map
->p
[j
]->n_ineq
,
1243 wraps_init(&wraps
, mat
, map
, i
, j
, eq_i
, ineq_i
, eq_j
, ineq_j
);
1244 bound
= isl_vec_alloc(map
->ctx
, 1 + total
);
1245 if (!set_i
|| !set_j
|| !wraps
.mat
|| !bound
)
1249 isl_seq_neg(bound
->el
, map
->p
[i
]->eq
[k
/ 2], 1 + total
);
1251 isl_seq_cpy(bound
->el
, map
->p
[i
]->eq
[k
/ 2], 1 + total
);
1252 isl_int_add_ui(bound
->el
[0], bound
->el
[0], 1);
1254 isl_seq_cpy(wraps
.mat
->row
[0], bound
->el
, 1 + total
);
1255 wraps
.mat
->n_row
= 1;
1257 if (add_wraps(&wraps
, map
->p
[j
], tabs
[j
], bound
->el
, set_i
) < 0)
1259 if (!wraps
.mat
->n_row
)
1262 isl_int_sub_ui(bound
->el
[0], bound
->el
[0], 1);
1263 isl_seq_neg(bound
->el
, bound
->el
, 1 + total
);
1265 isl_seq_cpy(wraps
.mat
->row
[wraps
.mat
->n_row
], bound
->el
, 1 + total
);
1268 if (add_wraps(&wraps
, map
->p
[i
], tabs
[i
], bound
->el
, set_j
) < 0)
1270 if (!wraps
.mat
->n_row
)
1273 changed
= fuse(map
, i
, j
, tabs
, eq_i
, ineq_i
, eq_j
, ineq_j
, wraps
.mat
);
1276 error
: changed
= -1;
1281 isl_set_free(set_i
);
1282 isl_set_free(set_j
);
1283 isl_vec_free(bound
);
1288 /* Check if the union of the given pair of basic maps
1289 * can be represented by a single basic map.
1290 * If so, replace the pair by the single basic map and return 1.
1291 * Otherwise, return 0;
1292 * The two basic maps are assumed to live in the same local space.
1294 * We first check the effect of each constraint of one basic map
1295 * on the other basic map.
1296 * The constraint may be
1297 * redundant the constraint is redundant in its own
1298 * basic map and should be ignore and removed
1300 * valid all (integer) points of the other basic map
1301 * satisfy the constraint
1302 * separate no (integer) point of the other basic map
1303 * satisfies the constraint
1304 * cut some but not all points of the other basic map
1305 * satisfy the constraint
1306 * adj_eq the given constraint is adjacent (on the outside)
1307 * to an equality of the other basic map
1308 * adj_ineq the given constraint is adjacent (on the outside)
1309 * to an inequality of the other basic map
1311 * We consider seven cases in which we can replace the pair by a single
1312 * basic map. We ignore all "redundant" constraints.
1314 * 1. all constraints of one basic map are valid
1315 * => the other basic map is a subset and can be removed
1317 * 2. all constraints of both basic maps are either "valid" or "cut"
1318 * and the facets corresponding to the "cut" constraints
1319 * of one of the basic maps lies entirely inside the other basic map
1320 * => the pair can be replaced by a basic map consisting
1321 * of the valid constraints in both basic maps
1323 * 3. there is a single pair of adjacent inequalities
1324 * (all other constraints are "valid")
1325 * => the pair can be replaced by a basic map consisting
1326 * of the valid constraints in both basic maps
1328 * 4. one basic map has a single adjacent inequality, while the other
1329 * constraints are "valid". The other basic map has some
1330 * "cut" constraints, but replacing the adjacent inequality by
1331 * its opposite and adding the valid constraints of the other
1332 * basic map results in a subset of the other basic map
1333 * => the pair can be replaced by a basic map consisting
1334 * of the valid constraints in both basic maps
1336 * 5. there is a single adjacent pair of an inequality and an equality,
1337 * the other constraints of the basic map containing the inequality are
1338 * "valid". Moreover, if the inequality the basic map is relaxed
1339 * and then turned into an equality, then resulting facet lies
1340 * entirely inside the other basic map
1341 * => the pair can be replaced by the basic map containing
1342 * the inequality, with the inequality relaxed.
1344 * 6. there is a single adjacent pair of an inequality and an equality,
1345 * the other constraints of the basic map containing the inequality are
1346 * "valid". Moreover, the facets corresponding to both
1347 * the inequality and the equality can be wrapped around their
1348 * ridges to include the other basic map
1349 * => the pair can be replaced by a basic map consisting
1350 * of the valid constraints in both basic maps together
1351 * with all wrapping constraints
1353 * 7. one of the basic maps extends beyond the other by at most one.
1354 * Moreover, the facets corresponding to the cut constraints and
1355 * the pieces of the other basic map at offset one from these cut
1356 * constraints can be wrapped around their ridges to include
1357 * the union of the two basic maps
1358 * => the pair can be replaced by a basic map consisting
1359 * of the valid constraints in both basic maps together
1360 * with all wrapping constraints
1362 * 8. the two basic maps live in adjacent hyperplanes. In principle
1363 * such sets can always be combined through wrapping, but we impose
1364 * that there is only one such pair, to avoid overeager coalescing.
1366 * Throughout the computation, we maintain a collection of tableaus
1367 * corresponding to the basic maps. When the basic maps are dropped
1368 * or combined, the tableaus are modified accordingly.
1370 static int coalesce_local_pair(__isl_keep isl_map
*map
, int i
, int j
,
1371 struct isl_tab
**tabs
)
1379 eq_i
= eq_status_in(map
->p
[i
], tabs
[j
]);
1380 if (map
->p
[i
]->n_eq
&& !eq_i
)
1382 if (any(eq_i
, 2 * map
->p
[i
]->n_eq
, STATUS_ERROR
))
1384 if (any(eq_i
, 2 * map
->p
[i
]->n_eq
, STATUS_SEPARATE
))
1387 eq_j
= eq_status_in(map
->p
[j
], tabs
[i
]);
1388 if (map
->p
[j
]->n_eq
&& !eq_j
)
1390 if (any(eq_j
, 2 * map
->p
[j
]->n_eq
, STATUS_ERROR
))
1392 if (any(eq_j
, 2 * map
->p
[j
]->n_eq
, STATUS_SEPARATE
))
1395 ineq_i
= ineq_status_in(map
->p
[i
], tabs
[i
], tabs
[j
]);
1396 if (map
->p
[i
]->n_ineq
&& !ineq_i
)
1398 if (any(ineq_i
, map
->p
[i
]->n_ineq
, STATUS_ERROR
))
1400 if (any(ineq_i
, map
->p
[i
]->n_ineq
, STATUS_SEPARATE
))
1403 ineq_j
= ineq_status_in(map
->p
[j
], tabs
[j
], tabs
[i
]);
1404 if (map
->p
[j
]->n_ineq
&& !ineq_j
)
1406 if (any(ineq_j
, map
->p
[j
]->n_ineq
, STATUS_ERROR
))
1408 if (any(ineq_j
, map
->p
[j
]->n_ineq
, STATUS_SEPARATE
))
1411 if (all(eq_i
, 2 * map
->p
[i
]->n_eq
, STATUS_VALID
) &&
1412 all(ineq_i
, map
->p
[i
]->n_ineq
, STATUS_VALID
)) {
1415 } else if (all(eq_j
, 2 * map
->p
[j
]->n_eq
, STATUS_VALID
) &&
1416 all(ineq_j
, map
->p
[j
]->n_ineq
, STATUS_VALID
)) {
1419 } else if (any(eq_i
, 2 * map
->p
[i
]->n_eq
, STATUS_ADJ_EQ
)) {
1420 changed
= check_eq_adj_eq(map
, i
, j
, tabs
,
1421 eq_i
, ineq_i
, eq_j
, ineq_j
);
1422 } else if (any(eq_j
, 2 * map
->p
[j
]->n_eq
, STATUS_ADJ_EQ
)) {
1423 changed
= check_eq_adj_eq(map
, j
, i
, tabs
,
1424 eq_j
, ineq_j
, eq_i
, ineq_i
);
1425 } else if (any(eq_i
, 2 * map
->p
[i
]->n_eq
, STATUS_ADJ_INEQ
) ||
1426 any(eq_j
, 2 * map
->p
[j
]->n_eq
, STATUS_ADJ_INEQ
)) {
1427 changed
= check_adj_eq(map
, i
, j
, tabs
,
1428 eq_i
, ineq_i
, eq_j
, ineq_j
);
1429 } else if (any(ineq_i
, map
->p
[i
]->n_ineq
, STATUS_ADJ_EQ
) ||
1430 any(ineq_j
, map
->p
[j
]->n_ineq
, STATUS_ADJ_EQ
)) {
1433 } else if (any(ineq_i
, map
->p
[i
]->n_ineq
, STATUS_ADJ_INEQ
) ||
1434 any(ineq_j
, map
->p
[j
]->n_ineq
, STATUS_ADJ_INEQ
)) {
1435 changed
= check_adj_ineq(map
, i
, j
, tabs
,
1436 eq_i
, ineq_i
, eq_j
, ineq_j
);
1438 if (!any(eq_i
, 2 * map
->p
[i
]->n_eq
, STATUS_CUT
) &&
1439 !any(eq_j
, 2 * map
->p
[j
]->n_eq
, STATUS_CUT
))
1440 changed
= check_facets(map
, i
, j
, tabs
, ineq_i
, ineq_j
);
1442 changed
= check_wrap(map
, i
, j
, tabs
,
1443 eq_i
, ineq_i
, eq_j
, ineq_j
);
1460 /* Do the two basic maps live in the same local space, i.e.,
1461 * do they have the same (known) divs?
1462 * If either basic map has any unknown divs, then we can only assume
1463 * that they do not live in the same local space.
1465 static int same_divs(__isl_keep isl_basic_map
*bmap1
,
1466 __isl_keep isl_basic_map
*bmap2
)
1472 if (!bmap1
|| !bmap2
)
1474 if (bmap1
->n_div
!= bmap2
->n_div
)
1477 if (bmap1
->n_div
== 0)
1480 known
= isl_basic_map_divs_known(bmap1
);
1481 if (known
< 0 || !known
)
1483 known
= isl_basic_map_divs_known(bmap2
);
1484 if (known
< 0 || !known
)
1487 total
= isl_basic_map_total_dim(bmap1
);
1488 for (i
= 0; i
< bmap1
->n_div
; ++i
)
1489 if (!isl_seq_eq(bmap1
->div
[i
], bmap2
->div
[i
], 2 + total
))
1495 /* Given two basic maps "i" and "j", where the divs of "i" form a subset
1496 * of those of "j", check if basic map "j" is a subset of basic map "i"
1497 * and, if so, drop basic map "j".
1499 * We first expand the divs of basic map "i" to match those of basic map "j",
1500 * using the divs and expansion computed by the caller.
1501 * Then we check if all constraints of the expanded "i" are valid for "j".
1503 static int coalesce_subset(__isl_keep isl_map
*map
, int i
, int j
,
1504 struct isl_tab
**tabs
, __isl_keep isl_mat
*div
, int *exp
)
1506 isl_basic_map
*bmap
;
1511 bmap
= isl_basic_map_copy(map
->p
[i
]);
1512 bmap
= isl_basic_set_expand_divs(bmap
, isl_mat_copy(div
), exp
);
1517 eq_i
= eq_status_in(bmap
, tabs
[j
]);
1518 if (bmap
->n_eq
&& !eq_i
)
1520 if (any(eq_i
, 2 * bmap
->n_eq
, STATUS_ERROR
))
1522 if (any(eq_i
, 2 * bmap
->n_eq
, STATUS_SEPARATE
))
1525 ineq_i
= ineq_status_in(bmap
, NULL
, tabs
[j
]);
1526 if (bmap
->n_ineq
&& !ineq_i
)
1528 if (any(ineq_i
, bmap
->n_ineq
, STATUS_ERROR
))
1530 if (any(ineq_i
, bmap
->n_ineq
, STATUS_SEPARATE
))
1533 if (all(eq_i
, 2 * map
->p
[i
]->n_eq
, STATUS_VALID
) &&
1534 all(ineq_i
, map
->p
[i
]->n_ineq
, STATUS_VALID
)) {
1540 isl_basic_map_free(bmap
);
1545 isl_basic_map_free(bmap
);
1551 /* Check if the basic map "j" is a subset of basic map "i",
1552 * assuming that "i" has fewer divs that "j".
1553 * If not, then we change the order.
1555 * If the two basic maps have the same number of divs, then
1556 * they must necessarily be different. Otherwise, we would have
1557 * called coalesce_local_pair. We therefore don't try anything
1560 * We first check if the divs of "i" are all known and form a subset
1561 * of those of "j". If so, we pass control over to coalesce_subset.
1563 static int check_coalesce_subset(__isl_keep isl_map
*map
, int i
, int j
,
1564 struct isl_tab
**tabs
)
1567 isl_mat
*div_i
, *div_j
, *div
;
1573 if (map
->p
[i
]->n_div
== map
->p
[j
]->n_div
)
1575 if (map
->p
[j
]->n_div
< map
->p
[i
]->n_div
)
1576 return check_coalesce_subset(map
, j
, i
, tabs
);
1578 known
= isl_basic_map_divs_known(map
->p
[i
]);
1579 if (known
< 0 || !known
)
1582 ctx
= isl_map_get_ctx(map
);
1584 div_i
= isl_basic_map_get_divs(map
->p
[i
]);
1585 div_j
= isl_basic_map_get_divs(map
->p
[j
]);
1587 if (!div_i
|| !div_j
)
1590 exp1
= isl_alloc_array(ctx
, int, div_i
->n_row
);
1591 exp2
= isl_alloc_array(ctx
, int, div_j
->n_row
);
1592 if ((div_i
->n_row
&& !exp1
) || (div_j
->n_row
&& !exp2
))
1595 div
= isl_merge_divs(div_i
, div_j
, exp1
, exp2
);
1599 if (div
->n_row
== div_j
->n_row
)
1600 subset
= coalesce_subset(map
, i
, j
, tabs
, div
, exp1
);
1606 isl_mat_free(div_i
);
1607 isl_mat_free(div_j
);
1614 isl_mat_free(div_i
);
1615 isl_mat_free(div_j
);
1621 /* Check if the union of the given pair of basic maps
1622 * can be represented by a single basic map.
1623 * If so, replace the pair by the single basic map and return 1.
1624 * Otherwise, return 0;
1626 * We first check if the two basic maps live in the same local space.
1627 * If so, we do the complete check. Otherwise, we check if one is
1628 * an obvious subset of the other.
1630 static int coalesce_pair(__isl_keep isl_map
*map
, int i
, int j
,
1631 struct isl_tab
**tabs
)
1635 same
= same_divs(map
->p
[i
], map
->p
[j
]);
1639 return coalesce_local_pair(map
, i
, j
, tabs
);
1641 return check_coalesce_subset(map
, i
, j
, tabs
);
1644 static struct isl_map
*coalesce(struct isl_map
*map
, struct isl_tab
**tabs
)
1648 for (i
= map
->n
- 2; i
>= 0; --i
)
1650 for (j
= i
+ 1; j
< map
->n
; ++j
) {
1652 changed
= coalesce_pair(map
, i
, j
, tabs
);
1664 /* For each pair of basic maps in the map, check if the union of the two
1665 * can be represented by a single basic map.
1666 * If so, replace the pair by the single basic map and start over.
1668 * Since we are constructing the tableaus of the basic maps anyway,
1669 * we exploit them to detect implicit equalities and redundant constraints.
1670 * This also helps the coalescing as it can ignore the redundant constraints.
1671 * In order to avoid confusion, we make all implicit equalities explicit
1672 * in the basic maps. We don't call isl_basic_map_gauss, though,
1673 * as that may affect the number of constraints.
1674 * This means that we have to call isl_basic_map_gauss at the end
1675 * of the computation to ensure that the basic maps are not left
1676 * in an unexpected state.
1678 struct isl_map
*isl_map_coalesce(struct isl_map
*map
)
1682 struct isl_tab
**tabs
= NULL
;
1684 map
= isl_map_remove_empty_parts(map
);
1691 map
= isl_map_sort_divs(map
);
1692 map
= isl_map_cow(map
);
1697 tabs
= isl_calloc_array(map
->ctx
, struct isl_tab
*, map
->n
);
1702 for (i
= 0; i
< map
->n
; ++i
) {
1703 tabs
[i
] = isl_tab_from_basic_map(map
->p
[i
], 0);
1706 if (!ISL_F_ISSET(map
->p
[i
], ISL_BASIC_MAP_NO_IMPLICIT
))
1707 if (isl_tab_detect_implicit_equalities(tabs
[i
]) < 0)
1709 map
->p
[i
] = isl_tab_make_equalities_explicit(tabs
[i
],
1713 if (!ISL_F_ISSET(map
->p
[i
], ISL_BASIC_MAP_NO_REDUNDANT
))
1714 if (isl_tab_detect_redundant(tabs
[i
]) < 0)
1717 for (i
= map
->n
- 1; i
>= 0; --i
)
1721 map
= coalesce(map
, tabs
);
1724 for (i
= 0; i
< map
->n
; ++i
) {
1725 map
->p
[i
] = isl_basic_map_update_from_tab(map
->p
[i
],
1727 map
->p
[i
] = isl_basic_map_gauss(map
->p
[i
], NULL
);
1728 map
->p
[i
] = isl_basic_map_finalize(map
->p
[i
]);
1731 ISL_F_SET(map
->p
[i
], ISL_BASIC_MAP_NO_IMPLICIT
);
1732 ISL_F_SET(map
->p
[i
], ISL_BASIC_MAP_NO_REDUNDANT
);
1735 for (i
= 0; i
< n
; ++i
)
1736 isl_tab_free(tabs
[i
]);
1743 for (i
= 0; i
< n
; ++i
)
1744 isl_tab_free(tabs
[i
]);
1750 /* For each pair of basic sets in the set, check if the union of the two
1751 * can be represented by a single basic set.
1752 * If so, replace the pair by the single basic set and start over.
1754 struct isl_set
*isl_set_coalesce(struct isl_set
*set
)
1756 return (struct isl_set
*)isl_map_coalesce((struct isl_map
*)set
);