isl_qpolynomial_as_polynomial_on_domain: rename local variable
[isl.git] / isl_coalesce.c
blob5d0d173af9fe2fb7005dc6e719cf0220ff54a9ef
1 /*
2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2010 INRIA Saclay
4 * Copyright 2012-2013 Ecole Normale Superieure
5 * Copyright 2014 INRIA Rocquencourt
6 * Copyright 2016 INRIA Paris
7 * Copyright 2020 Cerebras Systems
9 * Use of this software is governed by the MIT license
11 * Written by Sven Verdoolaege, K.U.Leuven, Departement
12 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
13 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
14 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
15 * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
16 * and Inria Paris - Rocquencourt, Domaine de Voluceau - Rocquencourt,
17 * B.P. 105 - 78153 Le Chesnay, France
18 * and Centre de Recherche Inria de Paris, 2 rue Simone Iff - Voie DQ12,
19 * CS 42112, 75589 Paris Cedex 12, France
20 * and Cerebras Systems, 175 S San Antonio Rd, Los Altos, CA, USA
23 #include <isl_ctx_private.h>
24 #include "isl_map_private.h"
25 #include <isl_seq.h>
26 #include <isl/options.h>
27 #include "isl_tab.h"
28 #include <isl_mat_private.h>
29 #include <isl_local_space_private.h>
30 #include <isl_val_private.h>
31 #include <isl_vec_private.h>
32 #include <isl_aff_private.h>
33 #include <isl_equalities.h>
34 #include <isl_constraint_private.h>
36 #include <set_to_map.c>
37 #include <set_from_map.c>
39 #define STATUS_ERROR -1
40 #define STATUS_REDUNDANT 1
41 #define STATUS_VALID 2
42 #define STATUS_SEPARATE 3
43 #define STATUS_CUT 4
44 #define STATUS_ADJ_EQ 5
45 #define STATUS_ADJ_INEQ 6
47 static int status_in(isl_int *ineq, struct isl_tab *tab)
49 enum isl_ineq_type type = isl_tab_ineq_type(tab, ineq);
50 switch (type) {
51 default:
52 case isl_ineq_error: return STATUS_ERROR;
53 case isl_ineq_redundant: return STATUS_VALID;
54 case isl_ineq_separate: return STATUS_SEPARATE;
55 case isl_ineq_cut: return STATUS_CUT;
56 case isl_ineq_adj_eq: return STATUS_ADJ_EQ;
57 case isl_ineq_adj_ineq: return STATUS_ADJ_INEQ;
61 /* Compute the position of the equalities of basic map "bmap_i"
62 * with respect to the basic map represented by "tab_j".
63 * The resulting array has twice as many entries as the number
64 * of equalities corresponding to the two inequalities to which
65 * each equality corresponds.
67 static int *eq_status_in(__isl_keep isl_basic_map *bmap_i,
68 struct isl_tab *tab_j)
70 int k, l;
71 int *eq;
72 isl_size dim;
74 dim = isl_basic_map_dim(bmap_i, isl_dim_all);
75 if (dim < 0)
76 return NULL;
78 eq = isl_calloc_array(bmap_i->ctx, int, 2 * bmap_i->n_eq);
79 if (!eq)
80 return NULL;
82 for (k = 0; k < bmap_i->n_eq; ++k) {
83 for (l = 0; l < 2; ++l) {
84 isl_seq_neg(bmap_i->eq[k], bmap_i->eq[k], 1+dim);
85 eq[2 * k + l] = status_in(bmap_i->eq[k], tab_j);
86 if (eq[2 * k + l] == STATUS_ERROR)
87 goto error;
91 return eq;
92 error:
93 free(eq);
94 return NULL;
97 /* Compute the position of the inequalities of basic map "bmap_i"
98 * (also represented by "tab_i", if not NULL) with respect to the basic map
99 * represented by "tab_j".
101 static int *ineq_status_in(__isl_keep isl_basic_map *bmap_i,
102 struct isl_tab *tab_i, struct isl_tab *tab_j)
104 int k;
105 unsigned n_eq = bmap_i->n_eq;
106 int *ineq = isl_calloc_array(bmap_i->ctx, int, bmap_i->n_ineq);
108 if (!ineq)
109 return NULL;
111 for (k = 0; k < bmap_i->n_ineq; ++k) {
112 if (tab_i && isl_tab_is_redundant(tab_i, n_eq + k)) {
113 ineq[k] = STATUS_REDUNDANT;
114 continue;
116 ineq[k] = status_in(bmap_i->ineq[k], tab_j);
117 if (ineq[k] == STATUS_ERROR)
118 goto error;
119 if (ineq[k] == STATUS_SEPARATE)
120 break;
123 return ineq;
124 error:
125 free(ineq);
126 return NULL;
129 static int any(int *con, unsigned len, int status)
131 int i;
133 for (i = 0; i < len ; ++i)
134 if (con[i] == status)
135 return 1;
136 return 0;
139 /* Return the first position of "status" in the list "con" of length "len".
140 * Return -1 if there is no such entry.
142 static int find(int *con, unsigned len, int status)
144 int i;
146 for (i = 0; i < len ; ++i)
147 if (con[i] == status)
148 return i;
149 return -1;
152 static int count(int *con, unsigned len, int status)
154 int i;
155 int c = 0;
157 for (i = 0; i < len ; ++i)
158 if (con[i] == status)
159 c++;
160 return c;
163 static int all(int *con, unsigned len, int status)
165 int i;
167 for (i = 0; i < len ; ++i) {
168 if (con[i] == STATUS_REDUNDANT)
169 continue;
170 if (con[i] != status)
171 return 0;
173 return 1;
176 /* Internal information associated to a basic map in a map
177 * that is to be coalesced by isl_map_coalesce.
179 * "bmap" is the basic map itself (or NULL if "removed" is set)
180 * "tab" is the corresponding tableau (or NULL if "removed" is set)
181 * "hull_hash" identifies the affine space in which "bmap" lives.
182 * "modified" is set if this basic map may not be identical
183 * to any of the basic maps in the input.
184 * "removed" is set if this basic map has been removed from the map
185 * "simplify" is set if this basic map may have some unknown integer
186 * divisions that were not present in the input basic maps. The basic
187 * map should then be simplified such that we may be able to find
188 * a definition among the constraints.
190 * "eq" and "ineq" are only set if we are currently trying to coalesce
191 * this basic map with another basic map, in which case they represent
192 * the position of the inequalities of this basic map with respect to
193 * the other basic map. The number of elements in the "eq" array
194 * is twice the number of equalities in the "bmap", corresponding
195 * to the two inequalities that make up each equality.
197 struct isl_coalesce_info {
198 isl_basic_map *bmap;
199 struct isl_tab *tab;
200 uint32_t hull_hash;
201 int modified;
202 int removed;
203 int simplify;
204 int *eq;
205 int *ineq;
208 /* Is there any (half of an) equality constraint in the description
209 * of the basic map represented by "info" that
210 * has position "status" with respect to the other basic map?
212 static int any_eq(struct isl_coalesce_info *info, int status)
214 isl_size n_eq;
216 n_eq = isl_basic_map_n_equality(info->bmap);
217 return any(info->eq, 2 * n_eq, status);
220 /* Is there any inequality constraint in the description
221 * of the basic map represented by "info" that
222 * has position "status" with respect to the other basic map?
224 static int any_ineq(struct isl_coalesce_info *info, int status)
226 isl_size n_ineq;
228 n_ineq = isl_basic_map_n_inequality(info->bmap);
229 return any(info->ineq, n_ineq, status);
232 /* Return the position of the first half on an equality constraint
233 * in the description of the basic map represented by "info" that
234 * has position "status" with respect to the other basic map.
235 * The returned value is twice the position of the equality constraint
236 * plus zero for the negative half and plus one for the positive half.
237 * Return -1 if there is no such entry.
239 static int find_eq(struct isl_coalesce_info *info, int status)
241 isl_size n_eq;
243 n_eq = isl_basic_map_n_equality(info->bmap);
244 return find(info->eq, 2 * n_eq, status);
247 /* Return the position of the first inequality constraint in the description
248 * of the basic map represented by "info" that
249 * has position "status" with respect to the other basic map.
250 * Return -1 if there is no such entry.
252 static int find_ineq(struct isl_coalesce_info *info, int status)
254 isl_size n_ineq;
256 n_ineq = isl_basic_map_n_inequality(info->bmap);
257 return find(info->ineq, n_ineq, status);
260 /* Return the number of (halves of) equality constraints in the description
261 * of the basic map represented by "info" that
262 * have position "status" with respect to the other basic map.
264 static int count_eq(struct isl_coalesce_info *info, int status)
266 isl_size n_eq;
268 n_eq = isl_basic_map_n_equality(info->bmap);
269 return count(info->eq, 2 * n_eq, status);
272 /* Return the number of inequality constraints in the description
273 * of the basic map represented by "info" that
274 * have position "status" with respect to the other basic map.
276 static int count_ineq(struct isl_coalesce_info *info, int status)
278 isl_size n_ineq;
280 n_ineq = isl_basic_map_n_inequality(info->bmap);
281 return count(info->ineq, n_ineq, status);
284 /* Are all non-redundant constraints of the basic map represented by "info"
285 * either valid or cut constraints with respect to the other basic map?
287 static int all_valid_or_cut(struct isl_coalesce_info *info)
289 int i;
291 for (i = 0; i < 2 * info->bmap->n_eq; ++i) {
292 if (info->eq[i] == STATUS_REDUNDANT)
293 continue;
294 if (info->eq[i] == STATUS_VALID)
295 continue;
296 if (info->eq[i] == STATUS_CUT)
297 continue;
298 return 0;
301 for (i = 0; i < info->bmap->n_ineq; ++i) {
302 if (info->ineq[i] == STATUS_REDUNDANT)
303 continue;
304 if (info->ineq[i] == STATUS_VALID)
305 continue;
306 if (info->ineq[i] == STATUS_CUT)
307 continue;
308 return 0;
311 return 1;
314 /* Compute the hash of the (apparent) affine hull of info->bmap (with
315 * the existentially quantified variables removed) and store it
316 * in info->hash.
318 static int coalesce_info_set_hull_hash(struct isl_coalesce_info *info)
320 isl_basic_map *hull;
321 isl_size n_div;
323 hull = isl_basic_map_copy(info->bmap);
324 hull = isl_basic_map_plain_affine_hull(hull);
325 n_div = isl_basic_map_dim(hull, isl_dim_div);
326 if (n_div < 0)
327 hull = isl_basic_map_free(hull);
328 hull = isl_basic_map_drop_constraints_involving_dims(hull,
329 isl_dim_div, 0, n_div);
330 info->hull_hash = isl_basic_map_get_hash(hull);
331 isl_basic_map_free(hull);
333 return hull ? 0 : -1;
336 /* Free all the allocated memory in an array
337 * of "n" isl_coalesce_info elements.
339 static void clear_coalesce_info(int n, struct isl_coalesce_info *info)
341 int i;
343 if (!info)
344 return;
346 for (i = 0; i < n; ++i) {
347 isl_basic_map_free(info[i].bmap);
348 isl_tab_free(info[i].tab);
351 free(info);
354 /* Clear the memory associated to "info".
356 static void clear(struct isl_coalesce_info *info)
358 info->bmap = isl_basic_map_free(info->bmap);
359 isl_tab_free(info->tab);
360 info->tab = NULL;
363 /* Drop the basic map represented by "info".
364 * That is, clear the memory associated to the entry and
365 * mark it as having been removed.
367 static void drop(struct isl_coalesce_info *info)
369 clear(info);
370 info->removed = 1;
373 /* Exchange the information in "info1" with that in "info2".
375 static void exchange(struct isl_coalesce_info *info1,
376 struct isl_coalesce_info *info2)
378 struct isl_coalesce_info info;
380 info = *info1;
381 *info1 = *info2;
382 *info2 = info;
385 /* This type represents the kind of change that has been performed
386 * while trying to coalesce two basic maps.
388 * isl_change_none: nothing was changed
389 * isl_change_drop_first: the first basic map was removed
390 * isl_change_drop_second: the second basic map was removed
391 * isl_change_fuse: the two basic maps were replaced by a new basic map.
393 enum isl_change {
394 isl_change_error = -1,
395 isl_change_none = 0,
396 isl_change_drop_first,
397 isl_change_drop_second,
398 isl_change_fuse,
401 /* Update "change" based on an interchange of the first and the second
402 * basic map. That is, interchange isl_change_drop_first and
403 * isl_change_drop_second.
405 static enum isl_change invert_change(enum isl_change change)
407 switch (change) {
408 case isl_change_error:
409 return isl_change_error;
410 case isl_change_none:
411 return isl_change_none;
412 case isl_change_drop_first:
413 return isl_change_drop_second;
414 case isl_change_drop_second:
415 return isl_change_drop_first;
416 case isl_change_fuse:
417 return isl_change_fuse;
420 return isl_change_error;
423 /* Add the valid constraints of the basic map represented by "info"
424 * to "bmap". "len" is the size of the constraints.
425 * If only one of the pair of inequalities that make up an equality
426 * is valid, then add that inequality.
428 static __isl_give isl_basic_map *add_valid_constraints(
429 __isl_take isl_basic_map *bmap, struct isl_coalesce_info *info,
430 unsigned len)
432 int k, l;
434 if (!bmap)
435 return NULL;
437 for (k = 0; k < info->bmap->n_eq; ++k) {
438 if (info->eq[2 * k] == STATUS_VALID &&
439 info->eq[2 * k + 1] == STATUS_VALID) {
440 l = isl_basic_map_alloc_equality(bmap);
441 if (l < 0)
442 return isl_basic_map_free(bmap);
443 isl_seq_cpy(bmap->eq[l], info->bmap->eq[k], len);
444 } else if (info->eq[2 * k] == STATUS_VALID) {
445 l = isl_basic_map_alloc_inequality(bmap);
446 if (l < 0)
447 return isl_basic_map_free(bmap);
448 isl_seq_neg(bmap->ineq[l], info->bmap->eq[k], len);
449 } else if (info->eq[2 * k + 1] == STATUS_VALID) {
450 l = isl_basic_map_alloc_inequality(bmap);
451 if (l < 0)
452 return isl_basic_map_free(bmap);
453 isl_seq_cpy(bmap->ineq[l], info->bmap->eq[k], len);
457 for (k = 0; k < info->bmap->n_ineq; ++k) {
458 if (info->ineq[k] != STATUS_VALID)
459 continue;
460 l = isl_basic_map_alloc_inequality(bmap);
461 if (l < 0)
462 return isl_basic_map_free(bmap);
463 isl_seq_cpy(bmap->ineq[l], info->bmap->ineq[k], len);
466 return bmap;
469 /* Is "bmap" defined by a number of (non-redundant) constraints that
470 * is greater than the number of constraints of basic maps i and j combined?
471 * Equalities are counted as two inequalities.
473 static int number_of_constraints_increases(int i, int j,
474 struct isl_coalesce_info *info,
475 __isl_keep isl_basic_map *bmap, struct isl_tab *tab)
477 int k, n_old, n_new;
479 n_old = 2 * info[i].bmap->n_eq + info[i].bmap->n_ineq;
480 n_old += 2 * info[j].bmap->n_eq + info[j].bmap->n_ineq;
482 n_new = 2 * bmap->n_eq;
483 for (k = 0; k < bmap->n_ineq; ++k)
484 if (!isl_tab_is_redundant(tab, bmap->n_eq + k))
485 ++n_new;
487 return n_new > n_old;
490 /* Replace the pair of basic maps i and j by the basic map bounded
491 * by the valid constraints in both basic maps and the constraints
492 * in extra (if not NULL).
493 * Place the fused basic map in the position that is the smallest of i and j.
495 * If "detect_equalities" is set, then look for equalities encoded
496 * as pairs of inequalities.
497 * If "check_number" is set, then the original basic maps are only
498 * replaced if the total number of constraints does not increase.
499 * While the number of integer divisions in the two basic maps
500 * is assumed to be the same, the actual definitions may be different.
501 * We only copy the definition from one of the basic maps if it is
502 * the same as that of the other basic map. Otherwise, we mark
503 * the integer division as unknown and simplify the basic map
504 * in an attempt to recover the integer division definition.
505 * If any extra constraints get introduced, then these may
506 * involve integer divisions with a unit coefficient.
507 * Eliminate those that do not appear with any other coefficient
508 * in other constraints, to ensure they get eliminated completely,
509 * improving the chances of further coalescing.
511 static enum isl_change fuse(int i, int j, struct isl_coalesce_info *info,
512 __isl_keep isl_mat *extra, int detect_equalities, int check_number)
514 int k, l;
515 struct isl_basic_map *fused = NULL;
516 struct isl_tab *fused_tab = NULL;
517 isl_size total = isl_basic_map_dim(info[i].bmap, isl_dim_all);
518 unsigned extra_rows = extra ? extra->n_row : 0;
519 unsigned n_eq, n_ineq;
520 int simplify = 0;
522 if (total < 0)
523 return isl_change_error;
524 if (j < i)
525 return fuse(j, i, info, extra, detect_equalities, check_number);
527 n_eq = info[i].bmap->n_eq + info[j].bmap->n_eq;
528 n_ineq = info[i].bmap->n_ineq + info[j].bmap->n_ineq;
529 fused = isl_basic_map_alloc_space(isl_space_copy(info[i].bmap->dim),
530 info[i].bmap->n_div, n_eq, n_eq + n_ineq + extra_rows);
531 fused = add_valid_constraints(fused, &info[i], 1 + total);
532 fused = add_valid_constraints(fused, &info[j], 1 + total);
533 if (!fused)
534 goto error;
535 if (ISL_F_ISSET(info[i].bmap, ISL_BASIC_MAP_RATIONAL) &&
536 ISL_F_ISSET(info[j].bmap, ISL_BASIC_MAP_RATIONAL))
537 ISL_F_SET(fused, ISL_BASIC_MAP_RATIONAL);
539 for (k = 0; k < info[i].bmap->n_div; ++k) {
540 int l = isl_basic_map_alloc_div(fused);
541 if (l < 0)
542 goto error;
543 if (isl_seq_eq(info[i].bmap->div[k], info[j].bmap->div[k],
544 1 + 1 + total)) {
545 isl_seq_cpy(fused->div[l], info[i].bmap->div[k],
546 1 + 1 + total);
547 } else {
548 isl_int_set_si(fused->div[l][0], 0);
549 simplify = 1;
553 for (k = 0; k < extra_rows; ++k) {
554 l = isl_basic_map_alloc_inequality(fused);
555 if (l < 0)
556 goto error;
557 isl_seq_cpy(fused->ineq[l], extra->row[k], 1 + total);
560 if (detect_equalities)
561 fused = isl_basic_map_detect_inequality_pairs(fused, NULL);
562 fused = isl_basic_map_gauss(fused, NULL);
563 if (simplify || info[j].simplify) {
564 fused = isl_basic_map_simplify(fused);
565 info[i].simplify = 0;
566 } else if (extra_rows > 0) {
567 fused = isl_basic_map_eliminate_pure_unit_divs(fused);
569 fused = isl_basic_map_finalize(fused);
571 fused_tab = isl_tab_from_basic_map(fused, 0);
572 if (isl_tab_detect_redundant(fused_tab) < 0)
573 goto error;
575 if (check_number &&
576 number_of_constraints_increases(i, j, info, fused, fused_tab)) {
577 isl_tab_free(fused_tab);
578 isl_basic_map_free(fused);
579 return isl_change_none;
582 clear(&info[i]);
583 info[i].bmap = fused;
584 info[i].tab = fused_tab;
585 info[i].modified = 1;
586 drop(&info[j]);
588 return isl_change_fuse;
589 error:
590 isl_tab_free(fused_tab);
591 isl_basic_map_free(fused);
592 return isl_change_error;
595 /* Given a pair of basic maps i and j such that all constraints are either
596 * "valid" or "cut", check if the facets corresponding to the "cut"
597 * constraints of i lie entirely within basic map j.
598 * If so, replace the pair by the basic map consisting of the valid
599 * constraints in both basic maps.
600 * Checking whether the facet lies entirely within basic map j
601 * is performed by checking whether the constraints of basic map j
602 * are valid for the facet. These tests are performed on a rational
603 * tableau to avoid the theoretical possibility that a constraint
604 * that was considered to be a cut constraint for the entire basic map i
605 * happens to be considered to be a valid constraint for the facet,
606 * even though it cuts off the same rational points.
608 * To see that we are not introducing any extra points, call the
609 * two basic maps A and B and the resulting map U and let x
610 * be an element of U \setminus ( A \cup B ).
611 * A line connecting x with an element of A \cup B meets a facet F
612 * of either A or B. Assume it is a facet of B and let c_1 be
613 * the corresponding facet constraint. We have c_1(x) < 0 and
614 * so c_1 is a cut constraint. This implies that there is some
615 * (possibly rational) point x' satisfying the constraints of A
616 * and the opposite of c_1 as otherwise c_1 would have been marked
617 * valid for A. The line connecting x and x' meets a facet of A
618 * in a (possibly rational) point that also violates c_1, but this
619 * is impossible since all cut constraints of B are valid for all
620 * cut facets of A.
621 * In case F is a facet of A rather than B, then we can apply the
622 * above reasoning to find a facet of B separating x from A \cup B first.
624 static enum isl_change check_facets(int i, int j,
625 struct isl_coalesce_info *info)
627 int k, l;
628 struct isl_tab_undo *snap, *snap2;
629 unsigned n_eq = info[i].bmap->n_eq;
631 snap = isl_tab_snap(info[i].tab);
632 if (isl_tab_mark_rational(info[i].tab) < 0)
633 return isl_change_error;
634 snap2 = isl_tab_snap(info[i].tab);
636 for (k = 0; k < info[i].bmap->n_ineq; ++k) {
637 if (info[i].ineq[k] != STATUS_CUT)
638 continue;
639 if (isl_tab_select_facet(info[i].tab, n_eq + k) < 0)
640 return isl_change_error;
641 for (l = 0; l < info[j].bmap->n_ineq; ++l) {
642 int stat;
643 if (info[j].ineq[l] != STATUS_CUT)
644 continue;
645 stat = status_in(info[j].bmap->ineq[l], info[i].tab);
646 if (stat < 0)
647 return isl_change_error;
648 if (stat != STATUS_VALID)
649 break;
651 if (isl_tab_rollback(info[i].tab, snap2) < 0)
652 return isl_change_error;
653 if (l < info[j].bmap->n_ineq)
654 break;
657 if (k < info[i].bmap->n_ineq) {
658 if (isl_tab_rollback(info[i].tab, snap) < 0)
659 return isl_change_error;
660 return isl_change_none;
662 return fuse(i, j, info, NULL, 0, 0);
665 /* Check if info->bmap contains the basic map represented
666 * by the tableau "tab".
667 * For each equality, we check both the constraint itself
668 * (as an inequality) and its negation. Make sure the
669 * equality is returned to its original state before returning.
671 static isl_bool contains(struct isl_coalesce_info *info, struct isl_tab *tab)
673 int k;
674 isl_size dim;
675 isl_basic_map *bmap = info->bmap;
677 dim = isl_basic_map_dim(bmap, isl_dim_all);
678 if (dim < 0)
679 return isl_bool_error;
680 for (k = 0; k < bmap->n_eq; ++k) {
681 int stat;
682 isl_seq_neg(bmap->eq[k], bmap->eq[k], 1 + dim);
683 stat = status_in(bmap->eq[k], tab);
684 isl_seq_neg(bmap->eq[k], bmap->eq[k], 1 + dim);
685 if (stat < 0)
686 return isl_bool_error;
687 if (stat != STATUS_VALID)
688 return isl_bool_false;
689 stat = status_in(bmap->eq[k], tab);
690 if (stat < 0)
691 return isl_bool_error;
692 if (stat != STATUS_VALID)
693 return isl_bool_false;
696 for (k = 0; k < bmap->n_ineq; ++k) {
697 int stat;
698 if (info->ineq[k] == STATUS_REDUNDANT)
699 continue;
700 stat = status_in(bmap->ineq[k], tab);
701 if (stat < 0)
702 return isl_bool_error;
703 if (stat != STATUS_VALID)
704 return isl_bool_false;
706 return isl_bool_true;
709 /* Basic map "i" has an inequality "k" that is adjacent
710 * to some inequality of basic map "j". All the other inequalities
711 * are valid for "j".
712 * If not NULL, then "extra" contains extra wrapping constraints that are valid
713 * for both "i" and "j".
714 * Check if basic map "j" forms an extension of basic map "i",
715 * taking into account the extra constraints, if any.
717 * Note that this function is only called if some of the equalities or
718 * inequalities of basic map "j" do cut basic map "i". The function is
719 * correct even if there are no such cut constraints, but in that case
720 * the additional checks performed by this function are overkill.
722 * In particular, we replace constraint k, say f >= 0, by constraint
723 * f <= -1, add the inequalities of "j" that are valid for "i",
724 * as well as the "extra" constraints, if any,
725 * and check if the result is a subset of basic map "j".
726 * To improve the chances of the subset relation being detected,
727 * any variable that only attains a single integer value
728 * in the tableau of "i" is first fixed to that value.
729 * If the result is a subset, then we know that this result is exactly equal
730 * to basic map "j" since all its constraints are valid for basic map "j".
731 * By combining the valid constraints of "i" (all equalities and all
732 * inequalities except "k"), the valid constraints of "j" and
733 * the "extra" constraints, if any, we therefore
734 * obtain a basic map that is equal to their union.
735 * In this case, there is no need to perform a rollback of the tableau
736 * since it is going to be destroyed in fuse().
739 * |\__ |\__
740 * | \__ | \__
741 * | \_ => | \__
742 * |_______| _ |_________\
745 * |\ |\
746 * | \ | \
747 * | \ | \
748 * | | | \
749 * | ||\ => | \
750 * | || \ | \
751 * | || | | |
752 * |__||_/ |_____/
755 * _______ _______
756 * | | __ | \__
757 * | ||__| => | __|
758 * |_______| |_______/
760 static enum isl_change is_adj_ineq_extension_with_wraps(int i, int j, int k,
761 struct isl_coalesce_info *info, __isl_keep isl_mat *extra)
763 struct isl_tab_undo *snap;
764 isl_size n_eq_i, n_ineq_j, n_extra;
765 isl_size total = isl_basic_map_dim(info[i].bmap, isl_dim_all);
766 isl_stat r;
767 isl_bool super;
769 if (total < 0)
770 return isl_change_error;
772 n_eq_i = isl_basic_map_n_equality(info[i].bmap);
773 n_ineq_j = isl_basic_map_n_inequality(info[j].bmap);
774 n_extra = isl_mat_rows(extra);
775 if (n_eq_i < 0 || n_ineq_j < 0 || n_extra < 0)
776 return isl_change_error;
778 if (isl_tab_extend_cons(info[i].tab, 1 + n_ineq_j + n_extra) < 0)
779 return isl_change_error;
781 snap = isl_tab_snap(info[i].tab);
783 if (isl_tab_unrestrict(info[i].tab, n_eq_i + k) < 0)
784 return isl_change_error;
786 isl_seq_neg(info[i].bmap->ineq[k], info[i].bmap->ineq[k], 1 + total);
787 isl_int_sub_ui(info[i].bmap->ineq[k][0], info[i].bmap->ineq[k][0], 1);
788 r = isl_tab_add_ineq(info[i].tab, info[i].bmap->ineq[k]);
789 isl_seq_neg(info[i].bmap->ineq[k], info[i].bmap->ineq[k], 1 + total);
790 isl_int_sub_ui(info[i].bmap->ineq[k][0], info[i].bmap->ineq[k][0], 1);
791 if (r < 0)
792 return isl_change_error;
794 for (k = 0; k < n_ineq_j; ++k) {
795 if (info[j].ineq[k] != STATUS_VALID)
796 continue;
797 if (isl_tab_add_ineq(info[i].tab, info[j].bmap->ineq[k]) < 0)
798 return isl_change_error;
800 for (k = 0; k < n_extra; ++k) {
801 if (isl_tab_add_ineq(info[i].tab, extra->row[k]) < 0)
802 return isl_change_error;
804 if (isl_tab_detect_constants(info[i].tab) < 0)
805 return isl_change_error;
807 super = contains(&info[j], info[i].tab);
808 if (super < 0)
809 return isl_change_error;
810 if (super)
811 return fuse(i, j, info, extra, 0, 0);
813 if (isl_tab_rollback(info[i].tab, snap) < 0)
814 return isl_change_error;
816 return isl_change_none;
819 /* Given an affine transformation matrix "T", does row "row" represent
820 * anything other than a unit vector (possibly shifted by a constant)
821 * that is not involved in any of the other rows?
823 * That is, if a constraint involves the variable corresponding to
824 * the row, then could its preimage by "T" have any coefficients
825 * that are different from those in the original constraint?
827 static int not_unique_unit_row(__isl_keep isl_mat *T, int row)
829 int i, j;
830 int len = T->n_col - 1;
832 i = isl_seq_first_non_zero(T->row[row] + 1, len);
833 if (i < 0)
834 return 1;
835 if (!isl_int_is_one(T->row[row][1 + i]) &&
836 !isl_int_is_negone(T->row[row][1 + i]))
837 return 1;
839 j = isl_seq_first_non_zero(T->row[row] + 1 + i + 1, len - (i + 1));
840 if (j >= 0)
841 return 1;
843 for (j = 1; j < T->n_row; ++j) {
844 if (j == row)
845 continue;
846 if (!isl_int_is_zero(T->row[j][1 + i]))
847 return 1;
850 return 0;
853 /* Does inequality constraint "ineq" of "bmap" involve any of
854 * the variables marked in "affected"?
855 * "total" is the total number of variables, i.e., the number
856 * of entries in "affected".
858 static isl_bool is_affected(__isl_keep isl_basic_map *bmap, int ineq,
859 int *affected, int total)
861 int i;
863 for (i = 0; i < total; ++i) {
864 if (!affected[i])
865 continue;
866 if (!isl_int_is_zero(bmap->ineq[ineq][1 + i]))
867 return isl_bool_true;
870 return isl_bool_false;
873 /* Given the compressed version of inequality constraint "ineq"
874 * of info->bmap in "v", check if the constraint can be tightened,
875 * where the compression is based on an equality constraint valid
876 * for info->tab.
877 * If so, add the tightened version of the inequality constraint
878 * to info->tab. "v" may be modified by this function.
880 * That is, if the compressed constraint is of the form
882 * m f() + c >= 0
884 * with 0 < c < m, then it is equivalent to
886 * f() >= 0
888 * This means that c can also be subtracted from the original,
889 * uncompressed constraint without affecting the integer points
890 * in info->tab. Add this tightened constraint as an extra row
891 * to info->tab to make this information explicitly available.
893 static __isl_give isl_vec *try_tightening(struct isl_coalesce_info *info,
894 int ineq, __isl_take isl_vec *v)
896 isl_ctx *ctx;
897 isl_stat r;
899 if (!v)
900 return NULL;
902 ctx = isl_vec_get_ctx(v);
903 isl_seq_gcd(v->el + 1, v->size - 1, &ctx->normalize_gcd);
904 if (isl_int_is_zero(ctx->normalize_gcd) ||
905 isl_int_is_one(ctx->normalize_gcd)) {
906 return v;
909 v = isl_vec_cow(v);
910 if (!v)
911 return NULL;
913 isl_int_fdiv_r(v->el[0], v->el[0], ctx->normalize_gcd);
914 if (isl_int_is_zero(v->el[0]))
915 return v;
917 if (isl_tab_extend_cons(info->tab, 1) < 0)
918 return isl_vec_free(v);
920 isl_int_sub(info->bmap->ineq[ineq][0],
921 info->bmap->ineq[ineq][0], v->el[0]);
922 r = isl_tab_add_ineq(info->tab, info->bmap->ineq[ineq]);
923 isl_int_add(info->bmap->ineq[ineq][0],
924 info->bmap->ineq[ineq][0], v->el[0]);
926 if (r < 0)
927 return isl_vec_free(v);
929 return v;
932 /* Tighten the (non-redundant) constraints on the facet represented
933 * by info->tab.
934 * In particular, on input, info->tab represents the result
935 * of relaxing the "n" inequality constraints of info->bmap in "relaxed"
936 * by one, i.e., replacing f_i >= 0 by f_i + 1 >= 0, and then
937 * replacing the one at index "l" by the corresponding equality,
938 * i.e., f_k + 1 = 0, with k = relaxed[l].
940 * Compute a variable compression from the equality constraint f_k + 1 = 0
941 * and use it to tighten the other constraints of info->bmap
942 * (that is, all constraints that have not been relaxed),
943 * updating info->tab (and leaving info->bmap untouched).
944 * The compression handles essentially two cases, one where a variable
945 * is assigned a fixed value and can therefore be eliminated, and one
946 * where one variable is a shifted multiple of some other variable and
947 * can therefore be replaced by that multiple.
948 * Gaussian elimination would also work for the first case, but for
949 * the second case, the effectiveness would depend on the order
950 * of the variables.
951 * After compression, some of the constraints may have coefficients
952 * with a common divisor. If this divisor does not divide the constant
953 * term, then the constraint can be tightened.
954 * The tightening is performed on the tableau info->tab by introducing
955 * extra (temporary) constraints.
957 * Only constraints that are possibly affected by the compression are
958 * considered. In particular, if the constraint only involves variables
959 * that are directly mapped to a distinct set of other variables, then
960 * no common divisor can be introduced and no tightening can occur.
962 * It is important to only consider the non-redundant constraints
963 * since the facet constraint has been relaxed prior to the call
964 * to this function, meaning that the constraints that were redundant
965 * prior to the relaxation may no longer be redundant.
966 * These constraints will be ignored in the fused result, so
967 * the fusion detection should not exploit them.
969 static isl_stat tighten_on_relaxed_facet(struct isl_coalesce_info *info,
970 int n, int *relaxed, int l)
972 isl_size total;
973 isl_ctx *ctx;
974 isl_vec *v = NULL;
975 isl_mat *T;
976 int i;
977 int k;
978 int *affected;
980 k = relaxed[l];
981 ctx = isl_basic_map_get_ctx(info->bmap);
982 total = isl_basic_map_dim(info->bmap, isl_dim_all);
983 if (total < 0)
984 return isl_stat_error;
985 isl_int_add_ui(info->bmap->ineq[k][0], info->bmap->ineq[k][0], 1);
986 T = isl_mat_sub_alloc6(ctx, info->bmap->ineq, k, 1, 0, 1 + total);
987 T = isl_mat_variable_compression(T, NULL);
988 isl_int_sub_ui(info->bmap->ineq[k][0], info->bmap->ineq[k][0], 1);
989 if (!T)
990 return isl_stat_error;
991 if (T->n_col == 0) {
992 isl_mat_free(T);
993 return isl_stat_ok;
996 affected = isl_alloc_array(ctx, int, total);
997 if (!affected)
998 goto error;
1000 for (i = 0; i < total; ++i)
1001 affected[i] = not_unique_unit_row(T, 1 + i);
1003 for (i = 0; i < info->bmap->n_ineq; ++i) {
1004 isl_bool handle;
1005 if (any(relaxed, n, i))
1006 continue;
1007 if (info->ineq[i] == STATUS_REDUNDANT)
1008 continue;
1009 handle = is_affected(info->bmap, i, affected, total);
1010 if (handle < 0)
1011 goto error;
1012 if (!handle)
1013 continue;
1014 v = isl_vec_alloc(ctx, 1 + total);
1015 if (!v)
1016 goto error;
1017 isl_seq_cpy(v->el, info->bmap->ineq[i], 1 + total);
1018 v = isl_vec_mat_product(v, isl_mat_copy(T));
1019 v = try_tightening(info, i, v);
1020 isl_vec_free(v);
1021 if (!v)
1022 goto error;
1025 isl_mat_free(T);
1026 free(affected);
1027 return isl_stat_ok;
1028 error:
1029 isl_mat_free(T);
1030 free(affected);
1031 return isl_stat_error;
1034 /* Replace the basic maps "i" and "j" by an extension of "i"
1035 * along the "n" inequality constraints in "relax" by one.
1036 * The tableau info[i].tab has already been extended.
1037 * Extend info[i].bmap accordingly by relaxing all constraints in "relax"
1038 * by one.
1039 * Each integer division that does not have exactly the same
1040 * definition in "i" and "j" is marked unknown and the basic map
1041 * is scheduled to be simplified in an attempt to recover
1042 * the integer division definition.
1043 * Place the extension in the position that is the smallest of i and j.
1045 static enum isl_change extend(int i, int j, int n, int *relax,
1046 struct isl_coalesce_info *info)
1048 int l;
1049 isl_size total;
1051 info[i].bmap = isl_basic_map_cow(info[i].bmap);
1052 total = isl_basic_map_dim(info[i].bmap, isl_dim_all);
1053 if (total < 0)
1054 return isl_change_error;
1055 for (l = 0; l < info[i].bmap->n_div; ++l)
1056 if (!isl_seq_eq(info[i].bmap->div[l],
1057 info[j].bmap->div[l], 1 + 1 + total)) {
1058 isl_int_set_si(info[i].bmap->div[l][0], 0);
1059 info[i].simplify = 1;
1061 for (l = 0; l < n; ++l)
1062 isl_int_add_ui(info[i].bmap->ineq[relax[l]][0],
1063 info[i].bmap->ineq[relax[l]][0], 1);
1064 ISL_F_CLR(info[i].bmap, ISL_BASIC_MAP_NO_REDUNDANT);
1065 ISL_F_SET(info[i].bmap, ISL_BASIC_MAP_FINAL);
1066 drop(&info[j]);
1067 info[i].modified = 1;
1068 if (j < i)
1069 exchange(&info[i], &info[j]);
1070 return isl_change_fuse;
1073 /* Basic map "i" has "n" inequality constraints (collected in "relax")
1074 * that are such that they include basic map "j" if they are relaxed
1075 * by one. All the other inequalities are valid for "j".
1076 * Check if basic map "j" forms an extension of basic map "i".
1078 * In particular, relax the constraints in "relax", compute the corresponding
1079 * facets one by one and check whether each of these is included
1080 * in the other basic map.
1081 * Before testing for inclusion, the constraints on each facet
1082 * are tightened to increase the chance of an inclusion being detected.
1083 * (Adding the valid constraints of "j" to the tableau of "i", as is done
1084 * in is_adj_ineq_extension, may further increase those chances, but this
1085 * is not currently done.)
1086 * If each facet is included, we know that relaxing the constraints extends
1087 * the basic map with exactly the other basic map (we already know that this
1088 * other basic map is included in the extension, because all other
1089 * inequality constraints are valid of "j") and we can replace the
1090 * two basic maps by this extension.
1092 * If any of the relaxed constraints turn out to be redundant, then bail out.
1093 * isl_tab_select_facet refuses to handle such constraints. It may be
1094 * possible to handle them anyway by making a distinction between
1095 * redundant constraints with a corresponding facet that still intersects
1096 * the set (allowing isl_tab_select_facet to handle them) and
1097 * those where the facet does not intersect the set (which can be ignored
1098 * because the empty facet is trivially included in the other disjunct).
1099 * However, relaxed constraints that turn out to be redundant should
1100 * be fairly rare and no such instance has been reported where
1101 * coalescing would be successful.
1102 * ____ _____
1103 * / || / |
1104 * / || / |
1105 * \ || => \ |
1106 * \ || \ |
1107 * \___|| \____|
1110 * \ |\
1111 * |\\ | \
1112 * | \\ | \
1113 * | | => | /
1114 * | / | /
1115 * |/ |/
1117 static enum isl_change is_relaxed_extension(int i, int j, int n, int *relax,
1118 struct isl_coalesce_info *info)
1120 int l;
1121 isl_bool super;
1122 struct isl_tab_undo *snap, *snap2;
1123 unsigned n_eq = info[i].bmap->n_eq;
1125 for (l = 0; l < n; ++l)
1126 if (isl_tab_is_equality(info[i].tab, n_eq + relax[l]))
1127 return isl_change_none;
1129 snap = isl_tab_snap(info[i].tab);
1130 for (l = 0; l < n; ++l)
1131 if (isl_tab_relax(info[i].tab, n_eq + relax[l]) < 0)
1132 return isl_change_error;
1133 for (l = 0; l < n; ++l) {
1134 if (!isl_tab_is_redundant(info[i].tab, n_eq + relax[l]))
1135 continue;
1136 if (isl_tab_rollback(info[i].tab, snap) < 0)
1137 return isl_change_error;
1138 return isl_change_none;
1140 snap2 = isl_tab_snap(info[i].tab);
1141 for (l = 0; l < n; ++l) {
1142 if (isl_tab_rollback(info[i].tab, snap2) < 0)
1143 return isl_change_error;
1144 if (isl_tab_select_facet(info[i].tab, n_eq + relax[l]) < 0)
1145 return isl_change_error;
1146 if (tighten_on_relaxed_facet(&info[i], n, relax, l) < 0)
1147 return isl_change_error;
1148 super = contains(&info[j], info[i].tab);
1149 if (super < 0)
1150 return isl_change_error;
1151 if (super)
1152 continue;
1153 if (isl_tab_rollback(info[i].tab, snap) < 0)
1154 return isl_change_error;
1155 return isl_change_none;
1158 if (isl_tab_rollback(info[i].tab, snap2) < 0)
1159 return isl_change_error;
1160 return extend(i, j, n, relax, info);
1163 /* Data structure that keeps track of the wrapping constraints
1164 * and of information to bound the coefficients of those constraints.
1166 * "failed" is set if wrapping has failed.
1167 * bound is set if we want to apply a bound on the coefficients
1168 * mat contains the wrapping constraints
1169 * max is the bound on the coefficients (if bound is set)
1171 struct isl_wraps {
1172 int failed;
1173 int bound;
1174 isl_mat *mat;
1175 isl_int max;
1178 /* Update wraps->max to be greater than or equal to the coefficients
1179 * in the equalities and inequalities of info->bmap that can be removed
1180 * if we end up applying wrapping.
1182 static isl_stat wraps_update_max(struct isl_wraps *wraps,
1183 struct isl_coalesce_info *info)
1185 int k;
1186 isl_int max_k;
1187 isl_size total = isl_basic_map_dim(info->bmap, isl_dim_all);
1189 if (total < 0)
1190 return isl_stat_error;
1191 isl_int_init(max_k);
1193 for (k = 0; k < info->bmap->n_eq; ++k) {
1194 if (info->eq[2 * k] == STATUS_VALID &&
1195 info->eq[2 * k + 1] == STATUS_VALID)
1196 continue;
1197 isl_seq_abs_max(info->bmap->eq[k] + 1, total, &max_k);
1198 if (isl_int_abs_gt(max_k, wraps->max))
1199 isl_int_set(wraps->max, max_k);
1202 for (k = 0; k < info->bmap->n_ineq; ++k) {
1203 if (info->ineq[k] == STATUS_VALID ||
1204 info->ineq[k] == STATUS_REDUNDANT)
1205 continue;
1206 isl_seq_abs_max(info->bmap->ineq[k] + 1, total, &max_k);
1207 if (isl_int_abs_gt(max_k, wraps->max))
1208 isl_int_set(wraps->max, max_k);
1211 isl_int_clear(max_k);
1213 return isl_stat_ok;
1216 /* Initialize the isl_wraps data structure.
1217 * If we want to bound the coefficients of the wrapping constraints,
1218 * we set wraps->max to the largest coefficient
1219 * in the equalities and inequalities that can be removed if we end up
1220 * applying wrapping.
1222 static isl_stat wraps_init(struct isl_wraps *wraps, __isl_take isl_mat *mat,
1223 struct isl_coalesce_info *info, int i, int j)
1225 isl_ctx *ctx;
1227 wraps->failed = 0;
1228 wraps->bound = 0;
1229 wraps->mat = mat;
1230 if (!mat)
1231 return isl_stat_error;
1232 wraps->mat->n_row = 0;
1233 ctx = isl_mat_get_ctx(mat);
1234 wraps->bound = isl_options_get_coalesce_bounded_wrapping(ctx);
1235 if (!wraps->bound)
1236 return isl_stat_ok;
1237 isl_int_init(wraps->max);
1238 isl_int_set_si(wraps->max, 0);
1239 if (wraps_update_max(wraps, &info[i]) < 0)
1240 return isl_stat_error;
1241 if (wraps_update_max(wraps, &info[j]) < 0)
1242 return isl_stat_error;
1244 return isl_stat_ok;
1247 /* Free the contents of the isl_wraps data structure.
1249 static void wraps_free(struct isl_wraps *wraps)
1251 isl_mat_free(wraps->mat);
1252 if (wraps->bound)
1253 isl_int_clear(wraps->max);
1256 /* Mark the wrapping as failed.
1258 static isl_stat wraps_mark_failed(struct isl_wraps *wraps)
1260 wraps->failed = 1;
1261 return isl_stat_ok;
1264 /* Is the wrapping constraint in row "row" allowed?
1266 * If wraps->bound is set, we check that none of the coefficients
1267 * is greater than wraps->max.
1269 static int allow_wrap(struct isl_wraps *wraps, int row)
1271 int i;
1273 if (!wraps->bound)
1274 return 1;
1276 for (i = 1; i < wraps->mat->n_col; ++i)
1277 if (isl_int_abs_gt(wraps->mat->row[row][i], wraps->max))
1278 return 0;
1280 return 1;
1283 /* Wrap "ineq" (or its opposite if "negate" is set) around "bound"
1284 * to include "set" and add the result in position "w" of "wraps".
1285 * "len" is the total number of coefficients in "bound" and "ineq".
1286 * Return 1 on success, 0 on failure and -1 on error.
1287 * Wrapping can fail if the result of wrapping is equal to "bound"
1288 * or if we want to bound the sizes of the coefficients and
1289 * the wrapped constraint does not satisfy this bound.
1291 static int add_wrap(struct isl_wraps *wraps, int w, isl_int *bound,
1292 isl_int *ineq, unsigned len, __isl_keep isl_set *set, int negate)
1294 isl_seq_cpy(wraps->mat->row[w], bound, len);
1295 if (negate) {
1296 isl_seq_neg(wraps->mat->row[w + 1], ineq, len);
1297 ineq = wraps->mat->row[w + 1];
1299 if (!isl_set_wrap_facet(set, wraps->mat->row[w], ineq))
1300 return -1;
1301 if (isl_seq_eq(wraps->mat->row[w], bound, len))
1302 return 0;
1303 if (!allow_wrap(wraps, w))
1304 return 0;
1305 return 1;
1308 /* This function has two modes of operations.
1310 * If "add_valid" is set, then all the constraints of info->bmap
1311 * (except the opposite of "bound") are valid for the other basic map.
1312 * In this case, attempts are made to wrap some of these valid constraints
1313 * to more tightly fit around "set". Only successful wrappings are recorded
1314 * and failed wrappings are ignored.
1316 * If "add_valid" is not set, then some of the constraints of info->bmap
1317 * are not valid for the other basic map, and only those are considered
1318 * for wrapping. In this case all attempted wrappings need to succeed.
1319 * Otherwise "wraps" is marked as failed.
1320 * Note that the constraints that are valid for the other basic map
1321 * will be added to the combined basic map by default, so there is
1322 * no need to wrap them.
1323 * The caller wrap_in_facets even relies on this function not wrapping
1324 * any constraints that are already valid.
1326 * Only consider constraints that are not redundant (as determined
1327 * by info->tab) and that are valid or invalid depending on "add_valid".
1328 * Wrap each constraint around "bound" such that it includes the whole
1329 * set "set" and append the resulting constraint to "wraps".
1330 * "wraps" is assumed to have been pre-allocated to the appropriate size.
1331 * wraps->n_row is the number of actual wrapped constraints that have
1332 * been added.
1333 * If any of the wrapping problems results in a constraint that is
1334 * identical to "bound", then this means that "set" is unbounded in such
1335 * a way that no wrapping is possible.
1336 * Similarly, if we want to bound the coefficients of the wrapping
1337 * constraints and a newly added wrapping constraint does not
1338 * satisfy the bound, then the wrapping is considered to have failed.
1339 * Note though that "wraps" is only marked failed if "add_valid" is not set.
1341 static isl_stat add_selected_wraps(struct isl_wraps *wraps,
1342 struct isl_coalesce_info *info, isl_int *bound, __isl_keep isl_set *set,
1343 int add_valid)
1345 int l, m;
1346 int w;
1347 int added;
1348 isl_basic_map *bmap = info->bmap;
1349 isl_size total = isl_basic_map_dim(bmap, isl_dim_all);
1350 unsigned len = 1 + total;
1352 if (total < 0)
1353 return isl_stat_error;
1355 w = wraps->mat->n_row;
1357 for (l = 0; l < bmap->n_ineq; ++l) {
1358 int is_valid = info->ineq[l] == STATUS_VALID;
1359 if ((!add_valid && is_valid) ||
1360 info->ineq[l] == STATUS_REDUNDANT)
1361 continue;
1362 if (isl_seq_is_neg(bound, bmap->ineq[l], len))
1363 continue;
1364 if (isl_seq_eq(bound, bmap->ineq[l], len))
1365 continue;
1366 if (isl_tab_is_redundant(info->tab, bmap->n_eq + l))
1367 continue;
1369 added = add_wrap(wraps, w, bound, bmap->ineq[l], len, set, 0);
1370 if (added < 0)
1371 return isl_stat_error;
1372 if (!added && !is_valid)
1373 goto unbounded;
1374 if (added)
1375 ++w;
1377 for (l = 0; l < bmap->n_eq; ++l) {
1378 if (isl_seq_is_neg(bound, bmap->eq[l], len))
1379 continue;
1380 if (isl_seq_eq(bound, bmap->eq[l], len))
1381 continue;
1383 for (m = 0; m < 2; ++m) {
1384 if (info->eq[2 * l + m] == STATUS_VALID)
1385 continue;
1386 added = add_wrap(wraps, w, bound, bmap->eq[l], len,
1387 set, !m);
1388 if (added < 0)
1389 return isl_stat_error;
1390 if (!added)
1391 goto unbounded;
1392 ++w;
1396 wraps->mat->n_row = w;
1397 return isl_stat_ok;
1398 unbounded:
1399 return wraps_mark_failed(wraps);
1402 /* For each constraint in info->bmap that is not redundant (as determined
1403 * by info->tab) and that is not a valid constraint for the other basic map,
1404 * wrap the constraint around "bound" such that it includes the whole
1405 * set "set" and append the resulting constraint to "wraps".
1406 * Note that the constraints that are valid for the other basic map
1407 * will be added to the combined basic map by default, so there is
1408 * no need to wrap them.
1409 * The caller wrap_in_facets even relies on this function not wrapping
1410 * any constraints that are already valid.
1411 * "wraps" is assumed to have been pre-allocated to the appropriate size.
1412 * wraps->n_row is the number of actual wrapped constraints that have
1413 * been added.
1414 * If any of the wrapping problems results in a constraint that is
1415 * identical to "bound", then this means that "set" is unbounded in such
1416 * a way that no wrapping is possible. If this happens then "wraps"
1417 * is marked as failed.
1418 * Similarly, if we want to bound the coefficients of the wrapping
1419 * constraints and a newly added wrapping constraint does not
1420 * satisfy the bound, then "wraps" is also marked as failed.
1422 static isl_stat add_wraps(struct isl_wraps *wraps,
1423 struct isl_coalesce_info *info, isl_int *bound, __isl_keep isl_set *set)
1425 return add_selected_wraps(wraps, info, bound, set, 0);
1428 /* Check if the constraints in "wraps" from "first" until the last
1429 * are all valid for the basic set represented by "tab",
1430 * dropping the invalid constraints if "keep" is set and
1431 * marking the wrapping as failed if "keep" is not set and
1432 * any constraint turns out to be invalid.
1434 static isl_stat check_wraps(struct isl_wraps *wraps, int first,
1435 struct isl_tab *tab, int keep)
1437 int i;
1439 for (i = wraps->mat->n_row - 1; i >= first; --i) {
1440 enum isl_ineq_type type;
1441 type = isl_tab_ineq_type(tab, wraps->mat->row[i]);
1442 if (type == isl_ineq_error)
1443 return isl_stat_error;
1444 if (type == isl_ineq_redundant)
1445 continue;
1446 if (!keep)
1447 return wraps_mark_failed(wraps);
1448 wraps->mat = isl_mat_drop_rows(wraps->mat, i, 1);
1449 if (!wraps->mat)
1450 return isl_stat_error;
1453 return isl_stat_ok;
1456 /* Return a set that corresponds to the non-redundant constraints
1457 * (as recorded in tab) of bmap.
1459 * It's important to remove the redundant constraints as some
1460 * of the other constraints may have been modified after the
1461 * constraints were marked redundant.
1462 * In particular, a constraint may have been relaxed.
1463 * Redundant constraints are ignored when a constraint is relaxed
1464 * and should therefore continue to be ignored ever after.
1465 * Otherwise, the relaxation might be thwarted by some of
1466 * these constraints.
1468 * Update the underlying set to ensure that the dimension doesn't change.
1469 * Otherwise the integer divisions could get dropped if the tab
1470 * turns out to be empty.
1472 static __isl_give isl_set *set_from_updated_bmap(__isl_keep isl_basic_map *bmap,
1473 struct isl_tab *tab)
1475 isl_basic_set *bset;
1477 bmap = isl_basic_map_copy(bmap);
1478 bset = isl_basic_map_underlying_set(bmap);
1479 bset = isl_basic_set_cow(bset);
1480 bset = isl_basic_set_update_from_tab(bset, tab);
1481 return isl_set_from_basic_set(bset);
1484 /* Does "info" have any cut constraints that are redundant?
1486 static isl_bool has_redundant_cuts(struct isl_coalesce_info *info)
1488 int l;
1489 isl_size n_eq, n_ineq;
1491 n_eq = isl_basic_map_n_equality(info->bmap);
1492 n_ineq = isl_basic_map_n_inequality(info->bmap);
1493 if (n_eq < 0 || n_ineq < 0)
1494 return isl_bool_error;
1495 for (l = 0; l < n_ineq; ++l) {
1496 int red;
1498 if (info->ineq[l] != STATUS_CUT)
1499 continue;
1500 red = isl_tab_is_redundant(info->tab, n_eq + l);
1501 if (red < 0)
1502 return isl_bool_error;
1503 if (red)
1504 return isl_bool_true;
1507 return isl_bool_false;
1510 /* Wrap some constraints of info->bmap that bound the facet defined
1511 * by inequality "k" around (the opposite of) this inequality to
1512 * include "set". "bound" may be used to store the negated inequality.
1514 * If "add_valid" is set, then all ridges are already valid and
1515 * the purpose is to wrap "set" more tightly. In this case,
1516 * wrapping doesn't fail, although it is possible that no constraint
1517 * gets wrapped.
1519 * If "add_valid" is not set, then some of the ridges are cut constraints
1520 * and only those are wrapped around "set".
1522 * Since the wrapped constraints are not guaranteed to contain the whole
1523 * of info->bmap, we check them in check_wraps.
1524 * If any of the wrapped constraints turn out to be invalid, then
1525 * check_wraps will mark "wraps" as failed if "add_valid" is not set.
1526 * If "add_valid" is set, then the offending constraints are
1527 * simply removed.
1529 * If the facet turns out to be empty, then no wrapping can be performed.
1530 * This is considered a failure, unless "add_valid" is set.
1532 * If any of the cut constraints of info->bmap turn out
1533 * to be redundant with respect to other constraints
1534 * then these will neither be wrapped nor added directly to the result.
1535 * The result may therefore not be correct.
1536 * Skip wrapping and mark "wraps" as failed in this case.
1538 static isl_stat add_selected_wraps_around_facet(struct isl_wraps *wraps,
1539 struct isl_coalesce_info *info, int k, isl_int *bound,
1540 __isl_keep isl_set *set, int add_valid)
1542 isl_bool nowrap;
1543 struct isl_tab_undo *snap;
1544 int n;
1545 isl_size total = isl_basic_map_dim(info->bmap, isl_dim_all);
1547 if (total < 0)
1548 return isl_stat_error;
1550 snap = isl_tab_snap(info->tab);
1552 if (isl_tab_select_facet(info->tab, info->bmap->n_eq + k) < 0)
1553 return isl_stat_error;
1554 if (isl_tab_detect_redundant(info->tab) < 0)
1555 return isl_stat_error;
1556 if (info->tab->empty) {
1557 if (isl_tab_rollback(info->tab, snap) < 0)
1558 return isl_stat_error;
1559 if (!add_valid)
1560 return wraps_mark_failed(wraps);
1561 return isl_stat_ok;
1563 nowrap = has_redundant_cuts(info);
1564 if (nowrap < 0)
1565 return isl_stat_error;
1567 n = wraps->mat->n_row;
1568 if (!nowrap) {
1569 isl_seq_neg(bound, info->bmap->ineq[k], 1 + total);
1571 if (add_selected_wraps(wraps, info, bound, set, add_valid) < 0)
1572 return isl_stat_error;
1575 if (isl_tab_rollback(info->tab, snap) < 0)
1576 return isl_stat_error;
1577 if (nowrap)
1578 return wraps_mark_failed(wraps);
1579 if (check_wraps(wraps, n, info->tab, add_valid) < 0)
1580 return isl_stat_error;
1582 return isl_stat_ok;
1585 /* Wrap the constraints of info->bmap that bound the facet defined
1586 * by inequality "k" around (the opposite of) this inequality to
1587 * include "set". "bound" may be used to store the negated inequality.
1588 * If any of the wrapped constraints turn out to be invalid for info->bmap
1589 * itself, then mark "wraps" as failed.
1591 static isl_stat add_wraps_around_facet(struct isl_wraps *wraps,
1592 struct isl_coalesce_info *info, int k, isl_int *bound,
1593 __isl_keep isl_set *set)
1595 return add_selected_wraps_around_facet(wraps, info, k, bound, set, 0);
1598 /* Wrap the (valid) constraints of info->bmap that bound the facet defined
1599 * by inequality "k" around (the opposite of) this inequality to
1600 * include "set" more tightly.
1601 * "bound" may be used to store the negated inequality.
1602 * Remove any wrapping constraints that turn out to be invalid
1603 * for info->bmap itself.
1605 static isl_stat add_valid_wraps_around_facet(struct isl_wraps *wraps,
1606 struct isl_coalesce_info *info, int k, isl_int *bound,
1607 __isl_keep isl_set *set)
1609 return add_selected_wraps_around_facet(wraps, info, k, bound, set, 1);
1612 /* Basic map "i" has an inequality (say "k") that is adjacent
1613 * to some inequality of basic map "j". All the other inequalities
1614 * are valid for "j".
1615 * Check if basic map "j" forms an extension of basic map "i".
1617 * Note that this function is only called if some of the equalities or
1618 * inequalities of basic map "j" do cut basic map "i". The function is
1619 * correct even if there are no such cut constraints, but in that case
1620 * the additional checks performed by this function are overkill.
1622 * First try and wrap the ridges of "k" around "j".
1623 * Note that those ridges are already valid for "j",
1624 * but the wrapped versions may wrap "j" more tightly,
1625 * increasing the chances of "j" being detected as an extension of "i"
1627 static enum isl_change is_adj_ineq_extension(int i, int j,
1628 struct isl_coalesce_info *info)
1630 int k;
1631 enum isl_change change;
1632 isl_size total;
1633 isl_size n_eq_i, n_ineq_i;
1634 struct isl_wraps wraps;
1635 isl_ctx *ctx;
1636 isl_mat *mat;
1637 isl_vec *bound;
1638 isl_set *set_j;
1639 isl_stat r;
1641 k = find_ineq(&info[i], STATUS_ADJ_INEQ);
1642 if (k < 0)
1643 isl_die(isl_basic_map_get_ctx(info[i].bmap), isl_error_internal,
1644 "info[i].ineq should have exactly one STATUS_ADJ_INEQ",
1645 return isl_change_error);
1647 total = isl_basic_map_dim(info[i].bmap, isl_dim_all);
1648 n_eq_i = isl_basic_map_n_equality(info[i].bmap);
1649 n_ineq_i = isl_basic_map_n_inequality(info[i].bmap);
1650 if (total < 0 || n_eq_i < 0 || n_ineq_i < 0)
1651 return isl_change_error;
1653 set_j = set_from_updated_bmap(info[j].bmap, info[j].tab);
1654 ctx = isl_basic_map_get_ctx(info[i].bmap);
1655 bound = isl_vec_alloc(ctx, 1 + total);
1656 mat = isl_mat_alloc(ctx, 2 * n_eq_i + n_ineq_i, 1 + total);
1657 if (wraps_init(&wraps, mat, info, i, j) < 0)
1658 goto error;
1659 if (!bound || !set_j)
1660 goto error;
1661 r = add_valid_wraps_around_facet(&wraps, &info[i], k, bound->el, set_j);
1662 if (r < 0)
1663 goto error;
1665 change = is_adj_ineq_extension_with_wraps(i, j, k, info, wraps.mat);
1667 wraps_free(&wraps);
1668 isl_vec_free(bound);
1669 isl_set_free(set_j);
1671 return change;
1672 error:
1673 wraps_free(&wraps);
1674 isl_vec_free(bound);
1675 isl_set_free(set_j);
1676 return isl_change_error;
1679 /* Both basic maps have at least one inequality with and adjacent
1680 * (but opposite) inequality in the other basic map.
1681 * Check that there are no cut constraints and that there is only
1682 * a single pair of adjacent inequalities.
1683 * If so, we can replace the pair by a single basic map described
1684 * by all but the pair of adjacent inequalities.
1685 * Any additional points introduced lie strictly between the two
1686 * adjacent hyperplanes and can therefore be integral.
1688 * ____ _____
1689 * / ||\ / \
1690 * / || \ / \
1691 * \ || \ => \ \
1692 * \ || / \ /
1693 * \___||_/ \_____/
1695 * The test for a single pair of adjacent inequalities is important
1696 * for avoiding the combination of two basic maps like the following
1698 * /|
1699 * / |
1700 * /__|
1701 * _____
1702 * | |
1703 * | |
1704 * |___|
1706 * If there are some cut constraints on one side, then we may
1707 * still be able to fuse the two basic maps, but we need to perform
1708 * some additional checks in is_adj_ineq_extension.
1710 static enum isl_change check_adj_ineq(int i, int j,
1711 struct isl_coalesce_info *info)
1713 int count_i, count_j;
1714 int cut_i, cut_j;
1716 count_i = count_ineq(&info[i], STATUS_ADJ_INEQ);
1717 count_j = count_ineq(&info[j], STATUS_ADJ_INEQ);
1719 if (count_i != 1 && count_j != 1)
1720 return isl_change_none;
1722 cut_i = any_eq(&info[i], STATUS_CUT) || any_ineq(&info[i], STATUS_CUT);
1723 cut_j = any_eq(&info[j], STATUS_CUT) || any_ineq(&info[j], STATUS_CUT);
1725 if (!cut_i && !cut_j && count_i == 1 && count_j == 1)
1726 return fuse(i, j, info, NULL, 0, 0);
1728 if (count_i == 1 && !cut_i)
1729 return is_adj_ineq_extension(i, j, info);
1731 if (count_j == 1 && !cut_j)
1732 return is_adj_ineq_extension(j, i, info);
1734 return isl_change_none;
1737 /* Given a basic set i with a constraint k that is adjacent to
1738 * basic set j, check if we can wrap
1739 * both the facet corresponding to k (if "wrap_facet" is set) and basic map j
1740 * (always) around their ridges to include the other set.
1741 * If so, replace the pair of basic sets by their union.
1743 * All constraints of i (except k) are assumed to be valid or
1744 * cut constraints for j.
1745 * Wrapping the cut constraints to include basic map j may result
1746 * in constraints that are no longer valid of basic map i
1747 * we have to check that the resulting wrapping constraints are valid for i.
1748 * If "wrap_facet" is not set, then all constraints of i (except k)
1749 * are assumed to be valid for j.
1750 * ____ _____
1751 * / | / \
1752 * / || / |
1753 * \ || => \ |
1754 * \ || \ |
1755 * \___|| \____|
1758 static enum isl_change can_wrap_in_facet(int i, int j, int k,
1759 struct isl_coalesce_info *info, int wrap_facet)
1761 enum isl_change change = isl_change_none;
1762 struct isl_wraps wraps;
1763 isl_ctx *ctx;
1764 isl_mat *mat;
1765 struct isl_set *set_i = NULL;
1766 struct isl_set *set_j = NULL;
1767 struct isl_vec *bound = NULL;
1768 isl_size total = isl_basic_map_dim(info[i].bmap, isl_dim_all);
1770 if (total < 0)
1771 return isl_change_error;
1772 set_i = set_from_updated_bmap(info[i].bmap, info[i].tab);
1773 set_j = set_from_updated_bmap(info[j].bmap, info[j].tab);
1774 ctx = isl_basic_map_get_ctx(info[i].bmap);
1775 mat = isl_mat_alloc(ctx, 2 * (info[i].bmap->n_eq + info[j].bmap->n_eq) +
1776 info[i].bmap->n_ineq + info[j].bmap->n_ineq,
1777 1 + total);
1778 if (wraps_init(&wraps, mat, info, i, j) < 0)
1779 goto error;
1780 bound = isl_vec_alloc(ctx, 1 + total);
1781 if (!set_i || !set_j || !bound)
1782 goto error;
1784 isl_seq_cpy(bound->el, info[i].bmap->ineq[k], 1 + total);
1785 isl_int_add_ui(bound->el[0], bound->el[0], 1);
1786 isl_seq_normalize(ctx, bound->el, 1 + total);
1788 isl_seq_cpy(wraps.mat->row[0], bound->el, 1 + total);
1789 wraps.mat->n_row = 1;
1791 if (add_wraps(&wraps, &info[j], bound->el, set_i) < 0)
1792 goto error;
1793 if (wraps.failed)
1794 goto unbounded;
1796 if (wrap_facet) {
1797 if (add_wraps_around_facet(&wraps, &info[i], k,
1798 bound->el, set_j) < 0)
1799 goto error;
1800 if (wraps.failed)
1801 goto unbounded;
1804 change = fuse(i, j, info, wraps.mat, 0, 0);
1806 unbounded:
1807 wraps_free(&wraps);
1809 isl_set_free(set_i);
1810 isl_set_free(set_j);
1812 isl_vec_free(bound);
1814 return change;
1815 error:
1816 wraps_free(&wraps);
1817 isl_vec_free(bound);
1818 isl_set_free(set_i);
1819 isl_set_free(set_j);
1820 return isl_change_error;
1823 /* Given a cut constraint t(x) >= 0 of basic map i, stored in row "w"
1824 * of wrap.mat, replace it by its relaxed version t(x) + 1 >= 0, and
1825 * add wrapping constraints to wrap.mat for all constraints
1826 * of basic map j that bound the part of basic map j that sticks out
1827 * of the cut constraint.
1828 * "set_i" is the underlying set of basic map i.
1829 * If any wrapping fails, then wraps->mat.n_row is reset to zero.
1831 * In particular, we first intersect basic map j with t(x) + 1 = 0.
1832 * If the result is empty, then t(x) >= 0 was actually a valid constraint
1833 * (with respect to the integer points), so we add t(x) >= 0 instead.
1834 * Otherwise, we wrap the constraints of basic map j that are not
1835 * redundant in this intersection and that are not already valid
1836 * for basic map i over basic map i.
1837 * Note that it is sufficient to wrap the constraints to include
1838 * basic map i, because we will only wrap the constraints that do
1839 * not include basic map i already. The wrapped constraint will
1840 * therefore be more relaxed compared to the original constraint.
1841 * Since the original constraint is valid for basic map j, so is
1842 * the wrapped constraint.
1844 static isl_stat wrap_in_facet(struct isl_wraps *wraps, int w,
1845 struct isl_coalesce_info *info_j, __isl_keep isl_set *set_i,
1846 struct isl_tab_undo *snap)
1848 isl_int_add_ui(wraps->mat->row[w][0], wraps->mat->row[w][0], 1);
1849 if (isl_tab_add_eq(info_j->tab, wraps->mat->row[w]) < 0)
1850 return isl_stat_error;
1851 if (isl_tab_detect_redundant(info_j->tab) < 0)
1852 return isl_stat_error;
1854 if (info_j->tab->empty)
1855 isl_int_sub_ui(wraps->mat->row[w][0], wraps->mat->row[w][0], 1);
1856 else if (add_wraps(wraps, info_j, wraps->mat->row[w], set_i) < 0)
1857 return isl_stat_error;
1859 if (isl_tab_rollback(info_j->tab, snap) < 0)
1860 return isl_stat_error;
1862 return isl_stat_ok;
1865 /* Given a pair of basic maps i and j such that j sticks out
1866 * of i at n cut constraints, each time by at most one,
1867 * try to compute wrapping constraints and replace the two
1868 * basic maps by a single basic map.
1869 * The other constraints of i are assumed to be valid for j.
1870 * "set_i" is the underlying set of basic map i.
1871 * "wraps" has been initialized to be of the right size.
1873 * For each cut constraint t(x) >= 0 of i, we add the relaxed version
1874 * t(x) + 1 >= 0, along with wrapping constraints for all constraints
1875 * of basic map j that bound the part of basic map j that sticks out
1876 * of the cut constraint.
1878 * If any wrapping fails, i.e., if we cannot wrap to touch
1879 * the union, then we give up.
1880 * Otherwise, the pair of basic maps is replaced by their union.
1882 static enum isl_change try_wrap_in_facets(int i, int j,
1883 struct isl_coalesce_info *info, struct isl_wraps *wraps,
1884 __isl_keep isl_set *set_i)
1886 int k, l, w;
1887 isl_size total;
1888 struct isl_tab_undo *snap;
1890 total = isl_basic_map_dim(info[i].bmap, isl_dim_all);
1891 if (total < 0)
1892 return isl_change_error;
1894 snap = isl_tab_snap(info[j].tab);
1896 for (k = 0; k < info[i].bmap->n_eq; ++k) {
1897 for (l = 0; l < 2; ++l) {
1898 if (info[i].eq[2 * k + l] != STATUS_CUT)
1899 continue;
1900 w = wraps->mat->n_row++;
1901 if (l == 0)
1902 isl_seq_neg(wraps->mat->row[w],
1903 info[i].bmap->eq[k], 1 + total);
1904 else
1905 isl_seq_cpy(wraps->mat->row[w],
1906 info[i].bmap->eq[k], 1 + total);
1907 if (wrap_in_facet(wraps, w, &info[j], set_i, snap) < 0)
1908 return isl_change_error;
1910 if (wraps->failed)
1911 return isl_change_none;
1915 for (k = 0; k < info[i].bmap->n_ineq; ++k) {
1916 if (info[i].ineq[k] != STATUS_CUT)
1917 continue;
1918 w = wraps->mat->n_row++;
1919 isl_seq_cpy(wraps->mat->row[w],
1920 info[i].bmap->ineq[k], 1 + total);
1921 if (wrap_in_facet(wraps, w, &info[j], set_i, snap) < 0)
1922 return isl_change_error;
1924 if (wraps->failed)
1925 return isl_change_none;
1928 return fuse(i, j, info, wraps->mat, 0, 1);
1931 /* Given a pair of basic maps i and j such that j sticks out
1932 * of i at n cut constraints, each time by at most one,
1933 * try to compute wrapping constraints and replace the two
1934 * basic maps by a single basic map.
1935 * The other constraints of i are assumed to be valid for j.
1937 * The core computation is performed by try_wrap_in_facets.
1938 * This function simply extracts an underlying set representation
1939 * of basic map i and initializes the data structure for keeping
1940 * track of wrapping constraints.
1942 static enum isl_change wrap_in_facets(int i, int j, int n,
1943 struct isl_coalesce_info *info)
1945 enum isl_change change = isl_change_none;
1946 struct isl_wraps wraps;
1947 isl_ctx *ctx;
1948 isl_mat *mat;
1949 isl_set *set_i = NULL;
1950 isl_size total = isl_basic_map_dim(info[i].bmap, isl_dim_all);
1951 int max_wrap;
1953 if (total < 0)
1954 return isl_change_error;
1955 if (isl_tab_extend_cons(info[j].tab, 1) < 0)
1956 return isl_change_error;
1958 max_wrap = 1 + 2 * info[j].bmap->n_eq + info[j].bmap->n_ineq;
1959 max_wrap *= n;
1961 set_i = set_from_updated_bmap(info[i].bmap, info[i].tab);
1962 ctx = isl_basic_map_get_ctx(info[i].bmap);
1963 mat = isl_mat_alloc(ctx, max_wrap, 1 + total);
1964 if (wraps_init(&wraps, mat, info, i, j) < 0)
1965 goto error;
1966 if (!set_i)
1967 goto error;
1969 change = try_wrap_in_facets(i, j, info, &wraps, set_i);
1971 wraps_free(&wraps);
1972 isl_set_free(set_i);
1974 return change;
1975 error:
1976 wraps_free(&wraps);
1977 isl_set_free(set_i);
1978 return isl_change_error;
1981 /* Return the effect of inequality "ineq" on the tableau "tab",
1982 * after relaxing the constant term of "ineq" by one.
1984 static enum isl_ineq_type type_of_relaxed(struct isl_tab *tab, isl_int *ineq)
1986 enum isl_ineq_type type;
1988 isl_int_add_ui(ineq[0], ineq[0], 1);
1989 type = isl_tab_ineq_type(tab, ineq);
1990 isl_int_sub_ui(ineq[0], ineq[0], 1);
1992 return type;
1995 /* Given two basic sets i and j,
1996 * check if relaxing all the cut constraints of i by one turns
1997 * them into valid constraint for j and check if we can wrap in
1998 * the bits that are sticking out.
1999 * If so, replace the pair by their union.
2001 * We first check if all relaxed cut inequalities of i are valid for j
2002 * and then try to wrap in the intersections of the relaxed cut inequalities
2003 * with j.
2005 * During this wrapping, we consider the points of j that lie at a distance
2006 * of exactly 1 from i. In particular, we ignore the points that lie in
2007 * between this lower-dimensional space and the basic map i.
2008 * We can therefore only apply this to integer maps.
2009 * ____ _____
2010 * / ___|_ / \
2011 * / | | / |
2012 * \ | | => \ |
2013 * \|____| \ |
2014 * \___| \____/
2016 * _____ ______
2017 * | ____|_ | \
2018 * | | | | |
2019 * | | | => | |
2020 * |_| | | |
2021 * |_____| \______|
2023 * _______
2024 * | |
2025 * | |\ |
2026 * | | \ |
2027 * | | \ |
2028 * | | \|
2029 * | | \
2030 * | |_____\
2031 * | |
2032 * |_______|
2034 * Wrapping can fail if the result of wrapping one of the facets
2035 * around its edges does not produce any new facet constraint.
2036 * In particular, this happens when we try to wrap in unbounded sets.
2038 * _______________________________________________________________________
2040 * | ___
2041 * | | |
2042 * |_| |_________________________________________________________________
2043 * |___|
2045 * The following is not an acceptable result of coalescing the above two
2046 * sets as it includes extra integer points.
2047 * _______________________________________________________________________
2049 * |
2050 * |
2052 * \______________________________________________________________________
2054 static enum isl_change can_wrap_in_set(int i, int j,
2055 struct isl_coalesce_info *info)
2057 int k, l;
2058 int n;
2059 isl_size total;
2061 if (ISL_F_ISSET(info[i].bmap, ISL_BASIC_MAP_RATIONAL) ||
2062 ISL_F_ISSET(info[j].bmap, ISL_BASIC_MAP_RATIONAL))
2063 return isl_change_none;
2065 n = count_eq(&info[i], STATUS_CUT) + count_ineq(&info[i], STATUS_CUT);
2066 if (n == 0)
2067 return isl_change_none;
2069 total = isl_basic_map_dim(info[i].bmap, isl_dim_all);
2070 if (total < 0)
2071 return isl_change_error;
2072 for (k = 0; k < info[i].bmap->n_eq; ++k) {
2073 for (l = 0; l < 2; ++l) {
2074 enum isl_ineq_type type;
2076 if (info[i].eq[2 * k + l] != STATUS_CUT)
2077 continue;
2079 if (l == 0)
2080 isl_seq_neg(info[i].bmap->eq[k],
2081 info[i].bmap->eq[k], 1 + total);
2082 type = type_of_relaxed(info[j].tab,
2083 info[i].bmap->eq[k]);
2084 if (l == 0)
2085 isl_seq_neg(info[i].bmap->eq[k],
2086 info[i].bmap->eq[k], 1 + total);
2087 if (type == isl_ineq_error)
2088 return isl_change_error;
2089 if (type != isl_ineq_redundant)
2090 return isl_change_none;
2094 for (k = 0; k < info[i].bmap->n_ineq; ++k) {
2095 enum isl_ineq_type type;
2097 if (info[i].ineq[k] != STATUS_CUT)
2098 continue;
2100 type = type_of_relaxed(info[j].tab, info[i].bmap->ineq[k]);
2101 if (type == isl_ineq_error)
2102 return isl_change_error;
2103 if (type != isl_ineq_redundant)
2104 return isl_change_none;
2107 return wrap_in_facets(i, j, n, info);
2110 /* Check if either i or j has only cut constraints that can
2111 * be used to wrap in (a facet of) the other basic set.
2112 * if so, replace the pair by their union.
2114 static enum isl_change check_wrap(int i, int j, struct isl_coalesce_info *info)
2116 enum isl_change change = isl_change_none;
2118 change = can_wrap_in_set(i, j, info);
2119 if (change != isl_change_none)
2120 return change;
2122 change = can_wrap_in_set(j, i, info);
2123 return change;
2126 /* Check if all inequality constraints of "i" that cut "j" cease
2127 * to be cut constraints if they are relaxed by one.
2128 * If so, collect the cut constraints in "list".
2129 * The caller is responsible for allocating "list".
2131 static isl_bool all_cut_by_one(int i, int j, struct isl_coalesce_info *info,
2132 int *list)
2134 int l, n;
2136 n = 0;
2137 for (l = 0; l < info[i].bmap->n_ineq; ++l) {
2138 enum isl_ineq_type type;
2140 if (info[i].ineq[l] != STATUS_CUT)
2141 continue;
2142 type = type_of_relaxed(info[j].tab, info[i].bmap->ineq[l]);
2143 if (type == isl_ineq_error)
2144 return isl_bool_error;
2145 if (type != isl_ineq_redundant)
2146 return isl_bool_false;
2147 list[n++] = l;
2150 return isl_bool_true;
2153 /* Given two basic maps such that "j" has at least one equality constraint
2154 * that is adjacent to an inequality constraint of "i" and such that "i" has
2155 * exactly one inequality constraint that is adjacent to an equality
2156 * constraint of "j", check whether "i" can be extended to include "j" or
2157 * whether "j" can be wrapped into "i".
2158 * All remaining constraints of "i" and "j" are assumed to be valid
2159 * or cut constraints of the other basic map.
2160 * However, none of the equality constraints of "i" are cut constraints.
2162 * If "i" has any "cut" inequality constraints, then check if relaxing
2163 * each of them by one is sufficient for them to become valid.
2164 * If so, check if the inequality constraint adjacent to an equality
2165 * constraint of "j" along with all these cut constraints
2166 * can be relaxed by one to contain exactly "j".
2167 * Otherwise, or if this fails, check if "j" can be wrapped into "i".
2169 static enum isl_change check_single_adj_eq(int i, int j,
2170 struct isl_coalesce_info *info)
2172 enum isl_change change = isl_change_none;
2173 int k;
2174 int n_cut;
2175 int *relax;
2176 isl_ctx *ctx;
2177 isl_bool try_relax;
2179 n_cut = count_ineq(&info[i], STATUS_CUT);
2181 k = find_ineq(&info[i], STATUS_ADJ_EQ);
2183 if (n_cut > 0) {
2184 ctx = isl_basic_map_get_ctx(info[i].bmap);
2185 relax = isl_calloc_array(ctx, int, 1 + n_cut);
2186 if (!relax)
2187 return isl_change_error;
2188 relax[0] = k;
2189 try_relax = all_cut_by_one(i, j, info, relax + 1);
2190 if (try_relax < 0)
2191 change = isl_change_error;
2192 } else {
2193 try_relax = isl_bool_true;
2194 relax = &k;
2196 if (try_relax && change == isl_change_none)
2197 change = is_relaxed_extension(i, j, 1 + n_cut, relax, info);
2198 if (n_cut > 0)
2199 free(relax);
2200 if (change != isl_change_none)
2201 return change;
2203 change = can_wrap_in_facet(i, j, k, info, n_cut > 0);
2205 return change;
2208 /* At least one of the basic maps has an equality that is adjacent
2209 * to an inequality. Make sure that only one of the basic maps has
2210 * such an equality and that the other basic map has exactly one
2211 * inequality adjacent to an equality.
2212 * If the other basic map does not have such an inequality, then
2213 * check if all its constraints are either valid or cut constraints
2214 * and, if so, try wrapping in the first map into the second.
2215 * Otherwise, try to extend one basic map with the other or
2216 * wrap one basic map in the other.
2218 static enum isl_change check_adj_eq(int i, int j,
2219 struct isl_coalesce_info *info)
2221 if (any_eq(&info[i], STATUS_ADJ_INEQ) &&
2222 any_eq(&info[j], STATUS_ADJ_INEQ))
2223 /* ADJ EQ TOO MANY */
2224 return isl_change_none;
2226 if (any_eq(&info[i], STATUS_ADJ_INEQ))
2227 return check_adj_eq(j, i, info);
2229 /* j has an equality adjacent to an inequality in i */
2231 if (count_ineq(&info[i], STATUS_ADJ_EQ) != 1) {
2232 if (all_valid_or_cut(&info[i]))
2233 return can_wrap_in_set(i, j, info);
2234 return isl_change_none;
2236 if (any_eq(&info[i], STATUS_CUT))
2237 return isl_change_none;
2238 if (any_ineq(&info[j], STATUS_ADJ_EQ) ||
2239 any_ineq(&info[i], STATUS_ADJ_INEQ) ||
2240 any_ineq(&info[j], STATUS_ADJ_INEQ))
2241 /* ADJ EQ TOO MANY */
2242 return isl_change_none;
2244 return check_single_adj_eq(i, j, info);
2247 /* Disjunct "j" lies on a hyperplane that is adjacent to disjunct "i".
2248 * In particular, disjunct "i" has an inequality constraint that is adjacent
2249 * to a (combination of) equality constraint(s) of disjunct "j",
2250 * but disjunct "j" has no explicit equality constraint adjacent
2251 * to an inequality constraint of disjunct "i".
2253 * Disjunct "i" is already known not to have any equality constraints
2254 * that are adjacent to an equality or inequality constraint.
2255 * Check that, other than the inequality constraint mentioned above,
2256 * all other constraints of disjunct "i" are valid for disjunct "j".
2257 * If so, try and wrap in disjunct "j".
2259 static enum isl_change check_ineq_adj_eq(int i, int j,
2260 struct isl_coalesce_info *info)
2262 int k;
2264 if (any_eq(&info[i], STATUS_CUT))
2265 return isl_change_none;
2266 if (any_ineq(&info[i], STATUS_CUT))
2267 return isl_change_none;
2268 if (any_ineq(&info[i], STATUS_ADJ_INEQ))
2269 return isl_change_none;
2270 if (count_ineq(&info[i], STATUS_ADJ_EQ) != 1)
2271 return isl_change_none;
2273 k = find_ineq(&info[i], STATUS_ADJ_EQ);
2275 return can_wrap_in_facet(i, j, k, info, 0);
2278 /* The two basic maps lie on adjacent hyperplanes. In particular,
2279 * basic map "i" has an equality that lies parallel to basic map "j".
2280 * Check if we can wrap the facets around the parallel hyperplanes
2281 * to include the other set.
2283 * We perform basically the same operations as can_wrap_in_facet,
2284 * except that we don't need to select a facet of one of the sets.
2286 * \\ \\
2287 * \\ => \\
2288 * \ \|
2290 * If there is more than one equality of "i" adjacent to an equality of "j",
2291 * then the result will satisfy one or more equalities that are a linear
2292 * combination of these equalities. These will be encoded as pairs
2293 * of inequalities in the wrapping constraints and need to be made
2294 * explicit.
2296 static enum isl_change check_eq_adj_eq(int i, int j,
2297 struct isl_coalesce_info *info)
2299 int k;
2300 enum isl_change change = isl_change_none;
2301 int detect_equalities = 0;
2302 struct isl_wraps wraps;
2303 isl_ctx *ctx;
2304 isl_mat *mat;
2305 struct isl_set *set_i = NULL;
2306 struct isl_set *set_j = NULL;
2307 struct isl_vec *bound = NULL;
2308 isl_size total = isl_basic_map_dim(info[i].bmap, isl_dim_all);
2310 if (total < 0)
2311 return isl_change_error;
2312 if (count_eq(&info[i], STATUS_ADJ_EQ) != 1)
2313 detect_equalities = 1;
2315 k = find_eq(&info[i], STATUS_ADJ_EQ);
2317 set_i = set_from_updated_bmap(info[i].bmap, info[i].tab);
2318 set_j = set_from_updated_bmap(info[j].bmap, info[j].tab);
2319 ctx = isl_basic_map_get_ctx(info[i].bmap);
2320 mat = isl_mat_alloc(ctx, 2 * (info[i].bmap->n_eq + info[j].bmap->n_eq) +
2321 info[i].bmap->n_ineq + info[j].bmap->n_ineq,
2322 1 + total);
2323 if (wraps_init(&wraps, mat, info, i, j) < 0)
2324 goto error;
2325 bound = isl_vec_alloc(ctx, 1 + total);
2326 if (!set_i || !set_j || !bound)
2327 goto error;
2329 if (k % 2 == 0)
2330 isl_seq_neg(bound->el, info[i].bmap->eq[k / 2], 1 + total);
2331 else
2332 isl_seq_cpy(bound->el, info[i].bmap->eq[k / 2], 1 + total);
2333 isl_int_add_ui(bound->el[0], bound->el[0], 1);
2335 isl_seq_cpy(wraps.mat->row[0], bound->el, 1 + total);
2336 wraps.mat->n_row = 1;
2338 if (add_wraps(&wraps, &info[j], bound->el, set_i) < 0)
2339 goto error;
2340 if (wraps.failed)
2341 goto unbounded;
2343 isl_int_sub_ui(bound->el[0], bound->el[0], 1);
2344 isl_seq_neg(bound->el, bound->el, 1 + total);
2346 isl_seq_cpy(wraps.mat->row[wraps.mat->n_row], bound->el, 1 + total);
2347 wraps.mat->n_row++;
2349 if (add_wraps(&wraps, &info[i], bound->el, set_j) < 0)
2350 goto error;
2351 if (wraps.failed)
2352 goto unbounded;
2354 change = fuse(i, j, info, wraps.mat, detect_equalities, 0);
2356 if (0) {
2357 error: change = isl_change_error;
2359 unbounded:
2361 wraps_free(&wraps);
2362 isl_set_free(set_i);
2363 isl_set_free(set_j);
2364 isl_vec_free(bound);
2366 return change;
2369 /* Initialize the "eq" and "ineq" fields of "info".
2371 static void init_status(struct isl_coalesce_info *info)
2373 info->eq = info->ineq = NULL;
2376 /* Set info->eq to the positions of the equalities of info->bmap
2377 * with respect to the basic map represented by "tab".
2378 * If info->eq has already been computed, then do not compute it again.
2380 static void set_eq_status_in(struct isl_coalesce_info *info,
2381 struct isl_tab *tab)
2383 if (info->eq)
2384 return;
2385 info->eq = eq_status_in(info->bmap, tab);
2388 /* Set info->ineq to the positions of the inequalities of info->bmap
2389 * with respect to the basic map represented by "tab".
2390 * If info->ineq has already been computed, then do not compute it again.
2392 static void set_ineq_status_in(struct isl_coalesce_info *info,
2393 struct isl_tab *tab)
2395 if (info->ineq)
2396 return;
2397 info->ineq = ineq_status_in(info->bmap, info->tab, tab);
2400 /* Free the memory allocated by the "eq" and "ineq" fields of "info".
2401 * This function assumes that init_status has been called on "info" first,
2402 * after which the "eq" and "ineq" fields may or may not have been
2403 * assigned a newly allocated array.
2405 static void clear_status(struct isl_coalesce_info *info)
2407 free(info->eq);
2408 free(info->ineq);
2411 /* Are all inequality constraints of the basic map represented by "info"
2412 * valid for the other basic map, except for a single constraint
2413 * that is adjacent to an inequality constraint of the other basic map?
2415 static int all_ineq_valid_or_single_adj_ineq(struct isl_coalesce_info *info)
2417 int i;
2418 int k = -1;
2420 for (i = 0; i < info->bmap->n_ineq; ++i) {
2421 if (info->ineq[i] == STATUS_REDUNDANT)
2422 continue;
2423 if (info->ineq[i] == STATUS_VALID)
2424 continue;
2425 if (info->ineq[i] != STATUS_ADJ_INEQ)
2426 return 0;
2427 if (k != -1)
2428 return 0;
2429 k = i;
2432 return k != -1;
2435 /* Basic map "i" has one or more equality constraints that separate it
2436 * from basic map "j". Check if it happens to be an extension
2437 * of basic map "j".
2438 * In particular, check that all constraints of "j" are valid for "i",
2439 * except for one inequality constraint that is adjacent
2440 * to an inequality constraints of "i".
2441 * If so, check for "i" being an extension of "j" by calling
2442 * is_adj_ineq_extension.
2444 * Clean up the memory allocated for keeping track of the status
2445 * of the constraints before returning.
2447 static enum isl_change separating_equality(int i, int j,
2448 struct isl_coalesce_info *info)
2450 enum isl_change change = isl_change_none;
2452 if (all(info[j].eq, 2 * info[j].bmap->n_eq, STATUS_VALID) &&
2453 all_ineq_valid_or_single_adj_ineq(&info[j]))
2454 change = is_adj_ineq_extension(j, i, info);
2456 clear_status(&info[i]);
2457 clear_status(&info[j]);
2458 return change;
2461 /* Check if the union of the given pair of basic maps
2462 * can be represented by a single basic map.
2463 * If so, replace the pair by the single basic map and return
2464 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
2465 * Otherwise, return isl_change_none.
2466 * The two basic maps are assumed to live in the same local space.
2467 * The "eq" and "ineq" fields of info[i] and info[j] are assumed
2468 * to have been initialized by the caller, either to NULL or
2469 * to valid information.
2471 * We first check the effect of each constraint of one basic map
2472 * on the other basic map.
2473 * The constraint may be
2474 * redundant the constraint is redundant in its own
2475 * basic map and should be ignore and removed
2476 * in the end
2477 * valid all (integer) points of the other basic map
2478 * satisfy the constraint
2479 * separate no (integer) point of the other basic map
2480 * satisfies the constraint
2481 * cut some but not all points of the other basic map
2482 * satisfy the constraint
2483 * adj_eq the given constraint is adjacent (on the outside)
2484 * to an equality of the other basic map
2485 * adj_ineq the given constraint is adjacent (on the outside)
2486 * to an inequality of the other basic map
2488 * We consider seven cases in which we can replace the pair by a single
2489 * basic map. We ignore all "redundant" constraints.
2491 * 1. all constraints of one basic map are valid
2492 * => the other basic map is a subset and can be removed
2494 * 2. all constraints of both basic maps are either "valid" or "cut"
2495 * and the facets corresponding to the "cut" constraints
2496 * of one of the basic maps lies entirely inside the other basic map
2497 * => the pair can be replaced by a basic map consisting
2498 * of the valid constraints in both basic maps
2500 * 3. there is a single pair of adjacent inequalities
2501 * (all other constraints are "valid")
2502 * => the pair can be replaced by a basic map consisting
2503 * of the valid constraints in both basic maps
2505 * 4. one basic map has a single adjacent inequality, while the other
2506 * constraints are "valid". The other basic map has some
2507 * "cut" constraints, but replacing the adjacent inequality by
2508 * its opposite and adding the valid constraints of the other
2509 * basic map results in a subset of the other basic map
2510 * => the pair can be replaced by a basic map consisting
2511 * of the valid constraints in both basic maps
2513 * 5. there is a single adjacent pair of an inequality and an equality,
2514 * the other constraints of the basic map containing the inequality are
2515 * "valid". Moreover, if the inequality the basic map is relaxed
2516 * and then turned into an equality, then resulting facet lies
2517 * entirely inside the other basic map
2518 * => the pair can be replaced by the basic map containing
2519 * the inequality, with the inequality relaxed.
2521 * 6. there is a single inequality adjacent to an equality,
2522 * the other constraints of the basic map containing the inequality are
2523 * "valid". Moreover, the facets corresponding to both
2524 * the inequality and the equality can be wrapped around their
2525 * ridges to include the other basic map
2526 * => the pair can be replaced by a basic map consisting
2527 * of the valid constraints in both basic maps together
2528 * with all wrapping constraints
2530 * 7. one of the basic maps extends beyond the other by at most one.
2531 * Moreover, the facets corresponding to the cut constraints and
2532 * the pieces of the other basic map at offset one from these cut
2533 * constraints can be wrapped around their ridges to include
2534 * the union of the two basic maps
2535 * => the pair can be replaced by a basic map consisting
2536 * of the valid constraints in both basic maps together
2537 * with all wrapping constraints
2539 * 8. the two basic maps live in adjacent hyperplanes. In principle
2540 * such sets can always be combined through wrapping, but we impose
2541 * that there is only one such pair, to avoid overeager coalescing.
2543 * Throughout the computation, we maintain a collection of tableaus
2544 * corresponding to the basic maps. When the basic maps are dropped
2545 * or combined, the tableaus are modified accordingly.
2547 static enum isl_change coalesce_local_pair_reuse(int i, int j,
2548 struct isl_coalesce_info *info)
2550 enum isl_change change = isl_change_none;
2552 set_ineq_status_in(&info[i], info[j].tab);
2553 if (info[i].bmap->n_ineq && !info[i].ineq)
2554 goto error;
2555 if (any_ineq(&info[i], STATUS_ERROR))
2556 goto error;
2557 if (any_ineq(&info[i], STATUS_SEPARATE))
2558 goto done;
2560 set_ineq_status_in(&info[j], info[i].tab);
2561 if (info[j].bmap->n_ineq && !info[j].ineq)
2562 goto error;
2563 if (any_ineq(&info[j], STATUS_ERROR))
2564 goto error;
2565 if (any_ineq(&info[j], STATUS_SEPARATE))
2566 goto done;
2568 set_eq_status_in(&info[i], info[j].tab);
2569 if (info[i].bmap->n_eq && !info[i].eq)
2570 goto error;
2571 if (any_eq(&info[i], STATUS_ERROR))
2572 goto error;
2574 set_eq_status_in(&info[j], info[i].tab);
2575 if (info[j].bmap->n_eq && !info[j].eq)
2576 goto error;
2577 if (any_eq(&info[j], STATUS_ERROR))
2578 goto error;
2580 if (any_eq(&info[i], STATUS_SEPARATE))
2581 return separating_equality(i, j, info);
2582 if (any_eq(&info[j], STATUS_SEPARATE))
2583 return separating_equality(j, i, info);
2585 if (all(info[i].eq, 2 * info[i].bmap->n_eq, STATUS_VALID) &&
2586 all(info[i].ineq, info[i].bmap->n_ineq, STATUS_VALID)) {
2587 drop(&info[j]);
2588 change = isl_change_drop_second;
2589 } else if (all(info[j].eq, 2 * info[j].bmap->n_eq, STATUS_VALID) &&
2590 all(info[j].ineq, info[j].bmap->n_ineq, STATUS_VALID)) {
2591 drop(&info[i]);
2592 change = isl_change_drop_first;
2593 } else if (any_eq(&info[i], STATUS_ADJ_EQ)) {
2594 change = check_eq_adj_eq(i, j, info);
2595 } else if (any_eq(&info[j], STATUS_ADJ_EQ)) {
2596 change = check_eq_adj_eq(j, i, info);
2597 } else if (any_eq(&info[i], STATUS_ADJ_INEQ) ||
2598 any_eq(&info[j], STATUS_ADJ_INEQ)) {
2599 change = check_adj_eq(i, j, info);
2600 } else if (any_ineq(&info[i], STATUS_ADJ_EQ)) {
2601 change = check_ineq_adj_eq(i, j, info);
2602 } else if (any_ineq(&info[j], STATUS_ADJ_EQ)) {
2603 change = check_ineq_adj_eq(j, i, info);
2604 } else if (any_ineq(&info[i], STATUS_ADJ_INEQ) ||
2605 any_ineq(&info[j], STATUS_ADJ_INEQ)) {
2606 change = check_adj_ineq(i, j, info);
2607 } else {
2608 if (!any_eq(&info[i], STATUS_CUT) &&
2609 !any_eq(&info[j], STATUS_CUT))
2610 change = check_facets(i, j, info);
2611 if (change == isl_change_none)
2612 change = check_wrap(i, j, info);
2615 done:
2616 clear_status(&info[i]);
2617 clear_status(&info[j]);
2618 return change;
2619 error:
2620 clear_status(&info[i]);
2621 clear_status(&info[j]);
2622 return isl_change_error;
2625 /* Check if the union of the given pair of basic maps
2626 * can be represented by a single basic map.
2627 * If so, replace the pair by the single basic map and return
2628 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
2629 * Otherwise, return isl_change_none.
2630 * The two basic maps are assumed to live in the same local space.
2632 static enum isl_change coalesce_local_pair(int i, int j,
2633 struct isl_coalesce_info *info)
2635 init_status(&info[i]);
2636 init_status(&info[j]);
2637 return coalesce_local_pair_reuse(i, j, info);
2640 /* Shift the integer division at position "div" of the basic map
2641 * represented by "info" by "shift".
2643 * That is, if the integer division has the form
2645 * floor(f(x)/d)
2647 * then replace it by
2649 * floor((f(x) + shift * d)/d) - shift
2651 static isl_stat shift_div(struct isl_coalesce_info *info, int div,
2652 isl_int shift)
2654 isl_size total, n_div;
2656 info->bmap = isl_basic_map_shift_div(info->bmap, div, 0, shift);
2657 if (!info->bmap)
2658 return isl_stat_error;
2660 total = isl_basic_map_dim(info->bmap, isl_dim_all);
2661 n_div = isl_basic_map_dim(info->bmap, isl_dim_div);
2662 if (total < 0 || n_div < 0)
2663 return isl_stat_error;
2664 total -= n_div;
2665 if (isl_tab_shift_var(info->tab, total + div, shift) < 0)
2666 return isl_stat_error;
2668 return isl_stat_ok;
2671 /* If the integer division at position "div" is defined by an equality,
2672 * i.e., a stride constraint, then change the integer division expression
2673 * to have a constant term equal to zero.
2675 * Let the equality constraint be
2677 * c + f + m a = 0
2679 * The integer division expression is then typically of the form
2681 * a = floor((-f - c')/m)
2683 * The integer division is first shifted by t = floor(c/m),
2684 * turning the equality constraint into
2686 * c - m floor(c/m) + f + m a' = 0
2688 * i.e.,
2690 * (c mod m) + f + m a' = 0
2692 * That is,
2694 * a' = (-f - (c mod m))/m = floor((-f)/m)
2696 * because a' is an integer and 0 <= (c mod m) < m.
2697 * The constant term of a' can therefore be zeroed out,
2698 * but only if the integer division expression is of the expected form.
2700 static isl_stat normalize_stride_div(struct isl_coalesce_info *info, int div)
2702 isl_bool defined, valid;
2703 isl_stat r;
2704 isl_constraint *c;
2705 isl_int shift, stride;
2707 defined = isl_basic_map_has_defining_equality(info->bmap, isl_dim_div,
2708 div, &c);
2709 if (defined < 0)
2710 return isl_stat_error;
2711 if (!defined)
2712 return isl_stat_ok;
2713 if (!c)
2714 return isl_stat_error;
2715 valid = isl_constraint_is_div_equality(c, div);
2716 isl_int_init(shift);
2717 isl_int_init(stride);
2718 isl_constraint_get_constant(c, &shift);
2719 isl_constraint_get_coefficient(c, isl_dim_div, div, &stride);
2720 isl_int_fdiv_q(shift, shift, stride);
2721 r = shift_div(info, div, shift);
2722 isl_int_clear(stride);
2723 isl_int_clear(shift);
2724 isl_constraint_free(c);
2725 if (r < 0 || valid < 0)
2726 return isl_stat_error;
2727 if (!valid)
2728 return isl_stat_ok;
2729 info->bmap = isl_basic_map_set_div_expr_constant_num_si_inplace(
2730 info->bmap, div, 0);
2731 if (!info->bmap)
2732 return isl_stat_error;
2733 return isl_stat_ok;
2736 /* The basic maps represented by "info1" and "info2" are known
2737 * to have the same number of integer divisions.
2738 * Check if pairs of integer divisions are equal to each other
2739 * despite the fact that they differ by a rational constant.
2741 * In particular, look for any pair of integer divisions that
2742 * only differ in their constant terms.
2743 * If either of these integer divisions is defined
2744 * by stride constraints, then modify it to have a zero constant term.
2745 * If both are defined by stride constraints then in the end they will have
2746 * the same (zero) constant term.
2748 static isl_stat harmonize_stride_divs(struct isl_coalesce_info *info1,
2749 struct isl_coalesce_info *info2)
2751 int i;
2752 isl_size n;
2754 n = isl_basic_map_dim(info1->bmap, isl_dim_div);
2755 if (n < 0)
2756 return isl_stat_error;
2757 for (i = 0; i < n; ++i) {
2758 isl_bool known, harmonize;
2760 known = isl_basic_map_div_is_known(info1->bmap, i);
2761 if (known >= 0 && known)
2762 known = isl_basic_map_div_is_known(info2->bmap, i);
2763 if (known < 0)
2764 return isl_stat_error;
2765 if (!known)
2766 continue;
2767 harmonize = isl_basic_map_equal_div_expr_except_constant(
2768 info1->bmap, i, info2->bmap, i);
2769 if (harmonize < 0)
2770 return isl_stat_error;
2771 if (!harmonize)
2772 continue;
2773 if (normalize_stride_div(info1, i) < 0)
2774 return isl_stat_error;
2775 if (normalize_stride_div(info2, i) < 0)
2776 return isl_stat_error;
2779 return isl_stat_ok;
2782 /* If "shift" is an integer constant, then shift the integer division
2783 * at position "div" of the basic map represented by "info" by "shift".
2784 * If "shift" is not an integer constant, then do nothing.
2785 * If "shift" is equal to zero, then no shift needs to be performed either.
2787 * That is, if the integer division has the form
2789 * floor(f(x)/d)
2791 * then replace it by
2793 * floor((f(x) + shift * d)/d) - shift
2795 static isl_stat shift_if_cst_int(struct isl_coalesce_info *info, int div,
2796 __isl_keep isl_aff *shift)
2798 isl_bool cst;
2799 isl_stat r;
2800 isl_int d;
2801 isl_val *c;
2803 cst = isl_aff_is_cst(shift);
2804 if (cst < 0 || !cst)
2805 return cst < 0 ? isl_stat_error : isl_stat_ok;
2807 c = isl_aff_get_constant_val(shift);
2808 cst = isl_val_is_int(c);
2809 if (cst >= 0 && cst)
2810 cst = isl_bool_not(isl_val_is_zero(c));
2811 if (cst < 0 || !cst) {
2812 isl_val_free(c);
2813 return cst < 0 ? isl_stat_error : isl_stat_ok;
2816 isl_int_init(d);
2817 r = isl_val_get_num_isl_int(c, &d);
2818 if (r >= 0)
2819 r = shift_div(info, div, d);
2820 isl_int_clear(d);
2822 isl_val_free(c);
2824 return r;
2827 /* Check if some of the divs in the basic map represented by "info1"
2828 * are shifts of the corresponding divs in the basic map represented
2829 * by "info2", taking into account the equality constraints "eq1" of "info1"
2830 * and "eq2" of "info2". If so, align them with those of "info2".
2831 * "info1" and "info2" are assumed to have the same number
2832 * of integer divisions.
2834 * An integer division is considered to be a shift of another integer
2835 * division if, after simplification with respect to the equality
2836 * constraints of the other basic map, one is equal to the other
2837 * plus a constant.
2839 * In particular, for each pair of integer divisions, if both are known,
2840 * have the same denominator and are not already equal to each other,
2841 * simplify each with respect to the equality constraints
2842 * of the other basic map. If the difference is an integer constant,
2843 * then move this difference outside.
2844 * That is, if, after simplification, one integer division is of the form
2846 * floor((f(x) + c_1)/d)
2848 * while the other is of the form
2850 * floor((f(x) + c_2)/d)
2852 * and n = (c_2 - c_1)/d is an integer, then replace the first
2853 * integer division by
2855 * floor((f_1(x) + c_1 + n * d)/d) - n,
2857 * where floor((f_1(x) + c_1 + n * d)/d) = floor((f2(x) + c_2)/d)
2858 * after simplification with respect to the equality constraints.
2860 static isl_stat harmonize_divs_with_hulls(struct isl_coalesce_info *info1,
2861 struct isl_coalesce_info *info2, __isl_keep isl_basic_set *eq1,
2862 __isl_keep isl_basic_set *eq2)
2864 int i;
2865 isl_size total;
2866 isl_local_space *ls1, *ls2;
2868 total = isl_basic_map_dim(info1->bmap, isl_dim_all);
2869 if (total < 0)
2870 return isl_stat_error;
2871 ls1 = isl_local_space_wrap(isl_basic_map_get_local_space(info1->bmap));
2872 ls2 = isl_local_space_wrap(isl_basic_map_get_local_space(info2->bmap));
2873 for (i = 0; i < info1->bmap->n_div; ++i) {
2874 isl_stat r;
2875 isl_aff *div1, *div2;
2877 if (!isl_local_space_div_is_known(ls1, i) ||
2878 !isl_local_space_div_is_known(ls2, i))
2879 continue;
2880 if (isl_int_ne(info1->bmap->div[i][0], info2->bmap->div[i][0]))
2881 continue;
2882 if (isl_seq_eq(info1->bmap->div[i] + 1,
2883 info2->bmap->div[i] + 1, 1 + total))
2884 continue;
2885 div1 = isl_local_space_get_div(ls1, i);
2886 div2 = isl_local_space_get_div(ls2, i);
2887 div1 = isl_aff_substitute_equalities(div1,
2888 isl_basic_set_copy(eq2));
2889 div2 = isl_aff_substitute_equalities(div2,
2890 isl_basic_set_copy(eq1));
2891 div2 = isl_aff_sub(div2, div1);
2892 r = shift_if_cst_int(info1, i, div2);
2893 isl_aff_free(div2);
2894 if (r < 0)
2895 break;
2897 isl_local_space_free(ls1);
2898 isl_local_space_free(ls2);
2900 if (i < info1->bmap->n_div)
2901 return isl_stat_error;
2902 return isl_stat_ok;
2905 /* Check if some of the divs in the basic map represented by "info1"
2906 * are shifts of the corresponding divs in the basic map represented
2907 * by "info2". If so, align them with those of "info2".
2908 * Only do this if "info1" and "info2" have the same number
2909 * of integer divisions.
2911 * An integer division is considered to be a shift of another integer
2912 * division if, after simplification with respect to the equality
2913 * constraints of the other basic map, one is equal to the other
2914 * plus a constant.
2916 * First check if pairs of integer divisions are equal to each other
2917 * despite the fact that they differ by a rational constant.
2918 * If so, try and arrange for them to have the same constant term.
2920 * Then, extract the equality constraints and continue with
2921 * harmonize_divs_with_hulls.
2923 * If the equality constraints of both basic maps are the same,
2924 * then there is no need to perform any shifting since
2925 * the coefficients of the integer divisions should have been
2926 * reduced in the same way.
2928 static isl_stat harmonize_divs(struct isl_coalesce_info *info1,
2929 struct isl_coalesce_info *info2)
2931 isl_bool equal;
2932 isl_basic_map *bmap1, *bmap2;
2933 isl_basic_set *eq1, *eq2;
2934 isl_stat r;
2936 if (!info1->bmap || !info2->bmap)
2937 return isl_stat_error;
2939 if (info1->bmap->n_div != info2->bmap->n_div)
2940 return isl_stat_ok;
2941 if (info1->bmap->n_div == 0)
2942 return isl_stat_ok;
2944 if (harmonize_stride_divs(info1, info2) < 0)
2945 return isl_stat_error;
2947 bmap1 = isl_basic_map_copy(info1->bmap);
2948 bmap2 = isl_basic_map_copy(info2->bmap);
2949 eq1 = isl_basic_map_wrap(isl_basic_map_plain_affine_hull(bmap1));
2950 eq2 = isl_basic_map_wrap(isl_basic_map_plain_affine_hull(bmap2));
2951 equal = isl_basic_set_plain_is_equal(eq1, eq2);
2952 if (equal < 0)
2953 r = isl_stat_error;
2954 else if (equal)
2955 r = isl_stat_ok;
2956 else
2957 r = harmonize_divs_with_hulls(info1, info2, eq1, eq2);
2958 isl_basic_set_free(eq1);
2959 isl_basic_set_free(eq2);
2961 return r;
2964 /* Do the two basic maps live in the same local space, i.e.,
2965 * do they have the same (known) divs?
2966 * If either basic map has any unknown divs, then we can only assume
2967 * that they do not live in the same local space.
2969 static isl_bool same_divs(__isl_keep isl_basic_map *bmap1,
2970 __isl_keep isl_basic_map *bmap2)
2972 int i;
2973 isl_bool known;
2974 isl_size total;
2976 if (!bmap1 || !bmap2)
2977 return isl_bool_error;
2978 if (bmap1->n_div != bmap2->n_div)
2979 return isl_bool_false;
2981 if (bmap1->n_div == 0)
2982 return isl_bool_true;
2984 known = isl_basic_map_divs_known(bmap1);
2985 if (known < 0 || !known)
2986 return known;
2987 known = isl_basic_map_divs_known(bmap2);
2988 if (known < 0 || !known)
2989 return known;
2991 total = isl_basic_map_dim(bmap1, isl_dim_all);
2992 if (total < 0)
2993 return isl_bool_error;
2994 for (i = 0; i < bmap1->n_div; ++i)
2995 if (!isl_seq_eq(bmap1->div[i], bmap2->div[i], 2 + total))
2996 return isl_bool_false;
2998 return isl_bool_true;
3001 /* Assuming that "tab" contains the equality constraints and
3002 * the initial inequality constraints of "bmap", copy the remaining
3003 * inequality constraints of "bmap" to "Tab".
3005 static isl_stat copy_ineq(struct isl_tab *tab, __isl_keep isl_basic_map *bmap)
3007 int i, n_ineq;
3009 if (!bmap)
3010 return isl_stat_error;
3012 n_ineq = tab->n_con - tab->n_eq;
3013 for (i = n_ineq; i < bmap->n_ineq; ++i)
3014 if (isl_tab_add_ineq(tab, bmap->ineq[i]) < 0)
3015 return isl_stat_error;
3017 return isl_stat_ok;
3020 /* Description of an integer division that is added
3021 * during an expansion.
3022 * "pos" is the position of the corresponding variable.
3023 * "cst" indicates whether this integer division has a fixed value.
3024 * "val" contains the fixed value, if the value is fixed.
3026 struct isl_expanded {
3027 int pos;
3028 isl_bool cst;
3029 isl_int val;
3032 /* For each of the "n" integer division variables "expanded",
3033 * if the variable has a fixed value, then add two inequality
3034 * constraints expressing the fixed value.
3035 * Otherwise, add the corresponding div constraints.
3036 * The caller is responsible for removing the div constraints
3037 * that it added for all these "n" integer divisions.
3039 * The div constraints and the pair of inequality constraints
3040 * forcing the fixed value cannot both be added for a given variable
3041 * as the combination may render some of the original constraints redundant.
3042 * These would then be ignored during the coalescing detection,
3043 * while they could remain in the fused result.
3045 * The two added inequality constraints are
3047 * -a + v >= 0
3048 * a - v >= 0
3050 * with "a" the variable and "v" its fixed value.
3051 * The facet corresponding to one of these two constraints is selected
3052 * in the tableau to ensure that the pair of inequality constraints
3053 * is treated as an equality constraint.
3055 * The information in info->ineq is thrown away because it was
3056 * computed in terms of div constraints, while some of those
3057 * have now been replaced by these pairs of inequality constraints.
3059 static isl_stat fix_constant_divs(struct isl_coalesce_info *info,
3060 int n, struct isl_expanded *expanded)
3062 unsigned o_div;
3063 int i;
3064 isl_vec *ineq;
3066 o_div = isl_basic_map_offset(info->bmap, isl_dim_div) - 1;
3067 ineq = isl_vec_alloc(isl_tab_get_ctx(info->tab), 1 + info->tab->n_var);
3068 if (!ineq)
3069 return isl_stat_error;
3070 isl_seq_clr(ineq->el + 1, info->tab->n_var);
3072 for (i = 0; i < n; ++i) {
3073 if (!expanded[i].cst) {
3074 info->bmap = isl_basic_map_extend_constraints(
3075 info->bmap, 0, 2);
3076 info->bmap = isl_basic_map_add_div_constraints(
3077 info->bmap, expanded[i].pos - o_div);
3078 } else {
3079 isl_int_set_si(ineq->el[1 + expanded[i].pos], -1);
3080 isl_int_set(ineq->el[0], expanded[i].val);
3081 info->bmap = isl_basic_map_add_ineq(info->bmap,
3082 ineq->el);
3083 isl_int_set_si(ineq->el[1 + expanded[i].pos], 1);
3084 isl_int_neg(ineq->el[0], expanded[i].val);
3085 info->bmap = isl_basic_map_add_ineq(info->bmap,
3086 ineq->el);
3087 isl_int_set_si(ineq->el[1 + expanded[i].pos], 0);
3089 if (copy_ineq(info->tab, info->bmap) < 0)
3090 break;
3091 if (expanded[i].cst &&
3092 isl_tab_select_facet(info->tab, info->tab->n_con - 1) < 0)
3093 break;
3096 isl_vec_free(ineq);
3098 clear_status(info);
3099 init_status(info);
3101 return i < n ? isl_stat_error : isl_stat_ok;
3104 /* Insert the "n" integer division variables "expanded"
3105 * into info->tab and info->bmap and
3106 * update info->ineq with respect to the redundant constraints
3107 * in the resulting tableau.
3108 * "bmap" contains the result of this insertion in info->bmap,
3109 * while info->bmap is the original version
3110 * of "bmap", i.e., the one that corresponds to the current
3111 * state of info->tab. The number of constraints in info->bmap
3112 * is assumed to be the same as the number of constraints
3113 * in info->tab. This is required to be able to detect
3114 * the extra constraints in "bmap".
3116 * In particular, introduce extra variables corresponding
3117 * to the extra integer divisions and add the div constraints
3118 * that were added to "bmap" after info->tab was created
3119 * from info->bmap.
3120 * Furthermore, check if these extra integer divisions happen
3121 * to attain a fixed integer value in info->tab.
3122 * If so, replace the corresponding div constraints by pairs
3123 * of inequality constraints that fix these
3124 * integer divisions to their single integer values.
3125 * Replace info->bmap by "bmap" to match the changes to info->tab.
3126 * info->ineq was computed without a tableau and therefore
3127 * does not take into account the redundant constraints
3128 * in the tableau. Mark them here.
3129 * There is no need to check the newly added div constraints
3130 * since they cannot be redundant.
3131 * The redundancy check is not performed when constants have been discovered
3132 * since info->ineq is completely thrown away in this case.
3134 static isl_stat tab_insert_divs(struct isl_coalesce_info *info,
3135 int n, struct isl_expanded *expanded, __isl_take isl_basic_map *bmap)
3137 int i, n_ineq;
3138 unsigned n_eq;
3139 struct isl_tab_undo *snap;
3140 int any;
3142 if (!bmap)
3143 return isl_stat_error;
3144 if (info->bmap->n_eq + info->bmap->n_ineq != info->tab->n_con)
3145 isl_die(isl_basic_map_get_ctx(bmap), isl_error_internal,
3146 "original tableau does not correspond "
3147 "to original basic map", goto error);
3149 if (isl_tab_extend_vars(info->tab, n) < 0)
3150 goto error;
3151 if (isl_tab_extend_cons(info->tab, 2 * n) < 0)
3152 goto error;
3154 for (i = 0; i < n; ++i) {
3155 if (isl_tab_insert_var(info->tab, expanded[i].pos) < 0)
3156 goto error;
3159 snap = isl_tab_snap(info->tab);
3161 n_ineq = info->tab->n_con - info->tab->n_eq;
3162 if (copy_ineq(info->tab, bmap) < 0)
3163 goto error;
3165 isl_basic_map_free(info->bmap);
3166 info->bmap = bmap;
3168 any = 0;
3169 for (i = 0; i < n; ++i) {
3170 expanded[i].cst = isl_tab_is_constant(info->tab,
3171 expanded[i].pos, &expanded[i].val);
3172 if (expanded[i].cst < 0)
3173 return isl_stat_error;
3174 if (expanded[i].cst)
3175 any = 1;
3178 if (any) {
3179 if (isl_tab_rollback(info->tab, snap) < 0)
3180 return isl_stat_error;
3181 info->bmap = isl_basic_map_cow(info->bmap);
3182 info->bmap = isl_basic_map_free_inequality(info->bmap, 2 * n);
3183 if (!info->bmap)
3184 return isl_stat_error;
3186 return fix_constant_divs(info, n, expanded);
3189 n_eq = info->bmap->n_eq;
3190 for (i = 0; i < n_ineq; ++i) {
3191 if (isl_tab_is_redundant(info->tab, n_eq + i))
3192 info->ineq[i] = STATUS_REDUNDANT;
3195 return isl_stat_ok;
3196 error:
3197 isl_basic_map_free(bmap);
3198 return isl_stat_error;
3201 /* Expand info->tab and info->bmap in the same way "bmap" was expanded
3202 * in isl_basic_map_expand_divs using the expansion "exp" and
3203 * update info->ineq with respect to the redundant constraints
3204 * in the resulting tableau. info->bmap is the original version
3205 * of "bmap", i.e., the one that corresponds to the current
3206 * state of info->tab. The number of constraints in info->bmap
3207 * is assumed to be the same as the number of constraints
3208 * in info->tab. This is required to be able to detect
3209 * the extra constraints in "bmap".
3211 * Extract the positions where extra local variables are introduced
3212 * from "exp" and call tab_insert_divs.
3214 static isl_stat expand_tab(struct isl_coalesce_info *info, int *exp,
3215 __isl_take isl_basic_map *bmap)
3217 isl_ctx *ctx;
3218 struct isl_expanded *expanded;
3219 int i, j, k, n;
3220 int extra_var;
3221 isl_size total, n_div;
3222 unsigned pos;
3223 isl_stat r;
3225 total = isl_basic_map_dim(bmap, isl_dim_all);
3226 n_div = isl_basic_map_dim(bmap, isl_dim_div);
3227 if (total < 0 || n_div < 0)
3228 return isl_stat_error;
3229 pos = total - n_div;
3230 extra_var = total - info->tab->n_var;
3231 n = n_div - extra_var;
3233 ctx = isl_basic_map_get_ctx(bmap);
3234 expanded = isl_calloc_array(ctx, struct isl_expanded, extra_var);
3235 if (extra_var && !expanded)
3236 goto error;
3238 i = 0;
3239 k = 0;
3240 for (j = 0; j < n_div; ++j) {
3241 if (i < n && exp[i] == j) {
3242 ++i;
3243 continue;
3245 expanded[k++].pos = pos + j;
3248 for (k = 0; k < extra_var; ++k)
3249 isl_int_init(expanded[k].val);
3251 r = tab_insert_divs(info, extra_var, expanded, bmap);
3253 for (k = 0; k < extra_var; ++k)
3254 isl_int_clear(expanded[k].val);
3255 free(expanded);
3257 return r;
3258 error:
3259 isl_basic_map_free(bmap);
3260 return isl_stat_error;
3263 /* Check if the union of the basic maps represented by info[i] and info[j]
3264 * can be represented by a single basic map,
3265 * after expanding the divs of info[i] to match those of info[j].
3266 * If so, replace the pair by the single basic map and return
3267 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
3268 * Otherwise, return isl_change_none.
3270 * The caller has already checked for info[j] being a subset of info[i].
3271 * If some of the divs of info[j] are unknown, then the expanded info[i]
3272 * will not have the corresponding div constraints. The other patterns
3273 * therefore cannot apply. Skip the computation in this case.
3275 * The expansion is performed using the divs "div" and expansion "exp"
3276 * computed by the caller.
3277 * info[i].bmap has already been expanded and the result is passed in
3278 * as "bmap".
3279 * The "eq" and "ineq" fields of info[i] reflect the status of
3280 * the constraints of the expanded "bmap" with respect to info[j].tab.
3281 * However, inequality constraints that are redundant in info[i].tab
3282 * have not yet been marked as such because no tableau was available.
3284 * Replace info[i].bmap by "bmap" and expand info[i].tab as well,
3285 * updating info[i].ineq with respect to the redundant constraints.
3286 * Then try and coalesce the expanded info[i] with info[j],
3287 * reusing the information in info[i].eq and info[i].ineq.
3288 * If this does not result in any coalescing or if it results in info[j]
3289 * getting dropped (which should not happen in practice, since the case
3290 * of info[j] being a subset of info[i] has already been checked by
3291 * the caller), then revert info[i] to its original state.
3293 static enum isl_change coalesce_expand_tab_divs(__isl_take isl_basic_map *bmap,
3294 int i, int j, struct isl_coalesce_info *info, __isl_keep isl_mat *div,
3295 int *exp)
3297 isl_bool known;
3298 isl_basic_map *bmap_i;
3299 struct isl_tab_undo *snap;
3300 enum isl_change change = isl_change_none;
3302 known = isl_basic_map_divs_known(info[j].bmap);
3303 if (known < 0 || !known) {
3304 clear_status(&info[i]);
3305 isl_basic_map_free(bmap);
3306 return known < 0 ? isl_change_error : isl_change_none;
3309 bmap_i = isl_basic_map_copy(info[i].bmap);
3310 snap = isl_tab_snap(info[i].tab);
3311 if (expand_tab(&info[i], exp, bmap) < 0)
3312 change = isl_change_error;
3314 init_status(&info[j]);
3315 if (change == isl_change_none)
3316 change = coalesce_local_pair_reuse(i, j, info);
3317 else
3318 clear_status(&info[i]);
3319 if (change != isl_change_none && change != isl_change_drop_second) {
3320 isl_basic_map_free(bmap_i);
3321 } else {
3322 isl_basic_map_free(info[i].bmap);
3323 info[i].bmap = bmap_i;
3325 if (isl_tab_rollback(info[i].tab, snap) < 0)
3326 change = isl_change_error;
3329 return change;
3332 /* Check if the union of "bmap" and the basic map represented by info[j]
3333 * can be represented by a single basic map,
3334 * after expanding the divs of "bmap" to match those of info[j].
3335 * If so, replace the pair by the single basic map and return
3336 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
3337 * Otherwise, return isl_change_none.
3339 * In particular, check if the expanded "bmap" contains the basic map
3340 * represented by the tableau info[j].tab.
3341 * The expansion is performed using the divs "div" and expansion "exp"
3342 * computed by the caller.
3343 * Then we check if all constraints of the expanded "bmap" are valid for
3344 * info[j].tab.
3346 * If "i" is not equal to -1, then "bmap" is equal to info[i].bmap.
3347 * In this case, the positions of the constraints of info[i].bmap
3348 * with respect to the basic map represented by info[j] are stored
3349 * in info[i].
3351 * If the expanded "bmap" does not contain the basic map
3352 * represented by the tableau info[j].tab and if "i" is not -1,
3353 * i.e., if the original "bmap" is info[i].bmap, then expand info[i].tab
3354 * as well and check if that results in coalescing.
3356 static enum isl_change coalesce_with_expanded_divs(
3357 __isl_keep isl_basic_map *bmap, int i, int j,
3358 struct isl_coalesce_info *info, __isl_keep isl_mat *div, int *exp)
3360 enum isl_change change = isl_change_none;
3361 struct isl_coalesce_info info_local, *info_i;
3363 info_i = i >= 0 ? &info[i] : &info_local;
3364 init_status(info_i);
3365 bmap = isl_basic_map_copy(bmap);
3366 bmap = isl_basic_map_expand_divs(bmap, isl_mat_copy(div), exp);
3367 bmap = isl_basic_map_mark_final(bmap);
3369 if (!bmap)
3370 goto error;
3372 info_local.bmap = bmap;
3373 info_i->eq = eq_status_in(bmap, info[j].tab);
3374 if (bmap->n_eq && !info_i->eq)
3375 goto error;
3376 if (any_eq(info_i, STATUS_ERROR))
3377 goto error;
3378 if (any_eq(info_i, STATUS_SEPARATE))
3379 goto done;
3381 info_i->ineq = ineq_status_in(bmap, NULL, info[j].tab);
3382 if (bmap->n_ineq && !info_i->ineq)
3383 goto error;
3384 if (any_ineq(info_i, STATUS_ERROR))
3385 goto error;
3386 if (any_ineq(info_i, STATUS_SEPARATE))
3387 goto done;
3389 if (all(info_i->eq, 2 * bmap->n_eq, STATUS_VALID) &&
3390 all(info_i->ineq, bmap->n_ineq, STATUS_VALID)) {
3391 drop(&info[j]);
3392 change = isl_change_drop_second;
3395 if (change == isl_change_none && i != -1)
3396 return coalesce_expand_tab_divs(bmap, i, j, info, div, exp);
3398 done:
3399 isl_basic_map_free(bmap);
3400 clear_status(info_i);
3401 return change;
3402 error:
3403 isl_basic_map_free(bmap);
3404 clear_status(info_i);
3405 return isl_change_error;
3408 /* Check if the union of "bmap_i" and the basic map represented by info[j]
3409 * can be represented by a single basic map,
3410 * after aligning the divs of "bmap_i" to match those of info[j].
3411 * If so, replace the pair by the single basic map and return
3412 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
3413 * Otherwise, return isl_change_none.
3415 * In particular, check if "bmap_i" contains the basic map represented by
3416 * info[j] after aligning the divs of "bmap_i" to those of info[j].
3417 * Note that this can only succeed if the number of divs of "bmap_i"
3418 * is smaller than (or equal to) the number of divs of info[j].
3420 * We first check if the divs of "bmap_i" are all known and form a subset
3421 * of those of info[j].bmap. If so, we pass control over to
3422 * coalesce_with_expanded_divs.
3424 * If "i" is not equal to -1, then "bmap" is equal to info[i].bmap.
3426 static enum isl_change coalesce_after_aligning_divs(
3427 __isl_keep isl_basic_map *bmap_i, int i, int j,
3428 struct isl_coalesce_info *info)
3430 isl_bool known;
3431 isl_mat *div_i, *div_j, *div;
3432 int *exp1 = NULL;
3433 int *exp2 = NULL;
3434 isl_ctx *ctx;
3435 enum isl_change change;
3437 known = isl_basic_map_divs_known(bmap_i);
3438 if (known < 0)
3439 return isl_change_error;
3440 if (!known)
3441 return isl_change_none;
3443 ctx = isl_basic_map_get_ctx(bmap_i);
3445 div_i = isl_basic_map_get_divs(bmap_i);
3446 div_j = isl_basic_map_get_divs(info[j].bmap);
3448 if (!div_i || !div_j)
3449 goto error;
3451 exp1 = isl_alloc_array(ctx, int, div_i->n_row);
3452 exp2 = isl_alloc_array(ctx, int, div_j->n_row);
3453 if ((div_i->n_row && !exp1) || (div_j->n_row && !exp2))
3454 goto error;
3456 div = isl_merge_divs(div_i, div_j, exp1, exp2);
3457 if (!div)
3458 goto error;
3460 if (div->n_row == div_j->n_row)
3461 change = coalesce_with_expanded_divs(bmap_i,
3462 i, j, info, div, exp1);
3463 else
3464 change = isl_change_none;
3466 isl_mat_free(div);
3468 isl_mat_free(div_i);
3469 isl_mat_free(div_j);
3471 free(exp2);
3472 free(exp1);
3474 return change;
3475 error:
3476 isl_mat_free(div_i);
3477 isl_mat_free(div_j);
3478 free(exp1);
3479 free(exp2);
3480 return isl_change_error;
3483 /* Check if basic map "j" is a subset of basic map "i" after
3484 * exploiting the extra equalities of "j" to simplify the divs of "i".
3485 * If so, remove basic map "j" and return isl_change_drop_second.
3487 * If "j" does not have any equalities or if they are the same
3488 * as those of "i", then we cannot exploit them to simplify the divs.
3489 * Similarly, if there are no divs in "i", then they cannot be simplified.
3490 * If, on the other hand, the affine hulls of "i" and "j" do not intersect,
3491 * then "j" cannot be a subset of "i".
3493 * Otherwise, we intersect "i" with the affine hull of "j" and then
3494 * check if "j" is a subset of the result after aligning the divs.
3495 * If so, then "j" is definitely a subset of "i" and can be removed.
3496 * Note that if after intersection with the affine hull of "j".
3497 * "i" still has more divs than "j", then there is no way we can
3498 * align the divs of "i" to those of "j".
3500 static enum isl_change coalesce_subset_with_equalities(int i, int j,
3501 struct isl_coalesce_info *info)
3503 isl_basic_map *hull_i, *hull_j, *bmap_i;
3504 int equal, empty;
3505 enum isl_change change;
3507 if (info[j].bmap->n_eq == 0)
3508 return isl_change_none;
3509 if (info[i].bmap->n_div == 0)
3510 return isl_change_none;
3512 hull_i = isl_basic_map_copy(info[i].bmap);
3513 hull_i = isl_basic_map_plain_affine_hull(hull_i);
3514 hull_j = isl_basic_map_copy(info[j].bmap);
3515 hull_j = isl_basic_map_plain_affine_hull(hull_j);
3517 hull_j = isl_basic_map_intersect(hull_j, isl_basic_map_copy(hull_i));
3518 equal = isl_basic_map_plain_is_equal(hull_i, hull_j);
3519 empty = isl_basic_map_plain_is_empty(hull_j);
3520 isl_basic_map_free(hull_i);
3522 if (equal < 0 || equal || empty < 0 || empty) {
3523 isl_basic_map_free(hull_j);
3524 if (equal < 0 || empty < 0)
3525 return isl_change_error;
3526 return isl_change_none;
3529 bmap_i = isl_basic_map_copy(info[i].bmap);
3530 bmap_i = isl_basic_map_intersect(bmap_i, hull_j);
3531 if (!bmap_i)
3532 return isl_change_error;
3534 if (bmap_i->n_div > info[j].bmap->n_div) {
3535 isl_basic_map_free(bmap_i);
3536 return isl_change_none;
3539 change = coalesce_after_aligning_divs(bmap_i, -1, j, info);
3541 isl_basic_map_free(bmap_i);
3543 return change;
3546 /* Check if the union of the basic maps represented by info[i] and info[j]
3547 * can be represented by a single basic map, by aligning or equating
3548 * their integer divisions.
3549 * If so, replace the pair by the single basic map and return
3550 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
3551 * Otherwise, return isl_change_none.
3553 * Note that we only perform any test if the number of divs is different
3554 * in the two basic maps. In case the number of divs is the same,
3555 * we have already established that the divs are different
3556 * in the two basic maps.
3557 * In particular, if the number of divs of basic map i is smaller than
3558 * the number of divs of basic map j, then we check if j is a subset of i
3559 * and vice versa.
3561 static enum isl_change coalesce_divs(int i, int j,
3562 struct isl_coalesce_info *info)
3564 enum isl_change change = isl_change_none;
3566 if (info[i].bmap->n_div < info[j].bmap->n_div)
3567 change = coalesce_after_aligning_divs(info[i].bmap, i, j, info);
3568 if (change != isl_change_none)
3569 return change;
3571 if (info[j].bmap->n_div < info[i].bmap->n_div)
3572 change = coalesce_after_aligning_divs(info[j].bmap, j, i, info);
3573 if (change != isl_change_none)
3574 return invert_change(change);
3576 change = coalesce_subset_with_equalities(i, j, info);
3577 if (change != isl_change_none)
3578 return change;
3580 change = coalesce_subset_with_equalities(j, i, info);
3581 if (change != isl_change_none)
3582 return invert_change(change);
3584 return isl_change_none;
3587 /* Does "bmap" involve any divs that themselves refer to divs?
3589 static isl_bool has_nested_div(__isl_keep isl_basic_map *bmap)
3591 int i;
3592 isl_size total;
3593 isl_size n_div;
3595 total = isl_basic_map_dim(bmap, isl_dim_all);
3596 n_div = isl_basic_map_dim(bmap, isl_dim_div);
3597 if (total < 0 || n_div < 0)
3598 return isl_bool_error;
3599 total -= n_div;
3601 for (i = 0; i < n_div; ++i)
3602 if (isl_seq_first_non_zero(bmap->div[i] + 2 + total,
3603 n_div) != -1)
3604 return isl_bool_true;
3606 return isl_bool_false;
3609 /* Return a list of affine expressions, one for each integer division
3610 * in "bmap_i". For each integer division that also appears in "bmap_j",
3611 * the affine expression is set to NaN. The number of NaNs in the list
3612 * is equal to the number of integer divisions in "bmap_j".
3613 * For the other integer divisions of "bmap_i", the corresponding
3614 * element in the list is a purely affine expression equal to the integer
3615 * division in "hull".
3616 * If no such list can be constructed, then the number of elements
3617 * in the returned list is smaller than the number of integer divisions
3618 * in "bmap_i".
3619 * The integer division of "bmap_i" and "bmap_j" are assumed to be known and
3620 * not contain any nested divs.
3622 static __isl_give isl_aff_list *set_up_substitutions(
3623 __isl_keep isl_basic_map *bmap_i, __isl_keep isl_basic_map *bmap_j,
3624 __isl_take isl_basic_map *hull)
3626 isl_size n_div_i, n_div_j, total;
3627 isl_ctx *ctx;
3628 isl_local_space *ls;
3629 isl_basic_set *wrap_hull;
3630 isl_aff *aff_nan;
3631 isl_aff_list *list;
3632 int i, j;
3634 n_div_i = isl_basic_map_dim(bmap_i, isl_dim_div);
3635 n_div_j = isl_basic_map_dim(bmap_j, isl_dim_div);
3636 total = isl_basic_map_dim(bmap_i, isl_dim_all);
3637 if (!hull || n_div_i < 0 || n_div_j < 0 || total < 0)
3638 return NULL;
3640 ctx = isl_basic_map_get_ctx(hull);
3641 total -= n_div_i;
3643 ls = isl_basic_map_get_local_space(bmap_i);
3644 ls = isl_local_space_wrap(ls);
3645 wrap_hull = isl_basic_map_wrap(hull);
3647 aff_nan = isl_aff_nan_on_domain(isl_local_space_copy(ls));
3648 list = isl_aff_list_alloc(ctx, n_div_i);
3650 j = 0;
3651 for (i = 0; i < n_div_i; ++i) {
3652 isl_aff *aff;
3653 isl_size n_div;
3655 if (j < n_div_j &&
3656 isl_basic_map_equal_div_expr_part(bmap_i, i, bmap_j, j,
3657 0, 2 + total)) {
3658 ++j;
3659 list = isl_aff_list_add(list, isl_aff_copy(aff_nan));
3660 continue;
3662 if (n_div_i - i <= n_div_j - j)
3663 break;
3665 aff = isl_local_space_get_div(ls, i);
3666 aff = isl_aff_substitute_equalities(aff,
3667 isl_basic_set_copy(wrap_hull));
3668 aff = isl_aff_floor(aff);
3669 n_div = isl_aff_dim(aff, isl_dim_div);
3670 if (n_div < 0)
3671 goto error;
3672 if (n_div != 0) {
3673 isl_aff_free(aff);
3674 break;
3677 list = isl_aff_list_add(list, aff);
3680 isl_aff_free(aff_nan);
3681 isl_local_space_free(ls);
3682 isl_basic_set_free(wrap_hull);
3684 return list;
3685 error:
3686 isl_aff_free(aff_nan);
3687 isl_local_space_free(ls);
3688 isl_basic_set_free(wrap_hull);
3689 isl_aff_list_free(list);
3690 return NULL;
3693 /* Add variables to info->bmap and info->tab corresponding to the elements
3694 * in "list" that are not set to NaN.
3695 * "extra_var" is the number of these elements.
3696 * "dim" is the offset in the variables of "tab" where we should
3697 * start considering the elements in "list".
3698 * When this function returns, the total number of variables in "tab"
3699 * is equal to "dim" plus the number of elements in "list".
3701 * The newly added existentially quantified variables are not given
3702 * an explicit representation because the corresponding div constraints
3703 * do not appear in info->bmap. These constraints are not added
3704 * to info->bmap because for internal consistency, they would need to
3705 * be added to info->tab as well, where they could combine with the equality
3706 * that is added later to result in constraints that do not hold
3707 * in the original input.
3709 static isl_stat add_sub_vars(struct isl_coalesce_info *info,
3710 __isl_keep isl_aff_list *list, int dim, int extra_var)
3712 int i, j, d;
3713 isl_size n;
3715 info->bmap = isl_basic_map_cow(info->bmap);
3716 info->bmap = isl_basic_map_extend(info->bmap, extra_var, 0, 0);
3717 n = isl_aff_list_n_aff(list);
3718 if (!info->bmap || n < 0)
3719 return isl_stat_error;
3720 for (i = 0; i < n; ++i) {
3721 int is_nan;
3722 isl_aff *aff;
3724 aff = isl_aff_list_get_aff(list, i);
3725 is_nan = isl_aff_is_nan(aff);
3726 isl_aff_free(aff);
3727 if (is_nan < 0)
3728 return isl_stat_error;
3729 if (is_nan)
3730 continue;
3732 if (isl_tab_insert_var(info->tab, dim + i) < 0)
3733 return isl_stat_error;
3734 d = isl_basic_map_alloc_div(info->bmap);
3735 if (d < 0)
3736 return isl_stat_error;
3737 info->bmap = isl_basic_map_mark_div_unknown(info->bmap, d);
3738 for (j = d; j > i; --j)
3739 info->bmap = isl_basic_map_swap_div(info->bmap,
3740 j - 1, j);
3741 if (!info->bmap)
3742 return isl_stat_error;
3745 return isl_stat_ok;
3748 /* For each element in "list" that is not set to NaN, fix the corresponding
3749 * variable in "tab" to the purely affine expression defined by the element.
3750 * "dim" is the offset in the variables of "tab" where we should
3751 * start considering the elements in "list".
3753 * This function assumes that a sufficient number of rows and
3754 * elements in the constraint array are available in the tableau.
3756 static isl_stat add_sub_equalities(struct isl_tab *tab,
3757 __isl_keep isl_aff_list *list, int dim)
3759 int i;
3760 isl_size n;
3761 isl_ctx *ctx;
3762 isl_vec *sub;
3763 isl_aff *aff;
3765 n = isl_aff_list_n_aff(list);
3766 if (n < 0)
3767 return isl_stat_error;
3769 ctx = isl_tab_get_ctx(tab);
3770 sub = isl_vec_alloc(ctx, 1 + dim + n);
3771 if (!sub)
3772 return isl_stat_error;
3773 isl_seq_clr(sub->el + 1 + dim, n);
3775 for (i = 0; i < n; ++i) {
3776 aff = isl_aff_list_get_aff(list, i);
3777 if (!aff)
3778 goto error;
3779 if (isl_aff_is_nan(aff)) {
3780 isl_aff_free(aff);
3781 continue;
3783 isl_seq_cpy(sub->el, aff->v->el + 1, 1 + dim);
3784 isl_int_neg(sub->el[1 + dim + i], aff->v->el[0]);
3785 if (isl_tab_add_eq(tab, sub->el) < 0)
3786 goto error;
3787 isl_int_set_si(sub->el[1 + dim + i], 0);
3788 isl_aff_free(aff);
3791 isl_vec_free(sub);
3792 return isl_stat_ok;
3793 error:
3794 isl_aff_free(aff);
3795 isl_vec_free(sub);
3796 return isl_stat_error;
3799 /* Add variables to info->tab and info->bmap corresponding to the elements
3800 * in "list" that are not set to NaN. The value of the added variable
3801 * in info->tab is fixed to the purely affine expression defined by the element.
3802 * "dim" is the offset in the variables of info->tab where we should
3803 * start considering the elements in "list".
3804 * When this function returns, the total number of variables in info->tab
3805 * is equal to "dim" plus the number of elements in "list".
3807 static isl_stat add_subs(struct isl_coalesce_info *info,
3808 __isl_keep isl_aff_list *list, int dim)
3810 int extra_var;
3811 isl_size n;
3813 n = isl_aff_list_n_aff(list);
3814 if (n < 0)
3815 return isl_stat_error;
3817 extra_var = n - (info->tab->n_var - dim);
3819 if (isl_tab_extend_vars(info->tab, extra_var) < 0)
3820 return isl_stat_error;
3821 if (isl_tab_extend_cons(info->tab, 2 * extra_var) < 0)
3822 return isl_stat_error;
3823 if (add_sub_vars(info, list, dim, extra_var) < 0)
3824 return isl_stat_error;
3826 return add_sub_equalities(info->tab, list, dim);
3829 /* Coalesce basic map "j" into basic map "i" after adding the extra integer
3830 * divisions in "i" but not in "j" to basic map "j", with values
3831 * specified by "list". The total number of elements in "list"
3832 * is equal to the number of integer divisions in "i", while the number
3833 * of NaN elements in the list is equal to the number of integer divisions
3834 * in "j".
3836 * If no coalescing can be performed, then we need to revert basic map "j"
3837 * to its original state. We do the same if basic map "i" gets dropped
3838 * during the coalescing, even though this should not happen in practice
3839 * since we have already checked for "j" being a subset of "i"
3840 * before we reach this stage.
3842 static enum isl_change coalesce_with_subs(int i, int j,
3843 struct isl_coalesce_info *info, __isl_keep isl_aff_list *list)
3845 isl_basic_map *bmap_j;
3846 struct isl_tab_undo *snap;
3847 isl_size dim, n_div;
3848 enum isl_change change;
3850 bmap_j = isl_basic_map_copy(info[j].bmap);
3851 snap = isl_tab_snap(info[j].tab);
3853 dim = isl_basic_map_dim(bmap_j, isl_dim_all);
3854 n_div = isl_basic_map_dim(bmap_j, isl_dim_div);
3855 if (dim < 0 || n_div < 0)
3856 goto error;
3857 dim -= n_div;
3858 if (add_subs(&info[j], list, dim) < 0)
3859 goto error;
3861 change = coalesce_local_pair(i, j, info);
3862 if (change != isl_change_none && change != isl_change_drop_first) {
3863 isl_basic_map_free(bmap_j);
3864 } else {
3865 isl_basic_map_free(info[j].bmap);
3866 info[j].bmap = bmap_j;
3868 if (isl_tab_rollback(info[j].tab, snap) < 0)
3869 return isl_change_error;
3872 return change;
3873 error:
3874 isl_basic_map_free(bmap_j);
3875 return isl_change_error;
3878 /* Check if we can coalesce basic map "j" into basic map "i" after copying
3879 * those extra integer divisions in "i" that can be simplified away
3880 * using the extra equalities in "j".
3881 * All divs are assumed to be known and not contain any nested divs.
3883 * We first check if there are any extra equalities in "j" that we
3884 * can exploit. Then we check if every integer division in "i"
3885 * either already appears in "j" or can be simplified using the
3886 * extra equalities to a purely affine expression.
3887 * If these tests succeed, then we try to coalesce the two basic maps
3888 * by introducing extra dimensions in "j" corresponding to
3889 * the extra integer divisions "i" fixed to the corresponding
3890 * purely affine expression.
3892 static enum isl_change check_coalesce_into_eq(int i, int j,
3893 struct isl_coalesce_info *info)
3895 isl_size n_div_i, n_div_j, n;
3896 isl_basic_map *hull_i, *hull_j;
3897 isl_bool equal, empty;
3898 isl_aff_list *list;
3899 enum isl_change change;
3901 n_div_i = isl_basic_map_dim(info[i].bmap, isl_dim_div);
3902 n_div_j = isl_basic_map_dim(info[j].bmap, isl_dim_div);
3903 if (n_div_i < 0 || n_div_j < 0)
3904 return isl_change_error;
3905 if (n_div_i <= n_div_j)
3906 return isl_change_none;
3907 if (info[j].bmap->n_eq == 0)
3908 return isl_change_none;
3910 hull_i = isl_basic_map_copy(info[i].bmap);
3911 hull_i = isl_basic_map_plain_affine_hull(hull_i);
3912 hull_j = isl_basic_map_copy(info[j].bmap);
3913 hull_j = isl_basic_map_plain_affine_hull(hull_j);
3915 hull_j = isl_basic_map_intersect(hull_j, isl_basic_map_copy(hull_i));
3916 equal = isl_basic_map_plain_is_equal(hull_i, hull_j);
3917 empty = isl_basic_map_plain_is_empty(hull_j);
3918 isl_basic_map_free(hull_i);
3920 if (equal < 0 || empty < 0)
3921 goto error;
3922 if (equal || empty) {
3923 isl_basic_map_free(hull_j);
3924 return isl_change_none;
3927 list = set_up_substitutions(info[i].bmap, info[j].bmap, hull_j);
3928 if (!list)
3929 return isl_change_error;
3930 n = isl_aff_list_n_aff(list);
3931 if (n < 0)
3932 change = isl_change_error;
3933 else if (n < n_div_i)
3934 change = isl_change_none;
3935 else
3936 change = coalesce_with_subs(i, j, info, list);
3938 isl_aff_list_free(list);
3940 return change;
3941 error:
3942 isl_basic_map_free(hull_j);
3943 return isl_change_error;
3946 /* Check if we can coalesce basic maps "i" and "j" after copying
3947 * those extra integer divisions in one of the basic maps that can
3948 * be simplified away using the extra equalities in the other basic map.
3949 * We require all divs to be known in both basic maps.
3950 * Furthermore, to simplify the comparison of div expressions,
3951 * we do not allow any nested integer divisions.
3953 static enum isl_change check_coalesce_eq(int i, int j,
3954 struct isl_coalesce_info *info)
3956 isl_bool known, nested;
3957 enum isl_change change;
3959 known = isl_basic_map_divs_known(info[i].bmap);
3960 if (known < 0 || !known)
3961 return known < 0 ? isl_change_error : isl_change_none;
3962 known = isl_basic_map_divs_known(info[j].bmap);
3963 if (known < 0 || !known)
3964 return known < 0 ? isl_change_error : isl_change_none;
3965 nested = has_nested_div(info[i].bmap);
3966 if (nested < 0 || nested)
3967 return nested < 0 ? isl_change_error : isl_change_none;
3968 nested = has_nested_div(info[j].bmap);
3969 if (nested < 0 || nested)
3970 return nested < 0 ? isl_change_error : isl_change_none;
3972 change = check_coalesce_into_eq(i, j, info);
3973 if (change != isl_change_none)
3974 return change;
3975 change = check_coalesce_into_eq(j, i, info);
3976 if (change != isl_change_none)
3977 return invert_change(change);
3979 return isl_change_none;
3982 /* Check if the union of the given pair of basic maps
3983 * can be represented by a single basic map.
3984 * If so, replace the pair by the single basic map and return
3985 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
3986 * Otherwise, return isl_change_none.
3988 * We first check if the two basic maps live in the same local space,
3989 * after aligning the divs that differ by only an integer constant.
3990 * If so, we do the complete check. Otherwise, we check if they have
3991 * the same number of integer divisions and can be coalesced, if one is
3992 * an obvious subset of the other or if the extra integer divisions
3993 * of one basic map can be simplified away using the extra equalities
3994 * of the other basic map.
3996 * Note that trying to coalesce pairs of disjuncts with the same
3997 * number, but different local variables may drop the explicit
3998 * representation of some of these local variables.
3999 * This operation is therefore not performed when
4000 * the "coalesce_preserve_locals" option is set.
4002 static enum isl_change coalesce_pair(int i, int j,
4003 struct isl_coalesce_info *info)
4005 int preserve;
4006 isl_bool same;
4007 enum isl_change change;
4008 isl_ctx *ctx;
4010 if (harmonize_divs(&info[i], &info[j]) < 0)
4011 return isl_change_error;
4012 same = same_divs(info[i].bmap, info[j].bmap);
4013 if (same < 0)
4014 return isl_change_error;
4015 if (same)
4016 return coalesce_local_pair(i, j, info);
4018 ctx = isl_basic_map_get_ctx(info[i].bmap);
4019 preserve = isl_options_get_coalesce_preserve_locals(ctx);
4020 if (!preserve && info[i].bmap->n_div == info[j].bmap->n_div) {
4021 change = coalesce_local_pair(i, j, info);
4022 if (change != isl_change_none)
4023 return change;
4026 change = coalesce_divs(i, j, info);
4027 if (change != isl_change_none)
4028 return change;
4030 return check_coalesce_eq(i, j, info);
4033 /* Return the maximum of "a" and "b".
4035 static int isl_max(int a, int b)
4037 return a > b ? a : b;
4040 /* Pairwise coalesce the basic maps in the range [start1, end1[ of "info"
4041 * with those in the range [start2, end2[, skipping basic maps
4042 * that have been removed (either before or within this function).
4044 * For each basic map i in the first range, we check if it can be coalesced
4045 * with respect to any previously considered basic map j in the second range.
4046 * If i gets dropped (because it was a subset of some j), then
4047 * we can move on to the next basic map.
4048 * If j gets dropped, we need to continue checking against the other
4049 * previously considered basic maps.
4050 * If the two basic maps got fused, then we recheck the fused basic map
4051 * against the previously considered basic maps, starting at i + 1
4052 * (even if start2 is greater than i + 1).
4054 static int coalesce_range(isl_ctx *ctx, struct isl_coalesce_info *info,
4055 int start1, int end1, int start2, int end2)
4057 int i, j;
4059 for (i = end1 - 1; i >= start1; --i) {
4060 if (info[i].removed)
4061 continue;
4062 for (j = isl_max(i + 1, start2); j < end2; ++j) {
4063 enum isl_change changed;
4065 if (info[j].removed)
4066 continue;
4067 if (info[i].removed)
4068 isl_die(ctx, isl_error_internal,
4069 "basic map unexpectedly removed",
4070 return -1);
4071 changed = coalesce_pair(i, j, info);
4072 switch (changed) {
4073 case isl_change_error:
4074 return -1;
4075 case isl_change_none:
4076 case isl_change_drop_second:
4077 continue;
4078 case isl_change_drop_first:
4079 j = end2;
4080 break;
4081 case isl_change_fuse:
4082 j = i;
4083 break;
4088 return 0;
4091 /* Pairwise coalesce the basic maps described by the "n" elements of "info".
4093 * We consider groups of basic maps that live in the same apparent
4094 * affine hull and we first coalesce within such a group before we
4095 * coalesce the elements in the group with elements of previously
4096 * considered groups. If a fuse happens during the second phase,
4097 * then we also reconsider the elements within the group.
4099 static int coalesce(isl_ctx *ctx, int n, struct isl_coalesce_info *info)
4101 int start, end;
4103 for (end = n; end > 0; end = start) {
4104 start = end - 1;
4105 while (start >= 1 &&
4106 info[start - 1].hull_hash == info[start].hull_hash)
4107 start--;
4108 if (coalesce_range(ctx, info, start, end, start, end) < 0)
4109 return -1;
4110 if (coalesce_range(ctx, info, start, end, end, n) < 0)
4111 return -1;
4114 return 0;
4117 /* Update the basic maps in "map" based on the information in "info".
4118 * In particular, remove the basic maps that have been marked removed and
4119 * update the others based on the information in the corresponding tableau.
4120 * Since we detected implicit equalities without calling
4121 * isl_basic_map_gauss, we need to do it now.
4122 * Also call isl_basic_map_simplify if we may have lost the definition
4123 * of one or more integer divisions.
4124 * If a basic map is still equal to the one from which the corresponding "info"
4125 * entry was created, then redundant constraint and
4126 * implicit equality constraint detection have been performed
4127 * on the corresponding tableau and the basic map can be marked as such.
4129 static __isl_give isl_map *update_basic_maps(__isl_take isl_map *map,
4130 int n, struct isl_coalesce_info *info)
4132 int i;
4134 if (!map)
4135 return NULL;
4137 for (i = n - 1; i >= 0; --i) {
4138 if (info[i].removed) {
4139 isl_basic_map_free(map->p[i]);
4140 if (i != map->n - 1)
4141 map->p[i] = map->p[map->n - 1];
4142 map->n--;
4143 continue;
4146 info[i].bmap = isl_basic_map_update_from_tab(info[i].bmap,
4147 info[i].tab);
4148 info[i].bmap = isl_basic_map_gauss(info[i].bmap, NULL);
4149 if (info[i].simplify)
4150 info[i].bmap = isl_basic_map_simplify(info[i].bmap);
4151 info[i].bmap = isl_basic_map_finalize(info[i].bmap);
4152 if (!info[i].bmap)
4153 return isl_map_free(map);
4154 if (!info[i].modified) {
4155 ISL_F_SET(info[i].bmap, ISL_BASIC_MAP_NO_IMPLICIT);
4156 ISL_F_SET(info[i].bmap, ISL_BASIC_MAP_NO_REDUNDANT);
4158 isl_basic_map_free(map->p[i]);
4159 map->p[i] = info[i].bmap;
4160 info[i].bmap = NULL;
4163 return map;
4166 /* For each pair of basic maps in the map, check if the union of the two
4167 * can be represented by a single basic map.
4168 * If so, replace the pair by the single basic map and start over.
4170 * We factor out any (hidden) common factor from the constraint
4171 * coefficients to improve the detection of adjacent constraints.
4172 * Note that this function does not call isl_basic_map_gauss,
4173 * but it does make sure that only a single copy of the basic map
4174 * is affected. This means that isl_basic_map_gauss may have
4175 * to be called at the end of the computation (in update_basic_maps)
4176 * on this single copy to ensure that
4177 * the basic maps are not left in an unexpected state.
4179 * Since we are constructing the tableaus of the basic maps anyway,
4180 * we exploit them to detect implicit equalities and redundant constraints.
4181 * This also helps the coalescing as it can ignore the redundant constraints.
4182 * In order to avoid confusion, we make all implicit equalities explicit
4183 * in the basic maps. If the basic map only has a single reference
4184 * (this happens in particular if it was modified by
4185 * isl_basic_map_reduce_coefficients), then isl_basic_map_gauss
4186 * does not get called on the result. The call to
4187 * isl_basic_map_gauss in update_basic_maps resolves this as well.
4188 * For each basic map, we also compute the hash of the apparent affine hull
4189 * for use in coalesce.
4191 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map)
4193 int i;
4194 unsigned n;
4195 isl_ctx *ctx;
4196 struct isl_coalesce_info *info = NULL;
4198 map = isl_map_remove_empty_parts(map);
4199 if (!map)
4200 return NULL;
4202 if (map->n <= 1)
4203 return map;
4205 ctx = isl_map_get_ctx(map);
4206 map = isl_map_sort_divs(map);
4207 map = isl_map_cow(map);
4209 if (!map)
4210 return NULL;
4212 n = map->n;
4214 info = isl_calloc_array(map->ctx, struct isl_coalesce_info, n);
4215 if (!info)
4216 goto error;
4218 for (i = 0; i < map->n; ++i) {
4219 map->p[i] = isl_basic_map_reduce_coefficients(map->p[i]);
4220 if (!map->p[i])
4221 goto error;
4222 info[i].bmap = isl_basic_map_copy(map->p[i]);
4223 info[i].tab = isl_tab_from_basic_map(info[i].bmap, 0);
4224 if (!info[i].tab)
4225 goto error;
4226 if (!ISL_F_ISSET(info[i].bmap, ISL_BASIC_MAP_NO_IMPLICIT))
4227 if (isl_tab_detect_implicit_equalities(info[i].tab) < 0)
4228 goto error;
4229 info[i].bmap = isl_tab_make_equalities_explicit(info[i].tab,
4230 info[i].bmap);
4231 if (!info[i].bmap)
4232 goto error;
4233 if (!ISL_F_ISSET(info[i].bmap, ISL_BASIC_MAP_NO_REDUNDANT))
4234 if (isl_tab_detect_redundant(info[i].tab) < 0)
4235 goto error;
4236 if (coalesce_info_set_hull_hash(&info[i]) < 0)
4237 goto error;
4239 for (i = map->n - 1; i >= 0; --i)
4240 if (info[i].tab->empty)
4241 drop(&info[i]);
4243 if (coalesce(ctx, n, info) < 0)
4244 goto error;
4246 map = update_basic_maps(map, n, info);
4248 clear_coalesce_info(n, info);
4250 return map;
4251 error:
4252 clear_coalesce_info(n, info);
4253 isl_map_free(map);
4254 return NULL;
4257 /* For each pair of basic sets in the set, check if the union of the two
4258 * can be represented by a single basic set.
4259 * If so, replace the pair by the single basic set and start over.
4261 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set)
4263 return set_from_map(isl_map_coalesce(set_to_map(set)));