2 * Copyright 2005-2007 Universiteit Leiden
3 * Copyright 2008-2009 Katholieke Universiteit Leuven
4 * Copyright 2010 INRIA Saclay
6 * Use of this software is governed by the GNU LGPLv2.1 license
8 * Written by Sven Verdoolaege, Leiden Institute of Advanced Computer Science,
9 * Universiteit Leiden, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands
10 * and K.U.Leuven, Departement Computerwetenschappen, Celestijnenlaan 200A,
11 * B-3001 Leuven, Belgium
12 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
13 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
20 /* A private structure to keep track of a mapping together with
21 * a user-specified identifier and a boolean indicating whether
22 * the map represents a must or may access/dependence.
24 struct isl_labeled_map {
30 /* A structure containing the input for dependence analysis:
32 * - n_must + n_may (<= max_source) sources
33 * - a function for determining the relative order of sources and sink
34 * The must sources are placed before the may sources.
36 * domain_map is an auxiliary map that maps the sink access relation
37 * to the domain of this access relation.
39 * restrict_sources is a callback that (if not NULL) will be called
40 * right before any lexicographical maximization.
42 struct isl_access_info {
44 struct isl_labeled_map sink;
45 isl_access_level_before level_before;
46 isl_access_restrict_sources restrict_sources;
50 struct isl_labeled_map source[1];
53 /* A structure containing the output of dependence analysis:
54 * - n_source dependences
55 * - a wrapped subset of the sink for which definitely no source could be found
56 * - a wrapped subset of the sink for which possibly no source could be found
59 isl_set *must_no_source;
60 isl_set *may_no_source;
62 struct isl_labeled_map *dep;
65 /* Construct an isl_access_info structure and fill it up with
66 * the given data. The number of sources is set to 0.
68 __isl_give isl_access_info *isl_access_info_alloc(__isl_take isl_map *sink,
69 void *sink_user, isl_access_level_before fn, int max_source)
72 struct isl_access_info *acc;
77 ctx = isl_map_get_ctx(sink);
78 isl_assert(ctx, max_source >= 0, goto error);
80 acc = isl_calloc(ctx, struct isl_access_info,
81 sizeof(struct isl_access_info) +
82 (max_source - 1) * sizeof(struct isl_labeled_map));
87 acc->sink.data = sink_user;
88 acc->level_before = fn;
89 acc->max_source = max_source;
99 /* Free the given isl_access_info structure.
101 void isl_access_info_free(__isl_take isl_access_info *acc)
107 isl_map_free(acc->domain_map);
108 isl_map_free(acc->sink.map);
109 for (i = 0; i < acc->n_must + acc->n_may; ++i)
110 isl_map_free(acc->source[i].map);
114 isl_ctx *isl_access_info_get_ctx(__isl_keep isl_access_info *acc)
116 return acc ? isl_map_get_ctx(acc->sink.map) : NULL;
119 __isl_give isl_access_info *isl_access_info_set_restrict_sources(
120 __isl_take isl_access_info *acc, isl_access_restrict_sources fn)
124 acc->restrict_sources = fn;
128 /* Add another source to an isl_access_info structure, making
129 * sure the "must" sources are placed before the "may" sources.
130 * This function may be called at most max_source times on a
131 * given isl_access_info structure, with max_source as specified
132 * in the call to isl_access_info_alloc that constructed the structure.
134 __isl_give isl_access_info *isl_access_info_add_source(
135 __isl_take isl_access_info *acc, __isl_take isl_map *source,
136 int must, void *source_user)
142 ctx = isl_map_get_ctx(acc->sink.map);
143 isl_assert(ctx, acc->n_must + acc->n_may < acc->max_source, goto error);
147 acc->source[acc->n_must + acc->n_may] =
148 acc->source[acc->n_must];
149 acc->source[acc->n_must].map = source;
150 acc->source[acc->n_must].data = source_user;
151 acc->source[acc->n_must].must = 1;
154 acc->source[acc->n_must + acc->n_may].map = source;
155 acc->source[acc->n_must + acc->n_may].data = source_user;
156 acc->source[acc->n_must + acc->n_may].must = 0;
162 isl_map_free(source);
163 isl_access_info_free(acc);
167 /* A temporary structure used while sorting the accesses in an isl_access_info.
169 struct isl_access_sort_info {
170 struct isl_map *source_map;
172 struct isl_access_info *acc;
175 /* Return -n, 0 or n (with n a positive value), depending on whether
176 * the source access identified by p1 should be sorted before, together
177 * or after that identified by p2.
179 * If p1 and p2 share a different number of levels with the sink,
180 * then the one with the lowest number of shared levels should be
182 * If they both share no levels, then the order is irrelevant.
183 * Otherwise, if p1 appears before p2, then it should be sorted first.
184 * For more generic initial schedules, it is possible that neither
185 * p1 nor p2 appears before the other, or at least not in any obvious way.
186 * We therefore also check if p2 appears before p1, in which case p2
187 * should be sorted first.
188 * If not, we try to order the two statements based on the description
189 * of the iteration domains. This results in an arbitrary, but fairly
192 static int access_sort_cmp(const void *p1, const void *p2)
194 const struct isl_access_sort_info *i1, *i2;
197 i1 = (const struct isl_access_sort_info *) p1;
198 i2 = (const struct isl_access_sort_info *) p2;
200 level1 = i1->acc->level_before(i1->source_data, i1->acc->sink.data);
201 level2 = i2->acc->level_before(i2->source_data, i2->acc->sink.data);
203 if (level1 != level2 || !level1)
204 return level1 - level2;
206 level1 = i1->acc->level_before(i1->source_data, i2->source_data);
210 level2 = i1->acc->level_before(i2->source_data, i1->source_data);
214 h1 = isl_map_get_hash(i1->source_map);
215 h2 = isl_map_get_hash(i2->source_map);
216 return h1 > h2 ? 1 : h1 < h2 ? -1 : 0;
219 /* Sort the must source accesses in order of increasing number of shared
220 * levels with the sink access.
221 * Source accesses with the same number of shared levels are sorted
222 * in their textual order.
224 static __isl_give isl_access_info *isl_access_info_sort_sources(
225 __isl_take isl_access_info *acc)
229 struct isl_access_sort_info *array;
233 if (acc->n_must <= 1)
236 ctx = isl_map_get_ctx(acc->sink.map);
237 array = isl_alloc_array(ctx, struct isl_access_sort_info, acc->n_must);
241 for (i = 0; i < acc->n_must; ++i) {
242 array[i].source_map = acc->source[i].map;
243 array[i].source_data = acc->source[i].data;
247 qsort(array, acc->n_must, sizeof(struct isl_access_sort_info),
250 for (i = 0; i < acc->n_must; ++i) {
251 acc->source[i].map = array[i].source_map;
252 acc->source[i].data = array[i].source_data;
259 isl_access_info_free(acc);
263 /* Align the parameters of the two spaces if needed and then call
266 static __isl_give isl_space *space_align_and_join(__isl_take isl_space *left,
267 __isl_take isl_space *right)
269 if (isl_space_match(left, isl_dim_param, right, isl_dim_param))
270 return isl_space_join(left, right);
272 left = isl_space_align_params(left, isl_space_copy(right));
273 right = isl_space_align_params(right, isl_space_copy(left));
274 return isl_space_join(left, right);
277 /* Initialize an empty isl_flow structure corresponding to a given
278 * isl_access_info structure.
279 * For each must access, two dependences are created (initialized
280 * to the empty relation), one for the resulting must dependences
281 * and one for the resulting may dependences. May accesses can
282 * only lead to may dependences, so only one dependence is created
284 * This function is private as isl_flow structures are only supposed
285 * to be created by isl_access_info_compute_flow.
287 static __isl_give isl_flow *isl_flow_alloc(__isl_keep isl_access_info *acc)
291 struct isl_flow *dep;
296 ctx = isl_map_get_ctx(acc->sink.map);
297 dep = isl_calloc_type(ctx, struct isl_flow);
301 dep->dep = isl_calloc_array(ctx, struct isl_labeled_map,
302 2 * acc->n_must + acc->n_may);
306 dep->n_source = 2 * acc->n_must + acc->n_may;
307 for (i = 0; i < acc->n_must; ++i) {
309 dim = space_align_and_join(
310 isl_map_get_space(acc->source[i].map),
311 isl_space_reverse(isl_map_get_space(acc->sink.map)));
312 dep->dep[2 * i].map = isl_map_empty(dim);
313 dep->dep[2 * i + 1].map = isl_map_copy(dep->dep[2 * i].map);
314 dep->dep[2 * i].data = acc->source[i].data;
315 dep->dep[2 * i + 1].data = acc->source[i].data;
316 dep->dep[2 * i].must = 1;
317 dep->dep[2 * i + 1].must = 0;
318 if (!dep->dep[2 * i].map || !dep->dep[2 * i + 1].map)
321 for (i = acc->n_must; i < acc->n_must + acc->n_may; ++i) {
323 dim = space_align_and_join(
324 isl_map_get_space(acc->source[i].map),
325 isl_space_reverse(isl_map_get_space(acc->sink.map)));
326 dep->dep[acc->n_must + i].map = isl_map_empty(dim);
327 dep->dep[acc->n_must + i].data = acc->source[i].data;
328 dep->dep[acc->n_must + i].must = 0;
329 if (!dep->dep[acc->n_must + i].map)
339 /* Iterate over all sources and for each resulting flow dependence
340 * that is not empty, call the user specfied function.
341 * The second argument in this function call identifies the source,
342 * while the third argument correspond to the final argument of
343 * the isl_flow_foreach call.
345 int isl_flow_foreach(__isl_keep isl_flow *deps,
346 int (*fn)(__isl_take isl_map *dep, int must, void *dep_user, void *user),
354 for (i = 0; i < deps->n_source; ++i) {
355 if (isl_map_plain_is_empty(deps->dep[i].map))
357 if (fn(isl_map_copy(deps->dep[i].map), deps->dep[i].must,
358 deps->dep[i].data, user) < 0)
365 /* Return a copy of the subset of the sink for which no source could be found.
367 __isl_give isl_map *isl_flow_get_no_source(__isl_keep isl_flow *deps, int must)
373 return isl_set_unwrap(isl_set_copy(deps->must_no_source));
375 return isl_set_unwrap(isl_set_copy(deps->may_no_source));
378 void isl_flow_free(__isl_take isl_flow *deps)
384 isl_set_free(deps->must_no_source);
385 isl_set_free(deps->may_no_source);
387 for (i = 0; i < deps->n_source; ++i)
388 isl_map_free(deps->dep[i].map);
394 isl_ctx *isl_flow_get_ctx(__isl_keep isl_flow *deps)
396 return deps ? isl_set_get_ctx(deps->must_no_source) : NULL;
399 /* Return a map that enforces that the domain iteration occurs after
400 * the range iteration at the given level.
401 * If level is odd, then the domain iteration should occur after
402 * the target iteration in their shared level/2 outermost loops.
403 * In this case we simply need to enforce that these outermost
404 * loop iterations are the same.
405 * If level is even, then the loop iterator of the domain should
406 * be greater than the loop iterator of the range at the last
407 * of the level/2 shared loops, i.e., loop level/2 - 1.
409 static __isl_give isl_map *after_at_level(__isl_take isl_space *dim, int level)
411 struct isl_basic_map *bmap;
414 bmap = isl_basic_map_equal(dim, level/2);
416 bmap = isl_basic_map_more_at(dim, level/2 - 1);
418 return isl_map_from_basic_map(bmap);
421 /* Check if the user has set acc->restrict_sources and if so
422 * intersect the range of "dep" with the result of a call to this function.
424 * Since the user expects a mapping from sink iterations to source iterations,
425 * whereas the domain of "dep" is a wrapped map, mapping sink iterations
426 * to accessed array elements, we first need to project out the accessed
427 * sink array elements by applying acc->domain_map.
429 static __isl_give isl_map *restrict_sources(__isl_take isl_map *dep,
430 struct isl_access_info *acc, int source)
435 if (!acc->restrict_sources)
438 source_map = isl_map_copy(dep);
439 source_map = isl_map_apply_domain(source_map,
440 isl_map_copy(acc->domain_map));
441 param = acc->restrict_sources(source_map, acc->sink.data,
442 acc->source[source].data);
443 dep = isl_map_intersect_range(dep, param);
447 /* Compute the last iteration of must source j that precedes the sink
448 * at the given level for sink iterations in set_C.
449 * The subset of set_C for which no such iteration can be found is returned
452 static struct isl_map *last_source(struct isl_access_info *acc,
453 struct isl_set *set_C,
454 int j, int level, struct isl_set **empty)
456 struct isl_map *read_map;
457 struct isl_map *write_map;
458 struct isl_map *dep_map;
459 struct isl_map *after;
460 struct isl_map *result;
462 read_map = isl_map_copy(acc->sink.map);
463 write_map = isl_map_copy(acc->source[j].map);
464 write_map = isl_map_reverse(write_map);
465 dep_map = isl_map_apply_range(read_map, write_map);
466 after = after_at_level(isl_map_get_space(dep_map), level);
467 dep_map = isl_map_intersect(dep_map, after);
468 dep_map = restrict_sources(dep_map, acc, j);
469 result = isl_map_partial_lexmax(dep_map, set_C, empty);
470 result = isl_map_reverse(result);
475 /* For a given mapping between iterations of must source j and iterations
476 * of the sink, compute the last iteration of must source k preceding
477 * the sink at level before_level for any of the sink iterations,
478 * but following the corresponding iteration of must source j at level
481 static struct isl_map *last_later_source(struct isl_access_info *acc,
482 struct isl_map *old_map,
483 int j, int before_level,
484 int k, int after_level,
485 struct isl_set **empty)
488 struct isl_set *set_C;
489 struct isl_map *read_map;
490 struct isl_map *write_map;
491 struct isl_map *dep_map;
492 struct isl_map *after_write;
493 struct isl_map *before_read;
494 struct isl_map *result;
496 set_C = isl_map_range(isl_map_copy(old_map));
497 read_map = isl_map_copy(acc->sink.map);
498 write_map = isl_map_copy(acc->source[k].map);
500 write_map = isl_map_reverse(write_map);
501 dep_map = isl_map_apply_range(read_map, write_map);
502 dim = space_align_and_join(isl_map_get_space(acc->source[k].map),
503 isl_space_reverse(isl_map_get_space(acc->source[j].map)));
504 after_write = after_at_level(dim, after_level);
505 after_write = isl_map_apply_range(after_write, old_map);
506 after_write = isl_map_reverse(after_write);
507 dep_map = isl_map_intersect(dep_map, after_write);
508 before_read = after_at_level(isl_map_get_space(dep_map), before_level);
509 dep_map = isl_map_intersect(dep_map, before_read);
510 dep_map = restrict_sources(dep_map, acc, k);
511 result = isl_map_partial_lexmax(dep_map, set_C, empty);
512 result = isl_map_reverse(result);
517 /* Given a shared_level between two accesses, return 1 if the
518 * the first can precede the second at the requested target_level.
519 * If the target level is odd, i.e., refers to a statement level
520 * dimension, then first needs to precede second at the requested
521 * level, i.e., shared_level must be equal to target_level.
522 * If the target level is odd, then the two loops should share
523 * at least the requested number of outer loops.
525 static int can_precede_at_level(int shared_level, int target_level)
527 if (shared_level < target_level)
529 if ((target_level % 2) && shared_level > target_level)
534 /* Given a possible flow dependence temp_rel[j] between source j and the sink
535 * at level sink_level, remove those elements for which
536 * there is an iteration of another source k < j that is closer to the sink.
537 * The flow dependences temp_rel[k] are updated with the improved sources.
538 * Any improved source needs to precede the sink at the same level
539 * and needs to follow source j at the same or a deeper level.
540 * The lower this level, the later the execution date of source k.
541 * We therefore consider lower levels first.
543 * If temp_rel[j] is empty, then there can be no improvement and
544 * we return immediately.
546 static int intermediate_sources(__isl_keep isl_access_info *acc,
547 struct isl_map **temp_rel, int j, int sink_level)
550 int depth = 2 * isl_map_dim(acc->source[j].map, isl_dim_in) + 1;
552 if (isl_map_plain_is_empty(temp_rel[j]))
555 for (k = j - 1; k >= 0; --k) {
557 plevel = acc->level_before(acc->source[k].data, acc->sink.data);
558 if (!can_precede_at_level(plevel, sink_level))
561 plevel2 = acc->level_before(acc->source[j].data,
562 acc->source[k].data);
564 for (level = sink_level; level <= depth; ++level) {
566 struct isl_set *trest;
567 struct isl_map *copy;
569 if (!can_precede_at_level(plevel2, level))
572 copy = isl_map_copy(temp_rel[j]);
573 T = last_later_source(acc, copy, j, sink_level, k,
575 if (isl_map_plain_is_empty(T)) {
580 temp_rel[j] = isl_map_intersect_range(temp_rel[j], trest);
581 temp_rel[k] = isl_map_union_disjoint(temp_rel[k], T);
588 /* Compute all iterations of may source j that precedes the sink at the given
589 * level for sink iterations in set_C.
591 static __isl_give isl_map *all_sources(__isl_keep isl_access_info *acc,
592 __isl_take isl_set *set_C, int j, int level)
599 read_map = isl_map_copy(acc->sink.map);
600 read_map = isl_map_intersect_domain(read_map, set_C);
601 write_map = isl_map_copy(acc->source[acc->n_must + j].map);
602 write_map = isl_map_reverse(write_map);
603 dep_map = isl_map_apply_range(read_map, write_map);
604 after = after_at_level(isl_map_get_space(dep_map), level);
605 dep_map = isl_map_intersect(dep_map, after);
607 return isl_map_reverse(dep_map);
610 /* For a given mapping between iterations of must source k and iterations
611 * of the sink, compute the all iteration of may source j preceding
612 * the sink at level before_level for any of the sink iterations,
613 * but following the corresponding iteration of must source k at level
616 static __isl_give isl_map *all_later_sources(__isl_keep isl_access_info *acc,
617 __isl_keep isl_map *old_map,
618 int j, int before_level, int k, int after_level)
625 isl_map *after_write;
626 isl_map *before_read;
628 set_C = isl_map_range(isl_map_copy(old_map));
629 read_map = isl_map_copy(acc->sink.map);
630 read_map = isl_map_intersect_domain(read_map, set_C);
631 write_map = isl_map_copy(acc->source[acc->n_must + j].map);
633 write_map = isl_map_reverse(write_map);
634 dep_map = isl_map_apply_range(read_map, write_map);
635 dim = isl_space_join(isl_map_get_space(acc->source[acc->n_must + j].map),
636 isl_space_reverse(isl_map_get_space(acc->source[k].map)));
637 after_write = after_at_level(dim, after_level);
638 after_write = isl_map_apply_range(after_write, old_map);
639 after_write = isl_map_reverse(after_write);
640 dep_map = isl_map_intersect(dep_map, after_write);
641 before_read = after_at_level(isl_map_get_space(dep_map), before_level);
642 dep_map = isl_map_intersect(dep_map, before_read);
643 return isl_map_reverse(dep_map);
646 /* Given the must and may dependence relations for the must accesses
647 * for level sink_level, check if there are any accesses of may access j
648 * that occur in between and return their union.
649 * If some of these accesses are intermediate with respect to
650 * (previously thought to be) must dependences, then these
651 * must dependences are turned into may dependences.
653 static __isl_give isl_map *all_intermediate_sources(
654 __isl_keep isl_access_info *acc, __isl_take isl_map *map,
655 struct isl_map **must_rel, struct isl_map **may_rel,
656 int j, int sink_level)
659 int depth = 2 * isl_map_dim(acc->source[acc->n_must + j].map,
662 for (k = 0; k < acc->n_must; ++k) {
665 if (isl_map_plain_is_empty(may_rel[k]) &&
666 isl_map_plain_is_empty(must_rel[k]))
669 plevel = acc->level_before(acc->source[k].data,
670 acc->source[acc->n_must + j].data);
672 for (level = sink_level; level <= depth; ++level) {
677 if (!can_precede_at_level(plevel, level))
680 copy = isl_map_copy(may_rel[k]);
681 T = all_later_sources(acc, copy, j, sink_level, k, level);
682 map = isl_map_union(map, T);
684 copy = isl_map_copy(must_rel[k]);
685 T = all_later_sources(acc, copy, j, sink_level, k, level);
686 ran = isl_map_range(isl_map_copy(T));
687 map = isl_map_union(map, T);
688 may_rel[k] = isl_map_union_disjoint(may_rel[k],
689 isl_map_intersect_range(isl_map_copy(must_rel[k]),
691 T = isl_map_from_domain_and_range(
693 isl_space_domain(isl_map_get_space(must_rel[k]))),
695 must_rel[k] = isl_map_subtract(must_rel[k], T);
702 /* Compute dependences for the case where all accesses are "may"
703 * accesses, which boils down to computing memory based dependences.
704 * The generic algorithm would also work in this case, but it would
705 * be overkill to use it.
707 static __isl_give isl_flow *compute_mem_based_dependences(
708 __isl_keep isl_access_info *acc)
715 res = isl_flow_alloc(acc);
719 mustdo = isl_map_domain(isl_map_copy(acc->sink.map));
720 maydo = isl_set_copy(mustdo);
722 for (i = 0; i < acc->n_may; ++i) {
729 plevel = acc->level_before(acc->source[i].data, acc->sink.data);
730 is_before = plevel & 1;
733 dim = isl_map_get_space(res->dep[i].map);
735 before = isl_map_lex_le_first(dim, plevel);
737 before = isl_map_lex_lt_first(dim, plevel);
738 dep = isl_map_apply_range(isl_map_copy(acc->source[i].map),
739 isl_map_reverse(isl_map_copy(acc->sink.map)));
740 dep = isl_map_intersect(dep, before);
741 mustdo = isl_set_subtract(mustdo,
742 isl_map_range(isl_map_copy(dep)));
743 res->dep[i].map = isl_map_union(res->dep[i].map, dep);
746 res->may_no_source = isl_set_subtract(maydo, isl_set_copy(mustdo));
747 res->must_no_source = mustdo;
752 /* Compute dependences for the case where there is at least one
755 * The core algorithm considers all levels in which a source may precede
756 * the sink, where a level may either be a statement level or a loop level.
757 * The outermost statement level is 1, the first loop level is 2, etc...
758 * The algorithm basically does the following:
759 * for all levels l of the read access from innermost to outermost
760 * for all sources w that may precede the sink access at that level
761 * compute the last iteration of the source that precedes the sink access
763 * add result to possible last accesses at level l of source w
764 * for all sources w2 that we haven't considered yet at this level that may
765 * also precede the sink access
766 * for all levels l2 of w from l to innermost
767 * for all possible last accesses dep of w at l
768 * compute last iteration of w2 between the source and sink
770 * add result to possible last accesses at level l of write w2
771 * and replace possible last accesses dep by the remainder
774 * The above algorithm is applied to the must access. During the course
775 * of the algorithm, we keep track of sink iterations that still
776 * need to be considered. These iterations are split into those that
777 * haven't been matched to any source access (mustdo) and those that have only
778 * been matched to may accesses (maydo).
779 * At the end of each level, we also consider the may accesses.
780 * In particular, we consider may accesses that precede the remaining
781 * sink iterations, moving elements from mustdo to maydo when appropriate,
782 * and may accesses that occur between a must source and a sink of any
783 * dependences found at the current level, turning must dependences into
784 * may dependences when appropriate.
787 static __isl_give isl_flow *compute_val_based_dependences(
788 __isl_keep isl_access_info *acc)
792 isl_set *mustdo = NULL;
793 isl_set *maydo = NULL;
796 isl_map **must_rel = NULL;
797 isl_map **may_rel = NULL;
802 res = isl_flow_alloc(acc);
805 ctx = isl_map_get_ctx(acc->sink.map);
807 depth = 2 * isl_map_dim(acc->sink.map, isl_dim_in) + 1;
808 mustdo = isl_map_domain(isl_map_copy(acc->sink.map));
809 maydo = isl_set_empty_like(mustdo);
810 if (!mustdo || !maydo)
812 if (isl_set_plain_is_empty(mustdo))
815 must_rel = isl_alloc_array(ctx, struct isl_map *, acc->n_must);
816 may_rel = isl_alloc_array(ctx, struct isl_map *, acc->n_must);
817 if (!must_rel || !may_rel)
820 for (level = depth; level >= 1; --level) {
821 for (j = acc->n_must-1; j >=0; --j) {
822 must_rel[j] = isl_map_empty_like(res->dep[j].map);
823 may_rel[j] = isl_map_copy(must_rel[j]);
826 for (j = acc->n_must - 1; j >= 0; --j) {
828 struct isl_set *rest;
831 plevel = acc->level_before(acc->source[j].data,
833 if (!can_precede_at_level(plevel, level))
836 T = last_source(acc, mustdo, j, level, &rest);
837 must_rel[j] = isl_map_union_disjoint(must_rel[j], T);
840 intermediate_sources(acc, must_rel, j, level);
842 T = last_source(acc, maydo, j, level, &rest);
843 may_rel[j] = isl_map_union_disjoint(may_rel[j], T);
846 intermediate_sources(acc, may_rel, j, level);
848 if (isl_set_plain_is_empty(mustdo) &&
849 isl_set_plain_is_empty(maydo))
852 for (j = j - 1; j >= 0; --j) {
855 plevel = acc->level_before(acc->source[j].data,
857 if (!can_precede_at_level(plevel, level))
860 intermediate_sources(acc, must_rel, j, level);
861 intermediate_sources(acc, may_rel, j, level);
864 for (j = 0; j < acc->n_may; ++j) {
869 plevel = acc->level_before(acc->source[acc->n_must + j].data,
871 if (!can_precede_at_level(plevel, level))
874 T = all_sources(acc, isl_set_copy(maydo), j, level);
875 res->dep[2 * acc->n_must + j].map =
876 isl_map_union(res->dep[2 * acc->n_must + j].map, T);
877 T = all_sources(acc, isl_set_copy(mustdo), j, level);
878 ran = isl_map_range(isl_map_copy(T));
879 res->dep[2 * acc->n_must + j].map =
880 isl_map_union(res->dep[2 * acc->n_must + j].map, T);
881 mustdo = isl_set_subtract(mustdo, isl_set_copy(ran));
882 maydo = isl_set_union_disjoint(maydo, ran);
884 T = res->dep[2 * acc->n_must + j].map;
885 T = all_intermediate_sources(acc, T, must_rel, may_rel,
887 res->dep[2 * acc->n_must + j].map = T;
890 for (j = acc->n_must - 1; j >= 0; --j) {
891 res->dep[2 * j].map =
892 isl_map_union_disjoint(res->dep[2 * j].map,
894 res->dep[2 * j + 1].map =
895 isl_map_union_disjoint(res->dep[2 * j + 1].map,
899 if (isl_set_plain_is_empty(mustdo) &&
900 isl_set_plain_is_empty(maydo))
907 res->must_no_source = mustdo;
908 res->may_no_source = maydo;
912 isl_set_free(mustdo);
919 /* Given a "sink" access, a list of n "source" accesses,
920 * compute for each iteration of the sink access
921 * and for each element accessed by that iteration,
922 * the source access in the list that last accessed the
923 * element accessed by the sink access before this sink access.
924 * Each access is given as a map from the loop iterators
925 * to the array indices.
926 * The result is a list of n relations between source and sink
927 * iterations and a subset of the domain of the sink access,
928 * corresponding to those iterations that access an element
929 * not previously accessed.
931 * To deal with multi-valued sink access relations, the sink iteration
932 * domain is first extended with dimensions that correspond to the data
933 * space. After the computation is finished, these extra dimensions are
934 * projected out again.
936 __isl_give isl_flow *isl_access_info_compute_flow(__isl_take isl_access_info *acc)
939 struct isl_flow *res = NULL;
944 acc->domain_map = isl_map_domain_map(isl_map_copy(acc->sink.map));
945 acc->sink.map = isl_map_range_map(acc->sink.map);
949 if (acc->n_must == 0)
950 res = compute_mem_based_dependences(acc);
952 acc = isl_access_info_sort_sources(acc);
953 res = compute_val_based_dependences(acc);
958 for (j = 0; j < res->n_source; ++j) {
959 res->dep[j].map = isl_map_apply_range(res->dep[j].map,
960 isl_map_copy(acc->domain_map));
961 if (!res->dep[j].map)
964 if (!res->must_no_source || !res->may_no_source)
967 isl_access_info_free(acc);
970 isl_access_info_free(acc);
976 /* Keep track of some information about a schedule for a given
977 * access. In particular, keep track of which dimensions
978 * have a constant value and of the actual constant values.
980 struct isl_sched_info {
985 static void sched_info_free(__isl_take struct isl_sched_info *info)
989 isl_vec_free(info->cst);
994 /* Extract information on the constant dimensions of the schedule
995 * for a given access. The "map" is of the form
999 * with S the schedule domain, D the iteration domain and A the data domain.
1001 static __isl_give struct isl_sched_info *sched_info_alloc(
1002 __isl_keep isl_map *map)
1006 struct isl_sched_info *info;
1012 dim = isl_space_unwrap(isl_space_domain(isl_map_get_space(map)));
1015 n = isl_space_dim(dim, isl_dim_in);
1016 isl_space_free(dim);
1018 ctx = isl_map_get_ctx(map);
1019 info = isl_alloc_type(ctx, struct isl_sched_info);
1022 info->is_cst = isl_alloc_array(ctx, int, n);
1023 info->cst = isl_vec_alloc(ctx, n);
1024 if (!info->is_cst || !info->cst)
1027 for (i = 0; i < n; ++i)
1028 info->is_cst[i] = isl_map_plain_is_fixed(map, isl_dim_in, i,
1033 sched_info_free(info);
1037 struct isl_compute_flow_data {
1038 isl_union_map *must_source;
1039 isl_union_map *may_source;
1040 isl_union_map *must_dep;
1041 isl_union_map *may_dep;
1042 isl_union_map *must_no_source;
1043 isl_union_map *may_no_source;
1048 struct isl_sched_info *sink_info;
1049 struct isl_sched_info **source_info;
1050 isl_access_info *accesses;
1053 static int count_matching_array(__isl_take isl_map *map, void *user)
1057 struct isl_compute_flow_data *data;
1059 data = (struct isl_compute_flow_data *)user;
1061 dim = isl_space_range(isl_map_get_space(map));
1063 eq = isl_space_is_equal(dim, data->dim);
1065 isl_space_free(dim);
1076 static int collect_matching_array(__isl_take isl_map *map, void *user)
1080 struct isl_sched_info *info;
1081 struct isl_compute_flow_data *data;
1083 data = (struct isl_compute_flow_data *)user;
1085 dim = isl_space_range(isl_map_get_space(map));
1087 eq = isl_space_is_equal(dim, data->dim);
1089 isl_space_free(dim);
1098 info = sched_info_alloc(map);
1099 data->source_info[data->count] = info;
1101 data->accesses = isl_access_info_add_source(data->accesses,
1102 map, data->must, info);
1112 /* Determine the shared nesting level and the "textual order" of
1113 * the given accesses.
1115 * We first determine the minimal schedule dimension for both accesses.
1117 * If among those dimensions, we can find one where both have a fixed
1118 * value and if moreover those values are different, then the previous
1119 * dimension is the last shared nesting level and the textual order
1120 * is determined based on the order of the fixed values.
1121 * If no such fixed values can be found, then we set the shared
1122 * nesting level to the minimal schedule dimension, with no textual ordering.
1124 static int before(void *first, void *second)
1126 struct isl_sched_info *info1 = first;
1127 struct isl_sched_info *info2 = second;
1131 n1 = info1->cst->size;
1132 n2 = info2->cst->size;
1137 for (i = 0; i < n1; ++i) {
1138 if (!info1->is_cst[i])
1140 if (!info2->is_cst[i])
1142 if (isl_int_eq(info1->cst->el[i], info2->cst->el[i]))
1144 return 2 * i + isl_int_lt(info1->cst->el[i], info2->cst->el[i]);
1150 /* Given a sink access, look for all the source accesses that access
1151 * the same array and perform dataflow analysis on them using
1152 * isl_access_info_compute_flow.
1154 static int compute_flow(__isl_take isl_map *map, void *user)
1158 struct isl_compute_flow_data *data;
1161 data = (struct isl_compute_flow_data *)user;
1163 ctx = isl_map_get_ctx(map);
1165 data->accesses = NULL;
1166 data->sink_info = NULL;
1167 data->source_info = NULL;
1169 data->dim = isl_space_range(isl_map_get_space(map));
1171 if (isl_union_map_foreach_map(data->must_source,
1172 &count_matching_array, data) < 0)
1174 if (isl_union_map_foreach_map(data->may_source,
1175 &count_matching_array, data) < 0)
1178 data->sink_info = sched_info_alloc(map);
1179 data->source_info = isl_calloc_array(ctx, struct isl_sched_info *,
1182 data->accesses = isl_access_info_alloc(isl_map_copy(map),
1183 data->sink_info, &before, data->count);
1184 if (!data->sink_info || !data->source_info || !data->accesses)
1188 if (isl_union_map_foreach_map(data->must_source,
1189 &collect_matching_array, data) < 0)
1192 if (isl_union_map_foreach_map(data->may_source,
1193 &collect_matching_array, data) < 0)
1196 flow = isl_access_info_compute_flow(data->accesses);
1197 data->accesses = NULL;
1202 data->must_no_source = isl_union_map_union(data->must_no_source,
1203 isl_union_map_from_map(isl_flow_get_no_source(flow, 1)));
1204 data->may_no_source = isl_union_map_union(data->may_no_source,
1205 isl_union_map_from_map(isl_flow_get_no_source(flow, 0)));
1207 for (i = 0; i < flow->n_source; ++i) {
1209 dep = isl_union_map_from_map(isl_map_copy(flow->dep[i].map));
1210 if (flow->dep[i].must)
1211 data->must_dep = isl_union_map_union(data->must_dep, dep);
1213 data->may_dep = isl_union_map_union(data->may_dep, dep);
1216 isl_flow_free(flow);
1218 sched_info_free(data->sink_info);
1219 if (data->source_info) {
1220 for (i = 0; i < data->count; ++i)
1221 sched_info_free(data->source_info[i]);
1222 free(data->source_info);
1224 isl_space_free(data->dim);
1229 isl_access_info_free(data->accesses);
1230 sched_info_free(data->sink_info);
1231 if (data->source_info) {
1232 for (i = 0; i < data->count; ++i)
1233 sched_info_free(data->source_info[i]);
1234 free(data->source_info);
1236 isl_space_free(data->dim);
1242 /* Given a collection of "sink" and "source" accesses,
1243 * compute for each iteration of a sink access
1244 * and for each element accessed by that iteration,
1245 * the source access in the list that last accessed the
1246 * element accessed by the sink access before this sink access.
1247 * Each access is given as a map from the loop iterators
1248 * to the array indices.
1249 * The result is a relations between source and sink
1250 * iterations and a subset of the domain of the sink accesses,
1251 * corresponding to those iterations that access an element
1252 * not previously accessed.
1254 * We first prepend the schedule dimensions to the domain
1255 * of the accesses so that we can easily compare their relative order.
1256 * Then we consider each sink access individually in compute_flow.
1258 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
1259 __isl_take isl_union_map *must_source,
1260 __isl_take isl_union_map *may_source,
1261 __isl_take isl_union_map *schedule,
1262 __isl_give isl_union_map **must_dep, __isl_give isl_union_map **may_dep,
1263 __isl_give isl_union_map **must_no_source,
1264 __isl_give isl_union_map **may_no_source)
1267 isl_union_map *range_map = NULL;
1268 struct isl_compute_flow_data data;
1270 sink = isl_union_map_align_params(sink,
1271 isl_union_map_get_space(must_source));
1272 sink = isl_union_map_align_params(sink,
1273 isl_union_map_get_space(may_source));
1274 sink = isl_union_map_align_params(sink,
1275 isl_union_map_get_space(schedule));
1276 dim = isl_union_map_get_space(sink);
1277 must_source = isl_union_map_align_params(must_source, isl_space_copy(dim));
1278 may_source = isl_union_map_align_params(may_source, isl_space_copy(dim));
1279 schedule = isl_union_map_align_params(schedule, isl_space_copy(dim));
1281 schedule = isl_union_map_reverse(schedule);
1282 range_map = isl_union_map_range_map(schedule);
1283 schedule = isl_union_map_reverse(isl_union_map_copy(range_map));
1284 sink = isl_union_map_apply_domain(sink, isl_union_map_copy(schedule));
1285 must_source = isl_union_map_apply_domain(must_source,
1286 isl_union_map_copy(schedule));
1287 may_source = isl_union_map_apply_domain(may_source, schedule);
1289 data.must_source = must_source;
1290 data.may_source = may_source;
1291 data.must_dep = must_dep ?
1292 isl_union_map_empty(isl_space_copy(dim)) : NULL;
1293 data.may_dep = may_dep ? isl_union_map_empty(isl_space_copy(dim)) : NULL;
1294 data.must_no_source = must_no_source ?
1295 isl_union_map_empty(isl_space_copy(dim)) : NULL;
1296 data.may_no_source = may_no_source ?
1297 isl_union_map_empty(isl_space_copy(dim)) : NULL;
1299 isl_space_free(dim);
1301 if (isl_union_map_foreach_map(sink, &compute_flow, &data) < 0)
1304 isl_union_map_free(sink);
1305 isl_union_map_free(must_source);
1306 isl_union_map_free(may_source);
1309 data.must_dep = isl_union_map_apply_domain(data.must_dep,
1310 isl_union_map_copy(range_map));
1311 data.must_dep = isl_union_map_apply_range(data.must_dep,
1312 isl_union_map_copy(range_map));
1313 *must_dep = data.must_dep;
1316 data.may_dep = isl_union_map_apply_domain(data.may_dep,
1317 isl_union_map_copy(range_map));
1318 data.may_dep = isl_union_map_apply_range(data.may_dep,
1319 isl_union_map_copy(range_map));
1320 *may_dep = data.may_dep;
1322 if (must_no_source) {
1323 data.must_no_source = isl_union_map_apply_domain(
1324 data.must_no_source, isl_union_map_copy(range_map));
1325 *must_no_source = data.must_no_source;
1327 if (may_no_source) {
1328 data.may_no_source = isl_union_map_apply_domain(
1329 data.may_no_source, isl_union_map_copy(range_map));
1330 *may_no_source = data.may_no_source;
1333 isl_union_map_free(range_map);
1337 isl_union_map_free(range_map);
1338 isl_union_map_free(sink);
1339 isl_union_map_free(must_source);
1340 isl_union_map_free(may_source);
1341 isl_union_map_free(data.must_dep);
1342 isl_union_map_free(data.may_dep);
1343 isl_union_map_free(data.must_no_source);
1344 isl_union_map_free(data.may_no_source);
1351 *must_no_source = NULL;
1353 *may_no_source = NULL;