2 * Copyright 2005-2007 Universiteit Leiden
3 * Copyright 2008-2009 Katholieke Universiteit Leuven
4 * Copyright 2010 INRIA Saclay
5 * Copyright 2012 Universiteit Leiden
7 * Use of this software is governed by the GNU LGPLv2.1 license
9 * Written by Sven Verdoolaege, Leiden Institute of Advanced Computer Science,
10 * Universiteit Leiden, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands
11 * and K.U.Leuven, Departement Computerwetenschappen, Celestijnenlaan 200A,
12 * 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
20 #include <isl_qsort.h>
22 enum isl_restriction_type {
23 isl_restriction_type_empty,
24 isl_restriction_type_none,
25 isl_restriction_type_input,
26 isl_restriction_type_output
29 struct isl_restriction {
30 enum isl_restriction_type type;
36 /* Create a restriction of the given type.
38 static __isl_give isl_restriction *isl_restriction_alloc(
39 __isl_take isl_map *source_map, enum isl_restriction_type type)
42 isl_restriction *restr;
47 ctx = isl_map_get_ctx(source_map);
48 restr = isl_calloc_type(ctx, struct isl_restriction);
54 isl_map_free(source_map);
57 isl_map_free(source_map);
61 /* Create a restriction that doesn't restrict anything.
63 __isl_give isl_restriction *isl_restriction_none(__isl_take isl_map *source_map)
65 return isl_restriction_alloc(source_map, isl_restriction_type_none);
68 /* Create a restriction that removes everything.
70 __isl_give isl_restriction *isl_restriction_empty(
71 __isl_take isl_map *source_map)
73 return isl_restriction_alloc(source_map, isl_restriction_type_empty);
76 /* Create a restriction on the input of the maximization problem
77 * based on the given source and sink restrictions.
79 __isl_give isl_restriction *isl_restriction_input(
80 __isl_take isl_set *source_restr, __isl_take isl_set *sink_restr)
83 isl_restriction *restr;
85 if (!source_restr || !sink_restr)
88 ctx = isl_set_get_ctx(source_restr);
89 restr = isl_calloc_type(ctx, struct isl_restriction);
93 restr->type = isl_restriction_type_input;
94 restr->source = source_restr;
95 restr->sink = sink_restr;
99 isl_set_free(source_restr);
100 isl_set_free(sink_restr);
104 /* Create a restriction on the output of the maximization problem
105 * based on the given source restriction.
107 __isl_give isl_restriction *isl_restriction_output(
108 __isl_take isl_set *source_restr)
111 isl_restriction *restr;
116 ctx = isl_set_get_ctx(source_restr);
117 restr = isl_calloc_type(ctx, struct isl_restriction);
121 restr->type = isl_restriction_type_output;
122 restr->source = source_restr;
126 isl_set_free(source_restr);
130 void *isl_restriction_free(__isl_take isl_restriction *restr)
135 isl_set_free(restr->source);
136 isl_set_free(restr->sink);
141 isl_ctx *isl_restriction_get_ctx(__isl_keep isl_restriction *restr)
143 return restr ? isl_set_get_ctx(restr->source) : NULL;
146 /* A private structure to keep track of a mapping together with
147 * a user-specified identifier and a boolean indicating whether
148 * the map represents a must or may access/dependence.
150 struct isl_labeled_map {
156 /* A structure containing the input for dependence analysis:
158 * - n_must + n_may (<= max_source) sources
159 * - a function for determining the relative order of sources and sink
160 * The must sources are placed before the may sources.
162 * domain_map is an auxiliary map that maps the sink access relation
163 * to the domain of this access relation.
165 * restrict_fn is a callback that (if not NULL) will be called
166 * right before any lexicographical maximization.
168 struct isl_access_info {
170 struct isl_labeled_map sink;
171 isl_access_level_before level_before;
173 isl_access_restrict restrict_fn;
179 struct isl_labeled_map source[1];
182 /* A structure containing the output of dependence analysis:
183 * - n_source dependences
184 * - a wrapped subset of the sink for which definitely no source could be found
185 * - a wrapped subset of the sink for which possibly no source could be found
188 isl_set *must_no_source;
189 isl_set *may_no_source;
191 struct isl_labeled_map *dep;
194 /* Construct an isl_access_info structure and fill it up with
195 * the given data. The number of sources is set to 0.
197 __isl_give isl_access_info *isl_access_info_alloc(__isl_take isl_map *sink,
198 void *sink_user, isl_access_level_before fn, int max_source)
201 struct isl_access_info *acc;
206 ctx = isl_map_get_ctx(sink);
207 isl_assert(ctx, max_source >= 0, goto error);
209 acc = isl_calloc(ctx, struct isl_access_info,
210 sizeof(struct isl_access_info) +
211 (max_source - 1) * sizeof(struct isl_labeled_map));
215 acc->sink.map = sink;
216 acc->sink.data = sink_user;
217 acc->level_before = fn;
218 acc->max_source = max_source;
228 /* Free the given isl_access_info structure.
230 void isl_access_info_free(__isl_take isl_access_info *acc)
236 isl_map_free(acc->domain_map);
237 isl_map_free(acc->sink.map);
238 for (i = 0; i < acc->n_must + acc->n_may; ++i)
239 isl_map_free(acc->source[i].map);
243 isl_ctx *isl_access_info_get_ctx(__isl_keep isl_access_info *acc)
245 return acc ? isl_map_get_ctx(acc->sink.map) : NULL;
248 __isl_give isl_access_info *isl_access_info_set_restrict(
249 __isl_take isl_access_info *acc, isl_access_restrict fn, void *user)
253 acc->restrict_fn = fn;
254 acc->restrict_user = user;
258 /* Add another source to an isl_access_info structure, making
259 * sure the "must" sources are placed before the "may" sources.
260 * This function may be called at most max_source times on a
261 * given isl_access_info structure, with max_source as specified
262 * in the call to isl_access_info_alloc that constructed the structure.
264 __isl_give isl_access_info *isl_access_info_add_source(
265 __isl_take isl_access_info *acc, __isl_take isl_map *source,
266 int must, void *source_user)
272 ctx = isl_map_get_ctx(acc->sink.map);
273 isl_assert(ctx, acc->n_must + acc->n_may < acc->max_source, goto error);
277 acc->source[acc->n_must + acc->n_may] =
278 acc->source[acc->n_must];
279 acc->source[acc->n_must].map = source;
280 acc->source[acc->n_must].data = source_user;
281 acc->source[acc->n_must].must = 1;
284 acc->source[acc->n_must + acc->n_may].map = source;
285 acc->source[acc->n_must + acc->n_may].data = source_user;
286 acc->source[acc->n_must + acc->n_may].must = 0;
292 isl_map_free(source);
293 isl_access_info_free(acc);
297 /* Return -n, 0 or n (with n a positive value), depending on whether
298 * the source access identified by p1 should be sorted before, together
299 * or after that identified by p2.
301 * If p1 appears before p2, then it should be sorted first.
302 * For more generic initial schedules, it is possible that neither
303 * p1 nor p2 appears before the other, or at least not in any obvious way.
304 * We therefore also check if p2 appears before p1, in which case p2
305 * should be sorted first.
306 * If not, we try to order the two statements based on the description
307 * of the iteration domains. This results in an arbitrary, but fairly
310 static int access_sort_cmp(const void *p1, const void *p2, void *user)
312 isl_access_info *acc = user;
313 const struct isl_labeled_map *i1, *i2;
316 i1 = (const struct isl_labeled_map *) p1;
317 i2 = (const struct isl_labeled_map *) p2;
319 level1 = acc->level_before(i1->data, i2->data);
323 level2 = acc->level_before(i2->data, i1->data);
327 h1 = isl_map_get_hash(i1->map);
328 h2 = isl_map_get_hash(i2->map);
329 return h1 > h2 ? 1 : h1 < h2 ? -1 : 0;
332 /* Sort the must source accesses in their textual order.
334 static __isl_give isl_access_info *isl_access_info_sort_sources(
335 __isl_take isl_access_info *acc)
339 if (acc->n_must <= 1)
342 isl_quicksort(acc->source, acc->n_must, sizeof(struct isl_labeled_map),
343 access_sort_cmp, acc);
348 /* Align the parameters of the two spaces if needed and then call
351 static __isl_give isl_space *space_align_and_join(__isl_take isl_space *left,
352 __isl_take isl_space *right)
354 if (isl_space_match(left, isl_dim_param, right, isl_dim_param))
355 return isl_space_join(left, right);
357 left = isl_space_align_params(left, isl_space_copy(right));
358 right = isl_space_align_params(right, isl_space_copy(left));
359 return isl_space_join(left, right);
362 /* Initialize an empty isl_flow structure corresponding to a given
363 * isl_access_info structure.
364 * For each must access, two dependences are created (initialized
365 * to the empty relation), one for the resulting must dependences
366 * and one for the resulting may dependences. May accesses can
367 * only lead to may dependences, so only one dependence is created
369 * This function is private as isl_flow structures are only supposed
370 * to be created by isl_access_info_compute_flow.
372 static __isl_give isl_flow *isl_flow_alloc(__isl_keep isl_access_info *acc)
376 struct isl_flow *dep;
381 ctx = isl_map_get_ctx(acc->sink.map);
382 dep = isl_calloc_type(ctx, struct isl_flow);
386 dep->dep = isl_calloc_array(ctx, struct isl_labeled_map,
387 2 * acc->n_must + acc->n_may);
391 dep->n_source = 2 * acc->n_must + acc->n_may;
392 for (i = 0; i < acc->n_must; ++i) {
394 dim = space_align_and_join(
395 isl_map_get_space(acc->source[i].map),
396 isl_space_reverse(isl_map_get_space(acc->sink.map)));
397 dep->dep[2 * i].map = isl_map_empty(dim);
398 dep->dep[2 * i + 1].map = isl_map_copy(dep->dep[2 * i].map);
399 dep->dep[2 * i].data = acc->source[i].data;
400 dep->dep[2 * i + 1].data = acc->source[i].data;
401 dep->dep[2 * i].must = 1;
402 dep->dep[2 * i + 1].must = 0;
403 if (!dep->dep[2 * i].map || !dep->dep[2 * i + 1].map)
406 for (i = acc->n_must; i < acc->n_must + acc->n_may; ++i) {
408 dim = space_align_and_join(
409 isl_map_get_space(acc->source[i].map),
410 isl_space_reverse(isl_map_get_space(acc->sink.map)));
411 dep->dep[acc->n_must + i].map = isl_map_empty(dim);
412 dep->dep[acc->n_must + i].data = acc->source[i].data;
413 dep->dep[acc->n_must + i].must = 0;
414 if (!dep->dep[acc->n_must + i].map)
424 /* Iterate over all sources and for each resulting flow dependence
425 * that is not empty, call the user specfied function.
426 * The second argument in this function call identifies the source,
427 * while the third argument correspond to the final argument of
428 * the isl_flow_foreach call.
430 int isl_flow_foreach(__isl_keep isl_flow *deps,
431 int (*fn)(__isl_take isl_map *dep, int must, void *dep_user, void *user),
439 for (i = 0; i < deps->n_source; ++i) {
440 if (isl_map_plain_is_empty(deps->dep[i].map))
442 if (fn(isl_map_copy(deps->dep[i].map), deps->dep[i].must,
443 deps->dep[i].data, user) < 0)
450 /* Return a copy of the subset of the sink for which no source could be found.
452 __isl_give isl_map *isl_flow_get_no_source(__isl_keep isl_flow *deps, int must)
458 return isl_set_unwrap(isl_set_copy(deps->must_no_source));
460 return isl_set_unwrap(isl_set_copy(deps->may_no_source));
463 void isl_flow_free(__isl_take isl_flow *deps)
469 isl_set_free(deps->must_no_source);
470 isl_set_free(deps->may_no_source);
472 for (i = 0; i < deps->n_source; ++i)
473 isl_map_free(deps->dep[i].map);
479 isl_ctx *isl_flow_get_ctx(__isl_keep isl_flow *deps)
481 return deps ? isl_set_get_ctx(deps->must_no_source) : NULL;
484 /* Return a map that enforces that the domain iteration occurs after
485 * the range iteration at the given level.
486 * If level is odd, then the domain iteration should occur after
487 * the target iteration in their shared level/2 outermost loops.
488 * In this case we simply need to enforce that these outermost
489 * loop iterations are the same.
490 * If level is even, then the loop iterator of the domain should
491 * be greater than the loop iterator of the range at the last
492 * of the level/2 shared loops, i.e., loop level/2 - 1.
494 static __isl_give isl_map *after_at_level(__isl_take isl_space *dim, int level)
496 struct isl_basic_map *bmap;
499 bmap = isl_basic_map_equal(dim, level/2);
501 bmap = isl_basic_map_more_at(dim, level/2 - 1);
503 return isl_map_from_basic_map(bmap);
506 /* Compute the partial lexicographic maximum of "dep" on domain "sink",
507 * but first check if the user has set acc->restrict_fn and if so
508 * update either the input or the output of the maximization problem
509 * with respect to the resulting restriction.
511 * Since the user expects a mapping from sink iterations to source iterations,
512 * whereas the domain of "dep" is a wrapped map, mapping sink iterations
513 * to accessed array elements, we first need to project out the accessed
514 * sink array elements by applying acc->domain_map.
515 * Similarly, the sink restriction specified by the user needs to be
516 * converted back to the wrapped map.
518 static __isl_give isl_map *restricted_partial_lexmax(
519 __isl_keep isl_access_info *acc, __isl_take isl_map *dep,
520 int source, __isl_take isl_set *sink, __isl_give isl_set **empty)
523 isl_restriction *restr;
524 isl_set *sink_domain;
528 if (!acc->restrict_fn)
529 return isl_map_partial_lexmax(dep, sink, empty);
531 source_map = isl_map_copy(dep);
532 source_map = isl_map_apply_domain(source_map,
533 isl_map_copy(acc->domain_map));
534 sink_domain = isl_set_copy(sink);
535 sink_domain = isl_set_apply(sink_domain, isl_map_copy(acc->domain_map));
536 restr = acc->restrict_fn(source_map, sink_domain,
537 acc->source[source].data, acc->restrict_user);
538 isl_set_free(sink_domain);
539 isl_map_free(source_map);
543 if (restr->type == isl_restriction_type_input) {
544 dep = isl_map_intersect_range(dep, isl_set_copy(restr->source));
545 sink_restr = isl_set_copy(restr->sink);
546 sink_restr = isl_set_apply(sink_restr,
547 isl_map_reverse(isl_map_copy(acc->domain_map)));
548 sink = isl_set_intersect(sink, sink_restr);
549 } else if (restr->type == isl_restriction_type_empty) {
550 isl_space *space = isl_map_get_space(dep);
552 dep = isl_map_empty(space);
555 res = isl_map_partial_lexmax(dep, sink, empty);
557 if (restr->type == isl_restriction_type_output)
558 res = isl_map_intersect_range(res, isl_set_copy(restr->source));
560 isl_restriction_free(restr);
569 /* Compute the last iteration of must source j that precedes the sink
570 * at the given level for sink iterations in set_C.
571 * The subset of set_C for which no such iteration can be found is returned
574 static struct isl_map *last_source(struct isl_access_info *acc,
575 struct isl_set *set_C,
576 int j, int level, struct isl_set **empty)
578 struct isl_map *read_map;
579 struct isl_map *write_map;
580 struct isl_map *dep_map;
581 struct isl_map *after;
582 struct isl_map *result;
584 read_map = isl_map_copy(acc->sink.map);
585 write_map = isl_map_copy(acc->source[j].map);
586 write_map = isl_map_reverse(write_map);
587 dep_map = isl_map_apply_range(read_map, write_map);
588 after = after_at_level(isl_map_get_space(dep_map), level);
589 dep_map = isl_map_intersect(dep_map, after);
590 result = restricted_partial_lexmax(acc, dep_map, j, set_C, empty);
591 result = isl_map_reverse(result);
596 /* For a given mapping between iterations of must source j and iterations
597 * of the sink, compute the last iteration of must source k preceding
598 * the sink at level before_level for any of the sink iterations,
599 * but following the corresponding iteration of must source j at level
602 static struct isl_map *last_later_source(struct isl_access_info *acc,
603 struct isl_map *old_map,
604 int j, int before_level,
605 int k, int after_level,
606 struct isl_set **empty)
609 struct isl_set *set_C;
610 struct isl_map *read_map;
611 struct isl_map *write_map;
612 struct isl_map *dep_map;
613 struct isl_map *after_write;
614 struct isl_map *before_read;
615 struct isl_map *result;
617 set_C = isl_map_range(isl_map_copy(old_map));
618 read_map = isl_map_copy(acc->sink.map);
619 write_map = isl_map_copy(acc->source[k].map);
621 write_map = isl_map_reverse(write_map);
622 dep_map = isl_map_apply_range(read_map, write_map);
623 dim = space_align_and_join(isl_map_get_space(acc->source[k].map),
624 isl_space_reverse(isl_map_get_space(acc->source[j].map)));
625 after_write = after_at_level(dim, after_level);
626 after_write = isl_map_apply_range(after_write, old_map);
627 after_write = isl_map_reverse(after_write);
628 dep_map = isl_map_intersect(dep_map, after_write);
629 before_read = after_at_level(isl_map_get_space(dep_map), before_level);
630 dep_map = isl_map_intersect(dep_map, before_read);
631 result = restricted_partial_lexmax(acc, dep_map, k, set_C, empty);
632 result = isl_map_reverse(result);
637 /* Given a shared_level between two accesses, return 1 if the
638 * the first can precede the second at the requested target_level.
639 * If the target level is odd, i.e., refers to a statement level
640 * dimension, then first needs to precede second at the requested
641 * level, i.e., shared_level must be equal to target_level.
642 * If the target level is odd, then the two loops should share
643 * at least the requested number of outer loops.
645 static int can_precede_at_level(int shared_level, int target_level)
647 if (shared_level < target_level)
649 if ((target_level % 2) && shared_level > target_level)
654 /* Given a possible flow dependence temp_rel[j] between source j and the sink
655 * at level sink_level, remove those elements for which
656 * there is an iteration of another source k < j that is closer to the sink.
657 * The flow dependences temp_rel[k] are updated with the improved sources.
658 * Any improved source needs to precede the sink at the same level
659 * and needs to follow source j at the same or a deeper level.
660 * The lower this level, the later the execution date of source k.
661 * We therefore consider lower levels first.
663 * If temp_rel[j] is empty, then there can be no improvement and
664 * we return immediately.
666 static int intermediate_sources(__isl_keep isl_access_info *acc,
667 struct isl_map **temp_rel, int j, int sink_level)
670 int depth = 2 * isl_map_dim(acc->source[j].map, isl_dim_in) + 1;
672 if (isl_map_plain_is_empty(temp_rel[j]))
675 for (k = j - 1; k >= 0; --k) {
677 plevel = acc->level_before(acc->source[k].data, acc->sink.data);
678 if (!can_precede_at_level(plevel, sink_level))
681 plevel2 = acc->level_before(acc->source[j].data,
682 acc->source[k].data);
684 for (level = sink_level; level <= depth; ++level) {
686 struct isl_set *trest;
687 struct isl_map *copy;
689 if (!can_precede_at_level(plevel2, level))
692 copy = isl_map_copy(temp_rel[j]);
693 T = last_later_source(acc, copy, j, sink_level, k,
695 if (isl_map_plain_is_empty(T)) {
700 temp_rel[j] = isl_map_intersect_range(temp_rel[j], trest);
701 temp_rel[k] = isl_map_union_disjoint(temp_rel[k], T);
708 /* Compute all iterations of may source j that precedes the sink at the given
709 * level for sink iterations in set_C.
711 static __isl_give isl_map *all_sources(__isl_keep isl_access_info *acc,
712 __isl_take isl_set *set_C, int j, int level)
719 read_map = isl_map_copy(acc->sink.map);
720 read_map = isl_map_intersect_domain(read_map, set_C);
721 write_map = isl_map_copy(acc->source[acc->n_must + j].map);
722 write_map = isl_map_reverse(write_map);
723 dep_map = isl_map_apply_range(read_map, write_map);
724 after = after_at_level(isl_map_get_space(dep_map), level);
725 dep_map = isl_map_intersect(dep_map, after);
727 return isl_map_reverse(dep_map);
730 /* For a given mapping between iterations of must source k and iterations
731 * of the sink, compute the all iteration of may source j preceding
732 * the sink at level before_level for any of the sink iterations,
733 * but following the corresponding iteration of must source k at level
736 static __isl_give isl_map *all_later_sources(__isl_keep isl_access_info *acc,
737 __isl_keep isl_map *old_map,
738 int j, int before_level, int k, int after_level)
745 isl_map *after_write;
746 isl_map *before_read;
748 set_C = isl_map_range(isl_map_copy(old_map));
749 read_map = isl_map_copy(acc->sink.map);
750 read_map = isl_map_intersect_domain(read_map, set_C);
751 write_map = isl_map_copy(acc->source[acc->n_must + j].map);
753 write_map = isl_map_reverse(write_map);
754 dep_map = isl_map_apply_range(read_map, write_map);
755 dim = isl_space_join(isl_map_get_space(acc->source[acc->n_must + j].map),
756 isl_space_reverse(isl_map_get_space(acc->source[k].map)));
757 after_write = after_at_level(dim, after_level);
758 after_write = isl_map_apply_range(after_write, old_map);
759 after_write = isl_map_reverse(after_write);
760 dep_map = isl_map_intersect(dep_map, after_write);
761 before_read = after_at_level(isl_map_get_space(dep_map), before_level);
762 dep_map = isl_map_intersect(dep_map, before_read);
763 return isl_map_reverse(dep_map);
766 /* Given the must and may dependence relations for the must accesses
767 * for level sink_level, check if there are any accesses of may access j
768 * that occur in between and return their union.
769 * If some of these accesses are intermediate with respect to
770 * (previously thought to be) must dependences, then these
771 * must dependences are turned into may dependences.
773 static __isl_give isl_map *all_intermediate_sources(
774 __isl_keep isl_access_info *acc, __isl_take isl_map *map,
775 struct isl_map **must_rel, struct isl_map **may_rel,
776 int j, int sink_level)
779 int depth = 2 * isl_map_dim(acc->source[acc->n_must + j].map,
782 for (k = 0; k < acc->n_must; ++k) {
785 if (isl_map_plain_is_empty(may_rel[k]) &&
786 isl_map_plain_is_empty(must_rel[k]))
789 plevel = acc->level_before(acc->source[k].data,
790 acc->source[acc->n_must + j].data);
792 for (level = sink_level; level <= depth; ++level) {
797 if (!can_precede_at_level(plevel, level))
800 copy = isl_map_copy(may_rel[k]);
801 T = all_later_sources(acc, copy, j, sink_level, k, level);
802 map = isl_map_union(map, T);
804 copy = isl_map_copy(must_rel[k]);
805 T = all_later_sources(acc, copy, j, sink_level, k, level);
806 ran = isl_map_range(isl_map_copy(T));
807 map = isl_map_union(map, T);
808 may_rel[k] = isl_map_union_disjoint(may_rel[k],
809 isl_map_intersect_range(isl_map_copy(must_rel[k]),
811 T = isl_map_from_domain_and_range(
813 isl_space_domain(isl_map_get_space(must_rel[k]))),
815 must_rel[k] = isl_map_subtract(must_rel[k], T);
822 /* Compute dependences for the case where all accesses are "may"
823 * accesses, which boils down to computing memory based dependences.
824 * The generic algorithm would also work in this case, but it would
825 * be overkill to use it.
827 static __isl_give isl_flow *compute_mem_based_dependences(
828 __isl_keep isl_access_info *acc)
835 res = isl_flow_alloc(acc);
839 mustdo = isl_map_domain(isl_map_copy(acc->sink.map));
840 maydo = isl_set_copy(mustdo);
842 for (i = 0; i < acc->n_may; ++i) {
849 plevel = acc->level_before(acc->source[i].data, acc->sink.data);
850 is_before = plevel & 1;
853 dim = isl_map_get_space(res->dep[i].map);
855 before = isl_map_lex_le_first(dim, plevel);
857 before = isl_map_lex_lt_first(dim, plevel);
858 dep = isl_map_apply_range(isl_map_copy(acc->source[i].map),
859 isl_map_reverse(isl_map_copy(acc->sink.map)));
860 dep = isl_map_intersect(dep, before);
861 mustdo = isl_set_subtract(mustdo,
862 isl_map_range(isl_map_copy(dep)));
863 res->dep[i].map = isl_map_union(res->dep[i].map, dep);
866 res->may_no_source = isl_set_subtract(maydo, isl_set_copy(mustdo));
867 res->must_no_source = mustdo;
872 /* Compute dependences for the case where there is at least one
875 * The core algorithm considers all levels in which a source may precede
876 * the sink, where a level may either be a statement level or a loop level.
877 * The outermost statement level is 1, the first loop level is 2, etc...
878 * The algorithm basically does the following:
879 * for all levels l of the read access from innermost to outermost
880 * for all sources w that may precede the sink access at that level
881 * compute the last iteration of the source that precedes the sink access
883 * add result to possible last accesses at level l of source w
884 * for all sources w2 that we haven't considered yet at this level that may
885 * also precede the sink access
886 * for all levels l2 of w from l to innermost
887 * for all possible last accesses dep of w at l
888 * compute last iteration of w2 between the source and sink
890 * add result to possible last accesses at level l of write w2
891 * and replace possible last accesses dep by the remainder
894 * The above algorithm is applied to the must access. During the course
895 * of the algorithm, we keep track of sink iterations that still
896 * need to be considered. These iterations are split into those that
897 * haven't been matched to any source access (mustdo) and those that have only
898 * been matched to may accesses (maydo).
899 * At the end of each level, we also consider the may accesses.
900 * In particular, we consider may accesses that precede the remaining
901 * sink iterations, moving elements from mustdo to maydo when appropriate,
902 * and may accesses that occur between a must source and a sink of any
903 * dependences found at the current level, turning must dependences into
904 * may dependences when appropriate.
907 static __isl_give isl_flow *compute_val_based_dependences(
908 __isl_keep isl_access_info *acc)
912 isl_set *mustdo = NULL;
913 isl_set *maydo = NULL;
916 isl_map **must_rel = NULL;
917 isl_map **may_rel = NULL;
922 res = isl_flow_alloc(acc);
925 ctx = isl_map_get_ctx(acc->sink.map);
927 depth = 2 * isl_map_dim(acc->sink.map, isl_dim_in) + 1;
928 mustdo = isl_map_domain(isl_map_copy(acc->sink.map));
929 maydo = isl_set_empty_like(mustdo);
930 if (!mustdo || !maydo)
932 if (isl_set_plain_is_empty(mustdo))
935 must_rel = isl_alloc_array(ctx, struct isl_map *, acc->n_must);
936 may_rel = isl_alloc_array(ctx, struct isl_map *, acc->n_must);
937 if (!must_rel || !may_rel)
940 for (level = depth; level >= 1; --level) {
941 for (j = acc->n_must-1; j >=0; --j) {
942 must_rel[j] = isl_map_empty_like(res->dep[j].map);
943 may_rel[j] = isl_map_copy(must_rel[j]);
946 for (j = acc->n_must - 1; j >= 0; --j) {
948 struct isl_set *rest;
951 plevel = acc->level_before(acc->source[j].data,
953 if (!can_precede_at_level(plevel, level))
956 T = last_source(acc, mustdo, j, level, &rest);
957 must_rel[j] = isl_map_union_disjoint(must_rel[j], T);
960 intermediate_sources(acc, must_rel, j, level);
962 T = last_source(acc, maydo, j, level, &rest);
963 may_rel[j] = isl_map_union_disjoint(may_rel[j], T);
966 intermediate_sources(acc, may_rel, j, level);
968 if (isl_set_plain_is_empty(mustdo) &&
969 isl_set_plain_is_empty(maydo))
972 for (j = j - 1; j >= 0; --j) {
975 plevel = acc->level_before(acc->source[j].data,
977 if (!can_precede_at_level(plevel, level))
980 intermediate_sources(acc, must_rel, j, level);
981 intermediate_sources(acc, may_rel, j, level);
984 for (j = 0; j < acc->n_may; ++j) {
989 plevel = acc->level_before(acc->source[acc->n_must + j].data,
991 if (!can_precede_at_level(plevel, level))
994 T = all_sources(acc, isl_set_copy(maydo), j, level);
995 res->dep[2 * acc->n_must + j].map =
996 isl_map_union(res->dep[2 * acc->n_must + j].map, T);
997 T = all_sources(acc, isl_set_copy(mustdo), j, level);
998 ran = isl_map_range(isl_map_copy(T));
999 res->dep[2 * acc->n_must + j].map =
1000 isl_map_union(res->dep[2 * acc->n_must + j].map, T);
1001 mustdo = isl_set_subtract(mustdo, isl_set_copy(ran));
1002 maydo = isl_set_union_disjoint(maydo, ran);
1004 T = res->dep[2 * acc->n_must + j].map;
1005 T = all_intermediate_sources(acc, T, must_rel, may_rel,
1007 res->dep[2 * acc->n_must + j].map = T;
1010 for (j = acc->n_must - 1; j >= 0; --j) {
1011 res->dep[2 * j].map =
1012 isl_map_union_disjoint(res->dep[2 * j].map,
1014 res->dep[2 * j + 1].map =
1015 isl_map_union_disjoint(res->dep[2 * j + 1].map,
1019 if (isl_set_plain_is_empty(mustdo) &&
1020 isl_set_plain_is_empty(maydo))
1027 res->must_no_source = mustdo;
1028 res->may_no_source = maydo;
1032 isl_set_free(mustdo);
1033 isl_set_free(maydo);
1039 /* Given a "sink" access, a list of n "source" accesses,
1040 * compute for each iteration of the sink access
1041 * and for each element accessed by that iteration,
1042 * the source access in the list that last accessed the
1043 * element accessed by the sink access before this sink access.
1044 * Each access is given as a map from the loop iterators
1045 * to the array indices.
1046 * The result is a list of n relations between source and sink
1047 * iterations and a subset of the domain of the sink access,
1048 * corresponding to those iterations that access an element
1049 * not previously accessed.
1051 * To deal with multi-valued sink access relations, the sink iteration
1052 * domain is first extended with dimensions that correspond to the data
1053 * space. After the computation is finished, these extra dimensions are
1054 * projected out again.
1056 __isl_give isl_flow *isl_access_info_compute_flow(__isl_take isl_access_info *acc)
1059 struct isl_flow *res = NULL;
1064 acc->domain_map = isl_map_domain_map(isl_map_copy(acc->sink.map));
1065 acc->sink.map = isl_map_range_map(acc->sink.map);
1069 if (acc->n_must == 0)
1070 res = compute_mem_based_dependences(acc);
1072 acc = isl_access_info_sort_sources(acc);
1073 res = compute_val_based_dependences(acc);
1078 for (j = 0; j < res->n_source; ++j) {
1079 res->dep[j].map = isl_map_apply_range(res->dep[j].map,
1080 isl_map_copy(acc->domain_map));
1081 if (!res->dep[j].map)
1084 if (!res->must_no_source || !res->may_no_source)
1087 isl_access_info_free(acc);
1090 isl_access_info_free(acc);
1096 /* Keep track of some information about a schedule for a given
1097 * access. In particular, keep track of which dimensions
1098 * have a constant value and of the actual constant values.
1100 struct isl_sched_info {
1105 static void sched_info_free(__isl_take struct isl_sched_info *info)
1109 isl_vec_free(info->cst);
1114 /* Extract information on the constant dimensions of the schedule
1115 * for a given access. The "map" is of the form
1119 * with S the schedule domain, D the iteration domain and A the data domain.
1121 static __isl_give struct isl_sched_info *sched_info_alloc(
1122 __isl_keep isl_map *map)
1126 struct isl_sched_info *info;
1133 dim = isl_space_unwrap(isl_space_domain(isl_map_get_space(map)));
1136 n = isl_space_dim(dim, isl_dim_in);
1137 isl_space_free(dim);
1139 ctx = isl_map_get_ctx(map);
1140 info = isl_alloc_type(ctx, struct isl_sched_info);
1143 info->is_cst = isl_alloc_array(ctx, int, n);
1144 info->cst = isl_vec_alloc(ctx, n);
1145 if (!info->is_cst || !info->cst)
1149 for (i = 0; i < n; ++i) {
1150 info->is_cst[i] = isl_map_plain_is_fixed(map, isl_dim_in, i,
1152 info->cst = isl_vec_set_element(info->cst, i, v);
1158 sched_info_free(info);
1162 struct isl_compute_flow_data {
1163 isl_union_map *must_source;
1164 isl_union_map *may_source;
1165 isl_union_map *must_dep;
1166 isl_union_map *may_dep;
1167 isl_union_map *must_no_source;
1168 isl_union_map *may_no_source;
1173 struct isl_sched_info *sink_info;
1174 struct isl_sched_info **source_info;
1175 isl_access_info *accesses;
1178 static int count_matching_array(__isl_take isl_map *map, void *user)
1182 struct isl_compute_flow_data *data;
1184 data = (struct isl_compute_flow_data *)user;
1186 dim = isl_space_range(isl_map_get_space(map));
1188 eq = isl_space_is_equal(dim, data->dim);
1190 isl_space_free(dim);
1201 static int collect_matching_array(__isl_take isl_map *map, void *user)
1205 struct isl_sched_info *info;
1206 struct isl_compute_flow_data *data;
1208 data = (struct isl_compute_flow_data *)user;
1210 dim = isl_space_range(isl_map_get_space(map));
1212 eq = isl_space_is_equal(dim, data->dim);
1214 isl_space_free(dim);
1223 info = sched_info_alloc(map);
1224 data->source_info[data->count] = info;
1226 data->accesses = isl_access_info_add_source(data->accesses,
1227 map, data->must, info);
1237 /* Determine the shared nesting level and the "textual order" of
1238 * the given accesses.
1240 * We first determine the minimal schedule dimension for both accesses.
1242 * If among those dimensions, we can find one where both have a fixed
1243 * value and if moreover those values are different, then the previous
1244 * dimension is the last shared nesting level and the textual order
1245 * is determined based on the order of the fixed values.
1246 * If no such fixed values can be found, then we set the shared
1247 * nesting level to the minimal schedule dimension, with no textual ordering.
1249 static int before(void *first, void *second)
1251 struct isl_sched_info *info1 = first;
1252 struct isl_sched_info *info2 = second;
1257 n1 = isl_vec_size(info1->cst);
1258 n2 = isl_vec_size(info2->cst);
1265 for (i = 0; i < n1; ++i) {
1268 if (!info1->is_cst[i])
1270 if (!info2->is_cst[i])
1272 isl_vec_get_element(info1->cst, i, &v1);
1273 isl_vec_get_element(info2->cst, i, &v2);
1274 if (isl_int_eq(v1, v2))
1277 r = 2 * i + isl_int_lt(v1, v2);
1289 /* Given a sink access, look for all the source accesses that access
1290 * the same array and perform dataflow analysis on them using
1291 * isl_access_info_compute_flow.
1293 static int compute_flow(__isl_take isl_map *map, void *user)
1297 struct isl_compute_flow_data *data;
1300 data = (struct isl_compute_flow_data *)user;
1302 ctx = isl_map_get_ctx(map);
1304 data->accesses = NULL;
1305 data->sink_info = NULL;
1306 data->source_info = NULL;
1308 data->dim = isl_space_range(isl_map_get_space(map));
1310 if (isl_union_map_foreach_map(data->must_source,
1311 &count_matching_array, data) < 0)
1313 if (isl_union_map_foreach_map(data->may_source,
1314 &count_matching_array, data) < 0)
1317 data->sink_info = sched_info_alloc(map);
1318 data->source_info = isl_calloc_array(ctx, struct isl_sched_info *,
1321 data->accesses = isl_access_info_alloc(isl_map_copy(map),
1322 data->sink_info, &before, data->count);
1323 if (!data->sink_info || !data->source_info || !data->accesses)
1327 if (isl_union_map_foreach_map(data->must_source,
1328 &collect_matching_array, data) < 0)
1331 if (isl_union_map_foreach_map(data->may_source,
1332 &collect_matching_array, data) < 0)
1335 flow = isl_access_info_compute_flow(data->accesses);
1336 data->accesses = NULL;
1341 data->must_no_source = isl_union_map_union(data->must_no_source,
1342 isl_union_map_from_map(isl_flow_get_no_source(flow, 1)));
1343 data->may_no_source = isl_union_map_union(data->may_no_source,
1344 isl_union_map_from_map(isl_flow_get_no_source(flow, 0)));
1346 for (i = 0; i < flow->n_source; ++i) {
1348 dep = isl_union_map_from_map(isl_map_copy(flow->dep[i].map));
1349 if (flow->dep[i].must)
1350 data->must_dep = isl_union_map_union(data->must_dep, dep);
1352 data->may_dep = isl_union_map_union(data->may_dep, dep);
1355 isl_flow_free(flow);
1357 sched_info_free(data->sink_info);
1358 if (data->source_info) {
1359 for (i = 0; i < data->count; ++i)
1360 sched_info_free(data->source_info[i]);
1361 free(data->source_info);
1363 isl_space_free(data->dim);
1368 isl_access_info_free(data->accesses);
1369 sched_info_free(data->sink_info);
1370 if (data->source_info) {
1371 for (i = 0; i < data->count; ++i)
1372 sched_info_free(data->source_info[i]);
1373 free(data->source_info);
1375 isl_space_free(data->dim);
1381 /* Given a collection of "sink" and "source" accesses,
1382 * compute for each iteration of a sink access
1383 * and for each element accessed by that iteration,
1384 * the source access in the list that last accessed the
1385 * element accessed by the sink access before this sink access.
1386 * Each access is given as a map from the loop iterators
1387 * to the array indices.
1388 * The result is a relations between source and sink
1389 * iterations and a subset of the domain of the sink accesses,
1390 * corresponding to those iterations that access an element
1391 * not previously accessed.
1393 * We first prepend the schedule dimensions to the domain
1394 * of the accesses so that we can easily compare their relative order.
1395 * Then we consider each sink access individually in compute_flow.
1397 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
1398 __isl_take isl_union_map *must_source,
1399 __isl_take isl_union_map *may_source,
1400 __isl_take isl_union_map *schedule,
1401 __isl_give isl_union_map **must_dep, __isl_give isl_union_map **may_dep,
1402 __isl_give isl_union_map **must_no_source,
1403 __isl_give isl_union_map **may_no_source)
1406 isl_union_map *range_map = NULL;
1407 struct isl_compute_flow_data data;
1409 sink = isl_union_map_align_params(sink,
1410 isl_union_map_get_space(must_source));
1411 sink = isl_union_map_align_params(sink,
1412 isl_union_map_get_space(may_source));
1413 sink = isl_union_map_align_params(sink,
1414 isl_union_map_get_space(schedule));
1415 dim = isl_union_map_get_space(sink);
1416 must_source = isl_union_map_align_params(must_source, isl_space_copy(dim));
1417 may_source = isl_union_map_align_params(may_source, isl_space_copy(dim));
1418 schedule = isl_union_map_align_params(schedule, isl_space_copy(dim));
1420 schedule = isl_union_map_reverse(schedule);
1421 range_map = isl_union_map_range_map(schedule);
1422 schedule = isl_union_map_reverse(isl_union_map_copy(range_map));
1423 sink = isl_union_map_apply_domain(sink, isl_union_map_copy(schedule));
1424 must_source = isl_union_map_apply_domain(must_source,
1425 isl_union_map_copy(schedule));
1426 may_source = isl_union_map_apply_domain(may_source, schedule);
1428 data.must_source = must_source;
1429 data.may_source = may_source;
1430 data.must_dep = must_dep ?
1431 isl_union_map_empty(isl_space_copy(dim)) : NULL;
1432 data.may_dep = may_dep ? isl_union_map_empty(isl_space_copy(dim)) : NULL;
1433 data.must_no_source = must_no_source ?
1434 isl_union_map_empty(isl_space_copy(dim)) : NULL;
1435 data.may_no_source = may_no_source ?
1436 isl_union_map_empty(isl_space_copy(dim)) : NULL;
1438 isl_space_free(dim);
1440 if (isl_union_map_foreach_map(sink, &compute_flow, &data) < 0)
1443 isl_union_map_free(sink);
1444 isl_union_map_free(must_source);
1445 isl_union_map_free(may_source);
1448 data.must_dep = isl_union_map_apply_domain(data.must_dep,
1449 isl_union_map_copy(range_map));
1450 data.must_dep = isl_union_map_apply_range(data.must_dep,
1451 isl_union_map_copy(range_map));
1452 *must_dep = data.must_dep;
1455 data.may_dep = isl_union_map_apply_domain(data.may_dep,
1456 isl_union_map_copy(range_map));
1457 data.may_dep = isl_union_map_apply_range(data.may_dep,
1458 isl_union_map_copy(range_map));
1459 *may_dep = data.may_dep;
1461 if (must_no_source) {
1462 data.must_no_source = isl_union_map_apply_domain(
1463 data.must_no_source, isl_union_map_copy(range_map));
1464 *must_no_source = data.must_no_source;
1466 if (may_no_source) {
1467 data.may_no_source = isl_union_map_apply_domain(
1468 data.may_no_source, isl_union_map_copy(range_map));
1469 *may_no_source = data.may_no_source;
1472 isl_union_map_free(range_map);
1476 isl_union_map_free(range_map);
1477 isl_union_map_free(sink);
1478 isl_union_map_free(must_source);
1479 isl_union_map_free(may_source);
1480 isl_union_map_free(data.must_dep);
1481 isl_union_map_free(data.may_dep);
1482 isl_union_map_free(data.must_no_source);
1483 isl_union_map_free(data.may_no_source);
1490 *must_no_source = NULL;
1492 *may_no_source = NULL;