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 that doesn't restrict anything.
38 __isl_give isl_restriction *isl_restriction_none(__isl_keep isl_map *source_map)
41 isl_restriction *restr;
46 ctx = isl_map_get_ctx(source_map);
47 restr = isl_calloc_type(ctx, struct isl_restriction);
51 restr->type = isl_restriction_type_none;
56 /* Create a restriction that removes everything.
58 __isl_give isl_restriction *isl_restriction_empty(
59 __isl_keep isl_map *source_map)
62 isl_restriction *restr;
67 ctx = isl_map_get_ctx(source_map);
68 restr = isl_calloc_type(ctx, struct isl_restriction);
72 restr->type = isl_restriction_type_empty;
77 /* Create a restriction on the input of the maximization problem
78 * based on the given source and sink restrictions.
80 __isl_give isl_restriction *isl_restriction_input(
81 __isl_take isl_set *source_restr, __isl_take isl_set *sink_restr)
84 isl_restriction *restr;
86 if (!source_restr || !sink_restr)
89 ctx = isl_set_get_ctx(source_restr);
90 restr = isl_calloc_type(ctx, struct isl_restriction);
94 restr->type = isl_restriction_type_input;
95 restr->source = source_restr;
96 restr->sink = sink_restr;
100 isl_set_free(source_restr);
101 isl_set_free(sink_restr);
105 /* Create a restriction on the output of the maximization problem
106 * based on the given source restriction.
108 __isl_give isl_restriction *isl_restriction_output(
109 __isl_take isl_set *source_restr)
112 isl_restriction *restr;
117 ctx = isl_set_get_ctx(source_restr);
118 restr = isl_calloc_type(ctx, struct isl_restriction);
122 restr->type = isl_restriction_type_output;
123 restr->source = source_restr;
127 isl_set_free(source_restr);
131 void *isl_restriction_free(__isl_take isl_restriction *restr)
136 isl_set_free(restr->source);
137 isl_set_free(restr->sink);
142 isl_ctx *isl_restriction_get_ctx(__isl_keep isl_restriction *restr)
144 return restr ? isl_set_get_ctx(restr->source) : NULL;
147 /* A private structure to keep track of a mapping together with
148 * a user-specified identifier and a boolean indicating whether
149 * the map represents a must or may access/dependence.
151 struct isl_labeled_map {
157 /* A structure containing the input for dependence analysis:
159 * - n_must + n_may (<= max_source) sources
160 * - a function for determining the relative order of sources and sink
161 * The must sources are placed before the may sources.
163 * domain_map is an auxiliary map that maps the sink access relation
164 * to the domain of this access relation.
166 * restrict_fn is a callback that (if not NULL) will be called
167 * right before any lexicographical maximization.
169 struct isl_access_info {
171 struct isl_labeled_map sink;
172 isl_access_level_before level_before;
174 isl_access_restrict restrict_fn;
180 struct isl_labeled_map source[1];
183 /* A structure containing the output of dependence analysis:
184 * - n_source dependences
185 * - a wrapped subset of the sink for which definitely no source could be found
186 * - a wrapped subset of the sink for which possibly no source could be found
189 isl_set *must_no_source;
190 isl_set *may_no_source;
192 struct isl_labeled_map *dep;
195 /* Construct an isl_access_info structure and fill it up with
196 * the given data. The number of sources is set to 0.
198 __isl_give isl_access_info *isl_access_info_alloc(__isl_take isl_map *sink,
199 void *sink_user, isl_access_level_before fn, int max_source)
202 struct isl_access_info *acc;
207 ctx = isl_map_get_ctx(sink);
208 isl_assert(ctx, max_source >= 0, goto error);
210 acc = isl_calloc(ctx, struct isl_access_info,
211 sizeof(struct isl_access_info) +
212 (max_source - 1) * sizeof(struct isl_labeled_map));
216 acc->sink.map = sink;
217 acc->sink.data = sink_user;
218 acc->level_before = fn;
219 acc->max_source = max_source;
229 /* Free the given isl_access_info structure.
231 void isl_access_info_free(__isl_take isl_access_info *acc)
237 isl_map_free(acc->domain_map);
238 isl_map_free(acc->sink.map);
239 for (i = 0; i < acc->n_must + acc->n_may; ++i)
240 isl_map_free(acc->source[i].map);
244 isl_ctx *isl_access_info_get_ctx(__isl_keep isl_access_info *acc)
246 return acc ? isl_map_get_ctx(acc->sink.map) : NULL;
249 __isl_give isl_access_info *isl_access_info_set_restrict(
250 __isl_take isl_access_info *acc, isl_access_restrict fn, void *user)
254 acc->restrict_fn = fn;
255 acc->restrict_user = user;
259 /* Add another source to an isl_access_info structure, making
260 * sure the "must" sources are placed before the "may" sources.
261 * This function may be called at most max_source times on a
262 * given isl_access_info structure, with max_source as specified
263 * in the call to isl_access_info_alloc that constructed the structure.
265 __isl_give isl_access_info *isl_access_info_add_source(
266 __isl_take isl_access_info *acc, __isl_take isl_map *source,
267 int must, void *source_user)
273 ctx = isl_map_get_ctx(acc->sink.map);
274 isl_assert(ctx, acc->n_must + acc->n_may < acc->max_source, goto error);
278 acc->source[acc->n_must + acc->n_may] =
279 acc->source[acc->n_must];
280 acc->source[acc->n_must].map = source;
281 acc->source[acc->n_must].data = source_user;
282 acc->source[acc->n_must].must = 1;
285 acc->source[acc->n_must + acc->n_may].map = source;
286 acc->source[acc->n_must + acc->n_may].data = source_user;
287 acc->source[acc->n_must + acc->n_may].must = 0;
293 isl_map_free(source);
294 isl_access_info_free(acc);
298 /* Return -n, 0 or n (with n a positive value), depending on whether
299 * the source access identified by p1 should be sorted before, together
300 * or after that identified by p2.
302 * If p1 appears before p2, then it should be sorted first.
303 * For more generic initial schedules, it is possible that neither
304 * p1 nor p2 appears before the other, or at least not in any obvious way.
305 * We therefore also check if p2 appears before p1, in which case p2
306 * should be sorted first.
307 * If not, we try to order the two statements based on the description
308 * of the iteration domains. This results in an arbitrary, but fairly
311 static int access_sort_cmp(const void *p1, const void *p2, void *user)
313 isl_access_info *acc = user;
314 const struct isl_labeled_map *i1, *i2;
317 i1 = (const struct isl_labeled_map *) p1;
318 i2 = (const struct isl_labeled_map *) p2;
320 level1 = acc->level_before(i1->data, i2->data);
324 level2 = acc->level_before(i2->data, i1->data);
328 h1 = isl_map_get_hash(i1->map);
329 h2 = isl_map_get_hash(i2->map);
330 return h1 > h2 ? 1 : h1 < h2 ? -1 : 0;
333 /* Sort the must source accesses in their textual order.
335 static __isl_give isl_access_info *isl_access_info_sort_sources(
336 __isl_take isl_access_info *acc)
340 if (acc->n_must <= 1)
343 isl_quicksort(acc->source, acc->n_must, sizeof(struct isl_labeled_map),
344 access_sort_cmp, acc);
349 /* Align the parameters of the two spaces if needed and then call
352 static __isl_give isl_space *space_align_and_join(__isl_take isl_space *left,
353 __isl_take isl_space *right)
355 if (isl_space_match(left, isl_dim_param, right, isl_dim_param))
356 return isl_space_join(left, right);
358 left = isl_space_align_params(left, isl_space_copy(right));
359 right = isl_space_align_params(right, isl_space_copy(left));
360 return isl_space_join(left, right);
363 /* Initialize an empty isl_flow structure corresponding to a given
364 * isl_access_info structure.
365 * For each must access, two dependences are created (initialized
366 * to the empty relation), one for the resulting must dependences
367 * and one for the resulting may dependences. May accesses can
368 * only lead to may dependences, so only one dependence is created
370 * This function is private as isl_flow structures are only supposed
371 * to be created by isl_access_info_compute_flow.
373 static __isl_give isl_flow *isl_flow_alloc(__isl_keep isl_access_info *acc)
377 struct isl_flow *dep;
382 ctx = isl_map_get_ctx(acc->sink.map);
383 dep = isl_calloc_type(ctx, struct isl_flow);
387 dep->dep = isl_calloc_array(ctx, struct isl_labeled_map,
388 2 * acc->n_must + acc->n_may);
392 dep->n_source = 2 * acc->n_must + acc->n_may;
393 for (i = 0; i < acc->n_must; ++i) {
395 dim = space_align_and_join(
396 isl_map_get_space(acc->source[i].map),
397 isl_space_reverse(isl_map_get_space(acc->sink.map)));
398 dep->dep[2 * i].map = isl_map_empty(dim);
399 dep->dep[2 * i + 1].map = isl_map_copy(dep->dep[2 * i].map);
400 dep->dep[2 * i].data = acc->source[i].data;
401 dep->dep[2 * i + 1].data = acc->source[i].data;
402 dep->dep[2 * i].must = 1;
403 dep->dep[2 * i + 1].must = 0;
404 if (!dep->dep[2 * i].map || !dep->dep[2 * i + 1].map)
407 for (i = acc->n_must; i < acc->n_must + acc->n_may; ++i) {
409 dim = space_align_and_join(
410 isl_map_get_space(acc->source[i].map),
411 isl_space_reverse(isl_map_get_space(acc->sink.map)));
412 dep->dep[acc->n_must + i].map = isl_map_empty(dim);
413 dep->dep[acc->n_must + i].data = acc->source[i].data;
414 dep->dep[acc->n_must + i].must = 0;
415 if (!dep->dep[acc->n_must + i].map)
425 /* Iterate over all sources and for each resulting flow dependence
426 * that is not empty, call the user specfied function.
427 * The second argument in this function call identifies the source,
428 * while the third argument correspond to the final argument of
429 * the isl_flow_foreach call.
431 int isl_flow_foreach(__isl_keep isl_flow *deps,
432 int (*fn)(__isl_take isl_map *dep, int must, void *dep_user, void *user),
440 for (i = 0; i < deps->n_source; ++i) {
441 if (isl_map_plain_is_empty(deps->dep[i].map))
443 if (fn(isl_map_copy(deps->dep[i].map), deps->dep[i].must,
444 deps->dep[i].data, user) < 0)
451 /* Return a copy of the subset of the sink for which no source could be found.
453 __isl_give isl_map *isl_flow_get_no_source(__isl_keep isl_flow *deps, int must)
459 return isl_set_unwrap(isl_set_copy(deps->must_no_source));
461 return isl_set_unwrap(isl_set_copy(deps->may_no_source));
464 void isl_flow_free(__isl_take isl_flow *deps)
470 isl_set_free(deps->must_no_source);
471 isl_set_free(deps->may_no_source);
473 for (i = 0; i < deps->n_source; ++i)
474 isl_map_free(deps->dep[i].map);
480 isl_ctx *isl_flow_get_ctx(__isl_keep isl_flow *deps)
482 return deps ? isl_set_get_ctx(deps->must_no_source) : NULL;
485 /* Return a map that enforces that the domain iteration occurs after
486 * the range iteration at the given level.
487 * If level is odd, then the domain iteration should occur after
488 * the target iteration in their shared level/2 outermost loops.
489 * In this case we simply need to enforce that these outermost
490 * loop iterations are the same.
491 * If level is even, then the loop iterator of the domain should
492 * be greater than the loop iterator of the range at the last
493 * of the level/2 shared loops, i.e., loop level/2 - 1.
495 static __isl_give isl_map *after_at_level(__isl_take isl_space *dim, int level)
497 struct isl_basic_map *bmap;
500 bmap = isl_basic_map_equal(dim, level/2);
502 bmap = isl_basic_map_more_at(dim, level/2 - 1);
504 return isl_map_from_basic_map(bmap);
507 /* Compute the partial lexicographic maximum of "dep" on domain "sink",
508 * but first check if the user has set acc->restrict_fn and if so
509 * update either the input or the output of the maximization problem
510 * with respect to the resulting restriction.
512 * Since the user expects a mapping from sink iterations to source iterations,
513 * whereas the domain of "dep" is a wrapped map, mapping sink iterations
514 * to accessed array elements, we first need to project out the accessed
515 * sink array elements by applying acc->domain_map.
516 * Similarly, the sink restriction specified by the user needs to be
517 * converted back to the wrapped map.
519 static __isl_give isl_map *restricted_partial_lexmax(
520 __isl_keep isl_access_info *acc, __isl_take isl_map *dep,
521 int source, __isl_take isl_set *sink, __isl_give isl_set **empty)
524 isl_restriction *restr;
525 isl_set *sink_domain;
529 if (!acc->restrict_fn)
530 return isl_map_partial_lexmax(dep, sink, empty);
532 source_map = isl_map_copy(dep);
533 source_map = isl_map_apply_domain(source_map,
534 isl_map_copy(acc->domain_map));
535 sink_domain = isl_set_copy(sink);
536 sink_domain = isl_set_apply(sink_domain, isl_map_copy(acc->domain_map));
537 restr = acc->restrict_fn(source_map, sink_domain,
538 acc->source[source].data, acc->restrict_user);
539 isl_set_free(sink_domain);
540 isl_map_free(source_map);
544 if (restr->type == isl_restriction_type_input) {
545 dep = isl_map_intersect_range(dep, isl_set_copy(restr->source));
546 sink_restr = isl_set_copy(restr->sink);
547 sink_restr = isl_set_apply(sink_restr,
548 isl_map_reverse(isl_map_copy(acc->domain_map)));
549 sink = isl_set_intersect(sink, sink_restr);
550 } else if (restr->type == isl_restriction_type_empty) {
551 isl_space *space = isl_map_get_space(dep);
553 dep = isl_map_empty(space);
556 res = isl_map_partial_lexmax(dep, sink, empty);
558 if (restr->type == isl_restriction_type_output)
559 res = isl_map_intersect_range(res, isl_set_copy(restr->source));
561 isl_restriction_free(restr);
570 /* Compute the last iteration of must source j that precedes the sink
571 * at the given level for sink iterations in set_C.
572 * The subset of set_C for which no such iteration can be found is returned
575 static struct isl_map *last_source(struct isl_access_info *acc,
576 struct isl_set *set_C,
577 int j, int level, struct isl_set **empty)
579 struct isl_map *read_map;
580 struct isl_map *write_map;
581 struct isl_map *dep_map;
582 struct isl_map *after;
583 struct isl_map *result;
585 read_map = isl_map_copy(acc->sink.map);
586 write_map = isl_map_copy(acc->source[j].map);
587 write_map = isl_map_reverse(write_map);
588 dep_map = isl_map_apply_range(read_map, write_map);
589 after = after_at_level(isl_map_get_space(dep_map), level);
590 dep_map = isl_map_intersect(dep_map, after);
591 result = restricted_partial_lexmax(acc, dep_map, j, set_C, empty);
592 result = isl_map_reverse(result);
597 /* For a given mapping between iterations of must source j and iterations
598 * of the sink, compute the last iteration of must source k preceding
599 * the sink at level before_level for any of the sink iterations,
600 * but following the corresponding iteration of must source j at level
603 static struct isl_map *last_later_source(struct isl_access_info *acc,
604 struct isl_map *old_map,
605 int j, int before_level,
606 int k, int after_level,
607 struct isl_set **empty)
610 struct isl_set *set_C;
611 struct isl_map *read_map;
612 struct isl_map *write_map;
613 struct isl_map *dep_map;
614 struct isl_map *after_write;
615 struct isl_map *before_read;
616 struct isl_map *result;
618 set_C = isl_map_range(isl_map_copy(old_map));
619 read_map = isl_map_copy(acc->sink.map);
620 write_map = isl_map_copy(acc->source[k].map);
622 write_map = isl_map_reverse(write_map);
623 dep_map = isl_map_apply_range(read_map, write_map);
624 dim = space_align_and_join(isl_map_get_space(acc->source[k].map),
625 isl_space_reverse(isl_map_get_space(acc->source[j].map)));
626 after_write = after_at_level(dim, after_level);
627 after_write = isl_map_apply_range(after_write, old_map);
628 after_write = isl_map_reverse(after_write);
629 dep_map = isl_map_intersect(dep_map, after_write);
630 before_read = after_at_level(isl_map_get_space(dep_map), before_level);
631 dep_map = isl_map_intersect(dep_map, before_read);
632 result = restricted_partial_lexmax(acc, dep_map, k, set_C, empty);
633 result = isl_map_reverse(result);
638 /* Given a shared_level between two accesses, return 1 if the
639 * the first can precede the second at the requested target_level.
640 * If the target level is odd, i.e., refers to a statement level
641 * dimension, then first needs to precede second at the requested
642 * level, i.e., shared_level must be equal to target_level.
643 * If the target level is odd, then the two loops should share
644 * at least the requested number of outer loops.
646 static int can_precede_at_level(int shared_level, int target_level)
648 if (shared_level < target_level)
650 if ((target_level % 2) && shared_level > target_level)
655 /* Given a possible flow dependence temp_rel[j] between source j and the sink
656 * at level sink_level, remove those elements for which
657 * there is an iteration of another source k < j that is closer to the sink.
658 * The flow dependences temp_rel[k] are updated with the improved sources.
659 * Any improved source needs to precede the sink at the same level
660 * and needs to follow source j at the same or a deeper level.
661 * The lower this level, the later the execution date of source k.
662 * We therefore consider lower levels first.
664 * If temp_rel[j] is empty, then there can be no improvement and
665 * we return immediately.
667 static int intermediate_sources(__isl_keep isl_access_info *acc,
668 struct isl_map **temp_rel, int j, int sink_level)
671 int depth = 2 * isl_map_dim(acc->source[j].map, isl_dim_in) + 1;
673 if (isl_map_plain_is_empty(temp_rel[j]))
676 for (k = j - 1; k >= 0; --k) {
678 plevel = acc->level_before(acc->source[k].data, acc->sink.data);
679 if (!can_precede_at_level(plevel, sink_level))
682 plevel2 = acc->level_before(acc->source[j].data,
683 acc->source[k].data);
685 for (level = sink_level; level <= depth; ++level) {
687 struct isl_set *trest;
688 struct isl_map *copy;
690 if (!can_precede_at_level(plevel2, level))
693 copy = isl_map_copy(temp_rel[j]);
694 T = last_later_source(acc, copy, j, sink_level, k,
696 if (isl_map_plain_is_empty(T)) {
701 temp_rel[j] = isl_map_intersect_range(temp_rel[j], trest);
702 temp_rel[k] = isl_map_union_disjoint(temp_rel[k], T);
709 /* Compute all iterations of may source j that precedes the sink at the given
710 * level for sink iterations in set_C.
712 static __isl_give isl_map *all_sources(__isl_keep isl_access_info *acc,
713 __isl_take isl_set *set_C, int j, int level)
720 read_map = isl_map_copy(acc->sink.map);
721 read_map = isl_map_intersect_domain(read_map, set_C);
722 write_map = isl_map_copy(acc->source[acc->n_must + j].map);
723 write_map = isl_map_reverse(write_map);
724 dep_map = isl_map_apply_range(read_map, write_map);
725 after = after_at_level(isl_map_get_space(dep_map), level);
726 dep_map = isl_map_intersect(dep_map, after);
728 return isl_map_reverse(dep_map);
731 /* For a given mapping between iterations of must source k and iterations
732 * of the sink, compute the all iteration of may source j preceding
733 * the sink at level before_level for any of the sink iterations,
734 * but following the corresponding iteration of must source k at level
737 static __isl_give isl_map *all_later_sources(__isl_keep isl_access_info *acc,
738 __isl_keep isl_map *old_map,
739 int j, int before_level, int k, int after_level)
746 isl_map *after_write;
747 isl_map *before_read;
749 set_C = isl_map_range(isl_map_copy(old_map));
750 read_map = isl_map_copy(acc->sink.map);
751 read_map = isl_map_intersect_domain(read_map, set_C);
752 write_map = isl_map_copy(acc->source[acc->n_must + j].map);
754 write_map = isl_map_reverse(write_map);
755 dep_map = isl_map_apply_range(read_map, write_map);
756 dim = isl_space_join(isl_map_get_space(acc->source[acc->n_must + j].map),
757 isl_space_reverse(isl_map_get_space(acc->source[k].map)));
758 after_write = after_at_level(dim, after_level);
759 after_write = isl_map_apply_range(after_write, old_map);
760 after_write = isl_map_reverse(after_write);
761 dep_map = isl_map_intersect(dep_map, after_write);
762 before_read = after_at_level(isl_map_get_space(dep_map), before_level);
763 dep_map = isl_map_intersect(dep_map, before_read);
764 return isl_map_reverse(dep_map);
767 /* Given the must and may dependence relations for the must accesses
768 * for level sink_level, check if there are any accesses of may access j
769 * that occur in between and return their union.
770 * If some of these accesses are intermediate with respect to
771 * (previously thought to be) must dependences, then these
772 * must dependences are turned into may dependences.
774 static __isl_give isl_map *all_intermediate_sources(
775 __isl_keep isl_access_info *acc, __isl_take isl_map *map,
776 struct isl_map **must_rel, struct isl_map **may_rel,
777 int j, int sink_level)
780 int depth = 2 * isl_map_dim(acc->source[acc->n_must + j].map,
783 for (k = 0; k < acc->n_must; ++k) {
786 if (isl_map_plain_is_empty(may_rel[k]) &&
787 isl_map_plain_is_empty(must_rel[k]))
790 plevel = acc->level_before(acc->source[k].data,
791 acc->source[acc->n_must + j].data);
793 for (level = sink_level; level <= depth; ++level) {
798 if (!can_precede_at_level(plevel, level))
801 copy = isl_map_copy(may_rel[k]);
802 T = all_later_sources(acc, copy, j, sink_level, k, level);
803 map = isl_map_union(map, T);
805 copy = isl_map_copy(must_rel[k]);
806 T = all_later_sources(acc, copy, j, sink_level, k, level);
807 ran = isl_map_range(isl_map_copy(T));
808 map = isl_map_union(map, T);
809 may_rel[k] = isl_map_union_disjoint(may_rel[k],
810 isl_map_intersect_range(isl_map_copy(must_rel[k]),
812 T = isl_map_from_domain_and_range(
814 isl_space_domain(isl_map_get_space(must_rel[k]))),
816 must_rel[k] = isl_map_subtract(must_rel[k], T);
823 /* Compute dependences for the case where all accesses are "may"
824 * accesses, which boils down to computing memory based dependences.
825 * The generic algorithm would also work in this case, but it would
826 * be overkill to use it.
828 static __isl_give isl_flow *compute_mem_based_dependences(
829 __isl_keep isl_access_info *acc)
836 res = isl_flow_alloc(acc);
840 mustdo = isl_map_domain(isl_map_copy(acc->sink.map));
841 maydo = isl_set_copy(mustdo);
843 for (i = 0; i < acc->n_may; ++i) {
850 plevel = acc->level_before(acc->source[i].data, acc->sink.data);
851 is_before = plevel & 1;
854 dim = isl_map_get_space(res->dep[i].map);
856 before = isl_map_lex_le_first(dim, plevel);
858 before = isl_map_lex_lt_first(dim, plevel);
859 dep = isl_map_apply_range(isl_map_copy(acc->source[i].map),
860 isl_map_reverse(isl_map_copy(acc->sink.map)));
861 dep = isl_map_intersect(dep, before);
862 mustdo = isl_set_subtract(mustdo,
863 isl_map_range(isl_map_copy(dep)));
864 res->dep[i].map = isl_map_union(res->dep[i].map, dep);
867 res->may_no_source = isl_set_subtract(maydo, isl_set_copy(mustdo));
868 res->must_no_source = mustdo;
873 /* Compute dependences for the case where there is at least one
876 * The core algorithm considers all levels in which a source may precede
877 * the sink, where a level may either be a statement level or a loop level.
878 * The outermost statement level is 1, the first loop level is 2, etc...
879 * The algorithm basically does the following:
880 * for all levels l of the read access from innermost to outermost
881 * for all sources w that may precede the sink access at that level
882 * compute the last iteration of the source that precedes the sink access
884 * add result to possible last accesses at level l of source w
885 * for all sources w2 that we haven't considered yet at this level that may
886 * also precede the sink access
887 * for all levels l2 of w from l to innermost
888 * for all possible last accesses dep of w at l
889 * compute last iteration of w2 between the source and sink
891 * add result to possible last accesses at level l of write w2
892 * and replace possible last accesses dep by the remainder
895 * The above algorithm is applied to the must access. During the course
896 * of the algorithm, we keep track of sink iterations that still
897 * need to be considered. These iterations are split into those that
898 * haven't been matched to any source access (mustdo) and those that have only
899 * been matched to may accesses (maydo).
900 * At the end of each level, we also consider the may accesses.
901 * In particular, we consider may accesses that precede the remaining
902 * sink iterations, moving elements from mustdo to maydo when appropriate,
903 * and may accesses that occur between a must source and a sink of any
904 * dependences found at the current level, turning must dependences into
905 * may dependences when appropriate.
908 static __isl_give isl_flow *compute_val_based_dependences(
909 __isl_keep isl_access_info *acc)
913 isl_set *mustdo = NULL;
914 isl_set *maydo = NULL;
917 isl_map **must_rel = NULL;
918 isl_map **may_rel = NULL;
923 res = isl_flow_alloc(acc);
926 ctx = isl_map_get_ctx(acc->sink.map);
928 depth = 2 * isl_map_dim(acc->sink.map, isl_dim_in) + 1;
929 mustdo = isl_map_domain(isl_map_copy(acc->sink.map));
930 maydo = isl_set_empty_like(mustdo);
931 if (!mustdo || !maydo)
933 if (isl_set_plain_is_empty(mustdo))
936 must_rel = isl_alloc_array(ctx, struct isl_map *, acc->n_must);
937 may_rel = isl_alloc_array(ctx, struct isl_map *, acc->n_must);
938 if (!must_rel || !may_rel)
941 for (level = depth; level >= 1; --level) {
942 for (j = acc->n_must-1; j >=0; --j) {
943 must_rel[j] = isl_map_empty_like(res->dep[j].map);
944 may_rel[j] = isl_map_copy(must_rel[j]);
947 for (j = acc->n_must - 1; j >= 0; --j) {
949 struct isl_set *rest;
952 plevel = acc->level_before(acc->source[j].data,
954 if (!can_precede_at_level(plevel, level))
957 T = last_source(acc, mustdo, j, level, &rest);
958 must_rel[j] = isl_map_union_disjoint(must_rel[j], T);
961 intermediate_sources(acc, must_rel, j, level);
963 T = last_source(acc, maydo, j, level, &rest);
964 may_rel[j] = isl_map_union_disjoint(may_rel[j], T);
967 intermediate_sources(acc, may_rel, j, level);
969 if (isl_set_plain_is_empty(mustdo) &&
970 isl_set_plain_is_empty(maydo))
973 for (j = j - 1; j >= 0; --j) {
976 plevel = acc->level_before(acc->source[j].data,
978 if (!can_precede_at_level(plevel, level))
981 intermediate_sources(acc, must_rel, j, level);
982 intermediate_sources(acc, may_rel, j, level);
985 for (j = 0; j < acc->n_may; ++j) {
990 plevel = acc->level_before(acc->source[acc->n_must + j].data,
992 if (!can_precede_at_level(plevel, level))
995 T = all_sources(acc, isl_set_copy(maydo), j, level);
996 res->dep[2 * acc->n_must + j].map =
997 isl_map_union(res->dep[2 * acc->n_must + j].map, T);
998 T = all_sources(acc, isl_set_copy(mustdo), j, level);
999 ran = isl_map_range(isl_map_copy(T));
1000 res->dep[2 * acc->n_must + j].map =
1001 isl_map_union(res->dep[2 * acc->n_must + j].map, T);
1002 mustdo = isl_set_subtract(mustdo, isl_set_copy(ran));
1003 maydo = isl_set_union_disjoint(maydo, ran);
1005 T = res->dep[2 * acc->n_must + j].map;
1006 T = all_intermediate_sources(acc, T, must_rel, may_rel,
1008 res->dep[2 * acc->n_must + j].map = T;
1011 for (j = acc->n_must - 1; j >= 0; --j) {
1012 res->dep[2 * j].map =
1013 isl_map_union_disjoint(res->dep[2 * j].map,
1015 res->dep[2 * j + 1].map =
1016 isl_map_union_disjoint(res->dep[2 * j + 1].map,
1020 if (isl_set_plain_is_empty(mustdo) &&
1021 isl_set_plain_is_empty(maydo))
1028 res->must_no_source = mustdo;
1029 res->may_no_source = maydo;
1033 isl_set_free(mustdo);
1034 isl_set_free(maydo);
1040 /* Given a "sink" access, a list of n "source" accesses,
1041 * compute for each iteration of the sink access
1042 * and for each element accessed by that iteration,
1043 * the source access in the list that last accessed the
1044 * element accessed by the sink access before this sink access.
1045 * Each access is given as a map from the loop iterators
1046 * to the array indices.
1047 * The result is a list of n relations between source and sink
1048 * iterations and a subset of the domain of the sink access,
1049 * corresponding to those iterations that access an element
1050 * not previously accessed.
1052 * To deal with multi-valued sink access relations, the sink iteration
1053 * domain is first extended with dimensions that correspond to the data
1054 * space. After the computation is finished, these extra dimensions are
1055 * projected out again.
1057 __isl_give isl_flow *isl_access_info_compute_flow(__isl_take isl_access_info *acc)
1060 struct isl_flow *res = NULL;
1065 acc->domain_map = isl_map_domain_map(isl_map_copy(acc->sink.map));
1066 acc->sink.map = isl_map_range_map(acc->sink.map);
1070 if (acc->n_must == 0)
1071 res = compute_mem_based_dependences(acc);
1073 acc = isl_access_info_sort_sources(acc);
1074 res = compute_val_based_dependences(acc);
1079 for (j = 0; j < res->n_source; ++j) {
1080 res->dep[j].map = isl_map_apply_range(res->dep[j].map,
1081 isl_map_copy(acc->domain_map));
1082 if (!res->dep[j].map)
1085 if (!res->must_no_source || !res->may_no_source)
1088 isl_access_info_free(acc);
1091 isl_access_info_free(acc);
1097 /* Keep track of some information about a schedule for a given
1098 * access. In particular, keep track of which dimensions
1099 * have a constant value and of the actual constant values.
1101 struct isl_sched_info {
1106 static void sched_info_free(__isl_take struct isl_sched_info *info)
1110 isl_vec_free(info->cst);
1115 /* Extract information on the constant dimensions of the schedule
1116 * for a given access. The "map" is of the form
1120 * with S the schedule domain, D the iteration domain and A the data domain.
1122 static __isl_give struct isl_sched_info *sched_info_alloc(
1123 __isl_keep isl_map *map)
1127 struct isl_sched_info *info;
1134 dim = isl_space_unwrap(isl_space_domain(isl_map_get_space(map)));
1137 n = isl_space_dim(dim, isl_dim_in);
1138 isl_space_free(dim);
1140 ctx = isl_map_get_ctx(map);
1141 info = isl_alloc_type(ctx, struct isl_sched_info);
1144 info->is_cst = isl_alloc_array(ctx, int, n);
1145 info->cst = isl_vec_alloc(ctx, n);
1146 if (!info->is_cst || !info->cst)
1150 for (i = 0; i < n; ++i) {
1151 info->is_cst[i] = isl_map_plain_is_fixed(map, isl_dim_in, i,
1153 info->cst = isl_vec_set_element(info->cst, i, v);
1159 sched_info_free(info);
1163 struct isl_compute_flow_data {
1164 isl_union_map *must_source;
1165 isl_union_map *may_source;
1166 isl_union_map *must_dep;
1167 isl_union_map *may_dep;
1168 isl_union_map *must_no_source;
1169 isl_union_map *may_no_source;
1174 struct isl_sched_info *sink_info;
1175 struct isl_sched_info **source_info;
1176 isl_access_info *accesses;
1179 static int count_matching_array(__isl_take isl_map *map, void *user)
1183 struct isl_compute_flow_data *data;
1185 data = (struct isl_compute_flow_data *)user;
1187 dim = isl_space_range(isl_map_get_space(map));
1189 eq = isl_space_is_equal(dim, data->dim);
1191 isl_space_free(dim);
1202 static int collect_matching_array(__isl_take isl_map *map, void *user)
1206 struct isl_sched_info *info;
1207 struct isl_compute_flow_data *data;
1209 data = (struct isl_compute_flow_data *)user;
1211 dim = isl_space_range(isl_map_get_space(map));
1213 eq = isl_space_is_equal(dim, data->dim);
1215 isl_space_free(dim);
1224 info = sched_info_alloc(map);
1225 data->source_info[data->count] = info;
1227 data->accesses = isl_access_info_add_source(data->accesses,
1228 map, data->must, info);
1238 /* Determine the shared nesting level and the "textual order" of
1239 * the given accesses.
1241 * We first determine the minimal schedule dimension for both accesses.
1243 * If among those dimensions, we can find one where both have a fixed
1244 * value and if moreover those values are different, then the previous
1245 * dimension is the last shared nesting level and the textual order
1246 * is determined based on the order of the fixed values.
1247 * If no such fixed values can be found, then we set the shared
1248 * nesting level to the minimal schedule dimension, with no textual ordering.
1250 static int before(void *first, void *second)
1252 struct isl_sched_info *info1 = first;
1253 struct isl_sched_info *info2 = second;
1258 n1 = isl_vec_size(info1->cst);
1259 n2 = isl_vec_size(info2->cst);
1266 for (i = 0; i < n1; ++i) {
1269 if (!info1->is_cst[i])
1271 if (!info2->is_cst[i])
1273 isl_vec_get_element(info1->cst, i, &v1);
1274 isl_vec_get_element(info2->cst, i, &v2);
1275 if (isl_int_eq(v1, v2))
1278 r = 2 * i + isl_int_lt(v1, v2);
1290 /* Given a sink access, look for all the source accesses that access
1291 * the same array and perform dataflow analysis on them using
1292 * isl_access_info_compute_flow.
1294 static int compute_flow(__isl_take isl_map *map, void *user)
1298 struct isl_compute_flow_data *data;
1301 data = (struct isl_compute_flow_data *)user;
1303 ctx = isl_map_get_ctx(map);
1305 data->accesses = NULL;
1306 data->sink_info = NULL;
1307 data->source_info = NULL;
1309 data->dim = isl_space_range(isl_map_get_space(map));
1311 if (isl_union_map_foreach_map(data->must_source,
1312 &count_matching_array, data) < 0)
1314 if (isl_union_map_foreach_map(data->may_source,
1315 &count_matching_array, data) < 0)
1318 data->sink_info = sched_info_alloc(map);
1319 data->source_info = isl_calloc_array(ctx, struct isl_sched_info *,
1322 data->accesses = isl_access_info_alloc(isl_map_copy(map),
1323 data->sink_info, &before, data->count);
1324 if (!data->sink_info || !data->source_info || !data->accesses)
1328 if (isl_union_map_foreach_map(data->must_source,
1329 &collect_matching_array, data) < 0)
1332 if (isl_union_map_foreach_map(data->may_source,
1333 &collect_matching_array, data) < 0)
1336 flow = isl_access_info_compute_flow(data->accesses);
1337 data->accesses = NULL;
1342 data->must_no_source = isl_union_map_union(data->must_no_source,
1343 isl_union_map_from_map(isl_flow_get_no_source(flow, 1)));
1344 data->may_no_source = isl_union_map_union(data->may_no_source,
1345 isl_union_map_from_map(isl_flow_get_no_source(flow, 0)));
1347 for (i = 0; i < flow->n_source; ++i) {
1349 dep = isl_union_map_from_map(isl_map_copy(flow->dep[i].map));
1350 if (flow->dep[i].must)
1351 data->must_dep = isl_union_map_union(data->must_dep, dep);
1353 data->may_dep = isl_union_map_union(data->may_dep, dep);
1356 isl_flow_free(flow);
1358 sched_info_free(data->sink_info);
1359 if (data->source_info) {
1360 for (i = 0; i < data->count; ++i)
1361 sched_info_free(data->source_info[i]);
1362 free(data->source_info);
1364 isl_space_free(data->dim);
1369 isl_access_info_free(data->accesses);
1370 sched_info_free(data->sink_info);
1371 if (data->source_info) {
1372 for (i = 0; i < data->count; ++i)
1373 sched_info_free(data->source_info[i]);
1374 free(data->source_info);
1376 isl_space_free(data->dim);
1382 /* Given a collection of "sink" and "source" accesses,
1383 * compute for each iteration of a sink access
1384 * and for each element accessed by that iteration,
1385 * the source access in the list that last accessed the
1386 * element accessed by the sink access before this sink access.
1387 * Each access is given as a map from the loop iterators
1388 * to the array indices.
1389 * The result is a relations between source and sink
1390 * iterations and a subset of the domain of the sink accesses,
1391 * corresponding to those iterations that access an element
1392 * not previously accessed.
1394 * We first prepend the schedule dimensions to the domain
1395 * of the accesses so that we can easily compare their relative order.
1396 * Then we consider each sink access individually in compute_flow.
1398 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
1399 __isl_take isl_union_map *must_source,
1400 __isl_take isl_union_map *may_source,
1401 __isl_take isl_union_map *schedule,
1402 __isl_give isl_union_map **must_dep, __isl_give isl_union_map **may_dep,
1403 __isl_give isl_union_map **must_no_source,
1404 __isl_give isl_union_map **may_no_source)
1407 isl_union_map *range_map = NULL;
1408 struct isl_compute_flow_data data;
1410 sink = isl_union_map_align_params(sink,
1411 isl_union_map_get_space(must_source));
1412 sink = isl_union_map_align_params(sink,
1413 isl_union_map_get_space(may_source));
1414 sink = isl_union_map_align_params(sink,
1415 isl_union_map_get_space(schedule));
1416 dim = isl_union_map_get_space(sink);
1417 must_source = isl_union_map_align_params(must_source, isl_space_copy(dim));
1418 may_source = isl_union_map_align_params(may_source, isl_space_copy(dim));
1419 schedule = isl_union_map_align_params(schedule, isl_space_copy(dim));
1421 schedule = isl_union_map_reverse(schedule);
1422 range_map = isl_union_map_range_map(schedule);
1423 schedule = isl_union_map_reverse(isl_union_map_copy(range_map));
1424 sink = isl_union_map_apply_domain(sink, isl_union_map_copy(schedule));
1425 must_source = isl_union_map_apply_domain(must_source,
1426 isl_union_map_copy(schedule));
1427 may_source = isl_union_map_apply_domain(may_source, schedule);
1429 data.must_source = must_source;
1430 data.may_source = may_source;
1431 data.must_dep = must_dep ?
1432 isl_union_map_empty(isl_space_copy(dim)) : NULL;
1433 data.may_dep = may_dep ? isl_union_map_empty(isl_space_copy(dim)) : NULL;
1434 data.must_no_source = must_no_source ?
1435 isl_union_map_empty(isl_space_copy(dim)) : NULL;
1436 data.may_no_source = may_no_source ?
1437 isl_union_map_empty(isl_space_copy(dim)) : NULL;
1439 isl_space_free(dim);
1441 if (isl_union_map_foreach_map(sink, &compute_flow, &data) < 0)
1444 isl_union_map_free(sink);
1445 isl_union_map_free(must_source);
1446 isl_union_map_free(may_source);
1449 data.must_dep = isl_union_map_apply_domain(data.must_dep,
1450 isl_union_map_copy(range_map));
1451 data.must_dep = isl_union_map_apply_range(data.must_dep,
1452 isl_union_map_copy(range_map));
1453 *must_dep = data.must_dep;
1456 data.may_dep = isl_union_map_apply_domain(data.may_dep,
1457 isl_union_map_copy(range_map));
1458 data.may_dep = isl_union_map_apply_range(data.may_dep,
1459 isl_union_map_copy(range_map));
1460 *may_dep = data.may_dep;
1462 if (must_no_source) {
1463 data.must_no_source = isl_union_map_apply_domain(
1464 data.must_no_source, isl_union_map_copy(range_map));
1465 *must_no_source = data.must_no_source;
1467 if (may_no_source) {
1468 data.may_no_source = isl_union_map_apply_domain(
1469 data.may_no_source, isl_union_map_copy(range_map));
1470 *may_no_source = data.may_no_source;
1473 isl_union_map_free(range_map);
1477 isl_union_map_free(range_map);
1478 isl_union_map_free(sink);
1479 isl_union_map_free(must_source);
1480 isl_union_map_free(may_source);
1481 isl_union_map_free(data.must_dep);
1482 isl_union_map_free(data.may_dep);
1483 isl_union_map_free(data.must_no_source);
1484 isl_union_map_free(data.may_no_source);
1491 *must_no_source = NULL;
1493 *may_no_source = NULL;