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 /* A private structure to keep track of a mapping together with
143 * a user-specified identifier and a boolean indicating whether
144 * the map represents a must or may access/dependence.
146 struct isl_labeled_map
{
152 /* A structure containing the input for dependence analysis:
154 * - n_must + n_may (<= max_source) sources
155 * - a function for determining the relative order of sources and sink
156 * The must sources are placed before the may sources.
158 * domain_map is an auxiliary map that maps the sink access relation
159 * to the domain of this access relation.
161 * restrict_fn is a callback that (if not NULL) will be called
162 * right before any lexicographical maximization.
164 struct isl_access_info
{
166 struct isl_labeled_map sink
;
167 isl_access_level_before level_before
;
169 isl_access_restrict restrict_fn
;
175 struct isl_labeled_map source
[1];
178 /* A structure containing the output of dependence analysis:
179 * - n_source dependences
180 * - a wrapped subset of the sink for which definitely no source could be found
181 * - a wrapped subset of the sink for which possibly no source could be found
184 isl_set
*must_no_source
;
185 isl_set
*may_no_source
;
187 struct isl_labeled_map
*dep
;
190 /* Construct an isl_access_info structure and fill it up with
191 * the given data. The number of sources is set to 0.
193 __isl_give isl_access_info
*isl_access_info_alloc(__isl_take isl_map
*sink
,
194 void *sink_user
, isl_access_level_before fn
, int max_source
)
197 struct isl_access_info
*acc
;
202 ctx
= isl_map_get_ctx(sink
);
203 isl_assert(ctx
, max_source
>= 0, goto error
);
205 acc
= isl_calloc(ctx
, struct isl_access_info
,
206 sizeof(struct isl_access_info
) +
207 (max_source
- 1) * sizeof(struct isl_labeled_map
));
211 acc
->sink
.map
= sink
;
212 acc
->sink
.data
= sink_user
;
213 acc
->level_before
= fn
;
214 acc
->max_source
= max_source
;
224 /* Free the given isl_access_info structure.
226 void isl_access_info_free(__isl_take isl_access_info
*acc
)
232 isl_map_free(acc
->domain_map
);
233 isl_map_free(acc
->sink
.map
);
234 for (i
= 0; i
< acc
->n_must
+ acc
->n_may
; ++i
)
235 isl_map_free(acc
->source
[i
].map
);
239 isl_ctx
*isl_access_info_get_ctx(__isl_keep isl_access_info
*acc
)
241 return acc
? isl_map_get_ctx(acc
->sink
.map
) : NULL
;
244 __isl_give isl_access_info
*isl_access_info_set_restrict(
245 __isl_take isl_access_info
*acc
, isl_access_restrict fn
, void *user
)
249 acc
->restrict_fn
= fn
;
250 acc
->restrict_user
= user
;
254 /* Add another source to an isl_access_info structure, making
255 * sure the "must" sources are placed before the "may" sources.
256 * This function may be called at most max_source times on a
257 * given isl_access_info structure, with max_source as specified
258 * in the call to isl_access_info_alloc that constructed the structure.
260 __isl_give isl_access_info
*isl_access_info_add_source(
261 __isl_take isl_access_info
*acc
, __isl_take isl_map
*source
,
262 int must
, void *source_user
)
268 ctx
= isl_map_get_ctx(acc
->sink
.map
);
269 isl_assert(ctx
, acc
->n_must
+ acc
->n_may
< acc
->max_source
, goto error
);
273 acc
->source
[acc
->n_must
+ acc
->n_may
] =
274 acc
->source
[acc
->n_must
];
275 acc
->source
[acc
->n_must
].map
= source
;
276 acc
->source
[acc
->n_must
].data
= source_user
;
277 acc
->source
[acc
->n_must
].must
= 1;
280 acc
->source
[acc
->n_must
+ acc
->n_may
].map
= source
;
281 acc
->source
[acc
->n_must
+ acc
->n_may
].data
= source_user
;
282 acc
->source
[acc
->n_must
+ acc
->n_may
].must
= 0;
288 isl_map_free(source
);
289 isl_access_info_free(acc
);
293 /* Return -n, 0 or n (with n a positive value), depending on whether
294 * the source access identified by p1 should be sorted before, together
295 * or after that identified by p2.
297 * If p1 appears before p2, then it should be sorted first.
298 * For more generic initial schedules, it is possible that neither
299 * p1 nor p2 appears before the other, or at least not in any obvious way.
300 * We therefore also check if p2 appears before p1, in which case p2
301 * should be sorted first.
302 * If not, we try to order the two statements based on the description
303 * of the iteration domains. This results in an arbitrary, but fairly
306 static int access_sort_cmp(const void *p1
, const void *p2
, void *user
)
308 isl_access_info
*acc
= user
;
309 const struct isl_labeled_map
*i1
, *i2
;
312 i1
= (const struct isl_labeled_map
*) p1
;
313 i2
= (const struct isl_labeled_map
*) p2
;
315 level1
= acc
->level_before(i1
->data
, i2
->data
);
319 level2
= acc
->level_before(i2
->data
, i1
->data
);
323 h1
= isl_map_get_hash(i1
->map
);
324 h2
= isl_map_get_hash(i2
->map
);
325 return h1
> h2
? 1 : h1
< h2
? -1 : 0;
328 /* Sort the must source accesses in their textual order.
330 static __isl_give isl_access_info
*isl_access_info_sort_sources(
331 __isl_take isl_access_info
*acc
)
335 if (acc
->n_must
<= 1)
338 isl_quicksort(acc
->source
, acc
->n_must
, sizeof(struct isl_labeled_map
),
339 access_sort_cmp
, acc
);
344 /* Align the parameters of the two spaces if needed and then call
347 static __isl_give isl_space
*space_align_and_join(__isl_take isl_space
*left
,
348 __isl_take isl_space
*right
)
350 if (isl_space_match(left
, isl_dim_param
, right
, isl_dim_param
))
351 return isl_space_join(left
, right
);
353 left
= isl_space_align_params(left
, isl_space_copy(right
));
354 right
= isl_space_align_params(right
, isl_space_copy(left
));
355 return isl_space_join(left
, right
);
358 /* Initialize an empty isl_flow structure corresponding to a given
359 * isl_access_info structure.
360 * For each must access, two dependences are created (initialized
361 * to the empty relation), one for the resulting must dependences
362 * and one for the resulting may dependences. May accesses can
363 * only lead to may dependences, so only one dependence is created
365 * This function is private as isl_flow structures are only supposed
366 * to be created by isl_access_info_compute_flow.
368 static __isl_give isl_flow
*isl_flow_alloc(__isl_keep isl_access_info
*acc
)
372 struct isl_flow
*dep
;
377 ctx
= isl_map_get_ctx(acc
->sink
.map
);
378 dep
= isl_calloc_type(ctx
, struct isl_flow
);
382 dep
->dep
= isl_calloc_array(ctx
, struct isl_labeled_map
,
383 2 * acc
->n_must
+ acc
->n_may
);
387 dep
->n_source
= 2 * acc
->n_must
+ acc
->n_may
;
388 for (i
= 0; i
< acc
->n_must
; ++i
) {
390 dim
= space_align_and_join(
391 isl_map_get_space(acc
->source
[i
].map
),
392 isl_space_reverse(isl_map_get_space(acc
->sink
.map
)));
393 dep
->dep
[2 * i
].map
= isl_map_empty(dim
);
394 dep
->dep
[2 * i
+ 1].map
= isl_map_copy(dep
->dep
[2 * i
].map
);
395 dep
->dep
[2 * i
].data
= acc
->source
[i
].data
;
396 dep
->dep
[2 * i
+ 1].data
= acc
->source
[i
].data
;
397 dep
->dep
[2 * i
].must
= 1;
398 dep
->dep
[2 * i
+ 1].must
= 0;
399 if (!dep
->dep
[2 * i
].map
|| !dep
->dep
[2 * i
+ 1].map
)
402 for (i
= acc
->n_must
; i
< acc
->n_must
+ acc
->n_may
; ++i
) {
404 dim
= space_align_and_join(
405 isl_map_get_space(acc
->source
[i
].map
),
406 isl_space_reverse(isl_map_get_space(acc
->sink
.map
)));
407 dep
->dep
[acc
->n_must
+ i
].map
= isl_map_empty(dim
);
408 dep
->dep
[acc
->n_must
+ i
].data
= acc
->source
[i
].data
;
409 dep
->dep
[acc
->n_must
+ i
].must
= 0;
410 if (!dep
->dep
[acc
->n_must
+ i
].map
)
420 /* Iterate over all sources and for each resulting flow dependence
421 * that is not empty, call the user specfied function.
422 * The second argument in this function call identifies the source,
423 * while the third argument correspond to the final argument of
424 * the isl_flow_foreach call.
426 int isl_flow_foreach(__isl_keep isl_flow
*deps
,
427 int (*fn
)(__isl_take isl_map
*dep
, int must
, void *dep_user
, void *user
),
435 for (i
= 0; i
< deps
->n_source
; ++i
) {
436 if (isl_map_plain_is_empty(deps
->dep
[i
].map
))
438 if (fn(isl_map_copy(deps
->dep
[i
].map
), deps
->dep
[i
].must
,
439 deps
->dep
[i
].data
, user
) < 0)
446 /* Return a copy of the subset of the sink for which no source could be found.
448 __isl_give isl_map
*isl_flow_get_no_source(__isl_keep isl_flow
*deps
, int must
)
454 return isl_set_unwrap(isl_set_copy(deps
->must_no_source
));
456 return isl_set_unwrap(isl_set_copy(deps
->may_no_source
));
459 void isl_flow_free(__isl_take isl_flow
*deps
)
465 isl_set_free(deps
->must_no_source
);
466 isl_set_free(deps
->may_no_source
);
468 for (i
= 0; i
< deps
->n_source
; ++i
)
469 isl_map_free(deps
->dep
[i
].map
);
475 isl_ctx
*isl_flow_get_ctx(__isl_keep isl_flow
*deps
)
477 return deps
? isl_set_get_ctx(deps
->must_no_source
) : NULL
;
480 /* Return a map that enforces that the domain iteration occurs after
481 * the range iteration at the given level.
482 * If level is odd, then the domain iteration should occur after
483 * the target iteration in their shared level/2 outermost loops.
484 * In this case we simply need to enforce that these outermost
485 * loop iterations are the same.
486 * If level is even, then the loop iterator of the domain should
487 * be greater than the loop iterator of the range at the last
488 * of the level/2 shared loops, i.e., loop level/2 - 1.
490 static __isl_give isl_map
*after_at_level(__isl_take isl_space
*dim
, int level
)
492 struct isl_basic_map
*bmap
;
495 bmap
= isl_basic_map_equal(dim
, level
/2);
497 bmap
= isl_basic_map_more_at(dim
, level
/2 - 1);
499 return isl_map_from_basic_map(bmap
);
502 /* Compute the partial lexicographic maximum of "dep" on domain "sink",
503 * but first check if the user has set acc->restrict_fn and if so
504 * update either the input or the output of the maximization problem
505 * with respect to the resulting restriction.
507 * Since the user expects a mapping from sink iterations to source iterations,
508 * whereas the domain of "dep" is a wrapped map, mapping sink iterations
509 * to accessed array elements, we first need to project out the accessed
510 * sink array elements by applying acc->domain_map.
511 * Similarly, the sink restriction specified by the user needs to be
512 * converted back to the wrapped map.
514 static __isl_give isl_map
*restricted_partial_lexmax(
515 __isl_keep isl_access_info
*acc
, __isl_take isl_map
*dep
,
516 int source
, __isl_take isl_set
*sink
, __isl_give isl_set
**empty
)
519 isl_restriction
*restr
;
520 isl_set
*sink_domain
;
524 if (!acc
->restrict_fn
)
525 return isl_map_partial_lexmax(dep
, sink
, empty
);
527 source_map
= isl_map_copy(dep
);
528 source_map
= isl_map_apply_domain(source_map
,
529 isl_map_copy(acc
->domain_map
));
530 sink_domain
= isl_set_copy(sink
);
531 sink_domain
= isl_set_apply(sink_domain
, isl_map_copy(acc
->domain_map
));
532 restr
= acc
->restrict_fn(source_map
, sink_domain
,
533 acc
->source
[source
].data
, acc
->restrict_user
);
534 isl_set_free(sink_domain
);
535 isl_map_free(source_map
);
539 if (restr
->type
== isl_restriction_type_input
) {
540 dep
= isl_map_intersect_range(dep
, isl_set_copy(restr
->source
));
541 sink_restr
= isl_set_copy(restr
->sink
);
542 sink_restr
= isl_set_apply(sink_restr
,
543 isl_map_reverse(isl_map_copy(acc
->domain_map
)));
544 sink
= isl_set_intersect(sink
, sink_restr
);
545 } else if (restr
->type
== isl_restriction_type_empty
) {
546 isl_space
*space
= isl_map_get_space(dep
);
548 dep
= isl_map_empty(space
);
551 res
= isl_map_partial_lexmax(dep
, sink
, empty
);
553 if (restr
->type
== isl_restriction_type_output
)
554 res
= isl_map_intersect_range(res
, isl_set_copy(restr
->source
));
556 isl_restriction_free(restr
);
565 /* Compute the last iteration of must source j that precedes the sink
566 * at the given level for sink iterations in set_C.
567 * The subset of set_C for which no such iteration can be found is returned
570 static struct isl_map
*last_source(struct isl_access_info
*acc
,
571 struct isl_set
*set_C
,
572 int j
, int level
, struct isl_set
**empty
)
574 struct isl_map
*read_map
;
575 struct isl_map
*write_map
;
576 struct isl_map
*dep_map
;
577 struct isl_map
*after
;
578 struct isl_map
*result
;
580 read_map
= isl_map_copy(acc
->sink
.map
);
581 write_map
= isl_map_copy(acc
->source
[j
].map
);
582 write_map
= isl_map_reverse(write_map
);
583 dep_map
= isl_map_apply_range(read_map
, write_map
);
584 after
= after_at_level(isl_map_get_space(dep_map
), level
);
585 dep_map
= isl_map_intersect(dep_map
, after
);
586 result
= restricted_partial_lexmax(acc
, dep_map
, j
, set_C
, empty
);
587 result
= isl_map_reverse(result
);
592 /* For a given mapping between iterations of must source j and iterations
593 * of the sink, compute the last iteration of must source k preceding
594 * the sink at level before_level for any of the sink iterations,
595 * but following the corresponding iteration of must source j at level
598 static struct isl_map
*last_later_source(struct isl_access_info
*acc
,
599 struct isl_map
*old_map
,
600 int j
, int before_level
,
601 int k
, int after_level
,
602 struct isl_set
**empty
)
605 struct isl_set
*set_C
;
606 struct isl_map
*read_map
;
607 struct isl_map
*write_map
;
608 struct isl_map
*dep_map
;
609 struct isl_map
*after_write
;
610 struct isl_map
*before_read
;
611 struct isl_map
*result
;
613 set_C
= isl_map_range(isl_map_copy(old_map
));
614 read_map
= isl_map_copy(acc
->sink
.map
);
615 write_map
= isl_map_copy(acc
->source
[k
].map
);
617 write_map
= isl_map_reverse(write_map
);
618 dep_map
= isl_map_apply_range(read_map
, write_map
);
619 dim
= space_align_and_join(isl_map_get_space(acc
->source
[k
].map
),
620 isl_space_reverse(isl_map_get_space(acc
->source
[j
].map
)));
621 after_write
= after_at_level(dim
, after_level
);
622 after_write
= isl_map_apply_range(after_write
, old_map
);
623 after_write
= isl_map_reverse(after_write
);
624 dep_map
= isl_map_intersect(dep_map
, after_write
);
625 before_read
= after_at_level(isl_map_get_space(dep_map
), before_level
);
626 dep_map
= isl_map_intersect(dep_map
, before_read
);
627 result
= restricted_partial_lexmax(acc
, dep_map
, k
, set_C
, empty
);
628 result
= isl_map_reverse(result
);
633 /* Given a shared_level between two accesses, return 1 if the
634 * the first can precede the second at the requested target_level.
635 * If the target level is odd, i.e., refers to a statement level
636 * dimension, then first needs to precede second at the requested
637 * level, i.e., shared_level must be equal to target_level.
638 * If the target level is odd, then the two loops should share
639 * at least the requested number of outer loops.
641 static int can_precede_at_level(int shared_level
, int target_level
)
643 if (shared_level
< target_level
)
645 if ((target_level
% 2) && shared_level
> target_level
)
650 /* Given a possible flow dependence temp_rel[j] between source j and the sink
651 * at level sink_level, remove those elements for which
652 * there is an iteration of another source k < j that is closer to the sink.
653 * The flow dependences temp_rel[k] are updated with the improved sources.
654 * Any improved source needs to precede the sink at the same level
655 * and needs to follow source j at the same or a deeper level.
656 * The lower this level, the later the execution date of source k.
657 * We therefore consider lower levels first.
659 * If temp_rel[j] is empty, then there can be no improvement and
660 * we return immediately.
662 static int intermediate_sources(__isl_keep isl_access_info
*acc
,
663 struct isl_map
**temp_rel
, int j
, int sink_level
)
666 int depth
= 2 * isl_map_dim(acc
->source
[j
].map
, isl_dim_in
) + 1;
668 if (isl_map_plain_is_empty(temp_rel
[j
]))
671 for (k
= j
- 1; k
>= 0; --k
) {
673 plevel
= acc
->level_before(acc
->source
[k
].data
, acc
->sink
.data
);
674 if (!can_precede_at_level(plevel
, sink_level
))
677 plevel2
= acc
->level_before(acc
->source
[j
].data
,
678 acc
->source
[k
].data
);
680 for (level
= sink_level
; level
<= depth
; ++level
) {
682 struct isl_set
*trest
;
683 struct isl_map
*copy
;
685 if (!can_precede_at_level(plevel2
, level
))
688 copy
= isl_map_copy(temp_rel
[j
]);
689 T
= last_later_source(acc
, copy
, j
, sink_level
, k
,
691 if (isl_map_plain_is_empty(T
)) {
696 temp_rel
[j
] = isl_map_intersect_range(temp_rel
[j
], trest
);
697 temp_rel
[k
] = isl_map_union_disjoint(temp_rel
[k
], T
);
704 /* Compute all iterations of may source j that precedes the sink at the given
705 * level for sink iterations in set_C.
707 static __isl_give isl_map
*all_sources(__isl_keep isl_access_info
*acc
,
708 __isl_take isl_set
*set_C
, int j
, int level
)
715 read_map
= isl_map_copy(acc
->sink
.map
);
716 read_map
= isl_map_intersect_domain(read_map
, set_C
);
717 write_map
= isl_map_copy(acc
->source
[acc
->n_must
+ j
].map
);
718 write_map
= isl_map_reverse(write_map
);
719 dep_map
= isl_map_apply_range(read_map
, write_map
);
720 after
= after_at_level(isl_map_get_space(dep_map
), level
);
721 dep_map
= isl_map_intersect(dep_map
, after
);
723 return isl_map_reverse(dep_map
);
726 /* For a given mapping between iterations of must source k and iterations
727 * of the sink, compute the all iteration of may source j preceding
728 * the sink at level before_level for any of the sink iterations,
729 * but following the corresponding iteration of must source k at level
732 static __isl_give isl_map
*all_later_sources(__isl_keep isl_access_info
*acc
,
733 __isl_keep isl_map
*old_map
,
734 int j
, int before_level
, int k
, int after_level
)
741 isl_map
*after_write
;
742 isl_map
*before_read
;
744 set_C
= isl_map_range(isl_map_copy(old_map
));
745 read_map
= isl_map_copy(acc
->sink
.map
);
746 read_map
= isl_map_intersect_domain(read_map
, set_C
);
747 write_map
= isl_map_copy(acc
->source
[acc
->n_must
+ j
].map
);
749 write_map
= isl_map_reverse(write_map
);
750 dep_map
= isl_map_apply_range(read_map
, write_map
);
751 dim
= isl_space_join(isl_map_get_space(acc
->source
[acc
->n_must
+ j
].map
),
752 isl_space_reverse(isl_map_get_space(acc
->source
[k
].map
)));
753 after_write
= after_at_level(dim
, after_level
);
754 after_write
= isl_map_apply_range(after_write
, old_map
);
755 after_write
= isl_map_reverse(after_write
);
756 dep_map
= isl_map_intersect(dep_map
, after_write
);
757 before_read
= after_at_level(isl_map_get_space(dep_map
), before_level
);
758 dep_map
= isl_map_intersect(dep_map
, before_read
);
759 return isl_map_reverse(dep_map
);
762 /* Given the must and may dependence relations for the must accesses
763 * for level sink_level, check if there are any accesses of may access j
764 * that occur in between and return their union.
765 * If some of these accesses are intermediate with respect to
766 * (previously thought to be) must dependences, then these
767 * must dependences are turned into may dependences.
769 static __isl_give isl_map
*all_intermediate_sources(
770 __isl_keep isl_access_info
*acc
, __isl_take isl_map
*map
,
771 struct isl_map
**must_rel
, struct isl_map
**may_rel
,
772 int j
, int sink_level
)
775 int depth
= 2 * isl_map_dim(acc
->source
[acc
->n_must
+ j
].map
,
778 for (k
= 0; k
< acc
->n_must
; ++k
) {
781 if (isl_map_plain_is_empty(may_rel
[k
]) &&
782 isl_map_plain_is_empty(must_rel
[k
]))
785 plevel
= acc
->level_before(acc
->source
[k
].data
,
786 acc
->source
[acc
->n_must
+ j
].data
);
788 for (level
= sink_level
; level
<= depth
; ++level
) {
793 if (!can_precede_at_level(plevel
, level
))
796 copy
= isl_map_copy(may_rel
[k
]);
797 T
= all_later_sources(acc
, copy
, j
, sink_level
, k
, level
);
798 map
= isl_map_union(map
, T
);
800 copy
= isl_map_copy(must_rel
[k
]);
801 T
= all_later_sources(acc
, copy
, j
, sink_level
, k
, level
);
802 ran
= isl_map_range(isl_map_copy(T
));
803 map
= isl_map_union(map
, T
);
804 may_rel
[k
] = isl_map_union_disjoint(may_rel
[k
],
805 isl_map_intersect_range(isl_map_copy(must_rel
[k
]),
807 T
= isl_map_from_domain_and_range(
809 isl_space_domain(isl_map_get_space(must_rel
[k
]))),
811 must_rel
[k
] = isl_map_subtract(must_rel
[k
], T
);
818 /* Compute dependences for the case where all accesses are "may"
819 * accesses, which boils down to computing memory based dependences.
820 * The generic algorithm would also work in this case, but it would
821 * be overkill to use it.
823 static __isl_give isl_flow
*compute_mem_based_dependences(
824 __isl_keep isl_access_info
*acc
)
831 res
= isl_flow_alloc(acc
);
835 mustdo
= isl_map_domain(isl_map_copy(acc
->sink
.map
));
836 maydo
= isl_set_copy(mustdo
);
838 for (i
= 0; i
< acc
->n_may
; ++i
) {
845 plevel
= acc
->level_before(acc
->source
[i
].data
, acc
->sink
.data
);
846 is_before
= plevel
& 1;
849 dim
= isl_map_get_space(res
->dep
[i
].map
);
851 before
= isl_map_lex_le_first(dim
, plevel
);
853 before
= isl_map_lex_lt_first(dim
, plevel
);
854 dep
= isl_map_apply_range(isl_map_copy(acc
->source
[i
].map
),
855 isl_map_reverse(isl_map_copy(acc
->sink
.map
)));
856 dep
= isl_map_intersect(dep
, before
);
857 mustdo
= isl_set_subtract(mustdo
,
858 isl_map_range(isl_map_copy(dep
)));
859 res
->dep
[i
].map
= isl_map_union(res
->dep
[i
].map
, dep
);
862 res
->may_no_source
= isl_set_subtract(maydo
, isl_set_copy(mustdo
));
863 res
->must_no_source
= mustdo
;
868 /* Compute dependences for the case where there is at least one
871 * The core algorithm considers all levels in which a source may precede
872 * the sink, where a level may either be a statement level or a loop level.
873 * The outermost statement level is 1, the first loop level is 2, etc...
874 * The algorithm basically does the following:
875 * for all levels l of the read access from innermost to outermost
876 * for all sources w that may precede the sink access at that level
877 * compute the last iteration of the source that precedes the sink access
879 * add result to possible last accesses at level l of source w
880 * for all sources w2 that we haven't considered yet at this level that may
881 * also precede the sink access
882 * for all levels l2 of w from l to innermost
883 * for all possible last accesses dep of w at l
884 * compute last iteration of w2 between the source and sink
886 * add result to possible last accesses at level l of write w2
887 * and replace possible last accesses dep by the remainder
890 * The above algorithm is applied to the must access. During the course
891 * of the algorithm, we keep track of sink iterations that still
892 * need to be considered. These iterations are split into those that
893 * haven't been matched to any source access (mustdo) and those that have only
894 * been matched to may accesses (maydo).
895 * At the end of each level, we also consider the may accesses.
896 * In particular, we consider may accesses that precede the remaining
897 * sink iterations, moving elements from mustdo to maydo when appropriate,
898 * and may accesses that occur between a must source and a sink of any
899 * dependences found at the current level, turning must dependences into
900 * may dependences when appropriate.
903 static __isl_give isl_flow
*compute_val_based_dependences(
904 __isl_keep isl_access_info
*acc
)
908 isl_set
*mustdo
= NULL
;
909 isl_set
*maydo
= NULL
;
912 isl_map
**must_rel
= NULL
;
913 isl_map
**may_rel
= NULL
;
918 res
= isl_flow_alloc(acc
);
921 ctx
= isl_map_get_ctx(acc
->sink
.map
);
923 depth
= 2 * isl_map_dim(acc
->sink
.map
, isl_dim_in
) + 1;
924 mustdo
= isl_map_domain(isl_map_copy(acc
->sink
.map
));
925 maydo
= isl_set_empty_like(mustdo
);
926 if (!mustdo
|| !maydo
)
928 if (isl_set_plain_is_empty(mustdo
))
931 must_rel
= isl_alloc_array(ctx
, struct isl_map
*, acc
->n_must
);
932 may_rel
= isl_alloc_array(ctx
, struct isl_map
*, acc
->n_must
);
933 if (!must_rel
|| !may_rel
)
936 for (level
= depth
; level
>= 1; --level
) {
937 for (j
= acc
->n_must
-1; j
>=0; --j
) {
938 must_rel
[j
] = isl_map_empty_like(res
->dep
[j
].map
);
939 may_rel
[j
] = isl_map_copy(must_rel
[j
]);
942 for (j
= acc
->n_must
- 1; j
>= 0; --j
) {
944 struct isl_set
*rest
;
947 plevel
= acc
->level_before(acc
->source
[j
].data
,
949 if (!can_precede_at_level(plevel
, level
))
952 T
= last_source(acc
, mustdo
, j
, level
, &rest
);
953 must_rel
[j
] = isl_map_union_disjoint(must_rel
[j
], T
);
956 intermediate_sources(acc
, must_rel
, j
, level
);
958 T
= last_source(acc
, maydo
, j
, level
, &rest
);
959 may_rel
[j
] = isl_map_union_disjoint(may_rel
[j
], T
);
962 intermediate_sources(acc
, may_rel
, j
, level
);
964 if (isl_set_plain_is_empty(mustdo
) &&
965 isl_set_plain_is_empty(maydo
))
968 for (j
= j
- 1; j
>= 0; --j
) {
971 plevel
= acc
->level_before(acc
->source
[j
].data
,
973 if (!can_precede_at_level(plevel
, level
))
976 intermediate_sources(acc
, must_rel
, j
, level
);
977 intermediate_sources(acc
, may_rel
, j
, level
);
980 for (j
= 0; j
< acc
->n_may
; ++j
) {
985 plevel
= acc
->level_before(acc
->source
[acc
->n_must
+ j
].data
,
987 if (!can_precede_at_level(plevel
, level
))
990 T
= all_sources(acc
, isl_set_copy(maydo
), j
, level
);
991 res
->dep
[2 * acc
->n_must
+ j
].map
=
992 isl_map_union(res
->dep
[2 * acc
->n_must
+ j
].map
, T
);
993 T
= all_sources(acc
, isl_set_copy(mustdo
), j
, level
);
994 ran
= isl_map_range(isl_map_copy(T
));
995 res
->dep
[2 * acc
->n_must
+ j
].map
=
996 isl_map_union(res
->dep
[2 * acc
->n_must
+ j
].map
, T
);
997 mustdo
= isl_set_subtract(mustdo
, isl_set_copy(ran
));
998 maydo
= isl_set_union_disjoint(maydo
, ran
);
1000 T
= res
->dep
[2 * acc
->n_must
+ j
].map
;
1001 T
= all_intermediate_sources(acc
, T
, must_rel
, may_rel
,
1003 res
->dep
[2 * acc
->n_must
+ j
].map
= T
;
1006 for (j
= acc
->n_must
- 1; j
>= 0; --j
) {
1007 res
->dep
[2 * j
].map
=
1008 isl_map_union_disjoint(res
->dep
[2 * j
].map
,
1010 res
->dep
[2 * j
+ 1].map
=
1011 isl_map_union_disjoint(res
->dep
[2 * j
+ 1].map
,
1015 if (isl_set_plain_is_empty(mustdo
) &&
1016 isl_set_plain_is_empty(maydo
))
1023 res
->must_no_source
= mustdo
;
1024 res
->may_no_source
= maydo
;
1028 isl_set_free(mustdo
);
1029 isl_set_free(maydo
);
1035 /* Given a "sink" access, a list of n "source" accesses,
1036 * compute for each iteration of the sink access
1037 * and for each element accessed by that iteration,
1038 * the source access in the list that last accessed the
1039 * element accessed by the sink access before this sink access.
1040 * Each access is given as a map from the loop iterators
1041 * to the array indices.
1042 * The result is a list of n relations between source and sink
1043 * iterations and a subset of the domain of the sink access,
1044 * corresponding to those iterations that access an element
1045 * not previously accessed.
1047 * To deal with multi-valued sink access relations, the sink iteration
1048 * domain is first extended with dimensions that correspond to the data
1049 * space. After the computation is finished, these extra dimensions are
1050 * projected out again.
1052 __isl_give isl_flow
*isl_access_info_compute_flow(__isl_take isl_access_info
*acc
)
1055 struct isl_flow
*res
= NULL
;
1060 acc
->domain_map
= isl_map_domain_map(isl_map_copy(acc
->sink
.map
));
1061 acc
->sink
.map
= isl_map_range_map(acc
->sink
.map
);
1065 if (acc
->n_must
== 0)
1066 res
= compute_mem_based_dependences(acc
);
1068 acc
= isl_access_info_sort_sources(acc
);
1069 res
= compute_val_based_dependences(acc
);
1074 for (j
= 0; j
< res
->n_source
; ++j
) {
1075 res
->dep
[j
].map
= isl_map_apply_range(res
->dep
[j
].map
,
1076 isl_map_copy(acc
->domain_map
));
1077 if (!res
->dep
[j
].map
)
1080 if (!res
->must_no_source
|| !res
->may_no_source
)
1083 isl_access_info_free(acc
);
1086 isl_access_info_free(acc
);
1092 /* Keep track of some information about a schedule for a given
1093 * access. In particular, keep track of which dimensions
1094 * have a constant value and of the actual constant values.
1096 struct isl_sched_info
{
1101 static void sched_info_free(__isl_take
struct isl_sched_info
*info
)
1105 isl_vec_free(info
->cst
);
1110 /* Extract information on the constant dimensions of the schedule
1111 * for a given access. The "map" is of the form
1115 * with S the schedule domain, D the iteration domain and A the data domain.
1117 static __isl_give
struct isl_sched_info
*sched_info_alloc(
1118 __isl_keep isl_map
*map
)
1122 struct isl_sched_info
*info
;
1129 dim
= isl_space_unwrap(isl_space_domain(isl_map_get_space(map
)));
1132 n
= isl_space_dim(dim
, isl_dim_in
);
1133 isl_space_free(dim
);
1135 ctx
= isl_map_get_ctx(map
);
1136 info
= isl_alloc_type(ctx
, struct isl_sched_info
);
1139 info
->is_cst
= isl_alloc_array(ctx
, int, n
);
1140 info
->cst
= isl_vec_alloc(ctx
, n
);
1141 if (!info
->is_cst
|| !info
->cst
)
1145 for (i
= 0; i
< n
; ++i
) {
1146 info
->is_cst
[i
] = isl_map_plain_is_fixed(map
, isl_dim_in
, i
,
1148 info
->cst
= isl_vec_set_element(info
->cst
, i
, v
);
1154 sched_info_free(info
);
1158 struct isl_compute_flow_data
{
1159 isl_union_map
*must_source
;
1160 isl_union_map
*may_source
;
1161 isl_union_map
*must_dep
;
1162 isl_union_map
*may_dep
;
1163 isl_union_map
*must_no_source
;
1164 isl_union_map
*may_no_source
;
1169 struct isl_sched_info
*sink_info
;
1170 struct isl_sched_info
**source_info
;
1171 isl_access_info
*accesses
;
1174 static int count_matching_array(__isl_take isl_map
*map
, void *user
)
1178 struct isl_compute_flow_data
*data
;
1180 data
= (struct isl_compute_flow_data
*)user
;
1182 dim
= isl_space_range(isl_map_get_space(map
));
1184 eq
= isl_space_is_equal(dim
, data
->dim
);
1186 isl_space_free(dim
);
1197 static int collect_matching_array(__isl_take isl_map
*map
, void *user
)
1201 struct isl_sched_info
*info
;
1202 struct isl_compute_flow_data
*data
;
1204 data
= (struct isl_compute_flow_data
*)user
;
1206 dim
= isl_space_range(isl_map_get_space(map
));
1208 eq
= isl_space_is_equal(dim
, data
->dim
);
1210 isl_space_free(dim
);
1219 info
= sched_info_alloc(map
);
1220 data
->source_info
[data
->count
] = info
;
1222 data
->accesses
= isl_access_info_add_source(data
->accesses
,
1223 map
, data
->must
, info
);
1233 /* Determine the shared nesting level and the "textual order" of
1234 * the given accesses.
1236 * We first determine the minimal schedule dimension for both accesses.
1238 * If among those dimensions, we can find one where both have a fixed
1239 * value and if moreover those values are different, then the previous
1240 * dimension is the last shared nesting level and the textual order
1241 * is determined based on the order of the fixed values.
1242 * If no such fixed values can be found, then we set the shared
1243 * nesting level to the minimal schedule dimension, with no textual ordering.
1245 static int before(void *first
, void *second
)
1247 struct isl_sched_info
*info1
= first
;
1248 struct isl_sched_info
*info2
= second
;
1253 n1
= isl_vec_size(info1
->cst
);
1254 n2
= isl_vec_size(info2
->cst
);
1261 for (i
= 0; i
< n1
; ++i
) {
1264 if (!info1
->is_cst
[i
])
1266 if (!info2
->is_cst
[i
])
1268 isl_vec_get_element(info1
->cst
, i
, &v1
);
1269 isl_vec_get_element(info2
->cst
, i
, &v2
);
1270 if (isl_int_eq(v1
, v2
))
1273 r
= 2 * i
+ isl_int_lt(v1
, v2
);
1285 /* Given a sink access, look for all the source accesses that access
1286 * the same array and perform dataflow analysis on them using
1287 * isl_access_info_compute_flow.
1289 static int compute_flow(__isl_take isl_map
*map
, void *user
)
1293 struct isl_compute_flow_data
*data
;
1296 data
= (struct isl_compute_flow_data
*)user
;
1298 ctx
= isl_map_get_ctx(map
);
1300 data
->accesses
= NULL
;
1301 data
->sink_info
= NULL
;
1302 data
->source_info
= NULL
;
1304 data
->dim
= isl_space_range(isl_map_get_space(map
));
1306 if (isl_union_map_foreach_map(data
->must_source
,
1307 &count_matching_array
, data
) < 0)
1309 if (isl_union_map_foreach_map(data
->may_source
,
1310 &count_matching_array
, data
) < 0)
1313 data
->sink_info
= sched_info_alloc(map
);
1314 data
->source_info
= isl_calloc_array(ctx
, struct isl_sched_info
*,
1317 data
->accesses
= isl_access_info_alloc(isl_map_copy(map
),
1318 data
->sink_info
, &before
, data
->count
);
1319 if (!data
->sink_info
|| !data
->source_info
|| !data
->accesses
)
1323 if (isl_union_map_foreach_map(data
->must_source
,
1324 &collect_matching_array
, data
) < 0)
1327 if (isl_union_map_foreach_map(data
->may_source
,
1328 &collect_matching_array
, data
) < 0)
1331 flow
= isl_access_info_compute_flow(data
->accesses
);
1332 data
->accesses
= NULL
;
1337 data
->must_no_source
= isl_union_map_union(data
->must_no_source
,
1338 isl_union_map_from_map(isl_flow_get_no_source(flow
, 1)));
1339 data
->may_no_source
= isl_union_map_union(data
->may_no_source
,
1340 isl_union_map_from_map(isl_flow_get_no_source(flow
, 0)));
1342 for (i
= 0; i
< flow
->n_source
; ++i
) {
1344 dep
= isl_union_map_from_map(isl_map_copy(flow
->dep
[i
].map
));
1345 if (flow
->dep
[i
].must
)
1346 data
->must_dep
= isl_union_map_union(data
->must_dep
, dep
);
1348 data
->may_dep
= isl_union_map_union(data
->may_dep
, dep
);
1351 isl_flow_free(flow
);
1353 sched_info_free(data
->sink_info
);
1354 if (data
->source_info
) {
1355 for (i
= 0; i
< data
->count
; ++i
)
1356 sched_info_free(data
->source_info
[i
]);
1357 free(data
->source_info
);
1359 isl_space_free(data
->dim
);
1364 isl_access_info_free(data
->accesses
);
1365 sched_info_free(data
->sink_info
);
1366 if (data
->source_info
) {
1367 for (i
= 0; i
< data
->count
; ++i
)
1368 sched_info_free(data
->source_info
[i
]);
1369 free(data
->source_info
);
1371 isl_space_free(data
->dim
);
1377 /* Given a collection of "sink" and "source" accesses,
1378 * compute for each iteration of a sink access
1379 * and for each element accessed by that iteration,
1380 * the source access in the list that last accessed the
1381 * element accessed by the sink access before this sink access.
1382 * Each access is given as a map from the loop iterators
1383 * to the array indices.
1384 * The result is a relations between source and sink
1385 * iterations and a subset of the domain of the sink accesses,
1386 * corresponding to those iterations that access an element
1387 * not previously accessed.
1389 * We first prepend the schedule dimensions to the domain
1390 * of the accesses so that we can easily compare their relative order.
1391 * Then we consider each sink access individually in compute_flow.
1393 int isl_union_map_compute_flow(__isl_take isl_union_map
*sink
,
1394 __isl_take isl_union_map
*must_source
,
1395 __isl_take isl_union_map
*may_source
,
1396 __isl_take isl_union_map
*schedule
,
1397 __isl_give isl_union_map
**must_dep
, __isl_give isl_union_map
**may_dep
,
1398 __isl_give isl_union_map
**must_no_source
,
1399 __isl_give isl_union_map
**may_no_source
)
1402 isl_union_map
*range_map
= NULL
;
1403 struct isl_compute_flow_data data
;
1405 sink
= isl_union_map_align_params(sink
,
1406 isl_union_map_get_space(must_source
));
1407 sink
= isl_union_map_align_params(sink
,
1408 isl_union_map_get_space(may_source
));
1409 sink
= isl_union_map_align_params(sink
,
1410 isl_union_map_get_space(schedule
));
1411 dim
= isl_union_map_get_space(sink
);
1412 must_source
= isl_union_map_align_params(must_source
, isl_space_copy(dim
));
1413 may_source
= isl_union_map_align_params(may_source
, isl_space_copy(dim
));
1414 schedule
= isl_union_map_align_params(schedule
, isl_space_copy(dim
));
1416 schedule
= isl_union_map_reverse(schedule
);
1417 range_map
= isl_union_map_range_map(schedule
);
1418 schedule
= isl_union_map_reverse(isl_union_map_copy(range_map
));
1419 sink
= isl_union_map_apply_domain(sink
, isl_union_map_copy(schedule
));
1420 must_source
= isl_union_map_apply_domain(must_source
,
1421 isl_union_map_copy(schedule
));
1422 may_source
= isl_union_map_apply_domain(may_source
, schedule
);
1424 data
.must_source
= must_source
;
1425 data
.may_source
= may_source
;
1426 data
.must_dep
= must_dep
?
1427 isl_union_map_empty(isl_space_copy(dim
)) : NULL
;
1428 data
.may_dep
= may_dep
? isl_union_map_empty(isl_space_copy(dim
)) : NULL
;
1429 data
.must_no_source
= must_no_source
?
1430 isl_union_map_empty(isl_space_copy(dim
)) : NULL
;
1431 data
.may_no_source
= may_no_source
?
1432 isl_union_map_empty(isl_space_copy(dim
)) : NULL
;
1434 isl_space_free(dim
);
1436 if (isl_union_map_foreach_map(sink
, &compute_flow
, &data
) < 0)
1439 isl_union_map_free(sink
);
1440 isl_union_map_free(must_source
);
1441 isl_union_map_free(may_source
);
1444 data
.must_dep
= isl_union_map_apply_domain(data
.must_dep
,
1445 isl_union_map_copy(range_map
));
1446 data
.must_dep
= isl_union_map_apply_range(data
.must_dep
,
1447 isl_union_map_copy(range_map
));
1448 *must_dep
= data
.must_dep
;
1451 data
.may_dep
= isl_union_map_apply_domain(data
.may_dep
,
1452 isl_union_map_copy(range_map
));
1453 data
.may_dep
= isl_union_map_apply_range(data
.may_dep
,
1454 isl_union_map_copy(range_map
));
1455 *may_dep
= data
.may_dep
;
1457 if (must_no_source
) {
1458 data
.must_no_source
= isl_union_map_apply_domain(
1459 data
.must_no_source
, isl_union_map_copy(range_map
));
1460 *must_no_source
= data
.must_no_source
;
1462 if (may_no_source
) {
1463 data
.may_no_source
= isl_union_map_apply_domain(
1464 data
.may_no_source
, isl_union_map_copy(range_map
));
1465 *may_no_source
= data
.may_no_source
;
1468 isl_union_map_free(range_map
);
1472 isl_union_map_free(range_map
);
1473 isl_union_map_free(sink
);
1474 isl_union_map_free(must_source
);
1475 isl_union_map_free(may_source
);
1476 isl_union_map_free(data
.must_dep
);
1477 isl_union_map_free(data
.may_dep
);
1478 isl_union_map_free(data
.must_no_source
);
1479 isl_union_map_free(data
.may_no_source
);
1486 *must_no_source
= NULL
;
1488 *may_no_source
= NULL
;