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
;