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_take 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
;
53 isl_map_free(source_map
);
56 isl_map_free(source_map
);
60 /* Create a restriction that removes everything.
62 __isl_give isl_restriction
*isl_restriction_empty(
63 __isl_take isl_map
*source_map
)
66 isl_restriction
*restr
;
71 ctx
= isl_map_get_ctx(source_map
);
72 restr
= isl_calloc_type(ctx
, struct isl_restriction
);
76 restr
->type
= isl_restriction_type_empty
;
78 isl_map_free(source_map
);
81 isl_map_free(source_map
);
85 /* Create a restriction on the input of the maximization problem
86 * based on the given source and sink restrictions.
88 __isl_give isl_restriction
*isl_restriction_input(
89 __isl_take isl_set
*source_restr
, __isl_take isl_set
*sink_restr
)
92 isl_restriction
*restr
;
94 if (!source_restr
|| !sink_restr
)
97 ctx
= isl_set_get_ctx(source_restr
);
98 restr
= isl_calloc_type(ctx
, struct isl_restriction
);
102 restr
->type
= isl_restriction_type_input
;
103 restr
->source
= source_restr
;
104 restr
->sink
= sink_restr
;
108 isl_set_free(source_restr
);
109 isl_set_free(sink_restr
);
113 /* Create a restriction on the output of the maximization problem
114 * based on the given source restriction.
116 __isl_give isl_restriction
*isl_restriction_output(
117 __isl_take isl_set
*source_restr
)
120 isl_restriction
*restr
;
125 ctx
= isl_set_get_ctx(source_restr
);
126 restr
= isl_calloc_type(ctx
, struct isl_restriction
);
130 restr
->type
= isl_restriction_type_output
;
131 restr
->source
= source_restr
;
135 isl_set_free(source_restr
);
139 void *isl_restriction_free(__isl_take isl_restriction
*restr
)
144 isl_set_free(restr
->source
);
145 isl_set_free(restr
->sink
);
150 isl_ctx
*isl_restriction_get_ctx(__isl_keep isl_restriction
*restr
)
152 return restr
? isl_set_get_ctx(restr
->source
) : NULL
;
155 /* A private structure to keep track of a mapping together with
156 * a user-specified identifier and a boolean indicating whether
157 * the map represents a must or may access/dependence.
159 struct isl_labeled_map
{
165 /* A structure containing the input for dependence analysis:
167 * - n_must + n_may (<= max_source) sources
168 * - a function for determining the relative order of sources and sink
169 * The must sources are placed before the may sources.
171 * domain_map is an auxiliary map that maps the sink access relation
172 * to the domain of this access relation.
174 * restrict_fn is a callback that (if not NULL) will be called
175 * right before any lexicographical maximization.
177 struct isl_access_info
{
179 struct isl_labeled_map sink
;
180 isl_access_level_before level_before
;
182 isl_access_restrict restrict_fn
;
188 struct isl_labeled_map source
[1];
191 /* A structure containing the output of dependence analysis:
192 * - n_source dependences
193 * - a wrapped subset of the sink for which definitely no source could be found
194 * - a wrapped subset of the sink for which possibly no source could be found
197 isl_set
*must_no_source
;
198 isl_set
*may_no_source
;
200 struct isl_labeled_map
*dep
;
203 /* Construct an isl_access_info structure and fill it up with
204 * the given data. The number of sources is set to 0.
206 __isl_give isl_access_info
*isl_access_info_alloc(__isl_take isl_map
*sink
,
207 void *sink_user
, isl_access_level_before fn
, int max_source
)
210 struct isl_access_info
*acc
;
215 ctx
= isl_map_get_ctx(sink
);
216 isl_assert(ctx
, max_source
>= 0, goto error
);
218 acc
= isl_calloc(ctx
, struct isl_access_info
,
219 sizeof(struct isl_access_info
) +
220 (max_source
- 1) * sizeof(struct isl_labeled_map
));
224 acc
->sink
.map
= sink
;
225 acc
->sink
.data
= sink_user
;
226 acc
->level_before
= fn
;
227 acc
->max_source
= max_source
;
237 /* Free the given isl_access_info structure.
239 void isl_access_info_free(__isl_take isl_access_info
*acc
)
245 isl_map_free(acc
->domain_map
);
246 isl_map_free(acc
->sink
.map
);
247 for (i
= 0; i
< acc
->n_must
+ acc
->n_may
; ++i
)
248 isl_map_free(acc
->source
[i
].map
);
252 isl_ctx
*isl_access_info_get_ctx(__isl_keep isl_access_info
*acc
)
254 return acc
? isl_map_get_ctx(acc
->sink
.map
) : NULL
;
257 __isl_give isl_access_info
*isl_access_info_set_restrict(
258 __isl_take isl_access_info
*acc
, isl_access_restrict fn
, void *user
)
262 acc
->restrict_fn
= fn
;
263 acc
->restrict_user
= user
;
267 /* Add another source to an isl_access_info structure, making
268 * sure the "must" sources are placed before the "may" sources.
269 * This function may be called at most max_source times on a
270 * given isl_access_info structure, with max_source as specified
271 * in the call to isl_access_info_alloc that constructed the structure.
273 __isl_give isl_access_info
*isl_access_info_add_source(
274 __isl_take isl_access_info
*acc
, __isl_take isl_map
*source
,
275 int must
, void *source_user
)
281 ctx
= isl_map_get_ctx(acc
->sink
.map
);
282 isl_assert(ctx
, acc
->n_must
+ acc
->n_may
< acc
->max_source
, goto error
);
286 acc
->source
[acc
->n_must
+ acc
->n_may
] =
287 acc
->source
[acc
->n_must
];
288 acc
->source
[acc
->n_must
].map
= source
;
289 acc
->source
[acc
->n_must
].data
= source_user
;
290 acc
->source
[acc
->n_must
].must
= 1;
293 acc
->source
[acc
->n_must
+ acc
->n_may
].map
= source
;
294 acc
->source
[acc
->n_must
+ acc
->n_may
].data
= source_user
;
295 acc
->source
[acc
->n_must
+ acc
->n_may
].must
= 0;
301 isl_map_free(source
);
302 isl_access_info_free(acc
);
306 /* Return -n, 0 or n (with n a positive value), depending on whether
307 * the source access identified by p1 should be sorted before, together
308 * or after that identified by p2.
310 * If p1 appears before p2, then it should be sorted first.
311 * For more generic initial schedules, it is possible that neither
312 * p1 nor p2 appears before the other, or at least not in any obvious way.
313 * We therefore also check if p2 appears before p1, in which case p2
314 * should be sorted first.
315 * If not, we try to order the two statements based on the description
316 * of the iteration domains. This results in an arbitrary, but fairly
319 static int access_sort_cmp(const void *p1
, const void *p2
, void *user
)
321 isl_access_info
*acc
= user
;
322 const struct isl_labeled_map
*i1
, *i2
;
325 i1
= (const struct isl_labeled_map
*) p1
;
326 i2
= (const struct isl_labeled_map
*) p2
;
328 level1
= acc
->level_before(i1
->data
, i2
->data
);
332 level2
= acc
->level_before(i2
->data
, i1
->data
);
336 h1
= isl_map_get_hash(i1
->map
);
337 h2
= isl_map_get_hash(i2
->map
);
338 return h1
> h2
? 1 : h1
< h2
? -1 : 0;
341 /* Sort the must source accesses in their textual order.
343 static __isl_give isl_access_info
*isl_access_info_sort_sources(
344 __isl_take isl_access_info
*acc
)
348 if (acc
->n_must
<= 1)
351 isl_quicksort(acc
->source
, acc
->n_must
, sizeof(struct isl_labeled_map
),
352 access_sort_cmp
, acc
);
357 /* Align the parameters of the two spaces if needed and then call
360 static __isl_give isl_space
*space_align_and_join(__isl_take isl_space
*left
,
361 __isl_take isl_space
*right
)
363 if (isl_space_match(left
, isl_dim_param
, right
, isl_dim_param
))
364 return isl_space_join(left
, right
);
366 left
= isl_space_align_params(left
, isl_space_copy(right
));
367 right
= isl_space_align_params(right
, isl_space_copy(left
));
368 return isl_space_join(left
, right
);
371 /* Initialize an empty isl_flow structure corresponding to a given
372 * isl_access_info structure.
373 * For each must access, two dependences are created (initialized
374 * to the empty relation), one for the resulting must dependences
375 * and one for the resulting may dependences. May accesses can
376 * only lead to may dependences, so only one dependence is created
378 * This function is private as isl_flow structures are only supposed
379 * to be created by isl_access_info_compute_flow.
381 static __isl_give isl_flow
*isl_flow_alloc(__isl_keep isl_access_info
*acc
)
385 struct isl_flow
*dep
;
390 ctx
= isl_map_get_ctx(acc
->sink
.map
);
391 dep
= isl_calloc_type(ctx
, struct isl_flow
);
395 dep
->dep
= isl_calloc_array(ctx
, struct isl_labeled_map
,
396 2 * acc
->n_must
+ acc
->n_may
);
400 dep
->n_source
= 2 * acc
->n_must
+ acc
->n_may
;
401 for (i
= 0; i
< acc
->n_must
; ++i
) {
403 dim
= space_align_and_join(
404 isl_map_get_space(acc
->source
[i
].map
),
405 isl_space_reverse(isl_map_get_space(acc
->sink
.map
)));
406 dep
->dep
[2 * i
].map
= isl_map_empty(dim
);
407 dep
->dep
[2 * i
+ 1].map
= isl_map_copy(dep
->dep
[2 * i
].map
);
408 dep
->dep
[2 * i
].data
= acc
->source
[i
].data
;
409 dep
->dep
[2 * i
+ 1].data
= acc
->source
[i
].data
;
410 dep
->dep
[2 * i
].must
= 1;
411 dep
->dep
[2 * i
+ 1].must
= 0;
412 if (!dep
->dep
[2 * i
].map
|| !dep
->dep
[2 * i
+ 1].map
)
415 for (i
= acc
->n_must
; i
< acc
->n_must
+ acc
->n_may
; ++i
) {
417 dim
= space_align_and_join(
418 isl_map_get_space(acc
->source
[i
].map
),
419 isl_space_reverse(isl_map_get_space(acc
->sink
.map
)));
420 dep
->dep
[acc
->n_must
+ i
].map
= isl_map_empty(dim
);
421 dep
->dep
[acc
->n_must
+ i
].data
= acc
->source
[i
].data
;
422 dep
->dep
[acc
->n_must
+ i
].must
= 0;
423 if (!dep
->dep
[acc
->n_must
+ i
].map
)
433 /* Iterate over all sources and for each resulting flow dependence
434 * that is not empty, call the user specfied function.
435 * The second argument in this function call identifies the source,
436 * while the third argument correspond to the final argument of
437 * the isl_flow_foreach call.
439 int isl_flow_foreach(__isl_keep isl_flow
*deps
,
440 int (*fn
)(__isl_take isl_map
*dep
, int must
, void *dep_user
, void *user
),
448 for (i
= 0; i
< deps
->n_source
; ++i
) {
449 if (isl_map_plain_is_empty(deps
->dep
[i
].map
))
451 if (fn(isl_map_copy(deps
->dep
[i
].map
), deps
->dep
[i
].must
,
452 deps
->dep
[i
].data
, user
) < 0)
459 /* Return a copy of the subset of the sink for which no source could be found.
461 __isl_give isl_map
*isl_flow_get_no_source(__isl_keep isl_flow
*deps
, int must
)
467 return isl_set_unwrap(isl_set_copy(deps
->must_no_source
));
469 return isl_set_unwrap(isl_set_copy(deps
->may_no_source
));
472 void isl_flow_free(__isl_take isl_flow
*deps
)
478 isl_set_free(deps
->must_no_source
);
479 isl_set_free(deps
->may_no_source
);
481 for (i
= 0; i
< deps
->n_source
; ++i
)
482 isl_map_free(deps
->dep
[i
].map
);
488 isl_ctx
*isl_flow_get_ctx(__isl_keep isl_flow
*deps
)
490 return deps
? isl_set_get_ctx(deps
->must_no_source
) : NULL
;
493 /* Return a map that enforces that the domain iteration occurs after
494 * the range iteration at the given level.
495 * If level is odd, then the domain iteration should occur after
496 * the target iteration in their shared level/2 outermost loops.
497 * In this case we simply need to enforce that these outermost
498 * loop iterations are the same.
499 * If level is even, then the loop iterator of the domain should
500 * be greater than the loop iterator of the range at the last
501 * of the level/2 shared loops, i.e., loop level/2 - 1.
503 static __isl_give isl_map
*after_at_level(__isl_take isl_space
*dim
, int level
)
505 struct isl_basic_map
*bmap
;
508 bmap
= isl_basic_map_equal(dim
, level
/2);
510 bmap
= isl_basic_map_more_at(dim
, level
/2 - 1);
512 return isl_map_from_basic_map(bmap
);
515 /* Compute the partial lexicographic maximum of "dep" on domain "sink",
516 * but first check if the user has set acc->restrict_fn and if so
517 * update either the input or the output of the maximization problem
518 * with respect to the resulting restriction.
520 * Since the user expects a mapping from sink iterations to source iterations,
521 * whereas the domain of "dep" is a wrapped map, mapping sink iterations
522 * to accessed array elements, we first need to project out the accessed
523 * sink array elements by applying acc->domain_map.
524 * Similarly, the sink restriction specified by the user needs to be
525 * converted back to the wrapped map.
527 static __isl_give isl_map
*restricted_partial_lexmax(
528 __isl_keep isl_access_info
*acc
, __isl_take isl_map
*dep
,
529 int source
, __isl_take isl_set
*sink
, __isl_give isl_set
**empty
)
532 isl_restriction
*restr
;
533 isl_set
*sink_domain
;
537 if (!acc
->restrict_fn
)
538 return isl_map_partial_lexmax(dep
, sink
, empty
);
540 source_map
= isl_map_copy(dep
);
541 source_map
= isl_map_apply_domain(source_map
,
542 isl_map_copy(acc
->domain_map
));
543 sink_domain
= isl_set_copy(sink
);
544 sink_domain
= isl_set_apply(sink_domain
, isl_map_copy(acc
->domain_map
));
545 restr
= acc
->restrict_fn(source_map
, sink_domain
,
546 acc
->source
[source
].data
, acc
->restrict_user
);
547 isl_set_free(sink_domain
);
548 isl_map_free(source_map
);
552 if (restr
->type
== isl_restriction_type_input
) {
553 dep
= isl_map_intersect_range(dep
, isl_set_copy(restr
->source
));
554 sink_restr
= isl_set_copy(restr
->sink
);
555 sink_restr
= isl_set_apply(sink_restr
,
556 isl_map_reverse(isl_map_copy(acc
->domain_map
)));
557 sink
= isl_set_intersect(sink
, sink_restr
);
558 } else if (restr
->type
== isl_restriction_type_empty
) {
559 isl_space
*space
= isl_map_get_space(dep
);
561 dep
= isl_map_empty(space
);
564 res
= isl_map_partial_lexmax(dep
, sink
, empty
);
566 if (restr
->type
== isl_restriction_type_output
)
567 res
= isl_map_intersect_range(res
, isl_set_copy(restr
->source
));
569 isl_restriction_free(restr
);
578 /* Compute the last iteration of must source j that precedes the sink
579 * at the given level for sink iterations in set_C.
580 * The subset of set_C for which no such iteration can be found is returned
583 static struct isl_map
*last_source(struct isl_access_info
*acc
,
584 struct isl_set
*set_C
,
585 int j
, int level
, struct isl_set
**empty
)
587 struct isl_map
*read_map
;
588 struct isl_map
*write_map
;
589 struct isl_map
*dep_map
;
590 struct isl_map
*after
;
591 struct isl_map
*result
;
593 read_map
= isl_map_copy(acc
->sink
.map
);
594 write_map
= isl_map_copy(acc
->source
[j
].map
);
595 write_map
= isl_map_reverse(write_map
);
596 dep_map
= isl_map_apply_range(read_map
, write_map
);
597 after
= after_at_level(isl_map_get_space(dep_map
), level
);
598 dep_map
= isl_map_intersect(dep_map
, after
);
599 result
= restricted_partial_lexmax(acc
, dep_map
, j
, set_C
, empty
);
600 result
= isl_map_reverse(result
);
605 /* For a given mapping between iterations of must source j and iterations
606 * of the sink, compute the last iteration of must source k preceding
607 * the sink at level before_level for any of the sink iterations,
608 * but following the corresponding iteration of must source j at level
611 static struct isl_map
*last_later_source(struct isl_access_info
*acc
,
612 struct isl_map
*old_map
,
613 int j
, int before_level
,
614 int k
, int after_level
,
615 struct isl_set
**empty
)
618 struct isl_set
*set_C
;
619 struct isl_map
*read_map
;
620 struct isl_map
*write_map
;
621 struct isl_map
*dep_map
;
622 struct isl_map
*after_write
;
623 struct isl_map
*before_read
;
624 struct isl_map
*result
;
626 set_C
= isl_map_range(isl_map_copy(old_map
));
627 read_map
= isl_map_copy(acc
->sink
.map
);
628 write_map
= isl_map_copy(acc
->source
[k
].map
);
630 write_map
= isl_map_reverse(write_map
);
631 dep_map
= isl_map_apply_range(read_map
, write_map
);
632 dim
= space_align_and_join(isl_map_get_space(acc
->source
[k
].map
),
633 isl_space_reverse(isl_map_get_space(acc
->source
[j
].map
)));
634 after_write
= after_at_level(dim
, after_level
);
635 after_write
= isl_map_apply_range(after_write
, old_map
);
636 after_write
= isl_map_reverse(after_write
);
637 dep_map
= isl_map_intersect(dep_map
, after_write
);
638 before_read
= after_at_level(isl_map_get_space(dep_map
), before_level
);
639 dep_map
= isl_map_intersect(dep_map
, before_read
);
640 result
= restricted_partial_lexmax(acc
, dep_map
, k
, set_C
, empty
);
641 result
= isl_map_reverse(result
);
646 /* Given a shared_level between two accesses, return 1 if the
647 * the first can precede the second at the requested target_level.
648 * If the target level is odd, i.e., refers to a statement level
649 * dimension, then first needs to precede second at the requested
650 * level, i.e., shared_level must be equal to target_level.
651 * If the target level is odd, then the two loops should share
652 * at least the requested number of outer loops.
654 static int can_precede_at_level(int shared_level
, int target_level
)
656 if (shared_level
< target_level
)
658 if ((target_level
% 2) && shared_level
> target_level
)
663 /* Given a possible flow dependence temp_rel[j] between source j and the sink
664 * at level sink_level, remove those elements for which
665 * there is an iteration of another source k < j that is closer to the sink.
666 * The flow dependences temp_rel[k] are updated with the improved sources.
667 * Any improved source needs to precede the sink at the same level
668 * and needs to follow source j at the same or a deeper level.
669 * The lower this level, the later the execution date of source k.
670 * We therefore consider lower levels first.
672 * If temp_rel[j] is empty, then there can be no improvement and
673 * we return immediately.
675 static int intermediate_sources(__isl_keep isl_access_info
*acc
,
676 struct isl_map
**temp_rel
, int j
, int sink_level
)
679 int depth
= 2 * isl_map_dim(acc
->source
[j
].map
, isl_dim_in
) + 1;
681 if (isl_map_plain_is_empty(temp_rel
[j
]))
684 for (k
= j
- 1; k
>= 0; --k
) {
686 plevel
= acc
->level_before(acc
->source
[k
].data
, acc
->sink
.data
);
687 if (!can_precede_at_level(plevel
, sink_level
))
690 plevel2
= acc
->level_before(acc
->source
[j
].data
,
691 acc
->source
[k
].data
);
693 for (level
= sink_level
; level
<= depth
; ++level
) {
695 struct isl_set
*trest
;
696 struct isl_map
*copy
;
698 if (!can_precede_at_level(plevel2
, level
))
701 copy
= isl_map_copy(temp_rel
[j
]);
702 T
= last_later_source(acc
, copy
, j
, sink_level
, k
,
704 if (isl_map_plain_is_empty(T
)) {
709 temp_rel
[j
] = isl_map_intersect_range(temp_rel
[j
], trest
);
710 temp_rel
[k
] = isl_map_union_disjoint(temp_rel
[k
], T
);
717 /* Compute all iterations of may source j that precedes the sink at the given
718 * level for sink iterations in set_C.
720 static __isl_give isl_map
*all_sources(__isl_keep isl_access_info
*acc
,
721 __isl_take isl_set
*set_C
, int j
, int level
)
728 read_map
= isl_map_copy(acc
->sink
.map
);
729 read_map
= isl_map_intersect_domain(read_map
, set_C
);
730 write_map
= isl_map_copy(acc
->source
[acc
->n_must
+ j
].map
);
731 write_map
= isl_map_reverse(write_map
);
732 dep_map
= isl_map_apply_range(read_map
, write_map
);
733 after
= after_at_level(isl_map_get_space(dep_map
), level
);
734 dep_map
= isl_map_intersect(dep_map
, after
);
736 return isl_map_reverse(dep_map
);
739 /* For a given mapping between iterations of must source k and iterations
740 * of the sink, compute the all iteration of may source j preceding
741 * the sink at level before_level for any of the sink iterations,
742 * but following the corresponding iteration of must source k at level
745 static __isl_give isl_map
*all_later_sources(__isl_keep isl_access_info
*acc
,
746 __isl_keep isl_map
*old_map
,
747 int j
, int before_level
, int k
, int after_level
)
754 isl_map
*after_write
;
755 isl_map
*before_read
;
757 set_C
= isl_map_range(isl_map_copy(old_map
));
758 read_map
= isl_map_copy(acc
->sink
.map
);
759 read_map
= isl_map_intersect_domain(read_map
, set_C
);
760 write_map
= isl_map_copy(acc
->source
[acc
->n_must
+ j
].map
);
762 write_map
= isl_map_reverse(write_map
);
763 dep_map
= isl_map_apply_range(read_map
, write_map
);
764 dim
= isl_space_join(isl_map_get_space(acc
->source
[acc
->n_must
+ j
].map
),
765 isl_space_reverse(isl_map_get_space(acc
->source
[k
].map
)));
766 after_write
= after_at_level(dim
, after_level
);
767 after_write
= isl_map_apply_range(after_write
, old_map
);
768 after_write
= isl_map_reverse(after_write
);
769 dep_map
= isl_map_intersect(dep_map
, after_write
);
770 before_read
= after_at_level(isl_map_get_space(dep_map
), before_level
);
771 dep_map
= isl_map_intersect(dep_map
, before_read
);
772 return isl_map_reverse(dep_map
);
775 /* Given the must and may dependence relations for the must accesses
776 * for level sink_level, check if there are any accesses of may access j
777 * that occur in between and return their union.
778 * If some of these accesses are intermediate with respect to
779 * (previously thought to be) must dependences, then these
780 * must dependences are turned into may dependences.
782 static __isl_give isl_map
*all_intermediate_sources(
783 __isl_keep isl_access_info
*acc
, __isl_take isl_map
*map
,
784 struct isl_map
**must_rel
, struct isl_map
**may_rel
,
785 int j
, int sink_level
)
788 int depth
= 2 * isl_map_dim(acc
->source
[acc
->n_must
+ j
].map
,
791 for (k
= 0; k
< acc
->n_must
; ++k
) {
794 if (isl_map_plain_is_empty(may_rel
[k
]) &&
795 isl_map_plain_is_empty(must_rel
[k
]))
798 plevel
= acc
->level_before(acc
->source
[k
].data
,
799 acc
->source
[acc
->n_must
+ j
].data
);
801 for (level
= sink_level
; level
<= depth
; ++level
) {
806 if (!can_precede_at_level(plevel
, level
))
809 copy
= isl_map_copy(may_rel
[k
]);
810 T
= all_later_sources(acc
, copy
, j
, sink_level
, k
, level
);
811 map
= isl_map_union(map
, T
);
813 copy
= isl_map_copy(must_rel
[k
]);
814 T
= all_later_sources(acc
, copy
, j
, sink_level
, k
, level
);
815 ran
= isl_map_range(isl_map_copy(T
));
816 map
= isl_map_union(map
, T
);
817 may_rel
[k
] = isl_map_union_disjoint(may_rel
[k
],
818 isl_map_intersect_range(isl_map_copy(must_rel
[k
]),
820 T
= isl_map_from_domain_and_range(
822 isl_space_domain(isl_map_get_space(must_rel
[k
]))),
824 must_rel
[k
] = isl_map_subtract(must_rel
[k
], T
);
831 /* Compute dependences for the case where all accesses are "may"
832 * accesses, which boils down to computing memory based dependences.
833 * The generic algorithm would also work in this case, but it would
834 * be overkill to use it.
836 static __isl_give isl_flow
*compute_mem_based_dependences(
837 __isl_keep isl_access_info
*acc
)
844 res
= isl_flow_alloc(acc
);
848 mustdo
= isl_map_domain(isl_map_copy(acc
->sink
.map
));
849 maydo
= isl_set_copy(mustdo
);
851 for (i
= 0; i
< acc
->n_may
; ++i
) {
858 plevel
= acc
->level_before(acc
->source
[i
].data
, acc
->sink
.data
);
859 is_before
= plevel
& 1;
862 dim
= isl_map_get_space(res
->dep
[i
].map
);
864 before
= isl_map_lex_le_first(dim
, plevel
);
866 before
= isl_map_lex_lt_first(dim
, plevel
);
867 dep
= isl_map_apply_range(isl_map_copy(acc
->source
[i
].map
),
868 isl_map_reverse(isl_map_copy(acc
->sink
.map
)));
869 dep
= isl_map_intersect(dep
, before
);
870 mustdo
= isl_set_subtract(mustdo
,
871 isl_map_range(isl_map_copy(dep
)));
872 res
->dep
[i
].map
= isl_map_union(res
->dep
[i
].map
, dep
);
875 res
->may_no_source
= isl_set_subtract(maydo
, isl_set_copy(mustdo
));
876 res
->must_no_source
= mustdo
;
881 /* Compute dependences for the case where there is at least one
884 * The core algorithm considers all levels in which a source may precede
885 * the sink, where a level may either be a statement level or a loop level.
886 * The outermost statement level is 1, the first loop level is 2, etc...
887 * The algorithm basically does the following:
888 * for all levels l of the read access from innermost to outermost
889 * for all sources w that may precede the sink access at that level
890 * compute the last iteration of the source that precedes the sink access
892 * add result to possible last accesses at level l of source w
893 * for all sources w2 that we haven't considered yet at this level that may
894 * also precede the sink access
895 * for all levels l2 of w from l to innermost
896 * for all possible last accesses dep of w at l
897 * compute last iteration of w2 between the source and sink
899 * add result to possible last accesses at level l of write w2
900 * and replace possible last accesses dep by the remainder
903 * The above algorithm is applied to the must access. During the course
904 * of the algorithm, we keep track of sink iterations that still
905 * need to be considered. These iterations are split into those that
906 * haven't been matched to any source access (mustdo) and those that have only
907 * been matched to may accesses (maydo).
908 * At the end of each level, we also consider the may accesses.
909 * In particular, we consider may accesses that precede the remaining
910 * sink iterations, moving elements from mustdo to maydo when appropriate,
911 * and may accesses that occur between a must source and a sink of any
912 * dependences found at the current level, turning must dependences into
913 * may dependences when appropriate.
916 static __isl_give isl_flow
*compute_val_based_dependences(
917 __isl_keep isl_access_info
*acc
)
921 isl_set
*mustdo
= NULL
;
922 isl_set
*maydo
= NULL
;
925 isl_map
**must_rel
= NULL
;
926 isl_map
**may_rel
= NULL
;
931 res
= isl_flow_alloc(acc
);
934 ctx
= isl_map_get_ctx(acc
->sink
.map
);
936 depth
= 2 * isl_map_dim(acc
->sink
.map
, isl_dim_in
) + 1;
937 mustdo
= isl_map_domain(isl_map_copy(acc
->sink
.map
));
938 maydo
= isl_set_empty_like(mustdo
);
939 if (!mustdo
|| !maydo
)
941 if (isl_set_plain_is_empty(mustdo
))
944 must_rel
= isl_alloc_array(ctx
, struct isl_map
*, acc
->n_must
);
945 may_rel
= isl_alloc_array(ctx
, struct isl_map
*, acc
->n_must
);
946 if (!must_rel
|| !may_rel
)
949 for (level
= depth
; level
>= 1; --level
) {
950 for (j
= acc
->n_must
-1; j
>=0; --j
) {
951 must_rel
[j
] = isl_map_empty_like(res
->dep
[j
].map
);
952 may_rel
[j
] = isl_map_copy(must_rel
[j
]);
955 for (j
= acc
->n_must
- 1; j
>= 0; --j
) {
957 struct isl_set
*rest
;
960 plevel
= acc
->level_before(acc
->source
[j
].data
,
962 if (!can_precede_at_level(plevel
, level
))
965 T
= last_source(acc
, mustdo
, j
, level
, &rest
);
966 must_rel
[j
] = isl_map_union_disjoint(must_rel
[j
], T
);
969 intermediate_sources(acc
, must_rel
, j
, level
);
971 T
= last_source(acc
, maydo
, j
, level
, &rest
);
972 may_rel
[j
] = isl_map_union_disjoint(may_rel
[j
], T
);
975 intermediate_sources(acc
, may_rel
, j
, level
);
977 if (isl_set_plain_is_empty(mustdo
) &&
978 isl_set_plain_is_empty(maydo
))
981 for (j
= j
- 1; j
>= 0; --j
) {
984 plevel
= acc
->level_before(acc
->source
[j
].data
,
986 if (!can_precede_at_level(plevel
, level
))
989 intermediate_sources(acc
, must_rel
, j
, level
);
990 intermediate_sources(acc
, may_rel
, j
, level
);
993 for (j
= 0; j
< acc
->n_may
; ++j
) {
998 plevel
= acc
->level_before(acc
->source
[acc
->n_must
+ j
].data
,
1000 if (!can_precede_at_level(plevel
, level
))
1003 T
= all_sources(acc
, isl_set_copy(maydo
), j
, level
);
1004 res
->dep
[2 * acc
->n_must
+ j
].map
=
1005 isl_map_union(res
->dep
[2 * acc
->n_must
+ j
].map
, T
);
1006 T
= all_sources(acc
, isl_set_copy(mustdo
), j
, level
);
1007 ran
= isl_map_range(isl_map_copy(T
));
1008 res
->dep
[2 * acc
->n_must
+ j
].map
=
1009 isl_map_union(res
->dep
[2 * acc
->n_must
+ j
].map
, T
);
1010 mustdo
= isl_set_subtract(mustdo
, isl_set_copy(ran
));
1011 maydo
= isl_set_union_disjoint(maydo
, ran
);
1013 T
= res
->dep
[2 * acc
->n_must
+ j
].map
;
1014 T
= all_intermediate_sources(acc
, T
, must_rel
, may_rel
,
1016 res
->dep
[2 * acc
->n_must
+ j
].map
= T
;
1019 for (j
= acc
->n_must
- 1; j
>= 0; --j
) {
1020 res
->dep
[2 * j
].map
=
1021 isl_map_union_disjoint(res
->dep
[2 * j
].map
,
1023 res
->dep
[2 * j
+ 1].map
=
1024 isl_map_union_disjoint(res
->dep
[2 * j
+ 1].map
,
1028 if (isl_set_plain_is_empty(mustdo
) &&
1029 isl_set_plain_is_empty(maydo
))
1036 res
->must_no_source
= mustdo
;
1037 res
->may_no_source
= maydo
;
1041 isl_set_free(mustdo
);
1042 isl_set_free(maydo
);
1048 /* Given a "sink" access, a list of n "source" accesses,
1049 * compute for each iteration of the sink access
1050 * and for each element accessed by that iteration,
1051 * the source access in the list that last accessed the
1052 * element accessed by the sink access before this sink access.
1053 * Each access is given as a map from the loop iterators
1054 * to the array indices.
1055 * The result is a list of n relations between source and sink
1056 * iterations and a subset of the domain of the sink access,
1057 * corresponding to those iterations that access an element
1058 * not previously accessed.
1060 * To deal with multi-valued sink access relations, the sink iteration
1061 * domain is first extended with dimensions that correspond to the data
1062 * space. After the computation is finished, these extra dimensions are
1063 * projected out again.
1065 __isl_give isl_flow
*isl_access_info_compute_flow(__isl_take isl_access_info
*acc
)
1068 struct isl_flow
*res
= NULL
;
1073 acc
->domain_map
= isl_map_domain_map(isl_map_copy(acc
->sink
.map
));
1074 acc
->sink
.map
= isl_map_range_map(acc
->sink
.map
);
1078 if (acc
->n_must
== 0)
1079 res
= compute_mem_based_dependences(acc
);
1081 acc
= isl_access_info_sort_sources(acc
);
1082 res
= compute_val_based_dependences(acc
);
1087 for (j
= 0; j
< res
->n_source
; ++j
) {
1088 res
->dep
[j
].map
= isl_map_apply_range(res
->dep
[j
].map
,
1089 isl_map_copy(acc
->domain_map
));
1090 if (!res
->dep
[j
].map
)
1093 if (!res
->must_no_source
|| !res
->may_no_source
)
1096 isl_access_info_free(acc
);
1099 isl_access_info_free(acc
);
1105 /* Keep track of some information about a schedule for a given
1106 * access. In particular, keep track of which dimensions
1107 * have a constant value and of the actual constant values.
1109 struct isl_sched_info
{
1114 static void sched_info_free(__isl_take
struct isl_sched_info
*info
)
1118 isl_vec_free(info
->cst
);
1123 /* Extract information on the constant dimensions of the schedule
1124 * for a given access. The "map" is of the form
1128 * with S the schedule domain, D the iteration domain and A the data domain.
1130 static __isl_give
struct isl_sched_info
*sched_info_alloc(
1131 __isl_keep isl_map
*map
)
1135 struct isl_sched_info
*info
;
1142 dim
= isl_space_unwrap(isl_space_domain(isl_map_get_space(map
)));
1145 n
= isl_space_dim(dim
, isl_dim_in
);
1146 isl_space_free(dim
);
1148 ctx
= isl_map_get_ctx(map
);
1149 info
= isl_alloc_type(ctx
, struct isl_sched_info
);
1152 info
->is_cst
= isl_alloc_array(ctx
, int, n
);
1153 info
->cst
= isl_vec_alloc(ctx
, n
);
1154 if (!info
->is_cst
|| !info
->cst
)
1158 for (i
= 0; i
< n
; ++i
) {
1159 info
->is_cst
[i
] = isl_map_plain_is_fixed(map
, isl_dim_in
, i
,
1161 info
->cst
= isl_vec_set_element(info
->cst
, i
, v
);
1167 sched_info_free(info
);
1171 struct isl_compute_flow_data
{
1172 isl_union_map
*must_source
;
1173 isl_union_map
*may_source
;
1174 isl_union_map
*must_dep
;
1175 isl_union_map
*may_dep
;
1176 isl_union_map
*must_no_source
;
1177 isl_union_map
*may_no_source
;
1182 struct isl_sched_info
*sink_info
;
1183 struct isl_sched_info
**source_info
;
1184 isl_access_info
*accesses
;
1187 static int count_matching_array(__isl_take isl_map
*map
, void *user
)
1191 struct isl_compute_flow_data
*data
;
1193 data
= (struct isl_compute_flow_data
*)user
;
1195 dim
= isl_space_range(isl_map_get_space(map
));
1197 eq
= isl_space_is_equal(dim
, data
->dim
);
1199 isl_space_free(dim
);
1210 static int collect_matching_array(__isl_take isl_map
*map
, void *user
)
1214 struct isl_sched_info
*info
;
1215 struct isl_compute_flow_data
*data
;
1217 data
= (struct isl_compute_flow_data
*)user
;
1219 dim
= isl_space_range(isl_map_get_space(map
));
1221 eq
= isl_space_is_equal(dim
, data
->dim
);
1223 isl_space_free(dim
);
1232 info
= sched_info_alloc(map
);
1233 data
->source_info
[data
->count
] = info
;
1235 data
->accesses
= isl_access_info_add_source(data
->accesses
,
1236 map
, data
->must
, info
);
1246 /* Determine the shared nesting level and the "textual order" of
1247 * the given accesses.
1249 * We first determine the minimal schedule dimension for both accesses.
1251 * If among those dimensions, we can find one where both have a fixed
1252 * value and if moreover those values are different, then the previous
1253 * dimension is the last shared nesting level and the textual order
1254 * is determined based on the order of the fixed values.
1255 * If no such fixed values can be found, then we set the shared
1256 * nesting level to the minimal schedule dimension, with no textual ordering.
1258 static int before(void *first
, void *second
)
1260 struct isl_sched_info
*info1
= first
;
1261 struct isl_sched_info
*info2
= second
;
1266 n1
= isl_vec_size(info1
->cst
);
1267 n2
= isl_vec_size(info2
->cst
);
1274 for (i
= 0; i
< n1
; ++i
) {
1277 if (!info1
->is_cst
[i
])
1279 if (!info2
->is_cst
[i
])
1281 isl_vec_get_element(info1
->cst
, i
, &v1
);
1282 isl_vec_get_element(info2
->cst
, i
, &v2
);
1283 if (isl_int_eq(v1
, v2
))
1286 r
= 2 * i
+ isl_int_lt(v1
, v2
);
1298 /* Given a sink access, look for all the source accesses that access
1299 * the same array and perform dataflow analysis on them using
1300 * isl_access_info_compute_flow.
1302 static int compute_flow(__isl_take isl_map
*map
, void *user
)
1306 struct isl_compute_flow_data
*data
;
1309 data
= (struct isl_compute_flow_data
*)user
;
1311 ctx
= isl_map_get_ctx(map
);
1313 data
->accesses
= NULL
;
1314 data
->sink_info
= NULL
;
1315 data
->source_info
= NULL
;
1317 data
->dim
= isl_space_range(isl_map_get_space(map
));
1319 if (isl_union_map_foreach_map(data
->must_source
,
1320 &count_matching_array
, data
) < 0)
1322 if (isl_union_map_foreach_map(data
->may_source
,
1323 &count_matching_array
, data
) < 0)
1326 data
->sink_info
= sched_info_alloc(map
);
1327 data
->source_info
= isl_calloc_array(ctx
, struct isl_sched_info
*,
1330 data
->accesses
= isl_access_info_alloc(isl_map_copy(map
),
1331 data
->sink_info
, &before
, data
->count
);
1332 if (!data
->sink_info
|| !data
->source_info
|| !data
->accesses
)
1336 if (isl_union_map_foreach_map(data
->must_source
,
1337 &collect_matching_array
, data
) < 0)
1340 if (isl_union_map_foreach_map(data
->may_source
,
1341 &collect_matching_array
, data
) < 0)
1344 flow
= isl_access_info_compute_flow(data
->accesses
);
1345 data
->accesses
= NULL
;
1350 data
->must_no_source
= isl_union_map_union(data
->must_no_source
,
1351 isl_union_map_from_map(isl_flow_get_no_source(flow
, 1)));
1352 data
->may_no_source
= isl_union_map_union(data
->may_no_source
,
1353 isl_union_map_from_map(isl_flow_get_no_source(flow
, 0)));
1355 for (i
= 0; i
< flow
->n_source
; ++i
) {
1357 dep
= isl_union_map_from_map(isl_map_copy(flow
->dep
[i
].map
));
1358 if (flow
->dep
[i
].must
)
1359 data
->must_dep
= isl_union_map_union(data
->must_dep
, dep
);
1361 data
->may_dep
= isl_union_map_union(data
->may_dep
, dep
);
1364 isl_flow_free(flow
);
1366 sched_info_free(data
->sink_info
);
1367 if (data
->source_info
) {
1368 for (i
= 0; i
< data
->count
; ++i
)
1369 sched_info_free(data
->source_info
[i
]);
1370 free(data
->source_info
);
1372 isl_space_free(data
->dim
);
1377 isl_access_info_free(data
->accesses
);
1378 sched_info_free(data
->sink_info
);
1379 if (data
->source_info
) {
1380 for (i
= 0; i
< data
->count
; ++i
)
1381 sched_info_free(data
->source_info
[i
]);
1382 free(data
->source_info
);
1384 isl_space_free(data
->dim
);
1390 /* Given a collection of "sink" and "source" accesses,
1391 * compute for each iteration of a sink access
1392 * and for each element accessed by that iteration,
1393 * the source access in the list that last accessed the
1394 * element accessed by the sink access before this sink access.
1395 * Each access is given as a map from the loop iterators
1396 * to the array indices.
1397 * The result is a relations between source and sink
1398 * iterations and a subset of the domain of the sink accesses,
1399 * corresponding to those iterations that access an element
1400 * not previously accessed.
1402 * We first prepend the schedule dimensions to the domain
1403 * of the accesses so that we can easily compare their relative order.
1404 * Then we consider each sink access individually in compute_flow.
1406 int isl_union_map_compute_flow(__isl_take isl_union_map
*sink
,
1407 __isl_take isl_union_map
*must_source
,
1408 __isl_take isl_union_map
*may_source
,
1409 __isl_take isl_union_map
*schedule
,
1410 __isl_give isl_union_map
**must_dep
, __isl_give isl_union_map
**may_dep
,
1411 __isl_give isl_union_map
**must_no_source
,
1412 __isl_give isl_union_map
**may_no_source
)
1415 isl_union_map
*range_map
= NULL
;
1416 struct isl_compute_flow_data data
;
1418 sink
= isl_union_map_align_params(sink
,
1419 isl_union_map_get_space(must_source
));
1420 sink
= isl_union_map_align_params(sink
,
1421 isl_union_map_get_space(may_source
));
1422 sink
= isl_union_map_align_params(sink
,
1423 isl_union_map_get_space(schedule
));
1424 dim
= isl_union_map_get_space(sink
);
1425 must_source
= isl_union_map_align_params(must_source
, isl_space_copy(dim
));
1426 may_source
= isl_union_map_align_params(may_source
, isl_space_copy(dim
));
1427 schedule
= isl_union_map_align_params(schedule
, isl_space_copy(dim
));
1429 schedule
= isl_union_map_reverse(schedule
);
1430 range_map
= isl_union_map_range_map(schedule
);
1431 schedule
= isl_union_map_reverse(isl_union_map_copy(range_map
));
1432 sink
= isl_union_map_apply_domain(sink
, isl_union_map_copy(schedule
));
1433 must_source
= isl_union_map_apply_domain(must_source
,
1434 isl_union_map_copy(schedule
));
1435 may_source
= isl_union_map_apply_domain(may_source
, schedule
);
1437 data
.must_source
= must_source
;
1438 data
.may_source
= may_source
;
1439 data
.must_dep
= must_dep
?
1440 isl_union_map_empty(isl_space_copy(dim
)) : NULL
;
1441 data
.may_dep
= may_dep
? isl_union_map_empty(isl_space_copy(dim
)) : NULL
;
1442 data
.must_no_source
= must_no_source
?
1443 isl_union_map_empty(isl_space_copy(dim
)) : NULL
;
1444 data
.may_no_source
= may_no_source
?
1445 isl_union_map_empty(isl_space_copy(dim
)) : NULL
;
1447 isl_space_free(dim
);
1449 if (isl_union_map_foreach_map(sink
, &compute_flow
, &data
) < 0)
1452 isl_union_map_free(sink
);
1453 isl_union_map_free(must_source
);
1454 isl_union_map_free(may_source
);
1457 data
.must_dep
= isl_union_map_apply_domain(data
.must_dep
,
1458 isl_union_map_copy(range_map
));
1459 data
.must_dep
= isl_union_map_apply_range(data
.must_dep
,
1460 isl_union_map_copy(range_map
));
1461 *must_dep
= data
.must_dep
;
1464 data
.may_dep
= isl_union_map_apply_domain(data
.may_dep
,
1465 isl_union_map_copy(range_map
));
1466 data
.may_dep
= isl_union_map_apply_range(data
.may_dep
,
1467 isl_union_map_copy(range_map
));
1468 *may_dep
= data
.may_dep
;
1470 if (must_no_source
) {
1471 data
.must_no_source
= isl_union_map_apply_domain(
1472 data
.must_no_source
, isl_union_map_copy(range_map
));
1473 *must_no_source
= data
.must_no_source
;
1475 if (may_no_source
) {
1476 data
.may_no_source
= isl_union_map_apply_domain(
1477 data
.may_no_source
, isl_union_map_copy(range_map
));
1478 *may_no_source
= data
.may_no_source
;
1481 isl_union_map_free(range_map
);
1485 isl_union_map_free(range_map
);
1486 isl_union_map_free(sink
);
1487 isl_union_map_free(must_source
);
1488 isl_union_map_free(may_source
);
1489 isl_union_map_free(data
.must_dep
);
1490 isl_union_map_free(data
.may_dep
);
1491 isl_union_map_free(data
.must_no_source
);
1492 isl_union_map_free(data
.may_no_source
);
1499 *must_no_source
= NULL
;
1501 *may_no_source
= NULL
;