2 * Copyright 2011 INRIA Saclay
3 * Copyright 2012-2014 Ecole Normale Superieure
4 * Copyright 2015-2016 Sven Verdoolaege
5 * Copyright 2016 INRIA Paris
6 * Copyright 2017 Sven Verdoolaege
8 * Use of this software is governed by the MIT license
10 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
11 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
13 * and Ecole Normale Superieure, 45 rue d'Ulm, 75230 Paris, France
14 * and Centre de Recherche Inria de Paris, 2 rue Simone Iff - Voie DQ12,
15 * CS 42112, 75589 Paris Cedex 12, France
18 #include <isl_ctx_private.h>
19 #include <isl_map_private.h>
20 #include <isl_space_private.h>
21 #include <isl_aff_private.h>
23 #include <isl/constraint.h>
24 #include <isl/schedule.h>
25 #include <isl_schedule_constraints.h>
26 #include <isl/schedule_node.h>
27 #include <isl_mat_private.h>
28 #include <isl_vec_private.h>
30 #include <isl_union_set_private.h>
33 #include <isl_dim_map.h>
34 #include <isl/map_to_basic_set.h>
36 #include <isl_options_private.h>
37 #include <isl_tarjan.h>
38 #include <isl_morph.h>
40 #include <isl_val_private.h>
43 * The scheduling algorithm implemented in this file was inspired by
44 * Bondhugula et al., "Automatic Transformations for Communication-Minimized
45 * Parallelization and Locality Optimization in the Polyhedral Model".
47 * For a detailed description of the variant implemented in isl,
48 * see Verdoolaege and Janssens, "Scheduling for PPCG" (2017).
52 /* Internal information about a node that is used during the construction
54 * space represents the original space in which the domain lives;
55 * that is, the space is not affected by compression
56 * sched is a matrix representation of the schedule being constructed
57 * for this node; if compressed is set, then this schedule is
58 * defined over the compressed domain space
59 * sched_map is an isl_map representation of the same (partial) schedule
60 * sched_map may be NULL; if compressed is set, then this map
61 * is defined over the uncompressed domain space
62 * rank is the number of linearly independent rows in the linear part
64 * the rows of "vmap" represent a change of basis for the node
65 * variables; the first rank rows span the linear part of
66 * the schedule rows; the remaining rows are linearly independent
67 * the rows of "indep" represent linear combinations of the schedule
68 * coefficients that are non-zero when the schedule coefficients are
69 * linearly independent of previously computed schedule rows.
70 * start is the first variable in the LP problem in the sequences that
71 * represents the schedule coefficients of this node
72 * nvar is the dimension of the (compressed) domain
73 * nparam is the number of parameters or 0 if we are not constructing
74 * a parametric schedule
76 * If compressed is set, then hull represents the constraints
77 * that were used to derive the compression, while compress and
78 * decompress map the original space to the compressed space and
81 * scc is the index of SCC (or WCC) this node belongs to
83 * "cluster" is only used inside extract_clusters and identifies
84 * the cluster of SCCs that the node belongs to.
86 * coincident contains a boolean for each of the rows of the schedule,
87 * indicating whether the corresponding scheduling dimension satisfies
88 * the coincidence constraints in the sense that the corresponding
89 * dependence distances are zero.
91 * If the schedule_treat_coalescing option is set, then
92 * "sizes" contains the sizes of the (compressed) instance set
93 * in each direction. If there is no fixed size in a given direction,
94 * then the corresponding size value is set to infinity.
95 * If the schedule_treat_coalescing option or the schedule_max_coefficient
96 * option is set, then "max" contains the maximal values for
97 * schedule coefficients of the (compressed) variables. If no bound
98 * needs to be imposed on a particular variable, then the corresponding
100 * If not NULL, then "bounds" contains a non-parametric set
101 * in the compressed space that is bounded by the size in each direction.
103 struct isl_sched_node
{
107 isl_multi_aff
*compress
;
108 isl_multi_aff
*decompress
;
123 isl_multi_val
*sizes
;
124 isl_basic_set
*bounds
;
128 static int node_has_tuples(const void *entry
, const void *val
)
130 struct isl_sched_node
*node
= (struct isl_sched_node
*)entry
;
131 isl_space
*space
= (isl_space
*) val
;
133 return isl_space_has_equal_tuples(node
->space
, space
);
136 static int node_scc_exactly(struct isl_sched_node
*node
, int scc
)
138 return node
->scc
== scc
;
141 static int node_scc_at_most(struct isl_sched_node
*node
, int scc
)
143 return node
->scc
<= scc
;
146 static int node_scc_at_least(struct isl_sched_node
*node
, int scc
)
148 return node
->scc
>= scc
;
151 /* An edge in the dependence graph. An edge may be used to
152 * ensure validity of the generated schedule, to minimize the dependence
155 * map is the dependence relation, with i -> j in the map if j depends on i
156 * tagged_condition and tagged_validity contain the union of all tagged
157 * condition or conditional validity dependence relations that
158 * specialize the dependence relation "map"; that is,
159 * if (i -> a) -> (j -> b) is an element of "tagged_condition"
160 * or "tagged_validity", then i -> j is an element of "map".
161 * If these fields are NULL, then they represent the empty relation.
162 * src is the source node
163 * dst is the sink node
165 * types is a bit vector containing the types of this edge.
166 * validity is set if the edge is used to ensure correctness
167 * coincidence is used to enforce zero dependence distances
168 * proximity is set if the edge is used to minimize dependence distances
169 * condition is set if the edge represents a condition
170 * for a conditional validity schedule constraint
171 * local can only be set for condition edges and indicates that
172 * the dependence distance over the edge should be zero
173 * conditional_validity is set if the edge is used to conditionally
176 * For validity edges, start and end mark the sequence of inequality
177 * constraints in the LP problem that encode the validity constraint
178 * corresponding to this edge.
180 * During clustering, an edge may be marked "no_merge" if it should
181 * not be used to merge clusters.
182 * The weight is also only used during clustering and it is
183 * an indication of how many schedule dimensions on either side
184 * of the schedule constraints can be aligned.
185 * If the weight is negative, then this means that this edge was postponed
186 * by has_bounded_distances or any_no_merge. The original weight can
187 * be retrieved by adding 1 + graph->max_weight, with "graph"
188 * the graph containing this edge.
190 struct isl_sched_edge
{
192 isl_union_map
*tagged_condition
;
193 isl_union_map
*tagged_validity
;
195 struct isl_sched_node
*src
;
196 struct isl_sched_node
*dst
;
207 /* Is "edge" marked as being of type "type"?
209 static int is_type(struct isl_sched_edge
*edge
, enum isl_edge_type type
)
211 return ISL_FL_ISSET(edge
->types
, 1 << type
);
214 /* Mark "edge" as being of type "type".
216 static void set_type(struct isl_sched_edge
*edge
, enum isl_edge_type type
)
218 ISL_FL_SET(edge
->types
, 1 << type
);
221 /* No longer mark "edge" as being of type "type"?
223 static void clear_type(struct isl_sched_edge
*edge
, enum isl_edge_type type
)
225 ISL_FL_CLR(edge
->types
, 1 << type
);
228 /* Is "edge" marked as a validity edge?
230 static int is_validity(struct isl_sched_edge
*edge
)
232 return is_type(edge
, isl_edge_validity
);
235 /* Mark "edge" as a validity edge.
237 static void set_validity(struct isl_sched_edge
*edge
)
239 set_type(edge
, isl_edge_validity
);
242 /* Is "edge" marked as a proximity edge?
244 static int is_proximity(struct isl_sched_edge
*edge
)
246 return is_type(edge
, isl_edge_proximity
);
249 /* Is "edge" marked as a local edge?
251 static int is_local(struct isl_sched_edge
*edge
)
253 return is_type(edge
, isl_edge_local
);
256 /* Mark "edge" as a local edge.
258 static void set_local(struct isl_sched_edge
*edge
)
260 set_type(edge
, isl_edge_local
);
263 /* No longer mark "edge" as a local edge.
265 static void clear_local(struct isl_sched_edge
*edge
)
267 clear_type(edge
, isl_edge_local
);
270 /* Is "edge" marked as a coincidence edge?
272 static int is_coincidence(struct isl_sched_edge
*edge
)
274 return is_type(edge
, isl_edge_coincidence
);
277 /* Is "edge" marked as a condition edge?
279 static int is_condition(struct isl_sched_edge
*edge
)
281 return is_type(edge
, isl_edge_condition
);
284 /* Is "edge" marked as a conditional validity edge?
286 static int is_conditional_validity(struct isl_sched_edge
*edge
)
288 return is_type(edge
, isl_edge_conditional_validity
);
291 /* Is "edge" of a type that can appear multiple times between
292 * the same pair of nodes?
294 * Condition edges and conditional validity edges may have tagged
295 * dependence relations, in which case an edge is added for each
298 static int is_multi_edge_type(struct isl_sched_edge
*edge
)
300 return is_condition(edge
) || is_conditional_validity(edge
);
303 /* Internal information about the dependence graph used during
304 * the construction of the schedule.
306 * intra_hmap is a cache, mapping dependence relations to their dual,
307 * for dependences from a node to itself, possibly without
308 * coefficients for the parameters
309 * intra_hmap_param is a cache, mapping dependence relations to their dual,
310 * for dependences from a node to itself, including coefficients
312 * inter_hmap is a cache, mapping dependence relations to their dual,
313 * for dependences between distinct nodes
314 * if compression is involved then the key for these maps
315 * is the original, uncompressed dependence relation, while
316 * the value is the dual of the compressed dependence relation.
318 * n is the number of nodes
319 * node is the list of nodes
320 * maxvar is the maximal number of variables over all nodes
321 * max_row is the allocated number of rows in the schedule
322 * n_row is the current (maximal) number of linearly independent
323 * rows in the node schedules
324 * n_total_row is the current number of rows in the node schedules
325 * band_start is the starting row in the node schedules of the current band
326 * root is set to the the original dependence graph from which this graph
327 * is derived through splitting. If this graph is not the result of
328 * splitting, then the root field points to the graph itself.
330 * sorted contains a list of node indices sorted according to the
331 * SCC to which a node belongs
333 * n_edge is the number of edges
334 * edge is the list of edges
335 * max_edge contains the maximal number of edges of each type;
336 * in particular, it contains the number of edges in the inital graph.
337 * edge_table contains pointers into the edge array, hashed on the source
338 * and sink spaces; there is one such table for each type;
339 * a given edge may be referenced from more than one table
340 * if the corresponding relation appears in more than one of the
341 * sets of dependences; however, for each type there is only
342 * a single edge between a given pair of source and sink space
343 * in the entire graph
345 * node_table contains pointers into the node array, hashed on the space tuples
347 * region contains a list of variable sequences that should be non-trivial
349 * lp contains the (I)LP problem used to obtain new schedule rows
351 * src_scc and dst_scc are the source and sink SCCs of an edge with
352 * conflicting constraints
354 * scc represents the number of components
355 * weak is set if the components are weakly connected
357 * max_weight is used during clustering and represents the maximal
358 * weight of the relevant proximity edges.
360 struct isl_sched_graph
{
361 isl_map_to_basic_set
*intra_hmap
;
362 isl_map_to_basic_set
*intra_hmap_param
;
363 isl_map_to_basic_set
*inter_hmap
;
365 struct isl_sched_node
*node
;
376 struct isl_sched_graph
*root
;
378 struct isl_sched_edge
*edge
;
380 int max_edge
[isl_edge_last
+ 1];
381 struct isl_hash_table
*edge_table
[isl_edge_last
+ 1];
383 struct isl_hash_table
*node_table
;
384 struct isl_trivial_region
*region
;
397 /* Initialize node_table based on the list of nodes.
399 static int graph_init_table(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
403 graph
->node_table
= isl_hash_table_alloc(ctx
, graph
->n
);
404 if (!graph
->node_table
)
407 for (i
= 0; i
< graph
->n
; ++i
) {
408 struct isl_hash_table_entry
*entry
;
411 hash
= isl_space_get_tuple_hash(graph
->node
[i
].space
);
412 entry
= isl_hash_table_find(ctx
, graph
->node_table
, hash
,
414 graph
->node
[i
].space
, 1);
417 entry
->data
= &graph
->node
[i
];
423 /* Return a pointer to the node that lives within the given space,
424 * or NULL if there is no such node.
426 static struct isl_sched_node
*graph_find_node(isl_ctx
*ctx
,
427 struct isl_sched_graph
*graph
, __isl_keep isl_space
*space
)
429 struct isl_hash_table_entry
*entry
;
432 hash
= isl_space_get_tuple_hash(space
);
433 entry
= isl_hash_table_find(ctx
, graph
->node_table
, hash
,
434 &node_has_tuples
, space
, 0);
436 return entry
? entry
->data
: NULL
;
439 /* Is "node" a node in "graph"?
441 static int is_node(struct isl_sched_graph
*graph
,
442 struct isl_sched_node
*node
)
444 return node
&& node
>= &graph
->node
[0] && node
< &graph
->node
[graph
->n
];
447 static int edge_has_src_and_dst(const void *entry
, const void *val
)
449 const struct isl_sched_edge
*edge
= entry
;
450 const struct isl_sched_edge
*temp
= val
;
452 return edge
->src
== temp
->src
&& edge
->dst
== temp
->dst
;
455 /* Add the given edge to graph->edge_table[type].
457 static isl_stat
graph_edge_table_add(isl_ctx
*ctx
,
458 struct isl_sched_graph
*graph
, enum isl_edge_type type
,
459 struct isl_sched_edge
*edge
)
461 struct isl_hash_table_entry
*entry
;
464 hash
= isl_hash_init();
465 hash
= isl_hash_builtin(hash
, edge
->src
);
466 hash
= isl_hash_builtin(hash
, edge
->dst
);
467 entry
= isl_hash_table_find(ctx
, graph
->edge_table
[type
], hash
,
468 &edge_has_src_and_dst
, edge
, 1);
470 return isl_stat_error
;
476 /* Add "edge" to all relevant edge tables.
477 * That is, for every type of the edge, add it to the corresponding table.
479 static isl_stat
graph_edge_tables_add(isl_ctx
*ctx
,
480 struct isl_sched_graph
*graph
, struct isl_sched_edge
*edge
)
482 enum isl_edge_type t
;
484 for (t
= isl_edge_first
; t
<= isl_edge_last
; ++t
) {
485 if (!is_type(edge
, t
))
487 if (graph_edge_table_add(ctx
, graph
, t
, edge
) < 0)
488 return isl_stat_error
;
494 /* Allocate the edge_tables based on the maximal number of edges of
497 static int graph_init_edge_tables(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
501 for (i
= 0; i
<= isl_edge_last
; ++i
) {
502 graph
->edge_table
[i
] = isl_hash_table_alloc(ctx
,
504 if (!graph
->edge_table
[i
])
511 /* If graph->edge_table[type] contains an edge from the given source
512 * to the given destination, then return the hash table entry of this edge.
513 * Otherwise, return NULL.
515 static struct isl_hash_table_entry
*graph_find_edge_entry(
516 struct isl_sched_graph
*graph
,
517 enum isl_edge_type type
,
518 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
520 isl_ctx
*ctx
= isl_space_get_ctx(src
->space
);
522 struct isl_sched_edge temp
= { .src
= src
, .dst
= dst
};
524 hash
= isl_hash_init();
525 hash
= isl_hash_builtin(hash
, temp
.src
);
526 hash
= isl_hash_builtin(hash
, temp
.dst
);
527 return isl_hash_table_find(ctx
, graph
->edge_table
[type
], hash
,
528 &edge_has_src_and_dst
, &temp
, 0);
532 /* If graph->edge_table[type] contains an edge from the given source
533 * to the given destination, then return this edge.
534 * Otherwise, return NULL.
536 static struct isl_sched_edge
*graph_find_edge(struct isl_sched_graph
*graph
,
537 enum isl_edge_type type
,
538 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
540 struct isl_hash_table_entry
*entry
;
542 entry
= graph_find_edge_entry(graph
, type
, src
, dst
);
549 /* Check whether the dependence graph has an edge of the given type
550 * between the given two nodes.
552 static isl_bool
graph_has_edge(struct isl_sched_graph
*graph
,
553 enum isl_edge_type type
,
554 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
556 struct isl_sched_edge
*edge
;
559 edge
= graph_find_edge(graph
, type
, src
, dst
);
563 empty
= isl_map_plain_is_empty(edge
->map
);
565 return isl_bool_error
;
570 /* Look for any edge with the same src, dst and map fields as "model".
572 * Return the matching edge if one can be found.
573 * Return "model" if no matching edge is found.
574 * Return NULL on error.
576 static struct isl_sched_edge
*graph_find_matching_edge(
577 struct isl_sched_graph
*graph
, struct isl_sched_edge
*model
)
579 enum isl_edge_type i
;
580 struct isl_sched_edge
*edge
;
582 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
585 edge
= graph_find_edge(graph
, i
, model
->src
, model
->dst
);
588 is_equal
= isl_map_plain_is_equal(model
->map
, edge
->map
);
598 /* Remove the given edge from all the edge_tables that refer to it.
600 static void graph_remove_edge(struct isl_sched_graph
*graph
,
601 struct isl_sched_edge
*edge
)
603 isl_ctx
*ctx
= isl_map_get_ctx(edge
->map
);
604 enum isl_edge_type i
;
606 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
607 struct isl_hash_table_entry
*entry
;
609 entry
= graph_find_edge_entry(graph
, i
, edge
->src
, edge
->dst
);
612 if (entry
->data
!= edge
)
614 isl_hash_table_remove(ctx
, graph
->edge_table
[i
], entry
);
618 /* Check whether the dependence graph has any edge
619 * between the given two nodes.
621 static isl_bool
graph_has_any_edge(struct isl_sched_graph
*graph
,
622 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
624 enum isl_edge_type i
;
627 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
628 r
= graph_has_edge(graph
, i
, src
, dst
);
636 /* Check whether the dependence graph has a validity edge
637 * between the given two nodes.
639 * Conditional validity edges are essentially validity edges that
640 * can be ignored if the corresponding condition edges are iteration private.
641 * Here, we are only checking for the presence of validity
642 * edges, so we need to consider the conditional validity edges too.
643 * In particular, this function is used during the detection
644 * of strongly connected components and we cannot ignore
645 * conditional validity edges during this detection.
647 static isl_bool
graph_has_validity_edge(struct isl_sched_graph
*graph
,
648 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
652 r
= graph_has_edge(graph
, isl_edge_validity
, src
, dst
);
656 return graph_has_edge(graph
, isl_edge_conditional_validity
, src
, dst
);
659 static int graph_alloc(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
660 int n_node
, int n_edge
)
665 graph
->n_edge
= n_edge
;
666 graph
->node
= isl_calloc_array(ctx
, struct isl_sched_node
, graph
->n
);
667 graph
->sorted
= isl_calloc_array(ctx
, int, graph
->n
);
668 graph
->region
= isl_alloc_array(ctx
,
669 struct isl_trivial_region
, graph
->n
);
670 graph
->edge
= isl_calloc_array(ctx
,
671 struct isl_sched_edge
, graph
->n_edge
);
673 graph
->intra_hmap
= isl_map_to_basic_set_alloc(ctx
, 2 * n_edge
);
674 graph
->intra_hmap_param
= isl_map_to_basic_set_alloc(ctx
, 2 * n_edge
);
675 graph
->inter_hmap
= isl_map_to_basic_set_alloc(ctx
, 2 * n_edge
);
677 if (!graph
->node
|| !graph
->region
|| (graph
->n_edge
&& !graph
->edge
) ||
681 for(i
= 0; i
< graph
->n
; ++i
)
682 graph
->sorted
[i
] = i
;
687 static void graph_free(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
691 isl_map_to_basic_set_free(graph
->intra_hmap
);
692 isl_map_to_basic_set_free(graph
->intra_hmap_param
);
693 isl_map_to_basic_set_free(graph
->inter_hmap
);
696 for (i
= 0; i
< graph
->n
; ++i
) {
697 isl_space_free(graph
->node
[i
].space
);
698 isl_set_free(graph
->node
[i
].hull
);
699 isl_multi_aff_free(graph
->node
[i
].compress
);
700 isl_multi_aff_free(graph
->node
[i
].decompress
);
701 isl_mat_free(graph
->node
[i
].sched
);
702 isl_map_free(graph
->node
[i
].sched_map
);
703 isl_mat_free(graph
->node
[i
].indep
);
704 isl_mat_free(graph
->node
[i
].vmap
);
705 if (graph
->root
== graph
)
706 free(graph
->node
[i
].coincident
);
707 isl_multi_val_free(graph
->node
[i
].sizes
);
708 isl_basic_set_free(graph
->node
[i
].bounds
);
709 isl_vec_free(graph
->node
[i
].max
);
714 for (i
= 0; i
< graph
->n_edge
; ++i
) {
715 isl_map_free(graph
->edge
[i
].map
);
716 isl_union_map_free(graph
->edge
[i
].tagged_condition
);
717 isl_union_map_free(graph
->edge
[i
].tagged_validity
);
721 for (i
= 0; i
<= isl_edge_last
; ++i
)
722 isl_hash_table_free(ctx
, graph
->edge_table
[i
]);
723 isl_hash_table_free(ctx
, graph
->node_table
);
724 isl_basic_set_free(graph
->lp
);
727 /* For each "set" on which this function is called, increment
728 * graph->n by one and update graph->maxvar.
730 static isl_stat
init_n_maxvar(__isl_take isl_set
*set
, void *user
)
732 struct isl_sched_graph
*graph
= user
;
733 int nvar
= isl_set_dim(set
, isl_dim_set
);
736 if (nvar
> graph
->maxvar
)
737 graph
->maxvar
= nvar
;
744 /* Compute the number of rows that should be allocated for the schedule.
745 * In particular, we need one row for each variable or one row
746 * for each basic map in the dependences.
747 * Note that it is practically impossible to exhaust both
748 * the number of dependences and the number of variables.
750 static isl_stat
compute_max_row(struct isl_sched_graph
*graph
,
751 __isl_keep isl_schedule_constraints
*sc
)
755 isl_union_set
*domain
;
759 domain
= isl_schedule_constraints_get_domain(sc
);
760 r
= isl_union_set_foreach_set(domain
, &init_n_maxvar
, graph
);
761 isl_union_set_free(domain
);
763 return isl_stat_error
;
764 n_edge
= isl_schedule_constraints_n_basic_map(sc
);
766 return isl_stat_error
;
767 graph
->max_row
= n_edge
+ graph
->maxvar
;
772 /* Does "bset" have any defining equalities for its set variables?
774 static isl_bool
has_any_defining_equality(__isl_keep isl_basic_set
*bset
)
779 return isl_bool_error
;
781 n
= isl_basic_set_dim(bset
, isl_dim_set
);
782 for (i
= 0; i
< n
; ++i
) {
785 has
= isl_basic_set_has_defining_equality(bset
, isl_dim_set
, i
,
791 return isl_bool_false
;
794 /* Set the entries of node->max to the value of the schedule_max_coefficient
797 static isl_stat
set_max_coefficient(isl_ctx
*ctx
, struct isl_sched_node
*node
)
801 max
= isl_options_get_schedule_max_coefficient(ctx
);
805 node
->max
= isl_vec_alloc(ctx
, node
->nvar
);
806 node
->max
= isl_vec_set_si(node
->max
, max
);
808 return isl_stat_error
;
813 /* Set the entries of node->max to the minimum of the schedule_max_coefficient
814 * option (if set) and half of the minimum of the sizes in the other
815 * dimensions. Round up when computing the half such that
816 * if the minimum of the sizes is one, half of the size is taken to be one
818 * If the global minimum is unbounded (i.e., if both
819 * the schedule_max_coefficient is not set and the sizes in the other
820 * dimensions are unbounded), then store a negative value.
821 * If the schedule coefficient is close to the size of the instance set
822 * in another dimension, then the schedule may represent a loop
823 * coalescing transformation (especially if the coefficient
824 * in that other dimension is one). Forcing the coefficient to be
825 * smaller than or equal to half the minimal size should avoid this
828 static isl_stat
compute_max_coefficient(isl_ctx
*ctx
,
829 struct isl_sched_node
*node
)
835 max
= isl_options_get_schedule_max_coefficient(ctx
);
836 v
= isl_vec_alloc(ctx
, node
->nvar
);
838 return isl_stat_error
;
840 for (i
= 0; i
< node
->nvar
; ++i
) {
841 isl_int_set_si(v
->el
[i
], max
);
842 isl_int_mul_si(v
->el
[i
], v
->el
[i
], 2);
845 for (i
= 0; i
< node
->nvar
; ++i
) {
848 size
= isl_multi_val_get_val(node
->sizes
, i
);
851 if (!isl_val_is_int(size
)) {
855 for (j
= 0; j
< node
->nvar
; ++j
) {
858 if (isl_int_is_neg(v
->el
[j
]) ||
859 isl_int_gt(v
->el
[j
], size
->n
))
860 isl_int_set(v
->el
[j
], size
->n
);
865 for (i
= 0; i
< node
->nvar
; ++i
)
866 isl_int_cdiv_q_ui(v
->el
[i
], v
->el
[i
], 2);
872 return isl_stat_error
;
875 /* Compute and return the size of "set" in dimension "dim".
876 * The size is taken to be the difference in values for that variable
877 * for fixed values of the other variables.
878 * This assumes that "set" is convex.
879 * In particular, the variable is first isolated from the other variables
880 * in the range of a map
882 * [i_0, ..., i_dim-1, i_dim+1, ...] -> [i_dim]
884 * and then duplicated
886 * [i_0, ..., i_dim-1, i_dim+1, ...] -> [[i_dim] -> [i_dim']]
888 * The shared variables are then projected out and the maximal value
889 * of i_dim' - i_dim is computed.
891 static __isl_give isl_val
*compute_size(__isl_take isl_set
*set
, int dim
)
898 map
= isl_set_project_onto_map(set
, isl_dim_set
, dim
, 1);
899 map
= isl_map_project_out(map
, isl_dim_in
, dim
, 1);
900 map
= isl_map_range_product(map
, isl_map_copy(map
));
901 map
= isl_set_unwrap(isl_map_range(map
));
902 set
= isl_map_deltas(map
);
903 ls
= isl_local_space_from_space(isl_set_get_space(set
));
904 obj
= isl_aff_var_on_domain(ls
, isl_dim_set
, 0);
905 v
= isl_set_max_val(set
, obj
);
912 /* Compute the size of the instance set "set" of "node", after compression,
913 * as well as bounds on the corresponding coefficients, if needed.
915 * The sizes are needed when the schedule_treat_coalescing option is set.
916 * The bounds are needed when the schedule_treat_coalescing option or
917 * the schedule_max_coefficient option is set.
919 * If the schedule_treat_coalescing option is not set, then at most
920 * the bounds need to be set and this is done in set_max_coefficient.
921 * Otherwise, compress the domain if needed, compute the size
922 * in each direction and store the results in node->size.
923 * If the domain is not convex, then the sizes are computed
924 * on a convex superset in order to avoid picking up sizes
925 * that are valid for the individual disjuncts, but not for
926 * the domain as a whole.
927 * Finally, set the bounds on the coefficients based on the sizes
928 * and the schedule_max_coefficient option in compute_max_coefficient.
930 static isl_stat
compute_sizes_and_max(isl_ctx
*ctx
, struct isl_sched_node
*node
,
931 __isl_take isl_set
*set
)
936 if (!isl_options_get_schedule_treat_coalescing(ctx
)) {
938 return set_max_coefficient(ctx
, node
);
941 if (node
->compressed
)
942 set
= isl_set_preimage_multi_aff(set
,
943 isl_multi_aff_copy(node
->decompress
));
944 set
= isl_set_from_basic_set(isl_set_simple_hull(set
));
945 mv
= isl_multi_val_zero(isl_set_get_space(set
));
946 n
= isl_set_dim(set
, isl_dim_set
);
947 for (j
= 0; j
< n
; ++j
) {
950 v
= compute_size(isl_set_copy(set
), j
);
951 mv
= isl_multi_val_set_val(mv
, j
, v
);
956 return isl_stat_error
;
957 return compute_max_coefficient(ctx
, node
);
960 /* Add a new node to the graph representing the given instance set.
961 * "nvar" is the (possibly compressed) number of variables and
962 * may be smaller than then number of set variables in "set"
963 * if "compressed" is set.
964 * If "compressed" is set, then "hull" represents the constraints
965 * that were used to derive the compression, while "compress" and
966 * "decompress" map the original space to the compressed space and
968 * If "compressed" is not set, then "hull", "compress" and "decompress"
971 * Compute the size of the instance set and bounds on the coefficients,
974 static isl_stat
add_node(struct isl_sched_graph
*graph
,
975 __isl_take isl_set
*set
, int nvar
, int compressed
,
976 __isl_take isl_set
*hull
, __isl_take isl_multi_aff
*compress
,
977 __isl_take isl_multi_aff
*decompress
)
984 struct isl_sched_node
*node
;
987 return isl_stat_error
;
989 ctx
= isl_set_get_ctx(set
);
990 nparam
= isl_set_dim(set
, isl_dim_param
);
991 if (!ctx
->opt
->schedule_parametric
)
993 sched
= isl_mat_alloc(ctx
, 0, 1 + nparam
+ nvar
);
994 node
= &graph
->node
[graph
->n
];
996 space
= isl_set_get_space(set
);
999 node
->nparam
= nparam
;
1000 node
->sched
= sched
;
1001 node
->sched_map
= NULL
;
1002 coincident
= isl_calloc_array(ctx
, int, graph
->max_row
);
1003 node
->coincident
= coincident
;
1004 node
->compressed
= compressed
;
1006 node
->compress
= compress
;
1007 node
->decompress
= decompress
;
1008 if (compute_sizes_and_max(ctx
, node
, set
) < 0)
1009 return isl_stat_error
;
1011 if (!space
|| !sched
|| (graph
->max_row
&& !coincident
))
1012 return isl_stat_error
;
1013 if (compressed
&& (!hull
|| !compress
|| !decompress
))
1014 return isl_stat_error
;
1019 /* Construct an identifier for node "node", which will represent "set".
1020 * The name of the identifier is either "compressed" or
1021 * "compressed_<name>", with <name> the name of the space of "set".
1022 * The user pointer of the identifier points to "node".
1024 static __isl_give isl_id
*construct_compressed_id(__isl_keep isl_set
*set
,
1025 struct isl_sched_node
*node
)
1034 has_name
= isl_set_has_tuple_name(set
);
1038 ctx
= isl_set_get_ctx(set
);
1040 return isl_id_alloc(ctx
, "compressed", node
);
1042 p
= isl_printer_to_str(ctx
);
1043 name
= isl_set_get_tuple_name(set
);
1044 p
= isl_printer_print_str(p
, "compressed_");
1045 p
= isl_printer_print_str(p
, name
);
1046 id_name
= isl_printer_get_str(p
);
1047 isl_printer_free(p
);
1049 id
= isl_id_alloc(ctx
, id_name
, node
);
1055 /* Add a new node to the graph representing the given set.
1057 * If any of the set variables is defined by an equality, then
1058 * we perform variable compression such that we can perform
1059 * the scheduling on the compressed domain.
1060 * In this case, an identifier is used that references the new node
1061 * such that each compressed space is unique and
1062 * such that the node can be recovered from the compressed space.
1064 static isl_stat
extract_node(__isl_take isl_set
*set
, void *user
)
1067 isl_bool has_equality
;
1069 isl_basic_set
*hull
;
1072 isl_multi_aff
*compress
, *decompress
;
1073 struct isl_sched_graph
*graph
= user
;
1075 hull
= isl_set_affine_hull(isl_set_copy(set
));
1076 hull
= isl_basic_set_remove_divs(hull
);
1077 nvar
= isl_set_dim(set
, isl_dim_set
);
1078 has_equality
= has_any_defining_equality(hull
);
1080 if (has_equality
< 0)
1082 if (!has_equality
) {
1083 isl_basic_set_free(hull
);
1084 return add_node(graph
, set
, nvar
, 0, NULL
, NULL
, NULL
);
1087 id
= construct_compressed_id(set
, &graph
->node
[graph
->n
]);
1088 morph
= isl_basic_set_variable_compression_with_id(hull
,
1091 nvar
= isl_morph_ran_dim(morph
, isl_dim_set
);
1092 compress
= isl_morph_get_var_multi_aff(morph
);
1093 morph
= isl_morph_inverse(morph
);
1094 decompress
= isl_morph_get_var_multi_aff(morph
);
1095 isl_morph_free(morph
);
1097 hull_set
= isl_set_from_basic_set(hull
);
1098 return add_node(graph
, set
, nvar
, 1, hull_set
, compress
, decompress
);
1100 isl_basic_set_free(hull
);
1102 return isl_stat_error
;
1105 struct isl_extract_edge_data
{
1106 enum isl_edge_type type
;
1107 struct isl_sched_graph
*graph
;
1110 /* Merge edge2 into edge1, freeing the contents of edge2.
1111 * Return 0 on success and -1 on failure.
1113 * edge1 and edge2 are assumed to have the same value for the map field.
1115 static int merge_edge(struct isl_sched_edge
*edge1
,
1116 struct isl_sched_edge
*edge2
)
1118 edge1
->types
|= edge2
->types
;
1119 isl_map_free(edge2
->map
);
1121 if (is_condition(edge2
)) {
1122 if (!edge1
->tagged_condition
)
1123 edge1
->tagged_condition
= edge2
->tagged_condition
;
1125 edge1
->tagged_condition
=
1126 isl_union_map_union(edge1
->tagged_condition
,
1127 edge2
->tagged_condition
);
1130 if (is_conditional_validity(edge2
)) {
1131 if (!edge1
->tagged_validity
)
1132 edge1
->tagged_validity
= edge2
->tagged_validity
;
1134 edge1
->tagged_validity
=
1135 isl_union_map_union(edge1
->tagged_validity
,
1136 edge2
->tagged_validity
);
1139 if (is_condition(edge2
) && !edge1
->tagged_condition
)
1141 if (is_conditional_validity(edge2
) && !edge1
->tagged_validity
)
1147 /* Insert dummy tags in domain and range of "map".
1149 * In particular, if "map" is of the form
1155 * [A -> dummy_tag] -> [B -> dummy_tag]
1157 * where the dummy_tags are identical and equal to any dummy tags
1158 * introduced by any other call to this function.
1160 static __isl_give isl_map
*insert_dummy_tags(__isl_take isl_map
*map
)
1166 isl_set
*domain
, *range
;
1168 ctx
= isl_map_get_ctx(map
);
1170 id
= isl_id_alloc(ctx
, NULL
, &dummy
);
1171 space
= isl_space_params(isl_map_get_space(map
));
1172 space
= isl_space_set_from_params(space
);
1173 space
= isl_space_set_tuple_id(space
, isl_dim_set
, id
);
1174 space
= isl_space_map_from_set(space
);
1176 domain
= isl_map_wrap(map
);
1177 range
= isl_map_wrap(isl_map_universe(space
));
1178 map
= isl_map_from_domain_and_range(domain
, range
);
1179 map
= isl_map_zip(map
);
1184 /* Given that at least one of "src" or "dst" is compressed, return
1185 * a map between the spaces of these nodes restricted to the affine
1186 * hull that was used in the compression.
1188 static __isl_give isl_map
*extract_hull(struct isl_sched_node
*src
,
1189 struct isl_sched_node
*dst
)
1193 if (src
->compressed
)
1194 dom
= isl_set_copy(src
->hull
);
1196 dom
= isl_set_universe(isl_space_copy(src
->space
));
1197 if (dst
->compressed
)
1198 ran
= isl_set_copy(dst
->hull
);
1200 ran
= isl_set_universe(isl_space_copy(dst
->space
));
1202 return isl_map_from_domain_and_range(dom
, ran
);
1205 /* Intersect the domains of the nested relations in domain and range
1206 * of "tagged" with "map".
1208 static __isl_give isl_map
*map_intersect_domains(__isl_take isl_map
*tagged
,
1209 __isl_keep isl_map
*map
)
1213 tagged
= isl_map_zip(tagged
);
1214 set
= isl_map_wrap(isl_map_copy(map
));
1215 tagged
= isl_map_intersect_domain(tagged
, set
);
1216 tagged
= isl_map_zip(tagged
);
1220 /* Return a pointer to the node that lives in the domain space of "map"
1221 * or NULL if there is no such node.
1223 static struct isl_sched_node
*find_domain_node(isl_ctx
*ctx
,
1224 struct isl_sched_graph
*graph
, __isl_keep isl_map
*map
)
1226 struct isl_sched_node
*node
;
1229 space
= isl_space_domain(isl_map_get_space(map
));
1230 node
= graph_find_node(ctx
, graph
, space
);
1231 isl_space_free(space
);
1236 /* Return a pointer to the node that lives in the range space of "map"
1237 * or NULL if there is no such node.
1239 static struct isl_sched_node
*find_range_node(isl_ctx
*ctx
,
1240 struct isl_sched_graph
*graph
, __isl_keep isl_map
*map
)
1242 struct isl_sched_node
*node
;
1245 space
= isl_space_range(isl_map_get_space(map
));
1246 node
= graph_find_node(ctx
, graph
, space
);
1247 isl_space_free(space
);
1252 /* Refrain from adding a new edge based on "map".
1253 * Instead, just free the map.
1254 * "tagged" is either a copy of "map" with additional tags or NULL.
1256 static isl_stat
skip_edge(__isl_take isl_map
*map
, __isl_take isl_map
*tagged
)
1259 isl_map_free(tagged
);
1264 /* Add a new edge to the graph based on the given map
1265 * and add it to data->graph->edge_table[data->type].
1266 * If a dependence relation of a given type happens to be identical
1267 * to one of the dependence relations of a type that was added before,
1268 * then we don't create a new edge, but instead mark the original edge
1269 * as also representing a dependence of the current type.
1271 * Edges of type isl_edge_condition or isl_edge_conditional_validity
1272 * may be specified as "tagged" dependence relations. That is, "map"
1273 * may contain elements (i -> a) -> (j -> b), where i -> j denotes
1274 * the dependence on iterations and a and b are tags.
1275 * edge->map is set to the relation containing the elements i -> j,
1276 * while edge->tagged_condition and edge->tagged_validity contain
1277 * the union of all the "map" relations
1278 * for which extract_edge is called that result in the same edge->map.
1280 * If the source or the destination node is compressed, then
1281 * intersect both "map" and "tagged" with the constraints that
1282 * were used to construct the compression.
1283 * This ensures that there are no schedule constraints defined
1284 * outside of these domains, while the scheduler no longer has
1285 * any control over those outside parts.
1287 static isl_stat
extract_edge(__isl_take isl_map
*map
, void *user
)
1290 isl_ctx
*ctx
= isl_map_get_ctx(map
);
1291 struct isl_extract_edge_data
*data
= user
;
1292 struct isl_sched_graph
*graph
= data
->graph
;
1293 struct isl_sched_node
*src
, *dst
;
1294 struct isl_sched_edge
*edge
;
1295 isl_map
*tagged
= NULL
;
1297 if (data
->type
== isl_edge_condition
||
1298 data
->type
== isl_edge_conditional_validity
) {
1299 if (isl_map_can_zip(map
)) {
1300 tagged
= isl_map_copy(map
);
1301 map
= isl_set_unwrap(isl_map_domain(isl_map_zip(map
)));
1303 tagged
= insert_dummy_tags(isl_map_copy(map
));
1307 src
= find_domain_node(ctx
, graph
, map
);
1308 dst
= find_range_node(ctx
, graph
, map
);
1311 return skip_edge(map
, tagged
);
1313 if (src
->compressed
|| dst
->compressed
) {
1315 hull
= extract_hull(src
, dst
);
1317 tagged
= map_intersect_domains(tagged
, hull
);
1318 map
= isl_map_intersect(map
, hull
);
1321 empty
= isl_map_plain_is_empty(map
);
1325 return skip_edge(map
, tagged
);
1327 graph
->edge
[graph
->n_edge
].src
= src
;
1328 graph
->edge
[graph
->n_edge
].dst
= dst
;
1329 graph
->edge
[graph
->n_edge
].map
= map
;
1330 graph
->edge
[graph
->n_edge
].types
= 0;
1331 graph
->edge
[graph
->n_edge
].tagged_condition
= NULL
;
1332 graph
->edge
[graph
->n_edge
].tagged_validity
= NULL
;
1333 set_type(&graph
->edge
[graph
->n_edge
], data
->type
);
1334 if (data
->type
== isl_edge_condition
)
1335 graph
->edge
[graph
->n_edge
].tagged_condition
=
1336 isl_union_map_from_map(tagged
);
1337 if (data
->type
== isl_edge_conditional_validity
)
1338 graph
->edge
[graph
->n_edge
].tagged_validity
=
1339 isl_union_map_from_map(tagged
);
1341 edge
= graph_find_matching_edge(graph
, &graph
->edge
[graph
->n_edge
]);
1344 return isl_stat_error
;
1346 if (edge
== &graph
->edge
[graph
->n_edge
])
1347 return graph_edge_table_add(ctx
, graph
, data
->type
,
1348 &graph
->edge
[graph
->n_edge
++]);
1350 if (merge_edge(edge
, &graph
->edge
[graph
->n_edge
]) < 0)
1351 return isl_stat_error
;
1353 return graph_edge_table_add(ctx
, graph
, data
->type
, edge
);
1356 isl_map_free(tagged
);
1357 return isl_stat_error
;
1360 /* Initialize the schedule graph "graph" from the schedule constraints "sc".
1362 * The context is included in the domain before the nodes of
1363 * the graphs are extracted in order to be able to exploit
1364 * any possible additional equalities.
1365 * Note that this intersection is only performed locally here.
1367 static isl_stat
graph_init(struct isl_sched_graph
*graph
,
1368 __isl_keep isl_schedule_constraints
*sc
)
1371 isl_union_set
*domain
;
1373 struct isl_extract_edge_data data
;
1374 enum isl_edge_type i
;
1378 return isl_stat_error
;
1380 ctx
= isl_schedule_constraints_get_ctx(sc
);
1382 domain
= isl_schedule_constraints_get_domain(sc
);
1383 graph
->n
= isl_union_set_n_set(domain
);
1384 isl_union_set_free(domain
);
1386 if (graph_alloc(ctx
, graph
, graph
->n
,
1387 isl_schedule_constraints_n_map(sc
)) < 0)
1388 return isl_stat_error
;
1390 if (compute_max_row(graph
, sc
) < 0)
1391 return isl_stat_error
;
1392 graph
->root
= graph
;
1394 domain
= isl_schedule_constraints_get_domain(sc
);
1395 domain
= isl_union_set_intersect_params(domain
,
1396 isl_schedule_constraints_get_context(sc
));
1397 r
= isl_union_set_foreach_set(domain
, &extract_node
, graph
);
1398 isl_union_set_free(domain
);
1400 return isl_stat_error
;
1401 if (graph_init_table(ctx
, graph
) < 0)
1402 return isl_stat_error
;
1403 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
1404 c
= isl_schedule_constraints_get(sc
, i
);
1405 graph
->max_edge
[i
] = isl_union_map_n_map(c
);
1406 isl_union_map_free(c
);
1408 return isl_stat_error
;
1410 if (graph_init_edge_tables(ctx
, graph
) < 0)
1411 return isl_stat_error
;
1414 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
1418 c
= isl_schedule_constraints_get(sc
, i
);
1419 r
= isl_union_map_foreach_map(c
, &extract_edge
, &data
);
1420 isl_union_map_free(c
);
1422 return isl_stat_error
;
1428 /* Check whether there is any dependence from node[j] to node[i]
1429 * or from node[i] to node[j].
1431 static isl_bool
node_follows_weak(int i
, int j
, void *user
)
1434 struct isl_sched_graph
*graph
= user
;
1436 f
= graph_has_any_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
1439 return graph_has_any_edge(graph
, &graph
->node
[i
], &graph
->node
[j
]);
1442 /* Check whether there is a (conditional) validity dependence from node[j]
1443 * to node[i], forcing node[i] to follow node[j].
1445 static isl_bool
node_follows_strong(int i
, int j
, void *user
)
1447 struct isl_sched_graph
*graph
= user
;
1449 return graph_has_validity_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
1452 /* Use Tarjan's algorithm for computing the strongly connected components
1453 * in the dependence graph only considering those edges defined by "follows".
1455 static isl_stat
detect_ccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
1456 isl_bool (*follows
)(int i
, int j
, void *user
))
1459 struct isl_tarjan_graph
*g
= NULL
;
1461 g
= isl_tarjan_graph_init(ctx
, graph
->n
, follows
, graph
);
1463 return isl_stat_error
;
1469 while (g
->order
[i
] != -1) {
1470 graph
->node
[g
->order
[i
]].scc
= graph
->scc
;
1478 isl_tarjan_graph_free(g
);
1483 /* Apply Tarjan's algorithm to detect the strongly connected components
1484 * in the dependence graph.
1485 * Only consider the (conditional) validity dependences and clear "weak".
1487 static isl_stat
detect_sccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
1490 return detect_ccs(ctx
, graph
, &node_follows_strong
);
1493 /* Apply Tarjan's algorithm to detect the (weakly) connected components
1494 * in the dependence graph.
1495 * Consider all dependences and set "weak".
1497 static isl_stat
detect_wccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
1500 return detect_ccs(ctx
, graph
, &node_follows_weak
);
1503 static int cmp_scc(const void *a
, const void *b
, void *data
)
1505 struct isl_sched_graph
*graph
= data
;
1509 return graph
->node
[*i1
].scc
- graph
->node
[*i2
].scc
;
1512 /* Sort the elements of graph->sorted according to the corresponding SCCs.
1514 static int sort_sccs(struct isl_sched_graph
*graph
)
1516 return isl_sort(graph
->sorted
, graph
->n
, sizeof(int), &cmp_scc
, graph
);
1519 /* Return a non-parametric set in the compressed space of "node" that is
1520 * bounded by the size in each direction
1522 * { [x] : -S_i <= x_i <= S_i }
1524 * If S_i is infinity in direction i, then there are no constraints
1525 * in that direction.
1527 * Cache the result in node->bounds.
1529 static __isl_give isl_basic_set
*get_size_bounds(struct isl_sched_node
*node
)
1532 isl_basic_set
*bounds
;
1537 return isl_basic_set_copy(node
->bounds
);
1539 if (node
->compressed
)
1540 space
= isl_multi_aff_get_domain_space(node
->decompress
);
1542 space
= isl_space_copy(node
->space
);
1543 nparam
= isl_space_dim(space
, isl_dim_param
);
1544 space
= isl_space_drop_dims(space
, isl_dim_param
, 0, nparam
);
1545 bounds
= isl_basic_set_universe(space
);
1547 for (i
= 0; i
< node
->nvar
; ++i
) {
1550 size
= isl_multi_val_get_val(node
->sizes
, i
);
1552 return isl_basic_set_free(bounds
);
1553 if (!isl_val_is_int(size
)) {
1557 bounds
= isl_basic_set_upper_bound_val(bounds
, isl_dim_set
, i
,
1558 isl_val_copy(size
));
1559 bounds
= isl_basic_set_lower_bound_val(bounds
, isl_dim_set
, i
,
1563 node
->bounds
= isl_basic_set_copy(bounds
);
1567 /* Drop some constraints from "delta" that could be exploited
1568 * to construct loop coalescing schedules.
1569 * In particular, drop those constraint that bound the difference
1570 * to the size of the domain.
1571 * First project out the parameters to improve the effectiveness.
1573 static __isl_give isl_set
*drop_coalescing_constraints(
1574 __isl_take isl_set
*delta
, struct isl_sched_node
*node
)
1577 isl_basic_set
*bounds
;
1579 bounds
= get_size_bounds(node
);
1581 nparam
= isl_set_dim(delta
, isl_dim_param
);
1582 delta
= isl_set_project_out(delta
, isl_dim_param
, 0, nparam
);
1583 delta
= isl_set_remove_divs(delta
);
1584 delta
= isl_set_plain_gist_basic_set(delta
, bounds
);
1588 /* Given a dependence relation R from "node" to itself,
1589 * construct the set of coefficients of valid constraints for elements
1590 * in that dependence relation.
1591 * In particular, the result contains tuples of coefficients
1592 * c_0, c_n, c_x such that
1594 * c_0 + c_n n + c_x y - c_x x >= 0 for each (x,y) in R
1598 * c_0 + c_n n + c_x d >= 0 for each d in delta R = { y - x | (x,y) in R }
1600 * We choose here to compute the dual of delta R.
1601 * Alternatively, we could have computed the dual of R, resulting
1602 * in a set of tuples c_0, c_n, c_x, c_y, and then
1603 * plugged in (c_0, c_n, c_x, -c_x).
1605 * If "need_param" is set, then the resulting coefficients effectively
1606 * include coefficients for the parameters c_n. Otherwise, they may
1607 * have been projected out already.
1608 * Since the constraints may be different for these two cases,
1609 * they are stored in separate caches.
1610 * In particular, if no parameter coefficients are required and
1611 * the schedule_treat_coalescing option is set, then the parameters
1612 * are projected out and some constraints that could be exploited
1613 * to construct coalescing schedules are removed before the dual
1616 * If "node" has been compressed, then the dependence relation
1617 * is also compressed before the set of coefficients is computed.
1619 static __isl_give isl_basic_set
*intra_coefficients(
1620 struct isl_sched_graph
*graph
, struct isl_sched_node
*node
,
1621 __isl_take isl_map
*map
, int need_param
)
1626 isl_basic_set
*coef
;
1627 isl_maybe_isl_basic_set m
;
1628 isl_map_to_basic_set
**hmap
= &graph
->intra_hmap
;
1634 ctx
= isl_map_get_ctx(map
);
1635 treat
= !need_param
&& isl_options_get_schedule_treat_coalescing(ctx
);
1637 hmap
= &graph
->intra_hmap_param
;
1638 m
= isl_map_to_basic_set_try_get(*hmap
, map
);
1639 if (m
.valid
< 0 || m
.valid
) {
1644 key
= isl_map_copy(map
);
1645 if (node
->compressed
) {
1646 map
= isl_map_preimage_domain_multi_aff(map
,
1647 isl_multi_aff_copy(node
->decompress
));
1648 map
= isl_map_preimage_range_multi_aff(map
,
1649 isl_multi_aff_copy(node
->decompress
));
1651 delta
= isl_map_deltas(map
);
1653 delta
= drop_coalescing_constraints(delta
, node
);
1654 delta
= isl_set_remove_divs(delta
);
1655 coef
= isl_set_coefficients(delta
);
1656 *hmap
= isl_map_to_basic_set_set(*hmap
, key
, isl_basic_set_copy(coef
));
1661 /* Given a dependence relation R, construct the set of coefficients
1662 * of valid constraints for elements in that dependence relation.
1663 * In particular, the result contains tuples of coefficients
1664 * c_0, c_n, c_x, c_y such that
1666 * c_0 + c_n n + c_x x + c_y y >= 0 for each (x,y) in R
1668 * If the source or destination nodes of "edge" have been compressed,
1669 * then the dependence relation is also compressed before
1670 * the set of coefficients is computed.
1672 static __isl_give isl_basic_set
*inter_coefficients(
1673 struct isl_sched_graph
*graph
, struct isl_sched_edge
*edge
,
1674 __isl_take isl_map
*map
)
1678 isl_basic_set
*coef
;
1679 isl_maybe_isl_basic_set m
;
1681 m
= isl_map_to_basic_set_try_get(graph
->inter_hmap
, map
);
1682 if (m
.valid
< 0 || m
.valid
) {
1687 key
= isl_map_copy(map
);
1688 if (edge
->src
->compressed
)
1689 map
= isl_map_preimage_domain_multi_aff(map
,
1690 isl_multi_aff_copy(edge
->src
->decompress
));
1691 if (edge
->dst
->compressed
)
1692 map
= isl_map_preimage_range_multi_aff(map
,
1693 isl_multi_aff_copy(edge
->dst
->decompress
));
1694 set
= isl_map_wrap(isl_map_remove_divs(map
));
1695 coef
= isl_set_coefficients(set
);
1696 graph
->inter_hmap
= isl_map_to_basic_set_set(graph
->inter_hmap
, key
,
1697 isl_basic_set_copy(coef
));
1702 /* Return the position of the coefficients of the variables in
1703 * the coefficients constraints "coef".
1705 * The space of "coef" is of the form
1707 * { coefficients[[cst, params] -> S] }
1709 * Return the position of S.
1711 static int coef_var_offset(__isl_keep isl_basic_set
*coef
)
1716 space
= isl_space_unwrap(isl_basic_set_get_space(coef
));
1717 offset
= isl_space_dim(space
, isl_dim_in
);
1718 isl_space_free(space
);
1723 /* Return the offset of the coefficient of the constant term of "node"
1726 * Within each node, the coefficients have the following order:
1727 * - positive and negative parts of c_i_x
1728 * - c_i_n (if parametric)
1731 static int node_cst_coef_offset(struct isl_sched_node
*node
)
1733 return node
->start
+ 2 * node
->nvar
+ node
->nparam
;
1736 /* Return the offset of the coefficients of the parameters of "node"
1739 * Within each node, the coefficients have the following order:
1740 * - positive and negative parts of c_i_x
1741 * - c_i_n (if parametric)
1744 static int node_par_coef_offset(struct isl_sched_node
*node
)
1746 return node
->start
+ 2 * node
->nvar
;
1749 /* Return the offset of the coefficients of the variables of "node"
1752 * Within each node, the coefficients have the following order:
1753 * - positive and negative parts of c_i_x
1754 * - c_i_n (if parametric)
1757 static int node_var_coef_offset(struct isl_sched_node
*node
)
1762 /* Return the position of the pair of variables encoding
1763 * coefficient "i" of "node".
1765 * The order of these variable pairs is the opposite of
1766 * that of the coefficients, with 2 variables per coefficient.
1768 static int node_var_coef_pos(struct isl_sched_node
*node
, int i
)
1770 return node_var_coef_offset(node
) + 2 * (node
->nvar
- 1 - i
);
1773 /* Construct an isl_dim_map for mapping constraints on coefficients
1774 * for "node" to the corresponding positions in graph->lp.
1775 * "offset" is the offset of the coefficients for the variables
1776 * in the input constraints.
1777 * "s" is the sign of the mapping.
1779 * The input constraints are given in terms of the coefficients
1780 * (c_0, c_x) or (c_0, c_n, c_x).
1781 * The mapping produced by this function essentially plugs in
1782 * (0, c_i_x^+ - c_i_x^-) if s = 1 and
1783 * (0, -c_i_x^+ + c_i_x^-) if s = -1 or
1784 * (0, 0, c_i_x^+ - c_i_x^-) if s = 1 and
1785 * (0, 0, -c_i_x^+ + c_i_x^-) if s = -1.
1786 * In graph->lp, the c_i_x^- appear before their c_i_x^+ counterpart.
1787 * Furthermore, the order of these pairs is the opposite of that
1788 * of the corresponding coefficients.
1790 * The caller can extend the mapping to also map the other coefficients
1791 * (and therefore not plug in 0).
1793 static __isl_give isl_dim_map
*intra_dim_map(isl_ctx
*ctx
,
1794 struct isl_sched_graph
*graph
, struct isl_sched_node
*node
,
1799 isl_dim_map
*dim_map
;
1801 if (!node
|| !graph
->lp
)
1804 total
= isl_basic_set_total_dim(graph
->lp
);
1805 pos
= node_var_coef_pos(node
, 0);
1806 dim_map
= isl_dim_map_alloc(ctx
, total
);
1807 isl_dim_map_range(dim_map
, pos
, -2, offset
, 1, node
->nvar
, -s
);
1808 isl_dim_map_range(dim_map
, pos
+ 1, -2, offset
, 1, node
->nvar
, s
);
1813 /* Construct an isl_dim_map for mapping constraints on coefficients
1814 * for "src" (node i) and "dst" (node j) to the corresponding positions
1816 * "offset" is the offset of the coefficients for the variables of "src"
1817 * in the input constraints.
1818 * "s" is the sign of the mapping.
1820 * The input constraints are given in terms of the coefficients
1821 * (c_0, c_n, c_x, c_y).
1822 * The mapping produced by this function essentially plugs in
1823 * (c_j_0 - c_i_0, c_j_n - c_i_n,
1824 * -(c_i_x^+ - c_i_x^-), c_j_x^+ - c_j_x^-) if s = 1 and
1825 * (-c_j_0 + c_i_0, -c_j_n + c_i_n,
1826 * c_i_x^+ - c_i_x^-, -(c_j_x^+ - c_j_x^-)) if s = -1.
1827 * In graph->lp, the c_*^- appear before their c_*^+ counterpart.
1828 * Furthermore, the order of these pairs is the opposite of that
1829 * of the corresponding coefficients.
1831 * The caller can further extend the mapping.
1833 static __isl_give isl_dim_map
*inter_dim_map(isl_ctx
*ctx
,
1834 struct isl_sched_graph
*graph
, struct isl_sched_node
*src
,
1835 struct isl_sched_node
*dst
, int offset
, int s
)
1839 isl_dim_map
*dim_map
;
1841 if (!src
|| !dst
|| !graph
->lp
)
1844 total
= isl_basic_set_total_dim(graph
->lp
);
1845 dim_map
= isl_dim_map_alloc(ctx
, total
);
1847 pos
= node_cst_coef_offset(dst
);
1848 isl_dim_map_range(dim_map
, pos
, 0, 0, 0, 1, s
);
1849 pos
= node_par_coef_offset(dst
);
1850 isl_dim_map_range(dim_map
, pos
, 1, 1, 1, dst
->nparam
, s
);
1851 pos
= node_var_coef_pos(dst
, 0);
1852 isl_dim_map_range(dim_map
, pos
, -2, offset
+ src
->nvar
, 1,
1854 isl_dim_map_range(dim_map
, pos
+ 1, -2, offset
+ src
->nvar
, 1,
1857 pos
= node_cst_coef_offset(src
);
1858 isl_dim_map_range(dim_map
, pos
, 0, 0, 0, 1, -s
);
1859 pos
= node_par_coef_offset(src
);
1860 isl_dim_map_range(dim_map
, pos
, 1, 1, 1, src
->nparam
, -s
);
1861 pos
= node_var_coef_pos(src
, 0);
1862 isl_dim_map_range(dim_map
, pos
, -2, offset
, 1, src
->nvar
, s
);
1863 isl_dim_map_range(dim_map
, pos
+ 1, -2, offset
, 1, src
->nvar
, -s
);
1868 /* Add the constraints from "src" to "dst" using "dim_map",
1869 * after making sure there is enough room in "dst" for the extra constraints.
1871 static __isl_give isl_basic_set
*add_constraints_dim_map(
1872 __isl_take isl_basic_set
*dst
, __isl_take isl_basic_set
*src
,
1873 __isl_take isl_dim_map
*dim_map
)
1877 n_eq
= isl_basic_set_n_equality(src
);
1878 n_ineq
= isl_basic_set_n_inequality(src
);
1879 dst
= isl_basic_set_extend_constraints(dst
, n_eq
, n_ineq
);
1880 dst
= isl_basic_set_add_constraints_dim_map(dst
, src
, dim_map
);
1884 /* Add constraints to graph->lp that force validity for the given
1885 * dependence from a node i to itself.
1886 * That is, add constraints that enforce
1888 * (c_i_0 + c_i_n n + c_i_x y) - (c_i_0 + c_i_n n + c_i_x x)
1889 * = c_i_x (y - x) >= 0
1891 * for each (x,y) in R.
1892 * We obtain general constraints on coefficients (c_0, c_x)
1893 * of valid constraints for (y - x) and then plug in (0, c_i_x^+ - c_i_x^-),
1894 * where c_i_x = c_i_x^+ - c_i_x^-, with c_i_x^+ and c_i_x^- non-negative.
1895 * In graph->lp, the c_i_x^- appear before their c_i_x^+ counterpart.
1896 * Note that the result of intra_coefficients may also contain
1897 * parameter coefficients c_n, in which case 0 is plugged in for them as well.
1899 static isl_stat
add_intra_validity_constraints(struct isl_sched_graph
*graph
,
1900 struct isl_sched_edge
*edge
)
1903 isl_map
*map
= isl_map_copy(edge
->map
);
1904 isl_ctx
*ctx
= isl_map_get_ctx(map
);
1905 isl_dim_map
*dim_map
;
1906 isl_basic_set
*coef
;
1907 struct isl_sched_node
*node
= edge
->src
;
1909 coef
= intra_coefficients(graph
, node
, map
, 0);
1911 offset
= coef_var_offset(coef
);
1914 return isl_stat_error
;
1916 dim_map
= intra_dim_map(ctx
, graph
, node
, offset
, 1);
1917 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
1922 /* Add constraints to graph->lp that force validity for the given
1923 * dependence from node i to node j.
1924 * That is, add constraints that enforce
1926 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) >= 0
1928 * for each (x,y) in R.
1929 * We obtain general constraints on coefficients (c_0, c_n, c_x, c_y)
1930 * of valid constraints for R and then plug in
1931 * (c_j_0 - c_i_0, c_j_n - c_i_n, -(c_i_x^+ - c_i_x^-), c_j_x^+ - c_j_x^-),
1932 * where c_* = c_*^+ - c_*^-, with c_*^+ and c_*^- non-negative.
1933 * In graph->lp, the c_*^- appear before their c_*^+ counterpart.
1935 static isl_stat
add_inter_validity_constraints(struct isl_sched_graph
*graph
,
1936 struct isl_sched_edge
*edge
)
1941 isl_dim_map
*dim_map
;
1942 isl_basic_set
*coef
;
1943 struct isl_sched_node
*src
= edge
->src
;
1944 struct isl_sched_node
*dst
= edge
->dst
;
1947 return isl_stat_error
;
1949 map
= isl_map_copy(edge
->map
);
1950 ctx
= isl_map_get_ctx(map
);
1951 coef
= inter_coefficients(graph
, edge
, map
);
1953 offset
= coef_var_offset(coef
);
1956 return isl_stat_error
;
1958 dim_map
= inter_dim_map(ctx
, graph
, src
, dst
, offset
, 1);
1960 edge
->start
= graph
->lp
->n_ineq
;
1961 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
1963 return isl_stat_error
;
1964 edge
->end
= graph
->lp
->n_ineq
;
1969 /* Add constraints to graph->lp that bound the dependence distance for the given
1970 * dependence from a node i to itself.
1971 * If s = 1, we add the constraint
1973 * c_i_x (y - x) <= m_0 + m_n n
1977 * -c_i_x (y - x) + m_0 + m_n n >= 0
1979 * for each (x,y) in R.
1980 * If s = -1, we add the constraint
1982 * -c_i_x (y - x) <= m_0 + m_n n
1986 * c_i_x (y - x) + m_0 + m_n n >= 0
1988 * for each (x,y) in R.
1989 * We obtain general constraints on coefficients (c_0, c_n, c_x)
1990 * of valid constraints for (y - x) and then plug in (m_0, m_n, -s * c_i_x),
1991 * with each coefficient (except m_0) represented as a pair of non-negative
1995 * If "local" is set, then we add constraints
1997 * c_i_x (y - x) <= 0
2001 * -c_i_x (y - x) <= 0
2003 * instead, forcing the dependence distance to be (less than or) equal to 0.
2004 * That is, we plug in (0, 0, -s * c_i_x),
2005 * intra_coefficients is not required to have c_n in its result when
2006 * "local" is set. If they are missing, then (0, -s * c_i_x) is plugged in.
2007 * Note that dependences marked local are treated as validity constraints
2008 * by add_all_validity_constraints and therefore also have
2009 * their distances bounded by 0 from below.
2011 static isl_stat
add_intra_proximity_constraints(struct isl_sched_graph
*graph
,
2012 struct isl_sched_edge
*edge
, int s
, int local
)
2016 isl_map
*map
= isl_map_copy(edge
->map
);
2017 isl_ctx
*ctx
= isl_map_get_ctx(map
);
2018 isl_dim_map
*dim_map
;
2019 isl_basic_set
*coef
;
2020 struct isl_sched_node
*node
= edge
->src
;
2022 coef
= intra_coefficients(graph
, node
, map
, !local
);
2024 offset
= coef_var_offset(coef
);
2027 return isl_stat_error
;
2029 nparam
= isl_space_dim(node
->space
, isl_dim_param
);
2030 dim_map
= intra_dim_map(ctx
, graph
, node
, offset
, -s
);
2033 isl_dim_map_range(dim_map
, 1, 0, 0, 0, 1, 1);
2034 isl_dim_map_range(dim_map
, 4, 2, 1, 1, nparam
, -1);
2035 isl_dim_map_range(dim_map
, 5, 2, 1, 1, nparam
, 1);
2037 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
2042 /* Add constraints to graph->lp that bound the dependence distance for the given
2043 * dependence from node i to node j.
2044 * If s = 1, we add the constraint
2046 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x)
2051 * -(c_j_0 + c_j_n n + c_j_x y) + (c_i_0 + c_i_n n + c_i_x x) +
2054 * for each (x,y) in R.
2055 * If s = -1, we add the constraint
2057 * -((c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x))
2062 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) +
2065 * for each (x,y) in R.
2066 * We obtain general constraints on coefficients (c_0, c_n, c_x, c_y)
2067 * of valid constraints for R and then plug in
2068 * (m_0 - s*c_j_0 + s*c_i_0, m_n - s*c_j_n + s*c_i_n,
2069 * s*c_i_x, -s*c_j_x)
2070 * with each coefficient (except m_0, c_*_0 and c_*_n)
2071 * represented as a pair of non-negative coefficients.
2074 * If "local" is set (and s = 1), then we add constraints
2076 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) <= 0
2080 * -((c_j_0 + c_j_n n + c_j_x y) + (c_i_0 + c_i_n n + c_i_x x)) >= 0
2082 * instead, forcing the dependence distance to be (less than or) equal to 0.
2083 * That is, we plug in
2084 * (-s*c_j_0 + s*c_i_0, -s*c_j_n + s*c_i_n, s*c_i_x, -s*c_j_x).
2085 * Note that dependences marked local are treated as validity constraints
2086 * by add_all_validity_constraints and therefore also have
2087 * their distances bounded by 0 from below.
2089 static isl_stat
add_inter_proximity_constraints(struct isl_sched_graph
*graph
,
2090 struct isl_sched_edge
*edge
, int s
, int local
)
2094 isl_map
*map
= isl_map_copy(edge
->map
);
2095 isl_ctx
*ctx
= isl_map_get_ctx(map
);
2096 isl_dim_map
*dim_map
;
2097 isl_basic_set
*coef
;
2098 struct isl_sched_node
*src
= edge
->src
;
2099 struct isl_sched_node
*dst
= edge
->dst
;
2101 coef
= inter_coefficients(graph
, edge
, map
);
2103 offset
= coef_var_offset(coef
);
2106 return isl_stat_error
;
2108 nparam
= isl_space_dim(src
->space
, isl_dim_param
);
2109 dim_map
= inter_dim_map(ctx
, graph
, src
, dst
, offset
, -s
);
2112 isl_dim_map_range(dim_map
, 1, 0, 0, 0, 1, 1);
2113 isl_dim_map_range(dim_map
, 4, 2, 1, 1, nparam
, -1);
2114 isl_dim_map_range(dim_map
, 5, 2, 1, 1, nparam
, 1);
2117 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
2122 /* Should the distance over "edge" be forced to zero?
2123 * That is, is it marked as a local edge?
2124 * If "use_coincidence" is set, then coincidence edges are treated
2127 static int force_zero(struct isl_sched_edge
*edge
, int use_coincidence
)
2129 return is_local(edge
) || (use_coincidence
&& is_coincidence(edge
));
2132 /* Add all validity constraints to graph->lp.
2134 * An edge that is forced to be local needs to have its dependence
2135 * distances equal to zero. We take care of bounding them by 0 from below
2136 * here. add_all_proximity_constraints takes care of bounding them by 0
2139 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2140 * Otherwise, we ignore them.
2142 static int add_all_validity_constraints(struct isl_sched_graph
*graph
,
2143 int use_coincidence
)
2147 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2148 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
2151 zero
= force_zero(edge
, use_coincidence
);
2152 if (!is_validity(edge
) && !zero
)
2154 if (edge
->src
!= edge
->dst
)
2156 if (add_intra_validity_constraints(graph
, edge
) < 0)
2160 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2161 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
2164 zero
= force_zero(edge
, use_coincidence
);
2165 if (!is_validity(edge
) && !zero
)
2167 if (edge
->src
== edge
->dst
)
2169 if (add_inter_validity_constraints(graph
, edge
) < 0)
2176 /* Add constraints to graph->lp that bound the dependence distance
2177 * for all dependence relations.
2178 * If a given proximity dependence is identical to a validity
2179 * dependence, then the dependence distance is already bounded
2180 * from below (by zero), so we only need to bound the distance
2181 * from above. (This includes the case of "local" dependences
2182 * which are treated as validity dependence by add_all_validity_constraints.)
2183 * Otherwise, we need to bound the distance both from above and from below.
2185 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2186 * Otherwise, we ignore them.
2188 static int add_all_proximity_constraints(struct isl_sched_graph
*graph
,
2189 int use_coincidence
)
2193 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2194 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
2197 zero
= force_zero(edge
, use_coincidence
);
2198 if (!is_proximity(edge
) && !zero
)
2200 if (edge
->src
== edge
->dst
&&
2201 add_intra_proximity_constraints(graph
, edge
, 1, zero
) < 0)
2203 if (edge
->src
!= edge
->dst
&&
2204 add_inter_proximity_constraints(graph
, edge
, 1, zero
) < 0)
2206 if (is_validity(edge
) || zero
)
2208 if (edge
->src
== edge
->dst
&&
2209 add_intra_proximity_constraints(graph
, edge
, -1, 0) < 0)
2211 if (edge
->src
!= edge
->dst
&&
2212 add_inter_proximity_constraints(graph
, edge
, -1, 0) < 0)
2219 /* Normalize the rows of "indep" such that all rows are lexicographically
2220 * positive and such that each row contains as many final zeros as possible,
2221 * given the choice for the previous rows.
2222 * Do this by performing elementary row operations.
2224 static __isl_give isl_mat
*normalize_independent(__isl_take isl_mat
*indep
)
2226 indep
= isl_mat_reverse_gauss(indep
);
2227 indep
= isl_mat_lexnonneg_rows(indep
);
2231 /* Compute a basis for the rows in the linear part of the schedule
2232 * and extend this basis to a full basis. The remaining rows
2233 * can then be used to force linear independence from the rows
2236 * In particular, given the schedule rows S, we compute
2241 * with H the Hermite normal form of S. That is, all but the
2242 * first rank columns of H are zero and so each row in S is
2243 * a linear combination of the first rank rows of Q.
2244 * The matrix Q can be used as a variable transformation
2245 * that isolates the directions of S in the first rank rows.
2246 * Transposing S U = H yields
2250 * with all but the first rank rows of H^T zero.
2251 * The last rows of U^T are therefore linear combinations
2252 * of schedule coefficients that are all zero on schedule
2253 * coefficients that are linearly dependent on the rows of S.
2254 * At least one of these combinations is non-zero on
2255 * linearly independent schedule coefficients.
2256 * The rows are normalized to involve as few of the last
2257 * coefficients as possible and to have a positive initial value.
2259 static int node_update_vmap(struct isl_sched_node
*node
)
2262 int n_row
= isl_mat_rows(node
->sched
);
2264 H
= isl_mat_sub_alloc(node
->sched
, 0, n_row
,
2265 1 + node
->nparam
, node
->nvar
);
2267 H
= isl_mat_left_hermite(H
, 0, &U
, &Q
);
2268 isl_mat_free(node
->indep
);
2269 isl_mat_free(node
->vmap
);
2271 node
->indep
= isl_mat_transpose(U
);
2272 node
->rank
= isl_mat_initial_non_zero_cols(H
);
2273 node
->indep
= isl_mat_drop_rows(node
->indep
, 0, node
->rank
);
2274 node
->indep
= normalize_independent(node
->indep
);
2277 if (!node
->indep
|| !node
->vmap
|| node
->rank
< 0)
2282 /* Is "edge" marked as a validity or a conditional validity edge?
2284 static int is_any_validity(struct isl_sched_edge
*edge
)
2286 return is_validity(edge
) || is_conditional_validity(edge
);
2289 /* How many times should we count the constraints in "edge"?
2291 * We count as follows
2292 * validity -> 1 (>= 0)
2293 * validity+proximity -> 2 (>= 0 and upper bound)
2294 * proximity -> 2 (lower and upper bound)
2295 * local(+any) -> 2 (>= 0 and <= 0)
2297 * If an edge is only marked conditional_validity then it counts
2298 * as zero since it is only checked afterwards.
2300 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2301 * Otherwise, we ignore them.
2303 static int edge_multiplicity(struct isl_sched_edge
*edge
, int use_coincidence
)
2305 if (is_proximity(edge
) || force_zero(edge
, use_coincidence
))
2307 if (is_validity(edge
))
2312 /* How many times should the constraints in "edge" be counted
2313 * as a parametric intra-node constraint?
2315 * Only proximity edges that are not forced zero need
2316 * coefficient constraints that include coefficients for parameters.
2317 * If the edge is also a validity edge, then only
2318 * an upper bound is introduced. Otherwise, both lower and upper bounds
2321 static int parametric_intra_edge_multiplicity(struct isl_sched_edge
*edge
,
2322 int use_coincidence
)
2324 if (edge
->src
!= edge
->dst
)
2326 if (!is_proximity(edge
))
2328 if (force_zero(edge
, use_coincidence
))
2330 if (is_validity(edge
))
2336 /* Add "f" times the number of equality and inequality constraints of "bset"
2337 * to "n_eq" and "n_ineq" and free "bset".
2339 static isl_stat
update_count(__isl_take isl_basic_set
*bset
,
2340 int f
, int *n_eq
, int *n_ineq
)
2343 return isl_stat_error
;
2345 *n_eq
+= isl_basic_set_n_equality(bset
);
2346 *n_ineq
+= isl_basic_set_n_inequality(bset
);
2347 isl_basic_set_free(bset
);
2352 /* Count the number of equality and inequality constraints
2353 * that will be added for the given map.
2355 * The edges that require parameter coefficients are counted separately.
2357 * "use_coincidence" is set if we should take into account coincidence edges.
2359 static isl_stat
count_map_constraints(struct isl_sched_graph
*graph
,
2360 struct isl_sched_edge
*edge
, __isl_take isl_map
*map
,
2361 int *n_eq
, int *n_ineq
, int use_coincidence
)
2364 isl_basic_set
*coef
;
2365 int f
= edge_multiplicity(edge
, use_coincidence
);
2366 int fp
= parametric_intra_edge_multiplicity(edge
, use_coincidence
);
2373 if (edge
->src
!= edge
->dst
) {
2374 coef
= inter_coefficients(graph
, edge
, map
);
2375 return update_count(coef
, f
, n_eq
, n_ineq
);
2379 copy
= isl_map_copy(map
);
2380 coef
= intra_coefficients(graph
, edge
->src
, copy
, 1);
2381 if (update_count(coef
, fp
, n_eq
, n_ineq
) < 0)
2386 copy
= isl_map_copy(map
);
2387 coef
= intra_coefficients(graph
, edge
->src
, copy
, 0);
2388 if (update_count(coef
, f
- fp
, n_eq
, n_ineq
) < 0)
2396 return isl_stat_error
;
2399 /* Count the number of equality and inequality constraints
2400 * that will be added to the main lp problem.
2401 * We count as follows
2402 * validity -> 1 (>= 0)
2403 * validity+proximity -> 2 (>= 0 and upper bound)
2404 * proximity -> 2 (lower and upper bound)
2405 * local(+any) -> 2 (>= 0 and <= 0)
2407 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2408 * Otherwise, we ignore them.
2410 static int count_constraints(struct isl_sched_graph
*graph
,
2411 int *n_eq
, int *n_ineq
, int use_coincidence
)
2415 *n_eq
= *n_ineq
= 0;
2416 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2417 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
2418 isl_map
*map
= isl_map_copy(edge
->map
);
2420 if (count_map_constraints(graph
, edge
, map
, n_eq
, n_ineq
,
2421 use_coincidence
) < 0)
2428 /* Count the number of constraints that will be added by
2429 * add_bound_constant_constraints to bound the values of the constant terms
2430 * and increment *n_eq and *n_ineq accordingly.
2432 * In practice, add_bound_constant_constraints only adds inequalities.
2434 static isl_stat
count_bound_constant_constraints(isl_ctx
*ctx
,
2435 struct isl_sched_graph
*graph
, int *n_eq
, int *n_ineq
)
2437 if (isl_options_get_schedule_max_constant_term(ctx
) == -1)
2440 *n_ineq
+= graph
->n
;
2445 /* Add constraints to bound the values of the constant terms in the schedule,
2446 * if requested by the user.
2448 * The maximal value of the constant terms is defined by the option
2449 * "schedule_max_constant_term".
2451 static isl_stat
add_bound_constant_constraints(isl_ctx
*ctx
,
2452 struct isl_sched_graph
*graph
)
2458 max
= isl_options_get_schedule_max_constant_term(ctx
);
2462 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2464 for (i
= 0; i
< graph
->n
; ++i
) {
2465 struct isl_sched_node
*node
= &graph
->node
[i
];
2468 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2470 return isl_stat_error
;
2471 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
2472 pos
= node_cst_coef_offset(node
);
2473 isl_int_set_si(graph
->lp
->ineq
[k
][1 + pos
], -1);
2474 isl_int_set_si(graph
->lp
->ineq
[k
][0], max
);
2480 /* Count the number of constraints that will be added by
2481 * add_bound_coefficient_constraints and increment *n_eq and *n_ineq
2484 * In practice, add_bound_coefficient_constraints only adds inequalities.
2486 static int count_bound_coefficient_constraints(isl_ctx
*ctx
,
2487 struct isl_sched_graph
*graph
, int *n_eq
, int *n_ineq
)
2491 if (isl_options_get_schedule_max_coefficient(ctx
) == -1 &&
2492 !isl_options_get_schedule_treat_coalescing(ctx
))
2495 for (i
= 0; i
< graph
->n
; ++i
)
2496 *n_ineq
+= graph
->node
[i
].nparam
+ 2 * graph
->node
[i
].nvar
;
2501 /* Add constraints to graph->lp that bound the values of
2502 * the parameter schedule coefficients of "node" to "max" and
2503 * the variable schedule coefficients to the corresponding entry
2505 * In either case, a negative value means that no bound needs to be imposed.
2507 * For parameter coefficients, this amounts to adding a constraint
2515 * The variables coefficients are, however, not represented directly.
2516 * Instead, the variable coefficients c_x are written as differences
2517 * c_x = c_x^+ - c_x^-.
2520 * -max_i <= c_x_i <= max_i
2524 * -max_i <= c_x_i^+ - c_x_i^- <= max_i
2528 * -(c_x_i^+ - c_x_i^-) + max_i >= 0
2529 * c_x_i^+ - c_x_i^- + max_i >= 0
2531 static isl_stat
node_add_coefficient_constraints(isl_ctx
*ctx
,
2532 struct isl_sched_graph
*graph
, struct isl_sched_node
*node
, int max
)
2538 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2540 for (j
= 0; j
< node
->nparam
; ++j
) {
2546 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2548 return isl_stat_error
;
2549 dim
= 1 + node_par_coef_offset(node
) + j
;
2550 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
2551 isl_int_set_si(graph
->lp
->ineq
[k
][dim
], -1);
2552 isl_int_set_si(graph
->lp
->ineq
[k
][0], max
);
2555 ineq
= isl_vec_alloc(ctx
, 1 + total
);
2556 ineq
= isl_vec_clr(ineq
);
2558 return isl_stat_error
;
2559 for (i
= 0; i
< node
->nvar
; ++i
) {
2560 int pos
= 1 + node_var_coef_pos(node
, i
);
2562 if (isl_int_is_neg(node
->max
->el
[i
]))
2565 isl_int_set_si(ineq
->el
[pos
], 1);
2566 isl_int_set_si(ineq
->el
[pos
+ 1], -1);
2567 isl_int_set(ineq
->el
[0], node
->max
->el
[i
]);
2569 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2572 isl_seq_cpy(graph
->lp
->ineq
[k
], ineq
->el
, 1 + total
);
2574 isl_seq_neg(ineq
->el
+ pos
, ineq
->el
+ pos
, 2);
2575 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2578 isl_seq_cpy(graph
->lp
->ineq
[k
], ineq
->el
, 1 + total
);
2580 isl_seq_clr(ineq
->el
+ pos
, 2);
2587 return isl_stat_error
;
2590 /* Add constraints that bound the values of the variable and parameter
2591 * coefficients of the schedule.
2593 * The maximal value of the coefficients is defined by the option
2594 * 'schedule_max_coefficient' and the entries in node->max.
2595 * These latter entries are only set if either the schedule_max_coefficient
2596 * option or the schedule_treat_coalescing option is set.
2598 static isl_stat
add_bound_coefficient_constraints(isl_ctx
*ctx
,
2599 struct isl_sched_graph
*graph
)
2604 max
= isl_options_get_schedule_max_coefficient(ctx
);
2606 if (max
== -1 && !isl_options_get_schedule_treat_coalescing(ctx
))
2609 for (i
= 0; i
< graph
->n
; ++i
) {
2610 struct isl_sched_node
*node
= &graph
->node
[i
];
2612 if (node_add_coefficient_constraints(ctx
, graph
, node
, max
) < 0)
2613 return isl_stat_error
;
2619 /* Add a constraint to graph->lp that equates the value at position
2620 * "sum_pos" to the sum of the "n" values starting at "first".
2622 static isl_stat
add_sum_constraint(struct isl_sched_graph
*graph
,
2623 int sum_pos
, int first
, int n
)
2628 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2630 k
= isl_basic_set_alloc_equality(graph
->lp
);
2632 return isl_stat_error
;
2633 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2634 isl_int_set_si(graph
->lp
->eq
[k
][1 + sum_pos
], -1);
2635 for (i
= 0; i
< n
; ++i
)
2636 isl_int_set_si(graph
->lp
->eq
[k
][1 + first
+ i
], 1);
2641 /* Add a constraint to graph->lp that equates the value at position
2642 * "sum_pos" to the sum of the parameter coefficients of all nodes.
2644 static isl_stat
add_param_sum_constraint(struct isl_sched_graph
*graph
,
2650 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2652 k
= isl_basic_set_alloc_equality(graph
->lp
);
2654 return isl_stat_error
;
2655 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2656 isl_int_set_si(graph
->lp
->eq
[k
][1 + sum_pos
], -1);
2657 for (i
= 0; i
< graph
->n
; ++i
) {
2658 int pos
= 1 + node_par_coef_offset(&graph
->node
[i
]);
2660 for (j
= 0; j
< graph
->node
[i
].nparam
; ++j
)
2661 isl_int_set_si(graph
->lp
->eq
[k
][pos
+ j
], 1);
2667 /* Add a constraint to graph->lp that equates the value at position
2668 * "sum_pos" to the sum of the variable coefficients of all nodes.
2670 static isl_stat
add_var_sum_constraint(struct isl_sched_graph
*graph
,
2676 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2678 k
= isl_basic_set_alloc_equality(graph
->lp
);
2680 return isl_stat_error
;
2681 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2682 isl_int_set_si(graph
->lp
->eq
[k
][1 + sum_pos
], -1);
2683 for (i
= 0; i
< graph
->n
; ++i
) {
2684 struct isl_sched_node
*node
= &graph
->node
[i
];
2685 int pos
= 1 + node_var_coef_offset(node
);
2687 for (j
= 0; j
< 2 * node
->nvar
; ++j
)
2688 isl_int_set_si(graph
->lp
->eq
[k
][pos
+ j
], 1);
2694 /* Construct an ILP problem for finding schedule coefficients
2695 * that result in non-negative, but small dependence distances
2696 * over all dependences.
2697 * In particular, the dependence distances over proximity edges
2698 * are bounded by m_0 + m_n n and we compute schedule coefficients
2699 * with small values (preferably zero) of m_n and m_0.
2701 * All variables of the ILP are non-negative. The actual coefficients
2702 * may be negative, so each coefficient is represented as the difference
2703 * of two non-negative variables. The negative part always appears
2704 * immediately before the positive part.
2705 * Other than that, the variables have the following order
2707 * - sum of positive and negative parts of m_n coefficients
2709 * - sum of all c_n coefficients
2710 * (unconstrained when computing non-parametric schedules)
2711 * - sum of positive and negative parts of all c_x coefficients
2712 * - positive and negative parts of m_n coefficients
2714 * - positive and negative parts of c_i_x, in opposite order
2715 * - c_i_n (if parametric)
2718 * The constraints are those from the edges plus two or three equalities
2719 * to express the sums.
2721 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2722 * Otherwise, we ignore them.
2724 static isl_stat
setup_lp(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
2725 int use_coincidence
)
2735 parametric
= ctx
->opt
->schedule_parametric
;
2736 nparam
= isl_space_dim(graph
->node
[0].space
, isl_dim_param
);
2738 total
= param_pos
+ 2 * nparam
;
2739 for (i
= 0; i
< graph
->n
; ++i
) {
2740 struct isl_sched_node
*node
= &graph
->node
[graph
->sorted
[i
]];
2741 if (node_update_vmap(node
) < 0)
2742 return isl_stat_error
;
2743 node
->start
= total
;
2744 total
+= 1 + node
->nparam
+ 2 * node
->nvar
;
2747 if (count_constraints(graph
, &n_eq
, &n_ineq
, use_coincidence
) < 0)
2748 return isl_stat_error
;
2749 if (count_bound_constant_constraints(ctx
, graph
, &n_eq
, &n_ineq
) < 0)
2750 return isl_stat_error
;
2751 if (count_bound_coefficient_constraints(ctx
, graph
, &n_eq
, &n_ineq
) < 0)
2752 return isl_stat_error
;
2754 space
= isl_space_set_alloc(ctx
, 0, total
);
2755 isl_basic_set_free(graph
->lp
);
2756 n_eq
+= 2 + parametric
;
2758 graph
->lp
= isl_basic_set_alloc_space(space
, 0, n_eq
, n_ineq
);
2760 if (add_sum_constraint(graph
, 0, param_pos
, 2 * nparam
) < 0)
2761 return isl_stat_error
;
2762 if (parametric
&& add_param_sum_constraint(graph
, 2) < 0)
2763 return isl_stat_error
;
2764 if (add_var_sum_constraint(graph
, 3) < 0)
2765 return isl_stat_error
;
2766 if (add_bound_constant_constraints(ctx
, graph
) < 0)
2767 return isl_stat_error
;
2768 if (add_bound_coefficient_constraints(ctx
, graph
) < 0)
2769 return isl_stat_error
;
2770 if (add_all_validity_constraints(graph
, use_coincidence
) < 0)
2771 return isl_stat_error
;
2772 if (add_all_proximity_constraints(graph
, use_coincidence
) < 0)
2773 return isl_stat_error
;
2778 /* Analyze the conflicting constraint found by
2779 * isl_tab_basic_set_non_trivial_lexmin. If it corresponds to the validity
2780 * constraint of one of the edges between distinct nodes, living, moreover
2781 * in distinct SCCs, then record the source and sink SCC as this may
2782 * be a good place to cut between SCCs.
2784 static int check_conflict(int con
, void *user
)
2787 struct isl_sched_graph
*graph
= user
;
2789 if (graph
->src_scc
>= 0)
2792 con
-= graph
->lp
->n_eq
;
2794 if (con
>= graph
->lp
->n_ineq
)
2797 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2798 if (!is_validity(&graph
->edge
[i
]))
2800 if (graph
->edge
[i
].src
== graph
->edge
[i
].dst
)
2802 if (graph
->edge
[i
].src
->scc
== graph
->edge
[i
].dst
->scc
)
2804 if (graph
->edge
[i
].start
> con
)
2806 if (graph
->edge
[i
].end
<= con
)
2808 graph
->src_scc
= graph
->edge
[i
].src
->scc
;
2809 graph
->dst_scc
= graph
->edge
[i
].dst
->scc
;
2815 /* Check whether the next schedule row of the given node needs to be
2816 * non-trivial. Lower-dimensional domains may have some trivial rows,
2817 * but as soon as the number of remaining required non-trivial rows
2818 * is as large as the number or remaining rows to be computed,
2819 * all remaining rows need to be non-trivial.
2821 static int needs_row(struct isl_sched_graph
*graph
, struct isl_sched_node
*node
)
2823 return node
->nvar
- node
->rank
>= graph
->maxvar
- graph
->n_row
;
2826 /* Construct a non-triviality region with triviality directions
2827 * corresponding to the rows of "indep".
2828 * The rows of "indep" are expressed in terms of the schedule coefficients c_i,
2829 * while the triviality directions are expressed in terms of
2830 * pairs of non-negative variables c^+_i - c^-_i, with c^-_i appearing
2831 * before c^+_i. Furthermore,
2832 * the pairs of non-negative variables representing the coefficients
2833 * are stored in the opposite order.
2835 static __isl_give isl_mat
*construct_trivial(__isl_keep isl_mat
*indep
)
2844 ctx
= isl_mat_get_ctx(indep
);
2845 n
= isl_mat_rows(indep
);
2846 n_var
= isl_mat_cols(indep
);
2847 mat
= isl_mat_alloc(ctx
, n
, 2 * n_var
);
2850 for (i
= 0; i
< n
; ++i
) {
2851 for (j
= 0; j
< n_var
; ++j
) {
2852 int nj
= n_var
- 1 - j
;
2853 isl_int_neg(mat
->row
[i
][2 * nj
], indep
->row
[i
][j
]);
2854 isl_int_set(mat
->row
[i
][2 * nj
+ 1], indep
->row
[i
][j
]);
2861 /* Solve the ILP problem constructed in setup_lp.
2862 * For each node such that all the remaining rows of its schedule
2863 * need to be non-trivial, we construct a non-triviality region.
2864 * This region imposes that the next row is independent of previous rows.
2865 * In particular, the non-triviality region enforces that at least
2866 * one of the linear combinations in the rows of node->indep is non-zero.
2868 static __isl_give isl_vec
*solve_lp(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2874 for (i
= 0; i
< graph
->n
; ++i
) {
2875 struct isl_sched_node
*node
= &graph
->node
[i
];
2878 graph
->region
[i
].pos
= node_var_coef_offset(node
);
2879 if (needs_row(graph
, node
))
2880 trivial
= construct_trivial(node
->indep
);
2882 trivial
= isl_mat_zero(ctx
, 0, 0);
2883 graph
->region
[i
].trivial
= trivial
;
2885 lp
= isl_basic_set_copy(graph
->lp
);
2886 sol
= isl_tab_basic_set_non_trivial_lexmin(lp
, 2, graph
->n
,
2887 graph
->region
, &check_conflict
, graph
);
2888 for (i
= 0; i
< graph
->n
; ++i
)
2889 isl_mat_free(graph
->region
[i
].trivial
);
2893 /* Extract the coefficients for the variables of "node" from "sol".
2895 * Each schedule coefficient c_i_x is represented as the difference
2896 * between two non-negative variables c_i_x^+ - c_i_x^-.
2897 * The c_i_x^- appear before their c_i_x^+ counterpart.
2898 * Furthermore, the order of these pairs is the opposite of that
2899 * of the corresponding coefficients.
2901 * Return c_i_x = c_i_x^+ - c_i_x^-
2903 static __isl_give isl_vec
*extract_var_coef(struct isl_sched_node
*node
,
2904 __isl_keep isl_vec
*sol
)
2912 csol
= isl_vec_alloc(isl_vec_get_ctx(sol
), node
->nvar
);
2916 pos
= 1 + node_var_coef_offset(node
);
2917 for (i
= 0; i
< node
->nvar
; ++i
)
2918 isl_int_sub(csol
->el
[node
->nvar
- 1 - i
],
2919 sol
->el
[pos
+ 2 * i
+ 1], sol
->el
[pos
+ 2 * i
]);
2924 /* Update the schedules of all nodes based on the given solution
2925 * of the LP problem.
2926 * The new row is added to the current band.
2927 * All possibly negative coefficients are encoded as a difference
2928 * of two non-negative variables, so we need to perform the subtraction
2931 * If coincident is set, then the caller guarantees that the new
2932 * row satisfies the coincidence constraints.
2934 static int update_schedule(struct isl_sched_graph
*graph
,
2935 __isl_take isl_vec
*sol
, int coincident
)
2938 isl_vec
*csol
= NULL
;
2943 isl_die(sol
->ctx
, isl_error_internal
,
2944 "no solution found", goto error
);
2945 if (graph
->n_total_row
>= graph
->max_row
)
2946 isl_die(sol
->ctx
, isl_error_internal
,
2947 "too many schedule rows", goto error
);
2949 for (i
= 0; i
< graph
->n
; ++i
) {
2950 struct isl_sched_node
*node
= &graph
->node
[i
];
2952 int row
= isl_mat_rows(node
->sched
);
2955 csol
= extract_var_coef(node
, sol
);
2959 isl_map_free(node
->sched_map
);
2960 node
->sched_map
= NULL
;
2961 node
->sched
= isl_mat_add_rows(node
->sched
, 1);
2964 pos
= node_cst_coef_offset(node
);
2965 node
->sched
= isl_mat_set_element(node
->sched
,
2966 row
, 0, sol
->el
[1 + pos
]);
2967 pos
= node_par_coef_offset(node
);
2968 for (j
= 0; j
< node
->nparam
; ++j
)
2969 node
->sched
= isl_mat_set_element(node
->sched
,
2970 row
, 1 + j
, sol
->el
[1 + pos
+ j
]);
2971 for (j
= 0; j
< node
->nvar
; ++j
)
2972 node
->sched
= isl_mat_set_element(node
->sched
,
2973 row
, 1 + node
->nparam
+ j
, csol
->el
[j
]);
2974 node
->coincident
[graph
->n_total_row
] = coincident
;
2980 graph
->n_total_row
++;
2989 /* Convert row "row" of node->sched into an isl_aff living in "ls"
2990 * and return this isl_aff.
2992 static __isl_give isl_aff
*extract_schedule_row(__isl_take isl_local_space
*ls
,
2993 struct isl_sched_node
*node
, int row
)
3001 aff
= isl_aff_zero_on_domain(ls
);
3002 if (isl_mat_get_element(node
->sched
, row
, 0, &v
) < 0)
3004 aff
= isl_aff_set_constant(aff
, v
);
3005 for (j
= 0; j
< node
->nparam
; ++j
) {
3006 if (isl_mat_get_element(node
->sched
, row
, 1 + j
, &v
) < 0)
3008 aff
= isl_aff_set_coefficient(aff
, isl_dim_param
, j
, v
);
3010 for (j
= 0; j
< node
->nvar
; ++j
) {
3011 if (isl_mat_get_element(node
->sched
, row
,
3012 1 + node
->nparam
+ j
, &v
) < 0)
3014 aff
= isl_aff_set_coefficient(aff
, isl_dim_in
, j
, v
);
3026 /* Convert the "n" rows starting at "first" of node->sched into a multi_aff
3027 * and return this multi_aff.
3029 * The result is defined over the uncompressed node domain.
3031 static __isl_give isl_multi_aff
*node_extract_partial_schedule_multi_aff(
3032 struct isl_sched_node
*node
, int first
, int n
)
3036 isl_local_space
*ls
;
3043 nrow
= isl_mat_rows(node
->sched
);
3044 if (node
->compressed
)
3045 space
= isl_multi_aff_get_domain_space(node
->decompress
);
3047 space
= isl_space_copy(node
->space
);
3048 ls
= isl_local_space_from_space(isl_space_copy(space
));
3049 space
= isl_space_from_domain(space
);
3050 space
= isl_space_add_dims(space
, isl_dim_out
, n
);
3051 ma
= isl_multi_aff_zero(space
);
3053 for (i
= first
; i
< first
+ n
; ++i
) {
3054 aff
= extract_schedule_row(isl_local_space_copy(ls
), node
, i
);
3055 ma
= isl_multi_aff_set_aff(ma
, i
- first
, aff
);
3058 isl_local_space_free(ls
);
3060 if (node
->compressed
)
3061 ma
= isl_multi_aff_pullback_multi_aff(ma
,
3062 isl_multi_aff_copy(node
->compress
));
3067 /* Convert node->sched into a multi_aff and return this multi_aff.
3069 * The result is defined over the uncompressed node domain.
3071 static __isl_give isl_multi_aff
*node_extract_schedule_multi_aff(
3072 struct isl_sched_node
*node
)
3076 nrow
= isl_mat_rows(node
->sched
);
3077 return node_extract_partial_schedule_multi_aff(node
, 0, nrow
);
3080 /* Convert node->sched into a map and return this map.
3082 * The result is cached in node->sched_map, which needs to be released
3083 * whenever node->sched is updated.
3084 * It is defined over the uncompressed node domain.
3086 static __isl_give isl_map
*node_extract_schedule(struct isl_sched_node
*node
)
3088 if (!node
->sched_map
) {
3091 ma
= node_extract_schedule_multi_aff(node
);
3092 node
->sched_map
= isl_map_from_multi_aff(ma
);
3095 return isl_map_copy(node
->sched_map
);
3098 /* Construct a map that can be used to update a dependence relation
3099 * based on the current schedule.
3100 * That is, construct a map expressing that source and sink
3101 * are executed within the same iteration of the current schedule.
3102 * This map can then be intersected with the dependence relation.
3103 * This is not the most efficient way, but this shouldn't be a critical
3106 static __isl_give isl_map
*specializer(struct isl_sched_node
*src
,
3107 struct isl_sched_node
*dst
)
3109 isl_map
*src_sched
, *dst_sched
;
3111 src_sched
= node_extract_schedule(src
);
3112 dst_sched
= node_extract_schedule(dst
);
3113 return isl_map_apply_range(src_sched
, isl_map_reverse(dst_sched
));
3116 /* Intersect the domains of the nested relations in domain and range
3117 * of "umap" with "map".
3119 static __isl_give isl_union_map
*intersect_domains(
3120 __isl_take isl_union_map
*umap
, __isl_keep isl_map
*map
)
3122 isl_union_set
*uset
;
3124 umap
= isl_union_map_zip(umap
);
3125 uset
= isl_union_set_from_set(isl_map_wrap(isl_map_copy(map
)));
3126 umap
= isl_union_map_intersect_domain(umap
, uset
);
3127 umap
= isl_union_map_zip(umap
);
3131 /* Update the dependence relation of the given edge based
3132 * on the current schedule.
3133 * If the dependence is carried completely by the current schedule, then
3134 * it is removed from the edge_tables. It is kept in the list of edges
3135 * as otherwise all edge_tables would have to be recomputed.
3137 * If the edge is of a type that can appear multiple times
3138 * between the same pair of nodes, then it is added to
3139 * the edge table (again). This prevents the situation
3140 * where none of these edges is referenced from the edge table
3141 * because the one that was referenced turned out to be empty and
3142 * was therefore removed from the table.
3144 static int update_edge(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
3145 struct isl_sched_edge
*edge
)
3150 id
= specializer(edge
->src
, edge
->dst
);
3151 edge
->map
= isl_map_intersect(edge
->map
, isl_map_copy(id
));
3155 if (edge
->tagged_condition
) {
3156 edge
->tagged_condition
=
3157 intersect_domains(edge
->tagged_condition
, id
);
3158 if (!edge
->tagged_condition
)
3161 if (edge
->tagged_validity
) {
3162 edge
->tagged_validity
=
3163 intersect_domains(edge
->tagged_validity
, id
);
3164 if (!edge
->tagged_validity
)
3168 empty
= isl_map_plain_is_empty(edge
->map
);
3172 graph_remove_edge(graph
, edge
);
3173 } else if (is_multi_edge_type(edge
)) {
3174 if (graph_edge_tables_add(ctx
, graph
, edge
) < 0)
3185 /* Does the domain of "umap" intersect "uset"?
3187 static int domain_intersects(__isl_keep isl_union_map
*umap
,
3188 __isl_keep isl_union_set
*uset
)
3192 umap
= isl_union_map_copy(umap
);
3193 umap
= isl_union_map_intersect_domain(umap
, isl_union_set_copy(uset
));
3194 empty
= isl_union_map_is_empty(umap
);
3195 isl_union_map_free(umap
);
3197 return empty
< 0 ? -1 : !empty
;
3200 /* Does the range of "umap" intersect "uset"?
3202 static int range_intersects(__isl_keep isl_union_map
*umap
,
3203 __isl_keep isl_union_set
*uset
)
3207 umap
= isl_union_map_copy(umap
);
3208 umap
= isl_union_map_intersect_range(umap
, isl_union_set_copy(uset
));
3209 empty
= isl_union_map_is_empty(umap
);
3210 isl_union_map_free(umap
);
3212 return empty
< 0 ? -1 : !empty
;
3215 /* Are the condition dependences of "edge" local with respect to
3216 * the current schedule?
3218 * That is, are domain and range of the condition dependences mapped
3219 * to the same point?
3221 * In other words, is the condition false?
3223 static int is_condition_false(struct isl_sched_edge
*edge
)
3225 isl_union_map
*umap
;
3226 isl_map
*map
, *sched
, *test
;
3229 empty
= isl_union_map_is_empty(edge
->tagged_condition
);
3230 if (empty
< 0 || empty
)
3233 umap
= isl_union_map_copy(edge
->tagged_condition
);
3234 umap
= isl_union_map_zip(umap
);
3235 umap
= isl_union_set_unwrap(isl_union_map_domain(umap
));
3236 map
= isl_map_from_union_map(umap
);
3238 sched
= node_extract_schedule(edge
->src
);
3239 map
= isl_map_apply_domain(map
, sched
);
3240 sched
= node_extract_schedule(edge
->dst
);
3241 map
= isl_map_apply_range(map
, sched
);
3243 test
= isl_map_identity(isl_map_get_space(map
));
3244 local
= isl_map_is_subset(map
, test
);
3251 /* For each conditional validity constraint that is adjacent
3252 * to a condition with domain in condition_source or range in condition_sink,
3253 * turn it into an unconditional validity constraint.
3255 static int unconditionalize_adjacent_validity(struct isl_sched_graph
*graph
,
3256 __isl_take isl_union_set
*condition_source
,
3257 __isl_take isl_union_set
*condition_sink
)
3261 condition_source
= isl_union_set_coalesce(condition_source
);
3262 condition_sink
= isl_union_set_coalesce(condition_sink
);
3264 for (i
= 0; i
< graph
->n_edge
; ++i
) {
3266 isl_union_map
*validity
;
3268 if (!is_conditional_validity(&graph
->edge
[i
]))
3270 if (is_validity(&graph
->edge
[i
]))
3273 validity
= graph
->edge
[i
].tagged_validity
;
3274 adjacent
= domain_intersects(validity
, condition_sink
);
3275 if (adjacent
>= 0 && !adjacent
)
3276 adjacent
= range_intersects(validity
, condition_source
);
3282 set_validity(&graph
->edge
[i
]);
3285 isl_union_set_free(condition_source
);
3286 isl_union_set_free(condition_sink
);
3289 isl_union_set_free(condition_source
);
3290 isl_union_set_free(condition_sink
);
3294 /* Update the dependence relations of all edges based on the current schedule
3295 * and enforce conditional validity constraints that are adjacent
3296 * to satisfied condition constraints.
3298 * First check if any of the condition constraints are satisfied
3299 * (i.e., not local to the outer schedule) and keep track of
3300 * their domain and range.
3301 * Then update all dependence relations (which removes the non-local
3303 * Finally, if any condition constraints turned out to be satisfied,
3304 * then turn all adjacent conditional validity constraints into
3305 * unconditional validity constraints.
3307 static int update_edges(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
3311 isl_union_set
*source
, *sink
;
3313 source
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
3314 sink
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
3315 for (i
= 0; i
< graph
->n_edge
; ++i
) {
3317 isl_union_set
*uset
;
3318 isl_union_map
*umap
;
3320 if (!is_condition(&graph
->edge
[i
]))
3322 if (is_local(&graph
->edge
[i
]))
3324 local
= is_condition_false(&graph
->edge
[i
]);
3332 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_condition
);
3333 uset
= isl_union_map_domain(umap
);
3334 source
= isl_union_set_union(source
, uset
);
3336 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_condition
);
3337 uset
= isl_union_map_range(umap
);
3338 sink
= isl_union_set_union(sink
, uset
);
3341 for (i
= 0; i
< graph
->n_edge
; ++i
) {
3342 if (update_edge(ctx
, graph
, &graph
->edge
[i
]) < 0)
3347 return unconditionalize_adjacent_validity(graph
, source
, sink
);
3349 isl_union_set_free(source
);
3350 isl_union_set_free(sink
);
3353 isl_union_set_free(source
);
3354 isl_union_set_free(sink
);
3358 static void next_band(struct isl_sched_graph
*graph
)
3360 graph
->band_start
= graph
->n_total_row
;
3363 /* Return the union of the universe domains of the nodes in "graph"
3364 * that satisfy "pred".
3366 static __isl_give isl_union_set
*isl_sched_graph_domain(isl_ctx
*ctx
,
3367 struct isl_sched_graph
*graph
,
3368 int (*pred
)(struct isl_sched_node
*node
, int data
), int data
)
3374 for (i
= 0; i
< graph
->n
; ++i
)
3375 if (pred(&graph
->node
[i
], data
))
3379 isl_die(ctx
, isl_error_internal
,
3380 "empty component", return NULL
);
3382 set
= isl_set_universe(isl_space_copy(graph
->node
[i
].space
));
3383 dom
= isl_union_set_from_set(set
);
3385 for (i
= i
+ 1; i
< graph
->n
; ++i
) {
3386 if (!pred(&graph
->node
[i
], data
))
3388 set
= isl_set_universe(isl_space_copy(graph
->node
[i
].space
));
3389 dom
= isl_union_set_union(dom
, isl_union_set_from_set(set
));
3395 /* Return a list of unions of universe domains, where each element
3396 * in the list corresponds to an SCC (or WCC) indexed by node->scc.
3398 static __isl_give isl_union_set_list
*extract_sccs(isl_ctx
*ctx
,
3399 struct isl_sched_graph
*graph
)
3402 isl_union_set_list
*filters
;
3404 filters
= isl_union_set_list_alloc(ctx
, graph
->scc
);
3405 for (i
= 0; i
< graph
->scc
; ++i
) {
3408 dom
= isl_sched_graph_domain(ctx
, graph
, &node_scc_exactly
, i
);
3409 filters
= isl_union_set_list_add(filters
, dom
);
3415 /* Return a list of two unions of universe domains, one for the SCCs up
3416 * to and including graph->src_scc and another for the other SCCs.
3418 static __isl_give isl_union_set_list
*extract_split(isl_ctx
*ctx
,
3419 struct isl_sched_graph
*graph
)
3422 isl_union_set_list
*filters
;
3424 filters
= isl_union_set_list_alloc(ctx
, 2);
3425 dom
= isl_sched_graph_domain(ctx
, graph
,
3426 &node_scc_at_most
, graph
->src_scc
);
3427 filters
= isl_union_set_list_add(filters
, dom
);
3428 dom
= isl_sched_graph_domain(ctx
, graph
,
3429 &node_scc_at_least
, graph
->src_scc
+ 1);
3430 filters
= isl_union_set_list_add(filters
, dom
);
3435 /* Copy nodes that satisfy node_pred from the src dependence graph
3436 * to the dst dependence graph.
3438 static isl_stat
copy_nodes(struct isl_sched_graph
*dst
,
3439 struct isl_sched_graph
*src
,
3440 int (*node_pred
)(struct isl_sched_node
*node
, int data
), int data
)
3445 for (i
= 0; i
< src
->n
; ++i
) {
3448 if (!node_pred(&src
->node
[i
], data
))
3452 dst
->node
[j
].space
= isl_space_copy(src
->node
[i
].space
);
3453 dst
->node
[j
].compressed
= src
->node
[i
].compressed
;
3454 dst
->node
[j
].hull
= isl_set_copy(src
->node
[i
].hull
);
3455 dst
->node
[j
].compress
=
3456 isl_multi_aff_copy(src
->node
[i
].compress
);
3457 dst
->node
[j
].decompress
=
3458 isl_multi_aff_copy(src
->node
[i
].decompress
);
3459 dst
->node
[j
].nvar
= src
->node
[i
].nvar
;
3460 dst
->node
[j
].nparam
= src
->node
[i
].nparam
;
3461 dst
->node
[j
].sched
= isl_mat_copy(src
->node
[i
].sched
);
3462 dst
->node
[j
].sched_map
= isl_map_copy(src
->node
[i
].sched_map
);
3463 dst
->node
[j
].coincident
= src
->node
[i
].coincident
;
3464 dst
->node
[j
].sizes
= isl_multi_val_copy(src
->node
[i
].sizes
);
3465 dst
->node
[j
].bounds
= isl_basic_set_copy(src
->node
[i
].bounds
);
3466 dst
->node
[j
].max
= isl_vec_copy(src
->node
[i
].max
);
3469 if (!dst
->node
[j
].space
|| !dst
->node
[j
].sched
)
3470 return isl_stat_error
;
3471 if (dst
->node
[j
].compressed
&&
3472 (!dst
->node
[j
].hull
|| !dst
->node
[j
].compress
||
3473 !dst
->node
[j
].decompress
))
3474 return isl_stat_error
;
3480 /* Copy non-empty edges that satisfy edge_pred from the src dependence graph
3481 * to the dst dependence graph.
3482 * If the source or destination node of the edge is not in the destination
3483 * graph, then it must be a backward proximity edge and it should simply
3486 static int copy_edges(isl_ctx
*ctx
, struct isl_sched_graph
*dst
,
3487 struct isl_sched_graph
*src
,
3488 int (*edge_pred
)(struct isl_sched_edge
*edge
, int data
), int data
)
3493 for (i
= 0; i
< src
->n_edge
; ++i
) {
3494 struct isl_sched_edge
*edge
= &src
->edge
[i
];
3496 isl_union_map
*tagged_condition
;
3497 isl_union_map
*tagged_validity
;
3498 struct isl_sched_node
*dst_src
, *dst_dst
;
3500 if (!edge_pred(edge
, data
))
3503 if (isl_map_plain_is_empty(edge
->map
))
3506 dst_src
= graph_find_node(ctx
, dst
, edge
->src
->space
);
3507 dst_dst
= graph_find_node(ctx
, dst
, edge
->dst
->space
);
3508 if (!dst_src
|| !dst_dst
) {
3509 if (is_validity(edge
) || is_conditional_validity(edge
))
3510 isl_die(ctx
, isl_error_internal
,
3511 "backward (conditional) validity edge",
3516 map
= isl_map_copy(edge
->map
);
3517 tagged_condition
= isl_union_map_copy(edge
->tagged_condition
);
3518 tagged_validity
= isl_union_map_copy(edge
->tagged_validity
);
3520 dst
->edge
[dst
->n_edge
].src
= dst_src
;
3521 dst
->edge
[dst
->n_edge
].dst
= dst_dst
;
3522 dst
->edge
[dst
->n_edge
].map
= map
;
3523 dst
->edge
[dst
->n_edge
].tagged_condition
= tagged_condition
;
3524 dst
->edge
[dst
->n_edge
].tagged_validity
= tagged_validity
;
3525 dst
->edge
[dst
->n_edge
].types
= edge
->types
;
3528 if (edge
->tagged_condition
&& !tagged_condition
)
3530 if (edge
->tagged_validity
&& !tagged_validity
)
3533 if (graph_edge_tables_add(ctx
, dst
,
3534 &dst
->edge
[dst
->n_edge
- 1]) < 0)
3541 /* Compute the maximal number of variables over all nodes.
3542 * This is the maximal number of linearly independent schedule
3543 * rows that we need to compute.
3544 * Just in case we end up in a part of the dependence graph
3545 * with only lower-dimensional domains, we make sure we will
3546 * compute the required amount of extra linearly independent rows.
3548 static int compute_maxvar(struct isl_sched_graph
*graph
)
3553 for (i
= 0; i
< graph
->n
; ++i
) {
3554 struct isl_sched_node
*node
= &graph
->node
[i
];
3557 if (node_update_vmap(node
) < 0)
3559 nvar
= node
->nvar
+ graph
->n_row
- node
->rank
;
3560 if (nvar
> graph
->maxvar
)
3561 graph
->maxvar
= nvar
;
3567 /* Extract the subgraph of "graph" that consists of the nodes satisfying
3568 * "node_pred" and the edges satisfying "edge_pred" and store
3569 * the result in "sub".
3571 static int extract_sub_graph(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
3572 int (*node_pred
)(struct isl_sched_node
*node
, int data
),
3573 int (*edge_pred
)(struct isl_sched_edge
*edge
, int data
),
3574 int data
, struct isl_sched_graph
*sub
)
3576 int i
, n
= 0, n_edge
= 0;
3579 for (i
= 0; i
< graph
->n
; ++i
)
3580 if (node_pred(&graph
->node
[i
], data
))
3582 for (i
= 0; i
< graph
->n_edge
; ++i
)
3583 if (edge_pred(&graph
->edge
[i
], data
))
3585 if (graph_alloc(ctx
, sub
, n
, n_edge
) < 0)
3587 sub
->root
= graph
->root
;
3588 if (copy_nodes(sub
, graph
, node_pred
, data
) < 0)
3590 if (graph_init_table(ctx
, sub
) < 0)
3592 for (t
= 0; t
<= isl_edge_last
; ++t
)
3593 sub
->max_edge
[t
] = graph
->max_edge
[t
];
3594 if (graph_init_edge_tables(ctx
, sub
) < 0)
3596 if (copy_edges(ctx
, sub
, graph
, edge_pred
, data
) < 0)
3598 sub
->n_row
= graph
->n_row
;
3599 sub
->max_row
= graph
->max_row
;
3600 sub
->n_total_row
= graph
->n_total_row
;
3601 sub
->band_start
= graph
->band_start
;
3606 static __isl_give isl_schedule_node
*compute_schedule(isl_schedule_node
*node
,
3607 struct isl_sched_graph
*graph
);
3608 static __isl_give isl_schedule_node
*compute_schedule_wcc(
3609 isl_schedule_node
*node
, struct isl_sched_graph
*graph
);
3611 /* Compute a schedule for a subgraph of "graph". In particular, for
3612 * the graph composed of nodes that satisfy node_pred and edges that
3613 * that satisfy edge_pred.
3614 * If the subgraph is known to consist of a single component, then wcc should
3615 * be set and then we call compute_schedule_wcc on the constructed subgraph.
3616 * Otherwise, we call compute_schedule, which will check whether the subgraph
3619 * The schedule is inserted at "node" and the updated schedule node
3622 static __isl_give isl_schedule_node
*compute_sub_schedule(
3623 __isl_take isl_schedule_node
*node
, isl_ctx
*ctx
,
3624 struct isl_sched_graph
*graph
,
3625 int (*node_pred
)(struct isl_sched_node
*node
, int data
),
3626 int (*edge_pred
)(struct isl_sched_edge
*edge
, int data
),
3629 struct isl_sched_graph split
= { 0 };
3631 if (extract_sub_graph(ctx
, graph
, node_pred
, edge_pred
, data
,
3636 node
= compute_schedule_wcc(node
, &split
);
3638 node
= compute_schedule(node
, &split
);
3640 graph_free(ctx
, &split
);
3643 graph_free(ctx
, &split
);
3644 return isl_schedule_node_free(node
);
3647 static int edge_scc_exactly(struct isl_sched_edge
*edge
, int scc
)
3649 return edge
->src
->scc
== scc
&& edge
->dst
->scc
== scc
;
3652 static int edge_dst_scc_at_most(struct isl_sched_edge
*edge
, int scc
)
3654 return edge
->dst
->scc
<= scc
;
3657 static int edge_src_scc_at_least(struct isl_sched_edge
*edge
, int scc
)
3659 return edge
->src
->scc
>= scc
;
3662 /* Reset the current band by dropping all its schedule rows.
3664 static isl_stat
reset_band(struct isl_sched_graph
*graph
)
3669 drop
= graph
->n_total_row
- graph
->band_start
;
3670 graph
->n_total_row
-= drop
;
3671 graph
->n_row
-= drop
;
3673 for (i
= 0; i
< graph
->n
; ++i
) {
3674 struct isl_sched_node
*node
= &graph
->node
[i
];
3676 isl_map_free(node
->sched_map
);
3677 node
->sched_map
= NULL
;
3679 node
->sched
= isl_mat_drop_rows(node
->sched
,
3680 graph
->band_start
, drop
);
3683 return isl_stat_error
;
3689 /* Split the current graph into two parts and compute a schedule for each
3690 * part individually. In particular, one part consists of all SCCs up
3691 * to and including graph->src_scc, while the other part contains the other
3692 * SCCs. The split is enforced by a sequence node inserted at position "node"
3693 * in the schedule tree. Return the updated schedule node.
3694 * If either of these two parts consists of a sequence, then it is spliced
3695 * into the sequence containing the two parts.
3697 * The current band is reset. It would be possible to reuse
3698 * the previously computed rows as the first rows in the next
3699 * band, but recomputing them may result in better rows as we are looking
3700 * at a smaller part of the dependence graph.
3702 static __isl_give isl_schedule_node
*compute_split_schedule(
3703 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
3707 isl_union_set_list
*filters
;
3712 if (reset_band(graph
) < 0)
3713 return isl_schedule_node_free(node
);
3717 ctx
= isl_schedule_node_get_ctx(node
);
3718 filters
= extract_split(ctx
, graph
);
3719 node
= isl_schedule_node_insert_sequence(node
, filters
);
3720 node
= isl_schedule_node_child(node
, 1);
3721 node
= isl_schedule_node_child(node
, 0);
3723 node
= compute_sub_schedule(node
, ctx
, graph
,
3724 &node_scc_at_least
, &edge_src_scc_at_least
,
3725 graph
->src_scc
+ 1, 0);
3726 is_seq
= isl_schedule_node_get_type(node
) == isl_schedule_node_sequence
;
3727 node
= isl_schedule_node_parent(node
);
3728 node
= isl_schedule_node_parent(node
);
3730 node
= isl_schedule_node_sequence_splice_child(node
, 1);
3731 node
= isl_schedule_node_child(node
, 0);
3732 node
= isl_schedule_node_child(node
, 0);
3733 node
= compute_sub_schedule(node
, ctx
, graph
,
3734 &node_scc_at_most
, &edge_dst_scc_at_most
,
3736 is_seq
= isl_schedule_node_get_type(node
) == isl_schedule_node_sequence
;
3737 node
= isl_schedule_node_parent(node
);
3738 node
= isl_schedule_node_parent(node
);
3740 node
= isl_schedule_node_sequence_splice_child(node
, 0);
3745 /* Insert a band node at position "node" in the schedule tree corresponding
3746 * to the current band in "graph". Mark the band node permutable
3747 * if "permutable" is set.
3748 * The partial schedules and the coincidence property are extracted
3749 * from the graph nodes.
3750 * Return the updated schedule node.
3752 static __isl_give isl_schedule_node
*insert_current_band(
3753 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
3759 isl_multi_pw_aff
*mpa
;
3760 isl_multi_union_pw_aff
*mupa
;
3766 isl_die(isl_schedule_node_get_ctx(node
), isl_error_internal
,
3767 "graph should have at least one node",
3768 return isl_schedule_node_free(node
));
3770 start
= graph
->band_start
;
3771 end
= graph
->n_total_row
;
3774 ma
= node_extract_partial_schedule_multi_aff(&graph
->node
[0], start
, n
);
3775 mpa
= isl_multi_pw_aff_from_multi_aff(ma
);
3776 mupa
= isl_multi_union_pw_aff_from_multi_pw_aff(mpa
);
3778 for (i
= 1; i
< graph
->n
; ++i
) {
3779 isl_multi_union_pw_aff
*mupa_i
;
3781 ma
= node_extract_partial_schedule_multi_aff(&graph
->node
[i
],
3783 mpa
= isl_multi_pw_aff_from_multi_aff(ma
);
3784 mupa_i
= isl_multi_union_pw_aff_from_multi_pw_aff(mpa
);
3785 mupa
= isl_multi_union_pw_aff_union_add(mupa
, mupa_i
);
3787 node
= isl_schedule_node_insert_partial_schedule(node
, mupa
);
3789 for (i
= 0; i
< n
; ++i
)
3790 node
= isl_schedule_node_band_member_set_coincident(node
, i
,
3791 graph
->node
[0].coincident
[start
+ i
]);
3792 node
= isl_schedule_node_band_set_permutable(node
, permutable
);
3797 /* Update the dependence relations based on the current schedule,
3798 * add the current band to "node" and then continue with the computation
3800 * Return the updated schedule node.
3802 static __isl_give isl_schedule_node
*compute_next_band(
3803 __isl_take isl_schedule_node
*node
,
3804 struct isl_sched_graph
*graph
, int permutable
)
3811 ctx
= isl_schedule_node_get_ctx(node
);
3812 if (update_edges(ctx
, graph
) < 0)
3813 return isl_schedule_node_free(node
);
3814 node
= insert_current_band(node
, graph
, permutable
);
3817 node
= isl_schedule_node_child(node
, 0);
3818 node
= compute_schedule(node
, graph
);
3819 node
= isl_schedule_node_parent(node
);
3824 /* Add the constraints "coef" derived from an edge from "node" to itself
3825 * to graph->lp in order to respect the dependences and to try and carry them.
3826 * "pos" is the sequence number of the edge that needs to be carried.
3827 * "coef" represents general constraints on coefficients (c_0, c_x)
3828 * of valid constraints for (y - x) with x and y instances of the node.
3830 * The constraints added to graph->lp need to enforce
3832 * (c_j_0 + c_j_x y) - (c_j_0 + c_j_x x)
3833 * = c_j_x (y - x) >= e_i
3835 * for each (x,y) in the dependence relation of the edge.
3836 * That is, (-e_i, c_j_x) needs to be plugged in for (c_0, c_x),
3837 * taking into account that each coefficient in c_j_x is represented
3838 * as a pair of non-negative coefficients.
3840 static isl_stat
add_intra_constraints(struct isl_sched_graph
*graph
,
3841 struct isl_sched_node
*node
, __isl_take isl_basic_set
*coef
, int pos
)
3845 isl_dim_map
*dim_map
;
3848 return isl_stat_error
;
3850 ctx
= isl_basic_set_get_ctx(coef
);
3851 offset
= coef_var_offset(coef
);
3852 dim_map
= intra_dim_map(ctx
, graph
, node
, offset
, 1);
3853 isl_dim_map_range(dim_map
, 3 + pos
, 0, 0, 0, 1, -1);
3854 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
3859 /* Add the constraints "coef" derived from an edge from "src" to "dst"
3860 * to graph->lp in order to respect the dependences and to try and carry them.
3861 * "pos" is the sequence number of the edge that needs to be carried or
3862 * -1 if no attempt should be made to carry the dependences.
3863 * "coef" represents general constraints on coefficients (c_0, c_n, c_x, c_y)
3864 * of valid constraints for (x, y) with x and y instances of "src" and "dst".
3866 * The constraints added to graph->lp need to enforce
3868 * (c_k_0 + c_k_n n + c_k_x y) - (c_j_0 + c_j_n n + c_j_x x) >= e_i
3870 * for each (x,y) in the dependence relation of the edge or
3872 * (c_k_0 + c_k_n n + c_k_x y) - (c_j_0 + c_j_n n + c_j_x x) >= 0
3876 * (-e_i + c_k_0 - c_j_0, c_k_n - c_j_n, -c_j_x, c_k_x)
3878 * (c_k_0 - c_j_0, c_k_n - c_j_n, -c_j_x, c_k_x)
3879 * needs to be plugged in for (c_0, c_n, c_x, c_y),
3880 * taking into account that each coefficient in c_j_x and c_k_x is represented
3881 * as a pair of non-negative coefficients.
3883 static isl_stat
add_inter_constraints(struct isl_sched_graph
*graph
,
3884 struct isl_sched_node
*src
, struct isl_sched_node
*dst
,
3885 __isl_take isl_basic_set
*coef
, int pos
)
3889 isl_dim_map
*dim_map
;
3892 return isl_stat_error
;
3894 ctx
= isl_basic_set_get_ctx(coef
);
3895 offset
= coef_var_offset(coef
);
3896 dim_map
= inter_dim_map(ctx
, graph
, src
, dst
, offset
, 1);
3898 isl_dim_map_range(dim_map
, 3 + pos
, 0, 0, 0, 1, -1);
3899 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
3904 /* Data structure for keeping track of the data needed
3905 * to exploit non-trivial lineality spaces.
3907 * "any_non_trivial" is true if there are any non-trivial lineality spaces.
3908 * If "any_non_trivial" is not true, then "equivalent" and "mask" may be NULL.
3909 * "equivalent" connects instances to other instances on the same line(s).
3910 * "mask" contains the domain spaces of "equivalent".
3911 * Any instance set not in "mask" does not have a non-trivial lineality space.
3913 struct isl_exploit_lineality_data
{
3914 isl_bool any_non_trivial
;
3915 isl_union_map
*equivalent
;
3916 isl_union_set
*mask
;
3919 /* Data structure collecting information used during the construction
3920 * of an LP for carrying dependences.
3922 * "intra" is a sequence of coefficient constraints for intra-node edges.
3923 * "inter" is a sequence of coefficient constraints for inter-node edges.
3924 * "lineality" contains data used to exploit non-trivial lineality spaces.
3927 isl_basic_set_list
*intra
;
3928 isl_basic_set_list
*inter
;
3929 struct isl_exploit_lineality_data lineality
;
3932 /* Free all the data stored in "carry".
3934 static void isl_carry_clear(struct isl_carry
*carry
)
3936 isl_basic_set_list_free(carry
->intra
);
3937 isl_basic_set_list_free(carry
->inter
);
3938 isl_union_map_free(carry
->lineality
.equivalent
);
3939 isl_union_set_free(carry
->lineality
.mask
);
3942 /* Return a pointer to the node in "graph" that lives in "space".
3943 * If the requested node has been compressed, then "space"
3944 * corresponds to the compressed space.
3946 * First try and see if "space" is the space of an uncompressed node.
3947 * If so, return that node.
3948 * Otherwise, "space" was constructed by construct_compressed_id and
3949 * contains a user pointer pointing to the node in the tuple id.
3950 * However, this node belongs to the original dependence graph.
3951 * If "graph" is a subgraph of this original dependence graph,
3952 * then the node with the same space still needs to be looked up
3953 * in the current graph.
3955 static struct isl_sched_node
*graph_find_compressed_node(isl_ctx
*ctx
,
3956 struct isl_sched_graph
*graph
, __isl_keep isl_space
*space
)
3959 struct isl_sched_node
*node
;
3964 node
= graph_find_node(ctx
, graph
, space
);
3968 id
= isl_space_get_tuple_id(space
, isl_dim_set
);
3969 node
= isl_id_get_user(id
);
3975 if (!is_node(graph
->root
, node
))
3976 isl_die(ctx
, isl_error_internal
,
3977 "space points to invalid node", return NULL
);
3978 if (graph
!= graph
->root
)
3979 node
= graph_find_node(ctx
, graph
, node
->space
);
3984 /* Internal data structure for add_all_constraints.
3986 * "graph" is the schedule constraint graph for which an LP problem
3987 * is being constructed.
3988 * "carry_inter" indicates whether inter-node edges should be carried.
3989 * "pos" is the position of the next edge that needs to be carried.
3991 struct isl_add_all_constraints_data
{
3993 struct isl_sched_graph
*graph
;
3998 /* Add the constraints "coef" derived from an edge from a node to itself
3999 * to data->graph->lp in order to respect the dependences and
4000 * to try and carry them.
4002 * The space of "coef" is of the form
4004 * coefficients[[c_cst] -> S[c_x]]
4006 * with S[c_x] the (compressed) space of the node.
4007 * Extract the node from the space and call add_intra_constraints.
4009 static isl_stat
lp_add_intra(__isl_take isl_basic_set
*coef
, void *user
)
4011 struct isl_add_all_constraints_data
*data
= user
;
4013 struct isl_sched_node
*node
;
4015 space
= isl_basic_set_get_space(coef
);
4016 space
= isl_space_range(isl_space_unwrap(space
));
4017 node
= graph_find_compressed_node(data
->ctx
, data
->graph
, space
);
4018 isl_space_free(space
);
4019 return add_intra_constraints(data
->graph
, node
, coef
, data
->pos
++);
4022 /* Add the constraints "coef" derived from an edge from a node j
4023 * to a node k to data->graph->lp in order to respect the dependences and
4024 * to try and carry them (provided data->carry_inter is set).
4026 * The space of "coef" is of the form
4028 * coefficients[[c_cst, c_n] -> [S_j[c_x] -> S_k[c_y]]]
4030 * with S_j[c_x] and S_k[c_y] the (compressed) spaces of the nodes.
4031 * Extract the nodes from the space and call add_inter_constraints.
4033 static isl_stat
lp_add_inter(__isl_take isl_basic_set
*coef
, void *user
)
4035 struct isl_add_all_constraints_data
*data
= user
;
4036 isl_space
*space
, *dom
;
4037 struct isl_sched_node
*src
, *dst
;
4040 space
= isl_basic_set_get_space(coef
);
4041 space
= isl_space_unwrap(isl_space_range(isl_space_unwrap(space
)));
4042 dom
= isl_space_domain(isl_space_copy(space
));
4043 src
= graph_find_compressed_node(data
->ctx
, data
->graph
, dom
);
4044 isl_space_free(dom
);
4045 space
= isl_space_range(space
);
4046 dst
= graph_find_compressed_node(data
->ctx
, data
->graph
, space
);
4047 isl_space_free(space
);
4049 pos
= data
->carry_inter
? data
->pos
++ : -1;
4050 return add_inter_constraints(data
->graph
, src
, dst
, coef
, pos
);
4053 /* Add constraints to graph->lp that force all (conditional) validity
4054 * dependences to be respected and attempt to carry them.
4055 * "intra" is the sequence of coefficient constraints for intra-node edges.
4056 * "inter" is the sequence of coefficient constraints for inter-node edges.
4057 * "carry_inter" indicates whether inter-node edges should be carried or
4060 static isl_stat
add_all_constraints(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
4061 __isl_keep isl_basic_set_list
*intra
,
4062 __isl_keep isl_basic_set_list
*inter
, int carry_inter
)
4064 struct isl_add_all_constraints_data data
= { ctx
, graph
, carry_inter
};
4067 if (isl_basic_set_list_foreach(intra
, &lp_add_intra
, &data
) < 0)
4068 return isl_stat_error
;
4069 if (isl_basic_set_list_foreach(inter
, &lp_add_inter
, &data
) < 0)
4070 return isl_stat_error
;
4074 /* Internal data structure for count_all_constraints
4075 * for keeping track of the number of equality and inequality constraints.
4077 struct isl_sched_count
{
4082 /* Add the number of equality and inequality constraints of "bset"
4083 * to data->n_eq and data->n_ineq.
4085 static isl_stat
bset_update_count(__isl_take isl_basic_set
*bset
, void *user
)
4087 struct isl_sched_count
*data
= user
;
4089 return update_count(bset
, 1, &data
->n_eq
, &data
->n_ineq
);
4092 /* Count the number of equality and inequality constraints
4093 * that will be added to the carry_lp problem.
4094 * We count each edge exactly once.
4095 * "intra" is the sequence of coefficient constraints for intra-node edges.
4096 * "inter" is the sequence of coefficient constraints for inter-node edges.
4098 static isl_stat
count_all_constraints(__isl_keep isl_basic_set_list
*intra
,
4099 __isl_keep isl_basic_set_list
*inter
, int *n_eq
, int *n_ineq
)
4101 struct isl_sched_count data
;
4103 data
.n_eq
= data
.n_ineq
= 0;
4104 if (isl_basic_set_list_foreach(inter
, &bset_update_count
, &data
) < 0)
4105 return isl_stat_error
;
4106 if (isl_basic_set_list_foreach(intra
, &bset_update_count
, &data
) < 0)
4107 return isl_stat_error
;
4110 *n_ineq
= data
.n_ineq
;
4115 /* Construct an LP problem for finding schedule coefficients
4116 * such that the schedule carries as many validity dependences as possible.
4117 * In particular, for each dependence i, we bound the dependence distance
4118 * from below by e_i, with 0 <= e_i <= 1 and then maximize the sum
4119 * of all e_i's. Dependences with e_i = 0 in the solution are simply
4120 * respected, while those with e_i > 0 (in practice e_i = 1) are carried.
4121 * "intra" is the sequence of coefficient constraints for intra-node edges.
4122 * "inter" is the sequence of coefficient constraints for inter-node edges.
4123 * "n_edge" is the total number of edges.
4124 * "carry_inter" indicates whether inter-node edges should be carried or
4125 * only respected. That is, if "carry_inter" is not set, then
4126 * no e_i variables are introduced for the inter-node edges.
4128 * All variables of the LP are non-negative. The actual coefficients
4129 * may be negative, so each coefficient is represented as the difference
4130 * of two non-negative variables. The negative part always appears
4131 * immediately before the positive part.
4132 * Other than that, the variables have the following order
4134 * - sum of (1 - e_i) over all edges
4135 * - sum of all c_n coefficients
4136 * (unconstrained when computing non-parametric schedules)
4137 * - sum of positive and negative parts of all c_x coefficients
4141 * - positive and negative parts of c_i_x, in opposite order
4142 * - c_i_n (if parametric)
4145 * The constraints are those from the (validity) edges plus three equalities
4146 * to express the sums and n_edge inequalities to express e_i <= 1.
4148 static isl_stat
setup_carry_lp(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
4149 int n_edge
, __isl_keep isl_basic_set_list
*intra
,
4150 __isl_keep isl_basic_set_list
*inter
, int carry_inter
)
4159 for (i
= 0; i
< graph
->n
; ++i
) {
4160 struct isl_sched_node
*node
= &graph
->node
[graph
->sorted
[i
]];
4161 node
->start
= total
;
4162 total
+= 1 + node
->nparam
+ 2 * node
->nvar
;
4165 if (count_all_constraints(intra
, inter
, &n_eq
, &n_ineq
) < 0)
4166 return isl_stat_error
;
4168 dim
= isl_space_set_alloc(ctx
, 0, total
);
4169 isl_basic_set_free(graph
->lp
);
4172 graph
->lp
= isl_basic_set_alloc_space(dim
, 0, n_eq
, n_ineq
);
4173 graph
->lp
= isl_basic_set_set_rational(graph
->lp
);
4175 k
= isl_basic_set_alloc_equality(graph
->lp
);
4177 return isl_stat_error
;
4178 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
4179 isl_int_set_si(graph
->lp
->eq
[k
][0], -n_edge
);
4180 isl_int_set_si(graph
->lp
->eq
[k
][1], 1);
4181 for (i
= 0; i
< n_edge
; ++i
)
4182 isl_int_set_si(graph
->lp
->eq
[k
][4 + i
], 1);
4184 if (add_param_sum_constraint(graph
, 1) < 0)
4185 return isl_stat_error
;
4186 if (add_var_sum_constraint(graph
, 2) < 0)
4187 return isl_stat_error
;
4189 for (i
= 0; i
< n_edge
; ++i
) {
4190 k
= isl_basic_set_alloc_inequality(graph
->lp
);
4192 return isl_stat_error
;
4193 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
4194 isl_int_set_si(graph
->lp
->ineq
[k
][4 + i
], -1);
4195 isl_int_set_si(graph
->lp
->ineq
[k
][0], 1);
4198 if (add_all_constraints(ctx
, graph
, intra
, inter
, carry_inter
) < 0)
4199 return isl_stat_error
;
4204 static __isl_give isl_schedule_node
*compute_component_schedule(
4205 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
4208 /* If the schedule_split_scaled option is set and if the linear
4209 * parts of the scheduling rows for all nodes in the graphs have
4210 * a non-trivial common divisor, then remove this
4211 * common divisor from the linear part.
4212 * Otherwise, insert a band node directly and continue with
4213 * the construction of the schedule.
4215 * If a non-trivial common divisor is found, then
4216 * the linear part is reduced and the remainder is ignored.
4217 * The pieces of the graph that are assigned different remainders
4218 * form (groups of) strongly connected components within
4219 * the scaled down band. If needed, they can therefore
4220 * be ordered along this remainder in a sequence node.
4221 * However, this ordering is not enforced here in order to allow
4222 * the scheduler to combine some of the strongly connected components.
4224 static __isl_give isl_schedule_node
*split_scaled(
4225 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
4235 ctx
= isl_schedule_node_get_ctx(node
);
4236 if (!ctx
->opt
->schedule_split_scaled
)
4237 return compute_next_band(node
, graph
, 0);
4239 return compute_next_band(node
, graph
, 0);
4242 isl_int_init(gcd_i
);
4244 isl_int_set_si(gcd
, 0);
4246 row
= isl_mat_rows(graph
->node
[0].sched
) - 1;
4248 for (i
= 0; i
< graph
->n
; ++i
) {
4249 struct isl_sched_node
*node
= &graph
->node
[i
];
4250 int cols
= isl_mat_cols(node
->sched
);
4252 isl_seq_gcd(node
->sched
->row
[row
] + 1, cols
- 1, &gcd_i
);
4253 isl_int_gcd(gcd
, gcd
, gcd_i
);
4256 isl_int_clear(gcd_i
);
4258 if (isl_int_cmp_si(gcd
, 1) <= 0) {
4260 return compute_next_band(node
, graph
, 0);
4263 for (i
= 0; i
< graph
->n
; ++i
) {
4264 struct isl_sched_node
*node
= &graph
->node
[i
];
4266 isl_int_fdiv_q(node
->sched
->row
[row
][0],
4267 node
->sched
->row
[row
][0], gcd
);
4268 isl_int_mul(node
->sched
->row
[row
][0],
4269 node
->sched
->row
[row
][0], gcd
);
4270 node
->sched
= isl_mat_scale_down_row(node
->sched
, row
, gcd
);
4277 return compute_next_band(node
, graph
, 0);
4280 return isl_schedule_node_free(node
);
4283 /* Is the schedule row "sol" trivial on node "node"?
4284 * That is, is the solution zero on the dimensions linearly independent of
4285 * the previously found solutions?
4286 * Return 1 if the solution is trivial, 0 if it is not and -1 on error.
4288 * Each coefficient is represented as the difference between
4289 * two non-negative values in "sol".
4290 * We construct the schedule row s and check if it is linearly
4291 * independent of previously computed schedule rows
4292 * by computing T s, with T the linear combinations that are zero
4293 * on linearly dependent schedule rows.
4294 * If the result consists of all zeros, then the solution is trivial.
4296 static int is_trivial(struct isl_sched_node
*node
, __isl_keep isl_vec
*sol
)
4303 if (node
->nvar
== node
->rank
)
4306 node_sol
= extract_var_coef(node
, sol
);
4307 node_sol
= isl_mat_vec_product(isl_mat_copy(node
->indep
), node_sol
);
4311 trivial
= isl_seq_first_non_zero(node_sol
->el
,
4312 node
->nvar
- node
->rank
) == -1;
4314 isl_vec_free(node_sol
);
4319 /* Is the schedule row "sol" trivial on any node where it should
4321 * Return 1 if any solution is trivial, 0 if they are not and -1 on error.
4323 static int is_any_trivial(struct isl_sched_graph
*graph
,
4324 __isl_keep isl_vec
*sol
)
4328 for (i
= 0; i
< graph
->n
; ++i
) {
4329 struct isl_sched_node
*node
= &graph
->node
[i
];
4332 if (!needs_row(graph
, node
))
4334 trivial
= is_trivial(node
, sol
);
4335 if (trivial
< 0 || trivial
)
4342 /* Does the schedule represented by "sol" perform loop coalescing on "node"?
4343 * If so, return the position of the coalesced dimension.
4344 * Otherwise, return node->nvar or -1 on error.
4346 * In particular, look for pairs of coefficients c_i and c_j such that
4347 * |c_j/c_i| > ceil(size_i/2), i.e., |c_j| > |c_i * ceil(size_i/2)|.
4348 * If any such pair is found, then return i.
4349 * If size_i is infinity, then no check on c_i needs to be performed.
4351 static int find_node_coalescing(struct isl_sched_node
*node
,
4352 __isl_keep isl_vec
*sol
)
4358 if (node
->nvar
<= 1)
4361 csol
= extract_var_coef(node
, sol
);
4365 for (i
= 0; i
< node
->nvar
; ++i
) {
4368 if (isl_int_is_zero(csol
->el
[i
]))
4370 v
= isl_multi_val_get_val(node
->sizes
, i
);
4373 if (!isl_val_is_int(v
)) {
4377 v
= isl_val_div_ui(v
, 2);
4378 v
= isl_val_ceil(v
);
4381 isl_int_mul(max
, v
->n
, csol
->el
[i
]);
4384 for (j
= 0; j
< node
->nvar
; ++j
) {
4387 if (isl_int_abs_gt(csol
->el
[j
], max
))
4403 /* Force the schedule coefficient at position "pos" of "node" to be zero
4405 * The coefficient is encoded as the difference between two non-negative
4406 * variables. Force these two variables to have the same value.
4408 static __isl_give isl_tab_lexmin
*zero_out_node_coef(
4409 __isl_take isl_tab_lexmin
*tl
, struct isl_sched_node
*node
, int pos
)
4415 ctx
= isl_space_get_ctx(node
->space
);
4416 dim
= isl_tab_lexmin_dim(tl
);
4418 return isl_tab_lexmin_free(tl
);
4419 eq
= isl_vec_alloc(ctx
, 1 + dim
);
4420 eq
= isl_vec_clr(eq
);
4422 return isl_tab_lexmin_free(tl
);
4424 pos
= 1 + node_var_coef_pos(node
, pos
);
4425 isl_int_set_si(eq
->el
[pos
], 1);
4426 isl_int_set_si(eq
->el
[pos
+ 1], -1);
4427 tl
= isl_tab_lexmin_add_eq(tl
, eq
->el
);
4433 /* Return the lexicographically smallest rational point in the basic set
4434 * from which "tl" was constructed, double checking that this input set
4437 static __isl_give isl_vec
*non_empty_solution(__isl_keep isl_tab_lexmin
*tl
)
4441 sol
= isl_tab_lexmin_get_solution(tl
);
4445 isl_die(isl_vec_get_ctx(sol
), isl_error_internal
,
4446 "error in schedule construction",
4447 return isl_vec_free(sol
));
4451 /* Does the solution "sol" of the LP problem constructed by setup_carry_lp
4452 * carry any of the "n_edge" groups of dependences?
4453 * The value in the first position is the sum of (1 - e_i) over all "n_edge"
4454 * edges, with 0 <= e_i <= 1 equal to 1 when the dependences represented
4455 * by the edge are carried by the solution.
4456 * If the sum of the (1 - e_i) is smaller than "n_edge" then at least
4457 * one of those is carried.
4459 * Note that despite the fact that the problem is solved using a rational
4460 * solver, the solution is guaranteed to be integral.
4461 * Specifically, the dependence distance lower bounds e_i (and therefore
4462 * also their sum) are integers. See Lemma 5 of [1].
4464 * Any potential denominator of the sum is cleared by this function.
4465 * The denominator is not relevant for any of the other elements
4468 * [1] P. Feautrier, Some Efficient Solutions to the Affine Scheduling
4469 * Problem, Part II: Multi-Dimensional Time.
4470 * In Intl. Journal of Parallel Programming, 1992.
4472 static int carries_dependences(__isl_keep isl_vec
*sol
, int n_edge
)
4474 isl_int_divexact(sol
->el
[1], sol
->el
[1], sol
->el
[0]);
4475 isl_int_set_si(sol
->el
[0], 1);
4476 return isl_int_cmp_si(sol
->el
[1], n_edge
) < 0;
4479 /* Return the lexicographically smallest rational point in "lp",
4480 * assuming that all variables are non-negative and performing some
4481 * additional sanity checks.
4482 * If "want_integral" is set, then compute the lexicographically smallest
4483 * integer point instead.
4484 * In particular, "lp" should not be empty by construction.
4485 * Double check that this is the case.
4486 * If dependences are not carried for any of the "n_edge" edges,
4487 * then return an empty vector.
4489 * If the schedule_treat_coalescing option is set and
4490 * if the computed schedule performs loop coalescing on a given node,
4491 * i.e., if it is of the form
4493 * c_i i + c_j j + ...
4495 * with |c_j/c_i| >= size_i, then force the coefficient c_i to be zero
4496 * to cut out this solution. Repeat this process until no more loop
4497 * coalescing occurs or until no more dependences can be carried.
4498 * In the latter case, revert to the previously computed solution.
4500 * If the caller requests an integral solution and if coalescing should
4501 * be treated, then perform the coalescing treatment first as
4502 * an integral solution computed before coalescing treatment
4503 * would carry the same number of edges and would therefore probably
4504 * also be coalescing.
4506 * To allow the coalescing treatment to be performed first,
4507 * the initial solution is allowed to be rational and it is only
4508 * cut out (if needed) in the next iteration, if no coalescing measures
4511 static __isl_give isl_vec
*non_neg_lexmin(struct isl_sched_graph
*graph
,
4512 __isl_take isl_basic_set
*lp
, int n_edge
, int want_integral
)
4517 isl_vec
*sol
= NULL
, *prev
;
4518 int treat_coalescing
;
4523 ctx
= isl_basic_set_get_ctx(lp
);
4524 treat_coalescing
= isl_options_get_schedule_treat_coalescing(ctx
);
4525 tl
= isl_tab_lexmin_from_basic_set(lp
);
4533 tl
= isl_tab_lexmin_cut_to_integer(tl
);
4535 sol
= non_empty_solution(tl
);
4539 integral
= isl_int_is_one(sol
->el
[0]);
4540 if (!carries_dependences(sol
, n_edge
)) {
4542 prev
= isl_vec_alloc(ctx
, 0);
4547 prev
= isl_vec_free(prev
);
4548 cut
= want_integral
&& !integral
;
4551 if (!treat_coalescing
)
4553 for (i
= 0; i
< graph
->n
; ++i
) {
4554 struct isl_sched_node
*node
= &graph
->node
[i
];
4556 pos
= find_node_coalescing(node
, sol
);
4559 if (pos
< node
->nvar
)
4564 tl
= zero_out_node_coef(tl
, &graph
->node
[i
], pos
);
4567 } while (try_again
);
4569 isl_tab_lexmin_free(tl
);
4573 isl_tab_lexmin_free(tl
);
4579 /* If "edge" is an edge from a node to itself, then add the corresponding
4580 * dependence relation to "umap".
4581 * If "node" has been compressed, then the dependence relation
4582 * is also compressed first.
4584 static __isl_give isl_union_map
*add_intra(__isl_take isl_union_map
*umap
,
4585 struct isl_sched_edge
*edge
)
4588 struct isl_sched_node
*node
= edge
->src
;
4590 if (edge
->src
!= edge
->dst
)
4593 map
= isl_map_copy(edge
->map
);
4594 if (node
->compressed
) {
4595 map
= isl_map_preimage_domain_multi_aff(map
,
4596 isl_multi_aff_copy(node
->decompress
));
4597 map
= isl_map_preimage_range_multi_aff(map
,
4598 isl_multi_aff_copy(node
->decompress
));
4600 umap
= isl_union_map_add_map(umap
, map
);
4604 /* If "edge" is an edge from a node to another node, then add the corresponding
4605 * dependence relation to "umap".
4606 * If the source or destination nodes of "edge" have been compressed,
4607 * then the dependence relation is also compressed first.
4609 static __isl_give isl_union_map
*add_inter(__isl_take isl_union_map
*umap
,
4610 struct isl_sched_edge
*edge
)
4614 if (edge
->src
== edge
->dst
)
4617 map
= isl_map_copy(edge
->map
);
4618 if (edge
->src
->compressed
)
4619 map
= isl_map_preimage_domain_multi_aff(map
,
4620 isl_multi_aff_copy(edge
->src
->decompress
));
4621 if (edge
->dst
->compressed
)
4622 map
= isl_map_preimage_range_multi_aff(map
,
4623 isl_multi_aff_copy(edge
->dst
->decompress
));
4624 umap
= isl_union_map_add_map(umap
, map
);
4628 /* Internal data structure used by union_drop_coalescing_constraints
4629 * to collect bounds on all relevant statements.
4631 * "graph" is the schedule constraint graph for which an LP problem
4632 * is being constructed.
4633 * "bounds" collects the bounds.
4635 struct isl_collect_bounds_data
{
4637 struct isl_sched_graph
*graph
;
4638 isl_union_set
*bounds
;
4641 /* Add the size bounds for the node with instance deltas in "set"
4644 static isl_stat
collect_bounds(__isl_take isl_set
*set
, void *user
)
4646 struct isl_collect_bounds_data
*data
= user
;
4647 struct isl_sched_node
*node
;
4651 space
= isl_set_get_space(set
);
4654 node
= graph_find_compressed_node(data
->ctx
, data
->graph
, space
);
4655 isl_space_free(space
);
4657 bounds
= isl_set_from_basic_set(get_size_bounds(node
));
4658 data
->bounds
= isl_union_set_add_set(data
->bounds
, bounds
);
4663 /* Drop some constraints from "delta" that could be exploited
4664 * to construct loop coalescing schedules.
4665 * In particular, drop those constraint that bound the difference
4666 * to the size of the domain.
4667 * Do this for each set/node in "delta" separately.
4668 * The parameters are assumed to have been projected out by the caller.
4670 static __isl_give isl_union_set
*union_drop_coalescing_constraints(isl_ctx
*ctx
,
4671 struct isl_sched_graph
*graph
, __isl_take isl_union_set
*delta
)
4673 struct isl_collect_bounds_data data
= { ctx
, graph
};
4675 data
.bounds
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
4676 if (isl_union_set_foreach_set(delta
, &collect_bounds
, &data
) < 0)
4677 data
.bounds
= isl_union_set_free(data
.bounds
);
4678 delta
= isl_union_set_plain_gist(delta
, data
.bounds
);
4683 /* Given a non-trivial lineality space "lineality", add the corresponding
4684 * universe set to data->mask and add a map from elements to
4685 * other elements along the lines in "lineality" to data->equivalent.
4686 * If this is the first time this function gets called
4687 * (data->any_non_trivial is still false), then set data->any_non_trivial and
4688 * initialize data->mask and data->equivalent.
4690 * In particular, if the lineality space is defined by equality constraints
4694 * then construct an affine mapping
4698 * and compute the equivalence relation of having the same image under f:
4700 * { x -> x' : E x = E x' }
4702 static isl_stat
add_non_trivial_lineality(__isl_take isl_basic_set
*lineality
,
4703 struct isl_exploit_lineality_data
*data
)
4709 isl_multi_pw_aff
*mpa
;
4714 return isl_stat_error
;
4715 if (isl_basic_set_dim(lineality
, isl_dim_div
) != 0)
4716 isl_die(isl_basic_set_get_ctx(lineality
), isl_error_internal
,
4717 "local variables not allowed", goto error
);
4719 space
= isl_basic_set_get_space(lineality
);
4720 if (!data
->any_non_trivial
) {
4721 data
->equivalent
= isl_union_map_empty(isl_space_copy(space
));
4722 data
->mask
= isl_union_set_empty(isl_space_copy(space
));
4724 data
->any_non_trivial
= isl_bool_true
;
4726 univ
= isl_set_universe(isl_space_copy(space
));
4727 data
->mask
= isl_union_set_add_set(data
->mask
, univ
);
4729 eq
= isl_basic_set_extract_equalities(lineality
);
4730 n
= isl_mat_rows(eq
);
4731 eq
= isl_mat_insert_zero_rows(eq
, 0, 1);
4732 eq
= isl_mat_set_element_si(eq
, 0, 0, 1);
4733 space
= isl_space_from_domain(space
);
4734 space
= isl_space_add_dims(space
, isl_dim_out
, n
);
4735 ma
= isl_multi_aff_from_aff_mat(space
, eq
);
4736 mpa
= isl_multi_pw_aff_from_multi_aff(ma
);
4737 map
= isl_multi_pw_aff_eq_map(mpa
, isl_multi_pw_aff_copy(mpa
));
4738 data
->equivalent
= isl_union_map_add_map(data
->equivalent
, map
);
4740 isl_basic_set_free(lineality
);
4743 isl_basic_set_free(lineality
);
4744 return isl_stat_error
;
4747 /* Check if the lineality space "set" is non-trivial (i.e., is not just
4748 * the origin or, in other words, satisfies a number of equality constraints
4749 * that is smaller than the dimension of the set).
4750 * If so, extend data->mask and data->equivalent accordingly.
4752 * The input should not have any local variables already, but
4753 * isl_set_remove_divs is called to make sure it does not.
4755 static isl_stat
add_lineality(__isl_take isl_set
*set
, void *user
)
4757 struct isl_exploit_lineality_data
*data
= user
;
4758 isl_basic_set
*hull
;
4761 set
= isl_set_remove_divs(set
);
4762 hull
= isl_set_unshifted_simple_hull(set
);
4763 dim
= isl_basic_set_dim(hull
, isl_dim_set
);
4764 n_eq
= isl_basic_set_n_equality(hull
);
4766 return isl_stat_error
;
4768 return add_non_trivial_lineality(hull
, data
);
4769 isl_basic_set_free(hull
);
4773 /* Check if the difference set on intra-node schedule constraints "intra"
4774 * has any non-trivial lineality space.
4775 * If so, then extend the difference set to a difference set
4776 * on equivalent elements. That is, if "intra" is
4778 * { y - x : (x,y) \in V }
4780 * and elements are equivalent if they have the same image under f,
4783 * { y' - x' : (x,y) \in V and f(x) = f(x') and f(y) = f(y') }
4785 * or, since f is linear,
4787 * { y' - x' : (x,y) \in V and f(y - x) = f(y' - x') }
4789 * The results of the search for non-trivial lineality spaces is stored
4792 static __isl_give isl_union_set
*exploit_intra_lineality(
4793 __isl_take isl_union_set
*intra
,
4794 struct isl_exploit_lineality_data
*data
)
4796 isl_union_set
*lineality
;
4797 isl_union_set
*uset
;
4799 data
->any_non_trivial
= isl_bool_false
;
4800 lineality
= isl_union_set_copy(intra
);
4801 lineality
= isl_union_set_combined_lineality_space(lineality
);
4802 if (isl_union_set_foreach_set(lineality
, &add_lineality
, data
) < 0)
4803 data
->any_non_trivial
= isl_bool_error
;
4804 isl_union_set_free(lineality
);
4806 if (data
->any_non_trivial
< 0)
4807 return isl_union_set_free(intra
);
4808 if (!data
->any_non_trivial
)
4811 uset
= isl_union_set_copy(intra
);
4812 intra
= isl_union_set_subtract(intra
, isl_union_set_copy(data
->mask
));
4813 uset
= isl_union_set_apply(uset
, isl_union_map_copy(data
->equivalent
));
4814 intra
= isl_union_set_union(intra
, uset
);
4816 intra
= isl_union_set_remove_divs(intra
);
4821 /* If the difference set on intra-node schedule constraints was found to have
4822 * any non-trivial lineality space by exploit_intra_lineality,
4823 * as recorded in "data", then extend the inter-node
4824 * schedule constraints "inter" to schedule constraints on equivalent elements.
4825 * That is, if "inter" is V and
4826 * elements are equivalent if they have the same image under f, then return
4828 * { (x', y') : (x,y) \in V and f(x) = f(x') and f(y) = f(y') }
4830 static __isl_give isl_union_map
*exploit_inter_lineality(
4831 __isl_take isl_union_map
*inter
,
4832 struct isl_exploit_lineality_data
*data
)
4834 isl_union_map
*umap
;
4836 if (data
->any_non_trivial
< 0)
4837 return isl_union_map_free(inter
);
4838 if (!data
->any_non_trivial
)
4841 umap
= isl_union_map_copy(inter
);
4842 inter
= isl_union_map_subtract_range(inter
,
4843 isl_union_set_copy(data
->mask
));
4844 umap
= isl_union_map_apply_range(umap
,
4845 isl_union_map_copy(data
->equivalent
));
4846 inter
= isl_union_map_union(inter
, umap
);
4847 umap
= isl_union_map_copy(inter
);
4848 inter
= isl_union_map_subtract_domain(inter
,
4849 isl_union_set_copy(data
->mask
));
4850 umap
= isl_union_map_apply_range(isl_union_map_copy(data
->equivalent
),
4852 inter
= isl_union_map_union(inter
, umap
);
4854 inter
= isl_union_map_remove_divs(inter
);
4859 /* For each (conditional) validity edge in "graph",
4860 * add the corresponding dependence relation using "add"
4861 * to a collection of dependence relations and return the result.
4862 * If "coincidence" is set, then coincidence edges are considered as well.
4864 static __isl_give isl_union_map
*collect_validity(struct isl_sched_graph
*graph
,
4865 __isl_give isl_union_map
*(*add
)(__isl_take isl_union_map
*umap
,
4866 struct isl_sched_edge
*edge
), int coincidence
)
4870 isl_union_map
*umap
;
4872 space
= isl_space_copy(graph
->node
[0].space
);
4873 umap
= isl_union_map_empty(space
);
4875 for (i
= 0; i
< graph
->n_edge
; ++i
) {
4876 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
4878 if (!is_any_validity(edge
) &&
4879 (!coincidence
|| !is_coincidence(edge
)))
4882 umap
= add(umap
, edge
);
4888 /* Project out all parameters from "uset" and return the result.
4890 static __isl_give isl_union_set
*union_set_drop_parameters(
4891 __isl_take isl_union_set
*uset
)
4895 nparam
= isl_union_set_dim(uset
, isl_dim_param
);
4896 return isl_union_set_project_out(uset
, isl_dim_param
, 0, nparam
);
4899 /* For each dependence relation on a (conditional) validity edge
4900 * from a node to itself,
4901 * construct the set of coefficients of valid constraints for elements
4902 * in that dependence relation and collect the results.
4903 * If "coincidence" is set, then coincidence edges are considered as well.
4905 * In particular, for each dependence relation R, constraints
4906 * on coefficients (c_0, c_x) are constructed such that
4908 * c_0 + c_x d >= 0 for each d in delta R = { y - x | (x,y) in R }
4910 * If the schedule_treat_coalescing option is set, then some constraints
4911 * that could be exploited to construct coalescing schedules
4912 * are removed before the dual is computed, but after the parameters
4913 * have been projected out.
4914 * The entire computation is essentially the same as that performed
4915 * by intra_coefficients, except that it operates on multiple
4916 * edges together and that the parameters are always projected out.
4918 * Additionally, exploit any non-trivial lineality space
4919 * in the difference set after removing coalescing constraints and
4920 * store the results of the non-trivial lineality space detection in "data".
4921 * The procedure is currently run unconditionally, but it is unlikely
4922 * to find any non-trivial lineality spaces if no coalescing constraints
4923 * have been removed.
4925 * Note that if a dependence relation is a union of basic maps,
4926 * then each basic map needs to be treated individually as it may only
4927 * be possible to carry the dependences expressed by some of those
4928 * basic maps and not all of them.
4929 * The collected validity constraints are therefore not coalesced and
4930 * it is assumed that they are not coalesced automatically.
4931 * Duplicate basic maps can be removed, however.
4932 * In particular, if the same basic map appears as a disjunct
4933 * in multiple edges, then it only needs to be carried once.
4935 static __isl_give isl_basic_set_list
*collect_intra_validity(isl_ctx
*ctx
,
4936 struct isl_sched_graph
*graph
, int coincidence
,
4937 struct isl_exploit_lineality_data
*data
)
4939 isl_union_map
*intra
;
4940 isl_union_set
*delta
;
4941 isl_basic_set_list
*list
;
4943 intra
= collect_validity(graph
, &add_intra
, coincidence
);
4944 delta
= isl_union_map_deltas(intra
);
4945 delta
= union_set_drop_parameters(delta
);
4946 delta
= isl_union_set_remove_divs(delta
);
4947 if (isl_options_get_schedule_treat_coalescing(ctx
))
4948 delta
= union_drop_coalescing_constraints(ctx
, graph
, delta
);
4949 delta
= exploit_intra_lineality(delta
, data
);
4950 list
= isl_union_set_get_basic_set_list(delta
);
4951 isl_union_set_free(delta
);
4953 return isl_basic_set_list_coefficients(list
);
4956 /* For each dependence relation on a (conditional) validity edge
4957 * from a node to some other node,
4958 * construct the set of coefficients of valid constraints for elements
4959 * in that dependence relation and collect the results.
4960 * If "coincidence" is set, then coincidence edges are considered as well.
4962 * In particular, for each dependence relation R, constraints
4963 * on coefficients (c_0, c_n, c_x, c_y) are constructed such that
4965 * c_0 + c_n n + c_x x + c_y y >= 0 for each (x,y) in R
4967 * This computation is essentially the same as that performed
4968 * by inter_coefficients, except that it operates on multiple
4971 * Additionally, exploit any non-trivial lineality space
4972 * that may have been discovered by collect_intra_validity
4973 * (as stored in "data").
4975 * Note that if a dependence relation is a union of basic maps,
4976 * then each basic map needs to be treated individually as it may only
4977 * be possible to carry the dependences expressed by some of those
4978 * basic maps and not all of them.
4979 * The collected validity constraints are therefore not coalesced and
4980 * it is assumed that they are not coalesced automatically.
4981 * Duplicate basic maps can be removed, however.
4982 * In particular, if the same basic map appears as a disjunct
4983 * in multiple edges, then it only needs to be carried once.
4985 static __isl_give isl_basic_set_list
*collect_inter_validity(
4986 struct isl_sched_graph
*graph
, int coincidence
,
4987 struct isl_exploit_lineality_data
*data
)
4989 isl_union_map
*inter
;
4990 isl_union_set
*wrap
;
4991 isl_basic_set_list
*list
;
4993 inter
= collect_validity(graph
, &add_inter
, coincidence
);
4994 inter
= exploit_inter_lineality(inter
, data
);
4995 inter
= isl_union_map_remove_divs(inter
);
4996 wrap
= isl_union_map_wrap(inter
);
4997 list
= isl_union_set_get_basic_set_list(wrap
);
4998 isl_union_set_free(wrap
);
4999 return isl_basic_set_list_coefficients(list
);
5002 /* Construct an LP problem for finding schedule coefficients
5003 * such that the schedule carries as many of the "n_edge" groups of
5004 * dependences as possible based on the corresponding coefficient
5005 * constraints and return the lexicographically smallest non-trivial solution.
5006 * "intra" is the sequence of coefficient constraints for intra-node edges.
5007 * "inter" is the sequence of coefficient constraints for inter-node edges.
5008 * If "want_integral" is set, then compute an integral solution
5009 * for the coefficients rather than using the numerators
5010 * of a rational solution.
5011 * "carry_inter" indicates whether inter-node edges should be carried or
5014 * If none of the "n_edge" groups can be carried
5015 * then return an empty vector.
5017 static __isl_give isl_vec
*compute_carrying_sol_coef(isl_ctx
*ctx
,
5018 struct isl_sched_graph
*graph
, int n_edge
,
5019 __isl_keep isl_basic_set_list
*intra
,
5020 __isl_keep isl_basic_set_list
*inter
, int want_integral
,
5025 if (setup_carry_lp(ctx
, graph
, n_edge
, intra
, inter
, carry_inter
) < 0)
5028 lp
= isl_basic_set_copy(graph
->lp
);
5029 return non_neg_lexmin(graph
, lp
, n_edge
, want_integral
);
5032 /* Construct an LP problem for finding schedule coefficients
5033 * such that the schedule carries as many of the validity dependences
5035 * return the lexicographically smallest non-trivial solution.
5036 * If "fallback" is set, then the carrying is performed as a fallback
5037 * for the Pluto-like scheduler.
5038 * If "coincidence" is set, then try and carry coincidence edges as well.
5040 * The variable "n_edge" stores the number of groups that should be carried.
5041 * If none of the "n_edge" groups can be carried
5042 * then return an empty vector.
5043 * If, moreover, "n_edge" is zero, then the LP problem does not even
5044 * need to be constructed.
5046 * If a fallback solution is being computed, then compute an integral solution
5047 * for the coefficients rather than using the numerators
5048 * of a rational solution.
5050 * If a fallback solution is being computed, if there are any intra-node
5051 * dependences, and if requested by the user, then first try
5052 * to only carry those intra-node dependences.
5053 * If this fails to carry any dependences, then try again
5054 * with the inter-node dependences included.
5056 static __isl_give isl_vec
*compute_carrying_sol(isl_ctx
*ctx
,
5057 struct isl_sched_graph
*graph
, int fallback
, int coincidence
)
5059 int n_intra
, n_inter
;
5061 struct isl_carry carry
= { 0 };
5064 carry
.intra
= collect_intra_validity(ctx
, graph
, coincidence
,
5066 carry
.inter
= collect_inter_validity(graph
, coincidence
,
5068 if (!carry
.intra
|| !carry
.inter
)
5070 n_intra
= isl_basic_set_list_n_basic_set(carry
.intra
);
5071 n_inter
= isl_basic_set_list_n_basic_set(carry
.inter
);
5073 if (fallback
&& n_intra
> 0 &&
5074 isl_options_get_schedule_carry_self_first(ctx
)) {
5075 sol
= compute_carrying_sol_coef(ctx
, graph
, n_intra
,
5076 carry
.intra
, carry
.inter
, fallback
, 0);
5077 if (!sol
|| sol
->size
!= 0 || n_inter
== 0) {
5078 isl_carry_clear(&carry
);
5084 n_edge
= n_intra
+ n_inter
;
5086 isl_carry_clear(&carry
);
5087 return isl_vec_alloc(ctx
, 0);
5090 sol
= compute_carrying_sol_coef(ctx
, graph
, n_edge
,
5091 carry
.intra
, carry
.inter
, fallback
, 1);
5092 isl_carry_clear(&carry
);
5095 isl_carry_clear(&carry
);
5099 /* Construct a schedule row for each node such that as many validity dependences
5100 * as possible are carried and then continue with the next band.
5101 * If "fallback" is set, then the carrying is performed as a fallback
5102 * for the Pluto-like scheduler.
5103 * If "coincidence" is set, then try and carry coincidence edges as well.
5105 * If there are no validity dependences, then no dependence can be carried and
5106 * the procedure is guaranteed to fail. If there is more than one component,
5107 * then try computing a schedule on each component separately
5108 * to prevent or at least postpone this failure.
5110 * If a schedule row is computed, then check that dependences are carried
5111 * for at least one of the edges.
5113 * If the computed schedule row turns out to be trivial on one or
5114 * more nodes where it should not be trivial, then we throw it away
5115 * and try again on each component separately.
5117 * If there is only one component, then we accept the schedule row anyway,
5118 * but we do not consider it as a complete row and therefore do not
5119 * increment graph->n_row. Note that the ranks of the nodes that
5120 * do get a non-trivial schedule part will get updated regardless and
5121 * graph->maxvar is computed based on these ranks. The test for
5122 * whether more schedule rows are required in compute_schedule_wcc
5123 * is therefore not affected.
5125 * Insert a band corresponding to the schedule row at position "node"
5126 * of the schedule tree and continue with the construction of the schedule.
5127 * This insertion and the continued construction is performed by split_scaled
5128 * after optionally checking for non-trivial common divisors.
5130 static __isl_give isl_schedule_node
*carry(__isl_take isl_schedule_node
*node
,
5131 struct isl_sched_graph
*graph
, int fallback
, int coincidence
)
5140 ctx
= isl_schedule_node_get_ctx(node
);
5141 sol
= compute_carrying_sol(ctx
, graph
, fallback
, coincidence
);
5143 return isl_schedule_node_free(node
);
5144 if (sol
->size
== 0) {
5147 return compute_component_schedule(node
, graph
, 1);
5148 isl_die(ctx
, isl_error_unknown
, "unable to carry dependences",
5149 return isl_schedule_node_free(node
));
5152 trivial
= is_any_trivial(graph
, sol
);
5154 sol
= isl_vec_free(sol
);
5155 } else if (trivial
&& graph
->scc
> 1) {
5157 return compute_component_schedule(node
, graph
, 1);
5160 if (update_schedule(graph
, sol
, 0) < 0)
5161 return isl_schedule_node_free(node
);
5165 return split_scaled(node
, graph
);
5168 /* Construct a schedule row for each node such that as many validity dependences
5169 * as possible are carried and then continue with the next band.
5170 * Do so as a fallback for the Pluto-like scheduler.
5171 * If "coincidence" is set, then try and carry coincidence edges as well.
5173 static __isl_give isl_schedule_node
*carry_fallback(
5174 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
5177 return carry(node
, graph
, 1, coincidence
);
5180 /* Construct a schedule row for each node such that as many validity dependences
5181 * as possible are carried and then continue with the next band.
5182 * Do so for the case where the Feautrier scheduler was selected
5185 static __isl_give isl_schedule_node
*carry_feautrier(
5186 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
5188 return carry(node
, graph
, 0, 0);
5191 /* Construct a schedule row for each node such that as many validity dependences
5192 * as possible are carried and then continue with the next band.
5193 * Do so as a fallback for the Pluto-like scheduler.
5195 static __isl_give isl_schedule_node
*carry_dependences(
5196 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
5198 return carry_fallback(node
, graph
, 0);
5201 /* Construct a schedule row for each node such that as many validity or
5202 * coincidence dependences as possible are carried and
5203 * then continue with the next band.
5204 * Do so as a fallback for the Pluto-like scheduler.
5206 static __isl_give isl_schedule_node
*carry_coincidence(
5207 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
5209 return carry_fallback(node
, graph
, 1);
5212 /* Topologically sort statements mapped to the same schedule iteration
5213 * and add insert a sequence node in front of "node"
5214 * corresponding to this order.
5215 * If "initialized" is set, then it may be assumed that compute_maxvar
5216 * has been called on the current band. Otherwise, call
5217 * compute_maxvar if and before carry_dependences gets called.
5219 * If it turns out to be impossible to sort the statements apart,
5220 * because different dependences impose different orderings
5221 * on the statements, then we extend the schedule such that
5222 * it carries at least one more dependence.
5224 static __isl_give isl_schedule_node
*sort_statements(
5225 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
5229 isl_union_set_list
*filters
;
5234 ctx
= isl_schedule_node_get_ctx(node
);
5236 isl_die(ctx
, isl_error_internal
,
5237 "graph should have at least one node",
5238 return isl_schedule_node_free(node
));
5243 if (update_edges(ctx
, graph
) < 0)
5244 return isl_schedule_node_free(node
);
5246 if (graph
->n_edge
== 0)
5249 if (detect_sccs(ctx
, graph
) < 0)
5250 return isl_schedule_node_free(node
);
5253 if (graph
->scc
< graph
->n
) {
5254 if (!initialized
&& compute_maxvar(graph
) < 0)
5255 return isl_schedule_node_free(node
);
5256 return carry_dependences(node
, graph
);
5259 filters
= extract_sccs(ctx
, graph
);
5260 node
= isl_schedule_node_insert_sequence(node
, filters
);
5265 /* Are there any (non-empty) (conditional) validity edges in the graph?
5267 static int has_validity_edges(struct isl_sched_graph
*graph
)
5271 for (i
= 0; i
< graph
->n_edge
; ++i
) {
5274 empty
= isl_map_plain_is_empty(graph
->edge
[i
].map
);
5279 if (is_any_validity(&graph
->edge
[i
]))
5286 /* Should we apply a Feautrier step?
5287 * That is, did the user request the Feautrier algorithm and are
5288 * there any validity dependences (left)?
5290 static int need_feautrier_step(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
5292 if (ctx
->opt
->schedule_algorithm
!= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
)
5295 return has_validity_edges(graph
);
5298 /* Compute a schedule for a connected dependence graph using Feautrier's
5299 * multi-dimensional scheduling algorithm and return the updated schedule node.
5301 * The original algorithm is described in [1].
5302 * The main idea is to minimize the number of scheduling dimensions, by
5303 * trying to satisfy as many dependences as possible per scheduling dimension.
5305 * [1] P. Feautrier, Some Efficient Solutions to the Affine Scheduling
5306 * Problem, Part II: Multi-Dimensional Time.
5307 * In Intl. Journal of Parallel Programming, 1992.
5309 static __isl_give isl_schedule_node
*compute_schedule_wcc_feautrier(
5310 isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
5312 return carry_feautrier(node
, graph
);
5315 /* Turn off the "local" bit on all (condition) edges.
5317 static void clear_local_edges(struct isl_sched_graph
*graph
)
5321 for (i
= 0; i
< graph
->n_edge
; ++i
)
5322 if (is_condition(&graph
->edge
[i
]))
5323 clear_local(&graph
->edge
[i
]);
5326 /* Does "graph" have both condition and conditional validity edges?
5328 static int need_condition_check(struct isl_sched_graph
*graph
)
5331 int any_condition
= 0;
5332 int any_conditional_validity
= 0;
5334 for (i
= 0; i
< graph
->n_edge
; ++i
) {
5335 if (is_condition(&graph
->edge
[i
]))
5337 if (is_conditional_validity(&graph
->edge
[i
]))
5338 any_conditional_validity
= 1;
5341 return any_condition
&& any_conditional_validity
;
5344 /* Does "graph" contain any coincidence edge?
5346 static int has_any_coincidence(struct isl_sched_graph
*graph
)
5350 for (i
= 0; i
< graph
->n_edge
; ++i
)
5351 if (is_coincidence(&graph
->edge
[i
]))
5357 /* Extract the final schedule row as a map with the iteration domain
5358 * of "node" as domain.
5360 static __isl_give isl_map
*final_row(struct isl_sched_node
*node
)
5365 row
= isl_mat_rows(node
->sched
) - 1;
5366 ma
= node_extract_partial_schedule_multi_aff(node
, row
, 1);
5367 return isl_map_from_multi_aff(ma
);
5370 /* Is the conditional validity dependence in the edge with index "edge_index"
5371 * violated by the latest (i.e., final) row of the schedule?
5372 * That is, is i scheduled after j
5373 * for any conditional validity dependence i -> j?
5375 static int is_violated(struct isl_sched_graph
*graph
, int edge_index
)
5377 isl_map
*src_sched
, *dst_sched
, *map
;
5378 struct isl_sched_edge
*edge
= &graph
->edge
[edge_index
];
5381 src_sched
= final_row(edge
->src
);
5382 dst_sched
= final_row(edge
->dst
);
5383 map
= isl_map_copy(edge
->map
);
5384 map
= isl_map_apply_domain(map
, src_sched
);
5385 map
= isl_map_apply_range(map
, dst_sched
);
5386 map
= isl_map_order_gt(map
, isl_dim_in
, 0, isl_dim_out
, 0);
5387 empty
= isl_map_is_empty(map
);
5396 /* Does "graph" have any satisfied condition edges that
5397 * are adjacent to the conditional validity constraint with
5398 * domain "conditional_source" and range "conditional_sink"?
5400 * A satisfied condition is one that is not local.
5401 * If a condition was forced to be local already (i.e., marked as local)
5402 * then there is no need to check if it is in fact local.
5404 * Additionally, mark all adjacent condition edges found as local.
5406 static int has_adjacent_true_conditions(struct isl_sched_graph
*graph
,
5407 __isl_keep isl_union_set
*conditional_source
,
5408 __isl_keep isl_union_set
*conditional_sink
)
5413 for (i
= 0; i
< graph
->n_edge
; ++i
) {
5414 int adjacent
, local
;
5415 isl_union_map
*condition
;
5417 if (!is_condition(&graph
->edge
[i
]))
5419 if (is_local(&graph
->edge
[i
]))
5422 condition
= graph
->edge
[i
].tagged_condition
;
5423 adjacent
= domain_intersects(condition
, conditional_sink
);
5424 if (adjacent
>= 0 && !adjacent
)
5425 adjacent
= range_intersects(condition
,
5426 conditional_source
);
5432 set_local(&graph
->edge
[i
]);
5434 local
= is_condition_false(&graph
->edge
[i
]);
5444 /* Are there any violated conditional validity dependences with
5445 * adjacent condition dependences that are not local with respect
5446 * to the current schedule?
5447 * That is, is the conditional validity constraint violated?
5449 * Additionally, mark all those adjacent condition dependences as local.
5450 * We also mark those adjacent condition dependences that were not marked
5451 * as local before, but just happened to be local already. This ensures
5452 * that they remain local if the schedule is recomputed.
5454 * We first collect domain and range of all violated conditional validity
5455 * dependences and then check if there are any adjacent non-local
5456 * condition dependences.
5458 static int has_violated_conditional_constraint(isl_ctx
*ctx
,
5459 struct isl_sched_graph
*graph
)
5463 isl_union_set
*source
, *sink
;
5465 source
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
5466 sink
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
5467 for (i
= 0; i
< graph
->n_edge
; ++i
) {
5468 isl_union_set
*uset
;
5469 isl_union_map
*umap
;
5472 if (!is_conditional_validity(&graph
->edge
[i
]))
5475 violated
= is_violated(graph
, i
);
5483 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_validity
);
5484 uset
= isl_union_map_domain(umap
);
5485 source
= isl_union_set_union(source
, uset
);
5486 source
= isl_union_set_coalesce(source
);
5488 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_validity
);
5489 uset
= isl_union_map_range(umap
);
5490 sink
= isl_union_set_union(sink
, uset
);
5491 sink
= isl_union_set_coalesce(sink
);
5495 any
= has_adjacent_true_conditions(graph
, source
, sink
);
5497 isl_union_set_free(source
);
5498 isl_union_set_free(sink
);
5501 isl_union_set_free(source
);
5502 isl_union_set_free(sink
);
5506 /* Examine the current band (the rows between graph->band_start and
5507 * graph->n_total_row), deciding whether to drop it or add it to "node"
5508 * and then continue with the computation of the next band, if any.
5509 * If "initialized" is set, then it may be assumed that compute_maxvar
5510 * has been called on the current band. Otherwise, call
5511 * compute_maxvar if and before carry_dependences gets called.
5513 * The caller keeps looking for a new row as long as
5514 * graph->n_row < graph->maxvar. If the latest attempt to find
5515 * such a row failed (i.e., we still have graph->n_row < graph->maxvar),
5517 * - split between SCCs and start over (assuming we found an interesting
5518 * pair of SCCs between which to split)
5519 * - continue with the next band (assuming the current band has at least
5521 * - if there is more than one SCC left, then split along all SCCs
5522 * - if outer coincidence needs to be enforced, then try to carry as many
5523 * validity or coincidence dependences as possible and
5524 * continue with the next band
5525 * - try to carry as many validity dependences as possible and
5526 * continue with the next band
5527 * In each case, we first insert a band node in the schedule tree
5528 * if any rows have been computed.
5530 * If the caller managed to complete the schedule and the current band
5531 * is empty, then finish off by topologically
5532 * sorting the statements based on the remaining dependences.
5533 * If, on the other hand, the current band has at least one row,
5534 * then continue with the next band. Note that this next band
5535 * will necessarily be empty, but the graph may still be split up
5536 * into weakly connected components before arriving back here.
5538 static __isl_give isl_schedule_node
*compute_schedule_finish_band(
5539 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
5547 empty
= graph
->n_total_row
== graph
->band_start
;
5548 if (graph
->n_row
< graph
->maxvar
) {
5551 ctx
= isl_schedule_node_get_ctx(node
);
5552 if (!ctx
->opt
->schedule_maximize_band_depth
&& !empty
)
5553 return compute_next_band(node
, graph
, 1);
5554 if (graph
->src_scc
>= 0)
5555 return compute_split_schedule(node
, graph
);
5557 return compute_next_band(node
, graph
, 1);
5559 return compute_component_schedule(node
, graph
, 1);
5560 if (!initialized
&& compute_maxvar(graph
) < 0)
5561 return isl_schedule_node_free(node
);
5562 if (isl_options_get_schedule_outer_coincidence(ctx
))
5563 return carry_coincidence(node
, graph
);
5564 return carry_dependences(node
, graph
);
5568 return compute_next_band(node
, graph
, 1);
5569 return sort_statements(node
, graph
, initialized
);
5572 /* Construct a band of schedule rows for a connected dependence graph.
5573 * The caller is responsible for determining the strongly connected
5574 * components and calling compute_maxvar first.
5576 * We try to find a sequence of as many schedule rows as possible that result
5577 * in non-negative dependence distances (independent of the previous rows
5578 * in the sequence, i.e., such that the sequence is tilable), with as
5579 * many of the initial rows as possible satisfying the coincidence constraints.
5580 * The computation stops if we can't find any more rows or if we have found
5581 * all the rows we wanted to find.
5583 * If ctx->opt->schedule_outer_coincidence is set, then we force the
5584 * outermost dimension to satisfy the coincidence constraints. If this
5585 * turns out to be impossible, we fall back on the general scheme above
5586 * and try to carry as many dependences as possible.
5588 * If "graph" contains both condition and conditional validity dependences,
5589 * then we need to check that that the conditional schedule constraint
5590 * is satisfied, i.e., there are no violated conditional validity dependences
5591 * that are adjacent to any non-local condition dependences.
5592 * If there are, then we mark all those adjacent condition dependences
5593 * as local and recompute the current band. Those dependences that
5594 * are marked local will then be forced to be local.
5595 * The initial computation is performed with no dependences marked as local.
5596 * If we are lucky, then there will be no violated conditional validity
5597 * dependences adjacent to any non-local condition dependences.
5598 * Otherwise, we mark some additional condition dependences as local and
5599 * recompute. We continue this process until there are no violations left or
5600 * until we are no longer able to compute a schedule.
5601 * Since there are only a finite number of dependences,
5602 * there will only be a finite number of iterations.
5604 static isl_stat
compute_schedule_wcc_band(isl_ctx
*ctx
,
5605 struct isl_sched_graph
*graph
)
5607 int has_coincidence
;
5608 int use_coincidence
;
5609 int force_coincidence
= 0;
5610 int check_conditional
;
5612 if (sort_sccs(graph
) < 0)
5613 return isl_stat_error
;
5615 clear_local_edges(graph
);
5616 check_conditional
= need_condition_check(graph
);
5617 has_coincidence
= has_any_coincidence(graph
);
5619 if (ctx
->opt
->schedule_outer_coincidence
)
5620 force_coincidence
= 1;
5622 use_coincidence
= has_coincidence
;
5623 while (graph
->n_row
< graph
->maxvar
) {
5628 graph
->src_scc
= -1;
5629 graph
->dst_scc
= -1;
5631 if (setup_lp(ctx
, graph
, use_coincidence
) < 0)
5632 return isl_stat_error
;
5633 sol
= solve_lp(ctx
, graph
);
5635 return isl_stat_error
;
5636 if (sol
->size
== 0) {
5637 int empty
= graph
->n_total_row
== graph
->band_start
;
5640 if (use_coincidence
&& (!force_coincidence
|| !empty
)) {
5641 use_coincidence
= 0;
5646 coincident
= !has_coincidence
|| use_coincidence
;
5647 if (update_schedule(graph
, sol
, coincident
) < 0)
5648 return isl_stat_error
;
5650 if (!check_conditional
)
5652 violated
= has_violated_conditional_constraint(ctx
, graph
);
5654 return isl_stat_error
;
5657 if (reset_band(graph
) < 0)
5658 return isl_stat_error
;
5659 use_coincidence
= has_coincidence
;
5665 /* Compute a schedule for a connected dependence graph by considering
5666 * the graph as a whole and return the updated schedule node.
5668 * The actual schedule rows of the current band are computed by
5669 * compute_schedule_wcc_band. compute_schedule_finish_band takes
5670 * care of integrating the band into "node" and continuing
5673 static __isl_give isl_schedule_node
*compute_schedule_wcc_whole(
5674 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
5681 ctx
= isl_schedule_node_get_ctx(node
);
5682 if (compute_schedule_wcc_band(ctx
, graph
) < 0)
5683 return isl_schedule_node_free(node
);
5685 return compute_schedule_finish_band(node
, graph
, 1);
5688 /* Clustering information used by compute_schedule_wcc_clustering.
5690 * "n" is the number of SCCs in the original dependence graph
5691 * "scc" is an array of "n" elements, each representing an SCC
5692 * of the original dependence graph. All entries in the same cluster
5693 * have the same number of schedule rows.
5694 * "scc_cluster" maps each SCC index to the cluster to which it belongs,
5695 * where each cluster is represented by the index of the first SCC
5696 * in the cluster. Initially, each SCC belongs to a cluster containing
5699 * "scc_in_merge" is used by merge_clusters_along_edge to keep
5700 * track of which SCCs need to be merged.
5702 * "cluster" contains the merged clusters of SCCs after the clustering
5705 * "scc_node" is a temporary data structure used inside copy_partial.
5706 * For each SCC, it keeps track of the number of nodes in the SCC
5707 * that have already been copied.
5709 struct isl_clustering
{
5711 struct isl_sched_graph
*scc
;
5712 struct isl_sched_graph
*cluster
;
5718 /* Initialize the clustering data structure "c" from "graph".
5720 * In particular, allocate memory, extract the SCCs from "graph"
5721 * into c->scc, initialize scc_cluster and construct
5722 * a band of schedule rows for each SCC.
5723 * Within each SCC, there is only one SCC by definition.
5724 * Each SCC initially belongs to a cluster containing only that SCC.
5726 static isl_stat
clustering_init(isl_ctx
*ctx
, struct isl_clustering
*c
,
5727 struct isl_sched_graph
*graph
)
5732 c
->scc
= isl_calloc_array(ctx
, struct isl_sched_graph
, c
->n
);
5733 c
->cluster
= isl_calloc_array(ctx
, struct isl_sched_graph
, c
->n
);
5734 c
->scc_cluster
= isl_calloc_array(ctx
, int, c
->n
);
5735 c
->scc_node
= isl_calloc_array(ctx
, int, c
->n
);
5736 c
->scc_in_merge
= isl_calloc_array(ctx
, int, c
->n
);
5737 if (!c
->scc
|| !c
->cluster
||
5738 !c
->scc_cluster
|| !c
->scc_node
|| !c
->scc_in_merge
)
5739 return isl_stat_error
;
5741 for (i
= 0; i
< c
->n
; ++i
) {
5742 if (extract_sub_graph(ctx
, graph
, &node_scc_exactly
,
5743 &edge_scc_exactly
, i
, &c
->scc
[i
]) < 0)
5744 return isl_stat_error
;
5746 if (compute_maxvar(&c
->scc
[i
]) < 0)
5747 return isl_stat_error
;
5748 if (compute_schedule_wcc_band(ctx
, &c
->scc
[i
]) < 0)
5749 return isl_stat_error
;
5750 c
->scc_cluster
[i
] = i
;
5756 /* Free all memory allocated for "c".
5758 static void clustering_free(isl_ctx
*ctx
, struct isl_clustering
*c
)
5763 for (i
= 0; i
< c
->n
; ++i
)
5764 graph_free(ctx
, &c
->scc
[i
]);
5767 for (i
= 0; i
< c
->n
; ++i
)
5768 graph_free(ctx
, &c
->cluster
[i
]);
5770 free(c
->scc_cluster
);
5772 free(c
->scc_in_merge
);
5775 /* Should we refrain from merging the cluster in "graph" with
5776 * any other cluster?
5777 * In particular, is its current schedule band empty and incomplete.
5779 static int bad_cluster(struct isl_sched_graph
*graph
)
5781 return graph
->n_row
< graph
->maxvar
&&
5782 graph
->n_total_row
== graph
->band_start
;
5785 /* Is "edge" a proximity edge with a non-empty dependence relation?
5787 static isl_bool
is_non_empty_proximity(struct isl_sched_edge
*edge
)
5789 if (!is_proximity(edge
))
5790 return isl_bool_false
;
5791 return isl_bool_not(isl_map_plain_is_empty(edge
->map
));
5794 /* Return the index of an edge in "graph" that can be used to merge
5795 * two clusters in "c".
5796 * Return graph->n_edge if no such edge can be found.
5797 * Return -1 on error.
5799 * In particular, return a proximity edge between two clusters
5800 * that is not marked "no_merge" and such that neither of the
5801 * two clusters has an incomplete, empty band.
5803 * If there are multiple such edges, then try and find the most
5804 * appropriate edge to use for merging. In particular, pick the edge
5805 * with the greatest weight. If there are multiple of those,
5806 * then pick one with the shortest distance between
5807 * the two cluster representatives.
5809 static int find_proximity(struct isl_sched_graph
*graph
,
5810 struct isl_clustering
*c
)
5812 int i
, best
= graph
->n_edge
, best_dist
, best_weight
;
5814 for (i
= 0; i
< graph
->n_edge
; ++i
) {
5815 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
5819 prox
= is_non_empty_proximity(edge
);
5826 if (bad_cluster(&c
->scc
[edge
->src
->scc
]) ||
5827 bad_cluster(&c
->scc
[edge
->dst
->scc
]))
5829 dist
= c
->scc_cluster
[edge
->dst
->scc
] -
5830 c
->scc_cluster
[edge
->src
->scc
];
5833 weight
= edge
->weight
;
5834 if (best
< graph
->n_edge
) {
5835 if (best_weight
> weight
)
5837 if (best_weight
== weight
&& best_dist
<= dist
)
5842 best_weight
= weight
;
5848 /* Internal data structure used in mark_merge_sccs.
5850 * "graph" is the dependence graph in which a strongly connected
5851 * component is constructed.
5852 * "scc_cluster" maps each SCC index to the cluster to which it belongs.
5853 * "src" and "dst" are the indices of the nodes that are being merged.
5855 struct isl_mark_merge_sccs_data
{
5856 struct isl_sched_graph
*graph
;
5862 /* Check whether the cluster containing node "i" depends on the cluster
5863 * containing node "j". If "i" and "j" belong to the same cluster,
5864 * then they are taken to depend on each other to ensure that
5865 * the resulting strongly connected component consists of complete
5866 * clusters. Furthermore, if "i" and "j" are the two nodes that
5867 * are being merged, then they are taken to depend on each other as well.
5868 * Otherwise, check if there is a (conditional) validity dependence
5869 * from node[j] to node[i], forcing node[i] to follow node[j].
5871 static isl_bool
cluster_follows(int i
, int j
, void *user
)
5873 struct isl_mark_merge_sccs_data
*data
= user
;
5874 struct isl_sched_graph
*graph
= data
->graph
;
5875 int *scc_cluster
= data
->scc_cluster
;
5877 if (data
->src
== i
&& data
->dst
== j
)
5878 return isl_bool_true
;
5879 if (data
->src
== j
&& data
->dst
== i
)
5880 return isl_bool_true
;
5881 if (scc_cluster
[graph
->node
[i
].scc
] == scc_cluster
[graph
->node
[j
].scc
])
5882 return isl_bool_true
;
5884 return graph_has_validity_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
5887 /* Mark all SCCs that belong to either of the two clusters in "c"
5888 * connected by the edge in "graph" with index "edge", or to any
5889 * of the intermediate clusters.
5890 * The marking is recorded in c->scc_in_merge.
5892 * The given edge has been selected for merging two clusters,
5893 * meaning that there is at least a proximity edge between the two nodes.
5894 * However, there may also be (indirect) validity dependences
5895 * between the two nodes. When merging the two clusters, all clusters
5896 * containing one or more of the intermediate nodes along the
5897 * indirect validity dependences need to be merged in as well.
5899 * First collect all such nodes by computing the strongly connected
5900 * component (SCC) containing the two nodes connected by the edge, where
5901 * the two nodes are considered to depend on each other to make
5902 * sure they end up in the same SCC. Similarly, each node is considered
5903 * to depend on every other node in the same cluster to ensure
5904 * that the SCC consists of complete clusters.
5906 * Then the original SCCs that contain any of these nodes are marked
5907 * in c->scc_in_merge.
5909 static isl_stat
mark_merge_sccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
5910 int edge
, struct isl_clustering
*c
)
5912 struct isl_mark_merge_sccs_data data
;
5913 struct isl_tarjan_graph
*g
;
5916 for (i
= 0; i
< c
->n
; ++i
)
5917 c
->scc_in_merge
[i
] = 0;
5920 data
.scc_cluster
= c
->scc_cluster
;
5921 data
.src
= graph
->edge
[edge
].src
- graph
->node
;
5922 data
.dst
= graph
->edge
[edge
].dst
- graph
->node
;
5924 g
= isl_tarjan_graph_component(ctx
, graph
->n
, data
.dst
,
5925 &cluster_follows
, &data
);
5931 isl_die(ctx
, isl_error_internal
,
5932 "expecting at least two nodes in component",
5934 if (g
->order
[--i
] != -1)
5935 isl_die(ctx
, isl_error_internal
,
5936 "expecting end of component marker", goto error
);
5938 for (--i
; i
>= 0 && g
->order
[i
] != -1; --i
) {
5939 int scc
= graph
->node
[g
->order
[i
]].scc
;
5940 c
->scc_in_merge
[scc
] = 1;
5943 isl_tarjan_graph_free(g
);
5946 isl_tarjan_graph_free(g
);
5947 return isl_stat_error
;
5950 /* Construct the identifier "cluster_i".
5952 static __isl_give isl_id
*cluster_id(isl_ctx
*ctx
, int i
)
5956 snprintf(name
, sizeof(name
), "cluster_%d", i
);
5957 return isl_id_alloc(ctx
, name
, NULL
);
5960 /* Construct the space of the cluster with index "i" containing
5961 * the strongly connected component "scc".
5963 * In particular, construct a space called cluster_i with dimension equal
5964 * to the number of schedule rows in the current band of "scc".
5966 static __isl_give isl_space
*cluster_space(struct isl_sched_graph
*scc
, int i
)
5972 nvar
= scc
->n_total_row
- scc
->band_start
;
5973 space
= isl_space_copy(scc
->node
[0].space
);
5974 space
= isl_space_params(space
);
5975 space
= isl_space_set_from_params(space
);
5976 space
= isl_space_add_dims(space
, isl_dim_set
, nvar
);
5977 id
= cluster_id(isl_space_get_ctx(space
), i
);
5978 space
= isl_space_set_tuple_id(space
, isl_dim_set
, id
);
5983 /* Collect the domain of the graph for merging clusters.
5985 * In particular, for each cluster with first SCC "i", construct
5986 * a set in the space called cluster_i with dimension equal
5987 * to the number of schedule rows in the current band of the cluster.
5989 static __isl_give isl_union_set
*collect_domain(isl_ctx
*ctx
,
5990 struct isl_sched_graph
*graph
, struct isl_clustering
*c
)
5994 isl_union_set
*domain
;
5996 space
= isl_space_params_alloc(ctx
, 0);
5997 domain
= isl_union_set_empty(space
);
5999 for (i
= 0; i
< graph
->scc
; ++i
) {
6002 if (!c
->scc_in_merge
[i
])
6004 if (c
->scc_cluster
[i
] != i
)
6006 space
= cluster_space(&c
->scc
[i
], i
);
6007 domain
= isl_union_set_add_set(domain
, isl_set_universe(space
));
6013 /* Construct a map from the original instances to the corresponding
6014 * cluster instance in the current bands of the clusters in "c".
6016 static __isl_give isl_union_map
*collect_cluster_map(isl_ctx
*ctx
,
6017 struct isl_sched_graph
*graph
, struct isl_clustering
*c
)
6021 isl_union_map
*cluster_map
;
6023 space
= isl_space_params_alloc(ctx
, 0);
6024 cluster_map
= isl_union_map_empty(space
);
6025 for (i
= 0; i
< graph
->scc
; ++i
) {
6029 if (!c
->scc_in_merge
[i
])
6032 id
= cluster_id(ctx
, c
->scc_cluster
[i
]);
6033 start
= c
->scc
[i
].band_start
;
6034 n
= c
->scc
[i
].n_total_row
- start
;
6035 for (j
= 0; j
< c
->scc
[i
].n
; ++j
) {
6038 struct isl_sched_node
*node
= &c
->scc
[i
].node
[j
];
6040 ma
= node_extract_partial_schedule_multi_aff(node
,
6042 ma
= isl_multi_aff_set_tuple_id(ma
, isl_dim_out
,
6044 map
= isl_map_from_multi_aff(ma
);
6045 cluster_map
= isl_union_map_add_map(cluster_map
, map
);
6053 /* Add "umap" to the schedule constraints "sc" of all types of "edge"
6054 * that are not isl_edge_condition or isl_edge_conditional_validity.
6056 static __isl_give isl_schedule_constraints
*add_non_conditional_constraints(
6057 struct isl_sched_edge
*edge
, __isl_keep isl_union_map
*umap
,
6058 __isl_take isl_schedule_constraints
*sc
)
6060 enum isl_edge_type t
;
6065 for (t
= isl_edge_first
; t
<= isl_edge_last
; ++t
) {
6066 if (t
== isl_edge_condition
||
6067 t
== isl_edge_conditional_validity
)
6069 if (!is_type(edge
, t
))
6071 sc
= isl_schedule_constraints_add(sc
, t
,
6072 isl_union_map_copy(umap
));
6078 /* Add schedule constraints of types isl_edge_condition and
6079 * isl_edge_conditional_validity to "sc" by applying "umap" to
6080 * the domains of the wrapped relations in domain and range
6081 * of the corresponding tagged constraints of "edge".
6083 static __isl_give isl_schedule_constraints
*add_conditional_constraints(
6084 struct isl_sched_edge
*edge
, __isl_keep isl_union_map
*umap
,
6085 __isl_take isl_schedule_constraints
*sc
)
6087 enum isl_edge_type t
;
6088 isl_union_map
*tagged
;
6090 for (t
= isl_edge_condition
; t
<= isl_edge_conditional_validity
; ++t
) {
6091 if (!is_type(edge
, t
))
6093 if (t
== isl_edge_condition
)
6094 tagged
= isl_union_map_copy(edge
->tagged_condition
);
6096 tagged
= isl_union_map_copy(edge
->tagged_validity
);
6097 tagged
= isl_union_map_zip(tagged
);
6098 tagged
= isl_union_map_apply_domain(tagged
,
6099 isl_union_map_copy(umap
));
6100 tagged
= isl_union_map_zip(tagged
);
6101 sc
= isl_schedule_constraints_add(sc
, t
, tagged
);
6109 /* Given a mapping "cluster_map" from the original instances to
6110 * the cluster instances, add schedule constraints on the clusters
6111 * to "sc" corresponding to the original constraints represented by "edge".
6113 * For non-tagged dependence constraints, the cluster constraints
6114 * are obtained by applying "cluster_map" to the edge->map.
6116 * For tagged dependence constraints, "cluster_map" needs to be applied
6117 * to the domains of the wrapped relations in domain and range
6118 * of the tagged dependence constraints. Pick out the mappings
6119 * from these domains from "cluster_map" and construct their product.
6120 * This mapping can then be applied to the pair of domains.
6122 static __isl_give isl_schedule_constraints
*collect_edge_constraints(
6123 struct isl_sched_edge
*edge
, __isl_keep isl_union_map
*cluster_map
,
6124 __isl_take isl_schedule_constraints
*sc
)
6126 isl_union_map
*umap
;
6128 isl_union_set
*uset
;
6129 isl_union_map
*umap1
, *umap2
;
6134 umap
= isl_union_map_from_map(isl_map_copy(edge
->map
));
6135 umap
= isl_union_map_apply_domain(umap
,
6136 isl_union_map_copy(cluster_map
));
6137 umap
= isl_union_map_apply_range(umap
,
6138 isl_union_map_copy(cluster_map
));
6139 sc
= add_non_conditional_constraints(edge
, umap
, sc
);
6140 isl_union_map_free(umap
);
6142 if (!sc
|| (!is_condition(edge
) && !is_conditional_validity(edge
)))
6145 space
= isl_space_domain(isl_map_get_space(edge
->map
));
6146 uset
= isl_union_set_from_set(isl_set_universe(space
));
6147 umap1
= isl_union_map_copy(cluster_map
);
6148 umap1
= isl_union_map_intersect_domain(umap1
, uset
);
6149 space
= isl_space_range(isl_map_get_space(edge
->map
));
6150 uset
= isl_union_set_from_set(isl_set_universe(space
));
6151 umap2
= isl_union_map_copy(cluster_map
);
6152 umap2
= isl_union_map_intersect_domain(umap2
, uset
);
6153 umap
= isl_union_map_product(umap1
, umap2
);
6155 sc
= add_conditional_constraints(edge
, umap
, sc
);
6157 isl_union_map_free(umap
);
6161 /* Given a mapping "cluster_map" from the original instances to
6162 * the cluster instances, add schedule constraints on the clusters
6163 * to "sc" corresponding to all edges in "graph" between nodes that
6164 * belong to SCCs that are marked for merging in "scc_in_merge".
6166 static __isl_give isl_schedule_constraints
*collect_constraints(
6167 struct isl_sched_graph
*graph
, int *scc_in_merge
,
6168 __isl_keep isl_union_map
*cluster_map
,
6169 __isl_take isl_schedule_constraints
*sc
)
6173 for (i
= 0; i
< graph
->n_edge
; ++i
) {
6174 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
6176 if (!scc_in_merge
[edge
->src
->scc
])
6178 if (!scc_in_merge
[edge
->dst
->scc
])
6180 sc
= collect_edge_constraints(edge
, cluster_map
, sc
);
6186 /* Construct a dependence graph for scheduling clusters with respect
6187 * to each other and store the result in "merge_graph".
6188 * In particular, the nodes of the graph correspond to the schedule
6189 * dimensions of the current bands of those clusters that have been
6190 * marked for merging in "c".
6192 * First construct an isl_schedule_constraints object for this domain
6193 * by transforming the edges in "graph" to the domain.
6194 * Then initialize a dependence graph for scheduling from these
6197 static isl_stat
init_merge_graph(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
6198 struct isl_clustering
*c
, struct isl_sched_graph
*merge_graph
)
6200 isl_union_set
*domain
;
6201 isl_union_map
*cluster_map
;
6202 isl_schedule_constraints
*sc
;
6205 domain
= collect_domain(ctx
, graph
, c
);
6206 sc
= isl_schedule_constraints_on_domain(domain
);
6208 return isl_stat_error
;
6209 cluster_map
= collect_cluster_map(ctx
, graph
, c
);
6210 sc
= collect_constraints(graph
, c
->scc_in_merge
, cluster_map
, sc
);
6211 isl_union_map_free(cluster_map
);
6213 r
= graph_init(merge_graph
, sc
);
6215 isl_schedule_constraints_free(sc
);
6220 /* Compute the maximal number of remaining schedule rows that still need
6221 * to be computed for the nodes that belong to clusters with the maximal
6222 * dimension for the current band (i.e., the band that is to be merged).
6223 * Only clusters that are about to be merged are considered.
6224 * "maxvar" is the maximal dimension for the current band.
6225 * "c" contains information about the clusters.
6227 * Return the maximal number of remaining schedule rows or -1 on error.
6229 static int compute_maxvar_max_slack(int maxvar
, struct isl_clustering
*c
)
6235 for (i
= 0; i
< c
->n
; ++i
) {
6237 struct isl_sched_graph
*scc
;
6239 if (!c
->scc_in_merge
[i
])
6242 nvar
= scc
->n_total_row
- scc
->band_start
;
6245 for (j
= 0; j
< scc
->n
; ++j
) {
6246 struct isl_sched_node
*node
= &scc
->node
[j
];
6249 if (node_update_vmap(node
) < 0)
6251 slack
= node
->nvar
- node
->rank
;
6252 if (slack
> max_slack
)
6260 /* If there are any clusters where the dimension of the current band
6261 * (i.e., the band that is to be merged) is smaller than "maxvar" and
6262 * if there are any nodes in such a cluster where the number
6263 * of remaining schedule rows that still need to be computed
6264 * is greater than "max_slack", then return the smallest current band
6265 * dimension of all these clusters. Otherwise return the original value
6266 * of "maxvar". Return -1 in case of any error.
6267 * Only clusters that are about to be merged are considered.
6268 * "c" contains information about the clusters.
6270 static int limit_maxvar_to_slack(int maxvar
, int max_slack
,
6271 struct isl_clustering
*c
)
6275 for (i
= 0; i
< c
->n
; ++i
) {
6277 struct isl_sched_graph
*scc
;
6279 if (!c
->scc_in_merge
[i
])
6282 nvar
= scc
->n_total_row
- scc
->band_start
;
6285 for (j
= 0; j
< scc
->n
; ++j
) {
6286 struct isl_sched_node
*node
= &scc
->node
[j
];
6289 if (node_update_vmap(node
) < 0)
6291 slack
= node
->nvar
- node
->rank
;
6292 if (slack
> max_slack
) {
6302 /* Adjust merge_graph->maxvar based on the number of remaining schedule rows
6303 * that still need to be computed. In particular, if there is a node
6304 * in a cluster where the dimension of the current band is smaller
6305 * than merge_graph->maxvar, but the number of remaining schedule rows
6306 * is greater than that of any node in a cluster with the maximal
6307 * dimension for the current band (i.e., merge_graph->maxvar),
6308 * then adjust merge_graph->maxvar to the (smallest) current band dimension
6309 * of those clusters. Without this adjustment, the total number of
6310 * schedule dimensions would be increased, resulting in a skewed view
6311 * of the number of coincident dimensions.
6312 * "c" contains information about the clusters.
6314 * If the maximize_band_depth option is set and merge_graph->maxvar is reduced,
6315 * then there is no point in attempting any merge since it will be rejected
6316 * anyway. Set merge_graph->maxvar to zero in such cases.
6318 static isl_stat
adjust_maxvar_to_slack(isl_ctx
*ctx
,
6319 struct isl_sched_graph
*merge_graph
, struct isl_clustering
*c
)
6321 int max_slack
, maxvar
;
6323 max_slack
= compute_maxvar_max_slack(merge_graph
->maxvar
, c
);
6325 return isl_stat_error
;
6326 maxvar
= limit_maxvar_to_slack(merge_graph
->maxvar
, max_slack
, c
);
6328 return isl_stat_error
;
6330 if (maxvar
< merge_graph
->maxvar
) {
6331 if (isl_options_get_schedule_maximize_band_depth(ctx
))
6332 merge_graph
->maxvar
= 0;
6334 merge_graph
->maxvar
= maxvar
;
6340 /* Return the number of coincident dimensions in the current band of "graph",
6341 * where the nodes of "graph" are assumed to be scheduled by a single band.
6343 static int get_n_coincident(struct isl_sched_graph
*graph
)
6347 for (i
= graph
->band_start
; i
< graph
->n_total_row
; ++i
)
6348 if (!graph
->node
[0].coincident
[i
])
6351 return i
- graph
->band_start
;
6354 /* Should the clusters be merged based on the cluster schedule
6355 * in the current (and only) band of "merge_graph", given that
6356 * coincidence should be maximized?
6358 * If the number of coincident schedule dimensions in the merged band
6359 * would be less than the maximal number of coincident schedule dimensions
6360 * in any of the merged clusters, then the clusters should not be merged.
6362 static isl_bool
ok_to_merge_coincident(struct isl_clustering
*c
,
6363 struct isl_sched_graph
*merge_graph
)
6370 for (i
= 0; i
< c
->n
; ++i
) {
6371 if (!c
->scc_in_merge
[i
])
6373 n_coincident
= get_n_coincident(&c
->scc
[i
]);
6374 if (n_coincident
> max_coincident
)
6375 max_coincident
= n_coincident
;
6378 n_coincident
= get_n_coincident(merge_graph
);
6380 return n_coincident
>= max_coincident
;
6383 /* Return the transformation on "node" expressed by the current (and only)
6384 * band of "merge_graph" applied to the clusters in "c".
6386 * First find the representation of "node" in its SCC in "c" and
6387 * extract the transformation expressed by the current band.
6388 * Then extract the transformation applied by "merge_graph"
6389 * to the cluster to which this SCC belongs.
6390 * Combine the two to obtain the complete transformation on the node.
6392 * Note that the range of the first transformation is an anonymous space,
6393 * while the domain of the second is named "cluster_X". The range
6394 * of the former therefore needs to be adjusted before the two
6397 static __isl_give isl_map
*extract_node_transformation(isl_ctx
*ctx
,
6398 struct isl_sched_node
*node
, struct isl_clustering
*c
,
6399 struct isl_sched_graph
*merge_graph
)
6401 struct isl_sched_node
*scc_node
, *cluster_node
;
6405 isl_multi_aff
*ma
, *ma2
;
6407 scc_node
= graph_find_node(ctx
, &c
->scc
[node
->scc
], node
->space
);
6408 start
= c
->scc
[node
->scc
].band_start
;
6409 n
= c
->scc
[node
->scc
].n_total_row
- start
;
6410 ma
= node_extract_partial_schedule_multi_aff(scc_node
, start
, n
);
6411 space
= cluster_space(&c
->scc
[node
->scc
], c
->scc_cluster
[node
->scc
]);
6412 cluster_node
= graph_find_node(ctx
, merge_graph
, space
);
6413 if (space
&& !cluster_node
)
6414 isl_die(ctx
, isl_error_internal
, "unable to find cluster",
6415 space
= isl_space_free(space
));
6416 id
= isl_space_get_tuple_id(space
, isl_dim_set
);
6417 ma
= isl_multi_aff_set_tuple_id(ma
, isl_dim_out
, id
);
6418 isl_space_free(space
);
6419 n
= merge_graph
->n_total_row
;
6420 ma2
= node_extract_partial_schedule_multi_aff(cluster_node
, 0, n
);
6421 ma
= isl_multi_aff_pullback_multi_aff(ma2
, ma
);
6423 return isl_map_from_multi_aff(ma
);
6426 /* Give a set of distances "set", are they bounded by a small constant
6427 * in direction "pos"?
6428 * In practice, check if they are bounded by 2 by checking that there
6429 * are no elements with a value greater than or equal to 3 or
6430 * smaller than or equal to -3.
6432 static isl_bool
distance_is_bounded(__isl_keep isl_set
*set
, int pos
)
6438 return isl_bool_error
;
6440 test
= isl_set_copy(set
);
6441 test
= isl_set_lower_bound_si(test
, isl_dim_set
, pos
, 3);
6442 bounded
= isl_set_is_empty(test
);
6445 if (bounded
< 0 || !bounded
)
6448 test
= isl_set_copy(set
);
6449 test
= isl_set_upper_bound_si(test
, isl_dim_set
, pos
, -3);
6450 bounded
= isl_set_is_empty(test
);
6456 /* Does the set "set" have a fixed (but possible parametric) value
6457 * at dimension "pos"?
6459 static isl_bool
has_single_value(__isl_keep isl_set
*set
, int pos
)
6465 return isl_bool_error
;
6466 set
= isl_set_copy(set
);
6467 n
= isl_set_dim(set
, isl_dim_set
);
6468 set
= isl_set_project_out(set
, isl_dim_set
, pos
+ 1, n
- (pos
+ 1));
6469 set
= isl_set_project_out(set
, isl_dim_set
, 0, pos
);
6470 single
= isl_set_is_singleton(set
);
6476 /* Does "map" have a fixed (but possible parametric) value
6477 * at dimension "pos" of either its domain or its range?
6479 static isl_bool
has_singular_src_or_dst(__isl_keep isl_map
*map
, int pos
)
6484 set
= isl_map_domain(isl_map_copy(map
));
6485 single
= has_single_value(set
, pos
);
6488 if (single
< 0 || single
)
6491 set
= isl_map_range(isl_map_copy(map
));
6492 single
= has_single_value(set
, pos
);
6498 /* Does the edge "edge" from "graph" have bounded dependence distances
6499 * in the merged graph "merge_graph" of a selection of clusters in "c"?
6501 * Extract the complete transformations of the source and destination
6502 * nodes of the edge, apply them to the edge constraints and
6503 * compute the differences. Finally, check if these differences are bounded
6504 * in each direction.
6506 * If the dimension of the band is greater than the number of
6507 * dimensions that can be expected to be optimized by the edge
6508 * (based on its weight), then also allow the differences to be unbounded
6509 * in the remaining dimensions, but only if either the source or
6510 * the destination has a fixed value in that direction.
6511 * This allows a statement that produces values that are used by
6512 * several instances of another statement to be merged with that
6514 * However, merging such clusters will introduce an inherently
6515 * large proximity distance inside the merged cluster, meaning
6516 * that proximity distances will no longer be optimized in
6517 * subsequent merges. These merges are therefore only allowed
6518 * after all other possible merges have been tried.
6519 * The first time such a merge is encountered, the weight of the edge
6520 * is replaced by a negative weight. The second time (i.e., after
6521 * all merges over edges with a non-negative weight have been tried),
6522 * the merge is allowed.
6524 static isl_bool
has_bounded_distances(isl_ctx
*ctx
, struct isl_sched_edge
*edge
,
6525 struct isl_sched_graph
*graph
, struct isl_clustering
*c
,
6526 struct isl_sched_graph
*merge_graph
)
6533 map
= isl_map_copy(edge
->map
);
6534 t
= extract_node_transformation(ctx
, edge
->src
, c
, merge_graph
);
6535 map
= isl_map_apply_domain(map
, t
);
6536 t
= extract_node_transformation(ctx
, edge
->dst
, c
, merge_graph
);
6537 map
= isl_map_apply_range(map
, t
);
6538 dist
= isl_map_deltas(isl_map_copy(map
));
6540 bounded
= isl_bool_true
;
6541 n
= isl_set_dim(dist
, isl_dim_set
);
6542 n_slack
= n
- edge
->weight
;
6543 if (edge
->weight
< 0)
6544 n_slack
-= graph
->max_weight
+ 1;
6545 for (i
= 0; i
< n
; ++i
) {
6546 isl_bool bounded_i
, singular_i
;
6548 bounded_i
= distance_is_bounded(dist
, i
);
6553 if (edge
->weight
>= 0)
6554 bounded
= isl_bool_false
;
6558 singular_i
= has_singular_src_or_dst(map
, i
);
6563 bounded
= isl_bool_false
;
6566 if (!bounded
&& i
>= n
&& edge
->weight
>= 0)
6567 edge
->weight
-= graph
->max_weight
+ 1;
6575 return isl_bool_error
;
6578 /* Should the clusters be merged based on the cluster schedule
6579 * in the current (and only) band of "merge_graph"?
6580 * "graph" is the original dependence graph, while "c" records
6581 * which SCCs are involved in the latest merge.
6583 * In particular, is there at least one proximity constraint
6584 * that is optimized by the merge?
6586 * A proximity constraint is considered to be optimized
6587 * if the dependence distances are small.
6589 static isl_bool
ok_to_merge_proximity(isl_ctx
*ctx
,
6590 struct isl_sched_graph
*graph
, struct isl_clustering
*c
,
6591 struct isl_sched_graph
*merge_graph
)
6595 for (i
= 0; i
< graph
->n_edge
; ++i
) {
6596 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
6599 if (!is_proximity(edge
))
6601 if (!c
->scc_in_merge
[edge
->src
->scc
])
6603 if (!c
->scc_in_merge
[edge
->dst
->scc
])
6605 if (c
->scc_cluster
[edge
->dst
->scc
] ==
6606 c
->scc_cluster
[edge
->src
->scc
])
6608 bounded
= has_bounded_distances(ctx
, edge
, graph
, c
,
6610 if (bounded
< 0 || bounded
)
6614 return isl_bool_false
;
6617 /* Should the clusters be merged based on the cluster schedule
6618 * in the current (and only) band of "merge_graph"?
6619 * "graph" is the original dependence graph, while "c" records
6620 * which SCCs are involved in the latest merge.
6622 * If the current band is empty, then the clusters should not be merged.
6624 * If the band depth should be maximized and the merge schedule
6625 * is incomplete (meaning that the dimension of some of the schedule
6626 * bands in the original schedule will be reduced), then the clusters
6627 * should not be merged.
6629 * If the schedule_maximize_coincidence option is set, then check that
6630 * the number of coincident schedule dimensions is not reduced.
6632 * Finally, only allow the merge if at least one proximity
6633 * constraint is optimized.
6635 static isl_bool
ok_to_merge(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
6636 struct isl_clustering
*c
, struct isl_sched_graph
*merge_graph
)
6638 if (merge_graph
->n_total_row
== merge_graph
->band_start
)
6639 return isl_bool_false
;
6641 if (isl_options_get_schedule_maximize_band_depth(ctx
) &&
6642 merge_graph
->n_total_row
< merge_graph
->maxvar
)
6643 return isl_bool_false
;
6645 if (isl_options_get_schedule_maximize_coincidence(ctx
)) {
6648 ok
= ok_to_merge_coincident(c
, merge_graph
);
6653 return ok_to_merge_proximity(ctx
, graph
, c
, merge_graph
);
6656 /* Apply the schedule in "t_node" to the "n" rows starting at "first"
6657 * of the schedule in "node" and return the result.
6659 * That is, essentially compute
6661 * T * N(first:first+n-1)
6663 * taking into account the constant term and the parameter coefficients
6666 static __isl_give isl_mat
*node_transformation(isl_ctx
*ctx
,
6667 struct isl_sched_node
*t_node
, struct isl_sched_node
*node
,
6672 int n_row
, n_col
, n_param
, n_var
;
6674 n_param
= node
->nparam
;
6676 n_row
= isl_mat_rows(t_node
->sched
);
6677 n_col
= isl_mat_cols(node
->sched
);
6678 t
= isl_mat_alloc(ctx
, n_row
, n_col
);
6681 for (i
= 0; i
< n_row
; ++i
) {
6682 isl_seq_cpy(t
->row
[i
], t_node
->sched
->row
[i
], 1 + n_param
);
6683 isl_seq_clr(t
->row
[i
] + 1 + n_param
, n_var
);
6684 for (j
= 0; j
< n
; ++j
)
6685 isl_seq_addmul(t
->row
[i
],
6686 t_node
->sched
->row
[i
][1 + n_param
+ j
],
6687 node
->sched
->row
[first
+ j
],
6688 1 + n_param
+ n_var
);
6693 /* Apply the cluster schedule in "t_node" to the current band
6694 * schedule of the nodes in "graph".
6696 * In particular, replace the rows starting at band_start
6697 * by the result of applying the cluster schedule in "t_node"
6698 * to the original rows.
6700 * The coincidence of the schedule is determined by the coincidence
6701 * of the cluster schedule.
6703 static isl_stat
transform(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
6704 struct isl_sched_node
*t_node
)
6710 start
= graph
->band_start
;
6711 n
= graph
->n_total_row
- start
;
6713 n_new
= isl_mat_rows(t_node
->sched
);
6714 for (i
= 0; i
< graph
->n
; ++i
) {
6715 struct isl_sched_node
*node
= &graph
->node
[i
];
6718 t
= node_transformation(ctx
, t_node
, node
, start
, n
);
6719 node
->sched
= isl_mat_drop_rows(node
->sched
, start
, n
);
6720 node
->sched
= isl_mat_concat(node
->sched
, t
);
6721 node
->sched_map
= isl_map_free(node
->sched_map
);
6723 return isl_stat_error
;
6724 for (j
= 0; j
< n_new
; ++j
)
6725 node
->coincident
[start
+ j
] = t_node
->coincident
[j
];
6727 graph
->n_total_row
-= n
;
6729 graph
->n_total_row
+= n_new
;
6730 graph
->n_row
+= n_new
;
6735 /* Merge the clusters marked for merging in "c" into a single
6736 * cluster using the cluster schedule in the current band of "merge_graph".
6737 * The representative SCC for the new cluster is the SCC with
6738 * the smallest index.
6740 * The current band schedule of each SCC in the new cluster is obtained
6741 * by applying the schedule of the corresponding original cluster
6742 * to the original band schedule.
6743 * All SCCs in the new cluster have the same number of schedule rows.
6745 static isl_stat
merge(isl_ctx
*ctx
, struct isl_clustering
*c
,
6746 struct isl_sched_graph
*merge_graph
)
6752 for (i
= 0; i
< c
->n
; ++i
) {
6753 struct isl_sched_node
*node
;
6755 if (!c
->scc_in_merge
[i
])
6759 space
= cluster_space(&c
->scc
[i
], c
->scc_cluster
[i
]);
6761 return isl_stat_error
;
6762 node
= graph_find_node(ctx
, merge_graph
, space
);
6763 isl_space_free(space
);
6765 isl_die(ctx
, isl_error_internal
,
6766 "unable to find cluster",
6767 return isl_stat_error
);
6768 if (transform(ctx
, &c
->scc
[i
], node
) < 0)
6769 return isl_stat_error
;
6770 c
->scc_cluster
[i
] = cluster
;
6776 /* Try and merge the clusters of SCCs marked in c->scc_in_merge
6777 * by scheduling the current cluster bands with respect to each other.
6779 * Construct a dependence graph with a space for each cluster and
6780 * with the coordinates of each space corresponding to the schedule
6781 * dimensions of the current band of that cluster.
6782 * Construct a cluster schedule in this cluster dependence graph and
6783 * apply it to the current cluster bands if it is applicable
6784 * according to ok_to_merge.
6786 * If the number of remaining schedule dimensions in a cluster
6787 * with a non-maximal current schedule dimension is greater than
6788 * the number of remaining schedule dimensions in clusters
6789 * with a maximal current schedule dimension, then restrict
6790 * the number of rows to be computed in the cluster schedule
6791 * to the minimal such non-maximal current schedule dimension.
6792 * Do this by adjusting merge_graph.maxvar.
6794 * Return isl_bool_true if the clusters have effectively been merged
6795 * into a single cluster.
6797 * Note that since the standard scheduling algorithm minimizes the maximal
6798 * distance over proximity constraints, the proximity constraints between
6799 * the merged clusters may not be optimized any further than what is
6800 * sufficient to bring the distances within the limits of the internal
6801 * proximity constraints inside the individual clusters.
6802 * It may therefore make sense to perform an additional translation step
6803 * to bring the clusters closer to each other, while maintaining
6804 * the linear part of the merging schedule found using the standard
6805 * scheduling algorithm.
6807 static isl_bool
try_merge(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
6808 struct isl_clustering
*c
)
6810 struct isl_sched_graph merge_graph
= { 0 };
6813 if (init_merge_graph(ctx
, graph
, c
, &merge_graph
) < 0)
6816 if (compute_maxvar(&merge_graph
) < 0)
6818 if (adjust_maxvar_to_slack(ctx
, &merge_graph
,c
) < 0)
6820 if (compute_schedule_wcc_band(ctx
, &merge_graph
) < 0)
6822 merged
= ok_to_merge(ctx
, graph
, c
, &merge_graph
);
6823 if (merged
&& merge(ctx
, c
, &merge_graph
) < 0)
6826 graph_free(ctx
, &merge_graph
);
6829 graph_free(ctx
, &merge_graph
);
6830 return isl_bool_error
;
6833 /* Is there any edge marked "no_merge" between two SCCs that are
6834 * about to be merged (i.e., that are set in "scc_in_merge")?
6835 * "merge_edge" is the proximity edge along which the clusters of SCCs
6836 * are going to be merged.
6838 * If there is any edge between two SCCs with a negative weight,
6839 * while the weight of "merge_edge" is non-negative, then this
6840 * means that the edge was postponed. "merge_edge" should then
6841 * also be postponed since merging along the edge with negative weight should
6842 * be postponed until all edges with non-negative weight have been tried.
6843 * Replace the weight of "merge_edge" by a negative weight as well and
6844 * tell the caller not to attempt a merge.
6846 static int any_no_merge(struct isl_sched_graph
*graph
, int *scc_in_merge
,
6847 struct isl_sched_edge
*merge_edge
)
6851 for (i
= 0; i
< graph
->n_edge
; ++i
) {
6852 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
6854 if (!scc_in_merge
[edge
->src
->scc
])
6856 if (!scc_in_merge
[edge
->dst
->scc
])
6860 if (merge_edge
->weight
>= 0 && edge
->weight
< 0) {
6861 merge_edge
->weight
-= graph
->max_weight
+ 1;
6869 /* Merge the two clusters in "c" connected by the edge in "graph"
6870 * with index "edge" into a single cluster.
6871 * If it turns out to be impossible to merge these two clusters,
6872 * then mark the edge as "no_merge" such that it will not be
6875 * First mark all SCCs that need to be merged. This includes the SCCs
6876 * in the two clusters, but it may also include the SCCs
6877 * of intermediate clusters.
6878 * If there is already a no_merge edge between any pair of such SCCs,
6879 * then simply mark the current edge as no_merge as well.
6880 * Likewise, if any of those edges was postponed by has_bounded_distances,
6881 * then postpone the current edge as well.
6882 * Otherwise, try and merge the clusters and mark "edge" as "no_merge"
6883 * if the clusters did not end up getting merged, unless the non-merge
6884 * is due to the fact that the edge was postponed. This postponement
6885 * can be recognized by a change in weight (from non-negative to negative).
6887 static isl_stat
merge_clusters_along_edge(isl_ctx
*ctx
,
6888 struct isl_sched_graph
*graph
, int edge
, struct isl_clustering
*c
)
6891 int edge_weight
= graph
->edge
[edge
].weight
;
6893 if (mark_merge_sccs(ctx
, graph
, edge
, c
) < 0)
6894 return isl_stat_error
;
6896 if (any_no_merge(graph
, c
->scc_in_merge
, &graph
->edge
[edge
]))
6897 merged
= isl_bool_false
;
6899 merged
= try_merge(ctx
, graph
, c
);
6901 return isl_stat_error
;
6902 if (!merged
&& edge_weight
== graph
->edge
[edge
].weight
)
6903 graph
->edge
[edge
].no_merge
= 1;
6908 /* Does "node" belong to the cluster identified by "cluster"?
6910 static int node_cluster_exactly(struct isl_sched_node
*node
, int cluster
)
6912 return node
->cluster
== cluster
;
6915 /* Does "edge" connect two nodes belonging to the cluster
6916 * identified by "cluster"?
6918 static int edge_cluster_exactly(struct isl_sched_edge
*edge
, int cluster
)
6920 return edge
->src
->cluster
== cluster
&& edge
->dst
->cluster
== cluster
;
6923 /* Swap the schedule of "node1" and "node2".
6924 * Both nodes have been derived from the same node in a common parent graph.
6925 * Since the "coincident" field is shared with that node
6926 * in the parent graph, there is no need to also swap this field.
6928 static void swap_sched(struct isl_sched_node
*node1
,
6929 struct isl_sched_node
*node2
)
6934 sched
= node1
->sched
;
6935 node1
->sched
= node2
->sched
;
6936 node2
->sched
= sched
;
6938 sched_map
= node1
->sched_map
;
6939 node1
->sched_map
= node2
->sched_map
;
6940 node2
->sched_map
= sched_map
;
6943 /* Copy the current band schedule from the SCCs that form the cluster
6944 * with index "pos" to the actual cluster at position "pos".
6945 * By construction, the index of the first SCC that belongs to the cluster
6948 * The order of the nodes inside both the SCCs and the cluster
6949 * is assumed to be same as the order in the original "graph".
6951 * Since the SCC graphs will no longer be used after this function,
6952 * the schedules are actually swapped rather than copied.
6954 static isl_stat
copy_partial(struct isl_sched_graph
*graph
,
6955 struct isl_clustering
*c
, int pos
)
6959 c
->cluster
[pos
].n_total_row
= c
->scc
[pos
].n_total_row
;
6960 c
->cluster
[pos
].n_row
= c
->scc
[pos
].n_row
;
6961 c
->cluster
[pos
].maxvar
= c
->scc
[pos
].maxvar
;
6963 for (i
= 0; i
< graph
->n
; ++i
) {
6967 if (graph
->node
[i
].cluster
!= pos
)
6969 s
= graph
->node
[i
].scc
;
6970 k
= c
->scc_node
[s
]++;
6971 swap_sched(&c
->cluster
[pos
].node
[j
], &c
->scc
[s
].node
[k
]);
6972 if (c
->scc
[s
].maxvar
> c
->cluster
[pos
].maxvar
)
6973 c
->cluster
[pos
].maxvar
= c
->scc
[s
].maxvar
;
6980 /* Is there a (conditional) validity dependence from node[j] to node[i],
6981 * forcing node[i] to follow node[j] or do the nodes belong to the same
6984 static isl_bool
node_follows_strong_or_same_cluster(int i
, int j
, void *user
)
6986 struct isl_sched_graph
*graph
= user
;
6988 if (graph
->node
[i
].cluster
== graph
->node
[j
].cluster
)
6989 return isl_bool_true
;
6990 return graph_has_validity_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
6993 /* Extract the merged clusters of SCCs in "graph", sort them, and
6994 * store them in c->clusters. Update c->scc_cluster accordingly.
6996 * First keep track of the cluster containing the SCC to which a node
6997 * belongs in the node itself.
6998 * Then extract the clusters into c->clusters, copying the current
6999 * band schedule from the SCCs that belong to the cluster.
7000 * Do this only once per cluster.
7002 * Finally, topologically sort the clusters and update c->scc_cluster
7003 * to match the new scc numbering. While the SCCs were originally
7004 * sorted already, some SCCs that depend on some other SCCs may
7005 * have been merged with SCCs that appear before these other SCCs.
7006 * A reordering may therefore be required.
7008 static isl_stat
extract_clusters(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
7009 struct isl_clustering
*c
)
7013 for (i
= 0; i
< graph
->n
; ++i
)
7014 graph
->node
[i
].cluster
= c
->scc_cluster
[graph
->node
[i
].scc
];
7016 for (i
= 0; i
< graph
->scc
; ++i
) {
7017 if (c
->scc_cluster
[i
] != i
)
7019 if (extract_sub_graph(ctx
, graph
, &node_cluster_exactly
,
7020 &edge_cluster_exactly
, i
, &c
->cluster
[i
]) < 0)
7021 return isl_stat_error
;
7022 c
->cluster
[i
].src_scc
= -1;
7023 c
->cluster
[i
].dst_scc
= -1;
7024 if (copy_partial(graph
, c
, i
) < 0)
7025 return isl_stat_error
;
7028 if (detect_ccs(ctx
, graph
, &node_follows_strong_or_same_cluster
) < 0)
7029 return isl_stat_error
;
7030 for (i
= 0; i
< graph
->n
; ++i
)
7031 c
->scc_cluster
[graph
->node
[i
].scc
] = graph
->node
[i
].cluster
;
7036 /* Compute weights on the proximity edges of "graph" that can
7037 * be used by find_proximity to find the most appropriate
7038 * proximity edge to use to merge two clusters in "c".
7039 * The weights are also used by has_bounded_distances to determine
7040 * whether the merge should be allowed.
7041 * Store the maximum of the computed weights in graph->max_weight.
7043 * The computed weight is a measure for the number of remaining schedule
7044 * dimensions that can still be completely aligned.
7045 * In particular, compute the number of equalities between
7046 * input dimensions and output dimensions in the proximity constraints.
7047 * The directions that are already handled by outer schedule bands
7048 * are projected out prior to determining this number.
7050 * Edges that will never be considered by find_proximity are ignored.
7052 static isl_stat
compute_weights(struct isl_sched_graph
*graph
,
7053 struct isl_clustering
*c
)
7057 graph
->max_weight
= 0;
7059 for (i
= 0; i
< graph
->n_edge
; ++i
) {
7060 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
7061 struct isl_sched_node
*src
= edge
->src
;
7062 struct isl_sched_node
*dst
= edge
->dst
;
7063 isl_basic_map
*hull
;
7067 prox
= is_non_empty_proximity(edge
);
7069 return isl_stat_error
;
7072 if (bad_cluster(&c
->scc
[edge
->src
->scc
]) ||
7073 bad_cluster(&c
->scc
[edge
->dst
->scc
]))
7075 if (c
->scc_cluster
[edge
->dst
->scc
] ==
7076 c
->scc_cluster
[edge
->src
->scc
])
7079 hull
= isl_map_affine_hull(isl_map_copy(edge
->map
));
7080 hull
= isl_basic_map_transform_dims(hull
, isl_dim_in
, 0,
7081 isl_mat_copy(src
->vmap
));
7082 hull
= isl_basic_map_transform_dims(hull
, isl_dim_out
, 0,
7083 isl_mat_copy(dst
->vmap
));
7084 hull
= isl_basic_map_project_out(hull
,
7085 isl_dim_in
, 0, src
->rank
);
7086 hull
= isl_basic_map_project_out(hull
,
7087 isl_dim_out
, 0, dst
->rank
);
7088 hull
= isl_basic_map_remove_divs(hull
);
7089 n_in
= isl_basic_map_dim(hull
, isl_dim_in
);
7090 n_out
= isl_basic_map_dim(hull
, isl_dim_out
);
7091 hull
= isl_basic_map_drop_constraints_not_involving_dims(hull
,
7092 isl_dim_in
, 0, n_in
);
7093 hull
= isl_basic_map_drop_constraints_not_involving_dims(hull
,
7094 isl_dim_out
, 0, n_out
);
7096 return isl_stat_error
;
7097 edge
->weight
= isl_basic_map_n_equality(hull
);
7098 isl_basic_map_free(hull
);
7100 if (edge
->weight
> graph
->max_weight
)
7101 graph
->max_weight
= edge
->weight
;
7107 /* Call compute_schedule_finish_band on each of the clusters in "c"
7108 * in their topological order. This order is determined by the scc
7109 * fields of the nodes in "graph".
7110 * Combine the results in a sequence expressing the topological order.
7112 * If there is only one cluster left, then there is no need to introduce
7113 * a sequence node. Also, in this case, the cluster necessarily contains
7114 * the SCC at position 0 in the original graph and is therefore also
7115 * stored in the first cluster of "c".
7117 static __isl_give isl_schedule_node
*finish_bands_clustering(
7118 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
7119 struct isl_clustering
*c
)
7123 isl_union_set_list
*filters
;
7125 if (graph
->scc
== 1)
7126 return compute_schedule_finish_band(node
, &c
->cluster
[0], 0);
7128 ctx
= isl_schedule_node_get_ctx(node
);
7130 filters
= extract_sccs(ctx
, graph
);
7131 node
= isl_schedule_node_insert_sequence(node
, filters
);
7133 for (i
= 0; i
< graph
->scc
; ++i
) {
7134 int j
= c
->scc_cluster
[i
];
7135 node
= isl_schedule_node_child(node
, i
);
7136 node
= isl_schedule_node_child(node
, 0);
7137 node
= compute_schedule_finish_band(node
, &c
->cluster
[j
], 0);
7138 node
= isl_schedule_node_parent(node
);
7139 node
= isl_schedule_node_parent(node
);
7145 /* Compute a schedule for a connected dependence graph by first considering
7146 * each strongly connected component (SCC) in the graph separately and then
7147 * incrementally combining them into clusters.
7148 * Return the updated schedule node.
7150 * Initially, each cluster consists of a single SCC, each with its
7151 * own band schedule. The algorithm then tries to merge pairs
7152 * of clusters along a proximity edge until no more suitable
7153 * proximity edges can be found. During this merging, the schedule
7154 * is maintained in the individual SCCs.
7155 * After the merging is completed, the full resulting clusters
7156 * are extracted and in finish_bands_clustering,
7157 * compute_schedule_finish_band is called on each of them to integrate
7158 * the band into "node" and to continue the computation.
7160 * compute_weights initializes the weights that are used by find_proximity.
7162 static __isl_give isl_schedule_node
*compute_schedule_wcc_clustering(
7163 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
7166 struct isl_clustering c
;
7169 ctx
= isl_schedule_node_get_ctx(node
);
7171 if (clustering_init(ctx
, &c
, graph
) < 0)
7174 if (compute_weights(graph
, &c
) < 0)
7178 i
= find_proximity(graph
, &c
);
7181 if (i
>= graph
->n_edge
)
7183 if (merge_clusters_along_edge(ctx
, graph
, i
, &c
) < 0)
7187 if (extract_clusters(ctx
, graph
, &c
) < 0)
7190 node
= finish_bands_clustering(node
, graph
, &c
);
7192 clustering_free(ctx
, &c
);
7195 clustering_free(ctx
, &c
);
7196 return isl_schedule_node_free(node
);
7199 /* Compute a schedule for a connected dependence graph and return
7200 * the updated schedule node.
7202 * If Feautrier's algorithm is selected, we first recursively try to satisfy
7203 * as many validity dependences as possible. When all validity dependences
7204 * are satisfied we extend the schedule to a full-dimensional schedule.
7206 * Call compute_schedule_wcc_whole or compute_schedule_wcc_clustering
7207 * depending on whether the user has selected the option to try and
7208 * compute a schedule for the entire (weakly connected) component first.
7209 * If there is only a single strongly connected component (SCC), then
7210 * there is no point in trying to combine SCCs
7211 * in compute_schedule_wcc_clustering, so compute_schedule_wcc_whole
7212 * is called instead.
7214 static __isl_give isl_schedule_node
*compute_schedule_wcc(
7215 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
7222 ctx
= isl_schedule_node_get_ctx(node
);
7223 if (detect_sccs(ctx
, graph
) < 0)
7224 return isl_schedule_node_free(node
);
7226 if (compute_maxvar(graph
) < 0)
7227 return isl_schedule_node_free(node
);
7229 if (need_feautrier_step(ctx
, graph
))
7230 return compute_schedule_wcc_feautrier(node
, graph
);
7232 if (graph
->scc
<= 1 || isl_options_get_schedule_whole_component(ctx
))
7233 return compute_schedule_wcc_whole(node
, graph
);
7235 return compute_schedule_wcc_clustering(node
, graph
);
7238 /* Compute a schedule for each group of nodes identified by node->scc
7239 * separately and then combine them in a sequence node (or as set node
7240 * if graph->weak is set) inserted at position "node" of the schedule tree.
7241 * Return the updated schedule node.
7243 * If "wcc" is set then each of the groups belongs to a single
7244 * weakly connected component in the dependence graph so that
7245 * there is no need for compute_sub_schedule to look for weakly
7246 * connected components.
7248 * If a set node would be introduced and if the number of components
7249 * is equal to the number of nodes, then check if the schedule
7250 * is already complete. If so, a redundant set node would be introduced
7251 * (without any further descendants) stating that the statements
7252 * can be executed in arbitrary order, which is also expressed
7253 * by the absence of any node. Refrain from inserting any nodes
7254 * in this case and simply return.
7256 static __isl_give isl_schedule_node
*compute_component_schedule(
7257 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
7262 isl_union_set_list
*filters
;
7267 if (graph
->weak
&& graph
->scc
== graph
->n
) {
7268 if (compute_maxvar(graph
) < 0)
7269 return isl_schedule_node_free(node
);
7270 if (graph
->n_row
>= graph
->maxvar
)
7274 ctx
= isl_schedule_node_get_ctx(node
);
7275 filters
= extract_sccs(ctx
, graph
);
7277 node
= isl_schedule_node_insert_set(node
, filters
);
7279 node
= isl_schedule_node_insert_sequence(node
, filters
);
7281 for (component
= 0; component
< graph
->scc
; ++component
) {
7282 node
= isl_schedule_node_child(node
, component
);
7283 node
= isl_schedule_node_child(node
, 0);
7284 node
= compute_sub_schedule(node
, ctx
, graph
,
7286 &edge_scc_exactly
, component
, wcc
);
7287 node
= isl_schedule_node_parent(node
);
7288 node
= isl_schedule_node_parent(node
);
7294 /* Compute a schedule for the given dependence graph and insert it at "node".
7295 * Return the updated schedule node.
7297 * We first check if the graph is connected (through validity and conditional
7298 * validity dependences) and, if not, compute a schedule
7299 * for each component separately.
7300 * If the schedule_serialize_sccs option is set, then we check for strongly
7301 * connected components instead and compute a separate schedule for
7302 * each such strongly connected component.
7304 static __isl_give isl_schedule_node
*compute_schedule(isl_schedule_node
*node
,
7305 struct isl_sched_graph
*graph
)
7312 ctx
= isl_schedule_node_get_ctx(node
);
7313 if (isl_options_get_schedule_serialize_sccs(ctx
)) {
7314 if (detect_sccs(ctx
, graph
) < 0)
7315 return isl_schedule_node_free(node
);
7317 if (detect_wccs(ctx
, graph
) < 0)
7318 return isl_schedule_node_free(node
);
7322 return compute_component_schedule(node
, graph
, 1);
7324 return compute_schedule_wcc(node
, graph
);
7327 /* Compute a schedule on sc->domain that respects the given schedule
7330 * In particular, the schedule respects all the validity dependences.
7331 * If the default isl scheduling algorithm is used, it tries to minimize
7332 * the dependence distances over the proximity dependences.
7333 * If Feautrier's scheduling algorithm is used, the proximity dependence
7334 * distances are only minimized during the extension to a full-dimensional
7337 * If there are any condition and conditional validity dependences,
7338 * then the conditional validity dependences may be violated inside
7339 * a tilable band, provided they have no adjacent non-local
7340 * condition dependences.
7342 __isl_give isl_schedule
*isl_schedule_constraints_compute_schedule(
7343 __isl_take isl_schedule_constraints
*sc
)
7345 isl_ctx
*ctx
= isl_schedule_constraints_get_ctx(sc
);
7346 struct isl_sched_graph graph
= { 0 };
7347 isl_schedule
*sched
;
7348 isl_schedule_node
*node
;
7349 isl_union_set
*domain
;
7351 sc
= isl_schedule_constraints_align_params(sc
);
7353 domain
= isl_schedule_constraints_get_domain(sc
);
7354 if (isl_union_set_n_set(domain
) == 0) {
7355 isl_schedule_constraints_free(sc
);
7356 return isl_schedule_from_domain(domain
);
7359 if (graph_init(&graph
, sc
) < 0)
7360 domain
= isl_union_set_free(domain
);
7362 node
= isl_schedule_node_from_domain(domain
);
7363 node
= isl_schedule_node_child(node
, 0);
7365 node
= compute_schedule(node
, &graph
);
7366 sched
= isl_schedule_node_get_schedule(node
);
7367 isl_schedule_node_free(node
);
7369 graph_free(ctx
, &graph
);
7370 isl_schedule_constraints_free(sc
);
7375 /* Compute a schedule for the given union of domains that respects
7376 * all the validity dependences and minimizes
7377 * the dependence distances over the proximity dependences.
7379 * This function is kept for backward compatibility.
7381 __isl_give isl_schedule
*isl_union_set_compute_schedule(
7382 __isl_take isl_union_set
*domain
,
7383 __isl_take isl_union_map
*validity
,
7384 __isl_take isl_union_map
*proximity
)
7386 isl_schedule_constraints
*sc
;
7388 sc
= isl_schedule_constraints_on_domain(domain
);
7389 sc
= isl_schedule_constraints_set_validity(sc
, validity
);
7390 sc
= isl_schedule_constraints_set_proximity(sc
, proximity
);
7392 return isl_schedule_constraints_compute_schedule(sc
);