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>
24 #include <isl/constraint.h>
25 #include <isl/schedule.h>
26 #include <isl_schedule_constraints.h>
27 #include <isl/schedule_node.h>
28 #include <isl_mat_private.h>
29 #include <isl_vec_private.h>
31 #include <isl_union_set_private.h>
34 #include <isl_dim_map.h>
35 #include <isl/map_to_basic_set.h>
37 #include <isl_options_private.h>
38 #include <isl_tarjan.h>
39 #include <isl_morph.h>
41 #include <isl_val_private.h>
44 * The scheduling algorithm implemented in this file was inspired by
45 * Bondhugula et al., "Automatic Transformations for Communication-Minimized
46 * Parallelization and Locality Optimization in the Polyhedral Model".
48 * For a detailed description of the variant implemented in isl,
49 * see Verdoolaege and Janssens, "Scheduling for PPCG" (2017).
53 /* Internal information about a node that is used during the construction
55 * space represents the original space in which the domain lives;
56 * that is, the space is not affected by compression
57 * sched is a matrix representation of the schedule being constructed
58 * for this node; if compressed is set, then this schedule is
59 * defined over the compressed domain space
60 * sched_map is an isl_map representation of the same (partial) schedule
61 * sched_map may be NULL; if compressed is set, then this map
62 * is defined over the uncompressed domain space
63 * rank is the number of linearly independent rows in the linear part
65 * the rows of "vmap" represent a change of basis for the node
66 * variables; the first rank rows span the linear part of
67 * the schedule rows; the remaining rows are linearly independent
68 * the rows of "indep" represent linear combinations of the schedule
69 * coefficients that are non-zero when the schedule coefficients are
70 * linearly independent of previously computed schedule rows.
71 * start is the first variable in the LP problem in the sequences that
72 * represents the schedule coefficients of this node
73 * nvar is the dimension of the (compressed) domain
74 * nparam is the number of parameters or 0 if we are not constructing
75 * a parametric schedule
77 * If compressed is set, then hull represents the constraints
78 * that were used to derive the compression, while compress and
79 * decompress map the original space to the compressed space and
82 * scc is the index of SCC (or WCC) this node belongs to
84 * "cluster" is only used inside extract_clusters and identifies
85 * the cluster of SCCs that the node belongs to.
87 * coincident contains a boolean for each of the rows of the schedule,
88 * indicating whether the corresponding scheduling dimension satisfies
89 * the coincidence constraints in the sense that the corresponding
90 * dependence distances are zero.
92 * If the schedule_treat_coalescing option is set, then
93 * "sizes" contains the sizes of the (compressed) instance set
94 * in each direction. If there is no fixed size in a given direction,
95 * then the corresponding size value is set to infinity.
96 * If the schedule_treat_coalescing option or the schedule_max_coefficient
97 * option is set, then "max" contains the maximal values for
98 * schedule coefficients of the (compressed) variables. If no bound
99 * needs to be imposed on a particular variable, then the corresponding
101 * If not NULL, then "bounds" contains a non-parametric set
102 * in the compressed space that is bounded by the size in each direction.
104 struct isl_sched_node
{
108 isl_multi_aff
*compress
;
109 isl_pw_multi_aff
*decompress
;
124 isl_multi_val
*sizes
;
125 isl_basic_set
*bounds
;
129 static isl_bool
node_has_tuples(const void *entry
, const void *val
)
131 struct isl_sched_node
*node
= (struct isl_sched_node
*)entry
;
132 isl_space
*space
= (isl_space
*) val
;
134 return isl_space_has_equal_tuples(node
->space
, space
);
137 static int node_scc_exactly(struct isl_sched_node
*node
, int scc
)
139 return node
->scc
== scc
;
142 static int node_scc_at_most(struct isl_sched_node
*node
, int scc
)
144 return node
->scc
<= scc
;
147 static int node_scc_at_least(struct isl_sched_node
*node
, int scc
)
149 return node
->scc
>= scc
;
152 /* An edge in the dependence graph. An edge may be used to
153 * ensure validity of the generated schedule, to minimize the dependence
156 * map is the dependence relation, with i -> j in the map if j depends on i
157 * tagged_condition and tagged_validity contain the union of all tagged
158 * condition or conditional validity dependence relations that
159 * specialize the dependence relation "map"; that is,
160 * if (i -> a) -> (j -> b) is an element of "tagged_condition"
161 * or "tagged_validity", then i -> j is an element of "map".
162 * If these fields are NULL, then they represent the empty relation.
163 * src is the source node
164 * dst is the sink node
166 * types is a bit vector containing the types of this edge.
167 * validity is set if the edge is used to ensure correctness
168 * coincidence is used to enforce zero dependence distances
169 * proximity is set if the edge is used to minimize dependence distances
170 * condition is set if the edge represents a condition
171 * for a conditional validity schedule constraint
172 * local can only be set for condition edges and indicates that
173 * the dependence distance over the edge should be zero
174 * conditional_validity is set if the edge is used to conditionally
177 * For validity edges, start and end mark the sequence of inequality
178 * constraints in the LP problem that encode the validity constraint
179 * corresponding to this edge.
181 * During clustering, an edge may be marked "no_merge" if it should
182 * not be used to merge clusters.
183 * The weight is also only used during clustering and it is
184 * an indication of how many schedule dimensions on either side
185 * of the schedule constraints can be aligned.
186 * If the weight is negative, then this means that this edge was postponed
187 * by has_bounded_distances or any_no_merge. The original weight can
188 * be retrieved by adding 1 + graph->max_weight, with "graph"
189 * the graph containing this edge.
191 struct isl_sched_edge
{
193 isl_union_map
*tagged_condition
;
194 isl_union_map
*tagged_validity
;
196 struct isl_sched_node
*src
;
197 struct isl_sched_node
*dst
;
208 /* Is "edge" marked as being of type "type"?
210 static int is_type(struct isl_sched_edge
*edge
, enum isl_edge_type type
)
212 return ISL_FL_ISSET(edge
->types
, 1 << type
);
215 /* Mark "edge" as being of type "type".
217 static void set_type(struct isl_sched_edge
*edge
, enum isl_edge_type type
)
219 ISL_FL_SET(edge
->types
, 1 << type
);
222 /* No longer mark "edge" as being of type "type"?
224 static void clear_type(struct isl_sched_edge
*edge
, enum isl_edge_type type
)
226 ISL_FL_CLR(edge
->types
, 1 << type
);
229 /* Is "edge" marked as a validity edge?
231 static int is_validity(struct isl_sched_edge
*edge
)
233 return is_type(edge
, isl_edge_validity
);
236 /* Mark "edge" as a validity edge.
238 static void set_validity(struct isl_sched_edge
*edge
)
240 set_type(edge
, isl_edge_validity
);
243 /* Is "edge" marked as a proximity edge?
245 static int is_proximity(struct isl_sched_edge
*edge
)
247 return is_type(edge
, isl_edge_proximity
);
250 /* Is "edge" marked as a local edge?
252 static int is_local(struct isl_sched_edge
*edge
)
254 return is_type(edge
, isl_edge_local
);
257 /* Mark "edge" as a local edge.
259 static void set_local(struct isl_sched_edge
*edge
)
261 set_type(edge
, isl_edge_local
);
264 /* No longer mark "edge" as a local edge.
266 static void clear_local(struct isl_sched_edge
*edge
)
268 clear_type(edge
, isl_edge_local
);
271 /* Is "edge" marked as a coincidence edge?
273 static int is_coincidence(struct isl_sched_edge
*edge
)
275 return is_type(edge
, isl_edge_coincidence
);
278 /* Is "edge" marked as a condition edge?
280 static int is_condition(struct isl_sched_edge
*edge
)
282 return is_type(edge
, isl_edge_condition
);
285 /* Is "edge" marked as a conditional validity edge?
287 static int is_conditional_validity(struct isl_sched_edge
*edge
)
289 return is_type(edge
, isl_edge_conditional_validity
);
292 /* Is "edge" of a type that can appear multiple times between
293 * the same pair of nodes?
295 * Condition edges and conditional validity edges may have tagged
296 * dependence relations, in which case an edge is added for each
299 static int is_multi_edge_type(struct isl_sched_edge
*edge
)
301 return is_condition(edge
) || is_conditional_validity(edge
);
304 /* Internal information about the dependence graph used during
305 * the construction of the schedule.
307 * intra_hmap is a cache, mapping dependence relations to their dual,
308 * for dependences from a node to itself, possibly without
309 * coefficients for the parameters
310 * intra_hmap_param is a cache, mapping dependence relations to their dual,
311 * for dependences from a node to itself, including coefficients
313 * inter_hmap is a cache, mapping dependence relations to their dual,
314 * for dependences between distinct nodes
315 * if compression is involved then the key for these maps
316 * is the original, uncompressed dependence relation, while
317 * the value is the dual of the compressed dependence relation.
319 * n is the number of nodes
320 * node is the list of nodes
321 * maxvar is the maximal number of variables over all nodes
322 * max_row is the allocated number of rows in the schedule
323 * n_row is the current (maximal) number of linearly independent
324 * rows in the node schedules
325 * n_total_row is the current number of rows in the node schedules
326 * band_start is the starting row in the node schedules of the current band
327 * root is set to the original dependence graph from which this graph
328 * is derived through splitting. If this graph is not the result of
329 * splitting, then the root field points to the graph itself.
331 * sorted contains a list of node indices sorted according to the
332 * SCC to which a node belongs
334 * n_edge is the number of edges
335 * edge is the list of edges
336 * max_edge contains the maximal number of edges of each type;
337 * in particular, it contains the number of edges in the inital graph.
338 * edge_table contains pointers into the edge array, hashed on the source
339 * and sink spaces; there is one such table for each type;
340 * a given edge may be referenced from more than one table
341 * if the corresponding relation appears in more than one of the
342 * sets of dependences; however, for each type there is only
343 * a single edge between a given pair of source and sink space
344 * in the entire graph
346 * node_table contains pointers into the node array, hashed on the space tuples
348 * region contains a list of variable sequences that should be non-trivial
350 * lp contains the (I)LP problem used to obtain new schedule rows
352 * src_scc and dst_scc are the source and sink SCCs of an edge with
353 * conflicting constraints
355 * scc represents the number of components
356 * weak is set if the components are weakly connected
358 * max_weight is used during clustering and represents the maximal
359 * weight of the relevant proximity edges.
361 struct isl_sched_graph
{
362 isl_map_to_basic_set
*intra_hmap
;
363 isl_map_to_basic_set
*intra_hmap_param
;
364 isl_map_to_basic_set
*inter_hmap
;
366 struct isl_sched_node
*node
;
377 struct isl_sched_graph
*root
;
379 struct isl_sched_edge
*edge
;
381 int max_edge
[isl_edge_last
+ 1];
382 struct isl_hash_table
*edge_table
[isl_edge_last
+ 1];
384 struct isl_hash_table
*node_table
;
385 struct isl_trivial_region
*region
;
398 /* Initialize node_table based on the list of nodes.
400 static int graph_init_table(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
404 graph
->node_table
= isl_hash_table_alloc(ctx
, graph
->n
);
405 if (!graph
->node_table
)
408 for (i
= 0; i
< graph
->n
; ++i
) {
409 struct isl_hash_table_entry
*entry
;
412 hash
= isl_space_get_tuple_hash(graph
->node
[i
].space
);
413 entry
= isl_hash_table_find(ctx
, graph
->node_table
, hash
,
415 graph
->node
[i
].space
, 1);
418 entry
->data
= &graph
->node
[i
];
424 /* Return a pointer to the node that lives within the given space,
425 * an invalid node if there is no such node, or NULL in case of error.
427 static struct isl_sched_node
*graph_find_node(isl_ctx
*ctx
,
428 struct isl_sched_graph
*graph
, __isl_keep isl_space
*space
)
430 struct isl_hash_table_entry
*entry
;
436 hash
= isl_space_get_tuple_hash(space
);
437 entry
= isl_hash_table_find(ctx
, graph
->node_table
, hash
,
438 &node_has_tuples
, space
, 0);
441 if (entry
== isl_hash_table_entry_none
)
442 return graph
->node
+ graph
->n
;
447 /* Is "node" a node in "graph"?
449 static int is_node(struct isl_sched_graph
*graph
,
450 struct isl_sched_node
*node
)
452 return node
&& node
>= &graph
->node
[0] && node
< &graph
->node
[graph
->n
];
455 static isl_bool
edge_has_src_and_dst(const void *entry
, const void *val
)
457 const struct isl_sched_edge
*edge
= entry
;
458 const struct isl_sched_edge
*temp
= val
;
460 return isl_bool_ok(edge
->src
== temp
->src
&& edge
->dst
== temp
->dst
);
463 /* Add the given edge to graph->edge_table[type].
465 static isl_stat
graph_edge_table_add(isl_ctx
*ctx
,
466 struct isl_sched_graph
*graph
, enum isl_edge_type type
,
467 struct isl_sched_edge
*edge
)
469 struct isl_hash_table_entry
*entry
;
472 hash
= isl_hash_init();
473 hash
= isl_hash_builtin(hash
, edge
->src
);
474 hash
= isl_hash_builtin(hash
, edge
->dst
);
475 entry
= isl_hash_table_find(ctx
, graph
->edge_table
[type
], hash
,
476 &edge_has_src_and_dst
, edge
, 1);
478 return isl_stat_error
;
484 /* Add "edge" to all relevant edge tables.
485 * That is, for every type of the edge, add it to the corresponding table.
487 static isl_stat
graph_edge_tables_add(isl_ctx
*ctx
,
488 struct isl_sched_graph
*graph
, struct isl_sched_edge
*edge
)
490 enum isl_edge_type t
;
492 for (t
= isl_edge_first
; t
<= isl_edge_last
; ++t
) {
493 if (!is_type(edge
, t
))
495 if (graph_edge_table_add(ctx
, graph
, t
, edge
) < 0)
496 return isl_stat_error
;
502 /* Allocate the edge_tables based on the maximal number of edges of
505 static int graph_init_edge_tables(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
509 for (i
= 0; i
<= isl_edge_last
; ++i
) {
510 graph
->edge_table
[i
] = isl_hash_table_alloc(ctx
,
512 if (!graph
->edge_table
[i
])
519 /* If graph->edge_table[type] contains an edge from the given source
520 * to the given destination, then return the hash table entry of this edge.
521 * Otherwise, return NULL.
523 static struct isl_hash_table_entry
*graph_find_edge_entry(
524 struct isl_sched_graph
*graph
,
525 enum isl_edge_type type
,
526 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
528 isl_ctx
*ctx
= isl_space_get_ctx(src
->space
);
530 struct isl_sched_edge temp
= { .src
= src
, .dst
= dst
};
532 hash
= isl_hash_init();
533 hash
= isl_hash_builtin(hash
, temp
.src
);
534 hash
= isl_hash_builtin(hash
, temp
.dst
);
535 return isl_hash_table_find(ctx
, graph
->edge_table
[type
], hash
,
536 &edge_has_src_and_dst
, &temp
, 0);
540 /* If graph->edge_table[type] contains an edge from the given source
541 * to the given destination, then return this edge.
542 * Return "none" if no such edge can be found.
543 * Return NULL on error.
545 static struct isl_sched_edge
*graph_find_edge(struct isl_sched_graph
*graph
,
546 enum isl_edge_type type
,
547 struct isl_sched_node
*src
, struct isl_sched_node
*dst
,
548 struct isl_sched_edge
*none
)
550 struct isl_hash_table_entry
*entry
;
552 entry
= graph_find_edge_entry(graph
, type
, src
, dst
);
555 if (entry
== isl_hash_table_entry_none
)
561 /* Check whether the dependence graph has an edge of the given type
562 * between the given two nodes.
564 static isl_bool
graph_has_edge(struct isl_sched_graph
*graph
,
565 enum isl_edge_type type
,
566 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
568 struct isl_sched_edge dummy
;
569 struct isl_sched_edge
*edge
;
572 edge
= graph_find_edge(graph
, type
, src
, dst
, &dummy
);
574 return isl_bool_error
;
576 return isl_bool_false
;
578 empty
= isl_map_plain_is_empty(edge
->map
);
580 return isl_bool_not(empty
);
583 /* Look for any edge with the same src, dst and map fields as "model".
585 * Return the matching edge if one can be found.
586 * Return "model" if no matching edge is found.
587 * Return NULL on error.
589 static struct isl_sched_edge
*graph_find_matching_edge(
590 struct isl_sched_graph
*graph
, struct isl_sched_edge
*model
)
592 enum isl_edge_type i
;
593 struct isl_sched_edge
*edge
;
595 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
598 edge
= graph_find_edge(graph
, i
, model
->src
, model
->dst
, model
);
603 is_equal
= isl_map_plain_is_equal(model
->map
, edge
->map
);
613 /* Remove the given edge from all the edge_tables that refer to it.
615 static isl_stat
graph_remove_edge(struct isl_sched_graph
*graph
,
616 struct isl_sched_edge
*edge
)
618 isl_ctx
*ctx
= isl_map_get_ctx(edge
->map
);
619 enum isl_edge_type i
;
621 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
622 struct isl_hash_table_entry
*entry
;
624 entry
= graph_find_edge_entry(graph
, i
, edge
->src
, edge
->dst
);
626 return isl_stat_error
;
627 if (entry
== isl_hash_table_entry_none
)
629 if (entry
->data
!= edge
)
631 isl_hash_table_remove(ctx
, graph
->edge_table
[i
], entry
);
637 /* Check whether the dependence graph has any edge
638 * between the given two nodes.
640 static isl_bool
graph_has_any_edge(struct isl_sched_graph
*graph
,
641 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
643 enum isl_edge_type i
;
646 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
647 r
= graph_has_edge(graph
, i
, src
, dst
);
655 /* Check whether the dependence graph has a validity edge
656 * between the given two nodes.
658 * Conditional validity edges are essentially validity edges that
659 * can be ignored if the corresponding condition edges are iteration private.
660 * Here, we are only checking for the presence of validity
661 * edges, so we need to consider the conditional validity edges too.
662 * In particular, this function is used during the detection
663 * of strongly connected components and we cannot ignore
664 * conditional validity edges during this detection.
666 static isl_bool
graph_has_validity_edge(struct isl_sched_graph
*graph
,
667 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
671 r
= graph_has_edge(graph
, isl_edge_validity
, src
, dst
);
675 return graph_has_edge(graph
, isl_edge_conditional_validity
, src
, dst
);
678 /* Perform all the required memory allocations for a schedule graph "graph"
679 * with "n_node" nodes and "n_edge" edge and initialize the corresponding
682 static isl_stat
graph_alloc(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
683 int n_node
, int n_edge
)
688 graph
->n_edge
= n_edge
;
689 graph
->node
= isl_calloc_array(ctx
, struct isl_sched_node
, graph
->n
);
690 graph
->sorted
= isl_calloc_array(ctx
, int, graph
->n
);
691 graph
->region
= isl_alloc_array(ctx
,
692 struct isl_trivial_region
, graph
->n
);
693 graph
->edge
= isl_calloc_array(ctx
,
694 struct isl_sched_edge
, graph
->n_edge
);
696 graph
->intra_hmap
= isl_map_to_basic_set_alloc(ctx
, 2 * n_edge
);
697 graph
->intra_hmap_param
= isl_map_to_basic_set_alloc(ctx
, 2 * n_edge
);
698 graph
->inter_hmap
= isl_map_to_basic_set_alloc(ctx
, 2 * n_edge
);
700 if (!graph
->node
|| !graph
->region
|| (graph
->n_edge
&& !graph
->edge
) ||
702 return isl_stat_error
;
704 for(i
= 0; i
< graph
->n
; ++i
)
705 graph
->sorted
[i
] = i
;
710 /* Free the memory associated to node "node" in "graph".
711 * The "coincident" field is shared by nodes in a graph and its subgraph.
712 * It therefore only needs to be freed for the original dependence graph,
713 * i.e., one that is not the result of splitting.
715 static void clear_node(struct isl_sched_graph
*graph
,
716 struct isl_sched_node
*node
)
718 isl_space_free(node
->space
);
719 isl_set_free(node
->hull
);
720 isl_multi_aff_free(node
->compress
);
721 isl_pw_multi_aff_free(node
->decompress
);
722 isl_mat_free(node
->sched
);
723 isl_map_free(node
->sched_map
);
724 isl_mat_free(node
->indep
);
725 isl_mat_free(node
->vmap
);
726 if (graph
->root
== graph
)
727 free(node
->coincident
);
728 isl_multi_val_free(node
->sizes
);
729 isl_basic_set_free(node
->bounds
);
730 isl_vec_free(node
->max
);
733 static void graph_free(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
737 isl_map_to_basic_set_free(graph
->intra_hmap
);
738 isl_map_to_basic_set_free(graph
->intra_hmap_param
);
739 isl_map_to_basic_set_free(graph
->inter_hmap
);
742 for (i
= 0; i
< graph
->n
; ++i
)
743 clear_node(graph
, &graph
->node
[i
]);
747 for (i
= 0; i
< graph
->n_edge
; ++i
) {
748 isl_map_free(graph
->edge
[i
].map
);
749 isl_union_map_free(graph
->edge
[i
].tagged_condition
);
750 isl_union_map_free(graph
->edge
[i
].tagged_validity
);
754 for (i
= 0; i
<= isl_edge_last
; ++i
)
755 isl_hash_table_free(ctx
, graph
->edge_table
[i
]);
756 isl_hash_table_free(ctx
, graph
->node_table
);
757 isl_basic_set_free(graph
->lp
);
760 /* For each "set" on which this function is called, increment
761 * graph->n by one and update graph->maxvar.
763 static isl_stat
init_n_maxvar(__isl_take isl_set
*set
, void *user
)
765 struct isl_sched_graph
*graph
= user
;
766 isl_size nvar
= isl_set_dim(set
, isl_dim_set
);
769 if (nvar
> graph
->maxvar
)
770 graph
->maxvar
= nvar
;
775 return isl_stat_error
;
779 /* Compute the number of rows that should be allocated for the schedule.
780 * In particular, we need one row for each variable or one row
781 * for each basic map in the dependences.
782 * Note that it is practically impossible to exhaust both
783 * the number of dependences and the number of variables.
785 static isl_stat
compute_max_row(struct isl_sched_graph
*graph
,
786 __isl_keep isl_schedule_constraints
*sc
)
790 isl_union_set
*domain
;
794 domain
= isl_schedule_constraints_get_domain(sc
);
795 r
= isl_union_set_foreach_set(domain
, &init_n_maxvar
, graph
);
796 isl_union_set_free(domain
);
798 return isl_stat_error
;
799 n_edge
= isl_schedule_constraints_n_basic_map(sc
);
801 return isl_stat_error
;
802 graph
->max_row
= n_edge
+ graph
->maxvar
;
807 /* Does "bset" have any defining equalities for its set variables?
809 static isl_bool
has_any_defining_equality(__isl_keep isl_basic_set
*bset
)
814 n
= isl_basic_set_dim(bset
, isl_dim_set
);
816 return isl_bool_error
;
818 for (i
= 0; i
< n
; ++i
) {
821 has
= isl_basic_set_has_defining_equality(bset
, isl_dim_set
, i
,
827 return isl_bool_false
;
830 /* Set the entries of node->max to the value of the schedule_max_coefficient
833 static isl_stat
set_max_coefficient(isl_ctx
*ctx
, struct isl_sched_node
*node
)
837 max
= isl_options_get_schedule_max_coefficient(ctx
);
841 node
->max
= isl_vec_alloc(ctx
, node
->nvar
);
842 node
->max
= isl_vec_set_si(node
->max
, max
);
844 return isl_stat_error
;
849 /* Set the entries of node->max to the minimum of the schedule_max_coefficient
850 * option (if set) and half of the minimum of the sizes in the other
851 * dimensions. Round up when computing the half such that
852 * if the minimum of the sizes is one, half of the size is taken to be one
854 * If the global minimum is unbounded (i.e., if both
855 * the schedule_max_coefficient is not set and the sizes in the other
856 * dimensions are unbounded), then store a negative value.
857 * If the schedule coefficient is close to the size of the instance set
858 * in another dimension, then the schedule may represent a loop
859 * coalescing transformation (especially if the coefficient
860 * in that other dimension is one). Forcing the coefficient to be
861 * smaller than or equal to half the minimal size should avoid this
864 static isl_stat
compute_max_coefficient(isl_ctx
*ctx
,
865 struct isl_sched_node
*node
)
871 max
= isl_options_get_schedule_max_coefficient(ctx
);
872 v
= isl_vec_alloc(ctx
, node
->nvar
);
874 return isl_stat_error
;
876 for (i
= 0; i
< node
->nvar
; ++i
) {
877 isl_int_set_si(v
->el
[i
], max
);
878 isl_int_mul_si(v
->el
[i
], v
->el
[i
], 2);
881 for (i
= 0; i
< node
->nvar
; ++i
) {
884 size
= isl_multi_val_get_val(node
->sizes
, i
);
887 if (!isl_val_is_int(size
)) {
891 for (j
= 0; j
< node
->nvar
; ++j
) {
894 if (isl_int_is_neg(v
->el
[j
]) ||
895 isl_int_gt(v
->el
[j
], size
->n
))
896 isl_int_set(v
->el
[j
], size
->n
);
901 for (i
= 0; i
< node
->nvar
; ++i
)
902 isl_int_cdiv_q_ui(v
->el
[i
], v
->el
[i
], 2);
908 return isl_stat_error
;
911 /* Construct an identifier for node "node", which will represent "set".
912 * The name of the identifier is either "compressed" or
913 * "compressed_<name>", with <name> the name of the space of "set".
914 * The user pointer of the identifier points to "node".
916 static __isl_give isl_id
*construct_compressed_id(__isl_keep isl_set
*set
,
917 struct isl_sched_node
*node
)
926 has_name
= isl_set_has_tuple_name(set
);
930 ctx
= isl_set_get_ctx(set
);
932 return isl_id_alloc(ctx
, "compressed", node
);
934 p
= isl_printer_to_str(ctx
);
935 name
= isl_set_get_tuple_name(set
);
936 p
= isl_printer_print_str(p
, "compressed_");
937 p
= isl_printer_print_str(p
, name
);
938 id_name
= isl_printer_get_str(p
);
941 id
= isl_id_alloc(ctx
, id_name
, node
);
947 /* Construct a map that isolates the variable in position "pos" in "set".
951 * [i_0, ..., i_pos-1, i_pos+1, ...] -> [i_pos]
953 static __isl_give isl_map
*isolate(__isl_take isl_set
*set
, int pos
)
957 map
= isl_set_project_onto_map(set
, isl_dim_set
, pos
, 1);
958 map
= isl_map_project_out(map
, isl_dim_in
, pos
, 1);
962 /* Compute and return the size of "set" in dimension "dim".
963 * The size is taken to be the difference in values for that variable
964 * for fixed values of the other variables.
965 * This assumes that "set" is convex.
966 * In particular, the variable is first isolated from the other variables
967 * in the range of a map
969 * [i_0, ..., i_dim-1, i_dim+1, ...] -> [i_dim]
971 * and then duplicated
973 * [i_0, ..., i_dim-1, i_dim+1, ...] -> [[i_dim] -> [i_dim']]
975 * The shared variables are then projected out and the maximal value
976 * of i_dim' - i_dim is computed.
978 static __isl_give isl_val
*compute_size(__isl_take isl_set
*set
, int dim
)
985 map
= isolate(set
, dim
);
986 map
= isl_map_range_product(map
, isl_map_copy(map
));
987 map
= isl_set_unwrap(isl_map_range(map
));
988 set
= isl_map_deltas(map
);
989 ls
= isl_local_space_from_space(isl_set_get_space(set
));
990 obj
= isl_aff_var_on_domain(ls
, isl_dim_set
, 0);
991 v
= isl_set_max_val(set
, obj
);
998 /* Perform a compression on "node" where "hull" represents the constraints
999 * that were used to derive the compression, while "compress" and
1000 * "decompress" map the original space to the compressed space and
1003 * If "node" was not compressed already, then simply store
1004 * the compression information.
1005 * Otherwise the "original" space is actually the result
1006 * of a previous compression, which is then combined
1007 * with the present compression.
1009 * The dimensionality of the compressed domain is also adjusted.
1010 * Other information, such as the sizes and the maximal coefficient values,
1011 * has not been computed yet and therefore does not need to be adjusted.
1013 static isl_stat
compress_node(struct isl_sched_node
*node
,
1014 __isl_take isl_set
*hull
, __isl_take isl_multi_aff
*compress
,
1015 __isl_take isl_pw_multi_aff
*decompress
)
1017 node
->nvar
= isl_multi_aff_dim(compress
, isl_dim_out
);
1018 if (!node
->compressed
) {
1019 node
->compressed
= 1;
1021 node
->compress
= compress
;
1022 node
->decompress
= decompress
;
1024 hull
= isl_set_preimage_multi_aff(hull
,
1025 isl_multi_aff_copy(node
->compress
));
1026 node
->hull
= isl_set_intersect(node
->hull
, hull
);
1027 node
->compress
= isl_multi_aff_pullback_multi_aff(
1028 compress
, node
->compress
);
1029 node
->decompress
= isl_pw_multi_aff_pullback_pw_multi_aff(
1030 node
->decompress
, decompress
);
1033 if (!node
->hull
|| !node
->compress
|| !node
->decompress
)
1034 return isl_stat_error
;
1039 /* Given that dimension "pos" in "set" has a fixed value
1040 * in terms of the other dimensions, (further) compress "node"
1041 * by projecting out this dimension.
1042 * "set" may be the result of a previous compression.
1043 * "uncompressed" is the original domain (without compression).
1045 * The compression function simply projects out the dimension.
1046 * The decompression function adds back the dimension
1047 * in the right position as an expression of the other dimensions
1048 * derived from "set".
1049 * As in extract_node, the compressed space has an identifier
1050 * that references "node" such that each compressed space is unique and
1051 * such that the node can be recovered from the compressed space.
1053 * The constraint removed through the compression is added to the "hull"
1054 * such that only edges that relate to the original domains
1055 * are taken into account.
1056 * In particular, it is obtained by composing compression and decompression and
1057 * taking the relation among the variables in the range.
1059 static isl_stat
project_out_fixed(struct isl_sched_node
*node
,
1060 __isl_keep isl_set
*uncompressed
, __isl_take isl_set
*set
, int pos
)
1066 isl_multi_aff
*compress
;
1067 isl_pw_multi_aff
*decompress
, *pma
;
1068 isl_multi_pw_aff
*mpa
;
1071 map
= isolate(isl_set_copy(set
), pos
);
1072 pma
= isl_pw_multi_aff_from_map(map
);
1073 domain
= isl_pw_multi_aff_domain(isl_pw_multi_aff_copy(pma
));
1074 pma
= isl_pw_multi_aff_gist(pma
, domain
);
1075 space
= isl_pw_multi_aff_get_domain_space(pma
);
1076 mpa
= isl_multi_pw_aff_identity(isl_space_map_from_set(space
));
1077 mpa
= isl_multi_pw_aff_range_splice(mpa
, pos
,
1078 isl_multi_pw_aff_from_pw_multi_aff(pma
));
1079 decompress
= isl_pw_multi_aff_from_multi_pw_aff(mpa
);
1080 space
= isl_set_get_space(set
);
1081 compress
= isl_multi_aff_project_out_map(space
, isl_dim_set
, pos
, 1);
1082 id
= construct_compressed_id(uncompressed
, node
);
1083 compress
= isl_multi_aff_set_tuple_id(compress
, isl_dim_out
, id
);
1084 space
= isl_space_reverse(isl_multi_aff_get_space(compress
));
1085 decompress
= isl_pw_multi_aff_reset_space(decompress
, space
);
1086 pma
= isl_pw_multi_aff_pullback_multi_aff(
1087 isl_pw_multi_aff_copy(decompress
), isl_multi_aff_copy(compress
));
1088 hull
= isl_map_range(isl_map_from_pw_multi_aff(pma
));
1092 return compress_node(node
, hull
, compress
, decompress
);
1095 /* Compute the size of the compressed domain in each dimension and
1096 * store the results in node->sizes.
1097 * "uncompressed" is the original domain (without compression).
1099 * First compress the domain if needed and then compute the size
1100 * in each direction.
1101 * If the domain is not convex, then the sizes are computed
1102 * on a convex superset in order to avoid picking up sizes
1103 * that are valid for the individual disjuncts, but not for
1104 * the domain as a whole.
1106 * If any of the sizes turns out to be zero, then this means
1107 * that this dimension has a fixed value in terms of
1108 * the other dimensions. Perform an (extra) compression
1109 * to remove this dimensions.
1111 static isl_stat
compute_sizes(struct isl_sched_node
*node
,
1112 __isl_keep isl_set
*uncompressed
)
1117 isl_set
*set
= isl_set_copy(uncompressed
);
1119 if (node
->compressed
)
1120 set
= isl_set_preimage_pw_multi_aff(set
,
1121 isl_pw_multi_aff_copy(node
->decompress
));
1122 set
= isl_set_from_basic_set(isl_set_simple_hull(set
));
1123 mv
= isl_multi_val_zero(isl_set_get_space(set
));
1124 n
= isl_set_dim(set
, isl_dim_set
);
1126 mv
= isl_multi_val_free(mv
);
1127 for (j
= 0; j
< n
; ++j
) {
1131 v
= compute_size(isl_set_copy(set
), j
);
1132 is_zero
= isl_val_is_zero(v
);
1133 mv
= isl_multi_val_set_val(mv
, j
, v
);
1134 if (is_zero
>= 0 && is_zero
) {
1135 isl_multi_val_free(mv
);
1136 if (project_out_fixed(node
, uncompressed
, set
, j
) < 0)
1137 return isl_stat_error
;
1138 return compute_sizes(node
, uncompressed
);
1144 return isl_stat_error
;
1148 /* Compute the size of the instance set "set" of "node", after compression,
1149 * as well as bounds on the corresponding coefficients, if needed.
1151 * The sizes are needed when the schedule_treat_coalescing option is set.
1152 * The bounds are needed when the schedule_treat_coalescing option or
1153 * the schedule_max_coefficient option is set.
1155 * If the schedule_treat_coalescing option is not set, then at most
1156 * the bounds need to be set and this is done in set_max_coefficient.
1157 * Otherwise, compute the size of the compressed domain
1158 * in each direction and store the results in node->size.
1159 * Finally, set the bounds on the coefficients based on the sizes
1160 * and the schedule_max_coefficient option in compute_max_coefficient.
1162 static isl_stat
compute_sizes_and_max(isl_ctx
*ctx
, struct isl_sched_node
*node
,
1163 __isl_take isl_set
*set
)
1167 if (!isl_options_get_schedule_treat_coalescing(ctx
)) {
1169 return set_max_coefficient(ctx
, node
);
1172 r
= compute_sizes(node
, set
);
1175 return isl_stat_error
;
1176 return compute_max_coefficient(ctx
, node
);
1179 /* Add a new node to the graph representing the given instance set.
1180 * "nvar" is the (possibly compressed) number of variables and
1181 * may be smaller than then number of set variables in "set"
1182 * if "compressed" is set.
1183 * If "compressed" is set, then "hull" represents the constraints
1184 * that were used to derive the compression, while "compress" and
1185 * "decompress" map the original space to the compressed space and
1187 * If "compressed" is not set, then "hull", "compress" and "decompress"
1190 * Compute the size of the instance set and bounds on the coefficients,
1193 static isl_stat
add_node(struct isl_sched_graph
*graph
,
1194 __isl_take isl_set
*set
, int nvar
, int compressed
,
1195 __isl_take isl_set
*hull
, __isl_take isl_multi_aff
*compress
,
1196 __isl_take isl_pw_multi_aff
*decompress
)
1203 struct isl_sched_node
*node
;
1205 nparam
= isl_set_dim(set
, isl_dim_param
);
1209 ctx
= isl_set_get_ctx(set
);
1210 if (!ctx
->opt
->schedule_parametric
)
1212 sched
= isl_mat_alloc(ctx
, 0, 1 + nparam
+ nvar
);
1213 node
= &graph
->node
[graph
->n
];
1215 space
= isl_set_get_space(set
);
1216 node
->space
= space
;
1218 node
->nparam
= nparam
;
1219 node
->sched
= sched
;
1220 node
->sched_map
= NULL
;
1221 coincident
= isl_calloc_array(ctx
, int, graph
->max_row
);
1222 node
->coincident
= coincident
;
1223 node
->compressed
= compressed
;
1225 node
->compress
= compress
;
1226 node
->decompress
= decompress
;
1227 if (compute_sizes_and_max(ctx
, node
, set
) < 0)
1228 return isl_stat_error
;
1230 if (!space
|| !sched
|| (graph
->max_row
&& !coincident
))
1231 return isl_stat_error
;
1232 if (compressed
&& (!hull
|| !compress
|| !decompress
))
1233 return isl_stat_error
;
1239 isl_multi_aff_free(compress
);
1240 isl_pw_multi_aff_free(decompress
);
1241 return isl_stat_error
;
1244 /* Add a new node to the graph representing the given set.
1246 * If any of the set variables is defined by an equality, then
1247 * we perform variable compression such that we can perform
1248 * the scheduling on the compressed domain.
1249 * In this case, an identifier is used that references the new node
1250 * such that each compressed space is unique and
1251 * such that the node can be recovered from the compressed space.
1253 static isl_stat
extract_node(__isl_take isl_set
*set
, void *user
)
1256 isl_bool has_equality
;
1258 isl_basic_set
*hull
;
1261 isl_multi_aff
*compress
, *decompress_ma
;
1262 isl_pw_multi_aff
*decompress
;
1263 struct isl_sched_graph
*graph
= user
;
1265 hull
= isl_set_affine_hull(isl_set_copy(set
));
1266 hull
= isl_basic_set_remove_divs(hull
);
1267 nvar
= isl_set_dim(set
, isl_dim_set
);
1268 has_equality
= has_any_defining_equality(hull
);
1270 if (nvar
< 0 || has_equality
< 0)
1272 if (!has_equality
) {
1273 isl_basic_set_free(hull
);
1274 return add_node(graph
, set
, nvar
, 0, NULL
, NULL
, NULL
);
1277 id
= construct_compressed_id(set
, &graph
->node
[graph
->n
]);
1278 morph
= isl_basic_set_variable_compression_with_id(hull
, id
);
1280 nvar
= isl_morph_ran_dim(morph
, isl_dim_set
);
1282 set
= isl_set_free(set
);
1283 compress
= isl_morph_get_var_multi_aff(morph
);
1284 morph
= isl_morph_inverse(morph
);
1285 decompress_ma
= isl_morph_get_var_multi_aff(morph
);
1286 decompress
= isl_pw_multi_aff_from_multi_aff(decompress_ma
);
1287 isl_morph_free(morph
);
1289 hull_set
= isl_set_from_basic_set(hull
);
1290 return add_node(graph
, set
, nvar
, 1, hull_set
, compress
, decompress
);
1292 isl_basic_set_free(hull
);
1294 return isl_stat_error
;
1297 struct isl_extract_edge_data
{
1298 enum isl_edge_type type
;
1299 struct isl_sched_graph
*graph
;
1302 /* Merge edge2 into edge1, freeing the contents of edge2.
1303 * Return 0 on success and -1 on failure.
1305 * edge1 and edge2 are assumed to have the same value for the map field.
1307 static int merge_edge(struct isl_sched_edge
*edge1
,
1308 struct isl_sched_edge
*edge2
)
1310 edge1
->types
|= edge2
->types
;
1311 isl_map_free(edge2
->map
);
1313 if (is_condition(edge2
)) {
1314 if (!edge1
->tagged_condition
)
1315 edge1
->tagged_condition
= edge2
->tagged_condition
;
1317 edge1
->tagged_condition
=
1318 isl_union_map_union(edge1
->tagged_condition
,
1319 edge2
->tagged_condition
);
1322 if (is_conditional_validity(edge2
)) {
1323 if (!edge1
->tagged_validity
)
1324 edge1
->tagged_validity
= edge2
->tagged_validity
;
1326 edge1
->tagged_validity
=
1327 isl_union_map_union(edge1
->tagged_validity
,
1328 edge2
->tagged_validity
);
1331 if (is_condition(edge2
) && !edge1
->tagged_condition
)
1333 if (is_conditional_validity(edge2
) && !edge1
->tagged_validity
)
1339 /* Insert dummy tags in domain and range of "map".
1341 * In particular, if "map" is of the form
1347 * [A -> dummy_tag] -> [B -> dummy_tag]
1349 * where the dummy_tags are identical and equal to any dummy tags
1350 * introduced by any other call to this function.
1352 static __isl_give isl_map
*insert_dummy_tags(__isl_take isl_map
*map
)
1358 isl_set
*domain
, *range
;
1360 ctx
= isl_map_get_ctx(map
);
1362 id
= isl_id_alloc(ctx
, NULL
, &dummy
);
1363 space
= isl_space_params(isl_map_get_space(map
));
1364 space
= isl_space_set_from_params(space
);
1365 space
= isl_space_set_tuple_id(space
, isl_dim_set
, id
);
1366 space
= isl_space_map_from_set(space
);
1368 domain
= isl_map_wrap(map
);
1369 range
= isl_map_wrap(isl_map_universe(space
));
1370 map
= isl_map_from_domain_and_range(domain
, range
);
1371 map
= isl_map_zip(map
);
1376 /* Given that at least one of "src" or "dst" is compressed, return
1377 * a map between the spaces of these nodes restricted to the affine
1378 * hull that was used in the compression.
1380 static __isl_give isl_map
*extract_hull(struct isl_sched_node
*src
,
1381 struct isl_sched_node
*dst
)
1385 if (src
->compressed
)
1386 dom
= isl_set_copy(src
->hull
);
1388 dom
= isl_set_universe(isl_space_copy(src
->space
));
1389 if (dst
->compressed
)
1390 ran
= isl_set_copy(dst
->hull
);
1392 ran
= isl_set_universe(isl_space_copy(dst
->space
));
1394 return isl_map_from_domain_and_range(dom
, ran
);
1397 /* Intersect the domains of the nested relations in domain and range
1398 * of "tagged" with "map".
1400 static __isl_give isl_map
*map_intersect_domains(__isl_take isl_map
*tagged
,
1401 __isl_keep isl_map
*map
)
1405 tagged
= isl_map_zip(tagged
);
1406 set
= isl_map_wrap(isl_map_copy(map
));
1407 tagged
= isl_map_intersect_domain(tagged
, set
);
1408 tagged
= isl_map_zip(tagged
);
1412 /* Return a pointer to the node that lives in the domain space of "map",
1413 * an invalid node if there is no such node, or NULL in case of error.
1415 static struct isl_sched_node
*find_domain_node(isl_ctx
*ctx
,
1416 struct isl_sched_graph
*graph
, __isl_keep isl_map
*map
)
1418 struct isl_sched_node
*node
;
1421 space
= isl_space_domain(isl_map_get_space(map
));
1422 node
= graph_find_node(ctx
, graph
, space
);
1423 isl_space_free(space
);
1428 /* Return a pointer to the node that lives in the range space of "map",
1429 * an invalid node if there is no such node, or NULL in case of error.
1431 static struct isl_sched_node
*find_range_node(isl_ctx
*ctx
,
1432 struct isl_sched_graph
*graph
, __isl_keep isl_map
*map
)
1434 struct isl_sched_node
*node
;
1437 space
= isl_space_range(isl_map_get_space(map
));
1438 node
= graph_find_node(ctx
, graph
, space
);
1439 isl_space_free(space
);
1444 /* Refrain from adding a new edge based on "map".
1445 * Instead, just free the map.
1446 * "tagged" is either a copy of "map" with additional tags or NULL.
1448 static isl_stat
skip_edge(__isl_take isl_map
*map
, __isl_take isl_map
*tagged
)
1451 isl_map_free(tagged
);
1456 /* Add a new edge to the graph based on the given map
1457 * and add it to data->graph->edge_table[data->type].
1458 * If a dependence relation of a given type happens to be identical
1459 * to one of the dependence relations of a type that was added before,
1460 * then we don't create a new edge, but instead mark the original edge
1461 * as also representing a dependence of the current type.
1463 * Edges of type isl_edge_condition or isl_edge_conditional_validity
1464 * may be specified as "tagged" dependence relations. That is, "map"
1465 * may contain elements (i -> a) -> (j -> b), where i -> j denotes
1466 * the dependence on iterations and a and b are tags.
1467 * edge->map is set to the relation containing the elements i -> j,
1468 * while edge->tagged_condition and edge->tagged_validity contain
1469 * the union of all the "map" relations
1470 * for which extract_edge is called that result in the same edge->map.
1472 * If the source or the destination node is compressed, then
1473 * intersect both "map" and "tagged" with the constraints that
1474 * were used to construct the compression.
1475 * This ensures that there are no schedule constraints defined
1476 * outside of these domains, while the scheduler no longer has
1477 * any control over those outside parts.
1479 static isl_stat
extract_edge(__isl_take isl_map
*map
, void *user
)
1482 isl_ctx
*ctx
= isl_map_get_ctx(map
);
1483 struct isl_extract_edge_data
*data
= user
;
1484 struct isl_sched_graph
*graph
= data
->graph
;
1485 struct isl_sched_node
*src
, *dst
;
1486 struct isl_sched_edge
*edge
;
1487 isl_map
*tagged
= NULL
;
1489 if (data
->type
== isl_edge_condition
||
1490 data
->type
== isl_edge_conditional_validity
) {
1491 if (isl_map_can_zip(map
)) {
1492 tagged
= isl_map_copy(map
);
1493 map
= isl_set_unwrap(isl_map_domain(isl_map_zip(map
)));
1495 tagged
= insert_dummy_tags(isl_map_copy(map
));
1499 src
= find_domain_node(ctx
, graph
, map
);
1500 dst
= find_range_node(ctx
, graph
, map
);
1504 if (!is_node(graph
, src
) || !is_node(graph
, dst
))
1505 return skip_edge(map
, tagged
);
1507 if (src
->compressed
|| dst
->compressed
) {
1509 hull
= extract_hull(src
, dst
);
1511 tagged
= map_intersect_domains(tagged
, hull
);
1512 map
= isl_map_intersect(map
, hull
);
1515 empty
= isl_map_plain_is_empty(map
);
1519 return skip_edge(map
, tagged
);
1521 graph
->edge
[graph
->n_edge
].src
= src
;
1522 graph
->edge
[graph
->n_edge
].dst
= dst
;
1523 graph
->edge
[graph
->n_edge
].map
= map
;
1524 graph
->edge
[graph
->n_edge
].types
= 0;
1525 graph
->edge
[graph
->n_edge
].tagged_condition
= NULL
;
1526 graph
->edge
[graph
->n_edge
].tagged_validity
= NULL
;
1527 set_type(&graph
->edge
[graph
->n_edge
], data
->type
);
1528 if (data
->type
== isl_edge_condition
)
1529 graph
->edge
[graph
->n_edge
].tagged_condition
=
1530 isl_union_map_from_map(tagged
);
1531 if (data
->type
== isl_edge_conditional_validity
)
1532 graph
->edge
[graph
->n_edge
].tagged_validity
=
1533 isl_union_map_from_map(tagged
);
1535 edge
= graph_find_matching_edge(graph
, &graph
->edge
[graph
->n_edge
]);
1538 return isl_stat_error
;
1540 if (edge
== &graph
->edge
[graph
->n_edge
])
1541 return graph_edge_table_add(ctx
, graph
, data
->type
,
1542 &graph
->edge
[graph
->n_edge
++]);
1544 if (merge_edge(edge
, &graph
->edge
[graph
->n_edge
]) < 0)
1545 return isl_stat_error
;
1547 return graph_edge_table_add(ctx
, graph
, data
->type
, edge
);
1550 isl_map_free(tagged
);
1551 return isl_stat_error
;
1554 /* Initialize the schedule graph "graph" from the schedule constraints "sc".
1556 * The context is included in the domain before the nodes of
1557 * the graphs are extracted in order to be able to exploit
1558 * any possible additional equalities.
1559 * Note that this intersection is only performed locally here.
1561 static isl_stat
graph_init(struct isl_sched_graph
*graph
,
1562 __isl_keep isl_schedule_constraints
*sc
)
1565 isl_union_set
*domain
;
1567 struct isl_extract_edge_data data
;
1568 enum isl_edge_type i
;
1573 return isl_stat_error
;
1575 ctx
= isl_schedule_constraints_get_ctx(sc
);
1577 domain
= isl_schedule_constraints_get_domain(sc
);
1578 n
= isl_union_set_n_set(domain
);
1580 isl_union_set_free(domain
);
1582 return isl_stat_error
;
1584 n
= isl_schedule_constraints_n_map(sc
);
1585 if (n
< 0 || graph_alloc(ctx
, graph
, graph
->n
, n
) < 0)
1586 return isl_stat_error
;
1588 if (compute_max_row(graph
, sc
) < 0)
1589 return isl_stat_error
;
1590 graph
->root
= graph
;
1592 domain
= isl_schedule_constraints_get_domain(sc
);
1593 domain
= isl_union_set_intersect_params(domain
,
1594 isl_schedule_constraints_get_context(sc
));
1595 r
= isl_union_set_foreach_set(domain
, &extract_node
, graph
);
1596 isl_union_set_free(domain
);
1598 return isl_stat_error
;
1599 if (graph_init_table(ctx
, graph
) < 0)
1600 return isl_stat_error
;
1601 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
1604 c
= isl_schedule_constraints_get(sc
, i
);
1605 n
= isl_union_map_n_map(c
);
1606 graph
->max_edge
[i
] = n
;
1607 isl_union_map_free(c
);
1609 return isl_stat_error
;
1611 if (graph_init_edge_tables(ctx
, graph
) < 0)
1612 return isl_stat_error
;
1615 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
1619 c
= isl_schedule_constraints_get(sc
, i
);
1620 r
= isl_union_map_foreach_map(c
, &extract_edge
, &data
);
1621 isl_union_map_free(c
);
1623 return isl_stat_error
;
1629 /* Check whether there is any dependence from node[j] to node[i]
1630 * or from node[i] to node[j].
1632 static isl_bool
node_follows_weak(int i
, int j
, void *user
)
1635 struct isl_sched_graph
*graph
= user
;
1637 f
= graph_has_any_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
1640 return graph_has_any_edge(graph
, &graph
->node
[i
], &graph
->node
[j
]);
1643 /* Check whether there is a (conditional) validity dependence from node[j]
1644 * to node[i], forcing node[i] to follow node[j].
1646 static isl_bool
node_follows_strong(int i
, int j
, void *user
)
1648 struct isl_sched_graph
*graph
= user
;
1650 return graph_has_validity_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
1653 /* Use Tarjan's algorithm for computing the strongly connected components
1654 * in the dependence graph only considering those edges defined by "follows".
1656 static isl_stat
detect_ccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
1657 isl_bool (*follows
)(int i
, int j
, void *user
))
1660 struct isl_tarjan_graph
*g
= NULL
;
1662 g
= isl_tarjan_graph_init(ctx
, graph
->n
, follows
, graph
);
1664 return isl_stat_error
;
1670 while (g
->order
[i
] != -1) {
1671 graph
->node
[g
->order
[i
]].scc
= graph
->scc
;
1679 isl_tarjan_graph_free(g
);
1684 /* Apply Tarjan's algorithm to detect the strongly connected components
1685 * in the dependence graph.
1686 * Only consider the (conditional) validity dependences and clear "weak".
1688 static isl_stat
detect_sccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
1691 return detect_ccs(ctx
, graph
, &node_follows_strong
);
1694 /* Apply Tarjan's algorithm to detect the (weakly) connected components
1695 * in the dependence graph.
1696 * Consider all dependences and set "weak".
1698 static isl_stat
detect_wccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
1701 return detect_ccs(ctx
, graph
, &node_follows_weak
);
1704 static int cmp_scc(const void *a
, const void *b
, void *data
)
1706 struct isl_sched_graph
*graph
= data
;
1710 return graph
->node
[*i1
].scc
- graph
->node
[*i2
].scc
;
1713 /* Sort the elements of graph->sorted according to the corresponding SCCs.
1715 static int sort_sccs(struct isl_sched_graph
*graph
)
1717 return isl_sort(graph
->sorted
, graph
->n
, sizeof(int), &cmp_scc
, graph
);
1720 /* Return a non-parametric set in the compressed space of "node" that is
1721 * bounded by the size in each direction
1723 * { [x] : -S_i <= x_i <= S_i }
1725 * If S_i is infinity in direction i, then there are no constraints
1726 * in that direction.
1728 * Cache the result in node->bounds.
1730 static __isl_give isl_basic_set
*get_size_bounds(struct isl_sched_node
*node
)
1733 isl_basic_set
*bounds
;
1737 return isl_basic_set_copy(node
->bounds
);
1739 if (node
->compressed
)
1740 space
= isl_pw_multi_aff_get_domain_space(node
->decompress
);
1742 space
= isl_space_copy(node
->space
);
1743 space
= isl_space_drop_all_params(space
);
1744 bounds
= isl_basic_set_universe(space
);
1746 for (i
= 0; i
< node
->nvar
; ++i
) {
1749 size
= isl_multi_val_get_val(node
->sizes
, i
);
1751 return isl_basic_set_free(bounds
);
1752 if (!isl_val_is_int(size
)) {
1756 bounds
= isl_basic_set_upper_bound_val(bounds
, isl_dim_set
, i
,
1757 isl_val_copy(size
));
1758 bounds
= isl_basic_set_lower_bound_val(bounds
, isl_dim_set
, i
,
1762 node
->bounds
= isl_basic_set_copy(bounds
);
1766 /* Compress the dependence relation "map", if needed, i.e.,
1767 * when the source node "src" and/or the destination node "dst"
1768 * has been compressed.
1770 static __isl_give isl_map
*compress(__isl_take isl_map
*map
,
1771 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
1773 if (src
->compressed
)
1774 map
= isl_map_preimage_domain_pw_multi_aff(map
,
1775 isl_pw_multi_aff_copy(src
->decompress
));
1776 if (dst
->compressed
)
1777 map
= isl_map_preimage_range_pw_multi_aff(map
,
1778 isl_pw_multi_aff_copy(dst
->decompress
));
1782 /* Drop some constraints from "delta" that could be exploited
1783 * to construct loop coalescing schedules.
1784 * In particular, drop those constraint that bound the difference
1785 * to the size of the domain.
1786 * First project out the parameters to improve the effectiveness.
1788 static __isl_give isl_set
*drop_coalescing_constraints(
1789 __isl_take isl_set
*delta
, struct isl_sched_node
*node
)
1792 isl_basic_set
*bounds
;
1794 nparam
= isl_set_dim(delta
, isl_dim_param
);
1796 return isl_set_free(delta
);
1798 bounds
= get_size_bounds(node
);
1800 delta
= isl_set_project_out(delta
, isl_dim_param
, 0, nparam
);
1801 delta
= isl_set_remove_divs(delta
);
1802 delta
= isl_set_plain_gist_basic_set(delta
, bounds
);
1806 /* Given a dependence relation R from "node" to itself,
1807 * construct the set of coefficients of valid constraints for elements
1808 * in that dependence relation.
1809 * In particular, the result contains tuples of coefficients
1810 * c_0, c_n, c_x such that
1812 * c_0 + c_n n + c_x y - c_x x >= 0 for each (x,y) in R
1816 * c_0 + c_n n + c_x d >= 0 for each d in delta R = { y - x | (x,y) in R }
1818 * We choose here to compute the dual of delta R.
1819 * Alternatively, we could have computed the dual of R, resulting
1820 * in a set of tuples c_0, c_n, c_x, c_y, and then
1821 * plugged in (c_0, c_n, c_x, -c_x).
1823 * If "need_param" is set, then the resulting coefficients effectively
1824 * include coefficients for the parameters c_n. Otherwise, they may
1825 * have been projected out already.
1826 * Since the constraints may be different for these two cases,
1827 * they are stored in separate caches.
1828 * In particular, if no parameter coefficients are required and
1829 * the schedule_treat_coalescing option is set, then the parameters
1830 * are projected out and some constraints that could be exploited
1831 * to construct coalescing schedules are removed before the dual
1834 * If "node" has been compressed, then the dependence relation
1835 * is also compressed before the set of coefficients is computed.
1837 static __isl_give isl_basic_set
*intra_coefficients(
1838 struct isl_sched_graph
*graph
, struct isl_sched_node
*node
,
1839 __isl_take isl_map
*map
, int need_param
)
1844 isl_basic_set
*coef
;
1845 isl_maybe_isl_basic_set m
;
1846 isl_map_to_basic_set
**hmap
= &graph
->intra_hmap
;
1852 ctx
= isl_map_get_ctx(map
);
1853 treat
= !need_param
&& isl_options_get_schedule_treat_coalescing(ctx
);
1855 hmap
= &graph
->intra_hmap_param
;
1856 m
= isl_map_to_basic_set_try_get(*hmap
, map
);
1857 if (m
.valid
< 0 || m
.valid
) {
1862 key
= isl_map_copy(map
);
1863 map
= compress(map
, node
, node
);
1864 delta
= isl_map_deltas(map
);
1866 delta
= drop_coalescing_constraints(delta
, node
);
1867 delta
= isl_set_remove_divs(delta
);
1868 coef
= isl_set_coefficients(delta
);
1869 *hmap
= isl_map_to_basic_set_set(*hmap
, key
, isl_basic_set_copy(coef
));
1874 /* Given a dependence relation R, construct the set of coefficients
1875 * of valid constraints for elements in that dependence relation.
1876 * In particular, the result contains tuples of coefficients
1877 * c_0, c_n, c_x, c_y such that
1879 * c_0 + c_n n + c_x x + c_y y >= 0 for each (x,y) in R
1881 * If the source or destination nodes of "edge" have been compressed,
1882 * then the dependence relation is also compressed before
1883 * the set of coefficients is computed.
1885 static __isl_give isl_basic_set
*inter_coefficients(
1886 struct isl_sched_graph
*graph
, struct isl_sched_edge
*edge
,
1887 __isl_take isl_map
*map
)
1891 isl_basic_set
*coef
;
1892 isl_maybe_isl_basic_set m
;
1894 m
= isl_map_to_basic_set_try_get(graph
->inter_hmap
, map
);
1895 if (m
.valid
< 0 || m
.valid
) {
1900 key
= isl_map_copy(map
);
1901 map
= compress(map
, edge
->src
, edge
->dst
);
1902 set
= isl_map_wrap(isl_map_remove_divs(map
));
1903 coef
= isl_set_coefficients(set
);
1904 graph
->inter_hmap
= isl_map_to_basic_set_set(graph
->inter_hmap
, key
,
1905 isl_basic_set_copy(coef
));
1910 /* Return the position of the coefficients of the variables in
1911 * the coefficients constraints "coef".
1913 * The space of "coef" is of the form
1915 * { coefficients[[cst, params] -> S] }
1917 * Return the position of S.
1919 static isl_size
coef_var_offset(__isl_keep isl_basic_set
*coef
)
1924 space
= isl_space_unwrap(isl_basic_set_get_space(coef
));
1925 offset
= isl_space_dim(space
, isl_dim_in
);
1926 isl_space_free(space
);
1931 /* Return the offset of the coefficient of the constant term of "node"
1934 * Within each node, the coefficients have the following order:
1935 * - positive and negative parts of c_i_x
1936 * - c_i_n (if parametric)
1939 static int node_cst_coef_offset(struct isl_sched_node
*node
)
1941 return node
->start
+ 2 * node
->nvar
+ node
->nparam
;
1944 /* Return the offset of the coefficients of the parameters of "node"
1947 * Within each node, the coefficients have the following order:
1948 * - positive and negative parts of c_i_x
1949 * - c_i_n (if parametric)
1952 static int node_par_coef_offset(struct isl_sched_node
*node
)
1954 return node
->start
+ 2 * node
->nvar
;
1957 /* Return the offset of the coefficients of the variables of "node"
1960 * Within each node, the coefficients have the following order:
1961 * - positive and negative parts of c_i_x
1962 * - c_i_n (if parametric)
1965 static int node_var_coef_offset(struct isl_sched_node
*node
)
1970 /* Return the position of the pair of variables encoding
1971 * coefficient "i" of "node".
1973 * The order of these variable pairs is the opposite of
1974 * that of the coefficients, with 2 variables per coefficient.
1976 static int node_var_coef_pos(struct isl_sched_node
*node
, int i
)
1978 return node_var_coef_offset(node
) + 2 * (node
->nvar
- 1 - i
);
1981 /* Construct an isl_dim_map for mapping constraints on coefficients
1982 * for "node" to the corresponding positions in graph->lp.
1983 * "offset" is the offset of the coefficients for the variables
1984 * in the input constraints.
1985 * "s" is the sign of the mapping.
1987 * The input constraints are given in terms of the coefficients
1988 * (c_0, c_x) or (c_0, c_n, c_x).
1989 * The mapping produced by this function essentially plugs in
1990 * (0, c_i_x^+ - c_i_x^-) if s = 1 and
1991 * (0, -c_i_x^+ + c_i_x^-) if s = -1 or
1992 * (0, 0, c_i_x^+ - c_i_x^-) if s = 1 and
1993 * (0, 0, -c_i_x^+ + c_i_x^-) if s = -1.
1994 * In graph->lp, the c_i_x^- appear before their c_i_x^+ counterpart.
1995 * Furthermore, the order of these pairs is the opposite of that
1996 * of the corresponding coefficients.
1998 * The caller can extend the mapping to also map the other coefficients
1999 * (and therefore not plug in 0).
2001 static __isl_give isl_dim_map
*intra_dim_map(isl_ctx
*ctx
,
2002 struct isl_sched_graph
*graph
, struct isl_sched_node
*node
,
2007 isl_dim_map
*dim_map
;
2009 total
= isl_basic_set_dim(graph
->lp
, isl_dim_all
);
2010 if (!node
|| total
< 0)
2013 pos
= node_var_coef_pos(node
, 0);
2014 dim_map
= isl_dim_map_alloc(ctx
, total
);
2015 isl_dim_map_range(dim_map
, pos
, -2, offset
, 1, node
->nvar
, -s
);
2016 isl_dim_map_range(dim_map
, pos
+ 1, -2, offset
, 1, node
->nvar
, s
);
2021 /* Construct an isl_dim_map for mapping constraints on coefficients
2022 * for "src" (node i) and "dst" (node j) to the corresponding positions
2024 * "offset" is the offset of the coefficients for the variables of "src"
2025 * in the input constraints.
2026 * "s" is the sign of the mapping.
2028 * The input constraints are given in terms of the coefficients
2029 * (c_0, c_n, c_x, c_y).
2030 * The mapping produced by this function essentially plugs in
2031 * (c_j_0 - c_i_0, c_j_n - c_i_n,
2032 * -(c_i_x^+ - c_i_x^-), c_j_x^+ - c_j_x^-) if s = 1 and
2033 * (-c_j_0 + c_i_0, -c_j_n + c_i_n,
2034 * c_i_x^+ - c_i_x^-, -(c_j_x^+ - c_j_x^-)) if s = -1.
2035 * In graph->lp, the c_*^- appear before their c_*^+ counterpart.
2036 * Furthermore, the order of these pairs is the opposite of that
2037 * of the corresponding coefficients.
2039 * The caller can further extend the mapping.
2041 static __isl_give isl_dim_map
*inter_dim_map(isl_ctx
*ctx
,
2042 struct isl_sched_graph
*graph
, struct isl_sched_node
*src
,
2043 struct isl_sched_node
*dst
, int offset
, int s
)
2047 isl_dim_map
*dim_map
;
2049 total
= isl_basic_set_dim(graph
->lp
, isl_dim_all
);
2050 if (!src
|| !dst
|| total
< 0)
2053 dim_map
= isl_dim_map_alloc(ctx
, total
);
2055 pos
= node_cst_coef_offset(dst
);
2056 isl_dim_map_range(dim_map
, pos
, 0, 0, 0, 1, s
);
2057 pos
= node_par_coef_offset(dst
);
2058 isl_dim_map_range(dim_map
, pos
, 1, 1, 1, dst
->nparam
, s
);
2059 pos
= node_var_coef_pos(dst
, 0);
2060 isl_dim_map_range(dim_map
, pos
, -2, offset
+ src
->nvar
, 1,
2062 isl_dim_map_range(dim_map
, pos
+ 1, -2, offset
+ src
->nvar
, 1,
2065 pos
= node_cst_coef_offset(src
);
2066 isl_dim_map_range(dim_map
, pos
, 0, 0, 0, 1, -s
);
2067 pos
= node_par_coef_offset(src
);
2068 isl_dim_map_range(dim_map
, pos
, 1, 1, 1, src
->nparam
, -s
);
2069 pos
= node_var_coef_pos(src
, 0);
2070 isl_dim_map_range(dim_map
, pos
, -2, offset
, 1, src
->nvar
, s
);
2071 isl_dim_map_range(dim_map
, pos
+ 1, -2, offset
, 1, src
->nvar
, -s
);
2076 /* Add the constraints from "src" to "dst" using "dim_map",
2077 * after making sure there is enough room in "dst" for the extra constraints.
2079 static __isl_give isl_basic_set
*add_constraints_dim_map(
2080 __isl_take isl_basic_set
*dst
, __isl_take isl_basic_set
*src
,
2081 __isl_take isl_dim_map
*dim_map
)
2085 n_eq
= isl_basic_set_n_equality(src
);
2086 n_ineq
= isl_basic_set_n_inequality(src
);
2087 dst
= isl_basic_set_extend_constraints(dst
, n_eq
, n_ineq
);
2088 dst
= isl_basic_set_add_constraints_dim_map(dst
, src
, dim_map
);
2092 /* Add constraints to graph->lp that force validity for the given
2093 * dependence from a node i to itself.
2094 * That is, add constraints that enforce
2096 * (c_i_0 + c_i_n n + c_i_x y) - (c_i_0 + c_i_n n + c_i_x x)
2097 * = c_i_x (y - x) >= 0
2099 * for each (x,y) in R.
2100 * We obtain general constraints on coefficients (c_0, c_x)
2101 * of valid constraints for (y - x) and then plug in (0, c_i_x^+ - c_i_x^-),
2102 * where c_i_x = c_i_x^+ - c_i_x^-, with c_i_x^+ and c_i_x^- non-negative.
2103 * In graph->lp, the c_i_x^- appear before their c_i_x^+ counterpart.
2104 * Note that the result of intra_coefficients may also contain
2105 * parameter coefficients c_n, in which case 0 is plugged in for them as well.
2107 static isl_stat
add_intra_validity_constraints(struct isl_sched_graph
*graph
,
2108 struct isl_sched_edge
*edge
)
2111 isl_map
*map
= isl_map_copy(edge
->map
);
2112 isl_ctx
*ctx
= isl_map_get_ctx(map
);
2113 isl_dim_map
*dim_map
;
2114 isl_basic_set
*coef
;
2115 struct isl_sched_node
*node
= edge
->src
;
2117 coef
= intra_coefficients(graph
, node
, map
, 0);
2119 offset
= coef_var_offset(coef
);
2121 coef
= isl_basic_set_free(coef
);
2123 return isl_stat_error
;
2125 dim_map
= intra_dim_map(ctx
, graph
, node
, offset
, 1);
2126 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
2131 /* Add constraints to graph->lp that force validity for the given
2132 * dependence from node i to node j.
2133 * That is, add constraints that enforce
2135 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) >= 0
2137 * for each (x,y) in R.
2138 * We obtain general constraints on coefficients (c_0, c_n, c_x, c_y)
2139 * of valid constraints for R and then plug in
2140 * (c_j_0 - c_i_0, c_j_n - c_i_n, -(c_i_x^+ - c_i_x^-), c_j_x^+ - c_j_x^-),
2141 * where c_* = c_*^+ - c_*^-, with c_*^+ and c_*^- non-negative.
2142 * In graph->lp, the c_*^- appear before their c_*^+ counterpart.
2144 static isl_stat
add_inter_validity_constraints(struct isl_sched_graph
*graph
,
2145 struct isl_sched_edge
*edge
)
2150 isl_dim_map
*dim_map
;
2151 isl_basic_set
*coef
;
2152 struct isl_sched_node
*src
= edge
->src
;
2153 struct isl_sched_node
*dst
= edge
->dst
;
2156 return isl_stat_error
;
2158 map
= isl_map_copy(edge
->map
);
2159 ctx
= isl_map_get_ctx(map
);
2160 coef
= inter_coefficients(graph
, edge
, map
);
2162 offset
= coef_var_offset(coef
);
2164 coef
= isl_basic_set_free(coef
);
2166 return isl_stat_error
;
2168 dim_map
= inter_dim_map(ctx
, graph
, src
, dst
, offset
, 1);
2170 edge
->start
= graph
->lp
->n_ineq
;
2171 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
2173 return isl_stat_error
;
2174 edge
->end
= graph
->lp
->n_ineq
;
2179 /* Add constraints to graph->lp that bound the dependence distance for the given
2180 * dependence from a node i to itself.
2181 * If s = 1, we add the constraint
2183 * c_i_x (y - x) <= m_0 + m_n n
2187 * -c_i_x (y - x) + m_0 + m_n n >= 0
2189 * for each (x,y) in R.
2190 * If s = -1, we add the constraint
2192 * -c_i_x (y - x) <= m_0 + m_n n
2196 * c_i_x (y - x) + m_0 + m_n n >= 0
2198 * for each (x,y) in R.
2199 * We obtain general constraints on coefficients (c_0, c_n, c_x)
2200 * of valid constraints for (y - x) and then plug in (m_0, m_n, -s * c_i_x),
2201 * with each coefficient (except m_0) represented as a pair of non-negative
2205 * If "local" is set, then we add constraints
2207 * c_i_x (y - x) <= 0
2211 * -c_i_x (y - x) <= 0
2213 * instead, forcing the dependence distance to be (less than or) equal to 0.
2214 * That is, we plug in (0, 0, -s * c_i_x),
2215 * intra_coefficients is not required to have c_n in its result when
2216 * "local" is set. If they are missing, then (0, -s * c_i_x) is plugged in.
2217 * Note that dependences marked local are treated as validity constraints
2218 * by add_all_validity_constraints and therefore also have
2219 * their distances bounded by 0 from below.
2221 static isl_stat
add_intra_proximity_constraints(struct isl_sched_graph
*graph
,
2222 struct isl_sched_edge
*edge
, int s
, int local
)
2226 isl_map
*map
= isl_map_copy(edge
->map
);
2227 isl_ctx
*ctx
= isl_map_get_ctx(map
);
2228 isl_dim_map
*dim_map
;
2229 isl_basic_set
*coef
;
2230 struct isl_sched_node
*node
= edge
->src
;
2232 coef
= intra_coefficients(graph
, node
, map
, !local
);
2233 nparam
= isl_space_dim(node
->space
, isl_dim_param
);
2235 offset
= coef_var_offset(coef
);
2236 if (nparam
< 0 || offset
< 0)
2237 coef
= isl_basic_set_free(coef
);
2239 return isl_stat_error
;
2241 dim_map
= intra_dim_map(ctx
, graph
, node
, offset
, -s
);
2244 isl_dim_map_range(dim_map
, 1, 0, 0, 0, 1, 1);
2245 isl_dim_map_range(dim_map
, 4, 2, 1, 1, nparam
, -1);
2246 isl_dim_map_range(dim_map
, 5, 2, 1, 1, nparam
, 1);
2248 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
2253 /* Add constraints to graph->lp that bound the dependence distance for the given
2254 * dependence from node i to node j.
2255 * If s = 1, we add the constraint
2257 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x)
2262 * -(c_j_0 + c_j_n n + c_j_x y) + (c_i_0 + c_i_n n + c_i_x x) +
2265 * for each (x,y) in R.
2266 * If s = -1, we add the constraint
2268 * -((c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x))
2273 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) +
2276 * for each (x,y) in R.
2277 * We obtain general constraints on coefficients (c_0, c_n, c_x, c_y)
2278 * of valid constraints for R and then plug in
2279 * (m_0 - s*c_j_0 + s*c_i_0, m_n - s*c_j_n + s*c_i_n,
2280 * s*c_i_x, -s*c_j_x)
2281 * with each coefficient (except m_0, c_*_0 and c_*_n)
2282 * represented as a pair of non-negative coefficients.
2285 * If "local" is set (and s = 1), then we add constraints
2287 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) <= 0
2291 * -((c_j_0 + c_j_n n + c_j_x y) + (c_i_0 + c_i_n n + c_i_x x)) >= 0
2293 * instead, forcing the dependence distance to be (less than or) equal to 0.
2294 * That is, we plug in
2295 * (-s*c_j_0 + s*c_i_0, -s*c_j_n + s*c_i_n, s*c_i_x, -s*c_j_x).
2296 * Note that dependences marked local are treated as validity constraints
2297 * by add_all_validity_constraints and therefore also have
2298 * their distances bounded by 0 from below.
2300 static isl_stat
add_inter_proximity_constraints(struct isl_sched_graph
*graph
,
2301 struct isl_sched_edge
*edge
, int s
, int local
)
2305 isl_map
*map
= isl_map_copy(edge
->map
);
2306 isl_ctx
*ctx
= isl_map_get_ctx(map
);
2307 isl_dim_map
*dim_map
;
2308 isl_basic_set
*coef
;
2309 struct isl_sched_node
*src
= edge
->src
;
2310 struct isl_sched_node
*dst
= edge
->dst
;
2312 coef
= inter_coefficients(graph
, edge
, map
);
2313 nparam
= isl_space_dim(src
->space
, isl_dim_param
);
2315 offset
= coef_var_offset(coef
);
2316 if (nparam
< 0 || offset
< 0)
2317 coef
= isl_basic_set_free(coef
);
2319 return isl_stat_error
;
2321 dim_map
= inter_dim_map(ctx
, graph
, src
, dst
, offset
, -s
);
2324 isl_dim_map_range(dim_map
, 1, 0, 0, 0, 1, 1);
2325 isl_dim_map_range(dim_map
, 4, 2, 1, 1, nparam
, -1);
2326 isl_dim_map_range(dim_map
, 5, 2, 1, 1, nparam
, 1);
2329 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
2334 /* Should the distance over "edge" be forced to zero?
2335 * That is, is it marked as a local edge?
2336 * If "use_coincidence" is set, then coincidence edges are treated
2339 static int force_zero(struct isl_sched_edge
*edge
, int use_coincidence
)
2341 return is_local(edge
) || (use_coincidence
&& is_coincidence(edge
));
2344 /* Add all validity constraints to graph->lp.
2346 * An edge that is forced to be local needs to have its dependence
2347 * distances equal to zero. We take care of bounding them by 0 from below
2348 * here. add_all_proximity_constraints takes care of bounding them by 0
2351 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2352 * Otherwise, we ignore them.
2354 static int add_all_validity_constraints(struct isl_sched_graph
*graph
,
2355 int use_coincidence
)
2359 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2360 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
2363 zero
= force_zero(edge
, use_coincidence
);
2364 if (!is_validity(edge
) && !zero
)
2366 if (edge
->src
!= edge
->dst
)
2368 if (add_intra_validity_constraints(graph
, edge
) < 0)
2372 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2373 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
2376 zero
= force_zero(edge
, use_coincidence
);
2377 if (!is_validity(edge
) && !zero
)
2379 if (edge
->src
== edge
->dst
)
2381 if (add_inter_validity_constraints(graph
, edge
) < 0)
2388 /* Add constraints to graph->lp that bound the dependence distance
2389 * for all dependence relations.
2390 * If a given proximity dependence is identical to a validity
2391 * dependence, then the dependence distance is already bounded
2392 * from below (by zero), so we only need to bound the distance
2393 * from above. (This includes the case of "local" dependences
2394 * which are treated as validity dependence by add_all_validity_constraints.)
2395 * Otherwise, we need to bound the distance both from above and from below.
2397 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2398 * Otherwise, we ignore them.
2400 static int add_all_proximity_constraints(struct isl_sched_graph
*graph
,
2401 int use_coincidence
)
2405 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2406 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
2409 zero
= force_zero(edge
, use_coincidence
);
2410 if (!is_proximity(edge
) && !zero
)
2412 if (edge
->src
== edge
->dst
&&
2413 add_intra_proximity_constraints(graph
, edge
, 1, zero
) < 0)
2415 if (edge
->src
!= edge
->dst
&&
2416 add_inter_proximity_constraints(graph
, edge
, 1, zero
) < 0)
2418 if (is_validity(edge
) || zero
)
2420 if (edge
->src
== edge
->dst
&&
2421 add_intra_proximity_constraints(graph
, edge
, -1, 0) < 0)
2423 if (edge
->src
!= edge
->dst
&&
2424 add_inter_proximity_constraints(graph
, edge
, -1, 0) < 0)
2431 /* Normalize the rows of "indep" such that all rows are lexicographically
2432 * positive and such that each row contains as many final zeros as possible,
2433 * given the choice for the previous rows.
2434 * Do this by performing elementary row operations.
2436 static __isl_give isl_mat
*normalize_independent(__isl_take isl_mat
*indep
)
2438 indep
= isl_mat_reverse_gauss(indep
);
2439 indep
= isl_mat_lexnonneg_rows(indep
);
2443 /* Extract the linear part of the current schedule for node "node".
2445 static __isl_give isl_mat
*extract_linear_schedule(struct isl_sched_node
*node
)
2447 isl_size n_row
= isl_mat_rows(node
->sched
);
2451 return isl_mat_sub_alloc(node
->sched
, 0, n_row
,
2452 1 + node
->nparam
, node
->nvar
);
2455 /* Compute a basis for the rows in the linear part of the schedule
2456 * and extend this basis to a full basis. The remaining rows
2457 * can then be used to force linear independence from the rows
2460 * In particular, given the schedule rows S, we compute
2465 * with H the Hermite normal form of S. That is, all but the
2466 * first rank columns of H are zero and so each row in S is
2467 * a linear combination of the first rank rows of Q.
2468 * The matrix Q can be used as a variable transformation
2469 * that isolates the directions of S in the first rank rows.
2470 * Transposing S U = H yields
2474 * with all but the first rank rows of H^T zero.
2475 * The last rows of U^T are therefore linear combinations
2476 * of schedule coefficients that are all zero on schedule
2477 * coefficients that are linearly dependent on the rows of S.
2478 * At least one of these combinations is non-zero on
2479 * linearly independent schedule coefficients.
2480 * The rows are normalized to involve as few of the last
2481 * coefficients as possible and to have a positive initial value.
2483 static int node_update_vmap(struct isl_sched_node
*node
)
2487 H
= extract_linear_schedule(node
);
2489 H
= isl_mat_left_hermite(H
, 0, &U
, &Q
);
2490 isl_mat_free(node
->indep
);
2491 isl_mat_free(node
->vmap
);
2493 node
->indep
= isl_mat_transpose(U
);
2494 node
->rank
= isl_mat_initial_non_zero_cols(H
);
2495 node
->indep
= isl_mat_drop_rows(node
->indep
, 0, node
->rank
);
2496 node
->indep
= normalize_independent(node
->indep
);
2499 if (!node
->indep
|| !node
->vmap
|| node
->rank
< 0)
2504 /* Is "edge" marked as a validity or a conditional validity edge?
2506 static int is_any_validity(struct isl_sched_edge
*edge
)
2508 return is_validity(edge
) || is_conditional_validity(edge
);
2511 /* How many times should we count the constraints in "edge"?
2513 * We count as follows
2514 * validity -> 1 (>= 0)
2515 * validity+proximity -> 2 (>= 0 and upper bound)
2516 * proximity -> 2 (lower and upper bound)
2517 * local(+any) -> 2 (>= 0 and <= 0)
2519 * If an edge is only marked conditional_validity then it counts
2520 * as zero since it is only checked afterwards.
2522 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2523 * Otherwise, we ignore them.
2525 static int edge_multiplicity(struct isl_sched_edge
*edge
, int use_coincidence
)
2527 if (is_proximity(edge
) || force_zero(edge
, use_coincidence
))
2529 if (is_validity(edge
))
2534 /* How many times should the constraints in "edge" be counted
2535 * as a parametric intra-node constraint?
2537 * Only proximity edges that are not forced zero need
2538 * coefficient constraints that include coefficients for parameters.
2539 * If the edge is also a validity edge, then only
2540 * an upper bound is introduced. Otherwise, both lower and upper bounds
2543 static int parametric_intra_edge_multiplicity(struct isl_sched_edge
*edge
,
2544 int use_coincidence
)
2546 if (edge
->src
!= edge
->dst
)
2548 if (!is_proximity(edge
))
2550 if (force_zero(edge
, use_coincidence
))
2552 if (is_validity(edge
))
2558 /* Add "f" times the number of equality and inequality constraints of "bset"
2559 * to "n_eq" and "n_ineq" and free "bset".
2561 static isl_stat
update_count(__isl_take isl_basic_set
*bset
,
2562 int f
, int *n_eq
, int *n_ineq
)
2565 return isl_stat_error
;
2567 *n_eq
+= isl_basic_set_n_equality(bset
);
2568 *n_ineq
+= isl_basic_set_n_inequality(bset
);
2569 isl_basic_set_free(bset
);
2574 /* Count the number of equality and inequality constraints
2575 * that will be added for the given map.
2577 * The edges that require parameter coefficients are counted separately.
2579 * "use_coincidence" is set if we should take into account coincidence edges.
2581 static isl_stat
count_map_constraints(struct isl_sched_graph
*graph
,
2582 struct isl_sched_edge
*edge
, __isl_take isl_map
*map
,
2583 int *n_eq
, int *n_ineq
, int use_coincidence
)
2586 isl_basic_set
*coef
;
2587 int f
= edge_multiplicity(edge
, use_coincidence
);
2588 int fp
= parametric_intra_edge_multiplicity(edge
, use_coincidence
);
2595 if (edge
->src
!= edge
->dst
) {
2596 coef
= inter_coefficients(graph
, edge
, map
);
2597 return update_count(coef
, f
, n_eq
, n_ineq
);
2601 copy
= isl_map_copy(map
);
2602 coef
= intra_coefficients(graph
, edge
->src
, copy
, 1);
2603 if (update_count(coef
, fp
, n_eq
, n_ineq
) < 0)
2608 copy
= isl_map_copy(map
);
2609 coef
= intra_coefficients(graph
, edge
->src
, copy
, 0);
2610 if (update_count(coef
, f
- fp
, n_eq
, n_ineq
) < 0)
2618 return isl_stat_error
;
2621 /* Count the number of equality and inequality constraints
2622 * that will be added to the main lp problem.
2623 * We count as follows
2624 * validity -> 1 (>= 0)
2625 * validity+proximity -> 2 (>= 0 and upper bound)
2626 * proximity -> 2 (lower and upper bound)
2627 * local(+any) -> 2 (>= 0 and <= 0)
2629 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2630 * Otherwise, we ignore them.
2632 static int count_constraints(struct isl_sched_graph
*graph
,
2633 int *n_eq
, int *n_ineq
, int use_coincidence
)
2637 *n_eq
= *n_ineq
= 0;
2638 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2639 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
2640 isl_map
*map
= isl_map_copy(edge
->map
);
2642 if (count_map_constraints(graph
, edge
, map
, n_eq
, n_ineq
,
2643 use_coincidence
) < 0)
2650 /* Count the number of constraints that will be added by
2651 * add_bound_constant_constraints to bound the values of the constant terms
2652 * and increment *n_eq and *n_ineq accordingly.
2654 * In practice, add_bound_constant_constraints only adds inequalities.
2656 static isl_stat
count_bound_constant_constraints(isl_ctx
*ctx
,
2657 struct isl_sched_graph
*graph
, int *n_eq
, int *n_ineq
)
2659 if (isl_options_get_schedule_max_constant_term(ctx
) == -1)
2662 *n_ineq
+= graph
->n
;
2667 /* Add constraints to bound the values of the constant terms in the schedule,
2668 * if requested by the user.
2670 * The maximal value of the constant terms is defined by the option
2671 * "schedule_max_constant_term".
2673 static isl_stat
add_bound_constant_constraints(isl_ctx
*ctx
,
2674 struct isl_sched_graph
*graph
)
2680 max
= isl_options_get_schedule_max_constant_term(ctx
);
2684 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2686 return isl_stat_error
;
2688 for (i
= 0; i
< graph
->n
; ++i
) {
2689 struct isl_sched_node
*node
= &graph
->node
[i
];
2692 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2694 return isl_stat_error
;
2695 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
2696 pos
= node_cst_coef_offset(node
);
2697 isl_int_set_si(graph
->lp
->ineq
[k
][1 + pos
], -1);
2698 isl_int_set_si(graph
->lp
->ineq
[k
][0], max
);
2704 /* Count the number of constraints that will be added by
2705 * add_bound_coefficient_constraints and increment *n_eq and *n_ineq
2708 * In practice, add_bound_coefficient_constraints only adds inequalities.
2710 static int count_bound_coefficient_constraints(isl_ctx
*ctx
,
2711 struct isl_sched_graph
*graph
, int *n_eq
, int *n_ineq
)
2715 if (isl_options_get_schedule_max_coefficient(ctx
) == -1 &&
2716 !isl_options_get_schedule_treat_coalescing(ctx
))
2719 for (i
= 0; i
< graph
->n
; ++i
)
2720 *n_ineq
+= graph
->node
[i
].nparam
+ 2 * graph
->node
[i
].nvar
;
2725 /* Add constraints to graph->lp that bound the values of
2726 * the parameter schedule coefficients of "node" to "max" and
2727 * the variable schedule coefficients to the corresponding entry
2729 * In either case, a negative value means that no bound needs to be imposed.
2731 * For parameter coefficients, this amounts to adding a constraint
2739 * The variables coefficients are, however, not represented directly.
2740 * Instead, the variable coefficients c_x are written as differences
2741 * c_x = c_x^+ - c_x^-.
2744 * -max_i <= c_x_i <= max_i
2748 * -max_i <= c_x_i^+ - c_x_i^- <= max_i
2752 * -(c_x_i^+ - c_x_i^-) + max_i >= 0
2753 * c_x_i^+ - c_x_i^- + max_i >= 0
2755 static isl_stat
node_add_coefficient_constraints(isl_ctx
*ctx
,
2756 struct isl_sched_graph
*graph
, struct isl_sched_node
*node
, int max
)
2762 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2764 return isl_stat_error
;
2766 for (j
= 0; j
< node
->nparam
; ++j
) {
2772 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2774 return isl_stat_error
;
2775 dim
= 1 + node_par_coef_offset(node
) + j
;
2776 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
2777 isl_int_set_si(graph
->lp
->ineq
[k
][dim
], -1);
2778 isl_int_set_si(graph
->lp
->ineq
[k
][0], max
);
2781 ineq
= isl_vec_alloc(ctx
, 1 + total
);
2782 ineq
= isl_vec_clr(ineq
);
2784 return isl_stat_error
;
2785 for (i
= 0; i
< node
->nvar
; ++i
) {
2786 int pos
= 1 + node_var_coef_pos(node
, i
);
2788 if (isl_int_is_neg(node
->max
->el
[i
]))
2791 isl_int_set_si(ineq
->el
[pos
], 1);
2792 isl_int_set_si(ineq
->el
[pos
+ 1], -1);
2793 isl_int_set(ineq
->el
[0], node
->max
->el
[i
]);
2795 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2798 isl_seq_cpy(graph
->lp
->ineq
[k
], ineq
->el
, 1 + total
);
2800 isl_seq_neg(ineq
->el
+ pos
, ineq
->el
+ pos
, 2);
2801 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2804 isl_seq_cpy(graph
->lp
->ineq
[k
], ineq
->el
, 1 + total
);
2806 isl_seq_clr(ineq
->el
+ pos
, 2);
2813 return isl_stat_error
;
2816 /* Add constraints that bound the values of the variable and parameter
2817 * coefficients of the schedule.
2819 * The maximal value of the coefficients is defined by the option
2820 * 'schedule_max_coefficient' and the entries in node->max.
2821 * These latter entries are only set if either the schedule_max_coefficient
2822 * option or the schedule_treat_coalescing option is set.
2824 static isl_stat
add_bound_coefficient_constraints(isl_ctx
*ctx
,
2825 struct isl_sched_graph
*graph
)
2830 max
= isl_options_get_schedule_max_coefficient(ctx
);
2832 if (max
== -1 && !isl_options_get_schedule_treat_coalescing(ctx
))
2835 for (i
= 0; i
< graph
->n
; ++i
) {
2836 struct isl_sched_node
*node
= &graph
->node
[i
];
2838 if (node_add_coefficient_constraints(ctx
, graph
, node
, max
) < 0)
2839 return isl_stat_error
;
2845 /* Add a constraint to graph->lp that equates the value at position
2846 * "sum_pos" to the sum of the "n" values starting at "first".
2848 static isl_stat
add_sum_constraint(struct isl_sched_graph
*graph
,
2849 int sum_pos
, int first
, int n
)
2854 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2856 return isl_stat_error
;
2858 k
= isl_basic_set_alloc_equality(graph
->lp
);
2860 return isl_stat_error
;
2861 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2862 isl_int_set_si(graph
->lp
->eq
[k
][1 + sum_pos
], -1);
2863 for (i
= 0; i
< n
; ++i
)
2864 isl_int_set_si(graph
->lp
->eq
[k
][1 + first
+ i
], 1);
2869 /* Add a constraint to graph->lp that equates the value at position
2870 * "sum_pos" to the sum of the parameter coefficients of all nodes.
2872 static isl_stat
add_param_sum_constraint(struct isl_sched_graph
*graph
,
2878 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2880 return isl_stat_error
;
2882 k
= isl_basic_set_alloc_equality(graph
->lp
);
2884 return isl_stat_error
;
2885 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2886 isl_int_set_si(graph
->lp
->eq
[k
][1 + sum_pos
], -1);
2887 for (i
= 0; i
< graph
->n
; ++i
) {
2888 int pos
= 1 + node_par_coef_offset(&graph
->node
[i
]);
2890 for (j
= 0; j
< graph
->node
[i
].nparam
; ++j
)
2891 isl_int_set_si(graph
->lp
->eq
[k
][pos
+ j
], 1);
2897 /* Add a constraint to graph->lp that equates the value at position
2898 * "sum_pos" to the sum of the variable coefficients of all nodes.
2900 static isl_stat
add_var_sum_constraint(struct isl_sched_graph
*graph
,
2906 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2908 return isl_stat_error
;
2910 k
= isl_basic_set_alloc_equality(graph
->lp
);
2912 return isl_stat_error
;
2913 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2914 isl_int_set_si(graph
->lp
->eq
[k
][1 + sum_pos
], -1);
2915 for (i
= 0; i
< graph
->n
; ++i
) {
2916 struct isl_sched_node
*node
= &graph
->node
[i
];
2917 int pos
= 1 + node_var_coef_offset(node
);
2919 for (j
= 0; j
< 2 * node
->nvar
; ++j
)
2920 isl_int_set_si(graph
->lp
->eq
[k
][pos
+ j
], 1);
2926 /* Construct an ILP problem for finding schedule coefficients
2927 * that result in non-negative, but small dependence distances
2928 * over all dependences.
2929 * In particular, the dependence distances over proximity edges
2930 * are bounded by m_0 + m_n n and we compute schedule coefficients
2931 * with small values (preferably zero) of m_n and m_0.
2933 * All variables of the ILP are non-negative. The actual coefficients
2934 * may be negative, so each coefficient is represented as the difference
2935 * of two non-negative variables. The negative part always appears
2936 * immediately before the positive part.
2937 * Other than that, the variables have the following order
2939 * - sum of positive and negative parts of m_n coefficients
2941 * - sum of all c_n coefficients
2942 * (unconstrained when computing non-parametric schedules)
2943 * - sum of positive and negative parts of all c_x coefficients
2944 * - positive and negative parts of m_n coefficients
2946 * - positive and negative parts of c_i_x, in opposite order
2947 * - c_i_n (if parametric)
2950 * The constraints are those from the edges plus two or three equalities
2951 * to express the sums.
2953 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2954 * Otherwise, we ignore them.
2956 static isl_stat
setup_lp(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
2957 int use_coincidence
)
2967 parametric
= ctx
->opt
->schedule_parametric
;
2968 nparam
= isl_space_dim(graph
->node
[0].space
, isl_dim_param
);
2970 return isl_stat_error
;
2972 total
= param_pos
+ 2 * nparam
;
2973 for (i
= 0; i
< graph
->n
; ++i
) {
2974 struct isl_sched_node
*node
= &graph
->node
[graph
->sorted
[i
]];
2975 if (node_update_vmap(node
) < 0)
2976 return isl_stat_error
;
2977 node
->start
= total
;
2978 total
+= 1 + node
->nparam
+ 2 * node
->nvar
;
2981 if (count_constraints(graph
, &n_eq
, &n_ineq
, use_coincidence
) < 0)
2982 return isl_stat_error
;
2983 if (count_bound_constant_constraints(ctx
, graph
, &n_eq
, &n_ineq
) < 0)
2984 return isl_stat_error
;
2985 if (count_bound_coefficient_constraints(ctx
, graph
, &n_eq
, &n_ineq
) < 0)
2986 return isl_stat_error
;
2988 space
= isl_space_set_alloc(ctx
, 0, total
);
2989 isl_basic_set_free(graph
->lp
);
2990 n_eq
+= 2 + parametric
;
2992 graph
->lp
= isl_basic_set_alloc_space(space
, 0, n_eq
, n_ineq
);
2994 if (add_sum_constraint(graph
, 0, param_pos
, 2 * nparam
) < 0)
2995 return isl_stat_error
;
2996 if (parametric
&& add_param_sum_constraint(graph
, 2) < 0)
2997 return isl_stat_error
;
2998 if (add_var_sum_constraint(graph
, 3) < 0)
2999 return isl_stat_error
;
3000 if (add_bound_constant_constraints(ctx
, graph
) < 0)
3001 return isl_stat_error
;
3002 if (add_bound_coefficient_constraints(ctx
, graph
) < 0)
3003 return isl_stat_error
;
3004 if (add_all_validity_constraints(graph
, use_coincidence
) < 0)
3005 return isl_stat_error
;
3006 if (add_all_proximity_constraints(graph
, use_coincidence
) < 0)
3007 return isl_stat_error
;
3012 /* Analyze the conflicting constraint found by
3013 * isl_tab_basic_set_non_trivial_lexmin. If it corresponds to the validity
3014 * constraint of one of the edges between distinct nodes, living, moreover
3015 * in distinct SCCs, then record the source and sink SCC as this may
3016 * be a good place to cut between SCCs.
3018 static int check_conflict(int con
, void *user
)
3021 struct isl_sched_graph
*graph
= user
;
3023 if (graph
->src_scc
>= 0)
3026 con
-= graph
->lp
->n_eq
;
3028 if (con
>= graph
->lp
->n_ineq
)
3031 for (i
= 0; i
< graph
->n_edge
; ++i
) {
3032 if (!is_validity(&graph
->edge
[i
]))
3034 if (graph
->edge
[i
].src
== graph
->edge
[i
].dst
)
3036 if (graph
->edge
[i
].src
->scc
== graph
->edge
[i
].dst
->scc
)
3038 if (graph
->edge
[i
].start
> con
)
3040 if (graph
->edge
[i
].end
<= con
)
3042 graph
->src_scc
= graph
->edge
[i
].src
->scc
;
3043 graph
->dst_scc
= graph
->edge
[i
].dst
->scc
;
3049 /* Check whether the next schedule row of the given node needs to be
3050 * non-trivial. Lower-dimensional domains may have some trivial rows,
3051 * but as soon as the number of remaining required non-trivial rows
3052 * is as large as the number or remaining rows to be computed,
3053 * all remaining rows need to be non-trivial.
3055 static int needs_row(struct isl_sched_graph
*graph
, struct isl_sched_node
*node
)
3057 return node
->nvar
- node
->rank
>= graph
->maxvar
- graph
->n_row
;
3060 /* Construct a non-triviality region with triviality directions
3061 * corresponding to the rows of "indep".
3062 * The rows of "indep" are expressed in terms of the schedule coefficients c_i,
3063 * while the triviality directions are expressed in terms of
3064 * pairs of non-negative variables c^+_i - c^-_i, with c^-_i appearing
3065 * before c^+_i. Furthermore,
3066 * the pairs of non-negative variables representing the coefficients
3067 * are stored in the opposite order.
3069 static __isl_give isl_mat
*construct_trivial(__isl_keep isl_mat
*indep
)
3076 n
= isl_mat_rows(indep
);
3077 n_var
= isl_mat_cols(indep
);
3078 if (n
< 0 || n_var
< 0)
3081 ctx
= isl_mat_get_ctx(indep
);
3082 mat
= isl_mat_alloc(ctx
, n
, 2 * n_var
);
3085 for (i
= 0; i
< n
; ++i
) {
3086 for (j
= 0; j
< n_var
; ++j
) {
3087 int nj
= n_var
- 1 - j
;
3088 isl_int_neg(mat
->row
[i
][2 * nj
], indep
->row
[i
][j
]);
3089 isl_int_set(mat
->row
[i
][2 * nj
+ 1], indep
->row
[i
][j
]);
3096 /* Solve the ILP problem constructed in setup_lp.
3097 * For each node such that all the remaining rows of its schedule
3098 * need to be non-trivial, we construct a non-triviality region.
3099 * This region imposes that the next row is independent of previous rows.
3100 * In particular, the non-triviality region enforces that at least
3101 * one of the linear combinations in the rows of node->indep is non-zero.
3103 static __isl_give isl_vec
*solve_lp(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
3109 for (i
= 0; i
< graph
->n
; ++i
) {
3110 struct isl_sched_node
*node
= &graph
->node
[i
];
3113 graph
->region
[i
].pos
= node_var_coef_offset(node
);
3114 if (needs_row(graph
, node
))
3115 trivial
= construct_trivial(node
->indep
);
3117 trivial
= isl_mat_zero(ctx
, 0, 0);
3118 graph
->region
[i
].trivial
= trivial
;
3120 lp
= isl_basic_set_copy(graph
->lp
);
3121 sol
= isl_tab_basic_set_non_trivial_lexmin(lp
, 2, graph
->n
,
3122 graph
->region
, &check_conflict
, graph
);
3123 for (i
= 0; i
< graph
->n
; ++i
)
3124 isl_mat_free(graph
->region
[i
].trivial
);
3128 /* Extract the coefficients for the variables of "node" from "sol".
3130 * Each schedule coefficient c_i_x is represented as the difference
3131 * between two non-negative variables c_i_x^+ - c_i_x^-.
3132 * The c_i_x^- appear before their c_i_x^+ counterpart.
3133 * Furthermore, the order of these pairs is the opposite of that
3134 * of the corresponding coefficients.
3136 * Return c_i_x = c_i_x^+ - c_i_x^-
3138 static __isl_give isl_vec
*extract_var_coef(struct isl_sched_node
*node
,
3139 __isl_keep isl_vec
*sol
)
3147 csol
= isl_vec_alloc(isl_vec_get_ctx(sol
), node
->nvar
);
3151 pos
= 1 + node_var_coef_offset(node
);
3152 for (i
= 0; i
< node
->nvar
; ++i
)
3153 isl_int_sub(csol
->el
[node
->nvar
- 1 - i
],
3154 sol
->el
[pos
+ 2 * i
+ 1], sol
->el
[pos
+ 2 * i
]);
3159 /* Update the schedules of all nodes based on the given solution
3160 * of the LP problem.
3161 * The new row is added to the current band.
3162 * All possibly negative coefficients are encoded as a difference
3163 * of two non-negative variables, so we need to perform the subtraction
3166 * If coincident is set, then the caller guarantees that the new
3167 * row satisfies the coincidence constraints.
3169 static int update_schedule(struct isl_sched_graph
*graph
,
3170 __isl_take isl_vec
*sol
, int coincident
)
3173 isl_vec
*csol
= NULL
;
3178 isl_die(sol
->ctx
, isl_error_internal
,
3179 "no solution found", goto error
);
3180 if (graph
->n_total_row
>= graph
->max_row
)
3181 isl_die(sol
->ctx
, isl_error_internal
,
3182 "too many schedule rows", goto error
);
3184 for (i
= 0; i
< graph
->n
; ++i
) {
3185 struct isl_sched_node
*node
= &graph
->node
[i
];
3187 isl_size row
= isl_mat_rows(node
->sched
);
3190 csol
= extract_var_coef(node
, sol
);
3191 if (row
< 0 || !csol
)
3194 isl_map_free(node
->sched_map
);
3195 node
->sched_map
= NULL
;
3196 node
->sched
= isl_mat_add_rows(node
->sched
, 1);
3199 pos
= node_cst_coef_offset(node
);
3200 node
->sched
= isl_mat_set_element(node
->sched
,
3201 row
, 0, sol
->el
[1 + pos
]);
3202 pos
= node_par_coef_offset(node
);
3203 for (j
= 0; j
< node
->nparam
; ++j
)
3204 node
->sched
= isl_mat_set_element(node
->sched
,
3205 row
, 1 + j
, sol
->el
[1 + pos
+ j
]);
3206 for (j
= 0; j
< node
->nvar
; ++j
)
3207 node
->sched
= isl_mat_set_element(node
->sched
,
3208 row
, 1 + node
->nparam
+ j
, csol
->el
[j
]);
3209 node
->coincident
[graph
->n_total_row
] = coincident
;
3215 graph
->n_total_row
++;
3224 /* Convert row "row" of node->sched into an isl_aff living in "ls"
3225 * and return this isl_aff.
3227 static __isl_give isl_aff
*extract_schedule_row(__isl_take isl_local_space
*ls
,
3228 struct isl_sched_node
*node
, int row
)
3236 aff
= isl_aff_zero_on_domain(ls
);
3237 if (isl_mat_get_element(node
->sched
, row
, 0, &v
) < 0)
3239 aff
= isl_aff_set_constant(aff
, v
);
3240 for (j
= 0; j
< node
->nparam
; ++j
) {
3241 if (isl_mat_get_element(node
->sched
, row
, 1 + j
, &v
) < 0)
3243 aff
= isl_aff_set_coefficient(aff
, isl_dim_param
, j
, v
);
3245 for (j
= 0; j
< node
->nvar
; ++j
) {
3246 if (isl_mat_get_element(node
->sched
, row
,
3247 1 + node
->nparam
+ j
, &v
) < 0)
3249 aff
= isl_aff_set_coefficient(aff
, isl_dim_in
, j
, v
);
3261 /* Convert the "n" rows starting at "first" of node->sched into a multi_aff
3262 * and return this multi_aff.
3264 * The result is defined over the uncompressed node domain.
3266 static __isl_give isl_multi_aff
*node_extract_partial_schedule_multi_aff(
3267 struct isl_sched_node
*node
, int first
, int n
)
3271 isl_local_space
*ls
;
3278 nrow
= isl_mat_rows(node
->sched
);
3281 if (node
->compressed
)
3282 space
= isl_pw_multi_aff_get_domain_space(node
->decompress
);
3284 space
= isl_space_copy(node
->space
);
3285 ls
= isl_local_space_from_space(isl_space_copy(space
));
3286 space
= isl_space_from_domain(space
);
3287 space
= isl_space_add_dims(space
, isl_dim_out
, n
);
3288 ma
= isl_multi_aff_zero(space
);
3290 for (i
= first
; i
< first
+ n
; ++i
) {
3291 aff
= extract_schedule_row(isl_local_space_copy(ls
), node
, i
);
3292 ma
= isl_multi_aff_set_aff(ma
, i
- first
, aff
);
3295 isl_local_space_free(ls
);
3297 if (node
->compressed
)
3298 ma
= isl_multi_aff_pullback_multi_aff(ma
,
3299 isl_multi_aff_copy(node
->compress
));
3304 /* Convert node->sched into a multi_aff and return this multi_aff.
3306 * The result is defined over the uncompressed node domain.
3308 static __isl_give isl_multi_aff
*node_extract_schedule_multi_aff(
3309 struct isl_sched_node
*node
)
3313 nrow
= isl_mat_rows(node
->sched
);
3316 return node_extract_partial_schedule_multi_aff(node
, 0, nrow
);
3319 /* Convert node->sched into a map and return this map.
3321 * The result is cached in node->sched_map, which needs to be released
3322 * whenever node->sched is updated.
3323 * It is defined over the uncompressed node domain.
3325 static __isl_give isl_map
*node_extract_schedule(struct isl_sched_node
*node
)
3327 if (!node
->sched_map
) {
3330 ma
= node_extract_schedule_multi_aff(node
);
3331 node
->sched_map
= isl_map_from_multi_aff(ma
);
3334 return isl_map_copy(node
->sched_map
);
3337 /* Construct a map that can be used to update a dependence relation
3338 * based on the current schedule.
3339 * That is, construct a map expressing that source and sink
3340 * are executed within the same iteration of the current schedule.
3341 * This map can then be intersected with the dependence relation.
3342 * This is not the most efficient way, but this shouldn't be a critical
3345 static __isl_give isl_map
*specializer(struct isl_sched_node
*src
,
3346 struct isl_sched_node
*dst
)
3348 isl_map
*src_sched
, *dst_sched
;
3350 src_sched
= node_extract_schedule(src
);
3351 dst_sched
= node_extract_schedule(dst
);
3352 return isl_map_apply_range(src_sched
, isl_map_reverse(dst_sched
));
3355 /* Intersect the domains of the nested relations in domain and range
3356 * of "umap" with "map".
3358 static __isl_give isl_union_map
*intersect_domains(
3359 __isl_take isl_union_map
*umap
, __isl_keep isl_map
*map
)
3361 isl_union_set
*uset
;
3363 umap
= isl_union_map_zip(umap
);
3364 uset
= isl_union_set_from_set(isl_map_wrap(isl_map_copy(map
)));
3365 umap
= isl_union_map_intersect_domain(umap
, uset
);
3366 umap
= isl_union_map_zip(umap
);
3370 /* Update the dependence relation of the given edge based
3371 * on the current schedule.
3372 * If the dependence is carried completely by the current schedule, then
3373 * it is removed from the edge_tables. It is kept in the list of edges
3374 * as otherwise all edge_tables would have to be recomputed.
3376 * If the edge is of a type that can appear multiple times
3377 * between the same pair of nodes, then it is added to
3378 * the edge table (again). This prevents the situation
3379 * where none of these edges is referenced from the edge table
3380 * because the one that was referenced turned out to be empty and
3381 * was therefore removed from the table.
3383 static isl_stat
update_edge(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
3384 struct isl_sched_edge
*edge
)
3389 id
= specializer(edge
->src
, edge
->dst
);
3390 edge
->map
= isl_map_intersect(edge
->map
, isl_map_copy(id
));
3394 if (edge
->tagged_condition
) {
3395 edge
->tagged_condition
=
3396 intersect_domains(edge
->tagged_condition
, id
);
3397 if (!edge
->tagged_condition
)
3400 if (edge
->tagged_validity
) {
3401 edge
->tagged_validity
=
3402 intersect_domains(edge
->tagged_validity
, id
);
3403 if (!edge
->tagged_validity
)
3407 empty
= isl_map_plain_is_empty(edge
->map
);
3411 if (graph_remove_edge(graph
, edge
) < 0)
3413 } else if (is_multi_edge_type(edge
)) {
3414 if (graph_edge_tables_add(ctx
, graph
, edge
) < 0)
3422 return isl_stat_error
;
3425 /* Does the domain of "umap" intersect "uset"?
3427 static int domain_intersects(__isl_keep isl_union_map
*umap
,
3428 __isl_keep isl_union_set
*uset
)
3432 umap
= isl_union_map_copy(umap
);
3433 umap
= isl_union_map_intersect_domain(umap
, isl_union_set_copy(uset
));
3434 empty
= isl_union_map_is_empty(umap
);
3435 isl_union_map_free(umap
);
3437 return empty
< 0 ? -1 : !empty
;
3440 /* Does the range of "umap" intersect "uset"?
3442 static int range_intersects(__isl_keep isl_union_map
*umap
,
3443 __isl_keep isl_union_set
*uset
)
3447 umap
= isl_union_map_copy(umap
);
3448 umap
= isl_union_map_intersect_range(umap
, isl_union_set_copy(uset
));
3449 empty
= isl_union_map_is_empty(umap
);
3450 isl_union_map_free(umap
);
3452 return empty
< 0 ? -1 : !empty
;
3455 /* Are the condition dependences of "edge" local with respect to
3456 * the current schedule?
3458 * That is, are domain and range of the condition dependences mapped
3459 * to the same point?
3461 * In other words, is the condition false?
3463 static int is_condition_false(struct isl_sched_edge
*edge
)
3465 isl_union_map
*umap
;
3466 isl_map
*map
, *sched
, *test
;
3469 empty
= isl_union_map_is_empty(edge
->tagged_condition
);
3470 if (empty
< 0 || empty
)
3473 umap
= isl_union_map_copy(edge
->tagged_condition
);
3474 umap
= isl_union_map_zip(umap
);
3475 umap
= isl_union_set_unwrap(isl_union_map_domain(umap
));
3476 map
= isl_map_from_union_map(umap
);
3478 sched
= node_extract_schedule(edge
->src
);
3479 map
= isl_map_apply_domain(map
, sched
);
3480 sched
= node_extract_schedule(edge
->dst
);
3481 map
= isl_map_apply_range(map
, sched
);
3483 test
= isl_map_identity(isl_map_get_space(map
));
3484 local
= isl_map_is_subset(map
, test
);
3491 /* For each conditional validity constraint that is adjacent
3492 * to a condition with domain in condition_source or range in condition_sink,
3493 * turn it into an unconditional validity constraint.
3495 static int unconditionalize_adjacent_validity(struct isl_sched_graph
*graph
,
3496 __isl_take isl_union_set
*condition_source
,
3497 __isl_take isl_union_set
*condition_sink
)
3501 condition_source
= isl_union_set_coalesce(condition_source
);
3502 condition_sink
= isl_union_set_coalesce(condition_sink
);
3504 for (i
= 0; i
< graph
->n_edge
; ++i
) {
3506 isl_union_map
*validity
;
3508 if (!is_conditional_validity(&graph
->edge
[i
]))
3510 if (is_validity(&graph
->edge
[i
]))
3513 validity
= graph
->edge
[i
].tagged_validity
;
3514 adjacent
= domain_intersects(validity
, condition_sink
);
3515 if (adjacent
>= 0 && !adjacent
)
3516 adjacent
= range_intersects(validity
, condition_source
);
3522 set_validity(&graph
->edge
[i
]);
3525 isl_union_set_free(condition_source
);
3526 isl_union_set_free(condition_sink
);
3529 isl_union_set_free(condition_source
);
3530 isl_union_set_free(condition_sink
);
3534 /* Update the dependence relations of all edges based on the current schedule
3535 * and enforce conditional validity constraints that are adjacent
3536 * to satisfied condition constraints.
3538 * First check if any of the condition constraints are satisfied
3539 * (i.e., not local to the outer schedule) and keep track of
3540 * their domain and range.
3541 * Then update all dependence relations (which removes the non-local
3543 * Finally, if any condition constraints turned out to be satisfied,
3544 * then turn all adjacent conditional validity constraints into
3545 * unconditional validity constraints.
3547 static int update_edges(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
3551 isl_union_set
*source
, *sink
;
3553 source
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
3554 sink
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
3555 for (i
= 0; i
< graph
->n_edge
; ++i
) {
3557 isl_union_set
*uset
;
3558 isl_union_map
*umap
;
3560 if (!is_condition(&graph
->edge
[i
]))
3562 if (is_local(&graph
->edge
[i
]))
3564 local
= is_condition_false(&graph
->edge
[i
]);
3572 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_condition
);
3573 uset
= isl_union_map_domain(umap
);
3574 source
= isl_union_set_union(source
, uset
);
3576 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_condition
);
3577 uset
= isl_union_map_range(umap
);
3578 sink
= isl_union_set_union(sink
, uset
);
3581 for (i
= 0; i
< graph
->n_edge
; ++i
) {
3582 if (update_edge(ctx
, graph
, &graph
->edge
[i
]) < 0)
3587 return unconditionalize_adjacent_validity(graph
, source
, sink
);
3589 isl_union_set_free(source
);
3590 isl_union_set_free(sink
);
3593 isl_union_set_free(source
);
3594 isl_union_set_free(sink
);
3598 static void next_band(struct isl_sched_graph
*graph
)
3600 graph
->band_start
= graph
->n_total_row
;
3603 /* Return the union of the universe domains of the nodes in "graph"
3604 * that satisfy "pred".
3606 static __isl_give isl_union_set
*isl_sched_graph_domain(isl_ctx
*ctx
,
3607 struct isl_sched_graph
*graph
,
3608 int (*pred
)(struct isl_sched_node
*node
, int data
), int data
)
3614 for (i
= 0; i
< graph
->n
; ++i
)
3615 if (pred(&graph
->node
[i
], data
))
3619 isl_die(ctx
, isl_error_internal
,
3620 "empty component", return NULL
);
3622 set
= isl_set_universe(isl_space_copy(graph
->node
[i
].space
));
3623 dom
= isl_union_set_from_set(set
);
3625 for (i
= i
+ 1; i
< graph
->n
; ++i
) {
3626 if (!pred(&graph
->node
[i
], data
))
3628 set
= isl_set_universe(isl_space_copy(graph
->node
[i
].space
));
3629 dom
= isl_union_set_union(dom
, isl_union_set_from_set(set
));
3635 /* Return a list of unions of universe domains, where each element
3636 * in the list corresponds to an SCC (or WCC) indexed by node->scc.
3638 static __isl_give isl_union_set_list
*extract_sccs(isl_ctx
*ctx
,
3639 struct isl_sched_graph
*graph
)
3642 isl_union_set_list
*filters
;
3644 filters
= isl_union_set_list_alloc(ctx
, graph
->scc
);
3645 for (i
= 0; i
< graph
->scc
; ++i
) {
3648 dom
= isl_sched_graph_domain(ctx
, graph
, &node_scc_exactly
, i
);
3649 filters
= isl_union_set_list_add(filters
, dom
);
3655 /* Return a list of two unions of universe domains, one for the SCCs up
3656 * to and including graph->src_scc and another for the other SCCs.
3658 static __isl_give isl_union_set_list
*extract_split(isl_ctx
*ctx
,
3659 struct isl_sched_graph
*graph
)
3662 isl_union_set_list
*filters
;
3664 filters
= isl_union_set_list_alloc(ctx
, 2);
3665 dom
= isl_sched_graph_domain(ctx
, graph
,
3666 &node_scc_at_most
, graph
->src_scc
);
3667 filters
= isl_union_set_list_add(filters
, dom
);
3668 dom
= isl_sched_graph_domain(ctx
, graph
,
3669 &node_scc_at_least
, graph
->src_scc
+ 1);
3670 filters
= isl_union_set_list_add(filters
, dom
);
3675 /* Copy nodes that satisfy node_pred from the src dependence graph
3676 * to the dst dependence graph.
3678 static isl_stat
copy_nodes(struct isl_sched_graph
*dst
,
3679 struct isl_sched_graph
*src
,
3680 int (*node_pred
)(struct isl_sched_node
*node
, int data
), int data
)
3685 for (i
= 0; i
< src
->n
; ++i
) {
3688 if (!node_pred(&src
->node
[i
], data
))
3692 dst
->node
[j
].space
= isl_space_copy(src
->node
[i
].space
);
3693 dst
->node
[j
].compressed
= src
->node
[i
].compressed
;
3694 dst
->node
[j
].hull
= isl_set_copy(src
->node
[i
].hull
);
3695 dst
->node
[j
].compress
=
3696 isl_multi_aff_copy(src
->node
[i
].compress
);
3697 dst
->node
[j
].decompress
=
3698 isl_pw_multi_aff_copy(src
->node
[i
].decompress
);
3699 dst
->node
[j
].nvar
= src
->node
[i
].nvar
;
3700 dst
->node
[j
].nparam
= src
->node
[i
].nparam
;
3701 dst
->node
[j
].sched
= isl_mat_copy(src
->node
[i
].sched
);
3702 dst
->node
[j
].sched_map
= isl_map_copy(src
->node
[i
].sched_map
);
3703 dst
->node
[j
].coincident
= src
->node
[i
].coincident
;
3704 dst
->node
[j
].sizes
= isl_multi_val_copy(src
->node
[i
].sizes
);
3705 dst
->node
[j
].bounds
= isl_basic_set_copy(src
->node
[i
].bounds
);
3706 dst
->node
[j
].max
= isl_vec_copy(src
->node
[i
].max
);
3709 if (!dst
->node
[j
].space
|| !dst
->node
[j
].sched
)
3710 return isl_stat_error
;
3711 if (dst
->node
[j
].compressed
&&
3712 (!dst
->node
[j
].hull
|| !dst
->node
[j
].compress
||
3713 !dst
->node
[j
].decompress
))
3714 return isl_stat_error
;
3720 /* Copy non-empty edges that satisfy edge_pred from the src dependence graph
3721 * to the dst dependence graph.
3722 * If the source or destination node of the edge is not in the destination
3723 * graph, then it must be a backward proximity edge and it should simply
3726 static isl_stat
copy_edges(isl_ctx
*ctx
, struct isl_sched_graph
*dst
,
3727 struct isl_sched_graph
*src
,
3728 int (*edge_pred
)(struct isl_sched_edge
*edge
, int data
), int data
)
3733 for (i
= 0; i
< src
->n_edge
; ++i
) {
3734 struct isl_sched_edge
*edge
= &src
->edge
[i
];
3736 isl_union_map
*tagged_condition
;
3737 isl_union_map
*tagged_validity
;
3738 struct isl_sched_node
*dst_src
, *dst_dst
;
3740 if (!edge_pred(edge
, data
))
3743 if (isl_map_plain_is_empty(edge
->map
))
3746 dst_src
= graph_find_node(ctx
, dst
, edge
->src
->space
);
3747 dst_dst
= graph_find_node(ctx
, dst
, edge
->dst
->space
);
3748 if (!dst_src
|| !dst_dst
)
3749 return isl_stat_error
;
3750 if (!is_node(dst
, dst_src
) || !is_node(dst
, dst_dst
)) {
3751 if (is_validity(edge
) || is_conditional_validity(edge
))
3752 isl_die(ctx
, isl_error_internal
,
3753 "backward (conditional) validity edge",
3754 return isl_stat_error
);
3758 map
= isl_map_copy(edge
->map
);
3759 tagged_condition
= isl_union_map_copy(edge
->tagged_condition
);
3760 tagged_validity
= isl_union_map_copy(edge
->tagged_validity
);
3762 dst
->edge
[dst
->n_edge
].src
= dst_src
;
3763 dst
->edge
[dst
->n_edge
].dst
= dst_dst
;
3764 dst
->edge
[dst
->n_edge
].map
= map
;
3765 dst
->edge
[dst
->n_edge
].tagged_condition
= tagged_condition
;
3766 dst
->edge
[dst
->n_edge
].tagged_validity
= tagged_validity
;
3767 dst
->edge
[dst
->n_edge
].types
= edge
->types
;
3770 if (edge
->tagged_condition
&& !tagged_condition
)
3771 return isl_stat_error
;
3772 if (edge
->tagged_validity
&& !tagged_validity
)
3773 return isl_stat_error
;
3775 if (graph_edge_tables_add(ctx
, dst
,
3776 &dst
->edge
[dst
->n_edge
- 1]) < 0)
3777 return isl_stat_error
;
3783 /* Compute the maximal number of variables over all nodes.
3784 * This is the maximal number of linearly independent schedule
3785 * rows that we need to compute.
3786 * Just in case we end up in a part of the dependence graph
3787 * with only lower-dimensional domains, we make sure we will
3788 * compute the required amount of extra linearly independent rows.
3790 static int compute_maxvar(struct isl_sched_graph
*graph
)
3795 for (i
= 0; i
< graph
->n
; ++i
) {
3796 struct isl_sched_node
*node
= &graph
->node
[i
];
3799 if (node_update_vmap(node
) < 0)
3801 nvar
= node
->nvar
+ graph
->n_row
- node
->rank
;
3802 if (nvar
> graph
->maxvar
)
3803 graph
->maxvar
= nvar
;
3809 /* Extract the subgraph of "graph" that consists of the nodes satisfying
3810 * "node_pred" and the edges satisfying "edge_pred" and store
3811 * the result in "sub".
3813 static isl_stat
extract_sub_graph(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
3814 int (*node_pred
)(struct isl_sched_node
*node
, int data
),
3815 int (*edge_pred
)(struct isl_sched_edge
*edge
, int data
),
3816 int data
, struct isl_sched_graph
*sub
)
3818 int i
, n
= 0, n_edge
= 0;
3821 for (i
= 0; i
< graph
->n
; ++i
)
3822 if (node_pred(&graph
->node
[i
], data
))
3824 for (i
= 0; i
< graph
->n_edge
; ++i
)
3825 if (edge_pred(&graph
->edge
[i
], data
))
3827 if (graph_alloc(ctx
, sub
, n
, n_edge
) < 0)
3828 return isl_stat_error
;
3829 sub
->root
= graph
->root
;
3830 if (copy_nodes(sub
, graph
, node_pred
, data
) < 0)
3831 return isl_stat_error
;
3832 if (graph_init_table(ctx
, sub
) < 0)
3833 return isl_stat_error
;
3834 for (t
= 0; t
<= isl_edge_last
; ++t
)
3835 sub
->max_edge
[t
] = graph
->max_edge
[t
];
3836 if (graph_init_edge_tables(ctx
, sub
) < 0)
3837 return isl_stat_error
;
3838 if (copy_edges(ctx
, sub
, graph
, edge_pred
, data
) < 0)
3839 return isl_stat_error
;
3840 sub
->n_row
= graph
->n_row
;
3841 sub
->max_row
= graph
->max_row
;
3842 sub
->n_total_row
= graph
->n_total_row
;
3843 sub
->band_start
= graph
->band_start
;
3848 static __isl_give isl_schedule_node
*compute_schedule(isl_schedule_node
*node
,
3849 struct isl_sched_graph
*graph
);
3850 static __isl_give isl_schedule_node
*compute_schedule_wcc(
3851 isl_schedule_node
*node
, struct isl_sched_graph
*graph
);
3853 /* Compute a schedule for a subgraph of "graph". In particular, for
3854 * the graph composed of nodes that satisfy node_pred and edges that
3855 * that satisfy edge_pred.
3856 * If the subgraph is known to consist of a single component, then wcc should
3857 * be set and then we call compute_schedule_wcc on the constructed subgraph.
3858 * Otherwise, we call compute_schedule, which will check whether the subgraph
3861 * The schedule is inserted at "node" and the updated schedule node
3864 static __isl_give isl_schedule_node
*compute_sub_schedule(
3865 __isl_take isl_schedule_node
*node
, isl_ctx
*ctx
,
3866 struct isl_sched_graph
*graph
,
3867 int (*node_pred
)(struct isl_sched_node
*node
, int data
),
3868 int (*edge_pred
)(struct isl_sched_edge
*edge
, int data
),
3871 struct isl_sched_graph split
= { 0 };
3873 if (extract_sub_graph(ctx
, graph
, node_pred
, edge_pred
, data
,
3878 node
= compute_schedule_wcc(node
, &split
);
3880 node
= compute_schedule(node
, &split
);
3882 graph_free(ctx
, &split
);
3885 graph_free(ctx
, &split
);
3886 return isl_schedule_node_free(node
);
3889 static int edge_scc_exactly(struct isl_sched_edge
*edge
, int scc
)
3891 return edge
->src
->scc
== scc
&& edge
->dst
->scc
== scc
;
3894 static int edge_dst_scc_at_most(struct isl_sched_edge
*edge
, int scc
)
3896 return edge
->dst
->scc
<= scc
;
3899 static int edge_src_scc_at_least(struct isl_sched_edge
*edge
, int scc
)
3901 return edge
->src
->scc
>= scc
;
3904 /* Reset the current band by dropping all its schedule rows.
3906 static isl_stat
reset_band(struct isl_sched_graph
*graph
)
3911 drop
= graph
->n_total_row
- graph
->band_start
;
3912 graph
->n_total_row
-= drop
;
3913 graph
->n_row
-= drop
;
3915 for (i
= 0; i
< graph
->n
; ++i
) {
3916 struct isl_sched_node
*node
= &graph
->node
[i
];
3918 isl_map_free(node
->sched_map
);
3919 node
->sched_map
= NULL
;
3921 node
->sched
= isl_mat_drop_rows(node
->sched
,
3922 graph
->band_start
, drop
);
3925 return isl_stat_error
;
3931 /* Split the current graph into two parts and compute a schedule for each
3932 * part individually. In particular, one part consists of all SCCs up
3933 * to and including graph->src_scc, while the other part contains the other
3934 * SCCs. The split is enforced by a sequence node inserted at position "node"
3935 * in the schedule tree. Return the updated schedule node.
3936 * If either of these two parts consists of a sequence, then it is spliced
3937 * into the sequence containing the two parts.
3939 * The current band is reset. It would be possible to reuse
3940 * the previously computed rows as the first rows in the next
3941 * band, but recomputing them may result in better rows as we are looking
3942 * at a smaller part of the dependence graph.
3944 static __isl_give isl_schedule_node
*compute_split_schedule(
3945 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
3949 isl_union_set_list
*filters
;
3954 if (reset_band(graph
) < 0)
3955 return isl_schedule_node_free(node
);
3959 ctx
= isl_schedule_node_get_ctx(node
);
3960 filters
= extract_split(ctx
, graph
);
3961 node
= isl_schedule_node_insert_sequence(node
, filters
);
3962 node
= isl_schedule_node_child(node
, 1);
3963 node
= isl_schedule_node_child(node
, 0);
3965 node
= compute_sub_schedule(node
, ctx
, graph
,
3966 &node_scc_at_least
, &edge_src_scc_at_least
,
3967 graph
->src_scc
+ 1, 0);
3968 is_seq
= isl_schedule_node_get_type(node
) == isl_schedule_node_sequence
;
3969 node
= isl_schedule_node_parent(node
);
3970 node
= isl_schedule_node_parent(node
);
3972 node
= isl_schedule_node_sequence_splice_child(node
, 1);
3973 node
= isl_schedule_node_child(node
, 0);
3974 node
= isl_schedule_node_child(node
, 0);
3975 node
= compute_sub_schedule(node
, ctx
, graph
,
3976 &node_scc_at_most
, &edge_dst_scc_at_most
,
3978 is_seq
= isl_schedule_node_get_type(node
) == isl_schedule_node_sequence
;
3979 node
= isl_schedule_node_parent(node
);
3980 node
= isl_schedule_node_parent(node
);
3982 node
= isl_schedule_node_sequence_splice_child(node
, 0);
3987 /* Insert a band node at position "node" in the schedule tree corresponding
3988 * to the current band in "graph". Mark the band node permutable
3989 * if "permutable" is set.
3990 * The partial schedules and the coincidence property are extracted
3991 * from the graph nodes.
3992 * Return the updated schedule node.
3994 static __isl_give isl_schedule_node
*insert_current_band(
3995 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
4001 isl_multi_pw_aff
*mpa
;
4002 isl_multi_union_pw_aff
*mupa
;
4008 isl_die(isl_schedule_node_get_ctx(node
), isl_error_internal
,
4009 "graph should have at least one node",
4010 return isl_schedule_node_free(node
));
4012 start
= graph
->band_start
;
4013 end
= graph
->n_total_row
;
4016 ma
= node_extract_partial_schedule_multi_aff(&graph
->node
[0], start
, n
);
4017 mpa
= isl_multi_pw_aff_from_multi_aff(ma
);
4018 mupa
= isl_multi_union_pw_aff_from_multi_pw_aff(mpa
);
4020 for (i
= 1; i
< graph
->n
; ++i
) {
4021 isl_multi_union_pw_aff
*mupa_i
;
4023 ma
= node_extract_partial_schedule_multi_aff(&graph
->node
[i
],
4025 mpa
= isl_multi_pw_aff_from_multi_aff(ma
);
4026 mupa_i
= isl_multi_union_pw_aff_from_multi_pw_aff(mpa
);
4027 mupa
= isl_multi_union_pw_aff_union_add(mupa
, mupa_i
);
4029 node
= isl_schedule_node_insert_partial_schedule(node
, mupa
);
4031 for (i
= 0; i
< n
; ++i
)
4032 node
= isl_schedule_node_band_member_set_coincident(node
, i
,
4033 graph
->node
[0].coincident
[start
+ i
]);
4034 node
= isl_schedule_node_band_set_permutable(node
, permutable
);
4039 /* Update the dependence relations based on the current schedule,
4040 * add the current band to "node" and then continue with the computation
4042 * Return the updated schedule node.
4044 static __isl_give isl_schedule_node
*compute_next_band(
4045 __isl_take isl_schedule_node
*node
,
4046 struct isl_sched_graph
*graph
, int permutable
)
4053 ctx
= isl_schedule_node_get_ctx(node
);
4054 if (update_edges(ctx
, graph
) < 0)
4055 return isl_schedule_node_free(node
);
4056 node
= insert_current_band(node
, graph
, permutable
);
4059 node
= isl_schedule_node_child(node
, 0);
4060 node
= compute_schedule(node
, graph
);
4061 node
= isl_schedule_node_parent(node
);
4066 /* Add the constraints "coef" derived from an edge from "node" to itself
4067 * to graph->lp in order to respect the dependences and to try and carry them.
4068 * "pos" is the sequence number of the edge that needs to be carried.
4069 * "coef" represents general constraints on coefficients (c_0, c_x)
4070 * of valid constraints for (y - x) with x and y instances of the node.
4072 * The constraints added to graph->lp need to enforce
4074 * (c_j_0 + c_j_x y) - (c_j_0 + c_j_x x)
4075 * = c_j_x (y - x) >= e_i
4077 * for each (x,y) in the dependence relation of the edge.
4078 * That is, (-e_i, c_j_x) needs to be plugged in for (c_0, c_x),
4079 * taking into account that each coefficient in c_j_x is represented
4080 * as a pair of non-negative coefficients.
4082 static isl_stat
add_intra_constraints(struct isl_sched_graph
*graph
,
4083 struct isl_sched_node
*node
, __isl_take isl_basic_set
*coef
, int pos
)
4087 isl_dim_map
*dim_map
;
4089 offset
= coef_var_offset(coef
);
4091 coef
= isl_basic_set_free(coef
);
4093 return isl_stat_error
;
4095 ctx
= isl_basic_set_get_ctx(coef
);
4096 dim_map
= intra_dim_map(ctx
, graph
, node
, offset
, 1);
4097 isl_dim_map_range(dim_map
, 3 + pos
, 0, 0, 0, 1, -1);
4098 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
4103 /* Add the constraints "coef" derived from an edge from "src" to "dst"
4104 * to graph->lp in order to respect the dependences and to try and carry them.
4105 * "pos" is the sequence number of the edge that needs to be carried or
4106 * -1 if no attempt should be made to carry the dependences.
4107 * "coef" represents general constraints on coefficients (c_0, c_n, c_x, c_y)
4108 * of valid constraints for (x, y) with x and y instances of "src" and "dst".
4110 * The constraints added to graph->lp need to enforce
4112 * (c_k_0 + c_k_n n + c_k_x y) - (c_j_0 + c_j_n n + c_j_x x) >= e_i
4114 * for each (x,y) in the dependence relation of the edge or
4116 * (c_k_0 + c_k_n n + c_k_x y) - (c_j_0 + c_j_n n + c_j_x x) >= 0
4120 * (-e_i + c_k_0 - c_j_0, c_k_n - c_j_n, -c_j_x, c_k_x)
4122 * (c_k_0 - c_j_0, c_k_n - c_j_n, -c_j_x, c_k_x)
4123 * needs to be plugged in for (c_0, c_n, c_x, c_y),
4124 * taking into account that each coefficient in c_j_x and c_k_x is represented
4125 * as a pair of non-negative coefficients.
4127 static isl_stat
add_inter_constraints(struct isl_sched_graph
*graph
,
4128 struct isl_sched_node
*src
, struct isl_sched_node
*dst
,
4129 __isl_take isl_basic_set
*coef
, int pos
)
4133 isl_dim_map
*dim_map
;
4135 offset
= coef_var_offset(coef
);
4137 coef
= isl_basic_set_free(coef
);
4139 return isl_stat_error
;
4141 ctx
= isl_basic_set_get_ctx(coef
);
4142 dim_map
= inter_dim_map(ctx
, graph
, src
, dst
, offset
, 1);
4144 isl_dim_map_range(dim_map
, 3 + pos
, 0, 0, 0, 1, -1);
4145 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
4150 /* Data structure for keeping track of the data needed
4151 * to exploit non-trivial lineality spaces.
4153 * "any_non_trivial" is true if there are any non-trivial lineality spaces.
4154 * If "any_non_trivial" is not true, then "equivalent" and "mask" may be NULL.
4155 * "equivalent" connects instances to other instances on the same line(s).
4156 * "mask" contains the domain spaces of "equivalent".
4157 * Any instance set not in "mask" does not have a non-trivial lineality space.
4159 struct isl_exploit_lineality_data
{
4160 isl_bool any_non_trivial
;
4161 isl_union_map
*equivalent
;
4162 isl_union_set
*mask
;
4165 /* Data structure collecting information used during the construction
4166 * of an LP for carrying dependences.
4168 * "intra" is a sequence of coefficient constraints for intra-node edges.
4169 * "inter" is a sequence of coefficient constraints for inter-node edges.
4170 * "lineality" contains data used to exploit non-trivial lineality spaces.
4173 isl_basic_set_list
*intra
;
4174 isl_basic_set_list
*inter
;
4175 struct isl_exploit_lineality_data lineality
;
4178 /* Free all the data stored in "carry".
4180 static void isl_carry_clear(struct isl_carry
*carry
)
4182 isl_basic_set_list_free(carry
->intra
);
4183 isl_basic_set_list_free(carry
->inter
);
4184 isl_union_map_free(carry
->lineality
.equivalent
);
4185 isl_union_set_free(carry
->lineality
.mask
);
4188 /* Return a pointer to the node in "graph" that lives in "space".
4189 * If the requested node has been compressed, then "space"
4190 * corresponds to the compressed space.
4191 * The graph is assumed to have such a node.
4192 * Return NULL in case of error.
4194 * First try and see if "space" is the space of an uncompressed node.
4195 * If so, return that node.
4196 * Otherwise, "space" was constructed by construct_compressed_id and
4197 * contains a user pointer pointing to the node in the tuple id.
4198 * However, this node belongs to the original dependence graph.
4199 * If "graph" is a subgraph of this original dependence graph,
4200 * then the node with the same space still needs to be looked up
4201 * in the current graph.
4203 static struct isl_sched_node
*graph_find_compressed_node(isl_ctx
*ctx
,
4204 struct isl_sched_graph
*graph
, __isl_keep isl_space
*space
)
4207 struct isl_sched_node
*node
;
4212 node
= graph_find_node(ctx
, graph
, space
);
4215 if (is_node(graph
, node
))
4218 id
= isl_space_get_tuple_id(space
, isl_dim_set
);
4219 node
= isl_id_get_user(id
);
4225 if (!is_node(graph
->root
, node
))
4226 isl_die(ctx
, isl_error_internal
,
4227 "space points to invalid node", return NULL
);
4228 if (graph
!= graph
->root
)
4229 node
= graph_find_node(ctx
, graph
, node
->space
);
4230 if (!is_node(graph
, node
))
4231 isl_die(ctx
, isl_error_internal
,
4232 "unable to find node", return NULL
);
4237 /* Internal data structure for add_all_constraints.
4239 * "graph" is the schedule constraint graph for which an LP problem
4240 * is being constructed.
4241 * "carry_inter" indicates whether inter-node edges should be carried.
4242 * "pos" is the position of the next edge that needs to be carried.
4244 struct isl_add_all_constraints_data
{
4246 struct isl_sched_graph
*graph
;
4251 /* Add the constraints "coef" derived from an edge from a node to itself
4252 * to data->graph->lp in order to respect the dependences and
4253 * to try and carry them.
4255 * The space of "coef" is of the form
4257 * coefficients[[c_cst] -> S[c_x]]
4259 * with S[c_x] the (compressed) space of the node.
4260 * Extract the node from the space and call add_intra_constraints.
4262 static isl_stat
lp_add_intra(__isl_take isl_basic_set
*coef
, void *user
)
4264 struct isl_add_all_constraints_data
*data
= user
;
4266 struct isl_sched_node
*node
;
4268 space
= isl_basic_set_get_space(coef
);
4269 space
= isl_space_range(isl_space_unwrap(space
));
4270 node
= graph_find_compressed_node(data
->ctx
, data
->graph
, space
);
4271 isl_space_free(space
);
4272 return add_intra_constraints(data
->graph
, node
, coef
, data
->pos
++);
4275 /* Add the constraints "coef" derived from an edge from a node j
4276 * to a node k to data->graph->lp in order to respect the dependences and
4277 * to try and carry them (provided data->carry_inter is set).
4279 * The space of "coef" is of the form
4281 * coefficients[[c_cst, c_n] -> [S_j[c_x] -> S_k[c_y]]]
4283 * with S_j[c_x] and S_k[c_y] the (compressed) spaces of the nodes.
4284 * Extract the nodes from the space and call add_inter_constraints.
4286 static isl_stat
lp_add_inter(__isl_take isl_basic_set
*coef
, void *user
)
4288 struct isl_add_all_constraints_data
*data
= user
;
4289 isl_space
*space
, *dom
;
4290 struct isl_sched_node
*src
, *dst
;
4293 space
= isl_basic_set_get_space(coef
);
4294 space
= isl_space_unwrap(isl_space_range(isl_space_unwrap(space
)));
4295 dom
= isl_space_domain(isl_space_copy(space
));
4296 src
= graph_find_compressed_node(data
->ctx
, data
->graph
, dom
);
4297 isl_space_free(dom
);
4298 space
= isl_space_range(space
);
4299 dst
= graph_find_compressed_node(data
->ctx
, data
->graph
, space
);
4300 isl_space_free(space
);
4302 pos
= data
->carry_inter
? data
->pos
++ : -1;
4303 return add_inter_constraints(data
->graph
, src
, dst
, coef
, pos
);
4306 /* Add constraints to graph->lp that force all (conditional) validity
4307 * dependences to be respected and attempt to carry them.
4308 * "intra" is the sequence of coefficient constraints for intra-node edges.
4309 * "inter" is the sequence of coefficient constraints for inter-node edges.
4310 * "carry_inter" indicates whether inter-node edges should be carried or
4313 static isl_stat
add_all_constraints(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
4314 __isl_keep isl_basic_set_list
*intra
,
4315 __isl_keep isl_basic_set_list
*inter
, int carry_inter
)
4317 struct isl_add_all_constraints_data data
= { ctx
, graph
, carry_inter
};
4320 if (isl_basic_set_list_foreach(intra
, &lp_add_intra
, &data
) < 0)
4321 return isl_stat_error
;
4322 if (isl_basic_set_list_foreach(inter
, &lp_add_inter
, &data
) < 0)
4323 return isl_stat_error
;
4327 /* Internal data structure for count_all_constraints
4328 * for keeping track of the number of equality and inequality constraints.
4330 struct isl_sched_count
{
4335 /* Add the number of equality and inequality constraints of "bset"
4336 * to data->n_eq and data->n_ineq.
4338 static isl_stat
bset_update_count(__isl_take isl_basic_set
*bset
, void *user
)
4340 struct isl_sched_count
*data
= user
;
4342 return update_count(bset
, 1, &data
->n_eq
, &data
->n_ineq
);
4345 /* Count the number of equality and inequality constraints
4346 * that will be added to the carry_lp problem.
4347 * We count each edge exactly once.
4348 * "intra" is the sequence of coefficient constraints for intra-node edges.
4349 * "inter" is the sequence of coefficient constraints for inter-node edges.
4351 static isl_stat
count_all_constraints(__isl_keep isl_basic_set_list
*intra
,
4352 __isl_keep isl_basic_set_list
*inter
, int *n_eq
, int *n_ineq
)
4354 struct isl_sched_count data
;
4356 data
.n_eq
= data
.n_ineq
= 0;
4357 if (isl_basic_set_list_foreach(inter
, &bset_update_count
, &data
) < 0)
4358 return isl_stat_error
;
4359 if (isl_basic_set_list_foreach(intra
, &bset_update_count
, &data
) < 0)
4360 return isl_stat_error
;
4363 *n_ineq
= data
.n_ineq
;
4368 /* Construct an LP problem for finding schedule coefficients
4369 * such that the schedule carries as many validity dependences as possible.
4370 * In particular, for each dependence i, we bound the dependence distance
4371 * from below by e_i, with 0 <= e_i <= 1 and then maximize the sum
4372 * of all e_i's. Dependences with e_i = 0 in the solution are simply
4373 * respected, while those with e_i > 0 (in practice e_i = 1) are carried.
4374 * "intra" is the sequence of coefficient constraints for intra-node edges.
4375 * "inter" is the sequence of coefficient constraints for inter-node edges.
4376 * "n_edge" is the total number of edges.
4377 * "carry_inter" indicates whether inter-node edges should be carried or
4378 * only respected. That is, if "carry_inter" is not set, then
4379 * no e_i variables are introduced for the inter-node edges.
4381 * All variables of the LP are non-negative. The actual coefficients
4382 * may be negative, so each coefficient is represented as the difference
4383 * of two non-negative variables. The negative part always appears
4384 * immediately before the positive part.
4385 * Other than that, the variables have the following order
4387 * - sum of (1 - e_i) over all edges
4388 * - sum of all c_n coefficients
4389 * (unconstrained when computing non-parametric schedules)
4390 * - sum of positive and negative parts of all c_x coefficients
4394 * - positive and negative parts of c_i_x, in opposite order
4395 * - c_i_n (if parametric)
4398 * The constraints are those from the (validity) edges plus three equalities
4399 * to express the sums and n_edge inequalities to express e_i <= 1.
4401 static isl_stat
setup_carry_lp(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
4402 int n_edge
, __isl_keep isl_basic_set_list
*intra
,
4403 __isl_keep isl_basic_set_list
*inter
, int carry_inter
)
4412 for (i
= 0; i
< graph
->n
; ++i
) {
4413 struct isl_sched_node
*node
= &graph
->node
[graph
->sorted
[i
]];
4414 node
->start
= total
;
4415 total
+= 1 + node
->nparam
+ 2 * node
->nvar
;
4418 if (count_all_constraints(intra
, inter
, &n_eq
, &n_ineq
) < 0)
4419 return isl_stat_error
;
4421 dim
= isl_space_set_alloc(ctx
, 0, total
);
4422 isl_basic_set_free(graph
->lp
);
4425 graph
->lp
= isl_basic_set_alloc_space(dim
, 0, n_eq
, n_ineq
);
4426 graph
->lp
= isl_basic_set_set_rational(graph
->lp
);
4428 k
= isl_basic_set_alloc_equality(graph
->lp
);
4430 return isl_stat_error
;
4431 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
4432 isl_int_set_si(graph
->lp
->eq
[k
][0], -n_edge
);
4433 isl_int_set_si(graph
->lp
->eq
[k
][1], 1);
4434 for (i
= 0; i
< n_edge
; ++i
)
4435 isl_int_set_si(graph
->lp
->eq
[k
][4 + i
], 1);
4437 if (add_param_sum_constraint(graph
, 1) < 0)
4438 return isl_stat_error
;
4439 if (add_var_sum_constraint(graph
, 2) < 0)
4440 return isl_stat_error
;
4442 for (i
= 0; i
< n_edge
; ++i
) {
4443 k
= isl_basic_set_alloc_inequality(graph
->lp
);
4445 return isl_stat_error
;
4446 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
4447 isl_int_set_si(graph
->lp
->ineq
[k
][4 + i
], -1);
4448 isl_int_set_si(graph
->lp
->ineq
[k
][0], 1);
4451 if (add_all_constraints(ctx
, graph
, intra
, inter
, carry_inter
) < 0)
4452 return isl_stat_error
;
4457 static __isl_give isl_schedule_node
*compute_component_schedule(
4458 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
4461 /* If the schedule_split_scaled option is set and if the linear
4462 * parts of the scheduling rows for all nodes in the graphs have
4463 * a non-trivial common divisor, then remove this
4464 * common divisor from the linear part.
4465 * Otherwise, insert a band node directly and continue with
4466 * the construction of the schedule.
4468 * If a non-trivial common divisor is found, then
4469 * the linear part is reduced and the remainder is ignored.
4470 * The pieces of the graph that are assigned different remainders
4471 * form (groups of) strongly connected components within
4472 * the scaled down band. If needed, they can therefore
4473 * be ordered along this remainder in a sequence node.
4474 * However, this ordering is not enforced here in order to allow
4475 * the scheduler to combine some of the strongly connected components.
4477 static __isl_give isl_schedule_node
*split_scaled(
4478 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
4489 ctx
= isl_schedule_node_get_ctx(node
);
4490 if (!ctx
->opt
->schedule_split_scaled
)
4491 return compute_next_band(node
, graph
, 0);
4493 return compute_next_band(node
, graph
, 0);
4494 n_row
= isl_mat_rows(graph
->node
[0].sched
);
4496 return isl_schedule_node_free(node
);
4499 isl_int_init(gcd_i
);
4501 isl_int_set_si(gcd
, 0);
4505 for (i
= 0; i
< graph
->n
; ++i
) {
4506 struct isl_sched_node
*node
= &graph
->node
[i
];
4507 isl_size cols
= isl_mat_cols(node
->sched
);
4511 isl_seq_gcd(node
->sched
->row
[row
] + 1, cols
- 1, &gcd_i
);
4512 isl_int_gcd(gcd
, gcd
, gcd_i
);
4515 isl_int_clear(gcd_i
);
4519 if (isl_int_cmp_si(gcd
, 1) <= 0) {
4521 return compute_next_band(node
, graph
, 0);
4524 for (i
= 0; i
< graph
->n
; ++i
) {
4525 struct isl_sched_node
*node
= &graph
->node
[i
];
4527 isl_int_fdiv_q(node
->sched
->row
[row
][0],
4528 node
->sched
->row
[row
][0], gcd
);
4529 isl_int_mul(node
->sched
->row
[row
][0],
4530 node
->sched
->row
[row
][0], gcd
);
4531 node
->sched
= isl_mat_scale_down_row(node
->sched
, row
, gcd
);
4538 return compute_next_band(node
, graph
, 0);
4541 return isl_schedule_node_free(node
);
4544 /* Is the schedule row "sol" trivial on node "node"?
4545 * That is, is the solution zero on the dimensions linearly independent of
4546 * the previously found solutions?
4547 * Return 1 if the solution is trivial, 0 if it is not and -1 on error.
4549 * Each coefficient is represented as the difference between
4550 * two non-negative values in "sol".
4551 * We construct the schedule row s and check if it is linearly
4552 * independent of previously computed schedule rows
4553 * by computing T s, with T the linear combinations that are zero
4554 * on linearly dependent schedule rows.
4555 * If the result consists of all zeros, then the solution is trivial.
4557 static int is_trivial(struct isl_sched_node
*node
, __isl_keep isl_vec
*sol
)
4564 if (node
->nvar
== node
->rank
)
4567 node_sol
= extract_var_coef(node
, sol
);
4568 node_sol
= isl_mat_vec_product(isl_mat_copy(node
->indep
), node_sol
);
4572 trivial
= isl_seq_first_non_zero(node_sol
->el
,
4573 node
->nvar
- node
->rank
) == -1;
4575 isl_vec_free(node_sol
);
4580 /* Is the schedule row "sol" trivial on any node where it should
4582 * Return 1 if any solution is trivial, 0 if they are not and -1 on error.
4584 static int is_any_trivial(struct isl_sched_graph
*graph
,
4585 __isl_keep isl_vec
*sol
)
4589 for (i
= 0; i
< graph
->n
; ++i
) {
4590 struct isl_sched_node
*node
= &graph
->node
[i
];
4593 if (!needs_row(graph
, node
))
4595 trivial
= is_trivial(node
, sol
);
4596 if (trivial
< 0 || trivial
)
4603 /* Does the schedule represented by "sol" perform loop coalescing on "node"?
4604 * If so, return the position of the coalesced dimension.
4605 * Otherwise, return node->nvar or -1 on error.
4607 * In particular, look for pairs of coefficients c_i and c_j such that
4608 * |c_j/c_i| > ceil(size_i/2), i.e., |c_j| > |c_i * ceil(size_i/2)|.
4609 * If any such pair is found, then return i.
4610 * If size_i is infinity, then no check on c_i needs to be performed.
4612 static int find_node_coalescing(struct isl_sched_node
*node
,
4613 __isl_keep isl_vec
*sol
)
4619 if (node
->nvar
<= 1)
4622 csol
= extract_var_coef(node
, sol
);
4626 for (i
= 0; i
< node
->nvar
; ++i
) {
4629 if (isl_int_is_zero(csol
->el
[i
]))
4631 v
= isl_multi_val_get_val(node
->sizes
, i
);
4634 if (!isl_val_is_int(v
)) {
4638 v
= isl_val_div_ui(v
, 2);
4639 v
= isl_val_ceil(v
);
4642 isl_int_mul(max
, v
->n
, csol
->el
[i
]);
4645 for (j
= 0; j
< node
->nvar
; ++j
) {
4648 if (isl_int_abs_gt(csol
->el
[j
], max
))
4664 /* Force the schedule coefficient at position "pos" of "node" to be zero
4666 * The coefficient is encoded as the difference between two non-negative
4667 * variables. Force these two variables to have the same value.
4669 static __isl_give isl_tab_lexmin
*zero_out_node_coef(
4670 __isl_take isl_tab_lexmin
*tl
, struct isl_sched_node
*node
, int pos
)
4676 ctx
= isl_space_get_ctx(node
->space
);
4677 dim
= isl_tab_lexmin_dim(tl
);
4679 return isl_tab_lexmin_free(tl
);
4680 eq
= isl_vec_alloc(ctx
, 1 + dim
);
4681 eq
= isl_vec_clr(eq
);
4683 return isl_tab_lexmin_free(tl
);
4685 pos
= 1 + node_var_coef_pos(node
, pos
);
4686 isl_int_set_si(eq
->el
[pos
], 1);
4687 isl_int_set_si(eq
->el
[pos
+ 1], -1);
4688 tl
= isl_tab_lexmin_add_eq(tl
, eq
->el
);
4694 /* Return the lexicographically smallest rational point in the basic set
4695 * from which "tl" was constructed, double checking that this input set
4698 static __isl_give isl_vec
*non_empty_solution(__isl_keep isl_tab_lexmin
*tl
)
4702 sol
= isl_tab_lexmin_get_solution(tl
);
4706 isl_die(isl_vec_get_ctx(sol
), isl_error_internal
,
4707 "error in schedule construction",
4708 return isl_vec_free(sol
));
4712 /* Does the solution "sol" of the LP problem constructed by setup_carry_lp
4713 * carry any of the "n_edge" groups of dependences?
4714 * The value in the first position is the sum of (1 - e_i) over all "n_edge"
4715 * edges, with 0 <= e_i <= 1 equal to 1 when the dependences represented
4716 * by the edge are carried by the solution.
4717 * If the sum of the (1 - e_i) is smaller than "n_edge" then at least
4718 * one of those is carried.
4720 * Note that despite the fact that the problem is solved using a rational
4721 * solver, the solution is guaranteed to be integral.
4722 * Specifically, the dependence distance lower bounds e_i (and therefore
4723 * also their sum) are integers. See Lemma 5 of [1].
4725 * Any potential denominator of the sum is cleared by this function.
4726 * The denominator is not relevant for any of the other elements
4729 * [1] P. Feautrier, Some Efficient Solutions to the Affine Scheduling
4730 * Problem, Part II: Multi-Dimensional Time.
4731 * In Intl. Journal of Parallel Programming, 1992.
4733 static int carries_dependences(__isl_keep isl_vec
*sol
, int n_edge
)
4735 isl_int_divexact(sol
->el
[1], sol
->el
[1], sol
->el
[0]);
4736 isl_int_set_si(sol
->el
[0], 1);
4737 return isl_int_cmp_si(sol
->el
[1], n_edge
) < 0;
4740 /* Return the lexicographically smallest rational point in "lp",
4741 * assuming that all variables are non-negative and performing some
4742 * additional sanity checks.
4743 * If "want_integral" is set, then compute the lexicographically smallest
4744 * integer point instead.
4745 * In particular, "lp" should not be empty by construction.
4746 * Double check that this is the case.
4747 * If dependences are not carried for any of the "n_edge" edges,
4748 * then return an empty vector.
4750 * If the schedule_treat_coalescing option is set and
4751 * if the computed schedule performs loop coalescing on a given node,
4752 * i.e., if it is of the form
4754 * c_i i + c_j j + ...
4756 * with |c_j/c_i| >= size_i, then force the coefficient c_i to be zero
4757 * to cut out this solution. Repeat this process until no more loop
4758 * coalescing occurs or until no more dependences can be carried.
4759 * In the latter case, revert to the previously computed solution.
4761 * If the caller requests an integral solution and if coalescing should
4762 * be treated, then perform the coalescing treatment first as
4763 * an integral solution computed before coalescing treatment
4764 * would carry the same number of edges and would therefore probably
4765 * also be coalescing.
4767 * To allow the coalescing treatment to be performed first,
4768 * the initial solution is allowed to be rational and it is only
4769 * cut out (if needed) in the next iteration, if no coalescing measures
4772 static __isl_give isl_vec
*non_neg_lexmin(struct isl_sched_graph
*graph
,
4773 __isl_take isl_basic_set
*lp
, int n_edge
, int want_integral
)
4778 isl_vec
*sol
= NULL
, *prev
;
4779 int treat_coalescing
;
4784 ctx
= isl_basic_set_get_ctx(lp
);
4785 treat_coalescing
= isl_options_get_schedule_treat_coalescing(ctx
);
4786 tl
= isl_tab_lexmin_from_basic_set(lp
);
4794 tl
= isl_tab_lexmin_cut_to_integer(tl
);
4796 sol
= non_empty_solution(tl
);
4800 integral
= isl_int_is_one(sol
->el
[0]);
4801 if (!carries_dependences(sol
, n_edge
)) {
4803 prev
= isl_vec_alloc(ctx
, 0);
4808 prev
= isl_vec_free(prev
);
4809 cut
= want_integral
&& !integral
;
4812 if (!treat_coalescing
)
4814 for (i
= 0; i
< graph
->n
; ++i
) {
4815 struct isl_sched_node
*node
= &graph
->node
[i
];
4817 pos
= find_node_coalescing(node
, sol
);
4820 if (pos
< node
->nvar
)
4825 tl
= zero_out_node_coef(tl
, &graph
->node
[i
], pos
);
4828 } while (try_again
);
4830 isl_tab_lexmin_free(tl
);
4834 isl_tab_lexmin_free(tl
);
4840 /* If "edge" is an edge from a node to itself, then add the corresponding
4841 * dependence relation to "umap".
4842 * If "node" has been compressed, then the dependence relation
4843 * is also compressed first.
4845 static __isl_give isl_union_map
*add_intra(__isl_take isl_union_map
*umap
,
4846 struct isl_sched_edge
*edge
)
4849 struct isl_sched_node
*node
= edge
->src
;
4851 if (edge
->src
!= edge
->dst
)
4854 map
= isl_map_copy(edge
->map
);
4855 map
= compress(map
, node
, node
);
4856 umap
= isl_union_map_add_map(umap
, map
);
4860 /* If "edge" is an edge from a node to another node, then add the corresponding
4861 * dependence relation to "umap".
4862 * If the source or destination nodes of "edge" have been compressed,
4863 * then the dependence relation is also compressed first.
4865 static __isl_give isl_union_map
*add_inter(__isl_take isl_union_map
*umap
,
4866 struct isl_sched_edge
*edge
)
4870 if (edge
->src
== edge
->dst
)
4873 map
= isl_map_copy(edge
->map
);
4874 map
= compress(map
, edge
->src
, edge
->dst
);
4875 umap
= isl_union_map_add_map(umap
, map
);
4879 /* Internal data structure used by union_drop_coalescing_constraints
4880 * to collect bounds on all relevant statements.
4882 * "graph" is the schedule constraint graph for which an LP problem
4883 * is being constructed.
4884 * "bounds" collects the bounds.
4886 struct isl_collect_bounds_data
{
4888 struct isl_sched_graph
*graph
;
4889 isl_union_set
*bounds
;
4892 /* Add the size bounds for the node with instance deltas in "set"
4895 static isl_stat
collect_bounds(__isl_take isl_set
*set
, void *user
)
4897 struct isl_collect_bounds_data
*data
= user
;
4898 struct isl_sched_node
*node
;
4902 space
= isl_set_get_space(set
);
4905 node
= graph_find_compressed_node(data
->ctx
, data
->graph
, space
);
4906 isl_space_free(space
);
4908 bounds
= isl_set_from_basic_set(get_size_bounds(node
));
4909 data
->bounds
= isl_union_set_add_set(data
->bounds
, bounds
);
4914 /* Drop some constraints from "delta" that could be exploited
4915 * to construct loop coalescing schedules.
4916 * In particular, drop those constraint that bound the difference
4917 * to the size of the domain.
4918 * Do this for each set/node in "delta" separately.
4919 * The parameters are assumed to have been projected out by the caller.
4921 static __isl_give isl_union_set
*union_drop_coalescing_constraints(isl_ctx
*ctx
,
4922 struct isl_sched_graph
*graph
, __isl_take isl_union_set
*delta
)
4924 struct isl_collect_bounds_data data
= { ctx
, graph
};
4926 data
.bounds
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
4927 if (isl_union_set_foreach_set(delta
, &collect_bounds
, &data
) < 0)
4928 data
.bounds
= isl_union_set_free(data
.bounds
);
4929 delta
= isl_union_set_plain_gist(delta
, data
.bounds
);
4934 /* Given a non-trivial lineality space "lineality", add the corresponding
4935 * universe set to data->mask and add a map from elements to
4936 * other elements along the lines in "lineality" to data->equivalent.
4937 * If this is the first time this function gets called
4938 * (data->any_non_trivial is still false), then set data->any_non_trivial and
4939 * initialize data->mask and data->equivalent.
4941 * In particular, if the lineality space is defined by equality constraints
4945 * then construct an affine mapping
4949 * and compute the equivalence relation of having the same image under f:
4951 * { x -> x' : E x = E x' }
4953 static isl_stat
add_non_trivial_lineality(__isl_take isl_basic_set
*lineality
,
4954 struct isl_exploit_lineality_data
*data
)
4960 isl_multi_pw_aff
*mpa
;
4964 if (isl_basic_set_check_no_locals(lineality
) < 0)
4967 space
= isl_basic_set_get_space(lineality
);
4968 if (!data
->any_non_trivial
) {
4969 data
->equivalent
= isl_union_map_empty(isl_space_copy(space
));
4970 data
->mask
= isl_union_set_empty(isl_space_copy(space
));
4972 data
->any_non_trivial
= isl_bool_true
;
4974 univ
= isl_set_universe(isl_space_copy(space
));
4975 data
->mask
= isl_union_set_add_set(data
->mask
, univ
);
4977 eq
= isl_basic_set_extract_equalities(lineality
);
4978 n
= isl_mat_rows(eq
);
4980 space
= isl_space_free(space
);
4981 eq
= isl_mat_insert_zero_rows(eq
, 0, 1);
4982 eq
= isl_mat_set_element_si(eq
, 0, 0, 1);
4983 space
= isl_space_from_domain(space
);
4984 space
= isl_space_add_dims(space
, isl_dim_out
, n
);
4985 ma
= isl_multi_aff_from_aff_mat(space
, eq
);
4986 mpa
= isl_multi_pw_aff_from_multi_aff(ma
);
4987 map
= isl_multi_pw_aff_eq_map(mpa
, isl_multi_pw_aff_copy(mpa
));
4988 data
->equivalent
= isl_union_map_add_map(data
->equivalent
, map
);
4990 isl_basic_set_free(lineality
);
4993 isl_basic_set_free(lineality
);
4994 return isl_stat_error
;
4997 /* Check if the lineality space "set" is non-trivial (i.e., is not just
4998 * the origin or, in other words, satisfies a number of equality constraints
4999 * that is smaller than the dimension of the set).
5000 * If so, extend data->mask and data->equivalent accordingly.
5002 * The input should not have any local variables already, but
5003 * isl_set_remove_divs is called to make sure it does not.
5005 static isl_stat
add_lineality(__isl_take isl_set
*set
, void *user
)
5007 struct isl_exploit_lineality_data
*data
= user
;
5008 isl_basic_set
*hull
;
5012 set
= isl_set_remove_divs(set
);
5013 hull
= isl_set_unshifted_simple_hull(set
);
5014 dim
= isl_basic_set_dim(hull
, isl_dim_set
);
5015 n_eq
= isl_basic_set_n_equality(hull
);
5019 return add_non_trivial_lineality(hull
, data
);
5020 isl_basic_set_free(hull
);
5023 isl_basic_set_free(hull
);
5024 return isl_stat_error
;
5027 /* Check if the difference set on intra-node schedule constraints "intra"
5028 * has any non-trivial lineality space.
5029 * If so, then extend the difference set to a difference set
5030 * on equivalent elements. That is, if "intra" is
5032 * { y - x : (x,y) \in V }
5034 * and elements are equivalent if they have the same image under f,
5037 * { y' - x' : (x,y) \in V and f(x) = f(x') and f(y) = f(y') }
5039 * or, since f is linear,
5041 * { y' - x' : (x,y) \in V and f(y - x) = f(y' - x') }
5043 * The results of the search for non-trivial lineality spaces is stored
5046 static __isl_give isl_union_set
*exploit_intra_lineality(
5047 __isl_take isl_union_set
*intra
,
5048 struct isl_exploit_lineality_data
*data
)
5050 isl_union_set
*lineality
;
5051 isl_union_set
*uset
;
5053 data
->any_non_trivial
= isl_bool_false
;
5054 lineality
= isl_union_set_copy(intra
);
5055 lineality
= isl_union_set_combined_lineality_space(lineality
);
5056 if (isl_union_set_foreach_set(lineality
, &add_lineality
, data
) < 0)
5057 data
->any_non_trivial
= isl_bool_error
;
5058 isl_union_set_free(lineality
);
5060 if (data
->any_non_trivial
< 0)
5061 return isl_union_set_free(intra
);
5062 if (!data
->any_non_trivial
)
5065 uset
= isl_union_set_copy(intra
);
5066 intra
= isl_union_set_subtract(intra
, isl_union_set_copy(data
->mask
));
5067 uset
= isl_union_set_apply(uset
, isl_union_map_copy(data
->equivalent
));
5068 intra
= isl_union_set_union(intra
, uset
);
5070 intra
= isl_union_set_remove_divs(intra
);
5075 /* If the difference set on intra-node schedule constraints was found to have
5076 * any non-trivial lineality space by exploit_intra_lineality,
5077 * as recorded in "data", then extend the inter-node
5078 * schedule constraints "inter" to schedule constraints on equivalent elements.
5079 * That is, if "inter" is V and
5080 * elements are equivalent if they have the same image under f, then return
5082 * { (x', y') : (x,y) \in V and f(x) = f(x') and f(y) = f(y') }
5084 static __isl_give isl_union_map
*exploit_inter_lineality(
5085 __isl_take isl_union_map
*inter
,
5086 struct isl_exploit_lineality_data
*data
)
5088 isl_union_map
*umap
;
5090 if (data
->any_non_trivial
< 0)
5091 return isl_union_map_free(inter
);
5092 if (!data
->any_non_trivial
)
5095 umap
= isl_union_map_copy(inter
);
5096 inter
= isl_union_map_subtract_range(inter
,
5097 isl_union_set_copy(data
->mask
));
5098 umap
= isl_union_map_apply_range(umap
,
5099 isl_union_map_copy(data
->equivalent
));
5100 inter
= isl_union_map_union(inter
, umap
);
5101 umap
= isl_union_map_copy(inter
);
5102 inter
= isl_union_map_subtract_domain(inter
,
5103 isl_union_set_copy(data
->mask
));
5104 umap
= isl_union_map_apply_range(isl_union_map_copy(data
->equivalent
),
5106 inter
= isl_union_map_union(inter
, umap
);
5108 inter
= isl_union_map_remove_divs(inter
);
5113 /* For each (conditional) validity edge in "graph",
5114 * add the corresponding dependence relation using "add"
5115 * to a collection of dependence relations and return the result.
5116 * If "coincidence" is set, then coincidence edges are considered as well.
5118 static __isl_give isl_union_map
*collect_validity(struct isl_sched_graph
*graph
,
5119 __isl_give isl_union_map
*(*add
)(__isl_take isl_union_map
*umap
,
5120 struct isl_sched_edge
*edge
), int coincidence
)
5124 isl_union_map
*umap
;
5126 space
= isl_space_copy(graph
->node
[0].space
);
5127 umap
= isl_union_map_empty(space
);
5129 for (i
= 0; i
< graph
->n_edge
; ++i
) {
5130 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
5132 if (!is_any_validity(edge
) &&
5133 (!coincidence
|| !is_coincidence(edge
)))
5136 umap
= add(umap
, edge
);
5142 /* For each dependence relation on a (conditional) validity edge
5143 * from a node to itself,
5144 * construct the set of coefficients of valid constraints for elements
5145 * in that dependence relation and collect the results.
5146 * If "coincidence" is set, then coincidence edges are considered as well.
5148 * In particular, for each dependence relation R, constraints
5149 * on coefficients (c_0, c_x) are constructed such that
5151 * c_0 + c_x d >= 0 for each d in delta R = { y - x | (x,y) in R }
5153 * If the schedule_treat_coalescing option is set, then some constraints
5154 * that could be exploited to construct coalescing schedules
5155 * are removed before the dual is computed, but after the parameters
5156 * have been projected out.
5157 * The entire computation is essentially the same as that performed
5158 * by intra_coefficients, except that it operates on multiple
5159 * edges together and that the parameters are always projected out.
5161 * Additionally, exploit any non-trivial lineality space
5162 * in the difference set after removing coalescing constraints and
5163 * store the results of the non-trivial lineality space detection in "data".
5164 * The procedure is currently run unconditionally, but it is unlikely
5165 * to find any non-trivial lineality spaces if no coalescing constraints
5166 * have been removed.
5168 * Note that if a dependence relation is a union of basic maps,
5169 * then each basic map needs to be treated individually as it may only
5170 * be possible to carry the dependences expressed by some of those
5171 * basic maps and not all of them.
5172 * The collected validity constraints are therefore not coalesced and
5173 * it is assumed that they are not coalesced automatically.
5174 * Duplicate basic maps can be removed, however.
5175 * In particular, if the same basic map appears as a disjunct
5176 * in multiple edges, then it only needs to be carried once.
5178 static __isl_give isl_basic_set_list
*collect_intra_validity(isl_ctx
*ctx
,
5179 struct isl_sched_graph
*graph
, int coincidence
,
5180 struct isl_exploit_lineality_data
*data
)
5182 isl_union_map
*intra
;
5183 isl_union_set
*delta
;
5184 isl_basic_set_list
*list
;
5186 intra
= collect_validity(graph
, &add_intra
, coincidence
);
5187 delta
= isl_union_map_deltas(intra
);
5188 delta
= isl_union_set_project_out_all_params(delta
);
5189 delta
= isl_union_set_remove_divs(delta
);
5190 if (isl_options_get_schedule_treat_coalescing(ctx
))
5191 delta
= union_drop_coalescing_constraints(ctx
, graph
, delta
);
5192 delta
= exploit_intra_lineality(delta
, data
);
5193 list
= isl_union_set_get_basic_set_list(delta
);
5194 isl_union_set_free(delta
);
5196 return isl_basic_set_list_coefficients(list
);
5199 /* For each dependence relation on a (conditional) validity edge
5200 * from a node to some other node,
5201 * construct the set of coefficients of valid constraints for elements
5202 * in that dependence relation and collect the results.
5203 * If "coincidence" is set, then coincidence edges are considered as well.
5205 * In particular, for each dependence relation R, constraints
5206 * on coefficients (c_0, c_n, c_x, c_y) are constructed such that
5208 * c_0 + c_n n + c_x x + c_y y >= 0 for each (x,y) in R
5210 * This computation is essentially the same as that performed
5211 * by inter_coefficients, except that it operates on multiple
5214 * Additionally, exploit any non-trivial lineality space
5215 * that may have been discovered by collect_intra_validity
5216 * (as stored in "data").
5218 * Note that if a dependence relation is a union of basic maps,
5219 * then each basic map needs to be treated individually as it may only
5220 * be possible to carry the dependences expressed by some of those
5221 * basic maps and not all of them.
5222 * The collected validity constraints are therefore not coalesced and
5223 * it is assumed that they are not coalesced automatically.
5224 * Duplicate basic maps can be removed, however.
5225 * In particular, if the same basic map appears as a disjunct
5226 * in multiple edges, then it only needs to be carried once.
5228 static __isl_give isl_basic_set_list
*collect_inter_validity(
5229 struct isl_sched_graph
*graph
, int coincidence
,
5230 struct isl_exploit_lineality_data
*data
)
5232 isl_union_map
*inter
;
5233 isl_union_set
*wrap
;
5234 isl_basic_set_list
*list
;
5236 inter
= collect_validity(graph
, &add_inter
, coincidence
);
5237 inter
= exploit_inter_lineality(inter
, data
);
5238 inter
= isl_union_map_remove_divs(inter
);
5239 wrap
= isl_union_map_wrap(inter
);
5240 list
= isl_union_set_get_basic_set_list(wrap
);
5241 isl_union_set_free(wrap
);
5242 return isl_basic_set_list_coefficients(list
);
5245 /* Construct an LP problem for finding schedule coefficients
5246 * such that the schedule carries as many of the "n_edge" groups of
5247 * dependences as possible based on the corresponding coefficient
5248 * constraints and return the lexicographically smallest non-trivial solution.
5249 * "intra" is the sequence of coefficient constraints for intra-node edges.
5250 * "inter" is the sequence of coefficient constraints for inter-node edges.
5251 * If "want_integral" is set, then compute an integral solution
5252 * for the coefficients rather than using the numerators
5253 * of a rational solution.
5254 * "carry_inter" indicates whether inter-node edges should be carried or
5257 * If none of the "n_edge" groups can be carried
5258 * then return an empty vector.
5260 static __isl_give isl_vec
*compute_carrying_sol_coef(isl_ctx
*ctx
,
5261 struct isl_sched_graph
*graph
, int n_edge
,
5262 __isl_keep isl_basic_set_list
*intra
,
5263 __isl_keep isl_basic_set_list
*inter
, int want_integral
,
5268 if (setup_carry_lp(ctx
, graph
, n_edge
, intra
, inter
, carry_inter
) < 0)
5271 lp
= isl_basic_set_copy(graph
->lp
);
5272 return non_neg_lexmin(graph
, lp
, n_edge
, want_integral
);
5275 /* Construct an LP problem for finding schedule coefficients
5276 * such that the schedule carries as many of the validity dependences
5278 * return the lexicographically smallest non-trivial solution.
5279 * If "fallback" is set, then the carrying is performed as a fallback
5280 * for the Pluto-like scheduler.
5281 * If "coincidence" is set, then try and carry coincidence edges as well.
5283 * The variable "n_edge" stores the number of groups that should be carried.
5284 * If none of the "n_edge" groups can be carried
5285 * then return an empty vector.
5286 * If, moreover, "n_edge" is zero, then the LP problem does not even
5287 * need to be constructed.
5289 * If a fallback solution is being computed, then compute an integral solution
5290 * for the coefficients rather than using the numerators
5291 * of a rational solution.
5293 * If a fallback solution is being computed, if there are any intra-node
5294 * dependences, and if requested by the user, then first try
5295 * to only carry those intra-node dependences.
5296 * If this fails to carry any dependences, then try again
5297 * with the inter-node dependences included.
5299 static __isl_give isl_vec
*compute_carrying_sol(isl_ctx
*ctx
,
5300 struct isl_sched_graph
*graph
, int fallback
, int coincidence
)
5302 isl_size n_intra
, n_inter
;
5304 struct isl_carry carry
= { 0 };
5307 carry
.intra
= collect_intra_validity(ctx
, graph
, coincidence
,
5309 carry
.inter
= collect_inter_validity(graph
, coincidence
,
5311 n_intra
= isl_basic_set_list_n_basic_set(carry
.intra
);
5312 n_inter
= isl_basic_set_list_n_basic_set(carry
.inter
);
5313 if (n_intra
< 0 || n_inter
< 0)
5316 if (fallback
&& n_intra
> 0 &&
5317 isl_options_get_schedule_carry_self_first(ctx
)) {
5318 sol
= compute_carrying_sol_coef(ctx
, graph
, n_intra
,
5319 carry
.intra
, carry
.inter
, fallback
, 0);
5320 if (!sol
|| sol
->size
!= 0 || n_inter
== 0) {
5321 isl_carry_clear(&carry
);
5327 n_edge
= n_intra
+ n_inter
;
5329 isl_carry_clear(&carry
);
5330 return isl_vec_alloc(ctx
, 0);
5333 sol
= compute_carrying_sol_coef(ctx
, graph
, n_edge
,
5334 carry
.intra
, carry
.inter
, fallback
, 1);
5335 isl_carry_clear(&carry
);
5338 isl_carry_clear(&carry
);
5342 /* Construct a schedule row for each node such that as many validity dependences
5343 * as possible are carried and then continue with the next band.
5344 * If "fallback" is set, then the carrying is performed as a fallback
5345 * for the Pluto-like scheduler.
5346 * If "coincidence" is set, then try and carry coincidence edges as well.
5348 * If there are no validity dependences, then no dependence can be carried and
5349 * the procedure is guaranteed to fail. If there is more than one component,
5350 * then try computing a schedule on each component separately
5351 * to prevent or at least postpone this failure.
5353 * If a schedule row is computed, then check that dependences are carried
5354 * for at least one of the edges.
5356 * If the computed schedule row turns out to be trivial on one or
5357 * more nodes where it should not be trivial, then we throw it away
5358 * and try again on each component separately.
5360 * If there is only one component, then we accept the schedule row anyway,
5361 * but we do not consider it as a complete row and therefore do not
5362 * increment graph->n_row. Note that the ranks of the nodes that
5363 * do get a non-trivial schedule part will get updated regardless and
5364 * graph->maxvar is computed based on these ranks. The test for
5365 * whether more schedule rows are required in compute_schedule_wcc
5366 * is therefore not affected.
5368 * Insert a band corresponding to the schedule row at position "node"
5369 * of the schedule tree and continue with the construction of the schedule.
5370 * This insertion and the continued construction is performed by split_scaled
5371 * after optionally checking for non-trivial common divisors.
5373 static __isl_give isl_schedule_node
*carry(__isl_take isl_schedule_node
*node
,
5374 struct isl_sched_graph
*graph
, int fallback
, int coincidence
)
5383 ctx
= isl_schedule_node_get_ctx(node
);
5384 sol
= compute_carrying_sol(ctx
, graph
, fallback
, coincidence
);
5386 return isl_schedule_node_free(node
);
5387 if (sol
->size
== 0) {
5390 return compute_component_schedule(node
, graph
, 1);
5391 isl_die(ctx
, isl_error_unknown
, "unable to carry dependences",
5392 return isl_schedule_node_free(node
));
5395 trivial
= is_any_trivial(graph
, sol
);
5397 sol
= isl_vec_free(sol
);
5398 } else if (trivial
&& graph
->scc
> 1) {
5400 return compute_component_schedule(node
, graph
, 1);
5403 if (update_schedule(graph
, sol
, 0) < 0)
5404 return isl_schedule_node_free(node
);
5408 return split_scaled(node
, graph
);
5411 /* Construct a schedule row for each node such that as many validity dependences
5412 * as possible are carried and then continue with the next band.
5413 * Do so as a fallback for the Pluto-like scheduler.
5414 * If "coincidence" is set, then try and carry coincidence edges as well.
5416 static __isl_give isl_schedule_node
*carry_fallback(
5417 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
5420 return carry(node
, graph
, 1, coincidence
);
5423 /* Construct a schedule row for each node such that as many validity dependences
5424 * as possible are carried and then continue with the next band.
5425 * Do so for the case where the Feautrier scheduler was selected
5428 static __isl_give isl_schedule_node
*carry_feautrier(
5429 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
5431 return carry(node
, graph
, 0, 0);
5434 /* Construct a schedule row for each node such that as many validity dependences
5435 * as possible are carried and then continue with the next band.
5436 * Do so as a fallback for the Pluto-like scheduler.
5438 static __isl_give isl_schedule_node
*carry_dependences(
5439 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
5441 return carry_fallback(node
, graph
, 0);
5444 /* Construct a schedule row for each node such that as many validity or
5445 * coincidence dependences as possible are carried and
5446 * then continue with the next band.
5447 * Do so as a fallback for the Pluto-like scheduler.
5449 static __isl_give isl_schedule_node
*carry_coincidence(
5450 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
5452 return carry_fallback(node
, graph
, 1);
5455 /* Topologically sort statements mapped to the same schedule iteration
5456 * and add insert a sequence node in front of "node"
5457 * corresponding to this order.
5458 * If "initialized" is set, then it may be assumed that compute_maxvar
5459 * has been called on the current band. Otherwise, call
5460 * compute_maxvar if and before carry_dependences gets called.
5462 * If it turns out to be impossible to sort the statements apart,
5463 * because different dependences impose different orderings
5464 * on the statements, then we extend the schedule such that
5465 * it carries at least one more dependence.
5467 static __isl_give isl_schedule_node
*sort_statements(
5468 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
5472 isl_union_set_list
*filters
;
5477 ctx
= isl_schedule_node_get_ctx(node
);
5479 isl_die(ctx
, isl_error_internal
,
5480 "graph should have at least one node",
5481 return isl_schedule_node_free(node
));
5486 if (update_edges(ctx
, graph
) < 0)
5487 return isl_schedule_node_free(node
);
5489 if (graph
->n_edge
== 0)
5492 if (detect_sccs(ctx
, graph
) < 0)
5493 return isl_schedule_node_free(node
);
5496 if (graph
->scc
< graph
->n
) {
5497 if (!initialized
&& compute_maxvar(graph
) < 0)
5498 return isl_schedule_node_free(node
);
5499 return carry_dependences(node
, graph
);
5502 filters
= extract_sccs(ctx
, graph
);
5503 node
= isl_schedule_node_insert_sequence(node
, filters
);
5508 /* Are there any (non-empty) (conditional) validity edges in the graph?
5510 static int has_validity_edges(struct isl_sched_graph
*graph
)
5514 for (i
= 0; i
< graph
->n_edge
; ++i
) {
5517 empty
= isl_map_plain_is_empty(graph
->edge
[i
].map
);
5522 if (is_any_validity(&graph
->edge
[i
]))
5529 /* Should we apply a Feautrier step?
5530 * That is, did the user request the Feautrier algorithm and are
5531 * there any validity dependences (left)?
5533 static int need_feautrier_step(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
5535 if (ctx
->opt
->schedule_algorithm
!= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
)
5538 return has_validity_edges(graph
);
5541 /* Compute a schedule for a connected dependence graph using Feautrier's
5542 * multi-dimensional scheduling algorithm and return the updated schedule node.
5544 * The original algorithm is described in [1].
5545 * The main idea is to minimize the number of scheduling dimensions, by
5546 * trying to satisfy as many dependences as possible per scheduling dimension.
5548 * [1] P. Feautrier, Some Efficient Solutions to the Affine Scheduling
5549 * Problem, Part II: Multi-Dimensional Time.
5550 * In Intl. Journal of Parallel Programming, 1992.
5552 static __isl_give isl_schedule_node
*compute_schedule_wcc_feautrier(
5553 isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
5555 return carry_feautrier(node
, graph
);
5558 /* Turn off the "local" bit on all (condition) edges.
5560 static void clear_local_edges(struct isl_sched_graph
*graph
)
5564 for (i
= 0; i
< graph
->n_edge
; ++i
)
5565 if (is_condition(&graph
->edge
[i
]))
5566 clear_local(&graph
->edge
[i
]);
5569 /* Does "graph" have both condition and conditional validity edges?
5571 static int need_condition_check(struct isl_sched_graph
*graph
)
5574 int any_condition
= 0;
5575 int any_conditional_validity
= 0;
5577 for (i
= 0; i
< graph
->n_edge
; ++i
) {
5578 if (is_condition(&graph
->edge
[i
]))
5580 if (is_conditional_validity(&graph
->edge
[i
]))
5581 any_conditional_validity
= 1;
5584 return any_condition
&& any_conditional_validity
;
5587 /* Does "graph" contain any coincidence edge?
5589 static int has_any_coincidence(struct isl_sched_graph
*graph
)
5593 for (i
= 0; i
< graph
->n_edge
; ++i
)
5594 if (is_coincidence(&graph
->edge
[i
]))
5600 /* Extract the final schedule row as a map with the iteration domain
5601 * of "node" as domain.
5603 static __isl_give isl_map
*final_row(struct isl_sched_node
*node
)
5608 n_row
= isl_mat_rows(node
->sched
);
5611 ma
= node_extract_partial_schedule_multi_aff(node
, n_row
- 1, 1);
5612 return isl_map_from_multi_aff(ma
);
5615 /* Is the conditional validity dependence in the edge with index "edge_index"
5616 * violated by the latest (i.e., final) row of the schedule?
5617 * That is, is i scheduled after j
5618 * for any conditional validity dependence i -> j?
5620 static int is_violated(struct isl_sched_graph
*graph
, int edge_index
)
5622 isl_map
*src_sched
, *dst_sched
, *map
;
5623 struct isl_sched_edge
*edge
= &graph
->edge
[edge_index
];
5626 src_sched
= final_row(edge
->src
);
5627 dst_sched
= final_row(edge
->dst
);
5628 map
= isl_map_copy(edge
->map
);
5629 map
= isl_map_apply_domain(map
, src_sched
);
5630 map
= isl_map_apply_range(map
, dst_sched
);
5631 map
= isl_map_order_gt(map
, isl_dim_in
, 0, isl_dim_out
, 0);
5632 empty
= isl_map_is_empty(map
);
5641 /* Does "graph" have any satisfied condition edges that
5642 * are adjacent to the conditional validity constraint with
5643 * domain "conditional_source" and range "conditional_sink"?
5645 * A satisfied condition is one that is not local.
5646 * If a condition was forced to be local already (i.e., marked as local)
5647 * then there is no need to check if it is in fact local.
5649 * Additionally, mark all adjacent condition edges found as local.
5651 static int has_adjacent_true_conditions(struct isl_sched_graph
*graph
,
5652 __isl_keep isl_union_set
*conditional_source
,
5653 __isl_keep isl_union_set
*conditional_sink
)
5658 for (i
= 0; i
< graph
->n_edge
; ++i
) {
5659 int adjacent
, local
;
5660 isl_union_map
*condition
;
5662 if (!is_condition(&graph
->edge
[i
]))
5664 if (is_local(&graph
->edge
[i
]))
5667 condition
= graph
->edge
[i
].tagged_condition
;
5668 adjacent
= domain_intersects(condition
, conditional_sink
);
5669 if (adjacent
>= 0 && !adjacent
)
5670 adjacent
= range_intersects(condition
,
5671 conditional_source
);
5677 set_local(&graph
->edge
[i
]);
5679 local
= is_condition_false(&graph
->edge
[i
]);
5689 /* Are there any violated conditional validity dependences with
5690 * adjacent condition dependences that are not local with respect
5691 * to the current schedule?
5692 * That is, is the conditional validity constraint violated?
5694 * Additionally, mark all those adjacent condition dependences as local.
5695 * We also mark those adjacent condition dependences that were not marked
5696 * as local before, but just happened to be local already. This ensures
5697 * that they remain local if the schedule is recomputed.
5699 * We first collect domain and range of all violated conditional validity
5700 * dependences and then check if there are any adjacent non-local
5701 * condition dependences.
5703 static int has_violated_conditional_constraint(isl_ctx
*ctx
,
5704 struct isl_sched_graph
*graph
)
5708 isl_union_set
*source
, *sink
;
5710 source
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
5711 sink
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
5712 for (i
= 0; i
< graph
->n_edge
; ++i
) {
5713 isl_union_set
*uset
;
5714 isl_union_map
*umap
;
5717 if (!is_conditional_validity(&graph
->edge
[i
]))
5720 violated
= is_violated(graph
, i
);
5728 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_validity
);
5729 uset
= isl_union_map_domain(umap
);
5730 source
= isl_union_set_union(source
, uset
);
5731 source
= isl_union_set_coalesce(source
);
5733 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_validity
);
5734 uset
= isl_union_map_range(umap
);
5735 sink
= isl_union_set_union(sink
, uset
);
5736 sink
= isl_union_set_coalesce(sink
);
5740 any
= has_adjacent_true_conditions(graph
, source
, sink
);
5742 isl_union_set_free(source
);
5743 isl_union_set_free(sink
);
5746 isl_union_set_free(source
);
5747 isl_union_set_free(sink
);
5751 /* Examine the current band (the rows between graph->band_start and
5752 * graph->n_total_row), deciding whether to drop it or add it to "node"
5753 * and then continue with the computation of the next band, if any.
5754 * If "initialized" is set, then it may be assumed that compute_maxvar
5755 * has been called on the current band. Otherwise, call
5756 * compute_maxvar if and before carry_dependences gets called.
5758 * The caller keeps looking for a new row as long as
5759 * graph->n_row < graph->maxvar. If the latest attempt to find
5760 * such a row failed (i.e., we still have graph->n_row < graph->maxvar),
5762 * - split between SCCs and start over (assuming we found an interesting
5763 * pair of SCCs between which to split)
5764 * - continue with the next band (assuming the current band has at least
5766 * - if there is more than one SCC left, then split along all SCCs
5767 * - if outer coincidence needs to be enforced, then try to carry as many
5768 * validity or coincidence dependences as possible and
5769 * continue with the next band
5770 * - try to carry as many validity dependences as possible and
5771 * continue with the next band
5772 * In each case, we first insert a band node in the schedule tree
5773 * if any rows have been computed.
5775 * If the caller managed to complete the schedule and the current band
5776 * is empty, then finish off by topologically
5777 * sorting the statements based on the remaining dependences.
5778 * If, on the other hand, the current band has at least one row,
5779 * then continue with the next band. Note that this next band
5780 * will necessarily be empty, but the graph may still be split up
5781 * into weakly connected components before arriving back here.
5783 static __isl_give isl_schedule_node
*compute_schedule_finish_band(
5784 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
5792 empty
= graph
->n_total_row
== graph
->band_start
;
5793 if (graph
->n_row
< graph
->maxvar
) {
5796 ctx
= isl_schedule_node_get_ctx(node
);
5797 if (!ctx
->opt
->schedule_maximize_band_depth
&& !empty
)
5798 return compute_next_band(node
, graph
, 1);
5799 if (graph
->src_scc
>= 0)
5800 return compute_split_schedule(node
, graph
);
5802 return compute_next_band(node
, graph
, 1);
5804 return compute_component_schedule(node
, graph
, 1);
5805 if (!initialized
&& compute_maxvar(graph
) < 0)
5806 return isl_schedule_node_free(node
);
5807 if (isl_options_get_schedule_outer_coincidence(ctx
))
5808 return carry_coincidence(node
, graph
);
5809 return carry_dependences(node
, graph
);
5813 return compute_next_band(node
, graph
, 1);
5814 return sort_statements(node
, graph
, initialized
);
5817 /* Construct a band of schedule rows for a connected dependence graph.
5818 * The caller is responsible for determining the strongly connected
5819 * components and calling compute_maxvar first.
5821 * We try to find a sequence of as many schedule rows as possible that result
5822 * in non-negative dependence distances (independent of the previous rows
5823 * in the sequence, i.e., such that the sequence is tilable), with as
5824 * many of the initial rows as possible satisfying the coincidence constraints.
5825 * The computation stops if we can't find any more rows or if we have found
5826 * all the rows we wanted to find.
5828 * If ctx->opt->schedule_outer_coincidence is set, then we force the
5829 * outermost dimension to satisfy the coincidence constraints. If this
5830 * turns out to be impossible, we fall back on the general scheme above
5831 * and try to carry as many dependences as possible.
5833 * If "graph" contains both condition and conditional validity dependences,
5834 * then we need to check that that the conditional schedule constraint
5835 * is satisfied, i.e., there are no violated conditional validity dependences
5836 * that are adjacent to any non-local condition dependences.
5837 * If there are, then we mark all those adjacent condition dependences
5838 * as local and recompute the current band. Those dependences that
5839 * are marked local will then be forced to be local.
5840 * The initial computation is performed with no dependences marked as local.
5841 * If we are lucky, then there will be no violated conditional validity
5842 * dependences adjacent to any non-local condition dependences.
5843 * Otherwise, we mark some additional condition dependences as local and
5844 * recompute. We continue this process until there are no violations left or
5845 * until we are no longer able to compute a schedule.
5846 * Since there are only a finite number of dependences,
5847 * there will only be a finite number of iterations.
5849 static isl_stat
compute_schedule_wcc_band(isl_ctx
*ctx
,
5850 struct isl_sched_graph
*graph
)
5852 int has_coincidence
;
5853 int use_coincidence
;
5854 int force_coincidence
= 0;
5855 int check_conditional
;
5857 if (sort_sccs(graph
) < 0)
5858 return isl_stat_error
;
5860 clear_local_edges(graph
);
5861 check_conditional
= need_condition_check(graph
);
5862 has_coincidence
= has_any_coincidence(graph
);
5864 if (ctx
->opt
->schedule_outer_coincidence
)
5865 force_coincidence
= 1;
5867 use_coincidence
= has_coincidence
;
5868 while (graph
->n_row
< graph
->maxvar
) {
5873 graph
->src_scc
= -1;
5874 graph
->dst_scc
= -1;
5876 if (setup_lp(ctx
, graph
, use_coincidence
) < 0)
5877 return isl_stat_error
;
5878 sol
= solve_lp(ctx
, graph
);
5880 return isl_stat_error
;
5881 if (sol
->size
== 0) {
5882 int empty
= graph
->n_total_row
== graph
->band_start
;
5885 if (use_coincidence
&& (!force_coincidence
|| !empty
)) {
5886 use_coincidence
= 0;
5891 coincident
= !has_coincidence
|| use_coincidence
;
5892 if (update_schedule(graph
, sol
, coincident
) < 0)
5893 return isl_stat_error
;
5895 if (!check_conditional
)
5897 violated
= has_violated_conditional_constraint(ctx
, graph
);
5899 return isl_stat_error
;
5902 if (reset_band(graph
) < 0)
5903 return isl_stat_error
;
5904 use_coincidence
= has_coincidence
;
5910 /* Compute a schedule for a connected dependence graph by considering
5911 * the graph as a whole and return the updated schedule node.
5913 * The actual schedule rows of the current band are computed by
5914 * compute_schedule_wcc_band. compute_schedule_finish_band takes
5915 * care of integrating the band into "node" and continuing
5918 static __isl_give isl_schedule_node
*compute_schedule_wcc_whole(
5919 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
5926 ctx
= isl_schedule_node_get_ctx(node
);
5927 if (compute_schedule_wcc_band(ctx
, graph
) < 0)
5928 return isl_schedule_node_free(node
);
5930 return compute_schedule_finish_band(node
, graph
, 1);
5933 /* Clustering information used by compute_schedule_wcc_clustering.
5935 * "n" is the number of SCCs in the original dependence graph
5936 * "scc" is an array of "n" elements, each representing an SCC
5937 * of the original dependence graph. All entries in the same cluster
5938 * have the same number of schedule rows.
5939 * "scc_cluster" maps each SCC index to the cluster to which it belongs,
5940 * where each cluster is represented by the index of the first SCC
5941 * in the cluster. Initially, each SCC belongs to a cluster containing
5944 * "scc_in_merge" is used by merge_clusters_along_edge to keep
5945 * track of which SCCs need to be merged.
5947 * "cluster" contains the merged clusters of SCCs after the clustering
5950 * "scc_node" is a temporary data structure used inside copy_partial.
5951 * For each SCC, it keeps track of the number of nodes in the SCC
5952 * that have already been copied.
5954 struct isl_clustering
{
5956 struct isl_sched_graph
*scc
;
5957 struct isl_sched_graph
*cluster
;
5963 /* Initialize the clustering data structure "c" from "graph".
5965 * In particular, allocate memory, extract the SCCs from "graph"
5966 * into c->scc, initialize scc_cluster and construct
5967 * a band of schedule rows for each SCC.
5968 * Within each SCC, there is only one SCC by definition.
5969 * Each SCC initially belongs to a cluster containing only that SCC.
5971 static isl_stat
clustering_init(isl_ctx
*ctx
, struct isl_clustering
*c
,
5972 struct isl_sched_graph
*graph
)
5977 c
->scc
= isl_calloc_array(ctx
, struct isl_sched_graph
, c
->n
);
5978 c
->cluster
= isl_calloc_array(ctx
, struct isl_sched_graph
, c
->n
);
5979 c
->scc_cluster
= isl_calloc_array(ctx
, int, c
->n
);
5980 c
->scc_node
= isl_calloc_array(ctx
, int, c
->n
);
5981 c
->scc_in_merge
= isl_calloc_array(ctx
, int, c
->n
);
5982 if (!c
->scc
|| !c
->cluster
||
5983 !c
->scc_cluster
|| !c
->scc_node
|| !c
->scc_in_merge
)
5984 return isl_stat_error
;
5986 for (i
= 0; i
< c
->n
; ++i
) {
5987 if (extract_sub_graph(ctx
, graph
, &node_scc_exactly
,
5988 &edge_scc_exactly
, i
, &c
->scc
[i
]) < 0)
5989 return isl_stat_error
;
5991 if (compute_maxvar(&c
->scc
[i
]) < 0)
5992 return isl_stat_error
;
5993 if (compute_schedule_wcc_band(ctx
, &c
->scc
[i
]) < 0)
5994 return isl_stat_error
;
5995 c
->scc_cluster
[i
] = i
;
6001 /* Free all memory allocated for "c".
6003 static void clustering_free(isl_ctx
*ctx
, struct isl_clustering
*c
)
6008 for (i
= 0; i
< c
->n
; ++i
)
6009 graph_free(ctx
, &c
->scc
[i
]);
6012 for (i
= 0; i
< c
->n
; ++i
)
6013 graph_free(ctx
, &c
->cluster
[i
]);
6015 free(c
->scc_cluster
);
6017 free(c
->scc_in_merge
);
6020 /* Should we refrain from merging the cluster in "graph" with
6021 * any other cluster?
6022 * In particular, is its current schedule band empty and incomplete.
6024 static int bad_cluster(struct isl_sched_graph
*graph
)
6026 return graph
->n_row
< graph
->maxvar
&&
6027 graph
->n_total_row
== graph
->band_start
;
6030 /* Is "edge" a proximity edge with a non-empty dependence relation?
6032 static isl_bool
is_non_empty_proximity(struct isl_sched_edge
*edge
)
6034 if (!is_proximity(edge
))
6035 return isl_bool_false
;
6036 return isl_bool_not(isl_map_plain_is_empty(edge
->map
));
6039 /* Return the index of an edge in "graph" that can be used to merge
6040 * two clusters in "c".
6041 * Return graph->n_edge if no such edge can be found.
6042 * Return -1 on error.
6044 * In particular, return a proximity edge between two clusters
6045 * that is not marked "no_merge" and such that neither of the
6046 * two clusters has an incomplete, empty band.
6048 * If there are multiple such edges, then try and find the most
6049 * appropriate edge to use for merging. In particular, pick the edge
6050 * with the greatest weight. If there are multiple of those,
6051 * then pick one with the shortest distance between
6052 * the two cluster representatives.
6054 static int find_proximity(struct isl_sched_graph
*graph
,
6055 struct isl_clustering
*c
)
6057 int i
, best
= graph
->n_edge
, best_dist
, best_weight
;
6059 for (i
= 0; i
< graph
->n_edge
; ++i
) {
6060 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
6064 prox
= is_non_empty_proximity(edge
);
6071 if (bad_cluster(&c
->scc
[edge
->src
->scc
]) ||
6072 bad_cluster(&c
->scc
[edge
->dst
->scc
]))
6074 dist
= c
->scc_cluster
[edge
->dst
->scc
] -
6075 c
->scc_cluster
[edge
->src
->scc
];
6078 weight
= edge
->weight
;
6079 if (best
< graph
->n_edge
) {
6080 if (best_weight
> weight
)
6082 if (best_weight
== weight
&& best_dist
<= dist
)
6087 best_weight
= weight
;
6093 /* Internal data structure used in mark_merge_sccs.
6095 * "graph" is the dependence graph in which a strongly connected
6096 * component is constructed.
6097 * "scc_cluster" maps each SCC index to the cluster to which it belongs.
6098 * "src" and "dst" are the indices of the nodes that are being merged.
6100 struct isl_mark_merge_sccs_data
{
6101 struct isl_sched_graph
*graph
;
6107 /* Check whether the cluster containing node "i" depends on the cluster
6108 * containing node "j". If "i" and "j" belong to the same cluster,
6109 * then they are taken to depend on each other to ensure that
6110 * the resulting strongly connected component consists of complete
6111 * clusters. Furthermore, if "i" and "j" are the two nodes that
6112 * are being merged, then they are taken to depend on each other as well.
6113 * Otherwise, check if there is a (conditional) validity dependence
6114 * from node[j] to node[i], forcing node[i] to follow node[j].
6116 static isl_bool
cluster_follows(int i
, int j
, void *user
)
6118 struct isl_mark_merge_sccs_data
*data
= user
;
6119 struct isl_sched_graph
*graph
= data
->graph
;
6120 int *scc_cluster
= data
->scc_cluster
;
6122 if (data
->src
== i
&& data
->dst
== j
)
6123 return isl_bool_true
;
6124 if (data
->src
== j
&& data
->dst
== i
)
6125 return isl_bool_true
;
6126 if (scc_cluster
[graph
->node
[i
].scc
] == scc_cluster
[graph
->node
[j
].scc
])
6127 return isl_bool_true
;
6129 return graph_has_validity_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
6132 /* Mark all SCCs that belong to either of the two clusters in "c"
6133 * connected by the edge in "graph" with index "edge", or to any
6134 * of the intermediate clusters.
6135 * The marking is recorded in c->scc_in_merge.
6137 * The given edge has been selected for merging two clusters,
6138 * meaning that there is at least a proximity edge between the two nodes.
6139 * However, there may also be (indirect) validity dependences
6140 * between the two nodes. When merging the two clusters, all clusters
6141 * containing one or more of the intermediate nodes along the
6142 * indirect validity dependences need to be merged in as well.
6144 * First collect all such nodes by computing the strongly connected
6145 * component (SCC) containing the two nodes connected by the edge, where
6146 * the two nodes are considered to depend on each other to make
6147 * sure they end up in the same SCC. Similarly, each node is considered
6148 * to depend on every other node in the same cluster to ensure
6149 * that the SCC consists of complete clusters.
6151 * Then the original SCCs that contain any of these nodes are marked
6152 * in c->scc_in_merge.
6154 static isl_stat
mark_merge_sccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
6155 int edge
, struct isl_clustering
*c
)
6157 struct isl_mark_merge_sccs_data data
;
6158 struct isl_tarjan_graph
*g
;
6161 for (i
= 0; i
< c
->n
; ++i
)
6162 c
->scc_in_merge
[i
] = 0;
6165 data
.scc_cluster
= c
->scc_cluster
;
6166 data
.src
= graph
->edge
[edge
].src
- graph
->node
;
6167 data
.dst
= graph
->edge
[edge
].dst
- graph
->node
;
6169 g
= isl_tarjan_graph_component(ctx
, graph
->n
, data
.dst
,
6170 &cluster_follows
, &data
);
6176 isl_die(ctx
, isl_error_internal
,
6177 "expecting at least two nodes in component",
6179 if (g
->order
[--i
] != -1)
6180 isl_die(ctx
, isl_error_internal
,
6181 "expecting end of component marker", goto error
);
6183 for (--i
; i
>= 0 && g
->order
[i
] != -1; --i
) {
6184 int scc
= graph
->node
[g
->order
[i
]].scc
;
6185 c
->scc_in_merge
[scc
] = 1;
6188 isl_tarjan_graph_free(g
);
6191 isl_tarjan_graph_free(g
);
6192 return isl_stat_error
;
6195 /* Construct the identifier "cluster_i".
6197 static __isl_give isl_id
*cluster_id(isl_ctx
*ctx
, int i
)
6201 snprintf(name
, sizeof(name
), "cluster_%d", i
);
6202 return isl_id_alloc(ctx
, name
, NULL
);
6205 /* Construct the space of the cluster with index "i" containing
6206 * the strongly connected component "scc".
6208 * In particular, construct a space called cluster_i with dimension equal
6209 * to the number of schedule rows in the current band of "scc".
6211 static __isl_give isl_space
*cluster_space(struct isl_sched_graph
*scc
, int i
)
6217 nvar
= scc
->n_total_row
- scc
->band_start
;
6218 space
= isl_space_copy(scc
->node
[0].space
);
6219 space
= isl_space_params(space
);
6220 space
= isl_space_set_from_params(space
);
6221 space
= isl_space_add_dims(space
, isl_dim_set
, nvar
);
6222 id
= cluster_id(isl_space_get_ctx(space
), i
);
6223 space
= isl_space_set_tuple_id(space
, isl_dim_set
, id
);
6228 /* Collect the domain of the graph for merging clusters.
6230 * In particular, for each cluster with first SCC "i", construct
6231 * a set in the space called cluster_i with dimension equal
6232 * to the number of schedule rows in the current band of the cluster.
6234 static __isl_give isl_union_set
*collect_domain(isl_ctx
*ctx
,
6235 struct isl_sched_graph
*graph
, struct isl_clustering
*c
)
6239 isl_union_set
*domain
;
6241 space
= isl_space_params_alloc(ctx
, 0);
6242 domain
= isl_union_set_empty(space
);
6244 for (i
= 0; i
< graph
->scc
; ++i
) {
6247 if (!c
->scc_in_merge
[i
])
6249 if (c
->scc_cluster
[i
] != i
)
6251 space
= cluster_space(&c
->scc
[i
], i
);
6252 domain
= isl_union_set_add_set(domain
, isl_set_universe(space
));
6258 /* Construct a map from the original instances to the corresponding
6259 * cluster instance in the current bands of the clusters in "c".
6261 static __isl_give isl_union_map
*collect_cluster_map(isl_ctx
*ctx
,
6262 struct isl_sched_graph
*graph
, struct isl_clustering
*c
)
6266 isl_union_map
*cluster_map
;
6268 space
= isl_space_params_alloc(ctx
, 0);
6269 cluster_map
= isl_union_map_empty(space
);
6270 for (i
= 0; i
< graph
->scc
; ++i
) {
6274 if (!c
->scc_in_merge
[i
])
6277 id
= cluster_id(ctx
, c
->scc_cluster
[i
]);
6278 start
= c
->scc
[i
].band_start
;
6279 n
= c
->scc
[i
].n_total_row
- start
;
6280 for (j
= 0; j
< c
->scc
[i
].n
; ++j
) {
6283 struct isl_sched_node
*node
= &c
->scc
[i
].node
[j
];
6285 ma
= node_extract_partial_schedule_multi_aff(node
,
6287 ma
= isl_multi_aff_set_tuple_id(ma
, isl_dim_out
,
6289 map
= isl_map_from_multi_aff(ma
);
6290 cluster_map
= isl_union_map_add_map(cluster_map
, map
);
6298 /* Add "umap" to the schedule constraints "sc" of all types of "edge"
6299 * that are not isl_edge_condition or isl_edge_conditional_validity.
6301 static __isl_give isl_schedule_constraints
*add_non_conditional_constraints(
6302 struct isl_sched_edge
*edge
, __isl_keep isl_union_map
*umap
,
6303 __isl_take isl_schedule_constraints
*sc
)
6305 enum isl_edge_type t
;
6310 for (t
= isl_edge_first
; t
<= isl_edge_last
; ++t
) {
6311 if (t
== isl_edge_condition
||
6312 t
== isl_edge_conditional_validity
)
6314 if (!is_type(edge
, t
))
6316 sc
= isl_schedule_constraints_add(sc
, t
,
6317 isl_union_map_copy(umap
));
6323 /* Add schedule constraints of types isl_edge_condition and
6324 * isl_edge_conditional_validity to "sc" by applying "umap" to
6325 * the domains of the wrapped relations in domain and range
6326 * of the corresponding tagged constraints of "edge".
6328 static __isl_give isl_schedule_constraints
*add_conditional_constraints(
6329 struct isl_sched_edge
*edge
, __isl_keep isl_union_map
*umap
,
6330 __isl_take isl_schedule_constraints
*sc
)
6332 enum isl_edge_type t
;
6333 isl_union_map
*tagged
;
6335 for (t
= isl_edge_condition
; t
<= isl_edge_conditional_validity
; ++t
) {
6336 if (!is_type(edge
, t
))
6338 if (t
== isl_edge_condition
)
6339 tagged
= isl_union_map_copy(edge
->tagged_condition
);
6341 tagged
= isl_union_map_copy(edge
->tagged_validity
);
6342 tagged
= isl_union_map_zip(tagged
);
6343 tagged
= isl_union_map_apply_domain(tagged
,
6344 isl_union_map_copy(umap
));
6345 tagged
= isl_union_map_zip(tagged
);
6346 sc
= isl_schedule_constraints_add(sc
, t
, tagged
);
6354 /* Given a mapping "cluster_map" from the original instances to
6355 * the cluster instances, add schedule constraints on the clusters
6356 * to "sc" corresponding to the original constraints represented by "edge".
6358 * For non-tagged dependence constraints, the cluster constraints
6359 * are obtained by applying "cluster_map" to the edge->map.
6361 * For tagged dependence constraints, "cluster_map" needs to be applied
6362 * to the domains of the wrapped relations in domain and range
6363 * of the tagged dependence constraints. Pick out the mappings
6364 * from these domains from "cluster_map" and construct their product.
6365 * This mapping can then be applied to the pair of domains.
6367 static __isl_give isl_schedule_constraints
*collect_edge_constraints(
6368 struct isl_sched_edge
*edge
, __isl_keep isl_union_map
*cluster_map
,
6369 __isl_take isl_schedule_constraints
*sc
)
6371 isl_union_map
*umap
;
6373 isl_union_set
*uset
;
6374 isl_union_map
*umap1
, *umap2
;
6379 umap
= isl_union_map_from_map(isl_map_copy(edge
->map
));
6380 umap
= isl_union_map_apply_domain(umap
,
6381 isl_union_map_copy(cluster_map
));
6382 umap
= isl_union_map_apply_range(umap
,
6383 isl_union_map_copy(cluster_map
));
6384 sc
= add_non_conditional_constraints(edge
, umap
, sc
);
6385 isl_union_map_free(umap
);
6387 if (!sc
|| (!is_condition(edge
) && !is_conditional_validity(edge
)))
6390 space
= isl_space_domain(isl_map_get_space(edge
->map
));
6391 uset
= isl_union_set_from_set(isl_set_universe(space
));
6392 umap1
= isl_union_map_copy(cluster_map
);
6393 umap1
= isl_union_map_intersect_domain(umap1
, uset
);
6394 space
= isl_space_range(isl_map_get_space(edge
->map
));
6395 uset
= isl_union_set_from_set(isl_set_universe(space
));
6396 umap2
= isl_union_map_copy(cluster_map
);
6397 umap2
= isl_union_map_intersect_domain(umap2
, uset
);
6398 umap
= isl_union_map_product(umap1
, umap2
);
6400 sc
= add_conditional_constraints(edge
, umap
, sc
);
6402 isl_union_map_free(umap
);
6406 /* Given a mapping "cluster_map" from the original instances to
6407 * the cluster instances, add schedule constraints on the clusters
6408 * to "sc" corresponding to all edges in "graph" between nodes that
6409 * belong to SCCs that are marked for merging in "scc_in_merge".
6411 static __isl_give isl_schedule_constraints
*collect_constraints(
6412 struct isl_sched_graph
*graph
, int *scc_in_merge
,
6413 __isl_keep isl_union_map
*cluster_map
,
6414 __isl_take isl_schedule_constraints
*sc
)
6418 for (i
= 0; i
< graph
->n_edge
; ++i
) {
6419 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
6421 if (!scc_in_merge
[edge
->src
->scc
])
6423 if (!scc_in_merge
[edge
->dst
->scc
])
6425 sc
= collect_edge_constraints(edge
, cluster_map
, sc
);
6431 /* Construct a dependence graph for scheduling clusters with respect
6432 * to each other and store the result in "merge_graph".
6433 * In particular, the nodes of the graph correspond to the schedule
6434 * dimensions of the current bands of those clusters that have been
6435 * marked for merging in "c".
6437 * First construct an isl_schedule_constraints object for this domain
6438 * by transforming the edges in "graph" to the domain.
6439 * Then initialize a dependence graph for scheduling from these
6442 static isl_stat
init_merge_graph(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
6443 struct isl_clustering
*c
, struct isl_sched_graph
*merge_graph
)
6445 isl_union_set
*domain
;
6446 isl_union_map
*cluster_map
;
6447 isl_schedule_constraints
*sc
;
6450 domain
= collect_domain(ctx
, graph
, c
);
6451 sc
= isl_schedule_constraints_on_domain(domain
);
6453 return isl_stat_error
;
6454 cluster_map
= collect_cluster_map(ctx
, graph
, c
);
6455 sc
= collect_constraints(graph
, c
->scc_in_merge
, cluster_map
, sc
);
6456 isl_union_map_free(cluster_map
);
6458 r
= graph_init(merge_graph
, sc
);
6460 isl_schedule_constraints_free(sc
);
6465 /* Compute the maximal number of remaining schedule rows that still need
6466 * to be computed for the nodes that belong to clusters with the maximal
6467 * dimension for the current band (i.e., the band that is to be merged).
6468 * Only clusters that are about to be merged are considered.
6469 * "maxvar" is the maximal dimension for the current band.
6470 * "c" contains information about the clusters.
6472 * Return the maximal number of remaining schedule rows or -1 on error.
6474 static int compute_maxvar_max_slack(int maxvar
, struct isl_clustering
*c
)
6480 for (i
= 0; i
< c
->n
; ++i
) {
6482 struct isl_sched_graph
*scc
;
6484 if (!c
->scc_in_merge
[i
])
6487 nvar
= scc
->n_total_row
- scc
->band_start
;
6490 for (j
= 0; j
< scc
->n
; ++j
) {
6491 struct isl_sched_node
*node
= &scc
->node
[j
];
6494 if (node_update_vmap(node
) < 0)
6496 slack
= node
->nvar
- node
->rank
;
6497 if (slack
> max_slack
)
6505 /* If there are any clusters where the dimension of the current band
6506 * (i.e., the band that is to be merged) is smaller than "maxvar" and
6507 * if there are any nodes in such a cluster where the number
6508 * of remaining schedule rows that still need to be computed
6509 * is greater than "max_slack", then return the smallest current band
6510 * dimension of all these clusters. Otherwise return the original value
6511 * of "maxvar". Return -1 in case of any error.
6512 * Only clusters that are about to be merged are considered.
6513 * "c" contains information about the clusters.
6515 static int limit_maxvar_to_slack(int maxvar
, int max_slack
,
6516 struct isl_clustering
*c
)
6520 for (i
= 0; i
< c
->n
; ++i
) {
6522 struct isl_sched_graph
*scc
;
6524 if (!c
->scc_in_merge
[i
])
6527 nvar
= scc
->n_total_row
- scc
->band_start
;
6530 for (j
= 0; j
< scc
->n
; ++j
) {
6531 struct isl_sched_node
*node
= &scc
->node
[j
];
6534 if (node_update_vmap(node
) < 0)
6536 slack
= node
->nvar
- node
->rank
;
6537 if (slack
> max_slack
) {
6547 /* Adjust merge_graph->maxvar based on the number of remaining schedule rows
6548 * that still need to be computed. In particular, if there is a node
6549 * in a cluster where the dimension of the current band is smaller
6550 * than merge_graph->maxvar, but the number of remaining schedule rows
6551 * is greater than that of any node in a cluster with the maximal
6552 * dimension for the current band (i.e., merge_graph->maxvar),
6553 * then adjust merge_graph->maxvar to the (smallest) current band dimension
6554 * of those clusters. Without this adjustment, the total number of
6555 * schedule dimensions would be increased, resulting in a skewed view
6556 * of the number of coincident dimensions.
6557 * "c" contains information about the clusters.
6559 * If the maximize_band_depth option is set and merge_graph->maxvar is reduced,
6560 * then there is no point in attempting any merge since it will be rejected
6561 * anyway. Set merge_graph->maxvar to zero in such cases.
6563 static isl_stat
adjust_maxvar_to_slack(isl_ctx
*ctx
,
6564 struct isl_sched_graph
*merge_graph
, struct isl_clustering
*c
)
6566 int max_slack
, maxvar
;
6568 max_slack
= compute_maxvar_max_slack(merge_graph
->maxvar
, c
);
6570 return isl_stat_error
;
6571 maxvar
= limit_maxvar_to_slack(merge_graph
->maxvar
, max_slack
, c
);
6573 return isl_stat_error
;
6575 if (maxvar
< merge_graph
->maxvar
) {
6576 if (isl_options_get_schedule_maximize_band_depth(ctx
))
6577 merge_graph
->maxvar
= 0;
6579 merge_graph
->maxvar
= maxvar
;
6585 /* Return the number of coincident dimensions in the current band of "graph",
6586 * where the nodes of "graph" are assumed to be scheduled by a single band.
6588 static int get_n_coincident(struct isl_sched_graph
*graph
)
6592 for (i
= graph
->band_start
; i
< graph
->n_total_row
; ++i
)
6593 if (!graph
->node
[0].coincident
[i
])
6596 return i
- graph
->band_start
;
6599 /* Should the clusters be merged based on the cluster schedule
6600 * in the current (and only) band of "merge_graph", given that
6601 * coincidence should be maximized?
6603 * If the number of coincident schedule dimensions in the merged band
6604 * would be less than the maximal number of coincident schedule dimensions
6605 * in any of the merged clusters, then the clusters should not be merged.
6607 static isl_bool
ok_to_merge_coincident(struct isl_clustering
*c
,
6608 struct isl_sched_graph
*merge_graph
)
6615 for (i
= 0; i
< c
->n
; ++i
) {
6616 if (!c
->scc_in_merge
[i
])
6618 n_coincident
= get_n_coincident(&c
->scc
[i
]);
6619 if (n_coincident
> max_coincident
)
6620 max_coincident
= n_coincident
;
6623 n_coincident
= get_n_coincident(merge_graph
);
6625 return isl_bool_ok(n_coincident
>= max_coincident
);
6628 /* Return the transformation on "node" expressed by the current (and only)
6629 * band of "merge_graph" applied to the clusters in "c".
6631 * First find the representation of "node" in its SCC in "c" and
6632 * extract the transformation expressed by the current band.
6633 * Then extract the transformation applied by "merge_graph"
6634 * to the cluster to which this SCC belongs.
6635 * Combine the two to obtain the complete transformation on the node.
6637 * Note that the range of the first transformation is an anonymous space,
6638 * while the domain of the second is named "cluster_X". The range
6639 * of the former therefore needs to be adjusted before the two
6642 static __isl_give isl_map
*extract_node_transformation(isl_ctx
*ctx
,
6643 struct isl_sched_node
*node
, struct isl_clustering
*c
,
6644 struct isl_sched_graph
*merge_graph
)
6646 struct isl_sched_node
*scc_node
, *cluster_node
;
6650 isl_multi_aff
*ma
, *ma2
;
6652 scc_node
= graph_find_node(ctx
, &c
->scc
[node
->scc
], node
->space
);
6653 if (scc_node
&& !is_node(&c
->scc
[node
->scc
], scc_node
))
6654 isl_die(ctx
, isl_error_internal
, "unable to find node",
6656 start
= c
->scc
[node
->scc
].band_start
;
6657 n
= c
->scc
[node
->scc
].n_total_row
- start
;
6658 ma
= node_extract_partial_schedule_multi_aff(scc_node
, start
, n
);
6659 space
= cluster_space(&c
->scc
[node
->scc
], c
->scc_cluster
[node
->scc
]);
6660 cluster_node
= graph_find_node(ctx
, merge_graph
, space
);
6661 if (cluster_node
&& !is_node(merge_graph
, cluster_node
))
6662 isl_die(ctx
, isl_error_internal
, "unable to find cluster",
6663 space
= isl_space_free(space
));
6664 id
= isl_space_get_tuple_id(space
, isl_dim_set
);
6665 ma
= isl_multi_aff_set_tuple_id(ma
, isl_dim_out
, id
);
6666 isl_space_free(space
);
6667 n
= merge_graph
->n_total_row
;
6668 ma2
= node_extract_partial_schedule_multi_aff(cluster_node
, 0, n
);
6669 ma
= isl_multi_aff_pullback_multi_aff(ma2
, ma
);
6671 return isl_map_from_multi_aff(ma
);
6674 /* Give a set of distances "set", are they bounded by a small constant
6675 * in direction "pos"?
6676 * In practice, check if they are bounded by 2 by checking that there
6677 * are no elements with a value greater than or equal to 3 or
6678 * smaller than or equal to -3.
6680 static isl_bool
distance_is_bounded(__isl_keep isl_set
*set
, int pos
)
6686 return isl_bool_error
;
6688 test
= isl_set_copy(set
);
6689 test
= isl_set_lower_bound_si(test
, isl_dim_set
, pos
, 3);
6690 bounded
= isl_set_is_empty(test
);
6693 if (bounded
< 0 || !bounded
)
6696 test
= isl_set_copy(set
);
6697 test
= isl_set_upper_bound_si(test
, isl_dim_set
, pos
, -3);
6698 bounded
= isl_set_is_empty(test
);
6704 /* Does the set "set" have a fixed (but possible parametric) value
6705 * at dimension "pos"?
6707 static isl_bool
has_single_value(__isl_keep isl_set
*set
, int pos
)
6712 n
= isl_set_dim(set
, isl_dim_set
);
6714 return isl_bool_error
;
6715 set
= isl_set_copy(set
);
6716 set
= isl_set_project_out(set
, isl_dim_set
, pos
+ 1, n
- (pos
+ 1));
6717 set
= isl_set_project_out(set
, isl_dim_set
, 0, pos
);
6718 single
= isl_set_is_singleton(set
);
6724 /* Does "map" have a fixed (but possible parametric) value
6725 * at dimension "pos" of either its domain or its range?
6727 static isl_bool
has_singular_src_or_dst(__isl_keep isl_map
*map
, int pos
)
6732 set
= isl_map_domain(isl_map_copy(map
));
6733 single
= has_single_value(set
, pos
);
6736 if (single
< 0 || single
)
6739 set
= isl_map_range(isl_map_copy(map
));
6740 single
= has_single_value(set
, pos
);
6746 /* Does the edge "edge" from "graph" have bounded dependence distances
6747 * in the merged graph "merge_graph" of a selection of clusters in "c"?
6749 * Extract the complete transformations of the source and destination
6750 * nodes of the edge, apply them to the edge constraints and
6751 * compute the differences. Finally, check if these differences are bounded
6752 * in each direction.
6754 * If the dimension of the band is greater than the number of
6755 * dimensions that can be expected to be optimized by the edge
6756 * (based on its weight), then also allow the differences to be unbounded
6757 * in the remaining dimensions, but only if either the source or
6758 * the destination has a fixed value in that direction.
6759 * This allows a statement that produces values that are used by
6760 * several instances of another statement to be merged with that
6762 * However, merging such clusters will introduce an inherently
6763 * large proximity distance inside the merged cluster, meaning
6764 * that proximity distances will no longer be optimized in
6765 * subsequent merges. These merges are therefore only allowed
6766 * after all other possible merges have been tried.
6767 * The first time such a merge is encountered, the weight of the edge
6768 * is replaced by a negative weight. The second time (i.e., after
6769 * all merges over edges with a non-negative weight have been tried),
6770 * the merge is allowed.
6772 static isl_bool
has_bounded_distances(isl_ctx
*ctx
, struct isl_sched_edge
*edge
,
6773 struct isl_sched_graph
*graph
, struct isl_clustering
*c
,
6774 struct isl_sched_graph
*merge_graph
)
6782 map
= isl_map_copy(edge
->map
);
6783 t
= extract_node_transformation(ctx
, edge
->src
, c
, merge_graph
);
6784 map
= isl_map_apply_domain(map
, t
);
6785 t
= extract_node_transformation(ctx
, edge
->dst
, c
, merge_graph
);
6786 map
= isl_map_apply_range(map
, t
);
6787 dist
= isl_map_deltas(isl_map_copy(map
));
6789 bounded
= isl_bool_true
;
6790 n
= isl_set_dim(dist
, isl_dim_set
);
6793 n_slack
= n
- edge
->weight
;
6794 if (edge
->weight
< 0)
6795 n_slack
-= graph
->max_weight
+ 1;
6796 for (i
= 0; i
< n
; ++i
) {
6797 isl_bool bounded_i
, singular_i
;
6799 bounded_i
= distance_is_bounded(dist
, i
);
6804 if (edge
->weight
>= 0)
6805 bounded
= isl_bool_false
;
6809 singular_i
= has_singular_src_or_dst(map
, i
);
6814 bounded
= isl_bool_false
;
6817 if (!bounded
&& i
>= n
&& edge
->weight
>= 0)
6818 edge
->weight
-= graph
->max_weight
+ 1;
6826 return isl_bool_error
;
6829 /* Should the clusters be merged based on the cluster schedule
6830 * in the current (and only) band of "merge_graph"?
6831 * "graph" is the original dependence graph, while "c" records
6832 * which SCCs are involved in the latest merge.
6834 * In particular, is there at least one proximity constraint
6835 * that is optimized by the merge?
6837 * A proximity constraint is considered to be optimized
6838 * if the dependence distances are small.
6840 static isl_bool
ok_to_merge_proximity(isl_ctx
*ctx
,
6841 struct isl_sched_graph
*graph
, struct isl_clustering
*c
,
6842 struct isl_sched_graph
*merge_graph
)
6846 for (i
= 0; i
< graph
->n_edge
; ++i
) {
6847 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
6850 if (!is_proximity(edge
))
6852 if (!c
->scc_in_merge
[edge
->src
->scc
])
6854 if (!c
->scc_in_merge
[edge
->dst
->scc
])
6856 if (c
->scc_cluster
[edge
->dst
->scc
] ==
6857 c
->scc_cluster
[edge
->src
->scc
])
6859 bounded
= has_bounded_distances(ctx
, edge
, graph
, c
,
6861 if (bounded
< 0 || bounded
)
6865 return isl_bool_false
;
6868 /* Should the clusters be merged based on the cluster schedule
6869 * in the current (and only) band of "merge_graph"?
6870 * "graph" is the original dependence graph, while "c" records
6871 * which SCCs are involved in the latest merge.
6873 * If the current band is empty, then the clusters should not be merged.
6875 * If the band depth should be maximized and the merge schedule
6876 * is incomplete (meaning that the dimension of some of the schedule
6877 * bands in the original schedule will be reduced), then the clusters
6878 * should not be merged.
6880 * If the schedule_maximize_coincidence option is set, then check that
6881 * the number of coincident schedule dimensions is not reduced.
6883 * Finally, only allow the merge if at least one proximity
6884 * constraint is optimized.
6886 static isl_bool
ok_to_merge(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
6887 struct isl_clustering
*c
, struct isl_sched_graph
*merge_graph
)
6889 if (merge_graph
->n_total_row
== merge_graph
->band_start
)
6890 return isl_bool_false
;
6892 if (isl_options_get_schedule_maximize_band_depth(ctx
) &&
6893 merge_graph
->n_total_row
< merge_graph
->maxvar
)
6894 return isl_bool_false
;
6896 if (isl_options_get_schedule_maximize_coincidence(ctx
)) {
6899 ok
= ok_to_merge_coincident(c
, merge_graph
);
6904 return ok_to_merge_proximity(ctx
, graph
, c
, merge_graph
);
6907 /* Apply the schedule in "t_node" to the "n" rows starting at "first"
6908 * of the schedule in "node" and return the result.
6910 * That is, essentially compute
6912 * T * N(first:first+n-1)
6914 * taking into account the constant term and the parameter coefficients
6917 static __isl_give isl_mat
*node_transformation(isl_ctx
*ctx
,
6918 struct isl_sched_node
*t_node
, struct isl_sched_node
*node
,
6923 isl_size n_row
, n_col
;
6926 n_param
= node
->nparam
;
6928 n_row
= isl_mat_rows(t_node
->sched
);
6929 n_col
= isl_mat_cols(node
->sched
);
6930 if (n_row
< 0 || n_col
< 0)
6932 t
= isl_mat_alloc(ctx
, n_row
, n_col
);
6935 for (i
= 0; i
< n_row
; ++i
) {
6936 isl_seq_cpy(t
->row
[i
], t_node
->sched
->row
[i
], 1 + n_param
);
6937 isl_seq_clr(t
->row
[i
] + 1 + n_param
, n_var
);
6938 for (j
= 0; j
< n
; ++j
)
6939 isl_seq_addmul(t
->row
[i
],
6940 t_node
->sched
->row
[i
][1 + n_param
+ j
],
6941 node
->sched
->row
[first
+ j
],
6942 1 + n_param
+ n_var
);
6947 /* Apply the cluster schedule in "t_node" to the current band
6948 * schedule of the nodes in "graph".
6950 * In particular, replace the rows starting at band_start
6951 * by the result of applying the cluster schedule in "t_node"
6952 * to the original rows.
6954 * The coincidence of the schedule is determined by the coincidence
6955 * of the cluster schedule.
6957 static isl_stat
transform(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
6958 struct isl_sched_node
*t_node
)
6964 start
= graph
->band_start
;
6965 n
= graph
->n_total_row
- start
;
6967 n_new
= isl_mat_rows(t_node
->sched
);
6969 return isl_stat_error
;
6970 for (i
= 0; i
< graph
->n
; ++i
) {
6971 struct isl_sched_node
*node
= &graph
->node
[i
];
6974 t
= node_transformation(ctx
, t_node
, node
, start
, n
);
6975 node
->sched
= isl_mat_drop_rows(node
->sched
, start
, n
);
6976 node
->sched
= isl_mat_concat(node
->sched
, t
);
6977 node
->sched_map
= isl_map_free(node
->sched_map
);
6979 return isl_stat_error
;
6980 for (j
= 0; j
< n_new
; ++j
)
6981 node
->coincident
[start
+ j
] = t_node
->coincident
[j
];
6983 graph
->n_total_row
-= n
;
6985 graph
->n_total_row
+= n_new
;
6986 graph
->n_row
+= n_new
;
6991 /* Merge the clusters marked for merging in "c" into a single
6992 * cluster using the cluster schedule in the current band of "merge_graph".
6993 * The representative SCC for the new cluster is the SCC with
6994 * the smallest index.
6996 * The current band schedule of each SCC in the new cluster is obtained
6997 * by applying the schedule of the corresponding original cluster
6998 * to the original band schedule.
6999 * All SCCs in the new cluster have the same number of schedule rows.
7001 static isl_stat
merge(isl_ctx
*ctx
, struct isl_clustering
*c
,
7002 struct isl_sched_graph
*merge_graph
)
7008 for (i
= 0; i
< c
->n
; ++i
) {
7009 struct isl_sched_node
*node
;
7011 if (!c
->scc_in_merge
[i
])
7015 space
= cluster_space(&c
->scc
[i
], c
->scc_cluster
[i
]);
7016 node
= graph_find_node(ctx
, merge_graph
, space
);
7017 isl_space_free(space
);
7019 return isl_stat_error
;
7020 if (!is_node(merge_graph
, node
))
7021 isl_die(ctx
, isl_error_internal
,
7022 "unable to find cluster",
7023 return isl_stat_error
);
7024 if (transform(ctx
, &c
->scc
[i
], node
) < 0)
7025 return isl_stat_error
;
7026 c
->scc_cluster
[i
] = cluster
;
7032 /* Try and merge the clusters of SCCs marked in c->scc_in_merge
7033 * by scheduling the current cluster bands with respect to each other.
7035 * Construct a dependence graph with a space for each cluster and
7036 * with the coordinates of each space corresponding to the schedule
7037 * dimensions of the current band of that cluster.
7038 * Construct a cluster schedule in this cluster dependence graph and
7039 * apply it to the current cluster bands if it is applicable
7040 * according to ok_to_merge.
7042 * If the number of remaining schedule dimensions in a cluster
7043 * with a non-maximal current schedule dimension is greater than
7044 * the number of remaining schedule dimensions in clusters
7045 * with a maximal current schedule dimension, then restrict
7046 * the number of rows to be computed in the cluster schedule
7047 * to the minimal such non-maximal current schedule dimension.
7048 * Do this by adjusting merge_graph.maxvar.
7050 * Return isl_bool_true if the clusters have effectively been merged
7051 * into a single cluster.
7053 * Note that since the standard scheduling algorithm minimizes the maximal
7054 * distance over proximity constraints, the proximity constraints between
7055 * the merged clusters may not be optimized any further than what is
7056 * sufficient to bring the distances within the limits of the internal
7057 * proximity constraints inside the individual clusters.
7058 * It may therefore make sense to perform an additional translation step
7059 * to bring the clusters closer to each other, while maintaining
7060 * the linear part of the merging schedule found using the standard
7061 * scheduling algorithm.
7063 static isl_bool
try_merge(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
7064 struct isl_clustering
*c
)
7066 struct isl_sched_graph merge_graph
= { 0 };
7069 if (init_merge_graph(ctx
, graph
, c
, &merge_graph
) < 0)
7072 if (compute_maxvar(&merge_graph
) < 0)
7074 if (adjust_maxvar_to_slack(ctx
, &merge_graph
,c
) < 0)
7076 if (compute_schedule_wcc_band(ctx
, &merge_graph
) < 0)
7078 merged
= ok_to_merge(ctx
, graph
, c
, &merge_graph
);
7079 if (merged
&& merge(ctx
, c
, &merge_graph
) < 0)
7082 graph_free(ctx
, &merge_graph
);
7085 graph_free(ctx
, &merge_graph
);
7086 return isl_bool_error
;
7089 /* Is there any edge marked "no_merge" between two SCCs that are
7090 * about to be merged (i.e., that are set in "scc_in_merge")?
7091 * "merge_edge" is the proximity edge along which the clusters of SCCs
7092 * are going to be merged.
7094 * If there is any edge between two SCCs with a negative weight,
7095 * while the weight of "merge_edge" is non-negative, then this
7096 * means that the edge was postponed. "merge_edge" should then
7097 * also be postponed since merging along the edge with negative weight should
7098 * be postponed until all edges with non-negative weight have been tried.
7099 * Replace the weight of "merge_edge" by a negative weight as well and
7100 * tell the caller not to attempt a merge.
7102 static int any_no_merge(struct isl_sched_graph
*graph
, int *scc_in_merge
,
7103 struct isl_sched_edge
*merge_edge
)
7107 for (i
= 0; i
< graph
->n_edge
; ++i
) {
7108 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
7110 if (!scc_in_merge
[edge
->src
->scc
])
7112 if (!scc_in_merge
[edge
->dst
->scc
])
7116 if (merge_edge
->weight
>= 0 && edge
->weight
< 0) {
7117 merge_edge
->weight
-= graph
->max_weight
+ 1;
7125 /* Merge the two clusters in "c" connected by the edge in "graph"
7126 * with index "edge" into a single cluster.
7127 * If it turns out to be impossible to merge these two clusters,
7128 * then mark the edge as "no_merge" such that it will not be
7131 * First mark all SCCs that need to be merged. This includes the SCCs
7132 * in the two clusters, but it may also include the SCCs
7133 * of intermediate clusters.
7134 * If there is already a no_merge edge between any pair of such SCCs,
7135 * then simply mark the current edge as no_merge as well.
7136 * Likewise, if any of those edges was postponed by has_bounded_distances,
7137 * then postpone the current edge as well.
7138 * Otherwise, try and merge the clusters and mark "edge" as "no_merge"
7139 * if the clusters did not end up getting merged, unless the non-merge
7140 * is due to the fact that the edge was postponed. This postponement
7141 * can be recognized by a change in weight (from non-negative to negative).
7143 static isl_stat
merge_clusters_along_edge(isl_ctx
*ctx
,
7144 struct isl_sched_graph
*graph
, int edge
, struct isl_clustering
*c
)
7147 int edge_weight
= graph
->edge
[edge
].weight
;
7149 if (mark_merge_sccs(ctx
, graph
, edge
, c
) < 0)
7150 return isl_stat_error
;
7152 if (any_no_merge(graph
, c
->scc_in_merge
, &graph
->edge
[edge
]))
7153 merged
= isl_bool_false
;
7155 merged
= try_merge(ctx
, graph
, c
);
7157 return isl_stat_error
;
7158 if (!merged
&& edge_weight
== graph
->edge
[edge
].weight
)
7159 graph
->edge
[edge
].no_merge
= 1;
7164 /* Does "node" belong to the cluster identified by "cluster"?
7166 static int node_cluster_exactly(struct isl_sched_node
*node
, int cluster
)
7168 return node
->cluster
== cluster
;
7171 /* Does "edge" connect two nodes belonging to the cluster
7172 * identified by "cluster"?
7174 static int edge_cluster_exactly(struct isl_sched_edge
*edge
, int cluster
)
7176 return edge
->src
->cluster
== cluster
&& edge
->dst
->cluster
== cluster
;
7179 /* Swap the schedule of "node1" and "node2".
7180 * Both nodes have been derived from the same node in a common parent graph.
7181 * Since the "coincident" field is shared with that node
7182 * in the parent graph, there is no need to also swap this field.
7184 static void swap_sched(struct isl_sched_node
*node1
,
7185 struct isl_sched_node
*node2
)
7190 sched
= node1
->sched
;
7191 node1
->sched
= node2
->sched
;
7192 node2
->sched
= sched
;
7194 sched_map
= node1
->sched_map
;
7195 node1
->sched_map
= node2
->sched_map
;
7196 node2
->sched_map
= sched_map
;
7199 /* Copy the current band schedule from the SCCs that form the cluster
7200 * with index "pos" to the actual cluster at position "pos".
7201 * By construction, the index of the first SCC that belongs to the cluster
7204 * The order of the nodes inside both the SCCs and the cluster
7205 * is assumed to be same as the order in the original "graph".
7207 * Since the SCC graphs will no longer be used after this function,
7208 * the schedules are actually swapped rather than copied.
7210 static isl_stat
copy_partial(struct isl_sched_graph
*graph
,
7211 struct isl_clustering
*c
, int pos
)
7215 c
->cluster
[pos
].n_total_row
= c
->scc
[pos
].n_total_row
;
7216 c
->cluster
[pos
].n_row
= c
->scc
[pos
].n_row
;
7217 c
->cluster
[pos
].maxvar
= c
->scc
[pos
].maxvar
;
7219 for (i
= 0; i
< graph
->n
; ++i
) {
7223 if (graph
->node
[i
].cluster
!= pos
)
7225 s
= graph
->node
[i
].scc
;
7226 k
= c
->scc_node
[s
]++;
7227 swap_sched(&c
->cluster
[pos
].node
[j
], &c
->scc
[s
].node
[k
]);
7228 if (c
->scc
[s
].maxvar
> c
->cluster
[pos
].maxvar
)
7229 c
->cluster
[pos
].maxvar
= c
->scc
[s
].maxvar
;
7236 /* Is there a (conditional) validity dependence from node[j] to node[i],
7237 * forcing node[i] to follow node[j] or do the nodes belong to the same
7240 static isl_bool
node_follows_strong_or_same_cluster(int i
, int j
, void *user
)
7242 struct isl_sched_graph
*graph
= user
;
7244 if (graph
->node
[i
].cluster
== graph
->node
[j
].cluster
)
7245 return isl_bool_true
;
7246 return graph_has_validity_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
7249 /* Extract the merged clusters of SCCs in "graph", sort them, and
7250 * store them in c->clusters. Update c->scc_cluster accordingly.
7252 * First keep track of the cluster containing the SCC to which a node
7253 * belongs in the node itself.
7254 * Then extract the clusters into c->clusters, copying the current
7255 * band schedule from the SCCs that belong to the cluster.
7256 * Do this only once per cluster.
7258 * Finally, topologically sort the clusters and update c->scc_cluster
7259 * to match the new scc numbering. While the SCCs were originally
7260 * sorted already, some SCCs that depend on some other SCCs may
7261 * have been merged with SCCs that appear before these other SCCs.
7262 * A reordering may therefore be required.
7264 static isl_stat
extract_clusters(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
7265 struct isl_clustering
*c
)
7269 for (i
= 0; i
< graph
->n
; ++i
)
7270 graph
->node
[i
].cluster
= c
->scc_cluster
[graph
->node
[i
].scc
];
7272 for (i
= 0; i
< graph
->scc
; ++i
) {
7273 if (c
->scc_cluster
[i
] != i
)
7275 if (extract_sub_graph(ctx
, graph
, &node_cluster_exactly
,
7276 &edge_cluster_exactly
, i
, &c
->cluster
[i
]) < 0)
7277 return isl_stat_error
;
7278 c
->cluster
[i
].src_scc
= -1;
7279 c
->cluster
[i
].dst_scc
= -1;
7280 if (copy_partial(graph
, c
, i
) < 0)
7281 return isl_stat_error
;
7284 if (detect_ccs(ctx
, graph
, &node_follows_strong_or_same_cluster
) < 0)
7285 return isl_stat_error
;
7286 for (i
= 0; i
< graph
->n
; ++i
)
7287 c
->scc_cluster
[graph
->node
[i
].scc
] = graph
->node
[i
].cluster
;
7292 /* Compute weights on the proximity edges of "graph" that can
7293 * be used by find_proximity to find the most appropriate
7294 * proximity edge to use to merge two clusters in "c".
7295 * The weights are also used by has_bounded_distances to determine
7296 * whether the merge should be allowed.
7297 * Store the maximum of the computed weights in graph->max_weight.
7299 * The computed weight is a measure for the number of remaining schedule
7300 * dimensions that can still be completely aligned.
7301 * In particular, compute the number of equalities between
7302 * input dimensions and output dimensions in the proximity constraints.
7303 * The directions that are already handled by outer schedule bands
7304 * are projected out prior to determining this number.
7306 * Edges that will never be considered by find_proximity are ignored.
7308 static isl_stat
compute_weights(struct isl_sched_graph
*graph
,
7309 struct isl_clustering
*c
)
7313 graph
->max_weight
= 0;
7315 for (i
= 0; i
< graph
->n_edge
; ++i
) {
7316 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
7317 struct isl_sched_node
*src
= edge
->src
;
7318 struct isl_sched_node
*dst
= edge
->dst
;
7319 isl_basic_map
*hull
;
7321 isl_size n_in
, n_out
;
7323 prox
= is_non_empty_proximity(edge
);
7325 return isl_stat_error
;
7328 if (bad_cluster(&c
->scc
[edge
->src
->scc
]) ||
7329 bad_cluster(&c
->scc
[edge
->dst
->scc
]))
7331 if (c
->scc_cluster
[edge
->dst
->scc
] ==
7332 c
->scc_cluster
[edge
->src
->scc
])
7335 hull
= isl_map_affine_hull(isl_map_copy(edge
->map
));
7336 hull
= isl_basic_map_transform_dims(hull
, isl_dim_in
, 0,
7337 isl_mat_copy(src
->vmap
));
7338 hull
= isl_basic_map_transform_dims(hull
, isl_dim_out
, 0,
7339 isl_mat_copy(dst
->vmap
));
7340 hull
= isl_basic_map_project_out(hull
,
7341 isl_dim_in
, 0, src
->rank
);
7342 hull
= isl_basic_map_project_out(hull
,
7343 isl_dim_out
, 0, dst
->rank
);
7344 hull
= isl_basic_map_remove_divs(hull
);
7345 n_in
= isl_basic_map_dim(hull
, isl_dim_in
);
7346 n_out
= isl_basic_map_dim(hull
, isl_dim_out
);
7347 if (n_in
< 0 || n_out
< 0)
7348 hull
= isl_basic_map_free(hull
);
7349 hull
= isl_basic_map_drop_constraints_not_involving_dims(hull
,
7350 isl_dim_in
, 0, n_in
);
7351 hull
= isl_basic_map_drop_constraints_not_involving_dims(hull
,
7352 isl_dim_out
, 0, n_out
);
7354 return isl_stat_error
;
7355 edge
->weight
= isl_basic_map_n_equality(hull
);
7356 isl_basic_map_free(hull
);
7358 if (edge
->weight
> graph
->max_weight
)
7359 graph
->max_weight
= edge
->weight
;
7365 /* Call compute_schedule_finish_band on each of the clusters in "c"
7366 * in their topological order. This order is determined by the scc
7367 * fields of the nodes in "graph".
7368 * Combine the results in a sequence expressing the topological order.
7370 * If there is only one cluster left, then there is no need to introduce
7371 * a sequence node. Also, in this case, the cluster necessarily contains
7372 * the SCC at position 0 in the original graph and is therefore also
7373 * stored in the first cluster of "c".
7375 static __isl_give isl_schedule_node
*finish_bands_clustering(
7376 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
7377 struct isl_clustering
*c
)
7381 isl_union_set_list
*filters
;
7383 if (graph
->scc
== 1)
7384 return compute_schedule_finish_band(node
, &c
->cluster
[0], 0);
7386 ctx
= isl_schedule_node_get_ctx(node
);
7388 filters
= extract_sccs(ctx
, graph
);
7389 node
= isl_schedule_node_insert_sequence(node
, filters
);
7391 for (i
= 0; i
< graph
->scc
; ++i
) {
7392 int j
= c
->scc_cluster
[i
];
7393 node
= isl_schedule_node_child(node
, i
);
7394 node
= isl_schedule_node_child(node
, 0);
7395 node
= compute_schedule_finish_band(node
, &c
->cluster
[j
], 0);
7396 node
= isl_schedule_node_parent(node
);
7397 node
= isl_schedule_node_parent(node
);
7403 /* Compute a schedule for a connected dependence graph by first considering
7404 * each strongly connected component (SCC) in the graph separately and then
7405 * incrementally combining them into clusters.
7406 * Return the updated schedule node.
7408 * Initially, each cluster consists of a single SCC, each with its
7409 * own band schedule. The algorithm then tries to merge pairs
7410 * of clusters along a proximity edge until no more suitable
7411 * proximity edges can be found. During this merging, the schedule
7412 * is maintained in the individual SCCs.
7413 * After the merging is completed, the full resulting clusters
7414 * are extracted and in finish_bands_clustering,
7415 * compute_schedule_finish_band is called on each of them to integrate
7416 * the band into "node" and to continue the computation.
7418 * compute_weights initializes the weights that are used by find_proximity.
7420 static __isl_give isl_schedule_node
*compute_schedule_wcc_clustering(
7421 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
7424 struct isl_clustering c
;
7427 ctx
= isl_schedule_node_get_ctx(node
);
7429 if (clustering_init(ctx
, &c
, graph
) < 0)
7432 if (compute_weights(graph
, &c
) < 0)
7436 i
= find_proximity(graph
, &c
);
7439 if (i
>= graph
->n_edge
)
7441 if (merge_clusters_along_edge(ctx
, graph
, i
, &c
) < 0)
7445 if (extract_clusters(ctx
, graph
, &c
) < 0)
7448 node
= finish_bands_clustering(node
, graph
, &c
);
7450 clustering_free(ctx
, &c
);
7453 clustering_free(ctx
, &c
);
7454 return isl_schedule_node_free(node
);
7457 /* Compute a schedule for a connected dependence graph and return
7458 * the updated schedule node.
7460 * If Feautrier's algorithm is selected, we first recursively try to satisfy
7461 * as many validity dependences as possible. When all validity dependences
7462 * are satisfied we extend the schedule to a full-dimensional schedule.
7464 * Call compute_schedule_wcc_whole or compute_schedule_wcc_clustering
7465 * depending on whether the user has selected the option to try and
7466 * compute a schedule for the entire (weakly connected) component first.
7467 * If there is only a single strongly connected component (SCC), then
7468 * there is no point in trying to combine SCCs
7469 * in compute_schedule_wcc_clustering, so compute_schedule_wcc_whole
7470 * is called instead.
7472 static __isl_give isl_schedule_node
*compute_schedule_wcc(
7473 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
7480 ctx
= isl_schedule_node_get_ctx(node
);
7481 if (detect_sccs(ctx
, graph
) < 0)
7482 return isl_schedule_node_free(node
);
7484 if (compute_maxvar(graph
) < 0)
7485 return isl_schedule_node_free(node
);
7487 if (need_feautrier_step(ctx
, graph
))
7488 return compute_schedule_wcc_feautrier(node
, graph
);
7490 if (graph
->scc
<= 1 || isl_options_get_schedule_whole_component(ctx
))
7491 return compute_schedule_wcc_whole(node
, graph
);
7493 return compute_schedule_wcc_clustering(node
, graph
);
7496 /* Compute a schedule for each group of nodes identified by node->scc
7497 * separately and then combine them in a sequence node (or as set node
7498 * if graph->weak is set) inserted at position "node" of the schedule tree.
7499 * Return the updated schedule node.
7501 * If "wcc" is set then each of the groups belongs to a single
7502 * weakly connected component in the dependence graph so that
7503 * there is no need for compute_sub_schedule to look for weakly
7504 * connected components.
7506 * If a set node would be introduced and if the number of components
7507 * is equal to the number of nodes, then check if the schedule
7508 * is already complete. If so, a redundant set node would be introduced
7509 * (without any further descendants) stating that the statements
7510 * can be executed in arbitrary order, which is also expressed
7511 * by the absence of any node. Refrain from inserting any nodes
7512 * in this case and simply return.
7514 static __isl_give isl_schedule_node
*compute_component_schedule(
7515 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
7520 isl_union_set_list
*filters
;
7525 if (graph
->weak
&& graph
->scc
== graph
->n
) {
7526 if (compute_maxvar(graph
) < 0)
7527 return isl_schedule_node_free(node
);
7528 if (graph
->n_row
>= graph
->maxvar
)
7532 ctx
= isl_schedule_node_get_ctx(node
);
7533 filters
= extract_sccs(ctx
, graph
);
7535 node
= isl_schedule_node_insert_set(node
, filters
);
7537 node
= isl_schedule_node_insert_sequence(node
, filters
);
7539 for (component
= 0; component
< graph
->scc
; ++component
) {
7540 node
= isl_schedule_node_child(node
, component
);
7541 node
= isl_schedule_node_child(node
, 0);
7542 node
= compute_sub_schedule(node
, ctx
, graph
,
7544 &edge_scc_exactly
, component
, wcc
);
7545 node
= isl_schedule_node_parent(node
);
7546 node
= isl_schedule_node_parent(node
);
7552 /* Compute a schedule for the given dependence graph and insert it at "node".
7553 * Return the updated schedule node.
7555 * We first check if the graph is connected (through validity and conditional
7556 * validity dependences) and, if not, compute a schedule
7557 * for each component separately.
7558 * If the schedule_serialize_sccs option is set, then we check for strongly
7559 * connected components instead and compute a separate schedule for
7560 * each such strongly connected component.
7562 static __isl_give isl_schedule_node
*compute_schedule(isl_schedule_node
*node
,
7563 struct isl_sched_graph
*graph
)
7570 ctx
= isl_schedule_node_get_ctx(node
);
7571 if (isl_options_get_schedule_serialize_sccs(ctx
)) {
7572 if (detect_sccs(ctx
, graph
) < 0)
7573 return isl_schedule_node_free(node
);
7575 if (detect_wccs(ctx
, graph
) < 0)
7576 return isl_schedule_node_free(node
);
7580 return compute_component_schedule(node
, graph
, 1);
7582 return compute_schedule_wcc(node
, graph
);
7585 /* Compute a schedule on sc->domain that respects the given schedule
7588 * In particular, the schedule respects all the validity dependences.
7589 * If the default isl scheduling algorithm is used, it tries to minimize
7590 * the dependence distances over the proximity dependences.
7591 * If Feautrier's scheduling algorithm is used, the proximity dependence
7592 * distances are only minimized during the extension to a full-dimensional
7595 * If there are any condition and conditional validity dependences,
7596 * then the conditional validity dependences may be violated inside
7597 * a tilable band, provided they have no adjacent non-local
7598 * condition dependences.
7600 __isl_give isl_schedule
*isl_schedule_constraints_compute_schedule(
7601 __isl_take isl_schedule_constraints
*sc
)
7603 isl_ctx
*ctx
= isl_schedule_constraints_get_ctx(sc
);
7604 struct isl_sched_graph graph
= { 0 };
7605 isl_schedule
*sched
;
7606 isl_schedule_node
*node
;
7607 isl_union_set
*domain
;
7610 sc
= isl_schedule_constraints_align_params(sc
);
7612 domain
= isl_schedule_constraints_get_domain(sc
);
7613 n
= isl_union_set_n_set(domain
);
7615 isl_schedule_constraints_free(sc
);
7616 return isl_schedule_from_domain(domain
);
7619 if (n
< 0 || graph_init(&graph
, sc
) < 0)
7620 domain
= isl_union_set_free(domain
);
7622 node
= isl_schedule_node_from_domain(domain
);
7623 node
= isl_schedule_node_child(node
, 0);
7625 node
= compute_schedule(node
, &graph
);
7626 sched
= isl_schedule_node_get_schedule(node
);
7627 isl_schedule_node_free(node
);
7629 graph_free(ctx
, &graph
);
7630 isl_schedule_constraints_free(sc
);
7635 /* Compute a schedule for the given union of domains that respects
7636 * all the validity dependences and minimizes
7637 * the dependence distances over the proximity dependences.
7639 * This function is kept for backward compatibility.
7641 __isl_give isl_schedule
*isl_union_set_compute_schedule(
7642 __isl_take isl_union_set
*domain
,
7643 __isl_take isl_union_map
*validity
,
7644 __isl_take isl_union_map
*proximity
)
7646 isl_schedule_constraints
*sc
;
7648 sc
= isl_schedule_constraints_on_domain(domain
);
7649 sc
= isl_schedule_constraints_set_validity(sc
, validity
);
7650 sc
= isl_schedule_constraints_set_proximity(sc
, proximity
);
7652 return isl_schedule_constraints_compute_schedule(sc
);