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_multi_aff
*decompress
;
124 isl_multi_val
*sizes
;
125 isl_basic_set
*bounds
;
129 static int 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);
440 return entry
? entry
->data
: graph
->node
+ graph
->n
;
443 /* Is "node" a node in "graph"?
445 static int is_node(struct isl_sched_graph
*graph
,
446 struct isl_sched_node
*node
)
448 return node
&& node
>= &graph
->node
[0] && node
< &graph
->node
[graph
->n
];
451 static int edge_has_src_and_dst(const void *entry
, const void *val
)
453 const struct isl_sched_edge
*edge
= entry
;
454 const struct isl_sched_edge
*temp
= val
;
456 return edge
->src
== temp
->src
&& edge
->dst
== temp
->dst
;
459 /* Add the given edge to graph->edge_table[type].
461 static isl_stat
graph_edge_table_add(isl_ctx
*ctx
,
462 struct isl_sched_graph
*graph
, enum isl_edge_type type
,
463 struct isl_sched_edge
*edge
)
465 struct isl_hash_table_entry
*entry
;
468 hash
= isl_hash_init();
469 hash
= isl_hash_builtin(hash
, edge
->src
);
470 hash
= isl_hash_builtin(hash
, edge
->dst
);
471 entry
= isl_hash_table_find(ctx
, graph
->edge_table
[type
], hash
,
472 &edge_has_src_and_dst
, edge
, 1);
474 return isl_stat_error
;
480 /* Add "edge" to all relevant edge tables.
481 * That is, for every type of the edge, add it to the corresponding table.
483 static isl_stat
graph_edge_tables_add(isl_ctx
*ctx
,
484 struct isl_sched_graph
*graph
, struct isl_sched_edge
*edge
)
486 enum isl_edge_type t
;
488 for (t
= isl_edge_first
; t
<= isl_edge_last
; ++t
) {
489 if (!is_type(edge
, t
))
491 if (graph_edge_table_add(ctx
, graph
, t
, edge
) < 0)
492 return isl_stat_error
;
498 /* Allocate the edge_tables based on the maximal number of edges of
501 static int graph_init_edge_tables(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
505 for (i
= 0; i
<= isl_edge_last
; ++i
) {
506 graph
->edge_table
[i
] = isl_hash_table_alloc(ctx
,
508 if (!graph
->edge_table
[i
])
515 /* If graph->edge_table[type] contains an edge from the given source
516 * to the given destination, then return the hash table entry of this edge.
517 * Otherwise, return NULL.
519 static struct isl_hash_table_entry
*graph_find_edge_entry(
520 struct isl_sched_graph
*graph
,
521 enum isl_edge_type type
,
522 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
524 isl_ctx
*ctx
= isl_space_get_ctx(src
->space
);
526 struct isl_sched_edge temp
= { .src
= src
, .dst
= dst
};
528 hash
= isl_hash_init();
529 hash
= isl_hash_builtin(hash
, temp
.src
);
530 hash
= isl_hash_builtin(hash
, temp
.dst
);
531 return isl_hash_table_find(ctx
, graph
->edge_table
[type
], hash
,
532 &edge_has_src_and_dst
, &temp
, 0);
536 /* If graph->edge_table[type] contains an edge from the given source
537 * to the given destination, then return this edge.
538 * Otherwise, return NULL.
540 static struct isl_sched_edge
*graph_find_edge(struct isl_sched_graph
*graph
,
541 enum isl_edge_type type
,
542 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
544 struct isl_hash_table_entry
*entry
;
546 entry
= graph_find_edge_entry(graph
, type
, src
, dst
);
553 /* Check whether the dependence graph has an edge of the given type
554 * between the given two nodes.
556 static isl_bool
graph_has_edge(struct isl_sched_graph
*graph
,
557 enum isl_edge_type type
,
558 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
560 struct isl_sched_edge
*edge
;
563 edge
= graph_find_edge(graph
, type
, src
, dst
);
565 return isl_bool_false
;
567 empty
= isl_map_plain_is_empty(edge
->map
);
569 return isl_bool_not(empty
);
572 /* Look for any edge with the same src, dst and map fields as "model".
574 * Return the matching edge if one can be found.
575 * Return "model" if no matching edge is found.
576 * Return NULL on error.
578 static struct isl_sched_edge
*graph_find_matching_edge(
579 struct isl_sched_graph
*graph
, struct isl_sched_edge
*model
)
581 enum isl_edge_type i
;
582 struct isl_sched_edge
*edge
;
584 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
587 edge
= graph_find_edge(graph
, i
, model
->src
, model
->dst
);
590 is_equal
= isl_map_plain_is_equal(model
->map
, edge
->map
);
600 /* Remove the given edge from all the edge_tables that refer to it.
602 static void graph_remove_edge(struct isl_sched_graph
*graph
,
603 struct isl_sched_edge
*edge
)
605 isl_ctx
*ctx
= isl_map_get_ctx(edge
->map
);
606 enum isl_edge_type i
;
608 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
609 struct isl_hash_table_entry
*entry
;
611 entry
= graph_find_edge_entry(graph
, i
, edge
->src
, edge
->dst
);
614 if (entry
->data
!= edge
)
616 isl_hash_table_remove(ctx
, graph
->edge_table
[i
], entry
);
620 /* Check whether the dependence graph has any edge
621 * between the given two nodes.
623 static isl_bool
graph_has_any_edge(struct isl_sched_graph
*graph
,
624 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
626 enum isl_edge_type i
;
629 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
630 r
= graph_has_edge(graph
, i
, src
, dst
);
638 /* Check whether the dependence graph has a validity edge
639 * between the given two nodes.
641 * Conditional validity edges are essentially validity edges that
642 * can be ignored if the corresponding condition edges are iteration private.
643 * Here, we are only checking for the presence of validity
644 * edges, so we need to consider the conditional validity edges too.
645 * In particular, this function is used during the detection
646 * of strongly connected components and we cannot ignore
647 * conditional validity edges during this detection.
649 static isl_bool
graph_has_validity_edge(struct isl_sched_graph
*graph
,
650 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
654 r
= graph_has_edge(graph
, isl_edge_validity
, src
, dst
);
658 return graph_has_edge(graph
, isl_edge_conditional_validity
, src
, dst
);
661 /* Perform all the required memory allocations for a schedule graph "graph"
662 * with "n_node" nodes and "n_edge" edge and initialize the corresponding
665 static isl_stat
graph_alloc(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
666 int n_node
, int n_edge
)
671 graph
->n_edge
= n_edge
;
672 graph
->node
= isl_calloc_array(ctx
, struct isl_sched_node
, graph
->n
);
673 graph
->sorted
= isl_calloc_array(ctx
, int, graph
->n
);
674 graph
->region
= isl_alloc_array(ctx
,
675 struct isl_trivial_region
, graph
->n
);
676 graph
->edge
= isl_calloc_array(ctx
,
677 struct isl_sched_edge
, graph
->n_edge
);
679 graph
->intra_hmap
= isl_map_to_basic_set_alloc(ctx
, 2 * n_edge
);
680 graph
->intra_hmap_param
= isl_map_to_basic_set_alloc(ctx
, 2 * n_edge
);
681 graph
->inter_hmap
= isl_map_to_basic_set_alloc(ctx
, 2 * n_edge
);
683 if (!graph
->node
|| !graph
->region
|| (graph
->n_edge
&& !graph
->edge
) ||
685 return isl_stat_error
;
687 for(i
= 0; i
< graph
->n
; ++i
)
688 graph
->sorted
[i
] = i
;
693 /* Free the memory associated to node "node" in "graph".
694 * The "coincident" field is shared by nodes in a graph and its subgraph.
695 * It therefore only needs to be freed for the original dependence graph,
696 * i.e., one that is not the result of splitting.
698 static void clear_node(struct isl_sched_graph
*graph
,
699 struct isl_sched_node
*node
)
701 isl_space_free(node
->space
);
702 isl_set_free(node
->hull
);
703 isl_multi_aff_free(node
->compress
);
704 isl_multi_aff_free(node
->decompress
);
705 isl_mat_free(node
->sched
);
706 isl_map_free(node
->sched_map
);
707 isl_mat_free(node
->indep
);
708 isl_mat_free(node
->vmap
);
709 if (graph
->root
== graph
)
710 free(node
->coincident
);
711 isl_multi_val_free(node
->sizes
);
712 isl_basic_set_free(node
->bounds
);
713 isl_vec_free(node
->max
);
716 static void graph_free(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
720 isl_map_to_basic_set_free(graph
->intra_hmap
);
721 isl_map_to_basic_set_free(graph
->intra_hmap_param
);
722 isl_map_to_basic_set_free(graph
->inter_hmap
);
725 for (i
= 0; i
< graph
->n
; ++i
)
726 clear_node(graph
, &graph
->node
[i
]);
730 for (i
= 0; i
< graph
->n_edge
; ++i
) {
731 isl_map_free(graph
->edge
[i
].map
);
732 isl_union_map_free(graph
->edge
[i
].tagged_condition
);
733 isl_union_map_free(graph
->edge
[i
].tagged_validity
);
737 for (i
= 0; i
<= isl_edge_last
; ++i
)
738 isl_hash_table_free(ctx
, graph
->edge_table
[i
]);
739 isl_hash_table_free(ctx
, graph
->node_table
);
740 isl_basic_set_free(graph
->lp
);
743 /* For each "set" on which this function is called, increment
744 * graph->n by one and update graph->maxvar.
746 static isl_stat
init_n_maxvar(__isl_take isl_set
*set
, void *user
)
748 struct isl_sched_graph
*graph
= user
;
749 isl_size nvar
= isl_set_dim(set
, isl_dim_set
);
752 if (nvar
> graph
->maxvar
)
753 graph
->maxvar
= nvar
;
758 return isl_stat_error
;
762 /* Compute the number of rows that should be allocated for the schedule.
763 * In particular, we need one row for each variable or one row
764 * for each basic map in the dependences.
765 * Note that it is practically impossible to exhaust both
766 * the number of dependences and the number of variables.
768 static isl_stat
compute_max_row(struct isl_sched_graph
*graph
,
769 __isl_keep isl_schedule_constraints
*sc
)
773 isl_union_set
*domain
;
777 domain
= isl_schedule_constraints_get_domain(sc
);
778 r
= isl_union_set_foreach_set(domain
, &init_n_maxvar
, graph
);
779 isl_union_set_free(domain
);
781 return isl_stat_error
;
782 n_edge
= isl_schedule_constraints_n_basic_map(sc
);
784 return isl_stat_error
;
785 graph
->max_row
= n_edge
+ graph
->maxvar
;
790 /* Does "bset" have any defining equalities for its set variables?
792 static isl_bool
has_any_defining_equality(__isl_keep isl_basic_set
*bset
)
797 n
= isl_basic_set_dim(bset
, isl_dim_set
);
799 return isl_bool_error
;
801 for (i
= 0; i
< n
; ++i
) {
804 has
= isl_basic_set_has_defining_equality(bset
, isl_dim_set
, i
,
810 return isl_bool_false
;
813 /* Set the entries of node->max to the value of the schedule_max_coefficient
816 static isl_stat
set_max_coefficient(isl_ctx
*ctx
, struct isl_sched_node
*node
)
820 max
= isl_options_get_schedule_max_coefficient(ctx
);
824 node
->max
= isl_vec_alloc(ctx
, node
->nvar
);
825 node
->max
= isl_vec_set_si(node
->max
, max
);
827 return isl_stat_error
;
832 /* Set the entries of node->max to the minimum of the schedule_max_coefficient
833 * option (if set) and half of the minimum of the sizes in the other
834 * dimensions. Round up when computing the half such that
835 * if the minimum of the sizes is one, half of the size is taken to be one
837 * If the global minimum is unbounded (i.e., if both
838 * the schedule_max_coefficient is not set and the sizes in the other
839 * dimensions are unbounded), then store a negative value.
840 * If the schedule coefficient is close to the size of the instance set
841 * in another dimension, then the schedule may represent a loop
842 * coalescing transformation (especially if the coefficient
843 * in that other dimension is one). Forcing the coefficient to be
844 * smaller than or equal to half the minimal size should avoid this
847 static isl_stat
compute_max_coefficient(isl_ctx
*ctx
,
848 struct isl_sched_node
*node
)
854 max
= isl_options_get_schedule_max_coefficient(ctx
);
855 v
= isl_vec_alloc(ctx
, node
->nvar
);
857 return isl_stat_error
;
859 for (i
= 0; i
< node
->nvar
; ++i
) {
860 isl_int_set_si(v
->el
[i
], max
);
861 isl_int_mul_si(v
->el
[i
], v
->el
[i
], 2);
864 for (i
= 0; i
< node
->nvar
; ++i
) {
867 size
= isl_multi_val_get_val(node
->sizes
, i
);
870 if (!isl_val_is_int(size
)) {
874 for (j
= 0; j
< node
->nvar
; ++j
) {
877 if (isl_int_is_neg(v
->el
[j
]) ||
878 isl_int_gt(v
->el
[j
], size
->n
))
879 isl_int_set(v
->el
[j
], size
->n
);
884 for (i
= 0; i
< node
->nvar
; ++i
)
885 isl_int_cdiv_q_ui(v
->el
[i
], v
->el
[i
], 2);
891 return isl_stat_error
;
894 /* Compute and return the size of "set" in dimension "dim".
895 * The size is taken to be the difference in values for that variable
896 * for fixed values of the other variables.
897 * This assumes that "set" is convex.
898 * In particular, the variable is first isolated from the other variables
899 * in the range of a map
901 * [i_0, ..., i_dim-1, i_dim+1, ...] -> [i_dim]
903 * and then duplicated
905 * [i_0, ..., i_dim-1, i_dim+1, ...] -> [[i_dim] -> [i_dim']]
907 * The shared variables are then projected out and the maximal value
908 * of i_dim' - i_dim is computed.
910 static __isl_give isl_val
*compute_size(__isl_take isl_set
*set
, int dim
)
917 map
= isl_set_project_onto_map(set
, isl_dim_set
, dim
, 1);
918 map
= isl_map_project_out(map
, isl_dim_in
, dim
, 1);
919 map
= isl_map_range_product(map
, isl_map_copy(map
));
920 map
= isl_set_unwrap(isl_map_range(map
));
921 set
= isl_map_deltas(map
);
922 ls
= isl_local_space_from_space(isl_set_get_space(set
));
923 obj
= isl_aff_var_on_domain(ls
, isl_dim_set
, 0);
924 v
= isl_set_max_val(set
, obj
);
931 /* Compute the size of the instance set "set" of "node", after compression,
932 * as well as bounds on the corresponding coefficients, if needed.
934 * The sizes are needed when the schedule_treat_coalescing option is set.
935 * The bounds are needed when the schedule_treat_coalescing option or
936 * the schedule_max_coefficient option is set.
938 * If the schedule_treat_coalescing option is not set, then at most
939 * the bounds need to be set and this is done in set_max_coefficient.
940 * Otherwise, compress the domain if needed, compute the size
941 * in each direction and store the results in node->size.
942 * If the domain is not convex, then the sizes are computed
943 * on a convex superset in order to avoid picking up sizes
944 * that are valid for the individual disjuncts, but not for
945 * the domain as a whole.
946 * Finally, set the bounds on the coefficients based on the sizes
947 * and the schedule_max_coefficient option in compute_max_coefficient.
949 static isl_stat
compute_sizes_and_max(isl_ctx
*ctx
, struct isl_sched_node
*node
,
950 __isl_take isl_set
*set
)
956 if (!isl_options_get_schedule_treat_coalescing(ctx
)) {
958 return set_max_coefficient(ctx
, node
);
961 if (node
->compressed
)
962 set
= isl_set_preimage_multi_aff(set
,
963 isl_multi_aff_copy(node
->decompress
));
964 set
= isl_set_from_basic_set(isl_set_simple_hull(set
));
965 mv
= isl_multi_val_zero(isl_set_get_space(set
));
966 n
= isl_set_dim(set
, isl_dim_set
);
968 mv
= isl_multi_val_free(mv
);
969 for (j
= 0; j
< n
; ++j
) {
972 v
= compute_size(isl_set_copy(set
), j
);
973 mv
= isl_multi_val_set_val(mv
, j
, v
);
978 return isl_stat_error
;
979 return compute_max_coefficient(ctx
, node
);
982 /* Add a new node to the graph representing the given instance set.
983 * "nvar" is the (possibly compressed) number of variables and
984 * may be smaller than then number of set variables in "set"
985 * if "compressed" is set.
986 * If "compressed" is set, then "hull" represents the constraints
987 * that were used to derive the compression, while "compress" and
988 * "decompress" map the original space to the compressed space and
990 * If "compressed" is not set, then "hull", "compress" and "decompress"
993 * Compute the size of the instance set and bounds on the coefficients,
996 static isl_stat
add_node(struct isl_sched_graph
*graph
,
997 __isl_take isl_set
*set
, int nvar
, int compressed
,
998 __isl_take isl_set
*hull
, __isl_take isl_multi_aff
*compress
,
999 __isl_take isl_multi_aff
*decompress
)
1006 struct isl_sched_node
*node
;
1008 nparam
= isl_set_dim(set
, isl_dim_param
);
1012 ctx
= isl_set_get_ctx(set
);
1013 if (!ctx
->opt
->schedule_parametric
)
1015 sched
= isl_mat_alloc(ctx
, 0, 1 + nparam
+ nvar
);
1016 node
= &graph
->node
[graph
->n
];
1018 space
= isl_set_get_space(set
);
1019 node
->space
= space
;
1021 node
->nparam
= nparam
;
1022 node
->sched
= sched
;
1023 node
->sched_map
= NULL
;
1024 coincident
= isl_calloc_array(ctx
, int, graph
->max_row
);
1025 node
->coincident
= coincident
;
1026 node
->compressed
= compressed
;
1028 node
->compress
= compress
;
1029 node
->decompress
= decompress
;
1030 if (compute_sizes_and_max(ctx
, node
, set
) < 0)
1031 return isl_stat_error
;
1033 if (!space
|| !sched
|| (graph
->max_row
&& !coincident
))
1034 return isl_stat_error
;
1035 if (compressed
&& (!hull
|| !compress
|| !decompress
))
1036 return isl_stat_error
;
1042 isl_multi_aff_free(compress
);
1043 isl_multi_aff_free(decompress
);
1044 return isl_stat_error
;
1047 /* Construct an identifier for node "node", which will represent "set".
1048 * The name of the identifier is either "compressed" or
1049 * "compressed_<name>", with <name> the name of the space of "set".
1050 * The user pointer of the identifier points to "node".
1052 static __isl_give isl_id
*construct_compressed_id(__isl_keep isl_set
*set
,
1053 struct isl_sched_node
*node
)
1062 has_name
= isl_set_has_tuple_name(set
);
1066 ctx
= isl_set_get_ctx(set
);
1068 return isl_id_alloc(ctx
, "compressed", node
);
1070 p
= isl_printer_to_str(ctx
);
1071 name
= isl_set_get_tuple_name(set
);
1072 p
= isl_printer_print_str(p
, "compressed_");
1073 p
= isl_printer_print_str(p
, name
);
1074 id_name
= isl_printer_get_str(p
);
1075 isl_printer_free(p
);
1077 id
= isl_id_alloc(ctx
, id_name
, node
);
1083 /* Add a new node to the graph representing the given set.
1085 * If any of the set variables is defined by an equality, then
1086 * we perform variable compression such that we can perform
1087 * the scheduling on the compressed domain.
1088 * In this case, an identifier is used that references the new node
1089 * such that each compressed space is unique and
1090 * such that the node can be recovered from the compressed space.
1092 static isl_stat
extract_node(__isl_take isl_set
*set
, void *user
)
1095 isl_bool has_equality
;
1097 isl_basic_set
*hull
;
1100 isl_multi_aff
*compress
, *decompress
;
1101 struct isl_sched_graph
*graph
= user
;
1103 hull
= isl_set_affine_hull(isl_set_copy(set
));
1104 hull
= isl_basic_set_remove_divs(hull
);
1105 nvar
= isl_set_dim(set
, isl_dim_set
);
1106 has_equality
= has_any_defining_equality(hull
);
1108 if (nvar
< 0 || has_equality
< 0)
1110 if (!has_equality
) {
1111 isl_basic_set_free(hull
);
1112 return add_node(graph
, set
, nvar
, 0, NULL
, NULL
, NULL
);
1115 id
= construct_compressed_id(set
, &graph
->node
[graph
->n
]);
1116 morph
= isl_basic_set_variable_compression_with_id(hull
, id
);
1118 nvar
= isl_morph_ran_dim(morph
, isl_dim_set
);
1120 set
= isl_set_free(set
);
1121 compress
= isl_morph_get_var_multi_aff(morph
);
1122 morph
= isl_morph_inverse(morph
);
1123 decompress
= isl_morph_get_var_multi_aff(morph
);
1124 isl_morph_free(morph
);
1126 hull_set
= isl_set_from_basic_set(hull
);
1127 return add_node(graph
, set
, nvar
, 1, hull_set
, compress
, decompress
);
1129 isl_basic_set_free(hull
);
1131 return isl_stat_error
;
1134 struct isl_extract_edge_data
{
1135 enum isl_edge_type type
;
1136 struct isl_sched_graph
*graph
;
1139 /* Merge edge2 into edge1, freeing the contents of edge2.
1140 * Return 0 on success and -1 on failure.
1142 * edge1 and edge2 are assumed to have the same value for the map field.
1144 static int merge_edge(struct isl_sched_edge
*edge1
,
1145 struct isl_sched_edge
*edge2
)
1147 edge1
->types
|= edge2
->types
;
1148 isl_map_free(edge2
->map
);
1150 if (is_condition(edge2
)) {
1151 if (!edge1
->tagged_condition
)
1152 edge1
->tagged_condition
= edge2
->tagged_condition
;
1154 edge1
->tagged_condition
=
1155 isl_union_map_union(edge1
->tagged_condition
,
1156 edge2
->tagged_condition
);
1159 if (is_conditional_validity(edge2
)) {
1160 if (!edge1
->tagged_validity
)
1161 edge1
->tagged_validity
= edge2
->tagged_validity
;
1163 edge1
->tagged_validity
=
1164 isl_union_map_union(edge1
->tagged_validity
,
1165 edge2
->tagged_validity
);
1168 if (is_condition(edge2
) && !edge1
->tagged_condition
)
1170 if (is_conditional_validity(edge2
) && !edge1
->tagged_validity
)
1176 /* Insert dummy tags in domain and range of "map".
1178 * In particular, if "map" is of the form
1184 * [A -> dummy_tag] -> [B -> dummy_tag]
1186 * where the dummy_tags are identical and equal to any dummy tags
1187 * introduced by any other call to this function.
1189 static __isl_give isl_map
*insert_dummy_tags(__isl_take isl_map
*map
)
1195 isl_set
*domain
, *range
;
1197 ctx
= isl_map_get_ctx(map
);
1199 id
= isl_id_alloc(ctx
, NULL
, &dummy
);
1200 space
= isl_space_params(isl_map_get_space(map
));
1201 space
= isl_space_set_from_params(space
);
1202 space
= isl_space_set_tuple_id(space
, isl_dim_set
, id
);
1203 space
= isl_space_map_from_set(space
);
1205 domain
= isl_map_wrap(map
);
1206 range
= isl_map_wrap(isl_map_universe(space
));
1207 map
= isl_map_from_domain_and_range(domain
, range
);
1208 map
= isl_map_zip(map
);
1213 /* Given that at least one of "src" or "dst" is compressed, return
1214 * a map between the spaces of these nodes restricted to the affine
1215 * hull that was used in the compression.
1217 static __isl_give isl_map
*extract_hull(struct isl_sched_node
*src
,
1218 struct isl_sched_node
*dst
)
1222 if (src
->compressed
)
1223 dom
= isl_set_copy(src
->hull
);
1225 dom
= isl_set_universe(isl_space_copy(src
->space
));
1226 if (dst
->compressed
)
1227 ran
= isl_set_copy(dst
->hull
);
1229 ran
= isl_set_universe(isl_space_copy(dst
->space
));
1231 return isl_map_from_domain_and_range(dom
, ran
);
1234 /* Intersect the domains of the nested relations in domain and range
1235 * of "tagged" with "map".
1237 static __isl_give isl_map
*map_intersect_domains(__isl_take isl_map
*tagged
,
1238 __isl_keep isl_map
*map
)
1242 tagged
= isl_map_zip(tagged
);
1243 set
= isl_map_wrap(isl_map_copy(map
));
1244 tagged
= isl_map_intersect_domain(tagged
, set
);
1245 tagged
= isl_map_zip(tagged
);
1249 /* Return a pointer to the node that lives in the domain space of "map",
1250 * an invalid node if there is no such node, or NULL in case of error.
1252 static struct isl_sched_node
*find_domain_node(isl_ctx
*ctx
,
1253 struct isl_sched_graph
*graph
, __isl_keep isl_map
*map
)
1255 struct isl_sched_node
*node
;
1258 space
= isl_space_domain(isl_map_get_space(map
));
1259 node
= graph_find_node(ctx
, graph
, space
);
1260 isl_space_free(space
);
1265 /* Return a pointer to the node that lives in the range space of "map",
1266 * an invalid node if there is no such node, or NULL in case of error.
1268 static struct isl_sched_node
*find_range_node(isl_ctx
*ctx
,
1269 struct isl_sched_graph
*graph
, __isl_keep isl_map
*map
)
1271 struct isl_sched_node
*node
;
1274 space
= isl_space_range(isl_map_get_space(map
));
1275 node
= graph_find_node(ctx
, graph
, space
);
1276 isl_space_free(space
);
1281 /* Refrain from adding a new edge based on "map".
1282 * Instead, just free the map.
1283 * "tagged" is either a copy of "map" with additional tags or NULL.
1285 static isl_stat
skip_edge(__isl_take isl_map
*map
, __isl_take isl_map
*tagged
)
1288 isl_map_free(tagged
);
1293 /* Add a new edge to the graph based on the given map
1294 * and add it to data->graph->edge_table[data->type].
1295 * If a dependence relation of a given type happens to be identical
1296 * to one of the dependence relations of a type that was added before,
1297 * then we don't create a new edge, but instead mark the original edge
1298 * as also representing a dependence of the current type.
1300 * Edges of type isl_edge_condition or isl_edge_conditional_validity
1301 * may be specified as "tagged" dependence relations. That is, "map"
1302 * may contain elements (i -> a) -> (j -> b), where i -> j denotes
1303 * the dependence on iterations and a and b are tags.
1304 * edge->map is set to the relation containing the elements i -> j,
1305 * while edge->tagged_condition and edge->tagged_validity contain
1306 * the union of all the "map" relations
1307 * for which extract_edge is called that result in the same edge->map.
1309 * If the source or the destination node is compressed, then
1310 * intersect both "map" and "tagged" with the constraints that
1311 * were used to construct the compression.
1312 * This ensures that there are no schedule constraints defined
1313 * outside of these domains, while the scheduler no longer has
1314 * any control over those outside parts.
1316 static isl_stat
extract_edge(__isl_take isl_map
*map
, void *user
)
1319 isl_ctx
*ctx
= isl_map_get_ctx(map
);
1320 struct isl_extract_edge_data
*data
= user
;
1321 struct isl_sched_graph
*graph
= data
->graph
;
1322 struct isl_sched_node
*src
, *dst
;
1323 struct isl_sched_edge
*edge
;
1324 isl_map
*tagged
= NULL
;
1326 if (data
->type
== isl_edge_condition
||
1327 data
->type
== isl_edge_conditional_validity
) {
1328 if (isl_map_can_zip(map
)) {
1329 tagged
= isl_map_copy(map
);
1330 map
= isl_set_unwrap(isl_map_domain(isl_map_zip(map
)));
1332 tagged
= insert_dummy_tags(isl_map_copy(map
));
1336 src
= find_domain_node(ctx
, graph
, map
);
1337 dst
= find_range_node(ctx
, graph
, map
);
1341 if (!is_node(graph
, src
) || !is_node(graph
, dst
))
1342 return skip_edge(map
, tagged
);
1344 if (src
->compressed
|| dst
->compressed
) {
1346 hull
= extract_hull(src
, dst
);
1348 tagged
= map_intersect_domains(tagged
, hull
);
1349 map
= isl_map_intersect(map
, hull
);
1352 empty
= isl_map_plain_is_empty(map
);
1356 return skip_edge(map
, tagged
);
1358 graph
->edge
[graph
->n_edge
].src
= src
;
1359 graph
->edge
[graph
->n_edge
].dst
= dst
;
1360 graph
->edge
[graph
->n_edge
].map
= map
;
1361 graph
->edge
[graph
->n_edge
].types
= 0;
1362 graph
->edge
[graph
->n_edge
].tagged_condition
= NULL
;
1363 graph
->edge
[graph
->n_edge
].tagged_validity
= NULL
;
1364 set_type(&graph
->edge
[graph
->n_edge
], data
->type
);
1365 if (data
->type
== isl_edge_condition
)
1366 graph
->edge
[graph
->n_edge
].tagged_condition
=
1367 isl_union_map_from_map(tagged
);
1368 if (data
->type
== isl_edge_conditional_validity
)
1369 graph
->edge
[graph
->n_edge
].tagged_validity
=
1370 isl_union_map_from_map(tagged
);
1372 edge
= graph_find_matching_edge(graph
, &graph
->edge
[graph
->n_edge
]);
1375 return isl_stat_error
;
1377 if (edge
== &graph
->edge
[graph
->n_edge
])
1378 return graph_edge_table_add(ctx
, graph
, data
->type
,
1379 &graph
->edge
[graph
->n_edge
++]);
1381 if (merge_edge(edge
, &graph
->edge
[graph
->n_edge
]) < 0)
1382 return isl_stat_error
;
1384 return graph_edge_table_add(ctx
, graph
, data
->type
, edge
);
1387 isl_map_free(tagged
);
1388 return isl_stat_error
;
1391 /* Initialize the schedule graph "graph" from the schedule constraints "sc".
1393 * The context is included in the domain before the nodes of
1394 * the graphs are extracted in order to be able to exploit
1395 * any possible additional equalities.
1396 * Note that this intersection is only performed locally here.
1398 static isl_stat
graph_init(struct isl_sched_graph
*graph
,
1399 __isl_keep isl_schedule_constraints
*sc
)
1402 isl_union_set
*domain
;
1404 struct isl_extract_edge_data data
;
1405 enum isl_edge_type i
;
1410 return isl_stat_error
;
1412 ctx
= isl_schedule_constraints_get_ctx(sc
);
1414 domain
= isl_schedule_constraints_get_domain(sc
);
1415 n
= isl_union_set_n_set(domain
);
1417 isl_union_set_free(domain
);
1419 return isl_stat_error
;
1421 n
= isl_schedule_constraints_n_map(sc
);
1422 if (n
< 0 || graph_alloc(ctx
, graph
, graph
->n
, n
) < 0)
1423 return isl_stat_error
;
1425 if (compute_max_row(graph
, sc
) < 0)
1426 return isl_stat_error
;
1427 graph
->root
= graph
;
1429 domain
= isl_schedule_constraints_get_domain(sc
);
1430 domain
= isl_union_set_intersect_params(domain
,
1431 isl_schedule_constraints_get_context(sc
));
1432 r
= isl_union_set_foreach_set(domain
, &extract_node
, graph
);
1433 isl_union_set_free(domain
);
1435 return isl_stat_error
;
1436 if (graph_init_table(ctx
, graph
) < 0)
1437 return isl_stat_error
;
1438 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
1441 c
= isl_schedule_constraints_get(sc
, i
);
1442 n
= isl_union_map_n_map(c
);
1443 graph
->max_edge
[i
] = n
;
1444 isl_union_map_free(c
);
1446 return isl_stat_error
;
1448 if (graph_init_edge_tables(ctx
, graph
) < 0)
1449 return isl_stat_error
;
1452 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
1456 c
= isl_schedule_constraints_get(sc
, i
);
1457 r
= isl_union_map_foreach_map(c
, &extract_edge
, &data
);
1458 isl_union_map_free(c
);
1460 return isl_stat_error
;
1466 /* Check whether there is any dependence from node[j] to node[i]
1467 * or from node[i] to node[j].
1469 static isl_bool
node_follows_weak(int i
, int j
, void *user
)
1472 struct isl_sched_graph
*graph
= user
;
1474 f
= graph_has_any_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
1477 return graph_has_any_edge(graph
, &graph
->node
[i
], &graph
->node
[j
]);
1480 /* Check whether there is a (conditional) validity dependence from node[j]
1481 * to node[i], forcing node[i] to follow node[j].
1483 static isl_bool
node_follows_strong(int i
, int j
, void *user
)
1485 struct isl_sched_graph
*graph
= user
;
1487 return graph_has_validity_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
1490 /* Use Tarjan's algorithm for computing the strongly connected components
1491 * in the dependence graph only considering those edges defined by "follows".
1493 static isl_stat
detect_ccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
1494 isl_bool (*follows
)(int i
, int j
, void *user
))
1497 struct isl_tarjan_graph
*g
= NULL
;
1499 g
= isl_tarjan_graph_init(ctx
, graph
->n
, follows
, graph
);
1501 return isl_stat_error
;
1507 while (g
->order
[i
] != -1) {
1508 graph
->node
[g
->order
[i
]].scc
= graph
->scc
;
1516 isl_tarjan_graph_free(g
);
1521 /* Apply Tarjan's algorithm to detect the strongly connected components
1522 * in the dependence graph.
1523 * Only consider the (conditional) validity dependences and clear "weak".
1525 static isl_stat
detect_sccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
1528 return detect_ccs(ctx
, graph
, &node_follows_strong
);
1531 /* Apply Tarjan's algorithm to detect the (weakly) connected components
1532 * in the dependence graph.
1533 * Consider all dependences and set "weak".
1535 static isl_stat
detect_wccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
1538 return detect_ccs(ctx
, graph
, &node_follows_weak
);
1541 static int cmp_scc(const void *a
, const void *b
, void *data
)
1543 struct isl_sched_graph
*graph
= data
;
1547 return graph
->node
[*i1
].scc
- graph
->node
[*i2
].scc
;
1550 /* Sort the elements of graph->sorted according to the corresponding SCCs.
1552 static int sort_sccs(struct isl_sched_graph
*graph
)
1554 return isl_sort(graph
->sorted
, graph
->n
, sizeof(int), &cmp_scc
, graph
);
1557 /* Return a non-parametric set in the compressed space of "node" that is
1558 * bounded by the size in each direction
1560 * { [x] : -S_i <= x_i <= S_i }
1562 * If S_i is infinity in direction i, then there are no constraints
1563 * in that direction.
1565 * Cache the result in node->bounds.
1567 static __isl_give isl_basic_set
*get_size_bounds(struct isl_sched_node
*node
)
1570 isl_basic_set
*bounds
;
1574 return isl_basic_set_copy(node
->bounds
);
1576 if (node
->compressed
)
1577 space
= isl_multi_aff_get_domain_space(node
->decompress
);
1579 space
= isl_space_copy(node
->space
);
1580 space
= isl_space_drop_all_params(space
);
1581 bounds
= isl_basic_set_universe(space
);
1583 for (i
= 0; i
< node
->nvar
; ++i
) {
1586 size
= isl_multi_val_get_val(node
->sizes
, i
);
1588 return isl_basic_set_free(bounds
);
1589 if (!isl_val_is_int(size
)) {
1593 bounds
= isl_basic_set_upper_bound_val(bounds
, isl_dim_set
, i
,
1594 isl_val_copy(size
));
1595 bounds
= isl_basic_set_lower_bound_val(bounds
, isl_dim_set
, i
,
1599 node
->bounds
= isl_basic_set_copy(bounds
);
1603 /* Drop some constraints from "delta" that could be exploited
1604 * to construct loop coalescing schedules.
1605 * In particular, drop those constraint that bound the difference
1606 * to the size of the domain.
1607 * First project out the parameters to improve the effectiveness.
1609 static __isl_give isl_set
*drop_coalescing_constraints(
1610 __isl_take isl_set
*delta
, struct isl_sched_node
*node
)
1613 isl_basic_set
*bounds
;
1615 nparam
= isl_set_dim(delta
, isl_dim_param
);
1617 return isl_set_free(delta
);
1619 bounds
= get_size_bounds(node
);
1621 delta
= isl_set_project_out(delta
, isl_dim_param
, 0, nparam
);
1622 delta
= isl_set_remove_divs(delta
);
1623 delta
= isl_set_plain_gist_basic_set(delta
, bounds
);
1627 /* Given a dependence relation R from "node" to itself,
1628 * construct the set of coefficients of valid constraints for elements
1629 * in that dependence relation.
1630 * In particular, the result contains tuples of coefficients
1631 * c_0, c_n, c_x such that
1633 * c_0 + c_n n + c_x y - c_x x >= 0 for each (x,y) in R
1637 * c_0 + c_n n + c_x d >= 0 for each d in delta R = { y - x | (x,y) in R }
1639 * We choose here to compute the dual of delta R.
1640 * Alternatively, we could have computed the dual of R, resulting
1641 * in a set of tuples c_0, c_n, c_x, c_y, and then
1642 * plugged in (c_0, c_n, c_x, -c_x).
1644 * If "need_param" is set, then the resulting coefficients effectively
1645 * include coefficients for the parameters c_n. Otherwise, they may
1646 * have been projected out already.
1647 * Since the constraints may be different for these two cases,
1648 * they are stored in separate caches.
1649 * In particular, if no parameter coefficients are required and
1650 * the schedule_treat_coalescing option is set, then the parameters
1651 * are projected out and some constraints that could be exploited
1652 * to construct coalescing schedules are removed before the dual
1655 * If "node" has been compressed, then the dependence relation
1656 * is also compressed before the set of coefficients is computed.
1658 static __isl_give isl_basic_set
*intra_coefficients(
1659 struct isl_sched_graph
*graph
, struct isl_sched_node
*node
,
1660 __isl_take isl_map
*map
, int need_param
)
1665 isl_basic_set
*coef
;
1666 isl_maybe_isl_basic_set m
;
1667 isl_map_to_basic_set
**hmap
= &graph
->intra_hmap
;
1673 ctx
= isl_map_get_ctx(map
);
1674 treat
= !need_param
&& isl_options_get_schedule_treat_coalescing(ctx
);
1676 hmap
= &graph
->intra_hmap_param
;
1677 m
= isl_map_to_basic_set_try_get(*hmap
, map
);
1678 if (m
.valid
< 0 || m
.valid
) {
1683 key
= isl_map_copy(map
);
1684 if (node
->compressed
) {
1685 map
= isl_map_preimage_domain_multi_aff(map
,
1686 isl_multi_aff_copy(node
->decompress
));
1687 map
= isl_map_preimage_range_multi_aff(map
,
1688 isl_multi_aff_copy(node
->decompress
));
1690 delta
= isl_map_deltas(map
);
1692 delta
= drop_coalescing_constraints(delta
, node
);
1693 delta
= isl_set_remove_divs(delta
);
1694 coef
= isl_set_coefficients(delta
);
1695 *hmap
= isl_map_to_basic_set_set(*hmap
, key
, isl_basic_set_copy(coef
));
1700 /* Given a dependence relation R, construct the set of coefficients
1701 * of valid constraints for elements in that dependence relation.
1702 * In particular, the result contains tuples of coefficients
1703 * c_0, c_n, c_x, c_y such that
1705 * c_0 + c_n n + c_x x + c_y y >= 0 for each (x,y) in R
1707 * If the source or destination nodes of "edge" have been compressed,
1708 * then the dependence relation is also compressed before
1709 * the set of coefficients is computed.
1711 static __isl_give isl_basic_set
*inter_coefficients(
1712 struct isl_sched_graph
*graph
, struct isl_sched_edge
*edge
,
1713 __isl_take isl_map
*map
)
1717 isl_basic_set
*coef
;
1718 isl_maybe_isl_basic_set m
;
1720 m
= isl_map_to_basic_set_try_get(graph
->inter_hmap
, map
);
1721 if (m
.valid
< 0 || m
.valid
) {
1726 key
= isl_map_copy(map
);
1727 if (edge
->src
->compressed
)
1728 map
= isl_map_preimage_domain_multi_aff(map
,
1729 isl_multi_aff_copy(edge
->src
->decompress
));
1730 if (edge
->dst
->compressed
)
1731 map
= isl_map_preimage_range_multi_aff(map
,
1732 isl_multi_aff_copy(edge
->dst
->decompress
));
1733 set
= isl_map_wrap(isl_map_remove_divs(map
));
1734 coef
= isl_set_coefficients(set
);
1735 graph
->inter_hmap
= isl_map_to_basic_set_set(graph
->inter_hmap
, key
,
1736 isl_basic_set_copy(coef
));
1741 /* Return the position of the coefficients of the variables in
1742 * the coefficients constraints "coef".
1744 * The space of "coef" is of the form
1746 * { coefficients[[cst, params] -> S] }
1748 * Return the position of S.
1750 static isl_size
coef_var_offset(__isl_keep isl_basic_set
*coef
)
1755 space
= isl_space_unwrap(isl_basic_set_get_space(coef
));
1756 offset
= isl_space_dim(space
, isl_dim_in
);
1757 isl_space_free(space
);
1762 /* Return the offset of the coefficient of the constant term of "node"
1765 * Within each node, the coefficients have the following order:
1766 * - positive and negative parts of c_i_x
1767 * - c_i_n (if parametric)
1770 static int node_cst_coef_offset(struct isl_sched_node
*node
)
1772 return node
->start
+ 2 * node
->nvar
+ node
->nparam
;
1775 /* Return the offset of the coefficients of the parameters of "node"
1778 * Within each node, the coefficients have the following order:
1779 * - positive and negative parts of c_i_x
1780 * - c_i_n (if parametric)
1783 static int node_par_coef_offset(struct isl_sched_node
*node
)
1785 return node
->start
+ 2 * node
->nvar
;
1788 /* Return the offset of the coefficients of the variables of "node"
1791 * Within each node, the coefficients have the following order:
1792 * - positive and negative parts of c_i_x
1793 * - c_i_n (if parametric)
1796 static int node_var_coef_offset(struct isl_sched_node
*node
)
1801 /* Return the position of the pair of variables encoding
1802 * coefficient "i" of "node".
1804 * The order of these variable pairs is the opposite of
1805 * that of the coefficients, with 2 variables per coefficient.
1807 static int node_var_coef_pos(struct isl_sched_node
*node
, int i
)
1809 return node_var_coef_offset(node
) + 2 * (node
->nvar
- 1 - i
);
1812 /* Construct an isl_dim_map for mapping constraints on coefficients
1813 * for "node" to the corresponding positions in graph->lp.
1814 * "offset" is the offset of the coefficients for the variables
1815 * in the input constraints.
1816 * "s" is the sign of the mapping.
1818 * The input constraints are given in terms of the coefficients
1819 * (c_0, c_x) or (c_0, c_n, c_x).
1820 * The mapping produced by this function essentially plugs in
1821 * (0, c_i_x^+ - c_i_x^-) if s = 1 and
1822 * (0, -c_i_x^+ + c_i_x^-) if s = -1 or
1823 * (0, 0, c_i_x^+ - c_i_x^-) if s = 1 and
1824 * (0, 0, -c_i_x^+ + c_i_x^-) if s = -1.
1825 * In graph->lp, the c_i_x^- appear before their c_i_x^+ counterpart.
1826 * Furthermore, the order of these pairs is the opposite of that
1827 * of the corresponding coefficients.
1829 * The caller can extend the mapping to also map the other coefficients
1830 * (and therefore not plug in 0).
1832 static __isl_give isl_dim_map
*intra_dim_map(isl_ctx
*ctx
,
1833 struct isl_sched_graph
*graph
, struct isl_sched_node
*node
,
1838 isl_dim_map
*dim_map
;
1840 total
= isl_basic_set_dim(graph
->lp
, isl_dim_all
);
1841 if (!node
|| total
< 0)
1844 pos
= node_var_coef_pos(node
, 0);
1845 dim_map
= isl_dim_map_alloc(ctx
, total
);
1846 isl_dim_map_range(dim_map
, pos
, -2, offset
, 1, node
->nvar
, -s
);
1847 isl_dim_map_range(dim_map
, pos
+ 1, -2, offset
, 1, node
->nvar
, s
);
1852 /* Construct an isl_dim_map for mapping constraints on coefficients
1853 * for "src" (node i) and "dst" (node j) to the corresponding positions
1855 * "offset" is the offset of the coefficients for the variables of "src"
1856 * in the input constraints.
1857 * "s" is the sign of the mapping.
1859 * The input constraints are given in terms of the coefficients
1860 * (c_0, c_n, c_x, c_y).
1861 * The mapping produced by this function essentially plugs in
1862 * (c_j_0 - c_i_0, c_j_n - c_i_n,
1863 * -(c_i_x^+ - c_i_x^-), c_j_x^+ - c_j_x^-) if s = 1 and
1864 * (-c_j_0 + c_i_0, -c_j_n + c_i_n,
1865 * c_i_x^+ - c_i_x^-, -(c_j_x^+ - c_j_x^-)) if s = -1.
1866 * In graph->lp, the c_*^- appear before their c_*^+ counterpart.
1867 * Furthermore, the order of these pairs is the opposite of that
1868 * of the corresponding coefficients.
1870 * The caller can further extend the mapping.
1872 static __isl_give isl_dim_map
*inter_dim_map(isl_ctx
*ctx
,
1873 struct isl_sched_graph
*graph
, struct isl_sched_node
*src
,
1874 struct isl_sched_node
*dst
, int offset
, int s
)
1878 isl_dim_map
*dim_map
;
1880 total
= isl_basic_set_dim(graph
->lp
, isl_dim_all
);
1881 if (!src
|| !dst
|| total
< 0)
1884 dim_map
= isl_dim_map_alloc(ctx
, total
);
1886 pos
= node_cst_coef_offset(dst
);
1887 isl_dim_map_range(dim_map
, pos
, 0, 0, 0, 1, s
);
1888 pos
= node_par_coef_offset(dst
);
1889 isl_dim_map_range(dim_map
, pos
, 1, 1, 1, dst
->nparam
, s
);
1890 pos
= node_var_coef_pos(dst
, 0);
1891 isl_dim_map_range(dim_map
, pos
, -2, offset
+ src
->nvar
, 1,
1893 isl_dim_map_range(dim_map
, pos
+ 1, -2, offset
+ src
->nvar
, 1,
1896 pos
= node_cst_coef_offset(src
);
1897 isl_dim_map_range(dim_map
, pos
, 0, 0, 0, 1, -s
);
1898 pos
= node_par_coef_offset(src
);
1899 isl_dim_map_range(dim_map
, pos
, 1, 1, 1, src
->nparam
, -s
);
1900 pos
= node_var_coef_pos(src
, 0);
1901 isl_dim_map_range(dim_map
, pos
, -2, offset
, 1, src
->nvar
, s
);
1902 isl_dim_map_range(dim_map
, pos
+ 1, -2, offset
, 1, src
->nvar
, -s
);
1907 /* Add the constraints from "src" to "dst" using "dim_map",
1908 * after making sure there is enough room in "dst" for the extra constraints.
1910 static __isl_give isl_basic_set
*add_constraints_dim_map(
1911 __isl_take isl_basic_set
*dst
, __isl_take isl_basic_set
*src
,
1912 __isl_take isl_dim_map
*dim_map
)
1916 n_eq
= isl_basic_set_n_equality(src
);
1917 n_ineq
= isl_basic_set_n_inequality(src
);
1918 dst
= isl_basic_set_extend_constraints(dst
, n_eq
, n_ineq
);
1919 dst
= isl_basic_set_add_constraints_dim_map(dst
, src
, dim_map
);
1923 /* Add constraints to graph->lp that force validity for the given
1924 * dependence from a node i to itself.
1925 * That is, add constraints that enforce
1927 * (c_i_0 + c_i_n n + c_i_x y) - (c_i_0 + c_i_n n + c_i_x x)
1928 * = c_i_x (y - x) >= 0
1930 * for each (x,y) in R.
1931 * We obtain general constraints on coefficients (c_0, c_x)
1932 * of valid constraints for (y - x) and then plug in (0, c_i_x^+ - c_i_x^-),
1933 * where c_i_x = c_i_x^+ - c_i_x^-, with c_i_x^+ and c_i_x^- non-negative.
1934 * In graph->lp, the c_i_x^- appear before their c_i_x^+ counterpart.
1935 * Note that the result of intra_coefficients may also contain
1936 * parameter coefficients c_n, in which case 0 is plugged in for them as well.
1938 static isl_stat
add_intra_validity_constraints(struct isl_sched_graph
*graph
,
1939 struct isl_sched_edge
*edge
)
1942 isl_map
*map
= isl_map_copy(edge
->map
);
1943 isl_ctx
*ctx
= isl_map_get_ctx(map
);
1944 isl_dim_map
*dim_map
;
1945 isl_basic_set
*coef
;
1946 struct isl_sched_node
*node
= edge
->src
;
1948 coef
= intra_coefficients(graph
, node
, map
, 0);
1950 offset
= coef_var_offset(coef
);
1952 coef
= isl_basic_set_free(coef
);
1954 return isl_stat_error
;
1956 dim_map
= intra_dim_map(ctx
, graph
, node
, offset
, 1);
1957 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
1962 /* Add constraints to graph->lp that force validity for the given
1963 * dependence from node i to node j.
1964 * That is, add constraints that enforce
1966 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) >= 0
1968 * for each (x,y) in R.
1969 * We obtain general constraints on coefficients (c_0, c_n, c_x, c_y)
1970 * of valid constraints for R and then plug in
1971 * (c_j_0 - c_i_0, c_j_n - c_i_n, -(c_i_x^+ - c_i_x^-), c_j_x^+ - c_j_x^-),
1972 * where c_* = c_*^+ - c_*^-, with c_*^+ and c_*^- non-negative.
1973 * In graph->lp, the c_*^- appear before their c_*^+ counterpart.
1975 static isl_stat
add_inter_validity_constraints(struct isl_sched_graph
*graph
,
1976 struct isl_sched_edge
*edge
)
1981 isl_dim_map
*dim_map
;
1982 isl_basic_set
*coef
;
1983 struct isl_sched_node
*src
= edge
->src
;
1984 struct isl_sched_node
*dst
= edge
->dst
;
1987 return isl_stat_error
;
1989 map
= isl_map_copy(edge
->map
);
1990 ctx
= isl_map_get_ctx(map
);
1991 coef
= inter_coefficients(graph
, edge
, map
);
1993 offset
= coef_var_offset(coef
);
1995 coef
= isl_basic_set_free(coef
);
1997 return isl_stat_error
;
1999 dim_map
= inter_dim_map(ctx
, graph
, src
, dst
, offset
, 1);
2001 edge
->start
= graph
->lp
->n_ineq
;
2002 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
2004 return isl_stat_error
;
2005 edge
->end
= graph
->lp
->n_ineq
;
2010 /* Add constraints to graph->lp that bound the dependence distance for the given
2011 * dependence from a node i to itself.
2012 * If s = 1, we add the constraint
2014 * c_i_x (y - x) <= m_0 + m_n n
2018 * -c_i_x (y - x) + m_0 + m_n n >= 0
2020 * for each (x,y) in R.
2021 * If s = -1, we add the constraint
2023 * -c_i_x (y - x) <= m_0 + m_n n
2027 * c_i_x (y - x) + m_0 + m_n n >= 0
2029 * for each (x,y) in R.
2030 * We obtain general constraints on coefficients (c_0, c_n, c_x)
2031 * of valid constraints for (y - x) and then plug in (m_0, m_n, -s * c_i_x),
2032 * with each coefficient (except m_0) represented as a pair of non-negative
2036 * If "local" is set, then we add constraints
2038 * c_i_x (y - x) <= 0
2042 * -c_i_x (y - x) <= 0
2044 * instead, forcing the dependence distance to be (less than or) equal to 0.
2045 * That is, we plug in (0, 0, -s * c_i_x),
2046 * intra_coefficients is not required to have c_n in its result when
2047 * "local" is set. If they are missing, then (0, -s * c_i_x) is plugged in.
2048 * Note that dependences marked local are treated as validity constraints
2049 * by add_all_validity_constraints and therefore also have
2050 * their distances bounded by 0 from below.
2052 static isl_stat
add_intra_proximity_constraints(struct isl_sched_graph
*graph
,
2053 struct isl_sched_edge
*edge
, int s
, int local
)
2057 isl_map
*map
= isl_map_copy(edge
->map
);
2058 isl_ctx
*ctx
= isl_map_get_ctx(map
);
2059 isl_dim_map
*dim_map
;
2060 isl_basic_set
*coef
;
2061 struct isl_sched_node
*node
= edge
->src
;
2063 coef
= intra_coefficients(graph
, node
, map
, !local
);
2064 nparam
= isl_space_dim(node
->space
, isl_dim_param
);
2066 offset
= coef_var_offset(coef
);
2067 if (nparam
< 0 || offset
< 0)
2068 coef
= isl_basic_set_free(coef
);
2070 return isl_stat_error
;
2072 dim_map
= intra_dim_map(ctx
, graph
, node
, offset
, -s
);
2075 isl_dim_map_range(dim_map
, 1, 0, 0, 0, 1, 1);
2076 isl_dim_map_range(dim_map
, 4, 2, 1, 1, nparam
, -1);
2077 isl_dim_map_range(dim_map
, 5, 2, 1, 1, nparam
, 1);
2079 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
2084 /* Add constraints to graph->lp that bound the dependence distance for the given
2085 * dependence from node i to node j.
2086 * If s = 1, we add the constraint
2088 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x)
2093 * -(c_j_0 + c_j_n n + c_j_x y) + (c_i_0 + c_i_n n + c_i_x x) +
2096 * for each (x,y) in R.
2097 * If s = -1, we add the constraint
2099 * -((c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x))
2104 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) +
2107 * for each (x,y) in R.
2108 * We obtain general constraints on coefficients (c_0, c_n, c_x, c_y)
2109 * of valid constraints for R and then plug in
2110 * (m_0 - s*c_j_0 + s*c_i_0, m_n - s*c_j_n + s*c_i_n,
2111 * s*c_i_x, -s*c_j_x)
2112 * with each coefficient (except m_0, c_*_0 and c_*_n)
2113 * represented as a pair of non-negative coefficients.
2116 * If "local" is set (and s = 1), then we add constraints
2118 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) <= 0
2122 * -((c_j_0 + c_j_n n + c_j_x y) + (c_i_0 + c_i_n n + c_i_x x)) >= 0
2124 * instead, forcing the dependence distance to be (less than or) equal to 0.
2125 * That is, we plug in
2126 * (-s*c_j_0 + s*c_i_0, -s*c_j_n + s*c_i_n, s*c_i_x, -s*c_j_x).
2127 * Note that dependences marked local are treated as validity constraints
2128 * by add_all_validity_constraints and therefore also have
2129 * their distances bounded by 0 from below.
2131 static isl_stat
add_inter_proximity_constraints(struct isl_sched_graph
*graph
,
2132 struct isl_sched_edge
*edge
, int s
, int local
)
2136 isl_map
*map
= isl_map_copy(edge
->map
);
2137 isl_ctx
*ctx
= isl_map_get_ctx(map
);
2138 isl_dim_map
*dim_map
;
2139 isl_basic_set
*coef
;
2140 struct isl_sched_node
*src
= edge
->src
;
2141 struct isl_sched_node
*dst
= edge
->dst
;
2143 coef
= inter_coefficients(graph
, edge
, map
);
2144 nparam
= isl_space_dim(src
->space
, isl_dim_param
);
2146 offset
= coef_var_offset(coef
);
2147 if (nparam
< 0 || offset
< 0)
2148 coef
= isl_basic_set_free(coef
);
2150 return isl_stat_error
;
2152 dim_map
= inter_dim_map(ctx
, graph
, src
, dst
, offset
, -s
);
2155 isl_dim_map_range(dim_map
, 1, 0, 0, 0, 1, 1);
2156 isl_dim_map_range(dim_map
, 4, 2, 1, 1, nparam
, -1);
2157 isl_dim_map_range(dim_map
, 5, 2, 1, 1, nparam
, 1);
2160 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
2165 /* Should the distance over "edge" be forced to zero?
2166 * That is, is it marked as a local edge?
2167 * If "use_coincidence" is set, then coincidence edges are treated
2170 static int force_zero(struct isl_sched_edge
*edge
, int use_coincidence
)
2172 return is_local(edge
) || (use_coincidence
&& is_coincidence(edge
));
2175 /* Add all validity constraints to graph->lp.
2177 * An edge that is forced to be local needs to have its dependence
2178 * distances equal to zero. We take care of bounding them by 0 from below
2179 * here. add_all_proximity_constraints takes care of bounding them by 0
2182 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2183 * Otherwise, we ignore them.
2185 static int add_all_validity_constraints(struct isl_sched_graph
*graph
,
2186 int use_coincidence
)
2190 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2191 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
2194 zero
= force_zero(edge
, use_coincidence
);
2195 if (!is_validity(edge
) && !zero
)
2197 if (edge
->src
!= edge
->dst
)
2199 if (add_intra_validity_constraints(graph
, edge
) < 0)
2203 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2204 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
2207 zero
= force_zero(edge
, use_coincidence
);
2208 if (!is_validity(edge
) && !zero
)
2210 if (edge
->src
== edge
->dst
)
2212 if (add_inter_validity_constraints(graph
, edge
) < 0)
2219 /* Add constraints to graph->lp that bound the dependence distance
2220 * for all dependence relations.
2221 * If a given proximity dependence is identical to a validity
2222 * dependence, then the dependence distance is already bounded
2223 * from below (by zero), so we only need to bound the distance
2224 * from above. (This includes the case of "local" dependences
2225 * which are treated as validity dependence by add_all_validity_constraints.)
2226 * Otherwise, we need to bound the distance both from above and from below.
2228 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2229 * Otherwise, we ignore them.
2231 static int add_all_proximity_constraints(struct isl_sched_graph
*graph
,
2232 int use_coincidence
)
2236 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2237 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
2240 zero
= force_zero(edge
, use_coincidence
);
2241 if (!is_proximity(edge
) && !zero
)
2243 if (edge
->src
== edge
->dst
&&
2244 add_intra_proximity_constraints(graph
, edge
, 1, zero
) < 0)
2246 if (edge
->src
!= edge
->dst
&&
2247 add_inter_proximity_constraints(graph
, edge
, 1, zero
) < 0)
2249 if (is_validity(edge
) || zero
)
2251 if (edge
->src
== edge
->dst
&&
2252 add_intra_proximity_constraints(graph
, edge
, -1, 0) < 0)
2254 if (edge
->src
!= edge
->dst
&&
2255 add_inter_proximity_constraints(graph
, edge
, -1, 0) < 0)
2262 /* Normalize the rows of "indep" such that all rows are lexicographically
2263 * positive and such that each row contains as many final zeros as possible,
2264 * given the choice for the previous rows.
2265 * Do this by performing elementary row operations.
2267 static __isl_give isl_mat
*normalize_independent(__isl_take isl_mat
*indep
)
2269 indep
= isl_mat_reverse_gauss(indep
);
2270 indep
= isl_mat_lexnonneg_rows(indep
);
2274 /* Extract the linear part of the current schedule for node "node".
2276 static __isl_give isl_mat
*extract_linear_schedule(struct isl_sched_node
*node
)
2278 isl_size n_row
= isl_mat_rows(node
->sched
);
2282 return isl_mat_sub_alloc(node
->sched
, 0, n_row
,
2283 1 + node
->nparam
, node
->nvar
);
2286 /* Compute a basis for the rows in the linear part of the schedule
2287 * and extend this basis to a full basis. The remaining rows
2288 * can then be used to force linear independence from the rows
2291 * In particular, given the schedule rows S, we compute
2296 * with H the Hermite normal form of S. That is, all but the
2297 * first rank columns of H are zero and so each row in S is
2298 * a linear combination of the first rank rows of Q.
2299 * The matrix Q can be used as a variable transformation
2300 * that isolates the directions of S in the first rank rows.
2301 * Transposing S U = H yields
2305 * with all but the first rank rows of H^T zero.
2306 * The last rows of U^T are therefore linear combinations
2307 * of schedule coefficients that are all zero on schedule
2308 * coefficients that are linearly dependent on the rows of S.
2309 * At least one of these combinations is non-zero on
2310 * linearly independent schedule coefficients.
2311 * The rows are normalized to involve as few of the last
2312 * coefficients as possible and to have a positive initial value.
2314 static int node_update_vmap(struct isl_sched_node
*node
)
2318 H
= extract_linear_schedule(node
);
2320 H
= isl_mat_left_hermite(H
, 0, &U
, &Q
);
2321 isl_mat_free(node
->indep
);
2322 isl_mat_free(node
->vmap
);
2324 node
->indep
= isl_mat_transpose(U
);
2325 node
->rank
= isl_mat_initial_non_zero_cols(H
);
2326 node
->indep
= isl_mat_drop_rows(node
->indep
, 0, node
->rank
);
2327 node
->indep
= normalize_independent(node
->indep
);
2330 if (!node
->indep
|| !node
->vmap
|| node
->rank
< 0)
2335 /* Is "edge" marked as a validity or a conditional validity edge?
2337 static int is_any_validity(struct isl_sched_edge
*edge
)
2339 return is_validity(edge
) || is_conditional_validity(edge
);
2342 /* How many times should we count the constraints in "edge"?
2344 * We count as follows
2345 * validity -> 1 (>= 0)
2346 * validity+proximity -> 2 (>= 0 and upper bound)
2347 * proximity -> 2 (lower and upper bound)
2348 * local(+any) -> 2 (>= 0 and <= 0)
2350 * If an edge is only marked conditional_validity then it counts
2351 * as zero since it is only checked afterwards.
2353 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2354 * Otherwise, we ignore them.
2356 static int edge_multiplicity(struct isl_sched_edge
*edge
, int use_coincidence
)
2358 if (is_proximity(edge
) || force_zero(edge
, use_coincidence
))
2360 if (is_validity(edge
))
2365 /* How many times should the constraints in "edge" be counted
2366 * as a parametric intra-node constraint?
2368 * Only proximity edges that are not forced zero need
2369 * coefficient constraints that include coefficients for parameters.
2370 * If the edge is also a validity edge, then only
2371 * an upper bound is introduced. Otherwise, both lower and upper bounds
2374 static int parametric_intra_edge_multiplicity(struct isl_sched_edge
*edge
,
2375 int use_coincidence
)
2377 if (edge
->src
!= edge
->dst
)
2379 if (!is_proximity(edge
))
2381 if (force_zero(edge
, use_coincidence
))
2383 if (is_validity(edge
))
2389 /* Add "f" times the number of equality and inequality constraints of "bset"
2390 * to "n_eq" and "n_ineq" and free "bset".
2392 static isl_stat
update_count(__isl_take isl_basic_set
*bset
,
2393 int f
, int *n_eq
, int *n_ineq
)
2396 return isl_stat_error
;
2398 *n_eq
+= isl_basic_set_n_equality(bset
);
2399 *n_ineq
+= isl_basic_set_n_inequality(bset
);
2400 isl_basic_set_free(bset
);
2405 /* Count the number of equality and inequality constraints
2406 * that will be added for the given map.
2408 * The edges that require parameter coefficients are counted separately.
2410 * "use_coincidence" is set if we should take into account coincidence edges.
2412 static isl_stat
count_map_constraints(struct isl_sched_graph
*graph
,
2413 struct isl_sched_edge
*edge
, __isl_take isl_map
*map
,
2414 int *n_eq
, int *n_ineq
, int use_coincidence
)
2417 isl_basic_set
*coef
;
2418 int f
= edge_multiplicity(edge
, use_coincidence
);
2419 int fp
= parametric_intra_edge_multiplicity(edge
, use_coincidence
);
2426 if (edge
->src
!= edge
->dst
) {
2427 coef
= inter_coefficients(graph
, edge
, map
);
2428 return update_count(coef
, f
, n_eq
, n_ineq
);
2432 copy
= isl_map_copy(map
);
2433 coef
= intra_coefficients(graph
, edge
->src
, copy
, 1);
2434 if (update_count(coef
, fp
, n_eq
, n_ineq
) < 0)
2439 copy
= isl_map_copy(map
);
2440 coef
= intra_coefficients(graph
, edge
->src
, copy
, 0);
2441 if (update_count(coef
, f
- fp
, n_eq
, n_ineq
) < 0)
2449 return isl_stat_error
;
2452 /* Count the number of equality and inequality constraints
2453 * that will be added to the main lp problem.
2454 * We count as follows
2455 * validity -> 1 (>= 0)
2456 * validity+proximity -> 2 (>= 0 and upper bound)
2457 * proximity -> 2 (lower and upper bound)
2458 * local(+any) -> 2 (>= 0 and <= 0)
2460 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2461 * Otherwise, we ignore them.
2463 static int count_constraints(struct isl_sched_graph
*graph
,
2464 int *n_eq
, int *n_ineq
, int use_coincidence
)
2468 *n_eq
= *n_ineq
= 0;
2469 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2470 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
2471 isl_map
*map
= isl_map_copy(edge
->map
);
2473 if (count_map_constraints(graph
, edge
, map
, n_eq
, n_ineq
,
2474 use_coincidence
) < 0)
2481 /* Count the number of constraints that will be added by
2482 * add_bound_constant_constraints to bound the values of the constant terms
2483 * and increment *n_eq and *n_ineq accordingly.
2485 * In practice, add_bound_constant_constraints only adds inequalities.
2487 static isl_stat
count_bound_constant_constraints(isl_ctx
*ctx
,
2488 struct isl_sched_graph
*graph
, int *n_eq
, int *n_ineq
)
2490 if (isl_options_get_schedule_max_constant_term(ctx
) == -1)
2493 *n_ineq
+= graph
->n
;
2498 /* Add constraints to bound the values of the constant terms in the schedule,
2499 * if requested by the user.
2501 * The maximal value of the constant terms is defined by the option
2502 * "schedule_max_constant_term".
2504 static isl_stat
add_bound_constant_constraints(isl_ctx
*ctx
,
2505 struct isl_sched_graph
*graph
)
2511 max
= isl_options_get_schedule_max_constant_term(ctx
);
2515 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2517 return isl_stat_error
;
2519 for (i
= 0; i
< graph
->n
; ++i
) {
2520 struct isl_sched_node
*node
= &graph
->node
[i
];
2523 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2525 return isl_stat_error
;
2526 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
2527 pos
= node_cst_coef_offset(node
);
2528 isl_int_set_si(graph
->lp
->ineq
[k
][1 + pos
], -1);
2529 isl_int_set_si(graph
->lp
->ineq
[k
][0], max
);
2535 /* Count the number of constraints that will be added by
2536 * add_bound_coefficient_constraints and increment *n_eq and *n_ineq
2539 * In practice, add_bound_coefficient_constraints only adds inequalities.
2541 static int count_bound_coefficient_constraints(isl_ctx
*ctx
,
2542 struct isl_sched_graph
*graph
, int *n_eq
, int *n_ineq
)
2546 if (isl_options_get_schedule_max_coefficient(ctx
) == -1 &&
2547 !isl_options_get_schedule_treat_coalescing(ctx
))
2550 for (i
= 0; i
< graph
->n
; ++i
)
2551 *n_ineq
+= graph
->node
[i
].nparam
+ 2 * graph
->node
[i
].nvar
;
2556 /* Add constraints to graph->lp that bound the values of
2557 * the parameter schedule coefficients of "node" to "max" and
2558 * the variable schedule coefficients to the corresponding entry
2560 * In either case, a negative value means that no bound needs to be imposed.
2562 * For parameter coefficients, this amounts to adding a constraint
2570 * The variables coefficients are, however, not represented directly.
2571 * Instead, the variable coefficients c_x are written as differences
2572 * c_x = c_x^+ - c_x^-.
2575 * -max_i <= c_x_i <= max_i
2579 * -max_i <= c_x_i^+ - c_x_i^- <= max_i
2583 * -(c_x_i^+ - c_x_i^-) + max_i >= 0
2584 * c_x_i^+ - c_x_i^- + max_i >= 0
2586 static isl_stat
node_add_coefficient_constraints(isl_ctx
*ctx
,
2587 struct isl_sched_graph
*graph
, struct isl_sched_node
*node
, int max
)
2593 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2595 return isl_stat_error
;
2597 for (j
= 0; j
< node
->nparam
; ++j
) {
2603 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2605 return isl_stat_error
;
2606 dim
= 1 + node_par_coef_offset(node
) + j
;
2607 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
2608 isl_int_set_si(graph
->lp
->ineq
[k
][dim
], -1);
2609 isl_int_set_si(graph
->lp
->ineq
[k
][0], max
);
2612 ineq
= isl_vec_alloc(ctx
, 1 + total
);
2613 ineq
= isl_vec_clr(ineq
);
2615 return isl_stat_error
;
2616 for (i
= 0; i
< node
->nvar
; ++i
) {
2617 int pos
= 1 + node_var_coef_pos(node
, i
);
2619 if (isl_int_is_neg(node
->max
->el
[i
]))
2622 isl_int_set_si(ineq
->el
[pos
], 1);
2623 isl_int_set_si(ineq
->el
[pos
+ 1], -1);
2624 isl_int_set(ineq
->el
[0], node
->max
->el
[i
]);
2626 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2629 isl_seq_cpy(graph
->lp
->ineq
[k
], ineq
->el
, 1 + total
);
2631 isl_seq_neg(ineq
->el
+ pos
, ineq
->el
+ pos
, 2);
2632 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2635 isl_seq_cpy(graph
->lp
->ineq
[k
], ineq
->el
, 1 + total
);
2637 isl_seq_clr(ineq
->el
+ pos
, 2);
2644 return isl_stat_error
;
2647 /* Add constraints that bound the values of the variable and parameter
2648 * coefficients of the schedule.
2650 * The maximal value of the coefficients is defined by the option
2651 * 'schedule_max_coefficient' and the entries in node->max.
2652 * These latter entries are only set if either the schedule_max_coefficient
2653 * option or the schedule_treat_coalescing option is set.
2655 static isl_stat
add_bound_coefficient_constraints(isl_ctx
*ctx
,
2656 struct isl_sched_graph
*graph
)
2661 max
= isl_options_get_schedule_max_coefficient(ctx
);
2663 if (max
== -1 && !isl_options_get_schedule_treat_coalescing(ctx
))
2666 for (i
= 0; i
< graph
->n
; ++i
) {
2667 struct isl_sched_node
*node
= &graph
->node
[i
];
2669 if (node_add_coefficient_constraints(ctx
, graph
, node
, max
) < 0)
2670 return isl_stat_error
;
2676 /* Add a constraint to graph->lp that equates the value at position
2677 * "sum_pos" to the sum of the "n" values starting at "first".
2679 static isl_stat
add_sum_constraint(struct isl_sched_graph
*graph
,
2680 int sum_pos
, int first
, int n
)
2685 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2687 return isl_stat_error
;
2689 k
= isl_basic_set_alloc_equality(graph
->lp
);
2691 return isl_stat_error
;
2692 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2693 isl_int_set_si(graph
->lp
->eq
[k
][1 + sum_pos
], -1);
2694 for (i
= 0; i
< n
; ++i
)
2695 isl_int_set_si(graph
->lp
->eq
[k
][1 + first
+ i
], 1);
2700 /* Add a constraint to graph->lp that equates the value at position
2701 * "sum_pos" to the sum of the parameter coefficients of all nodes.
2703 static isl_stat
add_param_sum_constraint(struct isl_sched_graph
*graph
,
2709 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2711 return isl_stat_error
;
2713 k
= isl_basic_set_alloc_equality(graph
->lp
);
2715 return isl_stat_error
;
2716 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2717 isl_int_set_si(graph
->lp
->eq
[k
][1 + sum_pos
], -1);
2718 for (i
= 0; i
< graph
->n
; ++i
) {
2719 int pos
= 1 + node_par_coef_offset(&graph
->node
[i
]);
2721 for (j
= 0; j
< graph
->node
[i
].nparam
; ++j
)
2722 isl_int_set_si(graph
->lp
->eq
[k
][pos
+ j
], 1);
2728 /* Add a constraint to graph->lp that equates the value at position
2729 * "sum_pos" to the sum of the variable coefficients of all nodes.
2731 static isl_stat
add_var_sum_constraint(struct isl_sched_graph
*graph
,
2737 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2739 return isl_stat_error
;
2741 k
= isl_basic_set_alloc_equality(graph
->lp
);
2743 return isl_stat_error
;
2744 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2745 isl_int_set_si(graph
->lp
->eq
[k
][1 + sum_pos
], -1);
2746 for (i
= 0; i
< graph
->n
; ++i
) {
2747 struct isl_sched_node
*node
= &graph
->node
[i
];
2748 int pos
= 1 + node_var_coef_offset(node
);
2750 for (j
= 0; j
< 2 * node
->nvar
; ++j
)
2751 isl_int_set_si(graph
->lp
->eq
[k
][pos
+ j
], 1);
2757 /* Construct an ILP problem for finding schedule coefficients
2758 * that result in non-negative, but small dependence distances
2759 * over all dependences.
2760 * In particular, the dependence distances over proximity edges
2761 * are bounded by m_0 + m_n n and we compute schedule coefficients
2762 * with small values (preferably zero) of m_n and m_0.
2764 * All variables of the ILP are non-negative. The actual coefficients
2765 * may be negative, so each coefficient is represented as the difference
2766 * of two non-negative variables. The negative part always appears
2767 * immediately before the positive part.
2768 * Other than that, the variables have the following order
2770 * - sum of positive and negative parts of m_n coefficients
2772 * - sum of all c_n coefficients
2773 * (unconstrained when computing non-parametric schedules)
2774 * - sum of positive and negative parts of all c_x coefficients
2775 * - positive and negative parts of m_n coefficients
2777 * - positive and negative parts of c_i_x, in opposite order
2778 * - c_i_n (if parametric)
2781 * The constraints are those from the edges plus two or three equalities
2782 * to express the sums.
2784 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2785 * Otherwise, we ignore them.
2787 static isl_stat
setup_lp(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
2788 int use_coincidence
)
2798 parametric
= ctx
->opt
->schedule_parametric
;
2799 nparam
= isl_space_dim(graph
->node
[0].space
, isl_dim_param
);
2801 return isl_stat_error
;
2803 total
= param_pos
+ 2 * nparam
;
2804 for (i
= 0; i
< graph
->n
; ++i
) {
2805 struct isl_sched_node
*node
= &graph
->node
[graph
->sorted
[i
]];
2806 if (node_update_vmap(node
) < 0)
2807 return isl_stat_error
;
2808 node
->start
= total
;
2809 total
+= 1 + node
->nparam
+ 2 * node
->nvar
;
2812 if (count_constraints(graph
, &n_eq
, &n_ineq
, use_coincidence
) < 0)
2813 return isl_stat_error
;
2814 if (count_bound_constant_constraints(ctx
, graph
, &n_eq
, &n_ineq
) < 0)
2815 return isl_stat_error
;
2816 if (count_bound_coefficient_constraints(ctx
, graph
, &n_eq
, &n_ineq
) < 0)
2817 return isl_stat_error
;
2819 space
= isl_space_set_alloc(ctx
, 0, total
);
2820 isl_basic_set_free(graph
->lp
);
2821 n_eq
+= 2 + parametric
;
2823 graph
->lp
= isl_basic_set_alloc_space(space
, 0, n_eq
, n_ineq
);
2825 if (add_sum_constraint(graph
, 0, param_pos
, 2 * nparam
) < 0)
2826 return isl_stat_error
;
2827 if (parametric
&& add_param_sum_constraint(graph
, 2) < 0)
2828 return isl_stat_error
;
2829 if (add_var_sum_constraint(graph
, 3) < 0)
2830 return isl_stat_error
;
2831 if (add_bound_constant_constraints(ctx
, graph
) < 0)
2832 return isl_stat_error
;
2833 if (add_bound_coefficient_constraints(ctx
, graph
) < 0)
2834 return isl_stat_error
;
2835 if (add_all_validity_constraints(graph
, use_coincidence
) < 0)
2836 return isl_stat_error
;
2837 if (add_all_proximity_constraints(graph
, use_coincidence
) < 0)
2838 return isl_stat_error
;
2843 /* Analyze the conflicting constraint found by
2844 * isl_tab_basic_set_non_trivial_lexmin. If it corresponds to the validity
2845 * constraint of one of the edges between distinct nodes, living, moreover
2846 * in distinct SCCs, then record the source and sink SCC as this may
2847 * be a good place to cut between SCCs.
2849 static int check_conflict(int con
, void *user
)
2852 struct isl_sched_graph
*graph
= user
;
2854 if (graph
->src_scc
>= 0)
2857 con
-= graph
->lp
->n_eq
;
2859 if (con
>= graph
->lp
->n_ineq
)
2862 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2863 if (!is_validity(&graph
->edge
[i
]))
2865 if (graph
->edge
[i
].src
== graph
->edge
[i
].dst
)
2867 if (graph
->edge
[i
].src
->scc
== graph
->edge
[i
].dst
->scc
)
2869 if (graph
->edge
[i
].start
> con
)
2871 if (graph
->edge
[i
].end
<= con
)
2873 graph
->src_scc
= graph
->edge
[i
].src
->scc
;
2874 graph
->dst_scc
= graph
->edge
[i
].dst
->scc
;
2880 /* Check whether the next schedule row of the given node needs to be
2881 * non-trivial. Lower-dimensional domains may have some trivial rows,
2882 * but as soon as the number of remaining required non-trivial rows
2883 * is as large as the number or remaining rows to be computed,
2884 * all remaining rows need to be non-trivial.
2886 static int needs_row(struct isl_sched_graph
*graph
, struct isl_sched_node
*node
)
2888 return node
->nvar
- node
->rank
>= graph
->maxvar
- graph
->n_row
;
2891 /* Construct a non-triviality region with triviality directions
2892 * corresponding to the rows of "indep".
2893 * The rows of "indep" are expressed in terms of the schedule coefficients c_i,
2894 * while the triviality directions are expressed in terms of
2895 * pairs of non-negative variables c^+_i - c^-_i, with c^-_i appearing
2896 * before c^+_i. Furthermore,
2897 * the pairs of non-negative variables representing the coefficients
2898 * are stored in the opposite order.
2900 static __isl_give isl_mat
*construct_trivial(__isl_keep isl_mat
*indep
)
2907 n
= isl_mat_rows(indep
);
2908 n_var
= isl_mat_cols(indep
);
2909 if (n
< 0 || n_var
< 0)
2912 ctx
= isl_mat_get_ctx(indep
);
2913 mat
= isl_mat_alloc(ctx
, n
, 2 * n_var
);
2916 for (i
= 0; i
< n
; ++i
) {
2917 for (j
= 0; j
< n_var
; ++j
) {
2918 int nj
= n_var
- 1 - j
;
2919 isl_int_neg(mat
->row
[i
][2 * nj
], indep
->row
[i
][j
]);
2920 isl_int_set(mat
->row
[i
][2 * nj
+ 1], indep
->row
[i
][j
]);
2927 /* Solve the ILP problem constructed in setup_lp.
2928 * For each node such that all the remaining rows of its schedule
2929 * need to be non-trivial, we construct a non-triviality region.
2930 * This region imposes that the next row is independent of previous rows.
2931 * In particular, the non-triviality region enforces that at least
2932 * one of the linear combinations in the rows of node->indep is non-zero.
2934 static __isl_give isl_vec
*solve_lp(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2940 for (i
= 0; i
< graph
->n
; ++i
) {
2941 struct isl_sched_node
*node
= &graph
->node
[i
];
2944 graph
->region
[i
].pos
= node_var_coef_offset(node
);
2945 if (needs_row(graph
, node
))
2946 trivial
= construct_trivial(node
->indep
);
2948 trivial
= isl_mat_zero(ctx
, 0, 0);
2949 graph
->region
[i
].trivial
= trivial
;
2951 lp
= isl_basic_set_copy(graph
->lp
);
2952 sol
= isl_tab_basic_set_non_trivial_lexmin(lp
, 2, graph
->n
,
2953 graph
->region
, &check_conflict
, graph
);
2954 for (i
= 0; i
< graph
->n
; ++i
)
2955 isl_mat_free(graph
->region
[i
].trivial
);
2959 /* Extract the coefficients for the variables of "node" from "sol".
2961 * Each schedule coefficient c_i_x is represented as the difference
2962 * between two non-negative variables c_i_x^+ - c_i_x^-.
2963 * The c_i_x^- appear before their c_i_x^+ counterpart.
2964 * Furthermore, the order of these pairs is the opposite of that
2965 * of the corresponding coefficients.
2967 * Return c_i_x = c_i_x^+ - c_i_x^-
2969 static __isl_give isl_vec
*extract_var_coef(struct isl_sched_node
*node
,
2970 __isl_keep isl_vec
*sol
)
2978 csol
= isl_vec_alloc(isl_vec_get_ctx(sol
), node
->nvar
);
2982 pos
= 1 + node_var_coef_offset(node
);
2983 for (i
= 0; i
< node
->nvar
; ++i
)
2984 isl_int_sub(csol
->el
[node
->nvar
- 1 - i
],
2985 sol
->el
[pos
+ 2 * i
+ 1], sol
->el
[pos
+ 2 * i
]);
2990 /* Update the schedules of all nodes based on the given solution
2991 * of the LP problem.
2992 * The new row is added to the current band.
2993 * All possibly negative coefficients are encoded as a difference
2994 * of two non-negative variables, so we need to perform the subtraction
2997 * If coincident is set, then the caller guarantees that the new
2998 * row satisfies the coincidence constraints.
3000 static int update_schedule(struct isl_sched_graph
*graph
,
3001 __isl_take isl_vec
*sol
, int coincident
)
3004 isl_vec
*csol
= NULL
;
3009 isl_die(sol
->ctx
, isl_error_internal
,
3010 "no solution found", goto error
);
3011 if (graph
->n_total_row
>= graph
->max_row
)
3012 isl_die(sol
->ctx
, isl_error_internal
,
3013 "too many schedule rows", goto error
);
3015 for (i
= 0; i
< graph
->n
; ++i
) {
3016 struct isl_sched_node
*node
= &graph
->node
[i
];
3018 isl_size row
= isl_mat_rows(node
->sched
);
3021 csol
= extract_var_coef(node
, sol
);
3022 if (row
< 0 || !csol
)
3025 isl_map_free(node
->sched_map
);
3026 node
->sched_map
= NULL
;
3027 node
->sched
= isl_mat_add_rows(node
->sched
, 1);
3030 pos
= node_cst_coef_offset(node
);
3031 node
->sched
= isl_mat_set_element(node
->sched
,
3032 row
, 0, sol
->el
[1 + pos
]);
3033 pos
= node_par_coef_offset(node
);
3034 for (j
= 0; j
< node
->nparam
; ++j
)
3035 node
->sched
= isl_mat_set_element(node
->sched
,
3036 row
, 1 + j
, sol
->el
[1 + pos
+ j
]);
3037 for (j
= 0; j
< node
->nvar
; ++j
)
3038 node
->sched
= isl_mat_set_element(node
->sched
,
3039 row
, 1 + node
->nparam
+ j
, csol
->el
[j
]);
3040 node
->coincident
[graph
->n_total_row
] = coincident
;
3046 graph
->n_total_row
++;
3055 /* Convert row "row" of node->sched into an isl_aff living in "ls"
3056 * and return this isl_aff.
3058 static __isl_give isl_aff
*extract_schedule_row(__isl_take isl_local_space
*ls
,
3059 struct isl_sched_node
*node
, int row
)
3067 aff
= isl_aff_zero_on_domain(ls
);
3068 if (isl_mat_get_element(node
->sched
, row
, 0, &v
) < 0)
3070 aff
= isl_aff_set_constant(aff
, v
);
3071 for (j
= 0; j
< node
->nparam
; ++j
) {
3072 if (isl_mat_get_element(node
->sched
, row
, 1 + j
, &v
) < 0)
3074 aff
= isl_aff_set_coefficient(aff
, isl_dim_param
, j
, v
);
3076 for (j
= 0; j
< node
->nvar
; ++j
) {
3077 if (isl_mat_get_element(node
->sched
, row
,
3078 1 + node
->nparam
+ j
, &v
) < 0)
3080 aff
= isl_aff_set_coefficient(aff
, isl_dim_in
, j
, v
);
3092 /* Convert the "n" rows starting at "first" of node->sched into a multi_aff
3093 * and return this multi_aff.
3095 * The result is defined over the uncompressed node domain.
3097 static __isl_give isl_multi_aff
*node_extract_partial_schedule_multi_aff(
3098 struct isl_sched_node
*node
, int first
, int n
)
3102 isl_local_space
*ls
;
3109 nrow
= isl_mat_rows(node
->sched
);
3112 if (node
->compressed
)
3113 space
= isl_multi_aff_get_domain_space(node
->decompress
);
3115 space
= isl_space_copy(node
->space
);
3116 ls
= isl_local_space_from_space(isl_space_copy(space
));
3117 space
= isl_space_from_domain(space
);
3118 space
= isl_space_add_dims(space
, isl_dim_out
, n
);
3119 ma
= isl_multi_aff_zero(space
);
3121 for (i
= first
; i
< first
+ n
; ++i
) {
3122 aff
= extract_schedule_row(isl_local_space_copy(ls
), node
, i
);
3123 ma
= isl_multi_aff_set_aff(ma
, i
- first
, aff
);
3126 isl_local_space_free(ls
);
3128 if (node
->compressed
)
3129 ma
= isl_multi_aff_pullback_multi_aff(ma
,
3130 isl_multi_aff_copy(node
->compress
));
3135 /* Convert node->sched into a multi_aff and return this multi_aff.
3137 * The result is defined over the uncompressed node domain.
3139 static __isl_give isl_multi_aff
*node_extract_schedule_multi_aff(
3140 struct isl_sched_node
*node
)
3144 nrow
= isl_mat_rows(node
->sched
);
3147 return node_extract_partial_schedule_multi_aff(node
, 0, nrow
);
3150 /* Convert node->sched into a map and return this map.
3152 * The result is cached in node->sched_map, which needs to be released
3153 * whenever node->sched is updated.
3154 * It is defined over the uncompressed node domain.
3156 static __isl_give isl_map
*node_extract_schedule(struct isl_sched_node
*node
)
3158 if (!node
->sched_map
) {
3161 ma
= node_extract_schedule_multi_aff(node
);
3162 node
->sched_map
= isl_map_from_multi_aff(ma
);
3165 return isl_map_copy(node
->sched_map
);
3168 /* Construct a map that can be used to update a dependence relation
3169 * based on the current schedule.
3170 * That is, construct a map expressing that source and sink
3171 * are executed within the same iteration of the current schedule.
3172 * This map can then be intersected with the dependence relation.
3173 * This is not the most efficient way, but this shouldn't be a critical
3176 static __isl_give isl_map
*specializer(struct isl_sched_node
*src
,
3177 struct isl_sched_node
*dst
)
3179 isl_map
*src_sched
, *dst_sched
;
3181 src_sched
= node_extract_schedule(src
);
3182 dst_sched
= node_extract_schedule(dst
);
3183 return isl_map_apply_range(src_sched
, isl_map_reverse(dst_sched
));
3186 /* Intersect the domains of the nested relations in domain and range
3187 * of "umap" with "map".
3189 static __isl_give isl_union_map
*intersect_domains(
3190 __isl_take isl_union_map
*umap
, __isl_keep isl_map
*map
)
3192 isl_union_set
*uset
;
3194 umap
= isl_union_map_zip(umap
);
3195 uset
= isl_union_set_from_set(isl_map_wrap(isl_map_copy(map
)));
3196 umap
= isl_union_map_intersect_domain(umap
, uset
);
3197 umap
= isl_union_map_zip(umap
);
3201 /* Update the dependence relation of the given edge based
3202 * on the current schedule.
3203 * If the dependence is carried completely by the current schedule, then
3204 * it is removed from the edge_tables. It is kept in the list of edges
3205 * as otherwise all edge_tables would have to be recomputed.
3207 * If the edge is of a type that can appear multiple times
3208 * between the same pair of nodes, then it is added to
3209 * the edge table (again). This prevents the situation
3210 * where none of these edges is referenced from the edge table
3211 * because the one that was referenced turned out to be empty and
3212 * was therefore removed from the table.
3214 static isl_stat
update_edge(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
3215 struct isl_sched_edge
*edge
)
3220 id
= specializer(edge
->src
, edge
->dst
);
3221 edge
->map
= isl_map_intersect(edge
->map
, isl_map_copy(id
));
3225 if (edge
->tagged_condition
) {
3226 edge
->tagged_condition
=
3227 intersect_domains(edge
->tagged_condition
, id
);
3228 if (!edge
->tagged_condition
)
3231 if (edge
->tagged_validity
) {
3232 edge
->tagged_validity
=
3233 intersect_domains(edge
->tagged_validity
, id
);
3234 if (!edge
->tagged_validity
)
3238 empty
= isl_map_plain_is_empty(edge
->map
);
3242 graph_remove_edge(graph
, edge
);
3243 } else if (is_multi_edge_type(edge
)) {
3244 if (graph_edge_tables_add(ctx
, graph
, edge
) < 0)
3252 return isl_stat_error
;
3255 /* Does the domain of "umap" intersect "uset"?
3257 static int domain_intersects(__isl_keep isl_union_map
*umap
,
3258 __isl_keep isl_union_set
*uset
)
3262 umap
= isl_union_map_copy(umap
);
3263 umap
= isl_union_map_intersect_domain(umap
, isl_union_set_copy(uset
));
3264 empty
= isl_union_map_is_empty(umap
);
3265 isl_union_map_free(umap
);
3267 return empty
< 0 ? -1 : !empty
;
3270 /* Does the range of "umap" intersect "uset"?
3272 static int range_intersects(__isl_keep isl_union_map
*umap
,
3273 __isl_keep isl_union_set
*uset
)
3277 umap
= isl_union_map_copy(umap
);
3278 umap
= isl_union_map_intersect_range(umap
, isl_union_set_copy(uset
));
3279 empty
= isl_union_map_is_empty(umap
);
3280 isl_union_map_free(umap
);
3282 return empty
< 0 ? -1 : !empty
;
3285 /* Are the condition dependences of "edge" local with respect to
3286 * the current schedule?
3288 * That is, are domain and range of the condition dependences mapped
3289 * to the same point?
3291 * In other words, is the condition false?
3293 static int is_condition_false(struct isl_sched_edge
*edge
)
3295 isl_union_map
*umap
;
3296 isl_map
*map
, *sched
, *test
;
3299 empty
= isl_union_map_is_empty(edge
->tagged_condition
);
3300 if (empty
< 0 || empty
)
3303 umap
= isl_union_map_copy(edge
->tagged_condition
);
3304 umap
= isl_union_map_zip(umap
);
3305 umap
= isl_union_set_unwrap(isl_union_map_domain(umap
));
3306 map
= isl_map_from_union_map(umap
);
3308 sched
= node_extract_schedule(edge
->src
);
3309 map
= isl_map_apply_domain(map
, sched
);
3310 sched
= node_extract_schedule(edge
->dst
);
3311 map
= isl_map_apply_range(map
, sched
);
3313 test
= isl_map_identity(isl_map_get_space(map
));
3314 local
= isl_map_is_subset(map
, test
);
3321 /* For each conditional validity constraint that is adjacent
3322 * to a condition with domain in condition_source or range in condition_sink,
3323 * turn it into an unconditional validity constraint.
3325 static int unconditionalize_adjacent_validity(struct isl_sched_graph
*graph
,
3326 __isl_take isl_union_set
*condition_source
,
3327 __isl_take isl_union_set
*condition_sink
)
3331 condition_source
= isl_union_set_coalesce(condition_source
);
3332 condition_sink
= isl_union_set_coalesce(condition_sink
);
3334 for (i
= 0; i
< graph
->n_edge
; ++i
) {
3336 isl_union_map
*validity
;
3338 if (!is_conditional_validity(&graph
->edge
[i
]))
3340 if (is_validity(&graph
->edge
[i
]))
3343 validity
= graph
->edge
[i
].tagged_validity
;
3344 adjacent
= domain_intersects(validity
, condition_sink
);
3345 if (adjacent
>= 0 && !adjacent
)
3346 adjacent
= range_intersects(validity
, condition_source
);
3352 set_validity(&graph
->edge
[i
]);
3355 isl_union_set_free(condition_source
);
3356 isl_union_set_free(condition_sink
);
3359 isl_union_set_free(condition_source
);
3360 isl_union_set_free(condition_sink
);
3364 /* Update the dependence relations of all edges based on the current schedule
3365 * and enforce conditional validity constraints that are adjacent
3366 * to satisfied condition constraints.
3368 * First check if any of the condition constraints are satisfied
3369 * (i.e., not local to the outer schedule) and keep track of
3370 * their domain and range.
3371 * Then update all dependence relations (which removes the non-local
3373 * Finally, if any condition constraints turned out to be satisfied,
3374 * then turn all adjacent conditional validity constraints into
3375 * unconditional validity constraints.
3377 static int update_edges(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
3381 isl_union_set
*source
, *sink
;
3383 source
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
3384 sink
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
3385 for (i
= 0; i
< graph
->n_edge
; ++i
) {
3387 isl_union_set
*uset
;
3388 isl_union_map
*umap
;
3390 if (!is_condition(&graph
->edge
[i
]))
3392 if (is_local(&graph
->edge
[i
]))
3394 local
= is_condition_false(&graph
->edge
[i
]);
3402 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_condition
);
3403 uset
= isl_union_map_domain(umap
);
3404 source
= isl_union_set_union(source
, uset
);
3406 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_condition
);
3407 uset
= isl_union_map_range(umap
);
3408 sink
= isl_union_set_union(sink
, uset
);
3411 for (i
= 0; i
< graph
->n_edge
; ++i
) {
3412 if (update_edge(ctx
, graph
, &graph
->edge
[i
]) < 0)
3417 return unconditionalize_adjacent_validity(graph
, source
, sink
);
3419 isl_union_set_free(source
);
3420 isl_union_set_free(sink
);
3423 isl_union_set_free(source
);
3424 isl_union_set_free(sink
);
3428 static void next_band(struct isl_sched_graph
*graph
)
3430 graph
->band_start
= graph
->n_total_row
;
3433 /* Return the union of the universe domains of the nodes in "graph"
3434 * that satisfy "pred".
3436 static __isl_give isl_union_set
*isl_sched_graph_domain(isl_ctx
*ctx
,
3437 struct isl_sched_graph
*graph
,
3438 int (*pred
)(struct isl_sched_node
*node
, int data
), int data
)
3444 for (i
= 0; i
< graph
->n
; ++i
)
3445 if (pred(&graph
->node
[i
], data
))
3449 isl_die(ctx
, isl_error_internal
,
3450 "empty component", return NULL
);
3452 set
= isl_set_universe(isl_space_copy(graph
->node
[i
].space
));
3453 dom
= isl_union_set_from_set(set
);
3455 for (i
= i
+ 1; i
< graph
->n
; ++i
) {
3456 if (!pred(&graph
->node
[i
], data
))
3458 set
= isl_set_universe(isl_space_copy(graph
->node
[i
].space
));
3459 dom
= isl_union_set_union(dom
, isl_union_set_from_set(set
));
3465 /* Return a list of unions of universe domains, where each element
3466 * in the list corresponds to an SCC (or WCC) indexed by node->scc.
3468 static __isl_give isl_union_set_list
*extract_sccs(isl_ctx
*ctx
,
3469 struct isl_sched_graph
*graph
)
3472 isl_union_set_list
*filters
;
3474 filters
= isl_union_set_list_alloc(ctx
, graph
->scc
);
3475 for (i
= 0; i
< graph
->scc
; ++i
) {
3478 dom
= isl_sched_graph_domain(ctx
, graph
, &node_scc_exactly
, i
);
3479 filters
= isl_union_set_list_add(filters
, dom
);
3485 /* Return a list of two unions of universe domains, one for the SCCs up
3486 * to and including graph->src_scc and another for the other SCCs.
3488 static __isl_give isl_union_set_list
*extract_split(isl_ctx
*ctx
,
3489 struct isl_sched_graph
*graph
)
3492 isl_union_set_list
*filters
;
3494 filters
= isl_union_set_list_alloc(ctx
, 2);
3495 dom
= isl_sched_graph_domain(ctx
, graph
,
3496 &node_scc_at_most
, graph
->src_scc
);
3497 filters
= isl_union_set_list_add(filters
, dom
);
3498 dom
= isl_sched_graph_domain(ctx
, graph
,
3499 &node_scc_at_least
, graph
->src_scc
+ 1);
3500 filters
= isl_union_set_list_add(filters
, dom
);
3505 /* Copy nodes that satisfy node_pred from the src dependence graph
3506 * to the dst dependence graph.
3508 static isl_stat
copy_nodes(struct isl_sched_graph
*dst
,
3509 struct isl_sched_graph
*src
,
3510 int (*node_pred
)(struct isl_sched_node
*node
, int data
), int data
)
3515 for (i
= 0; i
< src
->n
; ++i
) {
3518 if (!node_pred(&src
->node
[i
], data
))
3522 dst
->node
[j
].space
= isl_space_copy(src
->node
[i
].space
);
3523 dst
->node
[j
].compressed
= src
->node
[i
].compressed
;
3524 dst
->node
[j
].hull
= isl_set_copy(src
->node
[i
].hull
);
3525 dst
->node
[j
].compress
=
3526 isl_multi_aff_copy(src
->node
[i
].compress
);
3527 dst
->node
[j
].decompress
=
3528 isl_multi_aff_copy(src
->node
[i
].decompress
);
3529 dst
->node
[j
].nvar
= src
->node
[i
].nvar
;
3530 dst
->node
[j
].nparam
= src
->node
[i
].nparam
;
3531 dst
->node
[j
].sched
= isl_mat_copy(src
->node
[i
].sched
);
3532 dst
->node
[j
].sched_map
= isl_map_copy(src
->node
[i
].sched_map
);
3533 dst
->node
[j
].coincident
= src
->node
[i
].coincident
;
3534 dst
->node
[j
].sizes
= isl_multi_val_copy(src
->node
[i
].sizes
);
3535 dst
->node
[j
].bounds
= isl_basic_set_copy(src
->node
[i
].bounds
);
3536 dst
->node
[j
].max
= isl_vec_copy(src
->node
[i
].max
);
3539 if (!dst
->node
[j
].space
|| !dst
->node
[j
].sched
)
3540 return isl_stat_error
;
3541 if (dst
->node
[j
].compressed
&&
3542 (!dst
->node
[j
].hull
|| !dst
->node
[j
].compress
||
3543 !dst
->node
[j
].decompress
))
3544 return isl_stat_error
;
3550 /* Copy non-empty edges that satisfy edge_pred from the src dependence graph
3551 * to the dst dependence graph.
3552 * If the source or destination node of the edge is not in the destination
3553 * graph, then it must be a backward proximity edge and it should simply
3556 static isl_stat
copy_edges(isl_ctx
*ctx
, struct isl_sched_graph
*dst
,
3557 struct isl_sched_graph
*src
,
3558 int (*edge_pred
)(struct isl_sched_edge
*edge
, int data
), int data
)
3563 for (i
= 0; i
< src
->n_edge
; ++i
) {
3564 struct isl_sched_edge
*edge
= &src
->edge
[i
];
3566 isl_union_map
*tagged_condition
;
3567 isl_union_map
*tagged_validity
;
3568 struct isl_sched_node
*dst_src
, *dst_dst
;
3570 if (!edge_pred(edge
, data
))
3573 if (isl_map_plain_is_empty(edge
->map
))
3576 dst_src
= graph_find_node(ctx
, dst
, edge
->src
->space
);
3577 dst_dst
= graph_find_node(ctx
, dst
, edge
->dst
->space
);
3578 if (!dst_src
|| !dst_dst
)
3579 return isl_stat_error
;
3580 if (!is_node(dst
, dst_src
) || !is_node(dst
, dst_dst
)) {
3581 if (is_validity(edge
) || is_conditional_validity(edge
))
3582 isl_die(ctx
, isl_error_internal
,
3583 "backward (conditional) validity edge",
3584 return isl_stat_error
);
3588 map
= isl_map_copy(edge
->map
);
3589 tagged_condition
= isl_union_map_copy(edge
->tagged_condition
);
3590 tagged_validity
= isl_union_map_copy(edge
->tagged_validity
);
3592 dst
->edge
[dst
->n_edge
].src
= dst_src
;
3593 dst
->edge
[dst
->n_edge
].dst
= dst_dst
;
3594 dst
->edge
[dst
->n_edge
].map
= map
;
3595 dst
->edge
[dst
->n_edge
].tagged_condition
= tagged_condition
;
3596 dst
->edge
[dst
->n_edge
].tagged_validity
= tagged_validity
;
3597 dst
->edge
[dst
->n_edge
].types
= edge
->types
;
3600 if (edge
->tagged_condition
&& !tagged_condition
)
3601 return isl_stat_error
;
3602 if (edge
->tagged_validity
&& !tagged_validity
)
3603 return isl_stat_error
;
3605 if (graph_edge_tables_add(ctx
, dst
,
3606 &dst
->edge
[dst
->n_edge
- 1]) < 0)
3607 return isl_stat_error
;
3613 /* Compute the maximal number of variables over all nodes.
3614 * This is the maximal number of linearly independent schedule
3615 * rows that we need to compute.
3616 * Just in case we end up in a part of the dependence graph
3617 * with only lower-dimensional domains, we make sure we will
3618 * compute the required amount of extra linearly independent rows.
3620 static int compute_maxvar(struct isl_sched_graph
*graph
)
3625 for (i
= 0; i
< graph
->n
; ++i
) {
3626 struct isl_sched_node
*node
= &graph
->node
[i
];
3629 if (node_update_vmap(node
) < 0)
3631 nvar
= node
->nvar
+ graph
->n_row
- node
->rank
;
3632 if (nvar
> graph
->maxvar
)
3633 graph
->maxvar
= nvar
;
3639 /* Extract the subgraph of "graph" that consists of the nodes satisfying
3640 * "node_pred" and the edges satisfying "edge_pred" and store
3641 * the result in "sub".
3643 static isl_stat
extract_sub_graph(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
3644 int (*node_pred
)(struct isl_sched_node
*node
, int data
),
3645 int (*edge_pred
)(struct isl_sched_edge
*edge
, int data
),
3646 int data
, struct isl_sched_graph
*sub
)
3648 int i
, n
= 0, n_edge
= 0;
3651 for (i
= 0; i
< graph
->n
; ++i
)
3652 if (node_pred(&graph
->node
[i
], data
))
3654 for (i
= 0; i
< graph
->n_edge
; ++i
)
3655 if (edge_pred(&graph
->edge
[i
], data
))
3657 if (graph_alloc(ctx
, sub
, n
, n_edge
) < 0)
3658 return isl_stat_error
;
3659 sub
->root
= graph
->root
;
3660 if (copy_nodes(sub
, graph
, node_pred
, data
) < 0)
3661 return isl_stat_error
;
3662 if (graph_init_table(ctx
, sub
) < 0)
3663 return isl_stat_error
;
3664 for (t
= 0; t
<= isl_edge_last
; ++t
)
3665 sub
->max_edge
[t
] = graph
->max_edge
[t
];
3666 if (graph_init_edge_tables(ctx
, sub
) < 0)
3667 return isl_stat_error
;
3668 if (copy_edges(ctx
, sub
, graph
, edge_pred
, data
) < 0)
3669 return isl_stat_error
;
3670 sub
->n_row
= graph
->n_row
;
3671 sub
->max_row
= graph
->max_row
;
3672 sub
->n_total_row
= graph
->n_total_row
;
3673 sub
->band_start
= graph
->band_start
;
3678 static __isl_give isl_schedule_node
*compute_schedule(isl_schedule_node
*node
,
3679 struct isl_sched_graph
*graph
);
3680 static __isl_give isl_schedule_node
*compute_schedule_wcc(
3681 isl_schedule_node
*node
, struct isl_sched_graph
*graph
);
3683 /* Compute a schedule for a subgraph of "graph". In particular, for
3684 * the graph composed of nodes that satisfy node_pred and edges that
3685 * that satisfy edge_pred.
3686 * If the subgraph is known to consist of a single component, then wcc should
3687 * be set and then we call compute_schedule_wcc on the constructed subgraph.
3688 * Otherwise, we call compute_schedule, which will check whether the subgraph
3691 * The schedule is inserted at "node" and the updated schedule node
3694 static __isl_give isl_schedule_node
*compute_sub_schedule(
3695 __isl_take isl_schedule_node
*node
, isl_ctx
*ctx
,
3696 struct isl_sched_graph
*graph
,
3697 int (*node_pred
)(struct isl_sched_node
*node
, int data
),
3698 int (*edge_pred
)(struct isl_sched_edge
*edge
, int data
),
3701 struct isl_sched_graph split
= { 0 };
3703 if (extract_sub_graph(ctx
, graph
, node_pred
, edge_pred
, data
,
3708 node
= compute_schedule_wcc(node
, &split
);
3710 node
= compute_schedule(node
, &split
);
3712 graph_free(ctx
, &split
);
3715 graph_free(ctx
, &split
);
3716 return isl_schedule_node_free(node
);
3719 static int edge_scc_exactly(struct isl_sched_edge
*edge
, int scc
)
3721 return edge
->src
->scc
== scc
&& edge
->dst
->scc
== scc
;
3724 static int edge_dst_scc_at_most(struct isl_sched_edge
*edge
, int scc
)
3726 return edge
->dst
->scc
<= scc
;
3729 static int edge_src_scc_at_least(struct isl_sched_edge
*edge
, int scc
)
3731 return edge
->src
->scc
>= scc
;
3734 /* Reset the current band by dropping all its schedule rows.
3736 static isl_stat
reset_band(struct isl_sched_graph
*graph
)
3741 drop
= graph
->n_total_row
- graph
->band_start
;
3742 graph
->n_total_row
-= drop
;
3743 graph
->n_row
-= drop
;
3745 for (i
= 0; i
< graph
->n
; ++i
) {
3746 struct isl_sched_node
*node
= &graph
->node
[i
];
3748 isl_map_free(node
->sched_map
);
3749 node
->sched_map
= NULL
;
3751 node
->sched
= isl_mat_drop_rows(node
->sched
,
3752 graph
->band_start
, drop
);
3755 return isl_stat_error
;
3761 /* Split the current graph into two parts and compute a schedule for each
3762 * part individually. In particular, one part consists of all SCCs up
3763 * to and including graph->src_scc, while the other part contains the other
3764 * SCCs. The split is enforced by a sequence node inserted at position "node"
3765 * in the schedule tree. Return the updated schedule node.
3766 * If either of these two parts consists of a sequence, then it is spliced
3767 * into the sequence containing the two parts.
3769 * The current band is reset. It would be possible to reuse
3770 * the previously computed rows as the first rows in the next
3771 * band, but recomputing them may result in better rows as we are looking
3772 * at a smaller part of the dependence graph.
3774 static __isl_give isl_schedule_node
*compute_split_schedule(
3775 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
3779 isl_union_set_list
*filters
;
3784 if (reset_band(graph
) < 0)
3785 return isl_schedule_node_free(node
);
3789 ctx
= isl_schedule_node_get_ctx(node
);
3790 filters
= extract_split(ctx
, graph
);
3791 node
= isl_schedule_node_insert_sequence(node
, filters
);
3792 node
= isl_schedule_node_child(node
, 1);
3793 node
= isl_schedule_node_child(node
, 0);
3795 node
= compute_sub_schedule(node
, ctx
, graph
,
3796 &node_scc_at_least
, &edge_src_scc_at_least
,
3797 graph
->src_scc
+ 1, 0);
3798 is_seq
= isl_schedule_node_get_type(node
) == isl_schedule_node_sequence
;
3799 node
= isl_schedule_node_parent(node
);
3800 node
= isl_schedule_node_parent(node
);
3802 node
= isl_schedule_node_sequence_splice_child(node
, 1);
3803 node
= isl_schedule_node_child(node
, 0);
3804 node
= isl_schedule_node_child(node
, 0);
3805 node
= compute_sub_schedule(node
, ctx
, graph
,
3806 &node_scc_at_most
, &edge_dst_scc_at_most
,
3808 is_seq
= isl_schedule_node_get_type(node
) == isl_schedule_node_sequence
;
3809 node
= isl_schedule_node_parent(node
);
3810 node
= isl_schedule_node_parent(node
);
3812 node
= isl_schedule_node_sequence_splice_child(node
, 0);
3817 /* Insert a band node at position "node" in the schedule tree corresponding
3818 * to the current band in "graph". Mark the band node permutable
3819 * if "permutable" is set.
3820 * The partial schedules and the coincidence property are extracted
3821 * from the graph nodes.
3822 * Return the updated schedule node.
3824 static __isl_give isl_schedule_node
*insert_current_band(
3825 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
3831 isl_multi_pw_aff
*mpa
;
3832 isl_multi_union_pw_aff
*mupa
;
3838 isl_die(isl_schedule_node_get_ctx(node
), isl_error_internal
,
3839 "graph should have at least one node",
3840 return isl_schedule_node_free(node
));
3842 start
= graph
->band_start
;
3843 end
= graph
->n_total_row
;
3846 ma
= node_extract_partial_schedule_multi_aff(&graph
->node
[0], start
, n
);
3847 mpa
= isl_multi_pw_aff_from_multi_aff(ma
);
3848 mupa
= isl_multi_union_pw_aff_from_multi_pw_aff(mpa
);
3850 for (i
= 1; i
< graph
->n
; ++i
) {
3851 isl_multi_union_pw_aff
*mupa_i
;
3853 ma
= node_extract_partial_schedule_multi_aff(&graph
->node
[i
],
3855 mpa
= isl_multi_pw_aff_from_multi_aff(ma
);
3856 mupa_i
= isl_multi_union_pw_aff_from_multi_pw_aff(mpa
);
3857 mupa
= isl_multi_union_pw_aff_union_add(mupa
, mupa_i
);
3859 node
= isl_schedule_node_insert_partial_schedule(node
, mupa
);
3861 for (i
= 0; i
< n
; ++i
)
3862 node
= isl_schedule_node_band_member_set_coincident(node
, i
,
3863 graph
->node
[0].coincident
[start
+ i
]);
3864 node
= isl_schedule_node_band_set_permutable(node
, permutable
);
3869 /* Update the dependence relations based on the current schedule,
3870 * add the current band to "node" and then continue with the computation
3872 * Return the updated schedule node.
3874 static __isl_give isl_schedule_node
*compute_next_band(
3875 __isl_take isl_schedule_node
*node
,
3876 struct isl_sched_graph
*graph
, int permutable
)
3883 ctx
= isl_schedule_node_get_ctx(node
);
3884 if (update_edges(ctx
, graph
) < 0)
3885 return isl_schedule_node_free(node
);
3886 node
= insert_current_band(node
, graph
, permutable
);
3889 node
= isl_schedule_node_child(node
, 0);
3890 node
= compute_schedule(node
, graph
);
3891 node
= isl_schedule_node_parent(node
);
3896 /* Add the constraints "coef" derived from an edge from "node" to itself
3897 * to graph->lp in order to respect the dependences and to try and carry them.
3898 * "pos" is the sequence number of the edge that needs to be carried.
3899 * "coef" represents general constraints on coefficients (c_0, c_x)
3900 * of valid constraints for (y - x) with x and y instances of the node.
3902 * The constraints added to graph->lp need to enforce
3904 * (c_j_0 + c_j_x y) - (c_j_0 + c_j_x x)
3905 * = c_j_x (y - x) >= e_i
3907 * for each (x,y) in the dependence relation of the edge.
3908 * That is, (-e_i, c_j_x) needs to be plugged in for (c_0, c_x),
3909 * taking into account that each coefficient in c_j_x is represented
3910 * as a pair of non-negative coefficients.
3912 static isl_stat
add_intra_constraints(struct isl_sched_graph
*graph
,
3913 struct isl_sched_node
*node
, __isl_take isl_basic_set
*coef
, int pos
)
3917 isl_dim_map
*dim_map
;
3919 offset
= coef_var_offset(coef
);
3921 coef
= isl_basic_set_free(coef
);
3923 return isl_stat_error
;
3925 ctx
= isl_basic_set_get_ctx(coef
);
3926 dim_map
= intra_dim_map(ctx
, graph
, node
, offset
, 1);
3927 isl_dim_map_range(dim_map
, 3 + pos
, 0, 0, 0, 1, -1);
3928 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
3933 /* Add the constraints "coef" derived from an edge from "src" to "dst"
3934 * to graph->lp in order to respect the dependences and to try and carry them.
3935 * "pos" is the sequence number of the edge that needs to be carried or
3936 * -1 if no attempt should be made to carry the dependences.
3937 * "coef" represents general constraints on coefficients (c_0, c_n, c_x, c_y)
3938 * of valid constraints for (x, y) with x and y instances of "src" and "dst".
3940 * The constraints added to graph->lp need to enforce
3942 * (c_k_0 + c_k_n n + c_k_x y) - (c_j_0 + c_j_n n + c_j_x x) >= e_i
3944 * for each (x,y) in the dependence relation of the edge or
3946 * (c_k_0 + c_k_n n + c_k_x y) - (c_j_0 + c_j_n n + c_j_x x) >= 0
3950 * (-e_i + c_k_0 - c_j_0, c_k_n - c_j_n, -c_j_x, c_k_x)
3952 * (c_k_0 - c_j_0, c_k_n - c_j_n, -c_j_x, c_k_x)
3953 * needs to be plugged in for (c_0, c_n, c_x, c_y),
3954 * taking into account that each coefficient in c_j_x and c_k_x is represented
3955 * as a pair of non-negative coefficients.
3957 static isl_stat
add_inter_constraints(struct isl_sched_graph
*graph
,
3958 struct isl_sched_node
*src
, struct isl_sched_node
*dst
,
3959 __isl_take isl_basic_set
*coef
, int pos
)
3963 isl_dim_map
*dim_map
;
3965 offset
= coef_var_offset(coef
);
3967 coef
= isl_basic_set_free(coef
);
3969 return isl_stat_error
;
3971 ctx
= isl_basic_set_get_ctx(coef
);
3972 dim_map
= inter_dim_map(ctx
, graph
, src
, dst
, offset
, 1);
3974 isl_dim_map_range(dim_map
, 3 + pos
, 0, 0, 0, 1, -1);
3975 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
3980 /* Data structure for keeping track of the data needed
3981 * to exploit non-trivial lineality spaces.
3983 * "any_non_trivial" is true if there are any non-trivial lineality spaces.
3984 * If "any_non_trivial" is not true, then "equivalent" and "mask" may be NULL.
3985 * "equivalent" connects instances to other instances on the same line(s).
3986 * "mask" contains the domain spaces of "equivalent".
3987 * Any instance set not in "mask" does not have a non-trivial lineality space.
3989 struct isl_exploit_lineality_data
{
3990 isl_bool any_non_trivial
;
3991 isl_union_map
*equivalent
;
3992 isl_union_set
*mask
;
3995 /* Data structure collecting information used during the construction
3996 * of an LP for carrying dependences.
3998 * "intra" is a sequence of coefficient constraints for intra-node edges.
3999 * "inter" is a sequence of coefficient constraints for inter-node edges.
4000 * "lineality" contains data used to exploit non-trivial lineality spaces.
4003 isl_basic_set_list
*intra
;
4004 isl_basic_set_list
*inter
;
4005 struct isl_exploit_lineality_data lineality
;
4008 /* Free all the data stored in "carry".
4010 static void isl_carry_clear(struct isl_carry
*carry
)
4012 isl_basic_set_list_free(carry
->intra
);
4013 isl_basic_set_list_free(carry
->inter
);
4014 isl_union_map_free(carry
->lineality
.equivalent
);
4015 isl_union_set_free(carry
->lineality
.mask
);
4018 /* Return a pointer to the node in "graph" that lives in "space".
4019 * If the requested node has been compressed, then "space"
4020 * corresponds to the compressed space.
4021 * The graph is assumed to have such a node.
4022 * Return NULL in case of error.
4024 * First try and see if "space" is the space of an uncompressed node.
4025 * If so, return that node.
4026 * Otherwise, "space" was constructed by construct_compressed_id and
4027 * contains a user pointer pointing to the node in the tuple id.
4028 * However, this node belongs to the original dependence graph.
4029 * If "graph" is a subgraph of this original dependence graph,
4030 * then the node with the same space still needs to be looked up
4031 * in the current graph.
4033 static struct isl_sched_node
*graph_find_compressed_node(isl_ctx
*ctx
,
4034 struct isl_sched_graph
*graph
, __isl_keep isl_space
*space
)
4037 struct isl_sched_node
*node
;
4042 node
= graph_find_node(ctx
, graph
, space
);
4045 if (is_node(graph
, node
))
4048 id
= isl_space_get_tuple_id(space
, isl_dim_set
);
4049 node
= isl_id_get_user(id
);
4055 if (!is_node(graph
->root
, node
))
4056 isl_die(ctx
, isl_error_internal
,
4057 "space points to invalid node", return NULL
);
4058 if (graph
!= graph
->root
)
4059 node
= graph_find_node(ctx
, graph
, node
->space
);
4060 if (!is_node(graph
, node
))
4061 isl_die(ctx
, isl_error_internal
,
4062 "unable to find node", return NULL
);
4067 /* Internal data structure for add_all_constraints.
4069 * "graph" is the schedule constraint graph for which an LP problem
4070 * is being constructed.
4071 * "carry_inter" indicates whether inter-node edges should be carried.
4072 * "pos" is the position of the next edge that needs to be carried.
4074 struct isl_add_all_constraints_data
{
4076 struct isl_sched_graph
*graph
;
4081 /* Add the constraints "coef" derived from an edge from a node to itself
4082 * to data->graph->lp in order to respect the dependences and
4083 * to try and carry them.
4085 * The space of "coef" is of the form
4087 * coefficients[[c_cst] -> S[c_x]]
4089 * with S[c_x] the (compressed) space of the node.
4090 * Extract the node from the space and call add_intra_constraints.
4092 static isl_stat
lp_add_intra(__isl_take isl_basic_set
*coef
, void *user
)
4094 struct isl_add_all_constraints_data
*data
= user
;
4096 struct isl_sched_node
*node
;
4098 space
= isl_basic_set_get_space(coef
);
4099 space
= isl_space_range(isl_space_unwrap(space
));
4100 node
= graph_find_compressed_node(data
->ctx
, data
->graph
, space
);
4101 isl_space_free(space
);
4102 return add_intra_constraints(data
->graph
, node
, coef
, data
->pos
++);
4105 /* Add the constraints "coef" derived from an edge from a node j
4106 * to a node k to data->graph->lp in order to respect the dependences and
4107 * to try and carry them (provided data->carry_inter is set).
4109 * The space of "coef" is of the form
4111 * coefficients[[c_cst, c_n] -> [S_j[c_x] -> S_k[c_y]]]
4113 * with S_j[c_x] and S_k[c_y] the (compressed) spaces of the nodes.
4114 * Extract the nodes from the space and call add_inter_constraints.
4116 static isl_stat
lp_add_inter(__isl_take isl_basic_set
*coef
, void *user
)
4118 struct isl_add_all_constraints_data
*data
= user
;
4119 isl_space
*space
, *dom
;
4120 struct isl_sched_node
*src
, *dst
;
4123 space
= isl_basic_set_get_space(coef
);
4124 space
= isl_space_unwrap(isl_space_range(isl_space_unwrap(space
)));
4125 dom
= isl_space_domain(isl_space_copy(space
));
4126 src
= graph_find_compressed_node(data
->ctx
, data
->graph
, dom
);
4127 isl_space_free(dom
);
4128 space
= isl_space_range(space
);
4129 dst
= graph_find_compressed_node(data
->ctx
, data
->graph
, space
);
4130 isl_space_free(space
);
4132 pos
= data
->carry_inter
? data
->pos
++ : -1;
4133 return add_inter_constraints(data
->graph
, src
, dst
, coef
, pos
);
4136 /* Add constraints to graph->lp that force all (conditional) validity
4137 * dependences to be respected and attempt to carry them.
4138 * "intra" is the sequence of coefficient constraints for intra-node edges.
4139 * "inter" is the sequence of coefficient constraints for inter-node edges.
4140 * "carry_inter" indicates whether inter-node edges should be carried or
4143 static isl_stat
add_all_constraints(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
4144 __isl_keep isl_basic_set_list
*intra
,
4145 __isl_keep isl_basic_set_list
*inter
, int carry_inter
)
4147 struct isl_add_all_constraints_data data
= { ctx
, graph
, carry_inter
};
4150 if (isl_basic_set_list_foreach(intra
, &lp_add_intra
, &data
) < 0)
4151 return isl_stat_error
;
4152 if (isl_basic_set_list_foreach(inter
, &lp_add_inter
, &data
) < 0)
4153 return isl_stat_error
;
4157 /* Internal data structure for count_all_constraints
4158 * for keeping track of the number of equality and inequality constraints.
4160 struct isl_sched_count
{
4165 /* Add the number of equality and inequality constraints of "bset"
4166 * to data->n_eq and data->n_ineq.
4168 static isl_stat
bset_update_count(__isl_take isl_basic_set
*bset
, void *user
)
4170 struct isl_sched_count
*data
= user
;
4172 return update_count(bset
, 1, &data
->n_eq
, &data
->n_ineq
);
4175 /* Count the number of equality and inequality constraints
4176 * that will be added to the carry_lp problem.
4177 * We count each edge exactly once.
4178 * "intra" is the sequence of coefficient constraints for intra-node edges.
4179 * "inter" is the sequence of coefficient constraints for inter-node edges.
4181 static isl_stat
count_all_constraints(__isl_keep isl_basic_set_list
*intra
,
4182 __isl_keep isl_basic_set_list
*inter
, int *n_eq
, int *n_ineq
)
4184 struct isl_sched_count data
;
4186 data
.n_eq
= data
.n_ineq
= 0;
4187 if (isl_basic_set_list_foreach(inter
, &bset_update_count
, &data
) < 0)
4188 return isl_stat_error
;
4189 if (isl_basic_set_list_foreach(intra
, &bset_update_count
, &data
) < 0)
4190 return isl_stat_error
;
4193 *n_ineq
= data
.n_ineq
;
4198 /* Construct an LP problem for finding schedule coefficients
4199 * such that the schedule carries as many validity dependences as possible.
4200 * In particular, for each dependence i, we bound the dependence distance
4201 * from below by e_i, with 0 <= e_i <= 1 and then maximize the sum
4202 * of all e_i's. Dependences with e_i = 0 in the solution are simply
4203 * respected, while those with e_i > 0 (in practice e_i = 1) are carried.
4204 * "intra" is the sequence of coefficient constraints for intra-node edges.
4205 * "inter" is the sequence of coefficient constraints for inter-node edges.
4206 * "n_edge" is the total number of edges.
4207 * "carry_inter" indicates whether inter-node edges should be carried or
4208 * only respected. That is, if "carry_inter" is not set, then
4209 * no e_i variables are introduced for the inter-node edges.
4211 * All variables of the LP are non-negative. The actual coefficients
4212 * may be negative, so each coefficient is represented as the difference
4213 * of two non-negative variables. The negative part always appears
4214 * immediately before the positive part.
4215 * Other than that, the variables have the following order
4217 * - sum of (1 - e_i) over all edges
4218 * - sum of all c_n coefficients
4219 * (unconstrained when computing non-parametric schedules)
4220 * - sum of positive and negative parts of all c_x coefficients
4224 * - positive and negative parts of c_i_x, in opposite order
4225 * - c_i_n (if parametric)
4228 * The constraints are those from the (validity) edges plus three equalities
4229 * to express the sums and n_edge inequalities to express e_i <= 1.
4231 static isl_stat
setup_carry_lp(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
4232 int n_edge
, __isl_keep isl_basic_set_list
*intra
,
4233 __isl_keep isl_basic_set_list
*inter
, int carry_inter
)
4242 for (i
= 0; i
< graph
->n
; ++i
) {
4243 struct isl_sched_node
*node
= &graph
->node
[graph
->sorted
[i
]];
4244 node
->start
= total
;
4245 total
+= 1 + node
->nparam
+ 2 * node
->nvar
;
4248 if (count_all_constraints(intra
, inter
, &n_eq
, &n_ineq
) < 0)
4249 return isl_stat_error
;
4251 dim
= isl_space_set_alloc(ctx
, 0, total
);
4252 isl_basic_set_free(graph
->lp
);
4255 graph
->lp
= isl_basic_set_alloc_space(dim
, 0, n_eq
, n_ineq
);
4256 graph
->lp
= isl_basic_set_set_rational(graph
->lp
);
4258 k
= isl_basic_set_alloc_equality(graph
->lp
);
4260 return isl_stat_error
;
4261 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
4262 isl_int_set_si(graph
->lp
->eq
[k
][0], -n_edge
);
4263 isl_int_set_si(graph
->lp
->eq
[k
][1], 1);
4264 for (i
= 0; i
< n_edge
; ++i
)
4265 isl_int_set_si(graph
->lp
->eq
[k
][4 + i
], 1);
4267 if (add_param_sum_constraint(graph
, 1) < 0)
4268 return isl_stat_error
;
4269 if (add_var_sum_constraint(graph
, 2) < 0)
4270 return isl_stat_error
;
4272 for (i
= 0; i
< n_edge
; ++i
) {
4273 k
= isl_basic_set_alloc_inequality(graph
->lp
);
4275 return isl_stat_error
;
4276 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
4277 isl_int_set_si(graph
->lp
->ineq
[k
][4 + i
], -1);
4278 isl_int_set_si(graph
->lp
->ineq
[k
][0], 1);
4281 if (add_all_constraints(ctx
, graph
, intra
, inter
, carry_inter
) < 0)
4282 return isl_stat_error
;
4287 static __isl_give isl_schedule_node
*compute_component_schedule(
4288 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
4291 /* If the schedule_split_scaled option is set and if the linear
4292 * parts of the scheduling rows for all nodes in the graphs have
4293 * a non-trivial common divisor, then remove this
4294 * common divisor from the linear part.
4295 * Otherwise, insert a band node directly and continue with
4296 * the construction of the schedule.
4298 * If a non-trivial common divisor is found, then
4299 * the linear part is reduced and the remainder is ignored.
4300 * The pieces of the graph that are assigned different remainders
4301 * form (groups of) strongly connected components within
4302 * the scaled down band. If needed, they can therefore
4303 * be ordered along this remainder in a sequence node.
4304 * However, this ordering is not enforced here in order to allow
4305 * the scheduler to combine some of the strongly connected components.
4307 static __isl_give isl_schedule_node
*split_scaled(
4308 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
4319 ctx
= isl_schedule_node_get_ctx(node
);
4320 if (!ctx
->opt
->schedule_split_scaled
)
4321 return compute_next_band(node
, graph
, 0);
4323 return compute_next_band(node
, graph
, 0);
4324 n_row
= isl_mat_rows(graph
->node
[0].sched
);
4326 return isl_schedule_node_free(node
);
4329 isl_int_init(gcd_i
);
4331 isl_int_set_si(gcd
, 0);
4335 for (i
= 0; i
< graph
->n
; ++i
) {
4336 struct isl_sched_node
*node
= &graph
->node
[i
];
4337 isl_size cols
= isl_mat_cols(node
->sched
);
4341 isl_seq_gcd(node
->sched
->row
[row
] + 1, cols
- 1, &gcd_i
);
4342 isl_int_gcd(gcd
, gcd
, gcd_i
);
4345 isl_int_clear(gcd_i
);
4349 if (isl_int_cmp_si(gcd
, 1) <= 0) {
4351 return compute_next_band(node
, graph
, 0);
4354 for (i
= 0; i
< graph
->n
; ++i
) {
4355 struct isl_sched_node
*node
= &graph
->node
[i
];
4357 isl_int_fdiv_q(node
->sched
->row
[row
][0],
4358 node
->sched
->row
[row
][0], gcd
);
4359 isl_int_mul(node
->sched
->row
[row
][0],
4360 node
->sched
->row
[row
][0], gcd
);
4361 node
->sched
= isl_mat_scale_down_row(node
->sched
, row
, gcd
);
4368 return compute_next_band(node
, graph
, 0);
4371 return isl_schedule_node_free(node
);
4374 /* Is the schedule row "sol" trivial on node "node"?
4375 * That is, is the solution zero on the dimensions linearly independent of
4376 * the previously found solutions?
4377 * Return 1 if the solution is trivial, 0 if it is not and -1 on error.
4379 * Each coefficient is represented as the difference between
4380 * two non-negative values in "sol".
4381 * We construct the schedule row s and check if it is linearly
4382 * independent of previously computed schedule rows
4383 * by computing T s, with T the linear combinations that are zero
4384 * on linearly dependent schedule rows.
4385 * If the result consists of all zeros, then the solution is trivial.
4387 static int is_trivial(struct isl_sched_node
*node
, __isl_keep isl_vec
*sol
)
4394 if (node
->nvar
== node
->rank
)
4397 node_sol
= extract_var_coef(node
, sol
);
4398 node_sol
= isl_mat_vec_product(isl_mat_copy(node
->indep
), node_sol
);
4402 trivial
= isl_seq_first_non_zero(node_sol
->el
,
4403 node
->nvar
- node
->rank
) == -1;
4405 isl_vec_free(node_sol
);
4410 /* Is the schedule row "sol" trivial on any node where it should
4412 * Return 1 if any solution is trivial, 0 if they are not and -1 on error.
4414 static int is_any_trivial(struct isl_sched_graph
*graph
,
4415 __isl_keep isl_vec
*sol
)
4419 for (i
= 0; i
< graph
->n
; ++i
) {
4420 struct isl_sched_node
*node
= &graph
->node
[i
];
4423 if (!needs_row(graph
, node
))
4425 trivial
= is_trivial(node
, sol
);
4426 if (trivial
< 0 || trivial
)
4433 /* Does the schedule represented by "sol" perform loop coalescing on "node"?
4434 * If so, return the position of the coalesced dimension.
4435 * Otherwise, return node->nvar or -1 on error.
4437 * In particular, look for pairs of coefficients c_i and c_j such that
4438 * |c_j/c_i| > ceil(size_i/2), i.e., |c_j| > |c_i * ceil(size_i/2)|.
4439 * If any such pair is found, then return i.
4440 * If size_i is infinity, then no check on c_i needs to be performed.
4442 static int find_node_coalescing(struct isl_sched_node
*node
,
4443 __isl_keep isl_vec
*sol
)
4449 if (node
->nvar
<= 1)
4452 csol
= extract_var_coef(node
, sol
);
4456 for (i
= 0; i
< node
->nvar
; ++i
) {
4459 if (isl_int_is_zero(csol
->el
[i
]))
4461 v
= isl_multi_val_get_val(node
->sizes
, i
);
4464 if (!isl_val_is_int(v
)) {
4468 v
= isl_val_div_ui(v
, 2);
4469 v
= isl_val_ceil(v
);
4472 isl_int_mul(max
, v
->n
, csol
->el
[i
]);
4475 for (j
= 0; j
< node
->nvar
; ++j
) {
4478 if (isl_int_abs_gt(csol
->el
[j
], max
))
4494 /* Force the schedule coefficient at position "pos" of "node" to be zero
4496 * The coefficient is encoded as the difference between two non-negative
4497 * variables. Force these two variables to have the same value.
4499 static __isl_give isl_tab_lexmin
*zero_out_node_coef(
4500 __isl_take isl_tab_lexmin
*tl
, struct isl_sched_node
*node
, int pos
)
4506 ctx
= isl_space_get_ctx(node
->space
);
4507 dim
= isl_tab_lexmin_dim(tl
);
4509 return isl_tab_lexmin_free(tl
);
4510 eq
= isl_vec_alloc(ctx
, 1 + dim
);
4511 eq
= isl_vec_clr(eq
);
4513 return isl_tab_lexmin_free(tl
);
4515 pos
= 1 + node_var_coef_pos(node
, pos
);
4516 isl_int_set_si(eq
->el
[pos
], 1);
4517 isl_int_set_si(eq
->el
[pos
+ 1], -1);
4518 tl
= isl_tab_lexmin_add_eq(tl
, eq
->el
);
4524 /* Return the lexicographically smallest rational point in the basic set
4525 * from which "tl" was constructed, double checking that this input set
4528 static __isl_give isl_vec
*non_empty_solution(__isl_keep isl_tab_lexmin
*tl
)
4532 sol
= isl_tab_lexmin_get_solution(tl
);
4536 isl_die(isl_vec_get_ctx(sol
), isl_error_internal
,
4537 "error in schedule construction",
4538 return isl_vec_free(sol
));
4542 /* Does the solution "sol" of the LP problem constructed by setup_carry_lp
4543 * carry any of the "n_edge" groups of dependences?
4544 * The value in the first position is the sum of (1 - e_i) over all "n_edge"
4545 * edges, with 0 <= e_i <= 1 equal to 1 when the dependences represented
4546 * by the edge are carried by the solution.
4547 * If the sum of the (1 - e_i) is smaller than "n_edge" then at least
4548 * one of those is carried.
4550 * Note that despite the fact that the problem is solved using a rational
4551 * solver, the solution is guaranteed to be integral.
4552 * Specifically, the dependence distance lower bounds e_i (and therefore
4553 * also their sum) are integers. See Lemma 5 of [1].
4555 * Any potential denominator of the sum is cleared by this function.
4556 * The denominator is not relevant for any of the other elements
4559 * [1] P. Feautrier, Some Efficient Solutions to the Affine Scheduling
4560 * Problem, Part II: Multi-Dimensional Time.
4561 * In Intl. Journal of Parallel Programming, 1992.
4563 static int carries_dependences(__isl_keep isl_vec
*sol
, int n_edge
)
4565 isl_int_divexact(sol
->el
[1], sol
->el
[1], sol
->el
[0]);
4566 isl_int_set_si(sol
->el
[0], 1);
4567 return isl_int_cmp_si(sol
->el
[1], n_edge
) < 0;
4570 /* Return the lexicographically smallest rational point in "lp",
4571 * assuming that all variables are non-negative and performing some
4572 * additional sanity checks.
4573 * If "want_integral" is set, then compute the lexicographically smallest
4574 * integer point instead.
4575 * In particular, "lp" should not be empty by construction.
4576 * Double check that this is the case.
4577 * If dependences are not carried for any of the "n_edge" edges,
4578 * then return an empty vector.
4580 * If the schedule_treat_coalescing option is set and
4581 * if the computed schedule performs loop coalescing on a given node,
4582 * i.e., if it is of the form
4584 * c_i i + c_j j + ...
4586 * with |c_j/c_i| >= size_i, then force the coefficient c_i to be zero
4587 * to cut out this solution. Repeat this process until no more loop
4588 * coalescing occurs or until no more dependences can be carried.
4589 * In the latter case, revert to the previously computed solution.
4591 * If the caller requests an integral solution and if coalescing should
4592 * be treated, then perform the coalescing treatment first as
4593 * an integral solution computed before coalescing treatment
4594 * would carry the same number of edges and would therefore probably
4595 * also be coalescing.
4597 * To allow the coalescing treatment to be performed first,
4598 * the initial solution is allowed to be rational and it is only
4599 * cut out (if needed) in the next iteration, if no coalescing measures
4602 static __isl_give isl_vec
*non_neg_lexmin(struct isl_sched_graph
*graph
,
4603 __isl_take isl_basic_set
*lp
, int n_edge
, int want_integral
)
4608 isl_vec
*sol
= NULL
, *prev
;
4609 int treat_coalescing
;
4614 ctx
= isl_basic_set_get_ctx(lp
);
4615 treat_coalescing
= isl_options_get_schedule_treat_coalescing(ctx
);
4616 tl
= isl_tab_lexmin_from_basic_set(lp
);
4624 tl
= isl_tab_lexmin_cut_to_integer(tl
);
4626 sol
= non_empty_solution(tl
);
4630 integral
= isl_int_is_one(sol
->el
[0]);
4631 if (!carries_dependences(sol
, n_edge
)) {
4633 prev
= isl_vec_alloc(ctx
, 0);
4638 prev
= isl_vec_free(prev
);
4639 cut
= want_integral
&& !integral
;
4642 if (!treat_coalescing
)
4644 for (i
= 0; i
< graph
->n
; ++i
) {
4645 struct isl_sched_node
*node
= &graph
->node
[i
];
4647 pos
= find_node_coalescing(node
, sol
);
4650 if (pos
< node
->nvar
)
4655 tl
= zero_out_node_coef(tl
, &graph
->node
[i
], pos
);
4658 } while (try_again
);
4660 isl_tab_lexmin_free(tl
);
4664 isl_tab_lexmin_free(tl
);
4670 /* If "edge" is an edge from a node to itself, then add the corresponding
4671 * dependence relation to "umap".
4672 * If "node" has been compressed, then the dependence relation
4673 * is also compressed first.
4675 static __isl_give isl_union_map
*add_intra(__isl_take isl_union_map
*umap
,
4676 struct isl_sched_edge
*edge
)
4679 struct isl_sched_node
*node
= edge
->src
;
4681 if (edge
->src
!= edge
->dst
)
4684 map
= isl_map_copy(edge
->map
);
4685 if (node
->compressed
) {
4686 map
= isl_map_preimage_domain_multi_aff(map
,
4687 isl_multi_aff_copy(node
->decompress
));
4688 map
= isl_map_preimage_range_multi_aff(map
,
4689 isl_multi_aff_copy(node
->decompress
));
4691 umap
= isl_union_map_add_map(umap
, map
);
4695 /* If "edge" is an edge from a node to another node, then add the corresponding
4696 * dependence relation to "umap".
4697 * If the source or destination nodes of "edge" have been compressed,
4698 * then the dependence relation is also compressed first.
4700 static __isl_give isl_union_map
*add_inter(__isl_take isl_union_map
*umap
,
4701 struct isl_sched_edge
*edge
)
4705 if (edge
->src
== edge
->dst
)
4708 map
= isl_map_copy(edge
->map
);
4709 if (edge
->src
->compressed
)
4710 map
= isl_map_preimage_domain_multi_aff(map
,
4711 isl_multi_aff_copy(edge
->src
->decompress
));
4712 if (edge
->dst
->compressed
)
4713 map
= isl_map_preimage_range_multi_aff(map
,
4714 isl_multi_aff_copy(edge
->dst
->decompress
));
4715 umap
= isl_union_map_add_map(umap
, map
);
4719 /* Internal data structure used by union_drop_coalescing_constraints
4720 * to collect bounds on all relevant statements.
4722 * "graph" is the schedule constraint graph for which an LP problem
4723 * is being constructed.
4724 * "bounds" collects the bounds.
4726 struct isl_collect_bounds_data
{
4728 struct isl_sched_graph
*graph
;
4729 isl_union_set
*bounds
;
4732 /* Add the size bounds for the node with instance deltas in "set"
4735 static isl_stat
collect_bounds(__isl_take isl_set
*set
, void *user
)
4737 struct isl_collect_bounds_data
*data
= user
;
4738 struct isl_sched_node
*node
;
4742 space
= isl_set_get_space(set
);
4745 node
= graph_find_compressed_node(data
->ctx
, data
->graph
, space
);
4746 isl_space_free(space
);
4748 bounds
= isl_set_from_basic_set(get_size_bounds(node
));
4749 data
->bounds
= isl_union_set_add_set(data
->bounds
, bounds
);
4754 /* Drop some constraints from "delta" that could be exploited
4755 * to construct loop coalescing schedules.
4756 * In particular, drop those constraint that bound the difference
4757 * to the size of the domain.
4758 * Do this for each set/node in "delta" separately.
4759 * The parameters are assumed to have been projected out by the caller.
4761 static __isl_give isl_union_set
*union_drop_coalescing_constraints(isl_ctx
*ctx
,
4762 struct isl_sched_graph
*graph
, __isl_take isl_union_set
*delta
)
4764 struct isl_collect_bounds_data data
= { ctx
, graph
};
4766 data
.bounds
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
4767 if (isl_union_set_foreach_set(delta
, &collect_bounds
, &data
) < 0)
4768 data
.bounds
= isl_union_set_free(data
.bounds
);
4769 delta
= isl_union_set_plain_gist(delta
, data
.bounds
);
4774 /* Given a non-trivial lineality space "lineality", add the corresponding
4775 * universe set to data->mask and add a map from elements to
4776 * other elements along the lines in "lineality" to data->equivalent.
4777 * If this is the first time this function gets called
4778 * (data->any_non_trivial is still false), then set data->any_non_trivial and
4779 * initialize data->mask and data->equivalent.
4781 * In particular, if the lineality space is defined by equality constraints
4785 * then construct an affine mapping
4789 * and compute the equivalence relation of having the same image under f:
4791 * { x -> x' : E x = E x' }
4793 static isl_stat
add_non_trivial_lineality(__isl_take isl_basic_set
*lineality
,
4794 struct isl_exploit_lineality_data
*data
)
4800 isl_multi_pw_aff
*mpa
;
4804 if (isl_basic_set_check_no_locals(lineality
) < 0)
4807 space
= isl_basic_set_get_space(lineality
);
4808 if (!data
->any_non_trivial
) {
4809 data
->equivalent
= isl_union_map_empty(isl_space_copy(space
));
4810 data
->mask
= isl_union_set_empty(isl_space_copy(space
));
4812 data
->any_non_trivial
= isl_bool_true
;
4814 univ
= isl_set_universe(isl_space_copy(space
));
4815 data
->mask
= isl_union_set_add_set(data
->mask
, univ
);
4817 eq
= isl_basic_set_extract_equalities(lineality
);
4818 n
= isl_mat_rows(eq
);
4820 space
= isl_space_free(space
);
4821 eq
= isl_mat_insert_zero_rows(eq
, 0, 1);
4822 eq
= isl_mat_set_element_si(eq
, 0, 0, 1);
4823 space
= isl_space_from_domain(space
);
4824 space
= isl_space_add_dims(space
, isl_dim_out
, n
);
4825 ma
= isl_multi_aff_from_aff_mat(space
, eq
);
4826 mpa
= isl_multi_pw_aff_from_multi_aff(ma
);
4827 map
= isl_multi_pw_aff_eq_map(mpa
, isl_multi_pw_aff_copy(mpa
));
4828 data
->equivalent
= isl_union_map_add_map(data
->equivalent
, map
);
4830 isl_basic_set_free(lineality
);
4833 isl_basic_set_free(lineality
);
4834 return isl_stat_error
;
4837 /* Check if the lineality space "set" is non-trivial (i.e., is not just
4838 * the origin or, in other words, satisfies a number of equality constraints
4839 * that is smaller than the dimension of the set).
4840 * If so, extend data->mask and data->equivalent accordingly.
4842 * The input should not have any local variables already, but
4843 * isl_set_remove_divs is called to make sure it does not.
4845 static isl_stat
add_lineality(__isl_take isl_set
*set
, void *user
)
4847 struct isl_exploit_lineality_data
*data
= user
;
4848 isl_basic_set
*hull
;
4852 set
= isl_set_remove_divs(set
);
4853 hull
= isl_set_unshifted_simple_hull(set
);
4854 dim
= isl_basic_set_dim(hull
, isl_dim_set
);
4855 n_eq
= isl_basic_set_n_equality(hull
);
4859 return add_non_trivial_lineality(hull
, data
);
4860 isl_basic_set_free(hull
);
4863 isl_basic_set_free(hull
);
4864 return isl_stat_error
;
4867 /* Check if the difference set on intra-node schedule constraints "intra"
4868 * has any non-trivial lineality space.
4869 * If so, then extend the difference set to a difference set
4870 * on equivalent elements. That is, if "intra" is
4872 * { y - x : (x,y) \in V }
4874 * and elements are equivalent if they have the same image under f,
4877 * { y' - x' : (x,y) \in V and f(x) = f(x') and f(y) = f(y') }
4879 * or, since f is linear,
4881 * { y' - x' : (x,y) \in V and f(y - x) = f(y' - x') }
4883 * The results of the search for non-trivial lineality spaces is stored
4886 static __isl_give isl_union_set
*exploit_intra_lineality(
4887 __isl_take isl_union_set
*intra
,
4888 struct isl_exploit_lineality_data
*data
)
4890 isl_union_set
*lineality
;
4891 isl_union_set
*uset
;
4893 data
->any_non_trivial
= isl_bool_false
;
4894 lineality
= isl_union_set_copy(intra
);
4895 lineality
= isl_union_set_combined_lineality_space(lineality
);
4896 if (isl_union_set_foreach_set(lineality
, &add_lineality
, data
) < 0)
4897 data
->any_non_trivial
= isl_bool_error
;
4898 isl_union_set_free(lineality
);
4900 if (data
->any_non_trivial
< 0)
4901 return isl_union_set_free(intra
);
4902 if (!data
->any_non_trivial
)
4905 uset
= isl_union_set_copy(intra
);
4906 intra
= isl_union_set_subtract(intra
, isl_union_set_copy(data
->mask
));
4907 uset
= isl_union_set_apply(uset
, isl_union_map_copy(data
->equivalent
));
4908 intra
= isl_union_set_union(intra
, uset
);
4910 intra
= isl_union_set_remove_divs(intra
);
4915 /* If the difference set on intra-node schedule constraints was found to have
4916 * any non-trivial lineality space by exploit_intra_lineality,
4917 * as recorded in "data", then extend the inter-node
4918 * schedule constraints "inter" to schedule constraints on equivalent elements.
4919 * That is, if "inter" is V and
4920 * elements are equivalent if they have the same image under f, then return
4922 * { (x', y') : (x,y) \in V and f(x) = f(x') and f(y) = f(y') }
4924 static __isl_give isl_union_map
*exploit_inter_lineality(
4925 __isl_take isl_union_map
*inter
,
4926 struct isl_exploit_lineality_data
*data
)
4928 isl_union_map
*umap
;
4930 if (data
->any_non_trivial
< 0)
4931 return isl_union_map_free(inter
);
4932 if (!data
->any_non_trivial
)
4935 umap
= isl_union_map_copy(inter
);
4936 inter
= isl_union_map_subtract_range(inter
,
4937 isl_union_set_copy(data
->mask
));
4938 umap
= isl_union_map_apply_range(umap
,
4939 isl_union_map_copy(data
->equivalent
));
4940 inter
= isl_union_map_union(inter
, umap
);
4941 umap
= isl_union_map_copy(inter
);
4942 inter
= isl_union_map_subtract_domain(inter
,
4943 isl_union_set_copy(data
->mask
));
4944 umap
= isl_union_map_apply_range(isl_union_map_copy(data
->equivalent
),
4946 inter
= isl_union_map_union(inter
, umap
);
4948 inter
= isl_union_map_remove_divs(inter
);
4953 /* For each (conditional) validity edge in "graph",
4954 * add the corresponding dependence relation using "add"
4955 * to a collection of dependence relations and return the result.
4956 * If "coincidence" is set, then coincidence edges are considered as well.
4958 static __isl_give isl_union_map
*collect_validity(struct isl_sched_graph
*graph
,
4959 __isl_give isl_union_map
*(*add
)(__isl_take isl_union_map
*umap
,
4960 struct isl_sched_edge
*edge
), int coincidence
)
4964 isl_union_map
*umap
;
4966 space
= isl_space_copy(graph
->node
[0].space
);
4967 umap
= isl_union_map_empty(space
);
4969 for (i
= 0; i
< graph
->n_edge
; ++i
) {
4970 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
4972 if (!is_any_validity(edge
) &&
4973 (!coincidence
|| !is_coincidence(edge
)))
4976 umap
= add(umap
, edge
);
4982 /* For each dependence relation on a (conditional) validity edge
4983 * from a node to itself,
4984 * construct the set of coefficients of valid constraints for elements
4985 * in that dependence relation and collect the results.
4986 * If "coincidence" is set, then coincidence edges are considered as well.
4988 * In particular, for each dependence relation R, constraints
4989 * on coefficients (c_0, c_x) are constructed such that
4991 * c_0 + c_x d >= 0 for each d in delta R = { y - x | (x,y) in R }
4993 * If the schedule_treat_coalescing option is set, then some constraints
4994 * that could be exploited to construct coalescing schedules
4995 * are removed before the dual is computed, but after the parameters
4996 * have been projected out.
4997 * The entire computation is essentially the same as that performed
4998 * by intra_coefficients, except that it operates on multiple
4999 * edges together and that the parameters are always projected out.
5001 * Additionally, exploit any non-trivial lineality space
5002 * in the difference set after removing coalescing constraints and
5003 * store the results of the non-trivial lineality space detection in "data".
5004 * The procedure is currently run unconditionally, but it is unlikely
5005 * to find any non-trivial lineality spaces if no coalescing constraints
5006 * have been removed.
5008 * Note that if a dependence relation is a union of basic maps,
5009 * then each basic map needs to be treated individually as it may only
5010 * be possible to carry the dependences expressed by some of those
5011 * basic maps and not all of them.
5012 * The collected validity constraints are therefore not coalesced and
5013 * it is assumed that they are not coalesced automatically.
5014 * Duplicate basic maps can be removed, however.
5015 * In particular, if the same basic map appears as a disjunct
5016 * in multiple edges, then it only needs to be carried once.
5018 static __isl_give isl_basic_set_list
*collect_intra_validity(isl_ctx
*ctx
,
5019 struct isl_sched_graph
*graph
, int coincidence
,
5020 struct isl_exploit_lineality_data
*data
)
5022 isl_union_map
*intra
;
5023 isl_union_set
*delta
;
5024 isl_basic_set_list
*list
;
5026 intra
= collect_validity(graph
, &add_intra
, coincidence
);
5027 delta
= isl_union_map_deltas(intra
);
5028 delta
= isl_union_set_project_out_all_params(delta
);
5029 delta
= isl_union_set_remove_divs(delta
);
5030 if (isl_options_get_schedule_treat_coalescing(ctx
))
5031 delta
= union_drop_coalescing_constraints(ctx
, graph
, delta
);
5032 delta
= exploit_intra_lineality(delta
, data
);
5033 list
= isl_union_set_get_basic_set_list(delta
);
5034 isl_union_set_free(delta
);
5036 return isl_basic_set_list_coefficients(list
);
5039 /* For each dependence relation on a (conditional) validity edge
5040 * from a node to some other node,
5041 * construct the set of coefficients of valid constraints for elements
5042 * in that dependence relation and collect the results.
5043 * If "coincidence" is set, then coincidence edges are considered as well.
5045 * In particular, for each dependence relation R, constraints
5046 * on coefficients (c_0, c_n, c_x, c_y) are constructed such that
5048 * c_0 + c_n n + c_x x + c_y y >= 0 for each (x,y) in R
5050 * This computation is essentially the same as that performed
5051 * by inter_coefficients, except that it operates on multiple
5054 * Additionally, exploit any non-trivial lineality space
5055 * that may have been discovered by collect_intra_validity
5056 * (as stored in "data").
5058 * Note that if a dependence relation is a union of basic maps,
5059 * then each basic map needs to be treated individually as it may only
5060 * be possible to carry the dependences expressed by some of those
5061 * basic maps and not all of them.
5062 * The collected validity constraints are therefore not coalesced and
5063 * it is assumed that they are not coalesced automatically.
5064 * Duplicate basic maps can be removed, however.
5065 * In particular, if the same basic map appears as a disjunct
5066 * in multiple edges, then it only needs to be carried once.
5068 static __isl_give isl_basic_set_list
*collect_inter_validity(
5069 struct isl_sched_graph
*graph
, int coincidence
,
5070 struct isl_exploit_lineality_data
*data
)
5072 isl_union_map
*inter
;
5073 isl_union_set
*wrap
;
5074 isl_basic_set_list
*list
;
5076 inter
= collect_validity(graph
, &add_inter
, coincidence
);
5077 inter
= exploit_inter_lineality(inter
, data
);
5078 inter
= isl_union_map_remove_divs(inter
);
5079 wrap
= isl_union_map_wrap(inter
);
5080 list
= isl_union_set_get_basic_set_list(wrap
);
5081 isl_union_set_free(wrap
);
5082 return isl_basic_set_list_coefficients(list
);
5085 /* Construct an LP problem for finding schedule coefficients
5086 * such that the schedule carries as many of the "n_edge" groups of
5087 * dependences as possible based on the corresponding coefficient
5088 * constraints and return the lexicographically smallest non-trivial solution.
5089 * "intra" is the sequence of coefficient constraints for intra-node edges.
5090 * "inter" is the sequence of coefficient constraints for inter-node edges.
5091 * If "want_integral" is set, then compute an integral solution
5092 * for the coefficients rather than using the numerators
5093 * of a rational solution.
5094 * "carry_inter" indicates whether inter-node edges should be carried or
5097 * If none of the "n_edge" groups can be carried
5098 * then return an empty vector.
5100 static __isl_give isl_vec
*compute_carrying_sol_coef(isl_ctx
*ctx
,
5101 struct isl_sched_graph
*graph
, int n_edge
,
5102 __isl_keep isl_basic_set_list
*intra
,
5103 __isl_keep isl_basic_set_list
*inter
, int want_integral
,
5108 if (setup_carry_lp(ctx
, graph
, n_edge
, intra
, inter
, carry_inter
) < 0)
5111 lp
= isl_basic_set_copy(graph
->lp
);
5112 return non_neg_lexmin(graph
, lp
, n_edge
, want_integral
);
5115 /* Construct an LP problem for finding schedule coefficients
5116 * such that the schedule carries as many of the validity dependences
5118 * return the lexicographically smallest non-trivial solution.
5119 * If "fallback" is set, then the carrying is performed as a fallback
5120 * for the Pluto-like scheduler.
5121 * If "coincidence" is set, then try and carry coincidence edges as well.
5123 * The variable "n_edge" stores the number of groups that should be carried.
5124 * If none of the "n_edge" groups can be carried
5125 * then return an empty vector.
5126 * If, moreover, "n_edge" is zero, then the LP problem does not even
5127 * need to be constructed.
5129 * If a fallback solution is being computed, then compute an integral solution
5130 * for the coefficients rather than using the numerators
5131 * of a rational solution.
5133 * If a fallback solution is being computed, if there are any intra-node
5134 * dependences, and if requested by the user, then first try
5135 * to only carry those intra-node dependences.
5136 * If this fails to carry any dependences, then try again
5137 * with the inter-node dependences included.
5139 static __isl_give isl_vec
*compute_carrying_sol(isl_ctx
*ctx
,
5140 struct isl_sched_graph
*graph
, int fallback
, int coincidence
)
5142 isl_size n_intra
, n_inter
;
5144 struct isl_carry carry
= { 0 };
5147 carry
.intra
= collect_intra_validity(ctx
, graph
, coincidence
,
5149 carry
.inter
= collect_inter_validity(graph
, coincidence
,
5151 n_intra
= isl_basic_set_list_n_basic_set(carry
.intra
);
5152 n_inter
= isl_basic_set_list_n_basic_set(carry
.inter
);
5153 if (n_intra
< 0 || n_inter
< 0)
5156 if (fallback
&& n_intra
> 0 &&
5157 isl_options_get_schedule_carry_self_first(ctx
)) {
5158 sol
= compute_carrying_sol_coef(ctx
, graph
, n_intra
,
5159 carry
.intra
, carry
.inter
, fallback
, 0);
5160 if (!sol
|| sol
->size
!= 0 || n_inter
== 0) {
5161 isl_carry_clear(&carry
);
5167 n_edge
= n_intra
+ n_inter
;
5169 isl_carry_clear(&carry
);
5170 return isl_vec_alloc(ctx
, 0);
5173 sol
= compute_carrying_sol_coef(ctx
, graph
, n_edge
,
5174 carry
.intra
, carry
.inter
, fallback
, 1);
5175 isl_carry_clear(&carry
);
5178 isl_carry_clear(&carry
);
5182 /* Construct a schedule row for each node such that as many validity dependences
5183 * as possible are carried and then continue with the next band.
5184 * If "fallback" is set, then the carrying is performed as a fallback
5185 * for the Pluto-like scheduler.
5186 * If "coincidence" is set, then try and carry coincidence edges as well.
5188 * If there are no validity dependences, then no dependence can be carried and
5189 * the procedure is guaranteed to fail. If there is more than one component,
5190 * then try computing a schedule on each component separately
5191 * to prevent or at least postpone this failure.
5193 * If a schedule row is computed, then check that dependences are carried
5194 * for at least one of the edges.
5196 * If the computed schedule row turns out to be trivial on one or
5197 * more nodes where it should not be trivial, then we throw it away
5198 * and try again on each component separately.
5200 * If there is only one component, then we accept the schedule row anyway,
5201 * but we do not consider it as a complete row and therefore do not
5202 * increment graph->n_row. Note that the ranks of the nodes that
5203 * do get a non-trivial schedule part will get updated regardless and
5204 * graph->maxvar is computed based on these ranks. The test for
5205 * whether more schedule rows are required in compute_schedule_wcc
5206 * is therefore not affected.
5208 * Insert a band corresponding to the schedule row at position "node"
5209 * of the schedule tree and continue with the construction of the schedule.
5210 * This insertion and the continued construction is performed by split_scaled
5211 * after optionally checking for non-trivial common divisors.
5213 static __isl_give isl_schedule_node
*carry(__isl_take isl_schedule_node
*node
,
5214 struct isl_sched_graph
*graph
, int fallback
, int coincidence
)
5223 ctx
= isl_schedule_node_get_ctx(node
);
5224 sol
= compute_carrying_sol(ctx
, graph
, fallback
, coincidence
);
5226 return isl_schedule_node_free(node
);
5227 if (sol
->size
== 0) {
5230 return compute_component_schedule(node
, graph
, 1);
5231 isl_die(ctx
, isl_error_unknown
, "unable to carry dependences",
5232 return isl_schedule_node_free(node
));
5235 trivial
= is_any_trivial(graph
, sol
);
5237 sol
= isl_vec_free(sol
);
5238 } else if (trivial
&& graph
->scc
> 1) {
5240 return compute_component_schedule(node
, graph
, 1);
5243 if (update_schedule(graph
, sol
, 0) < 0)
5244 return isl_schedule_node_free(node
);
5248 return split_scaled(node
, graph
);
5251 /* Construct a schedule row for each node such that as many validity dependences
5252 * as possible are carried and then continue with the next band.
5253 * Do so as a fallback for the Pluto-like scheduler.
5254 * If "coincidence" is set, then try and carry coincidence edges as well.
5256 static __isl_give isl_schedule_node
*carry_fallback(
5257 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
5260 return carry(node
, graph
, 1, coincidence
);
5263 /* Construct a schedule row for each node such that as many validity dependences
5264 * as possible are carried and then continue with the next band.
5265 * Do so for the case where the Feautrier scheduler was selected
5268 static __isl_give isl_schedule_node
*carry_feautrier(
5269 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
5271 return carry(node
, graph
, 0, 0);
5274 /* Construct a schedule row for each node such that as many validity dependences
5275 * as possible are carried and then continue with the next band.
5276 * Do so as a fallback for the Pluto-like scheduler.
5278 static __isl_give isl_schedule_node
*carry_dependences(
5279 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
5281 return carry_fallback(node
, graph
, 0);
5284 /* Construct a schedule row for each node such that as many validity or
5285 * coincidence dependences as possible are carried and
5286 * then continue with the next band.
5287 * Do so as a fallback for the Pluto-like scheduler.
5289 static __isl_give isl_schedule_node
*carry_coincidence(
5290 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
5292 return carry_fallback(node
, graph
, 1);
5295 /* Topologically sort statements mapped to the same schedule iteration
5296 * and add insert a sequence node in front of "node"
5297 * corresponding to this order.
5298 * If "initialized" is set, then it may be assumed that compute_maxvar
5299 * has been called on the current band. Otherwise, call
5300 * compute_maxvar if and before carry_dependences gets called.
5302 * If it turns out to be impossible to sort the statements apart,
5303 * because different dependences impose different orderings
5304 * on the statements, then we extend the schedule such that
5305 * it carries at least one more dependence.
5307 static __isl_give isl_schedule_node
*sort_statements(
5308 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
5312 isl_union_set_list
*filters
;
5317 ctx
= isl_schedule_node_get_ctx(node
);
5319 isl_die(ctx
, isl_error_internal
,
5320 "graph should have at least one node",
5321 return isl_schedule_node_free(node
));
5326 if (update_edges(ctx
, graph
) < 0)
5327 return isl_schedule_node_free(node
);
5329 if (graph
->n_edge
== 0)
5332 if (detect_sccs(ctx
, graph
) < 0)
5333 return isl_schedule_node_free(node
);
5336 if (graph
->scc
< graph
->n
) {
5337 if (!initialized
&& compute_maxvar(graph
) < 0)
5338 return isl_schedule_node_free(node
);
5339 return carry_dependences(node
, graph
);
5342 filters
= extract_sccs(ctx
, graph
);
5343 node
= isl_schedule_node_insert_sequence(node
, filters
);
5348 /* Are there any (non-empty) (conditional) validity edges in the graph?
5350 static int has_validity_edges(struct isl_sched_graph
*graph
)
5354 for (i
= 0; i
< graph
->n_edge
; ++i
) {
5357 empty
= isl_map_plain_is_empty(graph
->edge
[i
].map
);
5362 if (is_any_validity(&graph
->edge
[i
]))
5369 /* Should we apply a Feautrier step?
5370 * That is, did the user request the Feautrier algorithm and are
5371 * there any validity dependences (left)?
5373 static int need_feautrier_step(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
5375 if (ctx
->opt
->schedule_algorithm
!= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
)
5378 return has_validity_edges(graph
);
5381 /* Compute a schedule for a connected dependence graph using Feautrier's
5382 * multi-dimensional scheduling algorithm and return the updated schedule node.
5384 * The original algorithm is described in [1].
5385 * The main idea is to minimize the number of scheduling dimensions, by
5386 * trying to satisfy as many dependences as possible per scheduling dimension.
5388 * [1] P. Feautrier, Some Efficient Solutions to the Affine Scheduling
5389 * Problem, Part II: Multi-Dimensional Time.
5390 * In Intl. Journal of Parallel Programming, 1992.
5392 static __isl_give isl_schedule_node
*compute_schedule_wcc_feautrier(
5393 isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
5395 return carry_feautrier(node
, graph
);
5398 /* Turn off the "local" bit on all (condition) edges.
5400 static void clear_local_edges(struct isl_sched_graph
*graph
)
5404 for (i
= 0; i
< graph
->n_edge
; ++i
)
5405 if (is_condition(&graph
->edge
[i
]))
5406 clear_local(&graph
->edge
[i
]);
5409 /* Does "graph" have both condition and conditional validity edges?
5411 static int need_condition_check(struct isl_sched_graph
*graph
)
5414 int any_condition
= 0;
5415 int any_conditional_validity
= 0;
5417 for (i
= 0; i
< graph
->n_edge
; ++i
) {
5418 if (is_condition(&graph
->edge
[i
]))
5420 if (is_conditional_validity(&graph
->edge
[i
]))
5421 any_conditional_validity
= 1;
5424 return any_condition
&& any_conditional_validity
;
5427 /* Does "graph" contain any coincidence edge?
5429 static int has_any_coincidence(struct isl_sched_graph
*graph
)
5433 for (i
= 0; i
< graph
->n_edge
; ++i
)
5434 if (is_coincidence(&graph
->edge
[i
]))
5440 /* Extract the final schedule row as a map with the iteration domain
5441 * of "node" as domain.
5443 static __isl_give isl_map
*final_row(struct isl_sched_node
*node
)
5448 n_row
= isl_mat_rows(node
->sched
);
5451 ma
= node_extract_partial_schedule_multi_aff(node
, n_row
- 1, 1);
5452 return isl_map_from_multi_aff(ma
);
5455 /* Is the conditional validity dependence in the edge with index "edge_index"
5456 * violated by the latest (i.e., final) row of the schedule?
5457 * That is, is i scheduled after j
5458 * for any conditional validity dependence i -> j?
5460 static int is_violated(struct isl_sched_graph
*graph
, int edge_index
)
5462 isl_map
*src_sched
, *dst_sched
, *map
;
5463 struct isl_sched_edge
*edge
= &graph
->edge
[edge_index
];
5466 src_sched
= final_row(edge
->src
);
5467 dst_sched
= final_row(edge
->dst
);
5468 map
= isl_map_copy(edge
->map
);
5469 map
= isl_map_apply_domain(map
, src_sched
);
5470 map
= isl_map_apply_range(map
, dst_sched
);
5471 map
= isl_map_order_gt(map
, isl_dim_in
, 0, isl_dim_out
, 0);
5472 empty
= isl_map_is_empty(map
);
5481 /* Does "graph" have any satisfied condition edges that
5482 * are adjacent to the conditional validity constraint with
5483 * domain "conditional_source" and range "conditional_sink"?
5485 * A satisfied condition is one that is not local.
5486 * If a condition was forced to be local already (i.e., marked as local)
5487 * then there is no need to check if it is in fact local.
5489 * Additionally, mark all adjacent condition edges found as local.
5491 static int has_adjacent_true_conditions(struct isl_sched_graph
*graph
,
5492 __isl_keep isl_union_set
*conditional_source
,
5493 __isl_keep isl_union_set
*conditional_sink
)
5498 for (i
= 0; i
< graph
->n_edge
; ++i
) {
5499 int adjacent
, local
;
5500 isl_union_map
*condition
;
5502 if (!is_condition(&graph
->edge
[i
]))
5504 if (is_local(&graph
->edge
[i
]))
5507 condition
= graph
->edge
[i
].tagged_condition
;
5508 adjacent
= domain_intersects(condition
, conditional_sink
);
5509 if (adjacent
>= 0 && !adjacent
)
5510 adjacent
= range_intersects(condition
,
5511 conditional_source
);
5517 set_local(&graph
->edge
[i
]);
5519 local
= is_condition_false(&graph
->edge
[i
]);
5529 /* Are there any violated conditional validity dependences with
5530 * adjacent condition dependences that are not local with respect
5531 * to the current schedule?
5532 * That is, is the conditional validity constraint violated?
5534 * Additionally, mark all those adjacent condition dependences as local.
5535 * We also mark those adjacent condition dependences that were not marked
5536 * as local before, but just happened to be local already. This ensures
5537 * that they remain local if the schedule is recomputed.
5539 * We first collect domain and range of all violated conditional validity
5540 * dependences and then check if there are any adjacent non-local
5541 * condition dependences.
5543 static int has_violated_conditional_constraint(isl_ctx
*ctx
,
5544 struct isl_sched_graph
*graph
)
5548 isl_union_set
*source
, *sink
;
5550 source
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
5551 sink
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
5552 for (i
= 0; i
< graph
->n_edge
; ++i
) {
5553 isl_union_set
*uset
;
5554 isl_union_map
*umap
;
5557 if (!is_conditional_validity(&graph
->edge
[i
]))
5560 violated
= is_violated(graph
, i
);
5568 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_validity
);
5569 uset
= isl_union_map_domain(umap
);
5570 source
= isl_union_set_union(source
, uset
);
5571 source
= isl_union_set_coalesce(source
);
5573 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_validity
);
5574 uset
= isl_union_map_range(umap
);
5575 sink
= isl_union_set_union(sink
, uset
);
5576 sink
= isl_union_set_coalesce(sink
);
5580 any
= has_adjacent_true_conditions(graph
, source
, sink
);
5582 isl_union_set_free(source
);
5583 isl_union_set_free(sink
);
5586 isl_union_set_free(source
);
5587 isl_union_set_free(sink
);
5591 /* Examine the current band (the rows between graph->band_start and
5592 * graph->n_total_row), deciding whether to drop it or add it to "node"
5593 * and then continue with the computation of the next band, if any.
5594 * If "initialized" is set, then it may be assumed that compute_maxvar
5595 * has been called on the current band. Otherwise, call
5596 * compute_maxvar if and before carry_dependences gets called.
5598 * The caller keeps looking for a new row as long as
5599 * graph->n_row < graph->maxvar. If the latest attempt to find
5600 * such a row failed (i.e., we still have graph->n_row < graph->maxvar),
5602 * - split between SCCs and start over (assuming we found an interesting
5603 * pair of SCCs between which to split)
5604 * - continue with the next band (assuming the current band has at least
5606 * - if there is more than one SCC left, then split along all SCCs
5607 * - if outer coincidence needs to be enforced, then try to carry as many
5608 * validity or coincidence dependences as possible and
5609 * continue with the next band
5610 * - try to carry as many validity dependences as possible and
5611 * continue with the next band
5612 * In each case, we first insert a band node in the schedule tree
5613 * if any rows have been computed.
5615 * If the caller managed to complete the schedule and the current band
5616 * is empty, then finish off by topologically
5617 * sorting the statements based on the remaining dependences.
5618 * If, on the other hand, the current band has at least one row,
5619 * then continue with the next band. Note that this next band
5620 * will necessarily be empty, but the graph may still be split up
5621 * into weakly connected components before arriving back here.
5623 static __isl_give isl_schedule_node
*compute_schedule_finish_band(
5624 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
5632 empty
= graph
->n_total_row
== graph
->band_start
;
5633 if (graph
->n_row
< graph
->maxvar
) {
5636 ctx
= isl_schedule_node_get_ctx(node
);
5637 if (!ctx
->opt
->schedule_maximize_band_depth
&& !empty
)
5638 return compute_next_band(node
, graph
, 1);
5639 if (graph
->src_scc
>= 0)
5640 return compute_split_schedule(node
, graph
);
5642 return compute_next_band(node
, graph
, 1);
5644 return compute_component_schedule(node
, graph
, 1);
5645 if (!initialized
&& compute_maxvar(graph
) < 0)
5646 return isl_schedule_node_free(node
);
5647 if (isl_options_get_schedule_outer_coincidence(ctx
))
5648 return carry_coincidence(node
, graph
);
5649 return carry_dependences(node
, graph
);
5653 return compute_next_band(node
, graph
, 1);
5654 return sort_statements(node
, graph
, initialized
);
5657 /* Construct a band of schedule rows for a connected dependence graph.
5658 * The caller is responsible for determining the strongly connected
5659 * components and calling compute_maxvar first.
5661 * We try to find a sequence of as many schedule rows as possible that result
5662 * in non-negative dependence distances (independent of the previous rows
5663 * in the sequence, i.e., such that the sequence is tilable), with as
5664 * many of the initial rows as possible satisfying the coincidence constraints.
5665 * The computation stops if we can't find any more rows or if we have found
5666 * all the rows we wanted to find.
5668 * If ctx->opt->schedule_outer_coincidence is set, then we force the
5669 * outermost dimension to satisfy the coincidence constraints. If this
5670 * turns out to be impossible, we fall back on the general scheme above
5671 * and try to carry as many dependences as possible.
5673 * If "graph" contains both condition and conditional validity dependences,
5674 * then we need to check that that the conditional schedule constraint
5675 * is satisfied, i.e., there are no violated conditional validity dependences
5676 * that are adjacent to any non-local condition dependences.
5677 * If there are, then we mark all those adjacent condition dependences
5678 * as local and recompute the current band. Those dependences that
5679 * are marked local will then be forced to be local.
5680 * The initial computation is performed with no dependences marked as local.
5681 * If we are lucky, then there will be no violated conditional validity
5682 * dependences adjacent to any non-local condition dependences.
5683 * Otherwise, we mark some additional condition dependences as local and
5684 * recompute. We continue this process until there are no violations left or
5685 * until we are no longer able to compute a schedule.
5686 * Since there are only a finite number of dependences,
5687 * there will only be a finite number of iterations.
5689 static isl_stat
compute_schedule_wcc_band(isl_ctx
*ctx
,
5690 struct isl_sched_graph
*graph
)
5692 int has_coincidence
;
5693 int use_coincidence
;
5694 int force_coincidence
= 0;
5695 int check_conditional
;
5697 if (sort_sccs(graph
) < 0)
5698 return isl_stat_error
;
5700 clear_local_edges(graph
);
5701 check_conditional
= need_condition_check(graph
);
5702 has_coincidence
= has_any_coincidence(graph
);
5704 if (ctx
->opt
->schedule_outer_coincidence
)
5705 force_coincidence
= 1;
5707 use_coincidence
= has_coincidence
;
5708 while (graph
->n_row
< graph
->maxvar
) {
5713 graph
->src_scc
= -1;
5714 graph
->dst_scc
= -1;
5716 if (setup_lp(ctx
, graph
, use_coincidence
) < 0)
5717 return isl_stat_error
;
5718 sol
= solve_lp(ctx
, graph
);
5720 return isl_stat_error
;
5721 if (sol
->size
== 0) {
5722 int empty
= graph
->n_total_row
== graph
->band_start
;
5725 if (use_coincidence
&& (!force_coincidence
|| !empty
)) {
5726 use_coincidence
= 0;
5731 coincident
= !has_coincidence
|| use_coincidence
;
5732 if (update_schedule(graph
, sol
, coincident
) < 0)
5733 return isl_stat_error
;
5735 if (!check_conditional
)
5737 violated
= has_violated_conditional_constraint(ctx
, graph
);
5739 return isl_stat_error
;
5742 if (reset_band(graph
) < 0)
5743 return isl_stat_error
;
5744 use_coincidence
= has_coincidence
;
5750 /* Compute a schedule for a connected dependence graph by considering
5751 * the graph as a whole and return the updated schedule node.
5753 * The actual schedule rows of the current band are computed by
5754 * compute_schedule_wcc_band. compute_schedule_finish_band takes
5755 * care of integrating the band into "node" and continuing
5758 static __isl_give isl_schedule_node
*compute_schedule_wcc_whole(
5759 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
5766 ctx
= isl_schedule_node_get_ctx(node
);
5767 if (compute_schedule_wcc_band(ctx
, graph
) < 0)
5768 return isl_schedule_node_free(node
);
5770 return compute_schedule_finish_band(node
, graph
, 1);
5773 /* Clustering information used by compute_schedule_wcc_clustering.
5775 * "n" is the number of SCCs in the original dependence graph
5776 * "scc" is an array of "n" elements, each representing an SCC
5777 * of the original dependence graph. All entries in the same cluster
5778 * have the same number of schedule rows.
5779 * "scc_cluster" maps each SCC index to the cluster to which it belongs,
5780 * where each cluster is represented by the index of the first SCC
5781 * in the cluster. Initially, each SCC belongs to a cluster containing
5784 * "scc_in_merge" is used by merge_clusters_along_edge to keep
5785 * track of which SCCs need to be merged.
5787 * "cluster" contains the merged clusters of SCCs after the clustering
5790 * "scc_node" is a temporary data structure used inside copy_partial.
5791 * For each SCC, it keeps track of the number of nodes in the SCC
5792 * that have already been copied.
5794 struct isl_clustering
{
5796 struct isl_sched_graph
*scc
;
5797 struct isl_sched_graph
*cluster
;
5803 /* Initialize the clustering data structure "c" from "graph".
5805 * In particular, allocate memory, extract the SCCs from "graph"
5806 * into c->scc, initialize scc_cluster and construct
5807 * a band of schedule rows for each SCC.
5808 * Within each SCC, there is only one SCC by definition.
5809 * Each SCC initially belongs to a cluster containing only that SCC.
5811 static isl_stat
clustering_init(isl_ctx
*ctx
, struct isl_clustering
*c
,
5812 struct isl_sched_graph
*graph
)
5817 c
->scc
= isl_calloc_array(ctx
, struct isl_sched_graph
, c
->n
);
5818 c
->cluster
= isl_calloc_array(ctx
, struct isl_sched_graph
, c
->n
);
5819 c
->scc_cluster
= isl_calloc_array(ctx
, int, c
->n
);
5820 c
->scc_node
= isl_calloc_array(ctx
, int, c
->n
);
5821 c
->scc_in_merge
= isl_calloc_array(ctx
, int, c
->n
);
5822 if (!c
->scc
|| !c
->cluster
||
5823 !c
->scc_cluster
|| !c
->scc_node
|| !c
->scc_in_merge
)
5824 return isl_stat_error
;
5826 for (i
= 0; i
< c
->n
; ++i
) {
5827 if (extract_sub_graph(ctx
, graph
, &node_scc_exactly
,
5828 &edge_scc_exactly
, i
, &c
->scc
[i
]) < 0)
5829 return isl_stat_error
;
5831 if (compute_maxvar(&c
->scc
[i
]) < 0)
5832 return isl_stat_error
;
5833 if (compute_schedule_wcc_band(ctx
, &c
->scc
[i
]) < 0)
5834 return isl_stat_error
;
5835 c
->scc_cluster
[i
] = i
;
5841 /* Free all memory allocated for "c".
5843 static void clustering_free(isl_ctx
*ctx
, struct isl_clustering
*c
)
5848 for (i
= 0; i
< c
->n
; ++i
)
5849 graph_free(ctx
, &c
->scc
[i
]);
5852 for (i
= 0; i
< c
->n
; ++i
)
5853 graph_free(ctx
, &c
->cluster
[i
]);
5855 free(c
->scc_cluster
);
5857 free(c
->scc_in_merge
);
5860 /* Should we refrain from merging the cluster in "graph" with
5861 * any other cluster?
5862 * In particular, is its current schedule band empty and incomplete.
5864 static int bad_cluster(struct isl_sched_graph
*graph
)
5866 return graph
->n_row
< graph
->maxvar
&&
5867 graph
->n_total_row
== graph
->band_start
;
5870 /* Is "edge" a proximity edge with a non-empty dependence relation?
5872 static isl_bool
is_non_empty_proximity(struct isl_sched_edge
*edge
)
5874 if (!is_proximity(edge
))
5875 return isl_bool_false
;
5876 return isl_bool_not(isl_map_plain_is_empty(edge
->map
));
5879 /* Return the index of an edge in "graph" that can be used to merge
5880 * two clusters in "c".
5881 * Return graph->n_edge if no such edge can be found.
5882 * Return -1 on error.
5884 * In particular, return a proximity edge between two clusters
5885 * that is not marked "no_merge" and such that neither of the
5886 * two clusters has an incomplete, empty band.
5888 * If there are multiple such edges, then try and find the most
5889 * appropriate edge to use for merging. In particular, pick the edge
5890 * with the greatest weight. If there are multiple of those,
5891 * then pick one with the shortest distance between
5892 * the two cluster representatives.
5894 static int find_proximity(struct isl_sched_graph
*graph
,
5895 struct isl_clustering
*c
)
5897 int i
, best
= graph
->n_edge
, best_dist
, best_weight
;
5899 for (i
= 0; i
< graph
->n_edge
; ++i
) {
5900 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
5904 prox
= is_non_empty_proximity(edge
);
5911 if (bad_cluster(&c
->scc
[edge
->src
->scc
]) ||
5912 bad_cluster(&c
->scc
[edge
->dst
->scc
]))
5914 dist
= c
->scc_cluster
[edge
->dst
->scc
] -
5915 c
->scc_cluster
[edge
->src
->scc
];
5918 weight
= edge
->weight
;
5919 if (best
< graph
->n_edge
) {
5920 if (best_weight
> weight
)
5922 if (best_weight
== weight
&& best_dist
<= dist
)
5927 best_weight
= weight
;
5933 /* Internal data structure used in mark_merge_sccs.
5935 * "graph" is the dependence graph in which a strongly connected
5936 * component is constructed.
5937 * "scc_cluster" maps each SCC index to the cluster to which it belongs.
5938 * "src" and "dst" are the indices of the nodes that are being merged.
5940 struct isl_mark_merge_sccs_data
{
5941 struct isl_sched_graph
*graph
;
5947 /* Check whether the cluster containing node "i" depends on the cluster
5948 * containing node "j". If "i" and "j" belong to the same cluster,
5949 * then they are taken to depend on each other to ensure that
5950 * the resulting strongly connected component consists of complete
5951 * clusters. Furthermore, if "i" and "j" are the two nodes that
5952 * are being merged, then they are taken to depend on each other as well.
5953 * Otherwise, check if there is a (conditional) validity dependence
5954 * from node[j] to node[i], forcing node[i] to follow node[j].
5956 static isl_bool
cluster_follows(int i
, int j
, void *user
)
5958 struct isl_mark_merge_sccs_data
*data
= user
;
5959 struct isl_sched_graph
*graph
= data
->graph
;
5960 int *scc_cluster
= data
->scc_cluster
;
5962 if (data
->src
== i
&& data
->dst
== j
)
5963 return isl_bool_true
;
5964 if (data
->src
== j
&& data
->dst
== i
)
5965 return isl_bool_true
;
5966 if (scc_cluster
[graph
->node
[i
].scc
] == scc_cluster
[graph
->node
[j
].scc
])
5967 return isl_bool_true
;
5969 return graph_has_validity_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
5972 /* Mark all SCCs that belong to either of the two clusters in "c"
5973 * connected by the edge in "graph" with index "edge", or to any
5974 * of the intermediate clusters.
5975 * The marking is recorded in c->scc_in_merge.
5977 * The given edge has been selected for merging two clusters,
5978 * meaning that there is at least a proximity edge between the two nodes.
5979 * However, there may also be (indirect) validity dependences
5980 * between the two nodes. When merging the two clusters, all clusters
5981 * containing one or more of the intermediate nodes along the
5982 * indirect validity dependences need to be merged in as well.
5984 * First collect all such nodes by computing the strongly connected
5985 * component (SCC) containing the two nodes connected by the edge, where
5986 * the two nodes are considered to depend on each other to make
5987 * sure they end up in the same SCC. Similarly, each node is considered
5988 * to depend on every other node in the same cluster to ensure
5989 * that the SCC consists of complete clusters.
5991 * Then the original SCCs that contain any of these nodes are marked
5992 * in c->scc_in_merge.
5994 static isl_stat
mark_merge_sccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
5995 int edge
, struct isl_clustering
*c
)
5997 struct isl_mark_merge_sccs_data data
;
5998 struct isl_tarjan_graph
*g
;
6001 for (i
= 0; i
< c
->n
; ++i
)
6002 c
->scc_in_merge
[i
] = 0;
6005 data
.scc_cluster
= c
->scc_cluster
;
6006 data
.src
= graph
->edge
[edge
].src
- graph
->node
;
6007 data
.dst
= graph
->edge
[edge
].dst
- graph
->node
;
6009 g
= isl_tarjan_graph_component(ctx
, graph
->n
, data
.dst
,
6010 &cluster_follows
, &data
);
6016 isl_die(ctx
, isl_error_internal
,
6017 "expecting at least two nodes in component",
6019 if (g
->order
[--i
] != -1)
6020 isl_die(ctx
, isl_error_internal
,
6021 "expecting end of component marker", goto error
);
6023 for (--i
; i
>= 0 && g
->order
[i
] != -1; --i
) {
6024 int scc
= graph
->node
[g
->order
[i
]].scc
;
6025 c
->scc_in_merge
[scc
] = 1;
6028 isl_tarjan_graph_free(g
);
6031 isl_tarjan_graph_free(g
);
6032 return isl_stat_error
;
6035 /* Construct the identifier "cluster_i".
6037 static __isl_give isl_id
*cluster_id(isl_ctx
*ctx
, int i
)
6041 snprintf(name
, sizeof(name
), "cluster_%d", i
);
6042 return isl_id_alloc(ctx
, name
, NULL
);
6045 /* Construct the space of the cluster with index "i" containing
6046 * the strongly connected component "scc".
6048 * In particular, construct a space called cluster_i with dimension equal
6049 * to the number of schedule rows in the current band of "scc".
6051 static __isl_give isl_space
*cluster_space(struct isl_sched_graph
*scc
, int i
)
6057 nvar
= scc
->n_total_row
- scc
->band_start
;
6058 space
= isl_space_copy(scc
->node
[0].space
);
6059 space
= isl_space_params(space
);
6060 space
= isl_space_set_from_params(space
);
6061 space
= isl_space_add_dims(space
, isl_dim_set
, nvar
);
6062 id
= cluster_id(isl_space_get_ctx(space
), i
);
6063 space
= isl_space_set_tuple_id(space
, isl_dim_set
, id
);
6068 /* Collect the domain of the graph for merging clusters.
6070 * In particular, for each cluster with first SCC "i", construct
6071 * a set in the space called cluster_i with dimension equal
6072 * to the number of schedule rows in the current band of the cluster.
6074 static __isl_give isl_union_set
*collect_domain(isl_ctx
*ctx
,
6075 struct isl_sched_graph
*graph
, struct isl_clustering
*c
)
6079 isl_union_set
*domain
;
6081 space
= isl_space_params_alloc(ctx
, 0);
6082 domain
= isl_union_set_empty(space
);
6084 for (i
= 0; i
< graph
->scc
; ++i
) {
6087 if (!c
->scc_in_merge
[i
])
6089 if (c
->scc_cluster
[i
] != i
)
6091 space
= cluster_space(&c
->scc
[i
], i
);
6092 domain
= isl_union_set_add_set(domain
, isl_set_universe(space
));
6098 /* Construct a map from the original instances to the corresponding
6099 * cluster instance in the current bands of the clusters in "c".
6101 static __isl_give isl_union_map
*collect_cluster_map(isl_ctx
*ctx
,
6102 struct isl_sched_graph
*graph
, struct isl_clustering
*c
)
6106 isl_union_map
*cluster_map
;
6108 space
= isl_space_params_alloc(ctx
, 0);
6109 cluster_map
= isl_union_map_empty(space
);
6110 for (i
= 0; i
< graph
->scc
; ++i
) {
6114 if (!c
->scc_in_merge
[i
])
6117 id
= cluster_id(ctx
, c
->scc_cluster
[i
]);
6118 start
= c
->scc
[i
].band_start
;
6119 n
= c
->scc
[i
].n_total_row
- start
;
6120 for (j
= 0; j
< c
->scc
[i
].n
; ++j
) {
6123 struct isl_sched_node
*node
= &c
->scc
[i
].node
[j
];
6125 ma
= node_extract_partial_schedule_multi_aff(node
,
6127 ma
= isl_multi_aff_set_tuple_id(ma
, isl_dim_out
,
6129 map
= isl_map_from_multi_aff(ma
);
6130 cluster_map
= isl_union_map_add_map(cluster_map
, map
);
6138 /* Add "umap" to the schedule constraints "sc" of all types of "edge"
6139 * that are not isl_edge_condition or isl_edge_conditional_validity.
6141 static __isl_give isl_schedule_constraints
*add_non_conditional_constraints(
6142 struct isl_sched_edge
*edge
, __isl_keep isl_union_map
*umap
,
6143 __isl_take isl_schedule_constraints
*sc
)
6145 enum isl_edge_type t
;
6150 for (t
= isl_edge_first
; t
<= isl_edge_last
; ++t
) {
6151 if (t
== isl_edge_condition
||
6152 t
== isl_edge_conditional_validity
)
6154 if (!is_type(edge
, t
))
6156 sc
= isl_schedule_constraints_add(sc
, t
,
6157 isl_union_map_copy(umap
));
6163 /* Add schedule constraints of types isl_edge_condition and
6164 * isl_edge_conditional_validity to "sc" by applying "umap" to
6165 * the domains of the wrapped relations in domain and range
6166 * of the corresponding tagged constraints of "edge".
6168 static __isl_give isl_schedule_constraints
*add_conditional_constraints(
6169 struct isl_sched_edge
*edge
, __isl_keep isl_union_map
*umap
,
6170 __isl_take isl_schedule_constraints
*sc
)
6172 enum isl_edge_type t
;
6173 isl_union_map
*tagged
;
6175 for (t
= isl_edge_condition
; t
<= isl_edge_conditional_validity
; ++t
) {
6176 if (!is_type(edge
, t
))
6178 if (t
== isl_edge_condition
)
6179 tagged
= isl_union_map_copy(edge
->tagged_condition
);
6181 tagged
= isl_union_map_copy(edge
->tagged_validity
);
6182 tagged
= isl_union_map_zip(tagged
);
6183 tagged
= isl_union_map_apply_domain(tagged
,
6184 isl_union_map_copy(umap
));
6185 tagged
= isl_union_map_zip(tagged
);
6186 sc
= isl_schedule_constraints_add(sc
, t
, tagged
);
6194 /* Given a mapping "cluster_map" from the original instances to
6195 * the cluster instances, add schedule constraints on the clusters
6196 * to "sc" corresponding to the original constraints represented by "edge".
6198 * For non-tagged dependence constraints, the cluster constraints
6199 * are obtained by applying "cluster_map" to the edge->map.
6201 * For tagged dependence constraints, "cluster_map" needs to be applied
6202 * to the domains of the wrapped relations in domain and range
6203 * of the tagged dependence constraints. Pick out the mappings
6204 * from these domains from "cluster_map" and construct their product.
6205 * This mapping can then be applied to the pair of domains.
6207 static __isl_give isl_schedule_constraints
*collect_edge_constraints(
6208 struct isl_sched_edge
*edge
, __isl_keep isl_union_map
*cluster_map
,
6209 __isl_take isl_schedule_constraints
*sc
)
6211 isl_union_map
*umap
;
6213 isl_union_set
*uset
;
6214 isl_union_map
*umap1
, *umap2
;
6219 umap
= isl_union_map_from_map(isl_map_copy(edge
->map
));
6220 umap
= isl_union_map_apply_domain(umap
,
6221 isl_union_map_copy(cluster_map
));
6222 umap
= isl_union_map_apply_range(umap
,
6223 isl_union_map_copy(cluster_map
));
6224 sc
= add_non_conditional_constraints(edge
, umap
, sc
);
6225 isl_union_map_free(umap
);
6227 if (!sc
|| (!is_condition(edge
) && !is_conditional_validity(edge
)))
6230 space
= isl_space_domain(isl_map_get_space(edge
->map
));
6231 uset
= isl_union_set_from_set(isl_set_universe(space
));
6232 umap1
= isl_union_map_copy(cluster_map
);
6233 umap1
= isl_union_map_intersect_domain(umap1
, uset
);
6234 space
= isl_space_range(isl_map_get_space(edge
->map
));
6235 uset
= isl_union_set_from_set(isl_set_universe(space
));
6236 umap2
= isl_union_map_copy(cluster_map
);
6237 umap2
= isl_union_map_intersect_domain(umap2
, uset
);
6238 umap
= isl_union_map_product(umap1
, umap2
);
6240 sc
= add_conditional_constraints(edge
, umap
, sc
);
6242 isl_union_map_free(umap
);
6246 /* Given a mapping "cluster_map" from the original instances to
6247 * the cluster instances, add schedule constraints on the clusters
6248 * to "sc" corresponding to all edges in "graph" between nodes that
6249 * belong to SCCs that are marked for merging in "scc_in_merge".
6251 static __isl_give isl_schedule_constraints
*collect_constraints(
6252 struct isl_sched_graph
*graph
, int *scc_in_merge
,
6253 __isl_keep isl_union_map
*cluster_map
,
6254 __isl_take isl_schedule_constraints
*sc
)
6258 for (i
= 0; i
< graph
->n_edge
; ++i
) {
6259 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
6261 if (!scc_in_merge
[edge
->src
->scc
])
6263 if (!scc_in_merge
[edge
->dst
->scc
])
6265 sc
= collect_edge_constraints(edge
, cluster_map
, sc
);
6271 /* Construct a dependence graph for scheduling clusters with respect
6272 * to each other and store the result in "merge_graph".
6273 * In particular, the nodes of the graph correspond to the schedule
6274 * dimensions of the current bands of those clusters that have been
6275 * marked for merging in "c".
6277 * First construct an isl_schedule_constraints object for this domain
6278 * by transforming the edges in "graph" to the domain.
6279 * Then initialize a dependence graph for scheduling from these
6282 static isl_stat
init_merge_graph(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
6283 struct isl_clustering
*c
, struct isl_sched_graph
*merge_graph
)
6285 isl_union_set
*domain
;
6286 isl_union_map
*cluster_map
;
6287 isl_schedule_constraints
*sc
;
6290 domain
= collect_domain(ctx
, graph
, c
);
6291 sc
= isl_schedule_constraints_on_domain(domain
);
6293 return isl_stat_error
;
6294 cluster_map
= collect_cluster_map(ctx
, graph
, c
);
6295 sc
= collect_constraints(graph
, c
->scc_in_merge
, cluster_map
, sc
);
6296 isl_union_map_free(cluster_map
);
6298 r
= graph_init(merge_graph
, sc
);
6300 isl_schedule_constraints_free(sc
);
6305 /* Compute the maximal number of remaining schedule rows that still need
6306 * to be computed for the nodes that belong to clusters with the maximal
6307 * dimension for the current band (i.e., the band that is to be merged).
6308 * Only clusters that are about to be merged are considered.
6309 * "maxvar" is the maximal dimension for the current band.
6310 * "c" contains information about the clusters.
6312 * Return the maximal number of remaining schedule rows or -1 on error.
6314 static int compute_maxvar_max_slack(int maxvar
, struct isl_clustering
*c
)
6320 for (i
= 0; i
< c
->n
; ++i
) {
6322 struct isl_sched_graph
*scc
;
6324 if (!c
->scc_in_merge
[i
])
6327 nvar
= scc
->n_total_row
- scc
->band_start
;
6330 for (j
= 0; j
< scc
->n
; ++j
) {
6331 struct isl_sched_node
*node
= &scc
->node
[j
];
6334 if (node_update_vmap(node
) < 0)
6336 slack
= node
->nvar
- node
->rank
;
6337 if (slack
> max_slack
)
6345 /* If there are any clusters where the dimension of the current band
6346 * (i.e., the band that is to be merged) is smaller than "maxvar" and
6347 * if there are any nodes in such a cluster where the number
6348 * of remaining schedule rows that still need to be computed
6349 * is greater than "max_slack", then return the smallest current band
6350 * dimension of all these clusters. Otherwise return the original value
6351 * of "maxvar". Return -1 in case of any error.
6352 * Only clusters that are about to be merged are considered.
6353 * "c" contains information about the clusters.
6355 static int limit_maxvar_to_slack(int maxvar
, int max_slack
,
6356 struct isl_clustering
*c
)
6360 for (i
= 0; i
< c
->n
; ++i
) {
6362 struct isl_sched_graph
*scc
;
6364 if (!c
->scc_in_merge
[i
])
6367 nvar
= scc
->n_total_row
- scc
->band_start
;
6370 for (j
= 0; j
< scc
->n
; ++j
) {
6371 struct isl_sched_node
*node
= &scc
->node
[j
];
6374 if (node_update_vmap(node
) < 0)
6376 slack
= node
->nvar
- node
->rank
;
6377 if (slack
> max_slack
) {
6387 /* Adjust merge_graph->maxvar based on the number of remaining schedule rows
6388 * that still need to be computed. In particular, if there is a node
6389 * in a cluster where the dimension of the current band is smaller
6390 * than merge_graph->maxvar, but the number of remaining schedule rows
6391 * is greater than that of any node in a cluster with the maximal
6392 * dimension for the current band (i.e., merge_graph->maxvar),
6393 * then adjust merge_graph->maxvar to the (smallest) current band dimension
6394 * of those clusters. Without this adjustment, the total number of
6395 * schedule dimensions would be increased, resulting in a skewed view
6396 * of the number of coincident dimensions.
6397 * "c" contains information about the clusters.
6399 * If the maximize_band_depth option is set and merge_graph->maxvar is reduced,
6400 * then there is no point in attempting any merge since it will be rejected
6401 * anyway. Set merge_graph->maxvar to zero in such cases.
6403 static isl_stat
adjust_maxvar_to_slack(isl_ctx
*ctx
,
6404 struct isl_sched_graph
*merge_graph
, struct isl_clustering
*c
)
6406 int max_slack
, maxvar
;
6408 max_slack
= compute_maxvar_max_slack(merge_graph
->maxvar
, c
);
6410 return isl_stat_error
;
6411 maxvar
= limit_maxvar_to_slack(merge_graph
->maxvar
, max_slack
, c
);
6413 return isl_stat_error
;
6415 if (maxvar
< merge_graph
->maxvar
) {
6416 if (isl_options_get_schedule_maximize_band_depth(ctx
))
6417 merge_graph
->maxvar
= 0;
6419 merge_graph
->maxvar
= maxvar
;
6425 /* Return the number of coincident dimensions in the current band of "graph",
6426 * where the nodes of "graph" are assumed to be scheduled by a single band.
6428 static int get_n_coincident(struct isl_sched_graph
*graph
)
6432 for (i
= graph
->band_start
; i
< graph
->n_total_row
; ++i
)
6433 if (!graph
->node
[0].coincident
[i
])
6436 return i
- graph
->band_start
;
6439 /* Should the clusters be merged based on the cluster schedule
6440 * in the current (and only) band of "merge_graph", given that
6441 * coincidence should be maximized?
6443 * If the number of coincident schedule dimensions in the merged band
6444 * would be less than the maximal number of coincident schedule dimensions
6445 * in any of the merged clusters, then the clusters should not be merged.
6447 static isl_bool
ok_to_merge_coincident(struct isl_clustering
*c
,
6448 struct isl_sched_graph
*merge_graph
)
6455 for (i
= 0; i
< c
->n
; ++i
) {
6456 if (!c
->scc_in_merge
[i
])
6458 n_coincident
= get_n_coincident(&c
->scc
[i
]);
6459 if (n_coincident
> max_coincident
)
6460 max_coincident
= n_coincident
;
6463 n_coincident
= get_n_coincident(merge_graph
);
6465 return isl_bool_ok(n_coincident
>= max_coincident
);
6468 /* Return the transformation on "node" expressed by the current (and only)
6469 * band of "merge_graph" applied to the clusters in "c".
6471 * First find the representation of "node" in its SCC in "c" and
6472 * extract the transformation expressed by the current band.
6473 * Then extract the transformation applied by "merge_graph"
6474 * to the cluster to which this SCC belongs.
6475 * Combine the two to obtain the complete transformation on the node.
6477 * Note that the range of the first transformation is an anonymous space,
6478 * while the domain of the second is named "cluster_X". The range
6479 * of the former therefore needs to be adjusted before the two
6482 static __isl_give isl_map
*extract_node_transformation(isl_ctx
*ctx
,
6483 struct isl_sched_node
*node
, struct isl_clustering
*c
,
6484 struct isl_sched_graph
*merge_graph
)
6486 struct isl_sched_node
*scc_node
, *cluster_node
;
6490 isl_multi_aff
*ma
, *ma2
;
6492 scc_node
= graph_find_node(ctx
, &c
->scc
[node
->scc
], node
->space
);
6493 if (scc_node
&& !is_node(&c
->scc
[node
->scc
], scc_node
))
6494 isl_die(ctx
, isl_error_internal
, "unable to find node",
6496 start
= c
->scc
[node
->scc
].band_start
;
6497 n
= c
->scc
[node
->scc
].n_total_row
- start
;
6498 ma
= node_extract_partial_schedule_multi_aff(scc_node
, start
, n
);
6499 space
= cluster_space(&c
->scc
[node
->scc
], c
->scc_cluster
[node
->scc
]);
6500 cluster_node
= graph_find_node(ctx
, merge_graph
, space
);
6501 if (cluster_node
&& !is_node(merge_graph
, cluster_node
))
6502 isl_die(ctx
, isl_error_internal
, "unable to find cluster",
6503 space
= isl_space_free(space
));
6504 id
= isl_space_get_tuple_id(space
, isl_dim_set
);
6505 ma
= isl_multi_aff_set_tuple_id(ma
, isl_dim_out
, id
);
6506 isl_space_free(space
);
6507 n
= merge_graph
->n_total_row
;
6508 ma2
= node_extract_partial_schedule_multi_aff(cluster_node
, 0, n
);
6509 ma
= isl_multi_aff_pullback_multi_aff(ma2
, ma
);
6511 return isl_map_from_multi_aff(ma
);
6514 /* Give a set of distances "set", are they bounded by a small constant
6515 * in direction "pos"?
6516 * In practice, check if they are bounded by 2 by checking that there
6517 * are no elements with a value greater than or equal to 3 or
6518 * smaller than or equal to -3.
6520 static isl_bool
distance_is_bounded(__isl_keep isl_set
*set
, int pos
)
6526 return isl_bool_error
;
6528 test
= isl_set_copy(set
);
6529 test
= isl_set_lower_bound_si(test
, isl_dim_set
, pos
, 3);
6530 bounded
= isl_set_is_empty(test
);
6533 if (bounded
< 0 || !bounded
)
6536 test
= isl_set_copy(set
);
6537 test
= isl_set_upper_bound_si(test
, isl_dim_set
, pos
, -3);
6538 bounded
= isl_set_is_empty(test
);
6544 /* Does the set "set" have a fixed (but possible parametric) value
6545 * at dimension "pos"?
6547 static isl_bool
has_single_value(__isl_keep isl_set
*set
, int pos
)
6552 n
= isl_set_dim(set
, isl_dim_set
);
6554 return isl_bool_error
;
6555 set
= isl_set_copy(set
);
6556 set
= isl_set_project_out(set
, isl_dim_set
, pos
+ 1, n
- (pos
+ 1));
6557 set
= isl_set_project_out(set
, isl_dim_set
, 0, pos
);
6558 single
= isl_set_is_singleton(set
);
6564 /* Does "map" have a fixed (but possible parametric) value
6565 * at dimension "pos" of either its domain or its range?
6567 static isl_bool
has_singular_src_or_dst(__isl_keep isl_map
*map
, int pos
)
6572 set
= isl_map_domain(isl_map_copy(map
));
6573 single
= has_single_value(set
, pos
);
6576 if (single
< 0 || single
)
6579 set
= isl_map_range(isl_map_copy(map
));
6580 single
= has_single_value(set
, pos
);
6586 /* Does the edge "edge" from "graph" have bounded dependence distances
6587 * in the merged graph "merge_graph" of a selection of clusters in "c"?
6589 * Extract the complete transformations of the source and destination
6590 * nodes of the edge, apply them to the edge constraints and
6591 * compute the differences. Finally, check if these differences are bounded
6592 * in each direction.
6594 * If the dimension of the band is greater than the number of
6595 * dimensions that can be expected to be optimized by the edge
6596 * (based on its weight), then also allow the differences to be unbounded
6597 * in the remaining dimensions, but only if either the source or
6598 * the destination has a fixed value in that direction.
6599 * This allows a statement that produces values that are used by
6600 * several instances of another statement to be merged with that
6602 * However, merging such clusters will introduce an inherently
6603 * large proximity distance inside the merged cluster, meaning
6604 * that proximity distances will no longer be optimized in
6605 * subsequent merges. These merges are therefore only allowed
6606 * after all other possible merges have been tried.
6607 * The first time such a merge is encountered, the weight of the edge
6608 * is replaced by a negative weight. The second time (i.e., after
6609 * all merges over edges with a non-negative weight have been tried),
6610 * the merge is allowed.
6612 static isl_bool
has_bounded_distances(isl_ctx
*ctx
, struct isl_sched_edge
*edge
,
6613 struct isl_sched_graph
*graph
, struct isl_clustering
*c
,
6614 struct isl_sched_graph
*merge_graph
)
6622 map
= isl_map_copy(edge
->map
);
6623 t
= extract_node_transformation(ctx
, edge
->src
, c
, merge_graph
);
6624 map
= isl_map_apply_domain(map
, t
);
6625 t
= extract_node_transformation(ctx
, edge
->dst
, c
, merge_graph
);
6626 map
= isl_map_apply_range(map
, t
);
6627 dist
= isl_map_deltas(isl_map_copy(map
));
6629 bounded
= isl_bool_true
;
6630 n
= isl_set_dim(dist
, isl_dim_set
);
6633 n_slack
= n
- edge
->weight
;
6634 if (edge
->weight
< 0)
6635 n_slack
-= graph
->max_weight
+ 1;
6636 for (i
= 0; i
< n
; ++i
) {
6637 isl_bool bounded_i
, singular_i
;
6639 bounded_i
= distance_is_bounded(dist
, i
);
6644 if (edge
->weight
>= 0)
6645 bounded
= isl_bool_false
;
6649 singular_i
= has_singular_src_or_dst(map
, i
);
6654 bounded
= isl_bool_false
;
6657 if (!bounded
&& i
>= n
&& edge
->weight
>= 0)
6658 edge
->weight
-= graph
->max_weight
+ 1;
6666 return isl_bool_error
;
6669 /* Should the clusters be merged based on the cluster schedule
6670 * in the current (and only) band of "merge_graph"?
6671 * "graph" is the original dependence graph, while "c" records
6672 * which SCCs are involved in the latest merge.
6674 * In particular, is there at least one proximity constraint
6675 * that is optimized by the merge?
6677 * A proximity constraint is considered to be optimized
6678 * if the dependence distances are small.
6680 static isl_bool
ok_to_merge_proximity(isl_ctx
*ctx
,
6681 struct isl_sched_graph
*graph
, struct isl_clustering
*c
,
6682 struct isl_sched_graph
*merge_graph
)
6686 for (i
= 0; i
< graph
->n_edge
; ++i
) {
6687 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
6690 if (!is_proximity(edge
))
6692 if (!c
->scc_in_merge
[edge
->src
->scc
])
6694 if (!c
->scc_in_merge
[edge
->dst
->scc
])
6696 if (c
->scc_cluster
[edge
->dst
->scc
] ==
6697 c
->scc_cluster
[edge
->src
->scc
])
6699 bounded
= has_bounded_distances(ctx
, edge
, graph
, c
,
6701 if (bounded
< 0 || bounded
)
6705 return isl_bool_false
;
6708 /* Should the clusters be merged based on the cluster schedule
6709 * in the current (and only) band of "merge_graph"?
6710 * "graph" is the original dependence graph, while "c" records
6711 * which SCCs are involved in the latest merge.
6713 * If the current band is empty, then the clusters should not be merged.
6715 * If the band depth should be maximized and the merge schedule
6716 * is incomplete (meaning that the dimension of some of the schedule
6717 * bands in the original schedule will be reduced), then the clusters
6718 * should not be merged.
6720 * If the schedule_maximize_coincidence option is set, then check that
6721 * the number of coincident schedule dimensions is not reduced.
6723 * Finally, only allow the merge if at least one proximity
6724 * constraint is optimized.
6726 static isl_bool
ok_to_merge(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
6727 struct isl_clustering
*c
, struct isl_sched_graph
*merge_graph
)
6729 if (merge_graph
->n_total_row
== merge_graph
->band_start
)
6730 return isl_bool_false
;
6732 if (isl_options_get_schedule_maximize_band_depth(ctx
) &&
6733 merge_graph
->n_total_row
< merge_graph
->maxvar
)
6734 return isl_bool_false
;
6736 if (isl_options_get_schedule_maximize_coincidence(ctx
)) {
6739 ok
= ok_to_merge_coincident(c
, merge_graph
);
6744 return ok_to_merge_proximity(ctx
, graph
, c
, merge_graph
);
6747 /* Apply the schedule in "t_node" to the "n" rows starting at "first"
6748 * of the schedule in "node" and return the result.
6750 * That is, essentially compute
6752 * T * N(first:first+n-1)
6754 * taking into account the constant term and the parameter coefficients
6757 static __isl_give isl_mat
*node_transformation(isl_ctx
*ctx
,
6758 struct isl_sched_node
*t_node
, struct isl_sched_node
*node
,
6763 isl_size n_row
, n_col
;
6766 n_param
= node
->nparam
;
6768 n_row
= isl_mat_rows(t_node
->sched
);
6769 n_col
= isl_mat_cols(node
->sched
);
6770 if (n_row
< 0 || n_col
< 0)
6772 t
= isl_mat_alloc(ctx
, n_row
, n_col
);
6775 for (i
= 0; i
< n_row
; ++i
) {
6776 isl_seq_cpy(t
->row
[i
], t_node
->sched
->row
[i
], 1 + n_param
);
6777 isl_seq_clr(t
->row
[i
] + 1 + n_param
, n_var
);
6778 for (j
= 0; j
< n
; ++j
)
6779 isl_seq_addmul(t
->row
[i
],
6780 t_node
->sched
->row
[i
][1 + n_param
+ j
],
6781 node
->sched
->row
[first
+ j
],
6782 1 + n_param
+ n_var
);
6787 /* Apply the cluster schedule in "t_node" to the current band
6788 * schedule of the nodes in "graph".
6790 * In particular, replace the rows starting at band_start
6791 * by the result of applying the cluster schedule in "t_node"
6792 * to the original rows.
6794 * The coincidence of the schedule is determined by the coincidence
6795 * of the cluster schedule.
6797 static isl_stat
transform(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
6798 struct isl_sched_node
*t_node
)
6804 start
= graph
->band_start
;
6805 n
= graph
->n_total_row
- start
;
6807 n_new
= isl_mat_rows(t_node
->sched
);
6809 return isl_stat_error
;
6810 for (i
= 0; i
< graph
->n
; ++i
) {
6811 struct isl_sched_node
*node
= &graph
->node
[i
];
6814 t
= node_transformation(ctx
, t_node
, node
, start
, n
);
6815 node
->sched
= isl_mat_drop_rows(node
->sched
, start
, n
);
6816 node
->sched
= isl_mat_concat(node
->sched
, t
);
6817 node
->sched_map
= isl_map_free(node
->sched_map
);
6819 return isl_stat_error
;
6820 for (j
= 0; j
< n_new
; ++j
)
6821 node
->coincident
[start
+ j
] = t_node
->coincident
[j
];
6823 graph
->n_total_row
-= n
;
6825 graph
->n_total_row
+= n_new
;
6826 graph
->n_row
+= n_new
;
6831 /* Merge the clusters marked for merging in "c" into a single
6832 * cluster using the cluster schedule in the current band of "merge_graph".
6833 * The representative SCC for the new cluster is the SCC with
6834 * the smallest index.
6836 * The current band schedule of each SCC in the new cluster is obtained
6837 * by applying the schedule of the corresponding original cluster
6838 * to the original band schedule.
6839 * All SCCs in the new cluster have the same number of schedule rows.
6841 static isl_stat
merge(isl_ctx
*ctx
, struct isl_clustering
*c
,
6842 struct isl_sched_graph
*merge_graph
)
6848 for (i
= 0; i
< c
->n
; ++i
) {
6849 struct isl_sched_node
*node
;
6851 if (!c
->scc_in_merge
[i
])
6855 space
= cluster_space(&c
->scc
[i
], c
->scc_cluster
[i
]);
6856 node
= graph_find_node(ctx
, merge_graph
, space
);
6857 isl_space_free(space
);
6859 return isl_stat_error
;
6860 if (!is_node(merge_graph
, node
))
6861 isl_die(ctx
, isl_error_internal
,
6862 "unable to find cluster",
6863 return isl_stat_error
);
6864 if (transform(ctx
, &c
->scc
[i
], node
) < 0)
6865 return isl_stat_error
;
6866 c
->scc_cluster
[i
] = cluster
;
6872 /* Try and merge the clusters of SCCs marked in c->scc_in_merge
6873 * by scheduling the current cluster bands with respect to each other.
6875 * Construct a dependence graph with a space for each cluster and
6876 * with the coordinates of each space corresponding to the schedule
6877 * dimensions of the current band of that cluster.
6878 * Construct a cluster schedule in this cluster dependence graph and
6879 * apply it to the current cluster bands if it is applicable
6880 * according to ok_to_merge.
6882 * If the number of remaining schedule dimensions in a cluster
6883 * with a non-maximal current schedule dimension is greater than
6884 * the number of remaining schedule dimensions in clusters
6885 * with a maximal current schedule dimension, then restrict
6886 * the number of rows to be computed in the cluster schedule
6887 * to the minimal such non-maximal current schedule dimension.
6888 * Do this by adjusting merge_graph.maxvar.
6890 * Return isl_bool_true if the clusters have effectively been merged
6891 * into a single cluster.
6893 * Note that since the standard scheduling algorithm minimizes the maximal
6894 * distance over proximity constraints, the proximity constraints between
6895 * the merged clusters may not be optimized any further than what is
6896 * sufficient to bring the distances within the limits of the internal
6897 * proximity constraints inside the individual clusters.
6898 * It may therefore make sense to perform an additional translation step
6899 * to bring the clusters closer to each other, while maintaining
6900 * the linear part of the merging schedule found using the standard
6901 * scheduling algorithm.
6903 static isl_bool
try_merge(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
6904 struct isl_clustering
*c
)
6906 struct isl_sched_graph merge_graph
= { 0 };
6909 if (init_merge_graph(ctx
, graph
, c
, &merge_graph
) < 0)
6912 if (compute_maxvar(&merge_graph
) < 0)
6914 if (adjust_maxvar_to_slack(ctx
, &merge_graph
,c
) < 0)
6916 if (compute_schedule_wcc_band(ctx
, &merge_graph
) < 0)
6918 merged
= ok_to_merge(ctx
, graph
, c
, &merge_graph
);
6919 if (merged
&& merge(ctx
, c
, &merge_graph
) < 0)
6922 graph_free(ctx
, &merge_graph
);
6925 graph_free(ctx
, &merge_graph
);
6926 return isl_bool_error
;
6929 /* Is there any edge marked "no_merge" between two SCCs that are
6930 * about to be merged (i.e., that are set in "scc_in_merge")?
6931 * "merge_edge" is the proximity edge along which the clusters of SCCs
6932 * are going to be merged.
6934 * If there is any edge between two SCCs with a negative weight,
6935 * while the weight of "merge_edge" is non-negative, then this
6936 * means that the edge was postponed. "merge_edge" should then
6937 * also be postponed since merging along the edge with negative weight should
6938 * be postponed until all edges with non-negative weight have been tried.
6939 * Replace the weight of "merge_edge" by a negative weight as well and
6940 * tell the caller not to attempt a merge.
6942 static int any_no_merge(struct isl_sched_graph
*graph
, int *scc_in_merge
,
6943 struct isl_sched_edge
*merge_edge
)
6947 for (i
= 0; i
< graph
->n_edge
; ++i
) {
6948 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
6950 if (!scc_in_merge
[edge
->src
->scc
])
6952 if (!scc_in_merge
[edge
->dst
->scc
])
6956 if (merge_edge
->weight
>= 0 && edge
->weight
< 0) {
6957 merge_edge
->weight
-= graph
->max_weight
+ 1;
6965 /* Merge the two clusters in "c" connected by the edge in "graph"
6966 * with index "edge" into a single cluster.
6967 * If it turns out to be impossible to merge these two clusters,
6968 * then mark the edge as "no_merge" such that it will not be
6971 * First mark all SCCs that need to be merged. This includes the SCCs
6972 * in the two clusters, but it may also include the SCCs
6973 * of intermediate clusters.
6974 * If there is already a no_merge edge between any pair of such SCCs,
6975 * then simply mark the current edge as no_merge as well.
6976 * Likewise, if any of those edges was postponed by has_bounded_distances,
6977 * then postpone the current edge as well.
6978 * Otherwise, try and merge the clusters and mark "edge" as "no_merge"
6979 * if the clusters did not end up getting merged, unless the non-merge
6980 * is due to the fact that the edge was postponed. This postponement
6981 * can be recognized by a change in weight (from non-negative to negative).
6983 static isl_stat
merge_clusters_along_edge(isl_ctx
*ctx
,
6984 struct isl_sched_graph
*graph
, int edge
, struct isl_clustering
*c
)
6987 int edge_weight
= graph
->edge
[edge
].weight
;
6989 if (mark_merge_sccs(ctx
, graph
, edge
, c
) < 0)
6990 return isl_stat_error
;
6992 if (any_no_merge(graph
, c
->scc_in_merge
, &graph
->edge
[edge
]))
6993 merged
= isl_bool_false
;
6995 merged
= try_merge(ctx
, graph
, c
);
6997 return isl_stat_error
;
6998 if (!merged
&& edge_weight
== graph
->edge
[edge
].weight
)
6999 graph
->edge
[edge
].no_merge
= 1;
7004 /* Does "node" belong to the cluster identified by "cluster"?
7006 static int node_cluster_exactly(struct isl_sched_node
*node
, int cluster
)
7008 return node
->cluster
== cluster
;
7011 /* Does "edge" connect two nodes belonging to the cluster
7012 * identified by "cluster"?
7014 static int edge_cluster_exactly(struct isl_sched_edge
*edge
, int cluster
)
7016 return edge
->src
->cluster
== cluster
&& edge
->dst
->cluster
== cluster
;
7019 /* Swap the schedule of "node1" and "node2".
7020 * Both nodes have been derived from the same node in a common parent graph.
7021 * Since the "coincident" field is shared with that node
7022 * in the parent graph, there is no need to also swap this field.
7024 static void swap_sched(struct isl_sched_node
*node1
,
7025 struct isl_sched_node
*node2
)
7030 sched
= node1
->sched
;
7031 node1
->sched
= node2
->sched
;
7032 node2
->sched
= sched
;
7034 sched_map
= node1
->sched_map
;
7035 node1
->sched_map
= node2
->sched_map
;
7036 node2
->sched_map
= sched_map
;
7039 /* Copy the current band schedule from the SCCs that form the cluster
7040 * with index "pos" to the actual cluster at position "pos".
7041 * By construction, the index of the first SCC that belongs to the cluster
7044 * The order of the nodes inside both the SCCs and the cluster
7045 * is assumed to be same as the order in the original "graph".
7047 * Since the SCC graphs will no longer be used after this function,
7048 * the schedules are actually swapped rather than copied.
7050 static isl_stat
copy_partial(struct isl_sched_graph
*graph
,
7051 struct isl_clustering
*c
, int pos
)
7055 c
->cluster
[pos
].n_total_row
= c
->scc
[pos
].n_total_row
;
7056 c
->cluster
[pos
].n_row
= c
->scc
[pos
].n_row
;
7057 c
->cluster
[pos
].maxvar
= c
->scc
[pos
].maxvar
;
7059 for (i
= 0; i
< graph
->n
; ++i
) {
7063 if (graph
->node
[i
].cluster
!= pos
)
7065 s
= graph
->node
[i
].scc
;
7066 k
= c
->scc_node
[s
]++;
7067 swap_sched(&c
->cluster
[pos
].node
[j
], &c
->scc
[s
].node
[k
]);
7068 if (c
->scc
[s
].maxvar
> c
->cluster
[pos
].maxvar
)
7069 c
->cluster
[pos
].maxvar
= c
->scc
[s
].maxvar
;
7076 /* Is there a (conditional) validity dependence from node[j] to node[i],
7077 * forcing node[i] to follow node[j] or do the nodes belong to the same
7080 static isl_bool
node_follows_strong_or_same_cluster(int i
, int j
, void *user
)
7082 struct isl_sched_graph
*graph
= user
;
7084 if (graph
->node
[i
].cluster
== graph
->node
[j
].cluster
)
7085 return isl_bool_true
;
7086 return graph_has_validity_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
7089 /* Extract the merged clusters of SCCs in "graph", sort them, and
7090 * store them in c->clusters. Update c->scc_cluster accordingly.
7092 * First keep track of the cluster containing the SCC to which a node
7093 * belongs in the node itself.
7094 * Then extract the clusters into c->clusters, copying the current
7095 * band schedule from the SCCs that belong to the cluster.
7096 * Do this only once per cluster.
7098 * Finally, topologically sort the clusters and update c->scc_cluster
7099 * to match the new scc numbering. While the SCCs were originally
7100 * sorted already, some SCCs that depend on some other SCCs may
7101 * have been merged with SCCs that appear before these other SCCs.
7102 * A reordering may therefore be required.
7104 static isl_stat
extract_clusters(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
7105 struct isl_clustering
*c
)
7109 for (i
= 0; i
< graph
->n
; ++i
)
7110 graph
->node
[i
].cluster
= c
->scc_cluster
[graph
->node
[i
].scc
];
7112 for (i
= 0; i
< graph
->scc
; ++i
) {
7113 if (c
->scc_cluster
[i
] != i
)
7115 if (extract_sub_graph(ctx
, graph
, &node_cluster_exactly
,
7116 &edge_cluster_exactly
, i
, &c
->cluster
[i
]) < 0)
7117 return isl_stat_error
;
7118 c
->cluster
[i
].src_scc
= -1;
7119 c
->cluster
[i
].dst_scc
= -1;
7120 if (copy_partial(graph
, c
, i
) < 0)
7121 return isl_stat_error
;
7124 if (detect_ccs(ctx
, graph
, &node_follows_strong_or_same_cluster
) < 0)
7125 return isl_stat_error
;
7126 for (i
= 0; i
< graph
->n
; ++i
)
7127 c
->scc_cluster
[graph
->node
[i
].scc
] = graph
->node
[i
].cluster
;
7132 /* Compute weights on the proximity edges of "graph" that can
7133 * be used by find_proximity to find the most appropriate
7134 * proximity edge to use to merge two clusters in "c".
7135 * The weights are also used by has_bounded_distances to determine
7136 * whether the merge should be allowed.
7137 * Store the maximum of the computed weights in graph->max_weight.
7139 * The computed weight is a measure for the number of remaining schedule
7140 * dimensions that can still be completely aligned.
7141 * In particular, compute the number of equalities between
7142 * input dimensions and output dimensions in the proximity constraints.
7143 * The directions that are already handled by outer schedule bands
7144 * are projected out prior to determining this number.
7146 * Edges that will never be considered by find_proximity are ignored.
7148 static isl_stat
compute_weights(struct isl_sched_graph
*graph
,
7149 struct isl_clustering
*c
)
7153 graph
->max_weight
= 0;
7155 for (i
= 0; i
< graph
->n_edge
; ++i
) {
7156 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
7157 struct isl_sched_node
*src
= edge
->src
;
7158 struct isl_sched_node
*dst
= edge
->dst
;
7159 isl_basic_map
*hull
;
7161 isl_size n_in
, n_out
;
7163 prox
= is_non_empty_proximity(edge
);
7165 return isl_stat_error
;
7168 if (bad_cluster(&c
->scc
[edge
->src
->scc
]) ||
7169 bad_cluster(&c
->scc
[edge
->dst
->scc
]))
7171 if (c
->scc_cluster
[edge
->dst
->scc
] ==
7172 c
->scc_cluster
[edge
->src
->scc
])
7175 hull
= isl_map_affine_hull(isl_map_copy(edge
->map
));
7176 hull
= isl_basic_map_transform_dims(hull
, isl_dim_in
, 0,
7177 isl_mat_copy(src
->vmap
));
7178 hull
= isl_basic_map_transform_dims(hull
, isl_dim_out
, 0,
7179 isl_mat_copy(dst
->vmap
));
7180 hull
= isl_basic_map_project_out(hull
,
7181 isl_dim_in
, 0, src
->rank
);
7182 hull
= isl_basic_map_project_out(hull
,
7183 isl_dim_out
, 0, dst
->rank
);
7184 hull
= isl_basic_map_remove_divs(hull
);
7185 n_in
= isl_basic_map_dim(hull
, isl_dim_in
);
7186 n_out
= isl_basic_map_dim(hull
, isl_dim_out
);
7187 if (n_in
< 0 || n_out
< 0)
7188 hull
= isl_basic_map_free(hull
);
7189 hull
= isl_basic_map_drop_constraints_not_involving_dims(hull
,
7190 isl_dim_in
, 0, n_in
);
7191 hull
= isl_basic_map_drop_constraints_not_involving_dims(hull
,
7192 isl_dim_out
, 0, n_out
);
7194 return isl_stat_error
;
7195 edge
->weight
= isl_basic_map_n_equality(hull
);
7196 isl_basic_map_free(hull
);
7198 if (edge
->weight
> graph
->max_weight
)
7199 graph
->max_weight
= edge
->weight
;
7205 /* Call compute_schedule_finish_band on each of the clusters in "c"
7206 * in their topological order. This order is determined by the scc
7207 * fields of the nodes in "graph".
7208 * Combine the results in a sequence expressing the topological order.
7210 * If there is only one cluster left, then there is no need to introduce
7211 * a sequence node. Also, in this case, the cluster necessarily contains
7212 * the SCC at position 0 in the original graph and is therefore also
7213 * stored in the first cluster of "c".
7215 static __isl_give isl_schedule_node
*finish_bands_clustering(
7216 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
7217 struct isl_clustering
*c
)
7221 isl_union_set_list
*filters
;
7223 if (graph
->scc
== 1)
7224 return compute_schedule_finish_band(node
, &c
->cluster
[0], 0);
7226 ctx
= isl_schedule_node_get_ctx(node
);
7228 filters
= extract_sccs(ctx
, graph
);
7229 node
= isl_schedule_node_insert_sequence(node
, filters
);
7231 for (i
= 0; i
< graph
->scc
; ++i
) {
7232 int j
= c
->scc_cluster
[i
];
7233 node
= isl_schedule_node_child(node
, i
);
7234 node
= isl_schedule_node_child(node
, 0);
7235 node
= compute_schedule_finish_band(node
, &c
->cluster
[j
], 0);
7236 node
= isl_schedule_node_parent(node
);
7237 node
= isl_schedule_node_parent(node
);
7243 /* Compute a schedule for a connected dependence graph by first considering
7244 * each strongly connected component (SCC) in the graph separately and then
7245 * incrementally combining them into clusters.
7246 * Return the updated schedule node.
7248 * Initially, each cluster consists of a single SCC, each with its
7249 * own band schedule. The algorithm then tries to merge pairs
7250 * of clusters along a proximity edge until no more suitable
7251 * proximity edges can be found. During this merging, the schedule
7252 * is maintained in the individual SCCs.
7253 * After the merging is completed, the full resulting clusters
7254 * are extracted and in finish_bands_clustering,
7255 * compute_schedule_finish_band is called on each of them to integrate
7256 * the band into "node" and to continue the computation.
7258 * compute_weights initializes the weights that are used by find_proximity.
7260 static __isl_give isl_schedule_node
*compute_schedule_wcc_clustering(
7261 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
7264 struct isl_clustering c
;
7267 ctx
= isl_schedule_node_get_ctx(node
);
7269 if (clustering_init(ctx
, &c
, graph
) < 0)
7272 if (compute_weights(graph
, &c
) < 0)
7276 i
= find_proximity(graph
, &c
);
7279 if (i
>= graph
->n_edge
)
7281 if (merge_clusters_along_edge(ctx
, graph
, i
, &c
) < 0)
7285 if (extract_clusters(ctx
, graph
, &c
) < 0)
7288 node
= finish_bands_clustering(node
, graph
, &c
);
7290 clustering_free(ctx
, &c
);
7293 clustering_free(ctx
, &c
);
7294 return isl_schedule_node_free(node
);
7297 /* Compute a schedule for a connected dependence graph and return
7298 * the updated schedule node.
7300 * If Feautrier's algorithm is selected, we first recursively try to satisfy
7301 * as many validity dependences as possible. When all validity dependences
7302 * are satisfied we extend the schedule to a full-dimensional schedule.
7304 * Call compute_schedule_wcc_whole or compute_schedule_wcc_clustering
7305 * depending on whether the user has selected the option to try and
7306 * compute a schedule for the entire (weakly connected) component first.
7307 * If there is only a single strongly connected component (SCC), then
7308 * there is no point in trying to combine SCCs
7309 * in compute_schedule_wcc_clustering, so compute_schedule_wcc_whole
7310 * is called instead.
7312 static __isl_give isl_schedule_node
*compute_schedule_wcc(
7313 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
7320 ctx
= isl_schedule_node_get_ctx(node
);
7321 if (detect_sccs(ctx
, graph
) < 0)
7322 return isl_schedule_node_free(node
);
7324 if (compute_maxvar(graph
) < 0)
7325 return isl_schedule_node_free(node
);
7327 if (need_feautrier_step(ctx
, graph
))
7328 return compute_schedule_wcc_feautrier(node
, graph
);
7330 if (graph
->scc
<= 1 || isl_options_get_schedule_whole_component(ctx
))
7331 return compute_schedule_wcc_whole(node
, graph
);
7333 return compute_schedule_wcc_clustering(node
, graph
);
7336 /* Compute a schedule for each group of nodes identified by node->scc
7337 * separately and then combine them in a sequence node (or as set node
7338 * if graph->weak is set) inserted at position "node" of the schedule tree.
7339 * Return the updated schedule node.
7341 * If "wcc" is set then each of the groups belongs to a single
7342 * weakly connected component in the dependence graph so that
7343 * there is no need for compute_sub_schedule to look for weakly
7344 * connected components.
7346 * If a set node would be introduced and if the number of components
7347 * is equal to the number of nodes, then check if the schedule
7348 * is already complete. If so, a redundant set node would be introduced
7349 * (without any further descendants) stating that the statements
7350 * can be executed in arbitrary order, which is also expressed
7351 * by the absence of any node. Refrain from inserting any nodes
7352 * in this case and simply return.
7354 static __isl_give isl_schedule_node
*compute_component_schedule(
7355 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
7360 isl_union_set_list
*filters
;
7365 if (graph
->weak
&& graph
->scc
== graph
->n
) {
7366 if (compute_maxvar(graph
) < 0)
7367 return isl_schedule_node_free(node
);
7368 if (graph
->n_row
>= graph
->maxvar
)
7372 ctx
= isl_schedule_node_get_ctx(node
);
7373 filters
= extract_sccs(ctx
, graph
);
7375 node
= isl_schedule_node_insert_set(node
, filters
);
7377 node
= isl_schedule_node_insert_sequence(node
, filters
);
7379 for (component
= 0; component
< graph
->scc
; ++component
) {
7380 node
= isl_schedule_node_child(node
, component
);
7381 node
= isl_schedule_node_child(node
, 0);
7382 node
= compute_sub_schedule(node
, ctx
, graph
,
7384 &edge_scc_exactly
, component
, wcc
);
7385 node
= isl_schedule_node_parent(node
);
7386 node
= isl_schedule_node_parent(node
);
7392 /* Compute a schedule for the given dependence graph and insert it at "node".
7393 * Return the updated schedule node.
7395 * We first check if the graph is connected (through validity and conditional
7396 * validity dependences) and, if not, compute a schedule
7397 * for each component separately.
7398 * If the schedule_serialize_sccs option is set, then we check for strongly
7399 * connected components instead and compute a separate schedule for
7400 * each such strongly connected component.
7402 static __isl_give isl_schedule_node
*compute_schedule(isl_schedule_node
*node
,
7403 struct isl_sched_graph
*graph
)
7410 ctx
= isl_schedule_node_get_ctx(node
);
7411 if (isl_options_get_schedule_serialize_sccs(ctx
)) {
7412 if (detect_sccs(ctx
, graph
) < 0)
7413 return isl_schedule_node_free(node
);
7415 if (detect_wccs(ctx
, graph
) < 0)
7416 return isl_schedule_node_free(node
);
7420 return compute_component_schedule(node
, graph
, 1);
7422 return compute_schedule_wcc(node
, graph
);
7425 /* Compute a schedule on sc->domain that respects the given schedule
7428 * In particular, the schedule respects all the validity dependences.
7429 * If the default isl scheduling algorithm is used, it tries to minimize
7430 * the dependence distances over the proximity dependences.
7431 * If Feautrier's scheduling algorithm is used, the proximity dependence
7432 * distances are only minimized during the extension to a full-dimensional
7435 * If there are any condition and conditional validity dependences,
7436 * then the conditional validity dependences may be violated inside
7437 * a tilable band, provided they have no adjacent non-local
7438 * condition dependences.
7440 __isl_give isl_schedule
*isl_schedule_constraints_compute_schedule(
7441 __isl_take isl_schedule_constraints
*sc
)
7443 isl_ctx
*ctx
= isl_schedule_constraints_get_ctx(sc
);
7444 struct isl_sched_graph graph
= { 0 };
7445 isl_schedule
*sched
;
7446 isl_schedule_node
*node
;
7447 isl_union_set
*domain
;
7450 sc
= isl_schedule_constraints_align_params(sc
);
7452 domain
= isl_schedule_constraints_get_domain(sc
);
7453 n
= isl_union_set_n_set(domain
);
7455 isl_schedule_constraints_free(sc
);
7456 return isl_schedule_from_domain(domain
);
7459 if (n
< 0 || graph_init(&graph
, sc
) < 0)
7460 domain
= isl_union_set_free(domain
);
7462 node
= isl_schedule_node_from_domain(domain
);
7463 node
= isl_schedule_node_child(node
, 0);
7465 node
= compute_schedule(node
, &graph
);
7466 sched
= isl_schedule_node_get_schedule(node
);
7467 isl_schedule_node_free(node
);
7469 graph_free(ctx
, &graph
);
7470 isl_schedule_constraints_free(sc
);
7475 /* Compute a schedule for the given union of domains that respects
7476 * all the validity dependences and minimizes
7477 * the dependence distances over the proximity dependences.
7479 * This function is kept for backward compatibility.
7481 __isl_give isl_schedule
*isl_union_set_compute_schedule(
7482 __isl_take isl_union_set
*domain
,
7483 __isl_take isl_union_map
*validity
,
7484 __isl_take isl_union_map
*proximity
)
7486 isl_schedule_constraints
*sc
;
7488 sc
= isl_schedule_constraints_on_domain(domain
);
7489 sc
= isl_schedule_constraints_set_validity(sc
, validity
);
7490 sc
= isl_schedule_constraints_set_proximity(sc
, proximity
);
7492 return isl_schedule_constraints_compute_schedule(sc
);