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
,
1119 nvar
= isl_morph_ran_dim(morph
, isl_dim_set
);
1121 set
= isl_set_free(set
);
1122 compress
= isl_morph_get_var_multi_aff(morph
);
1123 morph
= isl_morph_inverse(morph
);
1124 decompress
= isl_morph_get_var_multi_aff(morph
);
1125 isl_morph_free(morph
);
1127 hull_set
= isl_set_from_basic_set(hull
);
1128 return add_node(graph
, set
, nvar
, 1, hull_set
, compress
, decompress
);
1130 isl_basic_set_free(hull
);
1132 return isl_stat_error
;
1135 struct isl_extract_edge_data
{
1136 enum isl_edge_type type
;
1137 struct isl_sched_graph
*graph
;
1140 /* Merge edge2 into edge1, freeing the contents of edge2.
1141 * Return 0 on success and -1 on failure.
1143 * edge1 and edge2 are assumed to have the same value for the map field.
1145 static int merge_edge(struct isl_sched_edge
*edge1
,
1146 struct isl_sched_edge
*edge2
)
1148 edge1
->types
|= edge2
->types
;
1149 isl_map_free(edge2
->map
);
1151 if (is_condition(edge2
)) {
1152 if (!edge1
->tagged_condition
)
1153 edge1
->tagged_condition
= edge2
->tagged_condition
;
1155 edge1
->tagged_condition
=
1156 isl_union_map_union(edge1
->tagged_condition
,
1157 edge2
->tagged_condition
);
1160 if (is_conditional_validity(edge2
)) {
1161 if (!edge1
->tagged_validity
)
1162 edge1
->tagged_validity
= edge2
->tagged_validity
;
1164 edge1
->tagged_validity
=
1165 isl_union_map_union(edge1
->tagged_validity
,
1166 edge2
->tagged_validity
);
1169 if (is_condition(edge2
) && !edge1
->tagged_condition
)
1171 if (is_conditional_validity(edge2
) && !edge1
->tagged_validity
)
1177 /* Insert dummy tags in domain and range of "map".
1179 * In particular, if "map" is of the form
1185 * [A -> dummy_tag] -> [B -> dummy_tag]
1187 * where the dummy_tags are identical and equal to any dummy tags
1188 * introduced by any other call to this function.
1190 static __isl_give isl_map
*insert_dummy_tags(__isl_take isl_map
*map
)
1196 isl_set
*domain
, *range
;
1198 ctx
= isl_map_get_ctx(map
);
1200 id
= isl_id_alloc(ctx
, NULL
, &dummy
);
1201 space
= isl_space_params(isl_map_get_space(map
));
1202 space
= isl_space_set_from_params(space
);
1203 space
= isl_space_set_tuple_id(space
, isl_dim_set
, id
);
1204 space
= isl_space_map_from_set(space
);
1206 domain
= isl_map_wrap(map
);
1207 range
= isl_map_wrap(isl_map_universe(space
));
1208 map
= isl_map_from_domain_and_range(domain
, range
);
1209 map
= isl_map_zip(map
);
1214 /* Given that at least one of "src" or "dst" is compressed, return
1215 * a map between the spaces of these nodes restricted to the affine
1216 * hull that was used in the compression.
1218 static __isl_give isl_map
*extract_hull(struct isl_sched_node
*src
,
1219 struct isl_sched_node
*dst
)
1223 if (src
->compressed
)
1224 dom
= isl_set_copy(src
->hull
);
1226 dom
= isl_set_universe(isl_space_copy(src
->space
));
1227 if (dst
->compressed
)
1228 ran
= isl_set_copy(dst
->hull
);
1230 ran
= isl_set_universe(isl_space_copy(dst
->space
));
1232 return isl_map_from_domain_and_range(dom
, ran
);
1235 /* Intersect the domains of the nested relations in domain and range
1236 * of "tagged" with "map".
1238 static __isl_give isl_map
*map_intersect_domains(__isl_take isl_map
*tagged
,
1239 __isl_keep isl_map
*map
)
1243 tagged
= isl_map_zip(tagged
);
1244 set
= isl_map_wrap(isl_map_copy(map
));
1245 tagged
= isl_map_intersect_domain(tagged
, set
);
1246 tagged
= isl_map_zip(tagged
);
1250 /* Return a pointer to the node that lives in the domain space of "map",
1251 * an invalid node if there is no such node, or NULL in case of error.
1253 static struct isl_sched_node
*find_domain_node(isl_ctx
*ctx
,
1254 struct isl_sched_graph
*graph
, __isl_keep isl_map
*map
)
1256 struct isl_sched_node
*node
;
1259 space
= isl_space_domain(isl_map_get_space(map
));
1260 node
= graph_find_node(ctx
, graph
, space
);
1261 isl_space_free(space
);
1266 /* Return a pointer to the node that lives in the range space of "map",
1267 * an invalid node if there is no such node, or NULL in case of error.
1269 static struct isl_sched_node
*find_range_node(isl_ctx
*ctx
,
1270 struct isl_sched_graph
*graph
, __isl_keep isl_map
*map
)
1272 struct isl_sched_node
*node
;
1275 space
= isl_space_range(isl_map_get_space(map
));
1276 node
= graph_find_node(ctx
, graph
, space
);
1277 isl_space_free(space
);
1282 /* Refrain from adding a new edge based on "map".
1283 * Instead, just free the map.
1284 * "tagged" is either a copy of "map" with additional tags or NULL.
1286 static isl_stat
skip_edge(__isl_take isl_map
*map
, __isl_take isl_map
*tagged
)
1289 isl_map_free(tagged
);
1294 /* Add a new edge to the graph based on the given map
1295 * and add it to data->graph->edge_table[data->type].
1296 * If a dependence relation of a given type happens to be identical
1297 * to one of the dependence relations of a type that was added before,
1298 * then we don't create a new edge, but instead mark the original edge
1299 * as also representing a dependence of the current type.
1301 * Edges of type isl_edge_condition or isl_edge_conditional_validity
1302 * may be specified as "tagged" dependence relations. That is, "map"
1303 * may contain elements (i -> a) -> (j -> b), where i -> j denotes
1304 * the dependence on iterations and a and b are tags.
1305 * edge->map is set to the relation containing the elements i -> j,
1306 * while edge->tagged_condition and edge->tagged_validity contain
1307 * the union of all the "map" relations
1308 * for which extract_edge is called that result in the same edge->map.
1310 * If the source or the destination node is compressed, then
1311 * intersect both "map" and "tagged" with the constraints that
1312 * were used to construct the compression.
1313 * This ensures that there are no schedule constraints defined
1314 * outside of these domains, while the scheduler no longer has
1315 * any control over those outside parts.
1317 static isl_stat
extract_edge(__isl_take isl_map
*map
, void *user
)
1320 isl_ctx
*ctx
= isl_map_get_ctx(map
);
1321 struct isl_extract_edge_data
*data
= user
;
1322 struct isl_sched_graph
*graph
= data
->graph
;
1323 struct isl_sched_node
*src
, *dst
;
1324 struct isl_sched_edge
*edge
;
1325 isl_map
*tagged
= NULL
;
1327 if (data
->type
== isl_edge_condition
||
1328 data
->type
== isl_edge_conditional_validity
) {
1329 if (isl_map_can_zip(map
)) {
1330 tagged
= isl_map_copy(map
);
1331 map
= isl_set_unwrap(isl_map_domain(isl_map_zip(map
)));
1333 tagged
= insert_dummy_tags(isl_map_copy(map
));
1337 src
= find_domain_node(ctx
, graph
, map
);
1338 dst
= find_range_node(ctx
, graph
, map
);
1342 if (!is_node(graph
, src
) || !is_node(graph
, dst
))
1343 return skip_edge(map
, tagged
);
1345 if (src
->compressed
|| dst
->compressed
) {
1347 hull
= extract_hull(src
, dst
);
1349 tagged
= map_intersect_domains(tagged
, hull
);
1350 map
= isl_map_intersect(map
, hull
);
1353 empty
= isl_map_plain_is_empty(map
);
1357 return skip_edge(map
, tagged
);
1359 graph
->edge
[graph
->n_edge
].src
= src
;
1360 graph
->edge
[graph
->n_edge
].dst
= dst
;
1361 graph
->edge
[graph
->n_edge
].map
= map
;
1362 graph
->edge
[graph
->n_edge
].types
= 0;
1363 graph
->edge
[graph
->n_edge
].tagged_condition
= NULL
;
1364 graph
->edge
[graph
->n_edge
].tagged_validity
= NULL
;
1365 set_type(&graph
->edge
[graph
->n_edge
], data
->type
);
1366 if (data
->type
== isl_edge_condition
)
1367 graph
->edge
[graph
->n_edge
].tagged_condition
=
1368 isl_union_map_from_map(tagged
);
1369 if (data
->type
== isl_edge_conditional_validity
)
1370 graph
->edge
[graph
->n_edge
].tagged_validity
=
1371 isl_union_map_from_map(tagged
);
1373 edge
= graph_find_matching_edge(graph
, &graph
->edge
[graph
->n_edge
]);
1376 return isl_stat_error
;
1378 if (edge
== &graph
->edge
[graph
->n_edge
])
1379 return graph_edge_table_add(ctx
, graph
, data
->type
,
1380 &graph
->edge
[graph
->n_edge
++]);
1382 if (merge_edge(edge
, &graph
->edge
[graph
->n_edge
]) < 0)
1383 return isl_stat_error
;
1385 return graph_edge_table_add(ctx
, graph
, data
->type
, edge
);
1388 isl_map_free(tagged
);
1389 return isl_stat_error
;
1392 /* Initialize the schedule graph "graph" from the schedule constraints "sc".
1394 * The context is included in the domain before the nodes of
1395 * the graphs are extracted in order to be able to exploit
1396 * any possible additional equalities.
1397 * Note that this intersection is only performed locally here.
1399 static isl_stat
graph_init(struct isl_sched_graph
*graph
,
1400 __isl_keep isl_schedule_constraints
*sc
)
1403 isl_union_set
*domain
;
1405 struct isl_extract_edge_data data
;
1406 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 graph
->n
= isl_union_set_n_set(domain
);
1416 isl_union_set_free(domain
);
1418 if (graph_alloc(ctx
, graph
, graph
->n
,
1419 isl_schedule_constraints_n_map(sc
)) < 0)
1420 return isl_stat_error
;
1422 if (compute_max_row(graph
, sc
) < 0)
1423 return isl_stat_error
;
1424 graph
->root
= graph
;
1426 domain
= isl_schedule_constraints_get_domain(sc
);
1427 domain
= isl_union_set_intersect_params(domain
,
1428 isl_schedule_constraints_get_context(sc
));
1429 r
= isl_union_set_foreach_set(domain
, &extract_node
, graph
);
1430 isl_union_set_free(domain
);
1432 return isl_stat_error
;
1433 if (graph_init_table(ctx
, graph
) < 0)
1434 return isl_stat_error
;
1435 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
1436 c
= isl_schedule_constraints_get(sc
, i
);
1437 graph
->max_edge
[i
] = isl_union_map_n_map(c
);
1438 isl_union_map_free(c
);
1440 return isl_stat_error
;
1442 if (graph_init_edge_tables(ctx
, graph
) < 0)
1443 return isl_stat_error
;
1446 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
1450 c
= isl_schedule_constraints_get(sc
, i
);
1451 r
= isl_union_map_foreach_map(c
, &extract_edge
, &data
);
1452 isl_union_map_free(c
);
1454 return isl_stat_error
;
1460 /* Check whether there is any dependence from node[j] to node[i]
1461 * or from node[i] to node[j].
1463 static isl_bool
node_follows_weak(int i
, int j
, void *user
)
1466 struct isl_sched_graph
*graph
= user
;
1468 f
= graph_has_any_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
1471 return graph_has_any_edge(graph
, &graph
->node
[i
], &graph
->node
[j
]);
1474 /* Check whether there is a (conditional) validity dependence from node[j]
1475 * to node[i], forcing node[i] to follow node[j].
1477 static isl_bool
node_follows_strong(int i
, int j
, void *user
)
1479 struct isl_sched_graph
*graph
= user
;
1481 return graph_has_validity_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
1484 /* Use Tarjan's algorithm for computing the strongly connected components
1485 * in the dependence graph only considering those edges defined by "follows".
1487 static isl_stat
detect_ccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
1488 isl_bool (*follows
)(int i
, int j
, void *user
))
1491 struct isl_tarjan_graph
*g
= NULL
;
1493 g
= isl_tarjan_graph_init(ctx
, graph
->n
, follows
, graph
);
1495 return isl_stat_error
;
1501 while (g
->order
[i
] != -1) {
1502 graph
->node
[g
->order
[i
]].scc
= graph
->scc
;
1510 isl_tarjan_graph_free(g
);
1515 /* Apply Tarjan's algorithm to detect the strongly connected components
1516 * in the dependence graph.
1517 * Only consider the (conditional) validity dependences and clear "weak".
1519 static isl_stat
detect_sccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
1522 return detect_ccs(ctx
, graph
, &node_follows_strong
);
1525 /* Apply Tarjan's algorithm to detect the (weakly) connected components
1526 * in the dependence graph.
1527 * Consider all dependences and set "weak".
1529 static isl_stat
detect_wccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
1532 return detect_ccs(ctx
, graph
, &node_follows_weak
);
1535 static int cmp_scc(const void *a
, const void *b
, void *data
)
1537 struct isl_sched_graph
*graph
= data
;
1541 return graph
->node
[*i1
].scc
- graph
->node
[*i2
].scc
;
1544 /* Sort the elements of graph->sorted according to the corresponding SCCs.
1546 static int sort_sccs(struct isl_sched_graph
*graph
)
1548 return isl_sort(graph
->sorted
, graph
->n
, sizeof(int), &cmp_scc
, graph
);
1551 /* Return a non-parametric set in the compressed space of "node" that is
1552 * bounded by the size in each direction
1554 * { [x] : -S_i <= x_i <= S_i }
1556 * If S_i is infinity in direction i, then there are no constraints
1557 * in that direction.
1559 * Cache the result in node->bounds.
1561 static __isl_give isl_basic_set
*get_size_bounds(struct isl_sched_node
*node
)
1564 isl_basic_set
*bounds
;
1568 return isl_basic_set_copy(node
->bounds
);
1570 if (node
->compressed
)
1571 space
= isl_multi_aff_get_domain_space(node
->decompress
);
1573 space
= isl_space_copy(node
->space
);
1574 space
= isl_space_drop_all_params(space
);
1575 bounds
= isl_basic_set_universe(space
);
1577 for (i
= 0; i
< node
->nvar
; ++i
) {
1580 size
= isl_multi_val_get_val(node
->sizes
, i
);
1582 return isl_basic_set_free(bounds
);
1583 if (!isl_val_is_int(size
)) {
1587 bounds
= isl_basic_set_upper_bound_val(bounds
, isl_dim_set
, i
,
1588 isl_val_copy(size
));
1589 bounds
= isl_basic_set_lower_bound_val(bounds
, isl_dim_set
, i
,
1593 node
->bounds
= isl_basic_set_copy(bounds
);
1597 /* Drop some constraints from "delta" that could be exploited
1598 * to construct loop coalescing schedules.
1599 * In particular, drop those constraint that bound the difference
1600 * to the size of the domain.
1601 * First project out the parameters to improve the effectiveness.
1603 static __isl_give isl_set
*drop_coalescing_constraints(
1604 __isl_take isl_set
*delta
, struct isl_sched_node
*node
)
1607 isl_basic_set
*bounds
;
1609 nparam
= isl_set_dim(delta
, isl_dim_param
);
1611 return isl_set_free(delta
);
1613 bounds
= get_size_bounds(node
);
1615 delta
= isl_set_project_out(delta
, isl_dim_param
, 0, nparam
);
1616 delta
= isl_set_remove_divs(delta
);
1617 delta
= isl_set_plain_gist_basic_set(delta
, bounds
);
1621 /* Given a dependence relation R from "node" to itself,
1622 * construct the set of coefficients of valid constraints for elements
1623 * in that dependence relation.
1624 * In particular, the result contains tuples of coefficients
1625 * c_0, c_n, c_x such that
1627 * c_0 + c_n n + c_x y - c_x x >= 0 for each (x,y) in R
1631 * c_0 + c_n n + c_x d >= 0 for each d in delta R = { y - x | (x,y) in R }
1633 * We choose here to compute the dual of delta R.
1634 * Alternatively, we could have computed the dual of R, resulting
1635 * in a set of tuples c_0, c_n, c_x, c_y, and then
1636 * plugged in (c_0, c_n, c_x, -c_x).
1638 * If "need_param" is set, then the resulting coefficients effectively
1639 * include coefficients for the parameters c_n. Otherwise, they may
1640 * have been projected out already.
1641 * Since the constraints may be different for these two cases,
1642 * they are stored in separate caches.
1643 * In particular, if no parameter coefficients are required and
1644 * the schedule_treat_coalescing option is set, then the parameters
1645 * are projected out and some constraints that could be exploited
1646 * to construct coalescing schedules are removed before the dual
1649 * If "node" has been compressed, then the dependence relation
1650 * is also compressed before the set of coefficients is computed.
1652 static __isl_give isl_basic_set
*intra_coefficients(
1653 struct isl_sched_graph
*graph
, struct isl_sched_node
*node
,
1654 __isl_take isl_map
*map
, int need_param
)
1659 isl_basic_set
*coef
;
1660 isl_maybe_isl_basic_set m
;
1661 isl_map_to_basic_set
**hmap
= &graph
->intra_hmap
;
1667 ctx
= isl_map_get_ctx(map
);
1668 treat
= !need_param
&& isl_options_get_schedule_treat_coalescing(ctx
);
1670 hmap
= &graph
->intra_hmap_param
;
1671 m
= isl_map_to_basic_set_try_get(*hmap
, map
);
1672 if (m
.valid
< 0 || m
.valid
) {
1677 key
= isl_map_copy(map
);
1678 if (node
->compressed
) {
1679 map
= isl_map_preimage_domain_multi_aff(map
,
1680 isl_multi_aff_copy(node
->decompress
));
1681 map
= isl_map_preimage_range_multi_aff(map
,
1682 isl_multi_aff_copy(node
->decompress
));
1684 delta
= isl_map_deltas(map
);
1686 delta
= drop_coalescing_constraints(delta
, node
);
1687 delta
= isl_set_remove_divs(delta
);
1688 coef
= isl_set_coefficients(delta
);
1689 *hmap
= isl_map_to_basic_set_set(*hmap
, key
, isl_basic_set_copy(coef
));
1694 /* Given a dependence relation R, construct the set of coefficients
1695 * of valid constraints for elements in that dependence relation.
1696 * In particular, the result contains tuples of coefficients
1697 * c_0, c_n, c_x, c_y such that
1699 * c_0 + c_n n + c_x x + c_y y >= 0 for each (x,y) in R
1701 * If the source or destination nodes of "edge" have been compressed,
1702 * then the dependence relation is also compressed before
1703 * the set of coefficients is computed.
1705 static __isl_give isl_basic_set
*inter_coefficients(
1706 struct isl_sched_graph
*graph
, struct isl_sched_edge
*edge
,
1707 __isl_take isl_map
*map
)
1711 isl_basic_set
*coef
;
1712 isl_maybe_isl_basic_set m
;
1714 m
= isl_map_to_basic_set_try_get(graph
->inter_hmap
, map
);
1715 if (m
.valid
< 0 || m
.valid
) {
1720 key
= isl_map_copy(map
);
1721 if (edge
->src
->compressed
)
1722 map
= isl_map_preimage_domain_multi_aff(map
,
1723 isl_multi_aff_copy(edge
->src
->decompress
));
1724 if (edge
->dst
->compressed
)
1725 map
= isl_map_preimage_range_multi_aff(map
,
1726 isl_multi_aff_copy(edge
->dst
->decompress
));
1727 set
= isl_map_wrap(isl_map_remove_divs(map
));
1728 coef
= isl_set_coefficients(set
);
1729 graph
->inter_hmap
= isl_map_to_basic_set_set(graph
->inter_hmap
, key
,
1730 isl_basic_set_copy(coef
));
1735 /* Return the position of the coefficients of the variables in
1736 * the coefficients constraints "coef".
1738 * The space of "coef" is of the form
1740 * { coefficients[[cst, params] -> S] }
1742 * Return the position of S.
1744 static isl_size
coef_var_offset(__isl_keep isl_basic_set
*coef
)
1749 space
= isl_space_unwrap(isl_basic_set_get_space(coef
));
1750 offset
= isl_space_dim(space
, isl_dim_in
);
1751 isl_space_free(space
);
1756 /* Return the offset of the coefficient of the constant term of "node"
1759 * Within each node, the coefficients have the following order:
1760 * - positive and negative parts of c_i_x
1761 * - c_i_n (if parametric)
1764 static int node_cst_coef_offset(struct isl_sched_node
*node
)
1766 return node
->start
+ 2 * node
->nvar
+ node
->nparam
;
1769 /* Return the offset of the coefficients of the parameters of "node"
1772 * Within each node, the coefficients have the following order:
1773 * - positive and negative parts of c_i_x
1774 * - c_i_n (if parametric)
1777 static int node_par_coef_offset(struct isl_sched_node
*node
)
1779 return node
->start
+ 2 * node
->nvar
;
1782 /* Return the offset of the coefficients of the variables of "node"
1785 * Within each node, the coefficients have the following order:
1786 * - positive and negative parts of c_i_x
1787 * - c_i_n (if parametric)
1790 static int node_var_coef_offset(struct isl_sched_node
*node
)
1795 /* Return the position of the pair of variables encoding
1796 * coefficient "i" of "node".
1798 * The order of these variable pairs is the opposite of
1799 * that of the coefficients, with 2 variables per coefficient.
1801 static int node_var_coef_pos(struct isl_sched_node
*node
, int i
)
1803 return node_var_coef_offset(node
) + 2 * (node
->nvar
- 1 - i
);
1806 /* Construct an isl_dim_map for mapping constraints on coefficients
1807 * for "node" to the corresponding positions in graph->lp.
1808 * "offset" is the offset of the coefficients for the variables
1809 * in the input constraints.
1810 * "s" is the sign of the mapping.
1812 * The input constraints are given in terms of the coefficients
1813 * (c_0, c_x) or (c_0, c_n, c_x).
1814 * The mapping produced by this function essentially plugs in
1815 * (0, c_i_x^+ - c_i_x^-) if s = 1 and
1816 * (0, -c_i_x^+ + c_i_x^-) if s = -1 or
1817 * (0, 0, c_i_x^+ - c_i_x^-) if s = 1 and
1818 * (0, 0, -c_i_x^+ + c_i_x^-) if s = -1.
1819 * In graph->lp, the c_i_x^- appear before their c_i_x^+ counterpart.
1820 * Furthermore, the order of these pairs is the opposite of that
1821 * of the corresponding coefficients.
1823 * The caller can extend the mapping to also map the other coefficients
1824 * (and therefore not plug in 0).
1826 static __isl_give isl_dim_map
*intra_dim_map(isl_ctx
*ctx
,
1827 struct isl_sched_graph
*graph
, struct isl_sched_node
*node
,
1832 isl_dim_map
*dim_map
;
1834 total
= isl_basic_set_dim(graph
->lp
, isl_dim_all
);
1835 if (!node
|| total
< 0)
1838 pos
= node_var_coef_pos(node
, 0);
1839 dim_map
= isl_dim_map_alloc(ctx
, total
);
1840 isl_dim_map_range(dim_map
, pos
, -2, offset
, 1, node
->nvar
, -s
);
1841 isl_dim_map_range(dim_map
, pos
+ 1, -2, offset
, 1, node
->nvar
, s
);
1846 /* Construct an isl_dim_map for mapping constraints on coefficients
1847 * for "src" (node i) and "dst" (node j) to the corresponding positions
1849 * "offset" is the offset of the coefficients for the variables of "src"
1850 * in the input constraints.
1851 * "s" is the sign of the mapping.
1853 * The input constraints are given in terms of the coefficients
1854 * (c_0, c_n, c_x, c_y).
1855 * The mapping produced by this function essentially plugs in
1856 * (c_j_0 - c_i_0, c_j_n - c_i_n,
1857 * -(c_i_x^+ - c_i_x^-), c_j_x^+ - c_j_x^-) if s = 1 and
1858 * (-c_j_0 + c_i_0, -c_j_n + c_i_n,
1859 * c_i_x^+ - c_i_x^-, -(c_j_x^+ - c_j_x^-)) if s = -1.
1860 * In graph->lp, the c_*^- appear before their c_*^+ counterpart.
1861 * Furthermore, the order of these pairs is the opposite of that
1862 * of the corresponding coefficients.
1864 * The caller can further extend the mapping.
1866 static __isl_give isl_dim_map
*inter_dim_map(isl_ctx
*ctx
,
1867 struct isl_sched_graph
*graph
, struct isl_sched_node
*src
,
1868 struct isl_sched_node
*dst
, int offset
, int s
)
1872 isl_dim_map
*dim_map
;
1874 total
= isl_basic_set_dim(graph
->lp
, isl_dim_all
);
1875 if (!src
|| !dst
|| total
< 0)
1878 dim_map
= isl_dim_map_alloc(ctx
, total
);
1880 pos
= node_cst_coef_offset(dst
);
1881 isl_dim_map_range(dim_map
, pos
, 0, 0, 0, 1, s
);
1882 pos
= node_par_coef_offset(dst
);
1883 isl_dim_map_range(dim_map
, pos
, 1, 1, 1, dst
->nparam
, s
);
1884 pos
= node_var_coef_pos(dst
, 0);
1885 isl_dim_map_range(dim_map
, pos
, -2, offset
+ src
->nvar
, 1,
1887 isl_dim_map_range(dim_map
, pos
+ 1, -2, offset
+ src
->nvar
, 1,
1890 pos
= node_cst_coef_offset(src
);
1891 isl_dim_map_range(dim_map
, pos
, 0, 0, 0, 1, -s
);
1892 pos
= node_par_coef_offset(src
);
1893 isl_dim_map_range(dim_map
, pos
, 1, 1, 1, src
->nparam
, -s
);
1894 pos
= node_var_coef_pos(src
, 0);
1895 isl_dim_map_range(dim_map
, pos
, -2, offset
, 1, src
->nvar
, s
);
1896 isl_dim_map_range(dim_map
, pos
+ 1, -2, offset
, 1, src
->nvar
, -s
);
1901 /* Add the constraints from "src" to "dst" using "dim_map",
1902 * after making sure there is enough room in "dst" for the extra constraints.
1904 static __isl_give isl_basic_set
*add_constraints_dim_map(
1905 __isl_take isl_basic_set
*dst
, __isl_take isl_basic_set
*src
,
1906 __isl_take isl_dim_map
*dim_map
)
1910 n_eq
= isl_basic_set_n_equality(src
);
1911 n_ineq
= isl_basic_set_n_inequality(src
);
1912 dst
= isl_basic_set_extend_constraints(dst
, n_eq
, n_ineq
);
1913 dst
= isl_basic_set_add_constraints_dim_map(dst
, src
, dim_map
);
1917 /* Add constraints to graph->lp that force validity for the given
1918 * dependence from a node i to itself.
1919 * That is, add constraints that enforce
1921 * (c_i_0 + c_i_n n + c_i_x y) - (c_i_0 + c_i_n n + c_i_x x)
1922 * = c_i_x (y - x) >= 0
1924 * for each (x,y) in R.
1925 * We obtain general constraints on coefficients (c_0, c_x)
1926 * of valid constraints for (y - x) and then plug in (0, c_i_x^+ - c_i_x^-),
1927 * where c_i_x = c_i_x^+ - c_i_x^-, with c_i_x^+ and c_i_x^- non-negative.
1928 * In graph->lp, the c_i_x^- appear before their c_i_x^+ counterpart.
1929 * Note that the result of intra_coefficients may also contain
1930 * parameter coefficients c_n, in which case 0 is plugged in for them as well.
1932 static isl_stat
add_intra_validity_constraints(struct isl_sched_graph
*graph
,
1933 struct isl_sched_edge
*edge
)
1936 isl_map
*map
= isl_map_copy(edge
->map
);
1937 isl_ctx
*ctx
= isl_map_get_ctx(map
);
1938 isl_dim_map
*dim_map
;
1939 isl_basic_set
*coef
;
1940 struct isl_sched_node
*node
= edge
->src
;
1942 coef
= intra_coefficients(graph
, node
, map
, 0);
1944 offset
= coef_var_offset(coef
);
1946 coef
= isl_basic_set_free(coef
);
1948 return isl_stat_error
;
1950 dim_map
= intra_dim_map(ctx
, graph
, node
, offset
, 1);
1951 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
1956 /* Add constraints to graph->lp that force validity for the given
1957 * dependence from node i to node j.
1958 * That is, add constraints that enforce
1960 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) >= 0
1962 * for each (x,y) in R.
1963 * We obtain general constraints on coefficients (c_0, c_n, c_x, c_y)
1964 * of valid constraints for R and then plug in
1965 * (c_j_0 - c_i_0, c_j_n - c_i_n, -(c_i_x^+ - c_i_x^-), c_j_x^+ - c_j_x^-),
1966 * where c_* = c_*^+ - c_*^-, with c_*^+ and c_*^- non-negative.
1967 * In graph->lp, the c_*^- appear before their c_*^+ counterpart.
1969 static isl_stat
add_inter_validity_constraints(struct isl_sched_graph
*graph
,
1970 struct isl_sched_edge
*edge
)
1975 isl_dim_map
*dim_map
;
1976 isl_basic_set
*coef
;
1977 struct isl_sched_node
*src
= edge
->src
;
1978 struct isl_sched_node
*dst
= edge
->dst
;
1981 return isl_stat_error
;
1983 map
= isl_map_copy(edge
->map
);
1984 ctx
= isl_map_get_ctx(map
);
1985 coef
= inter_coefficients(graph
, edge
, map
);
1987 offset
= coef_var_offset(coef
);
1989 coef
= isl_basic_set_free(coef
);
1991 return isl_stat_error
;
1993 dim_map
= inter_dim_map(ctx
, graph
, src
, dst
, offset
, 1);
1995 edge
->start
= graph
->lp
->n_ineq
;
1996 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
1998 return isl_stat_error
;
1999 edge
->end
= graph
->lp
->n_ineq
;
2004 /* Add constraints to graph->lp that bound the dependence distance for the given
2005 * dependence from a node i to itself.
2006 * If s = 1, we add the constraint
2008 * c_i_x (y - x) <= m_0 + m_n n
2012 * -c_i_x (y - x) + m_0 + m_n n >= 0
2014 * for each (x,y) in R.
2015 * If s = -1, we add the constraint
2017 * -c_i_x (y - x) <= m_0 + m_n n
2021 * c_i_x (y - x) + m_0 + m_n n >= 0
2023 * for each (x,y) in R.
2024 * We obtain general constraints on coefficients (c_0, c_n, c_x)
2025 * of valid constraints for (y - x) and then plug in (m_0, m_n, -s * c_i_x),
2026 * with each coefficient (except m_0) represented as a pair of non-negative
2030 * If "local" is set, then we add constraints
2032 * c_i_x (y - x) <= 0
2036 * -c_i_x (y - x) <= 0
2038 * instead, forcing the dependence distance to be (less than or) equal to 0.
2039 * That is, we plug in (0, 0, -s * c_i_x),
2040 * intra_coefficients is not required to have c_n in its result when
2041 * "local" is set. If they are missing, then (0, -s * c_i_x) is plugged in.
2042 * Note that dependences marked local are treated as validity constraints
2043 * by add_all_validity_constraints and therefore also have
2044 * their distances bounded by 0 from below.
2046 static isl_stat
add_intra_proximity_constraints(struct isl_sched_graph
*graph
,
2047 struct isl_sched_edge
*edge
, int s
, int local
)
2051 isl_map
*map
= isl_map_copy(edge
->map
);
2052 isl_ctx
*ctx
= isl_map_get_ctx(map
);
2053 isl_dim_map
*dim_map
;
2054 isl_basic_set
*coef
;
2055 struct isl_sched_node
*node
= edge
->src
;
2057 coef
= intra_coefficients(graph
, node
, map
, !local
);
2058 nparam
= isl_space_dim(node
->space
, isl_dim_param
);
2060 offset
= coef_var_offset(coef
);
2061 if (nparam
< 0 || offset
< 0)
2062 coef
= isl_basic_set_free(coef
);
2064 return isl_stat_error
;
2066 dim_map
= intra_dim_map(ctx
, graph
, node
, offset
, -s
);
2069 isl_dim_map_range(dim_map
, 1, 0, 0, 0, 1, 1);
2070 isl_dim_map_range(dim_map
, 4, 2, 1, 1, nparam
, -1);
2071 isl_dim_map_range(dim_map
, 5, 2, 1, 1, nparam
, 1);
2073 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
2078 /* Add constraints to graph->lp that bound the dependence distance for the given
2079 * dependence from node i to node j.
2080 * If s = 1, we add the constraint
2082 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x)
2087 * -(c_j_0 + c_j_n n + c_j_x y) + (c_i_0 + c_i_n n + c_i_x x) +
2090 * for each (x,y) in R.
2091 * If s = -1, we add the constraint
2093 * -((c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x))
2098 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) +
2101 * for each (x,y) in R.
2102 * We obtain general constraints on coefficients (c_0, c_n, c_x, c_y)
2103 * of valid constraints for R and then plug in
2104 * (m_0 - s*c_j_0 + s*c_i_0, m_n - s*c_j_n + s*c_i_n,
2105 * s*c_i_x, -s*c_j_x)
2106 * with each coefficient (except m_0, c_*_0 and c_*_n)
2107 * represented as a pair of non-negative coefficients.
2110 * If "local" is set (and s = 1), then we add constraints
2112 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) <= 0
2116 * -((c_j_0 + c_j_n n + c_j_x y) + (c_i_0 + c_i_n n + c_i_x x)) >= 0
2118 * instead, forcing the dependence distance to be (less than or) equal to 0.
2119 * That is, we plug in
2120 * (-s*c_j_0 + s*c_i_0, -s*c_j_n + s*c_i_n, s*c_i_x, -s*c_j_x).
2121 * Note that dependences marked local are treated as validity constraints
2122 * by add_all_validity_constraints and therefore also have
2123 * their distances bounded by 0 from below.
2125 static isl_stat
add_inter_proximity_constraints(struct isl_sched_graph
*graph
,
2126 struct isl_sched_edge
*edge
, int s
, int local
)
2130 isl_map
*map
= isl_map_copy(edge
->map
);
2131 isl_ctx
*ctx
= isl_map_get_ctx(map
);
2132 isl_dim_map
*dim_map
;
2133 isl_basic_set
*coef
;
2134 struct isl_sched_node
*src
= edge
->src
;
2135 struct isl_sched_node
*dst
= edge
->dst
;
2137 coef
= inter_coefficients(graph
, edge
, map
);
2138 nparam
= isl_space_dim(src
->space
, isl_dim_param
);
2140 offset
= coef_var_offset(coef
);
2141 if (nparam
< 0 || offset
< 0)
2142 coef
= isl_basic_set_free(coef
);
2144 return isl_stat_error
;
2146 dim_map
= inter_dim_map(ctx
, graph
, src
, dst
, offset
, -s
);
2149 isl_dim_map_range(dim_map
, 1, 0, 0, 0, 1, 1);
2150 isl_dim_map_range(dim_map
, 4, 2, 1, 1, nparam
, -1);
2151 isl_dim_map_range(dim_map
, 5, 2, 1, 1, nparam
, 1);
2154 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
2159 /* Should the distance over "edge" be forced to zero?
2160 * That is, is it marked as a local edge?
2161 * If "use_coincidence" is set, then coincidence edges are treated
2164 static int force_zero(struct isl_sched_edge
*edge
, int use_coincidence
)
2166 return is_local(edge
) || (use_coincidence
&& is_coincidence(edge
));
2169 /* Add all validity constraints to graph->lp.
2171 * An edge that is forced to be local needs to have its dependence
2172 * distances equal to zero. We take care of bounding them by 0 from below
2173 * here. add_all_proximity_constraints takes care of bounding them by 0
2176 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2177 * Otherwise, we ignore them.
2179 static int add_all_validity_constraints(struct isl_sched_graph
*graph
,
2180 int use_coincidence
)
2184 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2185 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
2188 zero
= force_zero(edge
, use_coincidence
);
2189 if (!is_validity(edge
) && !zero
)
2191 if (edge
->src
!= edge
->dst
)
2193 if (add_intra_validity_constraints(graph
, edge
) < 0)
2197 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2198 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
2201 zero
= force_zero(edge
, use_coincidence
);
2202 if (!is_validity(edge
) && !zero
)
2204 if (edge
->src
== edge
->dst
)
2206 if (add_inter_validity_constraints(graph
, edge
) < 0)
2213 /* Add constraints to graph->lp that bound the dependence distance
2214 * for all dependence relations.
2215 * If a given proximity dependence is identical to a validity
2216 * dependence, then the dependence distance is already bounded
2217 * from below (by zero), so we only need to bound the distance
2218 * from above. (This includes the case of "local" dependences
2219 * which are treated as validity dependence by add_all_validity_constraints.)
2220 * Otherwise, we need to bound the distance both from above and from below.
2222 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2223 * Otherwise, we ignore them.
2225 static int add_all_proximity_constraints(struct isl_sched_graph
*graph
,
2226 int use_coincidence
)
2230 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2231 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
2234 zero
= force_zero(edge
, use_coincidence
);
2235 if (!is_proximity(edge
) && !zero
)
2237 if (edge
->src
== edge
->dst
&&
2238 add_intra_proximity_constraints(graph
, edge
, 1, zero
) < 0)
2240 if (edge
->src
!= edge
->dst
&&
2241 add_inter_proximity_constraints(graph
, edge
, 1, zero
) < 0)
2243 if (is_validity(edge
) || zero
)
2245 if (edge
->src
== edge
->dst
&&
2246 add_intra_proximity_constraints(graph
, edge
, -1, 0) < 0)
2248 if (edge
->src
!= edge
->dst
&&
2249 add_inter_proximity_constraints(graph
, edge
, -1, 0) < 0)
2256 /* Normalize the rows of "indep" such that all rows are lexicographically
2257 * positive and such that each row contains as many final zeros as possible,
2258 * given the choice for the previous rows.
2259 * Do this by performing elementary row operations.
2261 static __isl_give isl_mat
*normalize_independent(__isl_take isl_mat
*indep
)
2263 indep
= isl_mat_reverse_gauss(indep
);
2264 indep
= isl_mat_lexnonneg_rows(indep
);
2268 /* Extract the linear part of the current schedule for node "node".
2270 static __isl_give isl_mat
*extract_linear_schedule(struct isl_sched_node
*node
)
2272 int n_row
= isl_mat_rows(node
->sched
);
2274 return isl_mat_sub_alloc(node
->sched
, 0, n_row
,
2275 1 + node
->nparam
, node
->nvar
);
2278 /* Compute a basis for the rows in the linear part of the schedule
2279 * and extend this basis to a full basis. The remaining rows
2280 * can then be used to force linear independence from the rows
2283 * In particular, given the schedule rows S, we compute
2288 * with H the Hermite normal form of S. That is, all but the
2289 * first rank columns of H are zero and so each row in S is
2290 * a linear combination of the first rank rows of Q.
2291 * The matrix Q can be used as a variable transformation
2292 * that isolates the directions of S in the first rank rows.
2293 * Transposing S U = H yields
2297 * with all but the first rank rows of H^T zero.
2298 * The last rows of U^T are therefore linear combinations
2299 * of schedule coefficients that are all zero on schedule
2300 * coefficients that are linearly dependent on the rows of S.
2301 * At least one of these combinations is non-zero on
2302 * linearly independent schedule coefficients.
2303 * The rows are normalized to involve as few of the last
2304 * coefficients as possible and to have a positive initial value.
2306 static int node_update_vmap(struct isl_sched_node
*node
)
2310 H
= extract_linear_schedule(node
);
2312 H
= isl_mat_left_hermite(H
, 0, &U
, &Q
);
2313 isl_mat_free(node
->indep
);
2314 isl_mat_free(node
->vmap
);
2316 node
->indep
= isl_mat_transpose(U
);
2317 node
->rank
= isl_mat_initial_non_zero_cols(H
);
2318 node
->indep
= isl_mat_drop_rows(node
->indep
, 0, node
->rank
);
2319 node
->indep
= normalize_independent(node
->indep
);
2322 if (!node
->indep
|| !node
->vmap
|| node
->rank
< 0)
2327 /* Is "edge" marked as a validity or a conditional validity edge?
2329 static int is_any_validity(struct isl_sched_edge
*edge
)
2331 return is_validity(edge
) || is_conditional_validity(edge
);
2334 /* How many times should we count the constraints in "edge"?
2336 * We count as follows
2337 * validity -> 1 (>= 0)
2338 * validity+proximity -> 2 (>= 0 and upper bound)
2339 * proximity -> 2 (lower and upper bound)
2340 * local(+any) -> 2 (>= 0 and <= 0)
2342 * If an edge is only marked conditional_validity then it counts
2343 * as zero since it is only checked afterwards.
2345 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2346 * Otherwise, we ignore them.
2348 static int edge_multiplicity(struct isl_sched_edge
*edge
, int use_coincidence
)
2350 if (is_proximity(edge
) || force_zero(edge
, use_coincidence
))
2352 if (is_validity(edge
))
2357 /* How many times should the constraints in "edge" be counted
2358 * as a parametric intra-node constraint?
2360 * Only proximity edges that are not forced zero need
2361 * coefficient constraints that include coefficients for parameters.
2362 * If the edge is also a validity edge, then only
2363 * an upper bound is introduced. Otherwise, both lower and upper bounds
2366 static int parametric_intra_edge_multiplicity(struct isl_sched_edge
*edge
,
2367 int use_coincidence
)
2369 if (edge
->src
!= edge
->dst
)
2371 if (!is_proximity(edge
))
2373 if (force_zero(edge
, use_coincidence
))
2375 if (is_validity(edge
))
2381 /* Add "f" times the number of equality and inequality constraints of "bset"
2382 * to "n_eq" and "n_ineq" and free "bset".
2384 static isl_stat
update_count(__isl_take isl_basic_set
*bset
,
2385 int f
, int *n_eq
, int *n_ineq
)
2388 return isl_stat_error
;
2390 *n_eq
+= isl_basic_set_n_equality(bset
);
2391 *n_ineq
+= isl_basic_set_n_inequality(bset
);
2392 isl_basic_set_free(bset
);
2397 /* Count the number of equality and inequality constraints
2398 * that will be added for the given map.
2400 * The edges that require parameter coefficients are counted separately.
2402 * "use_coincidence" is set if we should take into account coincidence edges.
2404 static isl_stat
count_map_constraints(struct isl_sched_graph
*graph
,
2405 struct isl_sched_edge
*edge
, __isl_take isl_map
*map
,
2406 int *n_eq
, int *n_ineq
, int use_coincidence
)
2409 isl_basic_set
*coef
;
2410 int f
= edge_multiplicity(edge
, use_coincidence
);
2411 int fp
= parametric_intra_edge_multiplicity(edge
, use_coincidence
);
2418 if (edge
->src
!= edge
->dst
) {
2419 coef
= inter_coefficients(graph
, edge
, map
);
2420 return update_count(coef
, f
, n_eq
, n_ineq
);
2424 copy
= isl_map_copy(map
);
2425 coef
= intra_coefficients(graph
, edge
->src
, copy
, 1);
2426 if (update_count(coef
, fp
, n_eq
, n_ineq
) < 0)
2431 copy
= isl_map_copy(map
);
2432 coef
= intra_coefficients(graph
, edge
->src
, copy
, 0);
2433 if (update_count(coef
, f
- fp
, n_eq
, n_ineq
) < 0)
2441 return isl_stat_error
;
2444 /* Count the number of equality and inequality constraints
2445 * that will be added to the main lp problem.
2446 * We count as follows
2447 * validity -> 1 (>= 0)
2448 * validity+proximity -> 2 (>= 0 and upper bound)
2449 * proximity -> 2 (lower and upper bound)
2450 * local(+any) -> 2 (>= 0 and <= 0)
2452 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2453 * Otherwise, we ignore them.
2455 static int count_constraints(struct isl_sched_graph
*graph
,
2456 int *n_eq
, int *n_ineq
, int use_coincidence
)
2460 *n_eq
= *n_ineq
= 0;
2461 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2462 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
2463 isl_map
*map
= isl_map_copy(edge
->map
);
2465 if (count_map_constraints(graph
, edge
, map
, n_eq
, n_ineq
,
2466 use_coincidence
) < 0)
2473 /* Count the number of constraints that will be added by
2474 * add_bound_constant_constraints to bound the values of the constant terms
2475 * and increment *n_eq and *n_ineq accordingly.
2477 * In practice, add_bound_constant_constraints only adds inequalities.
2479 static isl_stat
count_bound_constant_constraints(isl_ctx
*ctx
,
2480 struct isl_sched_graph
*graph
, int *n_eq
, int *n_ineq
)
2482 if (isl_options_get_schedule_max_constant_term(ctx
) == -1)
2485 *n_ineq
+= graph
->n
;
2490 /* Add constraints to bound the values of the constant terms in the schedule,
2491 * if requested by the user.
2493 * The maximal value of the constant terms is defined by the option
2494 * "schedule_max_constant_term".
2496 static isl_stat
add_bound_constant_constraints(isl_ctx
*ctx
,
2497 struct isl_sched_graph
*graph
)
2503 max
= isl_options_get_schedule_max_constant_term(ctx
);
2507 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2509 return isl_stat_error
;
2511 for (i
= 0; i
< graph
->n
; ++i
) {
2512 struct isl_sched_node
*node
= &graph
->node
[i
];
2515 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2517 return isl_stat_error
;
2518 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
2519 pos
= node_cst_coef_offset(node
);
2520 isl_int_set_si(graph
->lp
->ineq
[k
][1 + pos
], -1);
2521 isl_int_set_si(graph
->lp
->ineq
[k
][0], max
);
2527 /* Count the number of constraints that will be added by
2528 * add_bound_coefficient_constraints and increment *n_eq and *n_ineq
2531 * In practice, add_bound_coefficient_constraints only adds inequalities.
2533 static int count_bound_coefficient_constraints(isl_ctx
*ctx
,
2534 struct isl_sched_graph
*graph
, int *n_eq
, int *n_ineq
)
2538 if (isl_options_get_schedule_max_coefficient(ctx
) == -1 &&
2539 !isl_options_get_schedule_treat_coalescing(ctx
))
2542 for (i
= 0; i
< graph
->n
; ++i
)
2543 *n_ineq
+= graph
->node
[i
].nparam
+ 2 * graph
->node
[i
].nvar
;
2548 /* Add constraints to graph->lp that bound the values of
2549 * the parameter schedule coefficients of "node" to "max" and
2550 * the variable schedule coefficients to the corresponding entry
2552 * In either case, a negative value means that no bound needs to be imposed.
2554 * For parameter coefficients, this amounts to adding a constraint
2562 * The variables coefficients are, however, not represented directly.
2563 * Instead, the variable coefficients c_x are written as differences
2564 * c_x = c_x^+ - c_x^-.
2567 * -max_i <= c_x_i <= max_i
2571 * -max_i <= c_x_i^+ - c_x_i^- <= max_i
2575 * -(c_x_i^+ - c_x_i^-) + max_i >= 0
2576 * c_x_i^+ - c_x_i^- + max_i >= 0
2578 static isl_stat
node_add_coefficient_constraints(isl_ctx
*ctx
,
2579 struct isl_sched_graph
*graph
, struct isl_sched_node
*node
, int max
)
2585 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2587 return isl_stat_error
;
2589 for (j
= 0; j
< node
->nparam
; ++j
) {
2595 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2597 return isl_stat_error
;
2598 dim
= 1 + node_par_coef_offset(node
) + j
;
2599 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
2600 isl_int_set_si(graph
->lp
->ineq
[k
][dim
], -1);
2601 isl_int_set_si(graph
->lp
->ineq
[k
][0], max
);
2604 ineq
= isl_vec_alloc(ctx
, 1 + total
);
2605 ineq
= isl_vec_clr(ineq
);
2607 return isl_stat_error
;
2608 for (i
= 0; i
< node
->nvar
; ++i
) {
2609 int pos
= 1 + node_var_coef_pos(node
, i
);
2611 if (isl_int_is_neg(node
->max
->el
[i
]))
2614 isl_int_set_si(ineq
->el
[pos
], 1);
2615 isl_int_set_si(ineq
->el
[pos
+ 1], -1);
2616 isl_int_set(ineq
->el
[0], node
->max
->el
[i
]);
2618 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2621 isl_seq_cpy(graph
->lp
->ineq
[k
], ineq
->el
, 1 + total
);
2623 isl_seq_neg(ineq
->el
+ pos
, ineq
->el
+ pos
, 2);
2624 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2627 isl_seq_cpy(graph
->lp
->ineq
[k
], ineq
->el
, 1 + total
);
2629 isl_seq_clr(ineq
->el
+ pos
, 2);
2636 return isl_stat_error
;
2639 /* Add constraints that bound the values of the variable and parameter
2640 * coefficients of the schedule.
2642 * The maximal value of the coefficients is defined by the option
2643 * 'schedule_max_coefficient' and the entries in node->max.
2644 * These latter entries are only set if either the schedule_max_coefficient
2645 * option or the schedule_treat_coalescing option is set.
2647 static isl_stat
add_bound_coefficient_constraints(isl_ctx
*ctx
,
2648 struct isl_sched_graph
*graph
)
2653 max
= isl_options_get_schedule_max_coefficient(ctx
);
2655 if (max
== -1 && !isl_options_get_schedule_treat_coalescing(ctx
))
2658 for (i
= 0; i
< graph
->n
; ++i
) {
2659 struct isl_sched_node
*node
= &graph
->node
[i
];
2661 if (node_add_coefficient_constraints(ctx
, graph
, node
, max
) < 0)
2662 return isl_stat_error
;
2668 /* Add a constraint to graph->lp that equates the value at position
2669 * "sum_pos" to the sum of the "n" values starting at "first".
2671 static isl_stat
add_sum_constraint(struct isl_sched_graph
*graph
,
2672 int sum_pos
, int first
, int n
)
2677 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2679 return isl_stat_error
;
2681 k
= isl_basic_set_alloc_equality(graph
->lp
);
2683 return isl_stat_error
;
2684 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2685 isl_int_set_si(graph
->lp
->eq
[k
][1 + sum_pos
], -1);
2686 for (i
= 0; i
< n
; ++i
)
2687 isl_int_set_si(graph
->lp
->eq
[k
][1 + first
+ i
], 1);
2692 /* Add a constraint to graph->lp that equates the value at position
2693 * "sum_pos" to the sum of the parameter coefficients of all nodes.
2695 static isl_stat
add_param_sum_constraint(struct isl_sched_graph
*graph
,
2701 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2703 return isl_stat_error
;
2705 k
= isl_basic_set_alloc_equality(graph
->lp
);
2707 return isl_stat_error
;
2708 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2709 isl_int_set_si(graph
->lp
->eq
[k
][1 + sum_pos
], -1);
2710 for (i
= 0; i
< graph
->n
; ++i
) {
2711 int pos
= 1 + node_par_coef_offset(&graph
->node
[i
]);
2713 for (j
= 0; j
< graph
->node
[i
].nparam
; ++j
)
2714 isl_int_set_si(graph
->lp
->eq
[k
][pos
+ j
], 1);
2720 /* Add a constraint to graph->lp that equates the value at position
2721 * "sum_pos" to the sum of the variable coefficients of all nodes.
2723 static isl_stat
add_var_sum_constraint(struct isl_sched_graph
*graph
,
2729 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2731 return isl_stat_error
;
2733 k
= isl_basic_set_alloc_equality(graph
->lp
);
2735 return isl_stat_error
;
2736 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2737 isl_int_set_si(graph
->lp
->eq
[k
][1 + sum_pos
], -1);
2738 for (i
= 0; i
< graph
->n
; ++i
) {
2739 struct isl_sched_node
*node
= &graph
->node
[i
];
2740 int pos
= 1 + node_var_coef_offset(node
);
2742 for (j
= 0; j
< 2 * node
->nvar
; ++j
)
2743 isl_int_set_si(graph
->lp
->eq
[k
][pos
+ j
], 1);
2749 /* Construct an ILP problem for finding schedule coefficients
2750 * that result in non-negative, but small dependence distances
2751 * over all dependences.
2752 * In particular, the dependence distances over proximity edges
2753 * are bounded by m_0 + m_n n and we compute schedule coefficients
2754 * with small values (preferably zero) of m_n and m_0.
2756 * All variables of the ILP are non-negative. The actual coefficients
2757 * may be negative, so each coefficient is represented as the difference
2758 * of two non-negative variables. The negative part always appears
2759 * immediately before the positive part.
2760 * Other than that, the variables have the following order
2762 * - sum of positive and negative parts of m_n coefficients
2764 * - sum of all c_n coefficients
2765 * (unconstrained when computing non-parametric schedules)
2766 * - sum of positive and negative parts of all c_x coefficients
2767 * - positive and negative parts of m_n coefficients
2769 * - positive and negative parts of c_i_x, in opposite order
2770 * - c_i_n (if parametric)
2773 * The constraints are those from the edges plus two or three equalities
2774 * to express the sums.
2776 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2777 * Otherwise, we ignore them.
2779 static isl_stat
setup_lp(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
2780 int use_coincidence
)
2790 parametric
= ctx
->opt
->schedule_parametric
;
2791 nparam
= isl_space_dim(graph
->node
[0].space
, isl_dim_param
);
2793 return isl_stat_error
;
2795 total
= param_pos
+ 2 * nparam
;
2796 for (i
= 0; i
< graph
->n
; ++i
) {
2797 struct isl_sched_node
*node
= &graph
->node
[graph
->sorted
[i
]];
2798 if (node_update_vmap(node
) < 0)
2799 return isl_stat_error
;
2800 node
->start
= total
;
2801 total
+= 1 + node
->nparam
+ 2 * node
->nvar
;
2804 if (count_constraints(graph
, &n_eq
, &n_ineq
, use_coincidence
) < 0)
2805 return isl_stat_error
;
2806 if (count_bound_constant_constraints(ctx
, graph
, &n_eq
, &n_ineq
) < 0)
2807 return isl_stat_error
;
2808 if (count_bound_coefficient_constraints(ctx
, graph
, &n_eq
, &n_ineq
) < 0)
2809 return isl_stat_error
;
2811 space
= isl_space_set_alloc(ctx
, 0, total
);
2812 isl_basic_set_free(graph
->lp
);
2813 n_eq
+= 2 + parametric
;
2815 graph
->lp
= isl_basic_set_alloc_space(space
, 0, n_eq
, n_ineq
);
2817 if (add_sum_constraint(graph
, 0, param_pos
, 2 * nparam
) < 0)
2818 return isl_stat_error
;
2819 if (parametric
&& add_param_sum_constraint(graph
, 2) < 0)
2820 return isl_stat_error
;
2821 if (add_var_sum_constraint(graph
, 3) < 0)
2822 return isl_stat_error
;
2823 if (add_bound_constant_constraints(ctx
, graph
) < 0)
2824 return isl_stat_error
;
2825 if (add_bound_coefficient_constraints(ctx
, graph
) < 0)
2826 return isl_stat_error
;
2827 if (add_all_validity_constraints(graph
, use_coincidence
) < 0)
2828 return isl_stat_error
;
2829 if (add_all_proximity_constraints(graph
, use_coincidence
) < 0)
2830 return isl_stat_error
;
2835 /* Analyze the conflicting constraint found by
2836 * isl_tab_basic_set_non_trivial_lexmin. If it corresponds to the validity
2837 * constraint of one of the edges between distinct nodes, living, moreover
2838 * in distinct SCCs, then record the source and sink SCC as this may
2839 * be a good place to cut between SCCs.
2841 static int check_conflict(int con
, void *user
)
2844 struct isl_sched_graph
*graph
= user
;
2846 if (graph
->src_scc
>= 0)
2849 con
-= graph
->lp
->n_eq
;
2851 if (con
>= graph
->lp
->n_ineq
)
2854 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2855 if (!is_validity(&graph
->edge
[i
]))
2857 if (graph
->edge
[i
].src
== graph
->edge
[i
].dst
)
2859 if (graph
->edge
[i
].src
->scc
== graph
->edge
[i
].dst
->scc
)
2861 if (graph
->edge
[i
].start
> con
)
2863 if (graph
->edge
[i
].end
<= con
)
2865 graph
->src_scc
= graph
->edge
[i
].src
->scc
;
2866 graph
->dst_scc
= graph
->edge
[i
].dst
->scc
;
2872 /* Check whether the next schedule row of the given node needs to be
2873 * non-trivial. Lower-dimensional domains may have some trivial rows,
2874 * but as soon as the number of remaining required non-trivial rows
2875 * is as large as the number or remaining rows to be computed,
2876 * all remaining rows need to be non-trivial.
2878 static int needs_row(struct isl_sched_graph
*graph
, struct isl_sched_node
*node
)
2880 return node
->nvar
- node
->rank
>= graph
->maxvar
- graph
->n_row
;
2883 /* Construct a non-triviality region with triviality directions
2884 * corresponding to the rows of "indep".
2885 * The rows of "indep" are expressed in terms of the schedule coefficients c_i,
2886 * while the triviality directions are expressed in terms of
2887 * pairs of non-negative variables c^+_i - c^-_i, with c^-_i appearing
2888 * before c^+_i. Furthermore,
2889 * the pairs of non-negative variables representing the coefficients
2890 * are stored in the opposite order.
2892 static __isl_give isl_mat
*construct_trivial(__isl_keep isl_mat
*indep
)
2901 ctx
= isl_mat_get_ctx(indep
);
2902 n
= isl_mat_rows(indep
);
2903 n_var
= isl_mat_cols(indep
);
2904 mat
= isl_mat_alloc(ctx
, n
, 2 * n_var
);
2907 for (i
= 0; i
< n
; ++i
) {
2908 for (j
= 0; j
< n_var
; ++j
) {
2909 int nj
= n_var
- 1 - j
;
2910 isl_int_neg(mat
->row
[i
][2 * nj
], indep
->row
[i
][j
]);
2911 isl_int_set(mat
->row
[i
][2 * nj
+ 1], indep
->row
[i
][j
]);
2918 /* Solve the ILP problem constructed in setup_lp.
2919 * For each node such that all the remaining rows of its schedule
2920 * need to be non-trivial, we construct a non-triviality region.
2921 * This region imposes that the next row is independent of previous rows.
2922 * In particular, the non-triviality region enforces that at least
2923 * one of the linear combinations in the rows of node->indep is non-zero.
2925 static __isl_give isl_vec
*solve_lp(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2931 for (i
= 0; i
< graph
->n
; ++i
) {
2932 struct isl_sched_node
*node
= &graph
->node
[i
];
2935 graph
->region
[i
].pos
= node_var_coef_offset(node
);
2936 if (needs_row(graph
, node
))
2937 trivial
= construct_trivial(node
->indep
);
2939 trivial
= isl_mat_zero(ctx
, 0, 0);
2940 graph
->region
[i
].trivial
= trivial
;
2942 lp
= isl_basic_set_copy(graph
->lp
);
2943 sol
= isl_tab_basic_set_non_trivial_lexmin(lp
, 2, graph
->n
,
2944 graph
->region
, &check_conflict
, graph
);
2945 for (i
= 0; i
< graph
->n
; ++i
)
2946 isl_mat_free(graph
->region
[i
].trivial
);
2950 /* Extract the coefficients for the variables of "node" from "sol".
2952 * Each schedule coefficient c_i_x is represented as the difference
2953 * between two non-negative variables c_i_x^+ - c_i_x^-.
2954 * The c_i_x^- appear before their c_i_x^+ counterpart.
2955 * Furthermore, the order of these pairs is the opposite of that
2956 * of the corresponding coefficients.
2958 * Return c_i_x = c_i_x^+ - c_i_x^-
2960 static __isl_give isl_vec
*extract_var_coef(struct isl_sched_node
*node
,
2961 __isl_keep isl_vec
*sol
)
2969 csol
= isl_vec_alloc(isl_vec_get_ctx(sol
), node
->nvar
);
2973 pos
= 1 + node_var_coef_offset(node
);
2974 for (i
= 0; i
< node
->nvar
; ++i
)
2975 isl_int_sub(csol
->el
[node
->nvar
- 1 - i
],
2976 sol
->el
[pos
+ 2 * i
+ 1], sol
->el
[pos
+ 2 * i
]);
2981 /* Update the schedules of all nodes based on the given solution
2982 * of the LP problem.
2983 * The new row is added to the current band.
2984 * All possibly negative coefficients are encoded as a difference
2985 * of two non-negative variables, so we need to perform the subtraction
2988 * If coincident is set, then the caller guarantees that the new
2989 * row satisfies the coincidence constraints.
2991 static int update_schedule(struct isl_sched_graph
*graph
,
2992 __isl_take isl_vec
*sol
, int coincident
)
2995 isl_vec
*csol
= NULL
;
3000 isl_die(sol
->ctx
, isl_error_internal
,
3001 "no solution found", goto error
);
3002 if (graph
->n_total_row
>= graph
->max_row
)
3003 isl_die(sol
->ctx
, isl_error_internal
,
3004 "too many schedule rows", goto error
);
3006 for (i
= 0; i
< graph
->n
; ++i
) {
3007 struct isl_sched_node
*node
= &graph
->node
[i
];
3009 int row
= isl_mat_rows(node
->sched
);
3012 csol
= extract_var_coef(node
, sol
);
3016 isl_map_free(node
->sched_map
);
3017 node
->sched_map
= NULL
;
3018 node
->sched
= isl_mat_add_rows(node
->sched
, 1);
3021 pos
= node_cst_coef_offset(node
);
3022 node
->sched
= isl_mat_set_element(node
->sched
,
3023 row
, 0, sol
->el
[1 + pos
]);
3024 pos
= node_par_coef_offset(node
);
3025 for (j
= 0; j
< node
->nparam
; ++j
)
3026 node
->sched
= isl_mat_set_element(node
->sched
,
3027 row
, 1 + j
, sol
->el
[1 + pos
+ j
]);
3028 for (j
= 0; j
< node
->nvar
; ++j
)
3029 node
->sched
= isl_mat_set_element(node
->sched
,
3030 row
, 1 + node
->nparam
+ j
, csol
->el
[j
]);
3031 node
->coincident
[graph
->n_total_row
] = coincident
;
3037 graph
->n_total_row
++;
3046 /* Convert row "row" of node->sched into an isl_aff living in "ls"
3047 * and return this isl_aff.
3049 static __isl_give isl_aff
*extract_schedule_row(__isl_take isl_local_space
*ls
,
3050 struct isl_sched_node
*node
, int row
)
3058 aff
= isl_aff_zero_on_domain(ls
);
3059 if (isl_mat_get_element(node
->sched
, row
, 0, &v
) < 0)
3061 aff
= isl_aff_set_constant(aff
, v
);
3062 for (j
= 0; j
< node
->nparam
; ++j
) {
3063 if (isl_mat_get_element(node
->sched
, row
, 1 + j
, &v
) < 0)
3065 aff
= isl_aff_set_coefficient(aff
, isl_dim_param
, j
, v
);
3067 for (j
= 0; j
< node
->nvar
; ++j
) {
3068 if (isl_mat_get_element(node
->sched
, row
,
3069 1 + node
->nparam
+ j
, &v
) < 0)
3071 aff
= isl_aff_set_coefficient(aff
, isl_dim_in
, j
, v
);
3083 /* Convert the "n" rows starting at "first" of node->sched into a multi_aff
3084 * and return this multi_aff.
3086 * The result is defined over the uncompressed node domain.
3088 static __isl_give isl_multi_aff
*node_extract_partial_schedule_multi_aff(
3089 struct isl_sched_node
*node
, int first
, int n
)
3093 isl_local_space
*ls
;
3100 nrow
= isl_mat_rows(node
->sched
);
3101 if (node
->compressed
)
3102 space
= isl_multi_aff_get_domain_space(node
->decompress
);
3104 space
= isl_space_copy(node
->space
);
3105 ls
= isl_local_space_from_space(isl_space_copy(space
));
3106 space
= isl_space_from_domain(space
);
3107 space
= isl_space_add_dims(space
, isl_dim_out
, n
);
3108 ma
= isl_multi_aff_zero(space
);
3110 for (i
= first
; i
< first
+ n
; ++i
) {
3111 aff
= extract_schedule_row(isl_local_space_copy(ls
), node
, i
);
3112 ma
= isl_multi_aff_set_aff(ma
, i
- first
, aff
);
3115 isl_local_space_free(ls
);
3117 if (node
->compressed
)
3118 ma
= isl_multi_aff_pullback_multi_aff(ma
,
3119 isl_multi_aff_copy(node
->compress
));
3124 /* Convert node->sched into a multi_aff and return this multi_aff.
3126 * The result is defined over the uncompressed node domain.
3128 static __isl_give isl_multi_aff
*node_extract_schedule_multi_aff(
3129 struct isl_sched_node
*node
)
3133 nrow
= isl_mat_rows(node
->sched
);
3134 return node_extract_partial_schedule_multi_aff(node
, 0, nrow
);
3137 /* Convert node->sched into a map and return this map.
3139 * The result is cached in node->sched_map, which needs to be released
3140 * whenever node->sched is updated.
3141 * It is defined over the uncompressed node domain.
3143 static __isl_give isl_map
*node_extract_schedule(struct isl_sched_node
*node
)
3145 if (!node
->sched_map
) {
3148 ma
= node_extract_schedule_multi_aff(node
);
3149 node
->sched_map
= isl_map_from_multi_aff(ma
);
3152 return isl_map_copy(node
->sched_map
);
3155 /* Construct a map that can be used to update a dependence relation
3156 * based on the current schedule.
3157 * That is, construct a map expressing that source and sink
3158 * are executed within the same iteration of the current schedule.
3159 * This map can then be intersected with the dependence relation.
3160 * This is not the most efficient way, but this shouldn't be a critical
3163 static __isl_give isl_map
*specializer(struct isl_sched_node
*src
,
3164 struct isl_sched_node
*dst
)
3166 isl_map
*src_sched
, *dst_sched
;
3168 src_sched
= node_extract_schedule(src
);
3169 dst_sched
= node_extract_schedule(dst
);
3170 return isl_map_apply_range(src_sched
, isl_map_reverse(dst_sched
));
3173 /* Intersect the domains of the nested relations in domain and range
3174 * of "umap" with "map".
3176 static __isl_give isl_union_map
*intersect_domains(
3177 __isl_take isl_union_map
*umap
, __isl_keep isl_map
*map
)
3179 isl_union_set
*uset
;
3181 umap
= isl_union_map_zip(umap
);
3182 uset
= isl_union_set_from_set(isl_map_wrap(isl_map_copy(map
)));
3183 umap
= isl_union_map_intersect_domain(umap
, uset
);
3184 umap
= isl_union_map_zip(umap
);
3188 /* Update the dependence relation of the given edge based
3189 * on the current schedule.
3190 * If the dependence is carried completely by the current schedule, then
3191 * it is removed from the edge_tables. It is kept in the list of edges
3192 * as otherwise all edge_tables would have to be recomputed.
3194 * If the edge is of a type that can appear multiple times
3195 * between the same pair of nodes, then it is added to
3196 * the edge table (again). This prevents the situation
3197 * where none of these edges is referenced from the edge table
3198 * because the one that was referenced turned out to be empty and
3199 * was therefore removed from the table.
3201 static isl_stat
update_edge(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
3202 struct isl_sched_edge
*edge
)
3207 id
= specializer(edge
->src
, edge
->dst
);
3208 edge
->map
= isl_map_intersect(edge
->map
, isl_map_copy(id
));
3212 if (edge
->tagged_condition
) {
3213 edge
->tagged_condition
=
3214 intersect_domains(edge
->tagged_condition
, id
);
3215 if (!edge
->tagged_condition
)
3218 if (edge
->tagged_validity
) {
3219 edge
->tagged_validity
=
3220 intersect_domains(edge
->tagged_validity
, id
);
3221 if (!edge
->tagged_validity
)
3225 empty
= isl_map_plain_is_empty(edge
->map
);
3229 graph_remove_edge(graph
, edge
);
3230 } else if (is_multi_edge_type(edge
)) {
3231 if (graph_edge_tables_add(ctx
, graph
, edge
) < 0)
3239 return isl_stat_error
;
3242 /* Does the domain of "umap" intersect "uset"?
3244 static int domain_intersects(__isl_keep isl_union_map
*umap
,
3245 __isl_keep isl_union_set
*uset
)
3249 umap
= isl_union_map_copy(umap
);
3250 umap
= isl_union_map_intersect_domain(umap
, isl_union_set_copy(uset
));
3251 empty
= isl_union_map_is_empty(umap
);
3252 isl_union_map_free(umap
);
3254 return empty
< 0 ? -1 : !empty
;
3257 /* Does the range of "umap" intersect "uset"?
3259 static int range_intersects(__isl_keep isl_union_map
*umap
,
3260 __isl_keep isl_union_set
*uset
)
3264 umap
= isl_union_map_copy(umap
);
3265 umap
= isl_union_map_intersect_range(umap
, isl_union_set_copy(uset
));
3266 empty
= isl_union_map_is_empty(umap
);
3267 isl_union_map_free(umap
);
3269 return empty
< 0 ? -1 : !empty
;
3272 /* Are the condition dependences of "edge" local with respect to
3273 * the current schedule?
3275 * That is, are domain and range of the condition dependences mapped
3276 * to the same point?
3278 * In other words, is the condition false?
3280 static int is_condition_false(struct isl_sched_edge
*edge
)
3282 isl_union_map
*umap
;
3283 isl_map
*map
, *sched
, *test
;
3286 empty
= isl_union_map_is_empty(edge
->tagged_condition
);
3287 if (empty
< 0 || empty
)
3290 umap
= isl_union_map_copy(edge
->tagged_condition
);
3291 umap
= isl_union_map_zip(umap
);
3292 umap
= isl_union_set_unwrap(isl_union_map_domain(umap
));
3293 map
= isl_map_from_union_map(umap
);
3295 sched
= node_extract_schedule(edge
->src
);
3296 map
= isl_map_apply_domain(map
, sched
);
3297 sched
= node_extract_schedule(edge
->dst
);
3298 map
= isl_map_apply_range(map
, sched
);
3300 test
= isl_map_identity(isl_map_get_space(map
));
3301 local
= isl_map_is_subset(map
, test
);
3308 /* For each conditional validity constraint that is adjacent
3309 * to a condition with domain in condition_source or range in condition_sink,
3310 * turn it into an unconditional validity constraint.
3312 static int unconditionalize_adjacent_validity(struct isl_sched_graph
*graph
,
3313 __isl_take isl_union_set
*condition_source
,
3314 __isl_take isl_union_set
*condition_sink
)
3318 condition_source
= isl_union_set_coalesce(condition_source
);
3319 condition_sink
= isl_union_set_coalesce(condition_sink
);
3321 for (i
= 0; i
< graph
->n_edge
; ++i
) {
3323 isl_union_map
*validity
;
3325 if (!is_conditional_validity(&graph
->edge
[i
]))
3327 if (is_validity(&graph
->edge
[i
]))
3330 validity
= graph
->edge
[i
].tagged_validity
;
3331 adjacent
= domain_intersects(validity
, condition_sink
);
3332 if (adjacent
>= 0 && !adjacent
)
3333 adjacent
= range_intersects(validity
, condition_source
);
3339 set_validity(&graph
->edge
[i
]);
3342 isl_union_set_free(condition_source
);
3343 isl_union_set_free(condition_sink
);
3346 isl_union_set_free(condition_source
);
3347 isl_union_set_free(condition_sink
);
3351 /* Update the dependence relations of all edges based on the current schedule
3352 * and enforce conditional validity constraints that are adjacent
3353 * to satisfied condition constraints.
3355 * First check if any of the condition constraints are satisfied
3356 * (i.e., not local to the outer schedule) and keep track of
3357 * their domain and range.
3358 * Then update all dependence relations (which removes the non-local
3360 * Finally, if any condition constraints turned out to be satisfied,
3361 * then turn all adjacent conditional validity constraints into
3362 * unconditional validity constraints.
3364 static int update_edges(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
3368 isl_union_set
*source
, *sink
;
3370 source
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
3371 sink
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
3372 for (i
= 0; i
< graph
->n_edge
; ++i
) {
3374 isl_union_set
*uset
;
3375 isl_union_map
*umap
;
3377 if (!is_condition(&graph
->edge
[i
]))
3379 if (is_local(&graph
->edge
[i
]))
3381 local
= is_condition_false(&graph
->edge
[i
]);
3389 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_condition
);
3390 uset
= isl_union_map_domain(umap
);
3391 source
= isl_union_set_union(source
, uset
);
3393 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_condition
);
3394 uset
= isl_union_map_range(umap
);
3395 sink
= isl_union_set_union(sink
, uset
);
3398 for (i
= 0; i
< graph
->n_edge
; ++i
) {
3399 if (update_edge(ctx
, graph
, &graph
->edge
[i
]) < 0)
3404 return unconditionalize_adjacent_validity(graph
, source
, sink
);
3406 isl_union_set_free(source
);
3407 isl_union_set_free(sink
);
3410 isl_union_set_free(source
);
3411 isl_union_set_free(sink
);
3415 static void next_band(struct isl_sched_graph
*graph
)
3417 graph
->band_start
= graph
->n_total_row
;
3420 /* Return the union of the universe domains of the nodes in "graph"
3421 * that satisfy "pred".
3423 static __isl_give isl_union_set
*isl_sched_graph_domain(isl_ctx
*ctx
,
3424 struct isl_sched_graph
*graph
,
3425 int (*pred
)(struct isl_sched_node
*node
, int data
), int data
)
3431 for (i
= 0; i
< graph
->n
; ++i
)
3432 if (pred(&graph
->node
[i
], data
))
3436 isl_die(ctx
, isl_error_internal
,
3437 "empty component", return NULL
);
3439 set
= isl_set_universe(isl_space_copy(graph
->node
[i
].space
));
3440 dom
= isl_union_set_from_set(set
);
3442 for (i
= i
+ 1; i
< graph
->n
; ++i
) {
3443 if (!pred(&graph
->node
[i
], data
))
3445 set
= isl_set_universe(isl_space_copy(graph
->node
[i
].space
));
3446 dom
= isl_union_set_union(dom
, isl_union_set_from_set(set
));
3452 /* Return a list of unions of universe domains, where each element
3453 * in the list corresponds to an SCC (or WCC) indexed by node->scc.
3455 static __isl_give isl_union_set_list
*extract_sccs(isl_ctx
*ctx
,
3456 struct isl_sched_graph
*graph
)
3459 isl_union_set_list
*filters
;
3461 filters
= isl_union_set_list_alloc(ctx
, graph
->scc
);
3462 for (i
= 0; i
< graph
->scc
; ++i
) {
3465 dom
= isl_sched_graph_domain(ctx
, graph
, &node_scc_exactly
, i
);
3466 filters
= isl_union_set_list_add(filters
, dom
);
3472 /* Return a list of two unions of universe domains, one for the SCCs up
3473 * to and including graph->src_scc and another for the other SCCs.
3475 static __isl_give isl_union_set_list
*extract_split(isl_ctx
*ctx
,
3476 struct isl_sched_graph
*graph
)
3479 isl_union_set_list
*filters
;
3481 filters
= isl_union_set_list_alloc(ctx
, 2);
3482 dom
= isl_sched_graph_domain(ctx
, graph
,
3483 &node_scc_at_most
, graph
->src_scc
);
3484 filters
= isl_union_set_list_add(filters
, dom
);
3485 dom
= isl_sched_graph_domain(ctx
, graph
,
3486 &node_scc_at_least
, graph
->src_scc
+ 1);
3487 filters
= isl_union_set_list_add(filters
, dom
);
3492 /* Copy nodes that satisfy node_pred from the src dependence graph
3493 * to the dst dependence graph.
3495 static isl_stat
copy_nodes(struct isl_sched_graph
*dst
,
3496 struct isl_sched_graph
*src
,
3497 int (*node_pred
)(struct isl_sched_node
*node
, int data
), int data
)
3502 for (i
= 0; i
< src
->n
; ++i
) {
3505 if (!node_pred(&src
->node
[i
], data
))
3509 dst
->node
[j
].space
= isl_space_copy(src
->node
[i
].space
);
3510 dst
->node
[j
].compressed
= src
->node
[i
].compressed
;
3511 dst
->node
[j
].hull
= isl_set_copy(src
->node
[i
].hull
);
3512 dst
->node
[j
].compress
=
3513 isl_multi_aff_copy(src
->node
[i
].compress
);
3514 dst
->node
[j
].decompress
=
3515 isl_multi_aff_copy(src
->node
[i
].decompress
);
3516 dst
->node
[j
].nvar
= src
->node
[i
].nvar
;
3517 dst
->node
[j
].nparam
= src
->node
[i
].nparam
;
3518 dst
->node
[j
].sched
= isl_mat_copy(src
->node
[i
].sched
);
3519 dst
->node
[j
].sched_map
= isl_map_copy(src
->node
[i
].sched_map
);
3520 dst
->node
[j
].coincident
= src
->node
[i
].coincident
;
3521 dst
->node
[j
].sizes
= isl_multi_val_copy(src
->node
[i
].sizes
);
3522 dst
->node
[j
].bounds
= isl_basic_set_copy(src
->node
[i
].bounds
);
3523 dst
->node
[j
].max
= isl_vec_copy(src
->node
[i
].max
);
3526 if (!dst
->node
[j
].space
|| !dst
->node
[j
].sched
)
3527 return isl_stat_error
;
3528 if (dst
->node
[j
].compressed
&&
3529 (!dst
->node
[j
].hull
|| !dst
->node
[j
].compress
||
3530 !dst
->node
[j
].decompress
))
3531 return isl_stat_error
;
3537 /* Copy non-empty edges that satisfy edge_pred from the src dependence graph
3538 * to the dst dependence graph.
3539 * If the source or destination node of the edge is not in the destination
3540 * graph, then it must be a backward proximity edge and it should simply
3543 static isl_stat
copy_edges(isl_ctx
*ctx
, struct isl_sched_graph
*dst
,
3544 struct isl_sched_graph
*src
,
3545 int (*edge_pred
)(struct isl_sched_edge
*edge
, int data
), int data
)
3550 for (i
= 0; i
< src
->n_edge
; ++i
) {
3551 struct isl_sched_edge
*edge
= &src
->edge
[i
];
3553 isl_union_map
*tagged_condition
;
3554 isl_union_map
*tagged_validity
;
3555 struct isl_sched_node
*dst_src
, *dst_dst
;
3557 if (!edge_pred(edge
, data
))
3560 if (isl_map_plain_is_empty(edge
->map
))
3563 dst_src
= graph_find_node(ctx
, dst
, edge
->src
->space
);
3564 dst_dst
= graph_find_node(ctx
, dst
, edge
->dst
->space
);
3565 if (!dst_src
|| !dst_dst
)
3566 return isl_stat_error
;
3567 if (!is_node(dst
, dst_src
) || !is_node(dst
, dst_dst
)) {
3568 if (is_validity(edge
) || is_conditional_validity(edge
))
3569 isl_die(ctx
, isl_error_internal
,
3570 "backward (conditional) validity edge",
3571 return isl_stat_error
);
3575 map
= isl_map_copy(edge
->map
);
3576 tagged_condition
= isl_union_map_copy(edge
->tagged_condition
);
3577 tagged_validity
= isl_union_map_copy(edge
->tagged_validity
);
3579 dst
->edge
[dst
->n_edge
].src
= dst_src
;
3580 dst
->edge
[dst
->n_edge
].dst
= dst_dst
;
3581 dst
->edge
[dst
->n_edge
].map
= map
;
3582 dst
->edge
[dst
->n_edge
].tagged_condition
= tagged_condition
;
3583 dst
->edge
[dst
->n_edge
].tagged_validity
= tagged_validity
;
3584 dst
->edge
[dst
->n_edge
].types
= edge
->types
;
3587 if (edge
->tagged_condition
&& !tagged_condition
)
3588 return isl_stat_error
;
3589 if (edge
->tagged_validity
&& !tagged_validity
)
3590 return isl_stat_error
;
3592 if (graph_edge_tables_add(ctx
, dst
,
3593 &dst
->edge
[dst
->n_edge
- 1]) < 0)
3594 return isl_stat_error
;
3600 /* Compute the maximal number of variables over all nodes.
3601 * This is the maximal number of linearly independent schedule
3602 * rows that we need to compute.
3603 * Just in case we end up in a part of the dependence graph
3604 * with only lower-dimensional domains, we make sure we will
3605 * compute the required amount of extra linearly independent rows.
3607 static int compute_maxvar(struct isl_sched_graph
*graph
)
3612 for (i
= 0; i
< graph
->n
; ++i
) {
3613 struct isl_sched_node
*node
= &graph
->node
[i
];
3616 if (node_update_vmap(node
) < 0)
3618 nvar
= node
->nvar
+ graph
->n_row
- node
->rank
;
3619 if (nvar
> graph
->maxvar
)
3620 graph
->maxvar
= nvar
;
3626 /* Extract the subgraph of "graph" that consists of the nodes satisfying
3627 * "node_pred" and the edges satisfying "edge_pred" and store
3628 * the result in "sub".
3630 static isl_stat
extract_sub_graph(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
3631 int (*node_pred
)(struct isl_sched_node
*node
, int data
),
3632 int (*edge_pred
)(struct isl_sched_edge
*edge
, int data
),
3633 int data
, struct isl_sched_graph
*sub
)
3635 int i
, n
= 0, n_edge
= 0;
3638 for (i
= 0; i
< graph
->n
; ++i
)
3639 if (node_pred(&graph
->node
[i
], data
))
3641 for (i
= 0; i
< graph
->n_edge
; ++i
)
3642 if (edge_pred(&graph
->edge
[i
], data
))
3644 if (graph_alloc(ctx
, sub
, n
, n_edge
) < 0)
3645 return isl_stat_error
;
3646 sub
->root
= graph
->root
;
3647 if (copy_nodes(sub
, graph
, node_pred
, data
) < 0)
3648 return isl_stat_error
;
3649 if (graph_init_table(ctx
, sub
) < 0)
3650 return isl_stat_error
;
3651 for (t
= 0; t
<= isl_edge_last
; ++t
)
3652 sub
->max_edge
[t
] = graph
->max_edge
[t
];
3653 if (graph_init_edge_tables(ctx
, sub
) < 0)
3654 return isl_stat_error
;
3655 if (copy_edges(ctx
, sub
, graph
, edge_pred
, data
) < 0)
3656 return isl_stat_error
;
3657 sub
->n_row
= graph
->n_row
;
3658 sub
->max_row
= graph
->max_row
;
3659 sub
->n_total_row
= graph
->n_total_row
;
3660 sub
->band_start
= graph
->band_start
;
3665 static __isl_give isl_schedule_node
*compute_schedule(isl_schedule_node
*node
,
3666 struct isl_sched_graph
*graph
);
3667 static __isl_give isl_schedule_node
*compute_schedule_wcc(
3668 isl_schedule_node
*node
, struct isl_sched_graph
*graph
);
3670 /* Compute a schedule for a subgraph of "graph". In particular, for
3671 * the graph composed of nodes that satisfy node_pred and edges that
3672 * that satisfy edge_pred.
3673 * If the subgraph is known to consist of a single component, then wcc should
3674 * be set and then we call compute_schedule_wcc on the constructed subgraph.
3675 * Otherwise, we call compute_schedule, which will check whether the subgraph
3678 * The schedule is inserted at "node" and the updated schedule node
3681 static __isl_give isl_schedule_node
*compute_sub_schedule(
3682 __isl_take isl_schedule_node
*node
, isl_ctx
*ctx
,
3683 struct isl_sched_graph
*graph
,
3684 int (*node_pred
)(struct isl_sched_node
*node
, int data
),
3685 int (*edge_pred
)(struct isl_sched_edge
*edge
, int data
),
3688 struct isl_sched_graph split
= { 0 };
3690 if (extract_sub_graph(ctx
, graph
, node_pred
, edge_pred
, data
,
3695 node
= compute_schedule_wcc(node
, &split
);
3697 node
= compute_schedule(node
, &split
);
3699 graph_free(ctx
, &split
);
3702 graph_free(ctx
, &split
);
3703 return isl_schedule_node_free(node
);
3706 static int edge_scc_exactly(struct isl_sched_edge
*edge
, int scc
)
3708 return edge
->src
->scc
== scc
&& edge
->dst
->scc
== scc
;
3711 static int edge_dst_scc_at_most(struct isl_sched_edge
*edge
, int scc
)
3713 return edge
->dst
->scc
<= scc
;
3716 static int edge_src_scc_at_least(struct isl_sched_edge
*edge
, int scc
)
3718 return edge
->src
->scc
>= scc
;
3721 /* Reset the current band by dropping all its schedule rows.
3723 static isl_stat
reset_band(struct isl_sched_graph
*graph
)
3728 drop
= graph
->n_total_row
- graph
->band_start
;
3729 graph
->n_total_row
-= drop
;
3730 graph
->n_row
-= drop
;
3732 for (i
= 0; i
< graph
->n
; ++i
) {
3733 struct isl_sched_node
*node
= &graph
->node
[i
];
3735 isl_map_free(node
->sched_map
);
3736 node
->sched_map
= NULL
;
3738 node
->sched
= isl_mat_drop_rows(node
->sched
,
3739 graph
->band_start
, drop
);
3742 return isl_stat_error
;
3748 /* Split the current graph into two parts and compute a schedule for each
3749 * part individually. In particular, one part consists of all SCCs up
3750 * to and including graph->src_scc, while the other part contains the other
3751 * SCCs. The split is enforced by a sequence node inserted at position "node"
3752 * in the schedule tree. Return the updated schedule node.
3753 * If either of these two parts consists of a sequence, then it is spliced
3754 * into the sequence containing the two parts.
3756 * The current band is reset. It would be possible to reuse
3757 * the previously computed rows as the first rows in the next
3758 * band, but recomputing them may result in better rows as we are looking
3759 * at a smaller part of the dependence graph.
3761 static __isl_give isl_schedule_node
*compute_split_schedule(
3762 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
3766 isl_union_set_list
*filters
;
3771 if (reset_band(graph
) < 0)
3772 return isl_schedule_node_free(node
);
3776 ctx
= isl_schedule_node_get_ctx(node
);
3777 filters
= extract_split(ctx
, graph
);
3778 node
= isl_schedule_node_insert_sequence(node
, filters
);
3779 node
= isl_schedule_node_child(node
, 1);
3780 node
= isl_schedule_node_child(node
, 0);
3782 node
= compute_sub_schedule(node
, ctx
, graph
,
3783 &node_scc_at_least
, &edge_src_scc_at_least
,
3784 graph
->src_scc
+ 1, 0);
3785 is_seq
= isl_schedule_node_get_type(node
) == isl_schedule_node_sequence
;
3786 node
= isl_schedule_node_parent(node
);
3787 node
= isl_schedule_node_parent(node
);
3789 node
= isl_schedule_node_sequence_splice_child(node
, 1);
3790 node
= isl_schedule_node_child(node
, 0);
3791 node
= isl_schedule_node_child(node
, 0);
3792 node
= compute_sub_schedule(node
, ctx
, graph
,
3793 &node_scc_at_most
, &edge_dst_scc_at_most
,
3795 is_seq
= isl_schedule_node_get_type(node
) == isl_schedule_node_sequence
;
3796 node
= isl_schedule_node_parent(node
);
3797 node
= isl_schedule_node_parent(node
);
3799 node
= isl_schedule_node_sequence_splice_child(node
, 0);
3804 /* Insert a band node at position "node" in the schedule tree corresponding
3805 * to the current band in "graph". Mark the band node permutable
3806 * if "permutable" is set.
3807 * The partial schedules and the coincidence property are extracted
3808 * from the graph nodes.
3809 * Return the updated schedule node.
3811 static __isl_give isl_schedule_node
*insert_current_band(
3812 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
3818 isl_multi_pw_aff
*mpa
;
3819 isl_multi_union_pw_aff
*mupa
;
3825 isl_die(isl_schedule_node_get_ctx(node
), isl_error_internal
,
3826 "graph should have at least one node",
3827 return isl_schedule_node_free(node
));
3829 start
= graph
->band_start
;
3830 end
= graph
->n_total_row
;
3833 ma
= node_extract_partial_schedule_multi_aff(&graph
->node
[0], start
, n
);
3834 mpa
= isl_multi_pw_aff_from_multi_aff(ma
);
3835 mupa
= isl_multi_union_pw_aff_from_multi_pw_aff(mpa
);
3837 for (i
= 1; i
< graph
->n
; ++i
) {
3838 isl_multi_union_pw_aff
*mupa_i
;
3840 ma
= node_extract_partial_schedule_multi_aff(&graph
->node
[i
],
3842 mpa
= isl_multi_pw_aff_from_multi_aff(ma
);
3843 mupa_i
= isl_multi_union_pw_aff_from_multi_pw_aff(mpa
);
3844 mupa
= isl_multi_union_pw_aff_union_add(mupa
, mupa_i
);
3846 node
= isl_schedule_node_insert_partial_schedule(node
, mupa
);
3848 for (i
= 0; i
< n
; ++i
)
3849 node
= isl_schedule_node_band_member_set_coincident(node
, i
,
3850 graph
->node
[0].coincident
[start
+ i
]);
3851 node
= isl_schedule_node_band_set_permutable(node
, permutable
);
3856 /* Update the dependence relations based on the current schedule,
3857 * add the current band to "node" and then continue with the computation
3859 * Return the updated schedule node.
3861 static __isl_give isl_schedule_node
*compute_next_band(
3862 __isl_take isl_schedule_node
*node
,
3863 struct isl_sched_graph
*graph
, int permutable
)
3870 ctx
= isl_schedule_node_get_ctx(node
);
3871 if (update_edges(ctx
, graph
) < 0)
3872 return isl_schedule_node_free(node
);
3873 node
= insert_current_band(node
, graph
, permutable
);
3876 node
= isl_schedule_node_child(node
, 0);
3877 node
= compute_schedule(node
, graph
);
3878 node
= isl_schedule_node_parent(node
);
3883 /* Add the constraints "coef" derived from an edge from "node" to itself
3884 * to graph->lp in order to respect the dependences and to try and carry them.
3885 * "pos" is the sequence number of the edge that needs to be carried.
3886 * "coef" represents general constraints on coefficients (c_0, c_x)
3887 * of valid constraints for (y - x) with x and y instances of the node.
3889 * The constraints added to graph->lp need to enforce
3891 * (c_j_0 + c_j_x y) - (c_j_0 + c_j_x x)
3892 * = c_j_x (y - x) >= e_i
3894 * for each (x,y) in the dependence relation of the edge.
3895 * That is, (-e_i, c_j_x) needs to be plugged in for (c_0, c_x),
3896 * taking into account that each coefficient in c_j_x is represented
3897 * as a pair of non-negative coefficients.
3899 static isl_stat
add_intra_constraints(struct isl_sched_graph
*graph
,
3900 struct isl_sched_node
*node
, __isl_take isl_basic_set
*coef
, int pos
)
3904 isl_dim_map
*dim_map
;
3906 offset
= coef_var_offset(coef
);
3908 coef
= isl_basic_set_free(coef
);
3910 return isl_stat_error
;
3912 ctx
= isl_basic_set_get_ctx(coef
);
3913 dim_map
= intra_dim_map(ctx
, graph
, node
, offset
, 1);
3914 isl_dim_map_range(dim_map
, 3 + pos
, 0, 0, 0, 1, -1);
3915 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
3920 /* Add the constraints "coef" derived from an edge from "src" to "dst"
3921 * to graph->lp in order to respect the dependences and to try and carry them.
3922 * "pos" is the sequence number of the edge that needs to be carried or
3923 * -1 if no attempt should be made to carry the dependences.
3924 * "coef" represents general constraints on coefficients (c_0, c_n, c_x, c_y)
3925 * of valid constraints for (x, y) with x and y instances of "src" and "dst".
3927 * The constraints added to graph->lp need to enforce
3929 * (c_k_0 + c_k_n n + c_k_x y) - (c_j_0 + c_j_n n + c_j_x x) >= e_i
3931 * for each (x,y) in the dependence relation of the edge or
3933 * (c_k_0 + c_k_n n + c_k_x y) - (c_j_0 + c_j_n n + c_j_x x) >= 0
3937 * (-e_i + c_k_0 - c_j_0, c_k_n - c_j_n, -c_j_x, c_k_x)
3939 * (c_k_0 - c_j_0, c_k_n - c_j_n, -c_j_x, c_k_x)
3940 * needs to be plugged in for (c_0, c_n, c_x, c_y),
3941 * taking into account that each coefficient in c_j_x and c_k_x is represented
3942 * as a pair of non-negative coefficients.
3944 static isl_stat
add_inter_constraints(struct isl_sched_graph
*graph
,
3945 struct isl_sched_node
*src
, struct isl_sched_node
*dst
,
3946 __isl_take isl_basic_set
*coef
, int pos
)
3950 isl_dim_map
*dim_map
;
3952 offset
= coef_var_offset(coef
);
3954 coef
= isl_basic_set_free(coef
);
3956 return isl_stat_error
;
3958 ctx
= isl_basic_set_get_ctx(coef
);
3959 dim_map
= inter_dim_map(ctx
, graph
, src
, dst
, offset
, 1);
3961 isl_dim_map_range(dim_map
, 3 + pos
, 0, 0, 0, 1, -1);
3962 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
3967 /* Data structure for keeping track of the data needed
3968 * to exploit non-trivial lineality spaces.
3970 * "any_non_trivial" is true if there are any non-trivial lineality spaces.
3971 * If "any_non_trivial" is not true, then "equivalent" and "mask" may be NULL.
3972 * "equivalent" connects instances to other instances on the same line(s).
3973 * "mask" contains the domain spaces of "equivalent".
3974 * Any instance set not in "mask" does not have a non-trivial lineality space.
3976 struct isl_exploit_lineality_data
{
3977 isl_bool any_non_trivial
;
3978 isl_union_map
*equivalent
;
3979 isl_union_set
*mask
;
3982 /* Data structure collecting information used during the construction
3983 * of an LP for carrying dependences.
3985 * "intra" is a sequence of coefficient constraints for intra-node edges.
3986 * "inter" is a sequence of coefficient constraints for inter-node edges.
3987 * "lineality" contains data used to exploit non-trivial lineality spaces.
3990 isl_basic_set_list
*intra
;
3991 isl_basic_set_list
*inter
;
3992 struct isl_exploit_lineality_data lineality
;
3995 /* Free all the data stored in "carry".
3997 static void isl_carry_clear(struct isl_carry
*carry
)
3999 isl_basic_set_list_free(carry
->intra
);
4000 isl_basic_set_list_free(carry
->inter
);
4001 isl_union_map_free(carry
->lineality
.equivalent
);
4002 isl_union_set_free(carry
->lineality
.mask
);
4005 /* Return a pointer to the node in "graph" that lives in "space".
4006 * If the requested node has been compressed, then "space"
4007 * corresponds to the compressed space.
4008 * The graph is assumed to have such a node.
4009 * Return NULL in case of error.
4011 * First try and see if "space" is the space of an uncompressed node.
4012 * If so, return that node.
4013 * Otherwise, "space" was constructed by construct_compressed_id and
4014 * contains a user pointer pointing to the node in the tuple id.
4015 * However, this node belongs to the original dependence graph.
4016 * If "graph" is a subgraph of this original dependence graph,
4017 * then the node with the same space still needs to be looked up
4018 * in the current graph.
4020 static struct isl_sched_node
*graph_find_compressed_node(isl_ctx
*ctx
,
4021 struct isl_sched_graph
*graph
, __isl_keep isl_space
*space
)
4024 struct isl_sched_node
*node
;
4029 node
= graph_find_node(ctx
, graph
, space
);
4032 if (is_node(graph
, node
))
4035 id
= isl_space_get_tuple_id(space
, isl_dim_set
);
4036 node
= isl_id_get_user(id
);
4042 if (!is_node(graph
->root
, node
))
4043 isl_die(ctx
, isl_error_internal
,
4044 "space points to invalid node", return NULL
);
4045 if (graph
!= graph
->root
)
4046 node
= graph_find_node(ctx
, graph
, node
->space
);
4047 if (!is_node(graph
, node
))
4048 isl_die(ctx
, isl_error_internal
,
4049 "unable to find node", return NULL
);
4054 /* Internal data structure for add_all_constraints.
4056 * "graph" is the schedule constraint graph for which an LP problem
4057 * is being constructed.
4058 * "carry_inter" indicates whether inter-node edges should be carried.
4059 * "pos" is the position of the next edge that needs to be carried.
4061 struct isl_add_all_constraints_data
{
4063 struct isl_sched_graph
*graph
;
4068 /* Add the constraints "coef" derived from an edge from a node to itself
4069 * to data->graph->lp in order to respect the dependences and
4070 * to try and carry them.
4072 * The space of "coef" is of the form
4074 * coefficients[[c_cst] -> S[c_x]]
4076 * with S[c_x] the (compressed) space of the node.
4077 * Extract the node from the space and call add_intra_constraints.
4079 static isl_stat
lp_add_intra(__isl_take isl_basic_set
*coef
, void *user
)
4081 struct isl_add_all_constraints_data
*data
= user
;
4083 struct isl_sched_node
*node
;
4085 space
= isl_basic_set_get_space(coef
);
4086 space
= isl_space_range(isl_space_unwrap(space
));
4087 node
= graph_find_compressed_node(data
->ctx
, data
->graph
, space
);
4088 isl_space_free(space
);
4089 return add_intra_constraints(data
->graph
, node
, coef
, data
->pos
++);
4092 /* Add the constraints "coef" derived from an edge from a node j
4093 * to a node k to data->graph->lp in order to respect the dependences and
4094 * to try and carry them (provided data->carry_inter is set).
4096 * The space of "coef" is of the form
4098 * coefficients[[c_cst, c_n] -> [S_j[c_x] -> S_k[c_y]]]
4100 * with S_j[c_x] and S_k[c_y] the (compressed) spaces of the nodes.
4101 * Extract the nodes from the space and call add_inter_constraints.
4103 static isl_stat
lp_add_inter(__isl_take isl_basic_set
*coef
, void *user
)
4105 struct isl_add_all_constraints_data
*data
= user
;
4106 isl_space
*space
, *dom
;
4107 struct isl_sched_node
*src
, *dst
;
4110 space
= isl_basic_set_get_space(coef
);
4111 space
= isl_space_unwrap(isl_space_range(isl_space_unwrap(space
)));
4112 dom
= isl_space_domain(isl_space_copy(space
));
4113 src
= graph_find_compressed_node(data
->ctx
, data
->graph
, dom
);
4114 isl_space_free(dom
);
4115 space
= isl_space_range(space
);
4116 dst
= graph_find_compressed_node(data
->ctx
, data
->graph
, space
);
4117 isl_space_free(space
);
4119 pos
= data
->carry_inter
? data
->pos
++ : -1;
4120 return add_inter_constraints(data
->graph
, src
, dst
, coef
, pos
);
4123 /* Add constraints to graph->lp that force all (conditional) validity
4124 * dependences to be respected and attempt to carry them.
4125 * "intra" is the sequence of coefficient constraints for intra-node edges.
4126 * "inter" is the sequence of coefficient constraints for inter-node edges.
4127 * "carry_inter" indicates whether inter-node edges should be carried or
4130 static isl_stat
add_all_constraints(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
4131 __isl_keep isl_basic_set_list
*intra
,
4132 __isl_keep isl_basic_set_list
*inter
, int carry_inter
)
4134 struct isl_add_all_constraints_data data
= { ctx
, graph
, carry_inter
};
4137 if (isl_basic_set_list_foreach(intra
, &lp_add_intra
, &data
) < 0)
4138 return isl_stat_error
;
4139 if (isl_basic_set_list_foreach(inter
, &lp_add_inter
, &data
) < 0)
4140 return isl_stat_error
;
4144 /* Internal data structure for count_all_constraints
4145 * for keeping track of the number of equality and inequality constraints.
4147 struct isl_sched_count
{
4152 /* Add the number of equality and inequality constraints of "bset"
4153 * to data->n_eq and data->n_ineq.
4155 static isl_stat
bset_update_count(__isl_take isl_basic_set
*bset
, void *user
)
4157 struct isl_sched_count
*data
= user
;
4159 return update_count(bset
, 1, &data
->n_eq
, &data
->n_ineq
);
4162 /* Count the number of equality and inequality constraints
4163 * that will be added to the carry_lp problem.
4164 * We count each edge exactly once.
4165 * "intra" is the sequence of coefficient constraints for intra-node edges.
4166 * "inter" is the sequence of coefficient constraints for inter-node edges.
4168 static isl_stat
count_all_constraints(__isl_keep isl_basic_set_list
*intra
,
4169 __isl_keep isl_basic_set_list
*inter
, int *n_eq
, int *n_ineq
)
4171 struct isl_sched_count data
;
4173 data
.n_eq
= data
.n_ineq
= 0;
4174 if (isl_basic_set_list_foreach(inter
, &bset_update_count
, &data
) < 0)
4175 return isl_stat_error
;
4176 if (isl_basic_set_list_foreach(intra
, &bset_update_count
, &data
) < 0)
4177 return isl_stat_error
;
4180 *n_ineq
= data
.n_ineq
;
4185 /* Construct an LP problem for finding schedule coefficients
4186 * such that the schedule carries as many validity dependences as possible.
4187 * In particular, for each dependence i, we bound the dependence distance
4188 * from below by e_i, with 0 <= e_i <= 1 and then maximize the sum
4189 * of all e_i's. Dependences with e_i = 0 in the solution are simply
4190 * respected, while those with e_i > 0 (in practice e_i = 1) are carried.
4191 * "intra" is the sequence of coefficient constraints for intra-node edges.
4192 * "inter" is the sequence of coefficient constraints for inter-node edges.
4193 * "n_edge" is the total number of edges.
4194 * "carry_inter" indicates whether inter-node edges should be carried or
4195 * only respected. That is, if "carry_inter" is not set, then
4196 * no e_i variables are introduced for the inter-node edges.
4198 * All variables of the LP are non-negative. The actual coefficients
4199 * may be negative, so each coefficient is represented as the difference
4200 * of two non-negative variables. The negative part always appears
4201 * immediately before the positive part.
4202 * Other than that, the variables have the following order
4204 * - sum of (1 - e_i) over all edges
4205 * - sum of all c_n coefficients
4206 * (unconstrained when computing non-parametric schedules)
4207 * - sum of positive and negative parts of all c_x coefficients
4211 * - positive and negative parts of c_i_x, in opposite order
4212 * - c_i_n (if parametric)
4215 * The constraints are those from the (validity) edges plus three equalities
4216 * to express the sums and n_edge inequalities to express e_i <= 1.
4218 static isl_stat
setup_carry_lp(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
4219 int n_edge
, __isl_keep isl_basic_set_list
*intra
,
4220 __isl_keep isl_basic_set_list
*inter
, int carry_inter
)
4229 for (i
= 0; i
< graph
->n
; ++i
) {
4230 struct isl_sched_node
*node
= &graph
->node
[graph
->sorted
[i
]];
4231 node
->start
= total
;
4232 total
+= 1 + node
->nparam
+ 2 * node
->nvar
;
4235 if (count_all_constraints(intra
, inter
, &n_eq
, &n_ineq
) < 0)
4236 return isl_stat_error
;
4238 dim
= isl_space_set_alloc(ctx
, 0, total
);
4239 isl_basic_set_free(graph
->lp
);
4242 graph
->lp
= isl_basic_set_alloc_space(dim
, 0, n_eq
, n_ineq
);
4243 graph
->lp
= isl_basic_set_set_rational(graph
->lp
);
4245 k
= isl_basic_set_alloc_equality(graph
->lp
);
4247 return isl_stat_error
;
4248 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
4249 isl_int_set_si(graph
->lp
->eq
[k
][0], -n_edge
);
4250 isl_int_set_si(graph
->lp
->eq
[k
][1], 1);
4251 for (i
= 0; i
< n_edge
; ++i
)
4252 isl_int_set_si(graph
->lp
->eq
[k
][4 + i
], 1);
4254 if (add_param_sum_constraint(graph
, 1) < 0)
4255 return isl_stat_error
;
4256 if (add_var_sum_constraint(graph
, 2) < 0)
4257 return isl_stat_error
;
4259 for (i
= 0; i
< n_edge
; ++i
) {
4260 k
= isl_basic_set_alloc_inequality(graph
->lp
);
4262 return isl_stat_error
;
4263 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
4264 isl_int_set_si(graph
->lp
->ineq
[k
][4 + i
], -1);
4265 isl_int_set_si(graph
->lp
->ineq
[k
][0], 1);
4268 if (add_all_constraints(ctx
, graph
, intra
, inter
, carry_inter
) < 0)
4269 return isl_stat_error
;
4274 static __isl_give isl_schedule_node
*compute_component_schedule(
4275 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
4278 /* If the schedule_split_scaled option is set and if the linear
4279 * parts of the scheduling rows for all nodes in the graphs have
4280 * a non-trivial common divisor, then remove this
4281 * common divisor from the linear part.
4282 * Otherwise, insert a band node directly and continue with
4283 * the construction of the schedule.
4285 * If a non-trivial common divisor is found, then
4286 * the linear part is reduced and the remainder is ignored.
4287 * The pieces of the graph that are assigned different remainders
4288 * form (groups of) strongly connected components within
4289 * the scaled down band. If needed, they can therefore
4290 * be ordered along this remainder in a sequence node.
4291 * However, this ordering is not enforced here in order to allow
4292 * the scheduler to combine some of the strongly connected components.
4294 static __isl_give isl_schedule_node
*split_scaled(
4295 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
4305 ctx
= isl_schedule_node_get_ctx(node
);
4306 if (!ctx
->opt
->schedule_split_scaled
)
4307 return compute_next_band(node
, graph
, 0);
4309 return compute_next_band(node
, graph
, 0);
4312 isl_int_init(gcd_i
);
4314 isl_int_set_si(gcd
, 0);
4316 row
= isl_mat_rows(graph
->node
[0].sched
) - 1;
4318 for (i
= 0; i
< graph
->n
; ++i
) {
4319 struct isl_sched_node
*node
= &graph
->node
[i
];
4320 int cols
= isl_mat_cols(node
->sched
);
4322 isl_seq_gcd(node
->sched
->row
[row
] + 1, cols
- 1, &gcd_i
);
4323 isl_int_gcd(gcd
, gcd
, gcd_i
);
4326 isl_int_clear(gcd_i
);
4328 if (isl_int_cmp_si(gcd
, 1) <= 0) {
4330 return compute_next_band(node
, graph
, 0);
4333 for (i
= 0; i
< graph
->n
; ++i
) {
4334 struct isl_sched_node
*node
= &graph
->node
[i
];
4336 isl_int_fdiv_q(node
->sched
->row
[row
][0],
4337 node
->sched
->row
[row
][0], gcd
);
4338 isl_int_mul(node
->sched
->row
[row
][0],
4339 node
->sched
->row
[row
][0], gcd
);
4340 node
->sched
= isl_mat_scale_down_row(node
->sched
, row
, gcd
);
4347 return compute_next_band(node
, graph
, 0);
4350 return isl_schedule_node_free(node
);
4353 /* Is the schedule row "sol" trivial on node "node"?
4354 * That is, is the solution zero on the dimensions linearly independent of
4355 * the previously found solutions?
4356 * Return 1 if the solution is trivial, 0 if it is not and -1 on error.
4358 * Each coefficient is represented as the difference between
4359 * two non-negative values in "sol".
4360 * We construct the schedule row s and check if it is linearly
4361 * independent of previously computed schedule rows
4362 * by computing T s, with T the linear combinations that are zero
4363 * on linearly dependent schedule rows.
4364 * If the result consists of all zeros, then the solution is trivial.
4366 static int is_trivial(struct isl_sched_node
*node
, __isl_keep isl_vec
*sol
)
4373 if (node
->nvar
== node
->rank
)
4376 node_sol
= extract_var_coef(node
, sol
);
4377 node_sol
= isl_mat_vec_product(isl_mat_copy(node
->indep
), node_sol
);
4381 trivial
= isl_seq_first_non_zero(node_sol
->el
,
4382 node
->nvar
- node
->rank
) == -1;
4384 isl_vec_free(node_sol
);
4389 /* Is the schedule row "sol" trivial on any node where it should
4391 * Return 1 if any solution is trivial, 0 if they are not and -1 on error.
4393 static int is_any_trivial(struct isl_sched_graph
*graph
,
4394 __isl_keep isl_vec
*sol
)
4398 for (i
= 0; i
< graph
->n
; ++i
) {
4399 struct isl_sched_node
*node
= &graph
->node
[i
];
4402 if (!needs_row(graph
, node
))
4404 trivial
= is_trivial(node
, sol
);
4405 if (trivial
< 0 || trivial
)
4412 /* Does the schedule represented by "sol" perform loop coalescing on "node"?
4413 * If so, return the position of the coalesced dimension.
4414 * Otherwise, return node->nvar or -1 on error.
4416 * In particular, look for pairs of coefficients c_i and c_j such that
4417 * |c_j/c_i| > ceil(size_i/2), i.e., |c_j| > |c_i * ceil(size_i/2)|.
4418 * If any such pair is found, then return i.
4419 * If size_i is infinity, then no check on c_i needs to be performed.
4421 static int find_node_coalescing(struct isl_sched_node
*node
,
4422 __isl_keep isl_vec
*sol
)
4428 if (node
->nvar
<= 1)
4431 csol
= extract_var_coef(node
, sol
);
4435 for (i
= 0; i
< node
->nvar
; ++i
) {
4438 if (isl_int_is_zero(csol
->el
[i
]))
4440 v
= isl_multi_val_get_val(node
->sizes
, i
);
4443 if (!isl_val_is_int(v
)) {
4447 v
= isl_val_div_ui(v
, 2);
4448 v
= isl_val_ceil(v
);
4451 isl_int_mul(max
, v
->n
, csol
->el
[i
]);
4454 for (j
= 0; j
< node
->nvar
; ++j
) {
4457 if (isl_int_abs_gt(csol
->el
[j
], max
))
4473 /* Force the schedule coefficient at position "pos" of "node" to be zero
4475 * The coefficient is encoded as the difference between two non-negative
4476 * variables. Force these two variables to have the same value.
4478 static __isl_give isl_tab_lexmin
*zero_out_node_coef(
4479 __isl_take isl_tab_lexmin
*tl
, struct isl_sched_node
*node
, int pos
)
4485 ctx
= isl_space_get_ctx(node
->space
);
4486 dim
= isl_tab_lexmin_dim(tl
);
4488 return isl_tab_lexmin_free(tl
);
4489 eq
= isl_vec_alloc(ctx
, 1 + dim
);
4490 eq
= isl_vec_clr(eq
);
4492 return isl_tab_lexmin_free(tl
);
4494 pos
= 1 + node_var_coef_pos(node
, pos
);
4495 isl_int_set_si(eq
->el
[pos
], 1);
4496 isl_int_set_si(eq
->el
[pos
+ 1], -1);
4497 tl
= isl_tab_lexmin_add_eq(tl
, eq
->el
);
4503 /* Return the lexicographically smallest rational point in the basic set
4504 * from which "tl" was constructed, double checking that this input set
4507 static __isl_give isl_vec
*non_empty_solution(__isl_keep isl_tab_lexmin
*tl
)
4511 sol
= isl_tab_lexmin_get_solution(tl
);
4515 isl_die(isl_vec_get_ctx(sol
), isl_error_internal
,
4516 "error in schedule construction",
4517 return isl_vec_free(sol
));
4521 /* Does the solution "sol" of the LP problem constructed by setup_carry_lp
4522 * carry any of the "n_edge" groups of dependences?
4523 * The value in the first position is the sum of (1 - e_i) over all "n_edge"
4524 * edges, with 0 <= e_i <= 1 equal to 1 when the dependences represented
4525 * by the edge are carried by the solution.
4526 * If the sum of the (1 - e_i) is smaller than "n_edge" then at least
4527 * one of those is carried.
4529 * Note that despite the fact that the problem is solved using a rational
4530 * solver, the solution is guaranteed to be integral.
4531 * Specifically, the dependence distance lower bounds e_i (and therefore
4532 * also their sum) are integers. See Lemma 5 of [1].
4534 * Any potential denominator of the sum is cleared by this function.
4535 * The denominator is not relevant for any of the other elements
4538 * [1] P. Feautrier, Some Efficient Solutions to the Affine Scheduling
4539 * Problem, Part II: Multi-Dimensional Time.
4540 * In Intl. Journal of Parallel Programming, 1992.
4542 static int carries_dependences(__isl_keep isl_vec
*sol
, int n_edge
)
4544 isl_int_divexact(sol
->el
[1], sol
->el
[1], sol
->el
[0]);
4545 isl_int_set_si(sol
->el
[0], 1);
4546 return isl_int_cmp_si(sol
->el
[1], n_edge
) < 0;
4549 /* Return the lexicographically smallest rational point in "lp",
4550 * assuming that all variables are non-negative and performing some
4551 * additional sanity checks.
4552 * If "want_integral" is set, then compute the lexicographically smallest
4553 * integer point instead.
4554 * In particular, "lp" should not be empty by construction.
4555 * Double check that this is the case.
4556 * If dependences are not carried for any of the "n_edge" edges,
4557 * then return an empty vector.
4559 * If the schedule_treat_coalescing option is set and
4560 * if the computed schedule performs loop coalescing on a given node,
4561 * i.e., if it is of the form
4563 * c_i i + c_j j + ...
4565 * with |c_j/c_i| >= size_i, then force the coefficient c_i to be zero
4566 * to cut out this solution. Repeat this process until no more loop
4567 * coalescing occurs or until no more dependences can be carried.
4568 * In the latter case, revert to the previously computed solution.
4570 * If the caller requests an integral solution and if coalescing should
4571 * be treated, then perform the coalescing treatment first as
4572 * an integral solution computed before coalescing treatment
4573 * would carry the same number of edges and would therefore probably
4574 * also be coalescing.
4576 * To allow the coalescing treatment to be performed first,
4577 * the initial solution is allowed to be rational and it is only
4578 * cut out (if needed) in the next iteration, if no coalescing measures
4581 static __isl_give isl_vec
*non_neg_lexmin(struct isl_sched_graph
*graph
,
4582 __isl_take isl_basic_set
*lp
, int n_edge
, int want_integral
)
4587 isl_vec
*sol
= NULL
, *prev
;
4588 int treat_coalescing
;
4593 ctx
= isl_basic_set_get_ctx(lp
);
4594 treat_coalescing
= isl_options_get_schedule_treat_coalescing(ctx
);
4595 tl
= isl_tab_lexmin_from_basic_set(lp
);
4603 tl
= isl_tab_lexmin_cut_to_integer(tl
);
4605 sol
= non_empty_solution(tl
);
4609 integral
= isl_int_is_one(sol
->el
[0]);
4610 if (!carries_dependences(sol
, n_edge
)) {
4612 prev
= isl_vec_alloc(ctx
, 0);
4617 prev
= isl_vec_free(prev
);
4618 cut
= want_integral
&& !integral
;
4621 if (!treat_coalescing
)
4623 for (i
= 0; i
< graph
->n
; ++i
) {
4624 struct isl_sched_node
*node
= &graph
->node
[i
];
4626 pos
= find_node_coalescing(node
, sol
);
4629 if (pos
< node
->nvar
)
4634 tl
= zero_out_node_coef(tl
, &graph
->node
[i
], pos
);
4637 } while (try_again
);
4639 isl_tab_lexmin_free(tl
);
4643 isl_tab_lexmin_free(tl
);
4649 /* If "edge" is an edge from a node to itself, then add the corresponding
4650 * dependence relation to "umap".
4651 * If "node" has been compressed, then the dependence relation
4652 * is also compressed first.
4654 static __isl_give isl_union_map
*add_intra(__isl_take isl_union_map
*umap
,
4655 struct isl_sched_edge
*edge
)
4658 struct isl_sched_node
*node
= edge
->src
;
4660 if (edge
->src
!= edge
->dst
)
4663 map
= isl_map_copy(edge
->map
);
4664 if (node
->compressed
) {
4665 map
= isl_map_preimage_domain_multi_aff(map
,
4666 isl_multi_aff_copy(node
->decompress
));
4667 map
= isl_map_preimage_range_multi_aff(map
,
4668 isl_multi_aff_copy(node
->decompress
));
4670 umap
= isl_union_map_add_map(umap
, map
);
4674 /* If "edge" is an edge from a node to another node, then add the corresponding
4675 * dependence relation to "umap".
4676 * If the source or destination nodes of "edge" have been compressed,
4677 * then the dependence relation is also compressed first.
4679 static __isl_give isl_union_map
*add_inter(__isl_take isl_union_map
*umap
,
4680 struct isl_sched_edge
*edge
)
4684 if (edge
->src
== edge
->dst
)
4687 map
= isl_map_copy(edge
->map
);
4688 if (edge
->src
->compressed
)
4689 map
= isl_map_preimage_domain_multi_aff(map
,
4690 isl_multi_aff_copy(edge
->src
->decompress
));
4691 if (edge
->dst
->compressed
)
4692 map
= isl_map_preimage_range_multi_aff(map
,
4693 isl_multi_aff_copy(edge
->dst
->decompress
));
4694 umap
= isl_union_map_add_map(umap
, map
);
4698 /* Internal data structure used by union_drop_coalescing_constraints
4699 * to collect bounds on all relevant statements.
4701 * "graph" is the schedule constraint graph for which an LP problem
4702 * is being constructed.
4703 * "bounds" collects the bounds.
4705 struct isl_collect_bounds_data
{
4707 struct isl_sched_graph
*graph
;
4708 isl_union_set
*bounds
;
4711 /* Add the size bounds for the node with instance deltas in "set"
4714 static isl_stat
collect_bounds(__isl_take isl_set
*set
, void *user
)
4716 struct isl_collect_bounds_data
*data
= user
;
4717 struct isl_sched_node
*node
;
4721 space
= isl_set_get_space(set
);
4724 node
= graph_find_compressed_node(data
->ctx
, data
->graph
, space
);
4725 isl_space_free(space
);
4727 bounds
= isl_set_from_basic_set(get_size_bounds(node
));
4728 data
->bounds
= isl_union_set_add_set(data
->bounds
, bounds
);
4733 /* Drop some constraints from "delta" that could be exploited
4734 * to construct loop coalescing schedules.
4735 * In particular, drop those constraint that bound the difference
4736 * to the size of the domain.
4737 * Do this for each set/node in "delta" separately.
4738 * The parameters are assumed to have been projected out by the caller.
4740 static __isl_give isl_union_set
*union_drop_coalescing_constraints(isl_ctx
*ctx
,
4741 struct isl_sched_graph
*graph
, __isl_take isl_union_set
*delta
)
4743 struct isl_collect_bounds_data data
= { ctx
, graph
};
4745 data
.bounds
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
4746 if (isl_union_set_foreach_set(delta
, &collect_bounds
, &data
) < 0)
4747 data
.bounds
= isl_union_set_free(data
.bounds
);
4748 delta
= isl_union_set_plain_gist(delta
, data
.bounds
);
4753 /* Given a non-trivial lineality space "lineality", add the corresponding
4754 * universe set to data->mask and add a map from elements to
4755 * other elements along the lines in "lineality" to data->equivalent.
4756 * If this is the first time this function gets called
4757 * (data->any_non_trivial is still false), then set data->any_non_trivial and
4758 * initialize data->mask and data->equivalent.
4760 * In particular, if the lineality space is defined by equality constraints
4764 * then construct an affine mapping
4768 * and compute the equivalence relation of having the same image under f:
4770 * { x -> x' : E x = E x' }
4772 static isl_stat
add_non_trivial_lineality(__isl_take isl_basic_set
*lineality
,
4773 struct isl_exploit_lineality_data
*data
)
4779 isl_multi_pw_aff
*mpa
;
4783 if (isl_basic_set_check_no_locals(lineality
) < 0)
4786 space
= isl_basic_set_get_space(lineality
);
4787 if (!data
->any_non_trivial
) {
4788 data
->equivalent
= isl_union_map_empty(isl_space_copy(space
));
4789 data
->mask
= isl_union_set_empty(isl_space_copy(space
));
4791 data
->any_non_trivial
= isl_bool_true
;
4793 univ
= isl_set_universe(isl_space_copy(space
));
4794 data
->mask
= isl_union_set_add_set(data
->mask
, univ
);
4796 eq
= isl_basic_set_extract_equalities(lineality
);
4797 n
= isl_mat_rows(eq
);
4798 eq
= isl_mat_insert_zero_rows(eq
, 0, 1);
4799 eq
= isl_mat_set_element_si(eq
, 0, 0, 1);
4800 space
= isl_space_from_domain(space
);
4801 space
= isl_space_add_dims(space
, isl_dim_out
, n
);
4802 ma
= isl_multi_aff_from_aff_mat(space
, eq
);
4803 mpa
= isl_multi_pw_aff_from_multi_aff(ma
);
4804 map
= isl_multi_pw_aff_eq_map(mpa
, isl_multi_pw_aff_copy(mpa
));
4805 data
->equivalent
= isl_union_map_add_map(data
->equivalent
, map
);
4807 isl_basic_set_free(lineality
);
4810 isl_basic_set_free(lineality
);
4811 return isl_stat_error
;
4814 /* Check if the lineality space "set" is non-trivial (i.e., is not just
4815 * the origin or, in other words, satisfies a number of equality constraints
4816 * that is smaller than the dimension of the set).
4817 * If so, extend data->mask and data->equivalent accordingly.
4819 * The input should not have any local variables already, but
4820 * isl_set_remove_divs is called to make sure it does not.
4822 static isl_stat
add_lineality(__isl_take isl_set
*set
, void *user
)
4824 struct isl_exploit_lineality_data
*data
= user
;
4825 isl_basic_set
*hull
;
4829 set
= isl_set_remove_divs(set
);
4830 hull
= isl_set_unshifted_simple_hull(set
);
4831 dim
= isl_basic_set_dim(hull
, isl_dim_set
);
4832 n_eq
= isl_basic_set_n_equality(hull
);
4836 return add_non_trivial_lineality(hull
, data
);
4837 isl_basic_set_free(hull
);
4840 isl_basic_set_free(hull
);
4841 return isl_stat_error
;
4844 /* Check if the difference set on intra-node schedule constraints "intra"
4845 * has any non-trivial lineality space.
4846 * If so, then extend the difference set to a difference set
4847 * on equivalent elements. That is, if "intra" is
4849 * { y - x : (x,y) \in V }
4851 * and elements are equivalent if they have the same image under f,
4854 * { y' - x' : (x,y) \in V and f(x) = f(x') and f(y) = f(y') }
4856 * or, since f is linear,
4858 * { y' - x' : (x,y) \in V and f(y - x) = f(y' - x') }
4860 * The results of the search for non-trivial lineality spaces is stored
4863 static __isl_give isl_union_set
*exploit_intra_lineality(
4864 __isl_take isl_union_set
*intra
,
4865 struct isl_exploit_lineality_data
*data
)
4867 isl_union_set
*lineality
;
4868 isl_union_set
*uset
;
4870 data
->any_non_trivial
= isl_bool_false
;
4871 lineality
= isl_union_set_copy(intra
);
4872 lineality
= isl_union_set_combined_lineality_space(lineality
);
4873 if (isl_union_set_foreach_set(lineality
, &add_lineality
, data
) < 0)
4874 data
->any_non_trivial
= isl_bool_error
;
4875 isl_union_set_free(lineality
);
4877 if (data
->any_non_trivial
< 0)
4878 return isl_union_set_free(intra
);
4879 if (!data
->any_non_trivial
)
4882 uset
= isl_union_set_copy(intra
);
4883 intra
= isl_union_set_subtract(intra
, isl_union_set_copy(data
->mask
));
4884 uset
= isl_union_set_apply(uset
, isl_union_map_copy(data
->equivalent
));
4885 intra
= isl_union_set_union(intra
, uset
);
4887 intra
= isl_union_set_remove_divs(intra
);
4892 /* If the difference set on intra-node schedule constraints was found to have
4893 * any non-trivial lineality space by exploit_intra_lineality,
4894 * as recorded in "data", then extend the inter-node
4895 * schedule constraints "inter" to schedule constraints on equivalent elements.
4896 * That is, if "inter" is V and
4897 * elements are equivalent if they have the same image under f, then return
4899 * { (x', y') : (x,y) \in V and f(x) = f(x') and f(y) = f(y') }
4901 static __isl_give isl_union_map
*exploit_inter_lineality(
4902 __isl_take isl_union_map
*inter
,
4903 struct isl_exploit_lineality_data
*data
)
4905 isl_union_map
*umap
;
4907 if (data
->any_non_trivial
< 0)
4908 return isl_union_map_free(inter
);
4909 if (!data
->any_non_trivial
)
4912 umap
= isl_union_map_copy(inter
);
4913 inter
= isl_union_map_subtract_range(inter
,
4914 isl_union_set_copy(data
->mask
));
4915 umap
= isl_union_map_apply_range(umap
,
4916 isl_union_map_copy(data
->equivalent
));
4917 inter
= isl_union_map_union(inter
, umap
);
4918 umap
= isl_union_map_copy(inter
);
4919 inter
= isl_union_map_subtract_domain(inter
,
4920 isl_union_set_copy(data
->mask
));
4921 umap
= isl_union_map_apply_range(isl_union_map_copy(data
->equivalent
),
4923 inter
= isl_union_map_union(inter
, umap
);
4925 inter
= isl_union_map_remove_divs(inter
);
4930 /* For each (conditional) validity edge in "graph",
4931 * add the corresponding dependence relation using "add"
4932 * to a collection of dependence relations and return the result.
4933 * If "coincidence" is set, then coincidence edges are considered as well.
4935 static __isl_give isl_union_map
*collect_validity(struct isl_sched_graph
*graph
,
4936 __isl_give isl_union_map
*(*add
)(__isl_take isl_union_map
*umap
,
4937 struct isl_sched_edge
*edge
), int coincidence
)
4941 isl_union_map
*umap
;
4943 space
= isl_space_copy(graph
->node
[0].space
);
4944 umap
= isl_union_map_empty(space
);
4946 for (i
= 0; i
< graph
->n_edge
; ++i
) {
4947 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
4949 if (!is_any_validity(edge
) &&
4950 (!coincidence
|| !is_coincidence(edge
)))
4953 umap
= add(umap
, edge
);
4959 /* For each dependence relation on a (conditional) validity edge
4960 * from a node to itself,
4961 * construct the set of coefficients of valid constraints for elements
4962 * in that dependence relation and collect the results.
4963 * If "coincidence" is set, then coincidence edges are considered as well.
4965 * In particular, for each dependence relation R, constraints
4966 * on coefficients (c_0, c_x) are constructed such that
4968 * c_0 + c_x d >= 0 for each d in delta R = { y - x | (x,y) in R }
4970 * If the schedule_treat_coalescing option is set, then some constraints
4971 * that could be exploited to construct coalescing schedules
4972 * are removed before the dual is computed, but after the parameters
4973 * have been projected out.
4974 * The entire computation is essentially the same as that performed
4975 * by intra_coefficients, except that it operates on multiple
4976 * edges together and that the parameters are always projected out.
4978 * Additionally, exploit any non-trivial lineality space
4979 * in the difference set after removing coalescing constraints and
4980 * store the results of the non-trivial lineality space detection in "data".
4981 * The procedure is currently run unconditionally, but it is unlikely
4982 * to find any non-trivial lineality spaces if no coalescing constraints
4983 * have been removed.
4985 * Note that if a dependence relation is a union of basic maps,
4986 * then each basic map needs to be treated individually as it may only
4987 * be possible to carry the dependences expressed by some of those
4988 * basic maps and not all of them.
4989 * The collected validity constraints are therefore not coalesced and
4990 * it is assumed that they are not coalesced automatically.
4991 * Duplicate basic maps can be removed, however.
4992 * In particular, if the same basic map appears as a disjunct
4993 * in multiple edges, then it only needs to be carried once.
4995 static __isl_give isl_basic_set_list
*collect_intra_validity(isl_ctx
*ctx
,
4996 struct isl_sched_graph
*graph
, int coincidence
,
4997 struct isl_exploit_lineality_data
*data
)
4999 isl_union_map
*intra
;
5000 isl_union_set
*delta
;
5001 isl_basic_set_list
*list
;
5003 intra
= collect_validity(graph
, &add_intra
, coincidence
);
5004 delta
= isl_union_map_deltas(intra
);
5005 delta
= isl_union_set_project_out_all_params(delta
);
5006 delta
= isl_union_set_remove_divs(delta
);
5007 if (isl_options_get_schedule_treat_coalescing(ctx
))
5008 delta
= union_drop_coalescing_constraints(ctx
, graph
, delta
);
5009 delta
= exploit_intra_lineality(delta
, data
);
5010 list
= isl_union_set_get_basic_set_list(delta
);
5011 isl_union_set_free(delta
);
5013 return isl_basic_set_list_coefficients(list
);
5016 /* For each dependence relation on a (conditional) validity edge
5017 * from a node to some other node,
5018 * construct the set of coefficients of valid constraints for elements
5019 * in that dependence relation and collect the results.
5020 * If "coincidence" is set, then coincidence edges are considered as well.
5022 * In particular, for each dependence relation R, constraints
5023 * on coefficients (c_0, c_n, c_x, c_y) are constructed such that
5025 * c_0 + c_n n + c_x x + c_y y >= 0 for each (x,y) in R
5027 * This computation is essentially the same as that performed
5028 * by inter_coefficients, except that it operates on multiple
5031 * Additionally, exploit any non-trivial lineality space
5032 * that may have been discovered by collect_intra_validity
5033 * (as stored in "data").
5035 * Note that if a dependence relation is a union of basic maps,
5036 * then each basic map needs to be treated individually as it may only
5037 * be possible to carry the dependences expressed by some of those
5038 * basic maps and not all of them.
5039 * The collected validity constraints are therefore not coalesced and
5040 * it is assumed that they are not coalesced automatically.
5041 * Duplicate basic maps can be removed, however.
5042 * In particular, if the same basic map appears as a disjunct
5043 * in multiple edges, then it only needs to be carried once.
5045 static __isl_give isl_basic_set_list
*collect_inter_validity(
5046 struct isl_sched_graph
*graph
, int coincidence
,
5047 struct isl_exploit_lineality_data
*data
)
5049 isl_union_map
*inter
;
5050 isl_union_set
*wrap
;
5051 isl_basic_set_list
*list
;
5053 inter
= collect_validity(graph
, &add_inter
, coincidence
);
5054 inter
= exploit_inter_lineality(inter
, data
);
5055 inter
= isl_union_map_remove_divs(inter
);
5056 wrap
= isl_union_map_wrap(inter
);
5057 list
= isl_union_set_get_basic_set_list(wrap
);
5058 isl_union_set_free(wrap
);
5059 return isl_basic_set_list_coefficients(list
);
5062 /* Construct an LP problem for finding schedule coefficients
5063 * such that the schedule carries as many of the "n_edge" groups of
5064 * dependences as possible based on the corresponding coefficient
5065 * constraints and return the lexicographically smallest non-trivial solution.
5066 * "intra" is the sequence of coefficient constraints for intra-node edges.
5067 * "inter" is the sequence of coefficient constraints for inter-node edges.
5068 * If "want_integral" is set, then compute an integral solution
5069 * for the coefficients rather than using the numerators
5070 * of a rational solution.
5071 * "carry_inter" indicates whether inter-node edges should be carried or
5074 * If none of the "n_edge" groups can be carried
5075 * then return an empty vector.
5077 static __isl_give isl_vec
*compute_carrying_sol_coef(isl_ctx
*ctx
,
5078 struct isl_sched_graph
*graph
, int n_edge
,
5079 __isl_keep isl_basic_set_list
*intra
,
5080 __isl_keep isl_basic_set_list
*inter
, int want_integral
,
5085 if (setup_carry_lp(ctx
, graph
, n_edge
, intra
, inter
, carry_inter
) < 0)
5088 lp
= isl_basic_set_copy(graph
->lp
);
5089 return non_neg_lexmin(graph
, lp
, n_edge
, want_integral
);
5092 /* Construct an LP problem for finding schedule coefficients
5093 * such that the schedule carries as many of the validity dependences
5095 * return the lexicographically smallest non-trivial solution.
5096 * If "fallback" is set, then the carrying is performed as a fallback
5097 * for the Pluto-like scheduler.
5098 * If "coincidence" is set, then try and carry coincidence edges as well.
5100 * The variable "n_edge" stores the number of groups that should be carried.
5101 * If none of the "n_edge" groups can be carried
5102 * then return an empty vector.
5103 * If, moreover, "n_edge" is zero, then the LP problem does not even
5104 * need to be constructed.
5106 * If a fallback solution is being computed, then compute an integral solution
5107 * for the coefficients rather than using the numerators
5108 * of a rational solution.
5110 * If a fallback solution is being computed, if there are any intra-node
5111 * dependences, and if requested by the user, then first try
5112 * to only carry those intra-node dependences.
5113 * If this fails to carry any dependences, then try again
5114 * with the inter-node dependences included.
5116 static __isl_give isl_vec
*compute_carrying_sol(isl_ctx
*ctx
,
5117 struct isl_sched_graph
*graph
, int fallback
, int coincidence
)
5119 int n_intra
, n_inter
;
5121 struct isl_carry carry
= { 0 };
5124 carry
.intra
= collect_intra_validity(ctx
, graph
, coincidence
,
5126 carry
.inter
= collect_inter_validity(graph
, coincidence
,
5128 if (!carry
.intra
|| !carry
.inter
)
5130 n_intra
= isl_basic_set_list_n_basic_set(carry
.intra
);
5131 n_inter
= isl_basic_set_list_n_basic_set(carry
.inter
);
5133 if (fallback
&& n_intra
> 0 &&
5134 isl_options_get_schedule_carry_self_first(ctx
)) {
5135 sol
= compute_carrying_sol_coef(ctx
, graph
, n_intra
,
5136 carry
.intra
, carry
.inter
, fallback
, 0);
5137 if (!sol
|| sol
->size
!= 0 || n_inter
== 0) {
5138 isl_carry_clear(&carry
);
5144 n_edge
= n_intra
+ n_inter
;
5146 isl_carry_clear(&carry
);
5147 return isl_vec_alloc(ctx
, 0);
5150 sol
= compute_carrying_sol_coef(ctx
, graph
, n_edge
,
5151 carry
.intra
, carry
.inter
, fallback
, 1);
5152 isl_carry_clear(&carry
);
5155 isl_carry_clear(&carry
);
5159 /* Construct a schedule row for each node such that as many validity dependences
5160 * as possible are carried and then continue with the next band.
5161 * If "fallback" is set, then the carrying is performed as a fallback
5162 * for the Pluto-like scheduler.
5163 * If "coincidence" is set, then try and carry coincidence edges as well.
5165 * If there are no validity dependences, then no dependence can be carried and
5166 * the procedure is guaranteed to fail. If there is more than one component,
5167 * then try computing a schedule on each component separately
5168 * to prevent or at least postpone this failure.
5170 * If a schedule row is computed, then check that dependences are carried
5171 * for at least one of the edges.
5173 * If the computed schedule row turns out to be trivial on one or
5174 * more nodes where it should not be trivial, then we throw it away
5175 * and try again on each component separately.
5177 * If there is only one component, then we accept the schedule row anyway,
5178 * but we do not consider it as a complete row and therefore do not
5179 * increment graph->n_row. Note that the ranks of the nodes that
5180 * do get a non-trivial schedule part will get updated regardless and
5181 * graph->maxvar is computed based on these ranks. The test for
5182 * whether more schedule rows are required in compute_schedule_wcc
5183 * is therefore not affected.
5185 * Insert a band corresponding to the schedule row at position "node"
5186 * of the schedule tree and continue with the construction of the schedule.
5187 * This insertion and the continued construction is performed by split_scaled
5188 * after optionally checking for non-trivial common divisors.
5190 static __isl_give isl_schedule_node
*carry(__isl_take isl_schedule_node
*node
,
5191 struct isl_sched_graph
*graph
, int fallback
, int coincidence
)
5200 ctx
= isl_schedule_node_get_ctx(node
);
5201 sol
= compute_carrying_sol(ctx
, graph
, fallback
, coincidence
);
5203 return isl_schedule_node_free(node
);
5204 if (sol
->size
== 0) {
5207 return compute_component_schedule(node
, graph
, 1);
5208 isl_die(ctx
, isl_error_unknown
, "unable to carry dependences",
5209 return isl_schedule_node_free(node
));
5212 trivial
= is_any_trivial(graph
, sol
);
5214 sol
= isl_vec_free(sol
);
5215 } else if (trivial
&& graph
->scc
> 1) {
5217 return compute_component_schedule(node
, graph
, 1);
5220 if (update_schedule(graph
, sol
, 0) < 0)
5221 return isl_schedule_node_free(node
);
5225 return split_scaled(node
, graph
);
5228 /* Construct a schedule row for each node such that as many validity dependences
5229 * as possible are carried and then continue with the next band.
5230 * Do so as a fallback for the Pluto-like scheduler.
5231 * If "coincidence" is set, then try and carry coincidence edges as well.
5233 static __isl_give isl_schedule_node
*carry_fallback(
5234 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
5237 return carry(node
, graph
, 1, coincidence
);
5240 /* Construct a schedule row for each node such that as many validity dependences
5241 * as possible are carried and then continue with the next band.
5242 * Do so for the case where the Feautrier scheduler was selected
5245 static __isl_give isl_schedule_node
*carry_feautrier(
5246 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
5248 return carry(node
, graph
, 0, 0);
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.
5255 static __isl_give isl_schedule_node
*carry_dependences(
5256 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
5258 return carry_fallback(node
, graph
, 0);
5261 /* Construct a schedule row for each node such that as many validity or
5262 * coincidence dependences as possible are carried and
5263 * then continue with the next band.
5264 * Do so as a fallback for the Pluto-like scheduler.
5266 static __isl_give isl_schedule_node
*carry_coincidence(
5267 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
5269 return carry_fallback(node
, graph
, 1);
5272 /* Topologically sort statements mapped to the same schedule iteration
5273 * and add insert a sequence node in front of "node"
5274 * corresponding to this order.
5275 * If "initialized" is set, then it may be assumed that compute_maxvar
5276 * has been called on the current band. Otherwise, call
5277 * compute_maxvar if and before carry_dependences gets called.
5279 * If it turns out to be impossible to sort the statements apart,
5280 * because different dependences impose different orderings
5281 * on the statements, then we extend the schedule such that
5282 * it carries at least one more dependence.
5284 static __isl_give isl_schedule_node
*sort_statements(
5285 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
5289 isl_union_set_list
*filters
;
5294 ctx
= isl_schedule_node_get_ctx(node
);
5296 isl_die(ctx
, isl_error_internal
,
5297 "graph should have at least one node",
5298 return isl_schedule_node_free(node
));
5303 if (update_edges(ctx
, graph
) < 0)
5304 return isl_schedule_node_free(node
);
5306 if (graph
->n_edge
== 0)
5309 if (detect_sccs(ctx
, graph
) < 0)
5310 return isl_schedule_node_free(node
);
5313 if (graph
->scc
< graph
->n
) {
5314 if (!initialized
&& compute_maxvar(graph
) < 0)
5315 return isl_schedule_node_free(node
);
5316 return carry_dependences(node
, graph
);
5319 filters
= extract_sccs(ctx
, graph
);
5320 node
= isl_schedule_node_insert_sequence(node
, filters
);
5325 /* Are there any (non-empty) (conditional) validity edges in the graph?
5327 static int has_validity_edges(struct isl_sched_graph
*graph
)
5331 for (i
= 0; i
< graph
->n_edge
; ++i
) {
5334 empty
= isl_map_plain_is_empty(graph
->edge
[i
].map
);
5339 if (is_any_validity(&graph
->edge
[i
]))
5346 /* Should we apply a Feautrier step?
5347 * That is, did the user request the Feautrier algorithm and are
5348 * there any validity dependences (left)?
5350 static int need_feautrier_step(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
5352 if (ctx
->opt
->schedule_algorithm
!= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
)
5355 return has_validity_edges(graph
);
5358 /* Compute a schedule for a connected dependence graph using Feautrier's
5359 * multi-dimensional scheduling algorithm and return the updated schedule node.
5361 * The original algorithm is described in [1].
5362 * The main idea is to minimize the number of scheduling dimensions, by
5363 * trying to satisfy as many dependences as possible per scheduling dimension.
5365 * [1] P. Feautrier, Some Efficient Solutions to the Affine Scheduling
5366 * Problem, Part II: Multi-Dimensional Time.
5367 * In Intl. Journal of Parallel Programming, 1992.
5369 static __isl_give isl_schedule_node
*compute_schedule_wcc_feautrier(
5370 isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
5372 return carry_feautrier(node
, graph
);
5375 /* Turn off the "local" bit on all (condition) edges.
5377 static void clear_local_edges(struct isl_sched_graph
*graph
)
5381 for (i
= 0; i
< graph
->n_edge
; ++i
)
5382 if (is_condition(&graph
->edge
[i
]))
5383 clear_local(&graph
->edge
[i
]);
5386 /* Does "graph" have both condition and conditional validity edges?
5388 static int need_condition_check(struct isl_sched_graph
*graph
)
5391 int any_condition
= 0;
5392 int any_conditional_validity
= 0;
5394 for (i
= 0; i
< graph
->n_edge
; ++i
) {
5395 if (is_condition(&graph
->edge
[i
]))
5397 if (is_conditional_validity(&graph
->edge
[i
]))
5398 any_conditional_validity
= 1;
5401 return any_condition
&& any_conditional_validity
;
5404 /* Does "graph" contain any coincidence edge?
5406 static int has_any_coincidence(struct isl_sched_graph
*graph
)
5410 for (i
= 0; i
< graph
->n_edge
; ++i
)
5411 if (is_coincidence(&graph
->edge
[i
]))
5417 /* Extract the final schedule row as a map with the iteration domain
5418 * of "node" as domain.
5420 static __isl_give isl_map
*final_row(struct isl_sched_node
*node
)
5425 row
= isl_mat_rows(node
->sched
) - 1;
5426 ma
= node_extract_partial_schedule_multi_aff(node
, row
, 1);
5427 return isl_map_from_multi_aff(ma
);
5430 /* Is the conditional validity dependence in the edge with index "edge_index"
5431 * violated by the latest (i.e., final) row of the schedule?
5432 * That is, is i scheduled after j
5433 * for any conditional validity dependence i -> j?
5435 static int is_violated(struct isl_sched_graph
*graph
, int edge_index
)
5437 isl_map
*src_sched
, *dst_sched
, *map
;
5438 struct isl_sched_edge
*edge
= &graph
->edge
[edge_index
];
5441 src_sched
= final_row(edge
->src
);
5442 dst_sched
= final_row(edge
->dst
);
5443 map
= isl_map_copy(edge
->map
);
5444 map
= isl_map_apply_domain(map
, src_sched
);
5445 map
= isl_map_apply_range(map
, dst_sched
);
5446 map
= isl_map_order_gt(map
, isl_dim_in
, 0, isl_dim_out
, 0);
5447 empty
= isl_map_is_empty(map
);
5456 /* Does "graph" have any satisfied condition edges that
5457 * are adjacent to the conditional validity constraint with
5458 * domain "conditional_source" and range "conditional_sink"?
5460 * A satisfied condition is one that is not local.
5461 * If a condition was forced to be local already (i.e., marked as local)
5462 * then there is no need to check if it is in fact local.
5464 * Additionally, mark all adjacent condition edges found as local.
5466 static int has_adjacent_true_conditions(struct isl_sched_graph
*graph
,
5467 __isl_keep isl_union_set
*conditional_source
,
5468 __isl_keep isl_union_set
*conditional_sink
)
5473 for (i
= 0; i
< graph
->n_edge
; ++i
) {
5474 int adjacent
, local
;
5475 isl_union_map
*condition
;
5477 if (!is_condition(&graph
->edge
[i
]))
5479 if (is_local(&graph
->edge
[i
]))
5482 condition
= graph
->edge
[i
].tagged_condition
;
5483 adjacent
= domain_intersects(condition
, conditional_sink
);
5484 if (adjacent
>= 0 && !adjacent
)
5485 adjacent
= range_intersects(condition
,
5486 conditional_source
);
5492 set_local(&graph
->edge
[i
]);
5494 local
= is_condition_false(&graph
->edge
[i
]);
5504 /* Are there any violated conditional validity dependences with
5505 * adjacent condition dependences that are not local with respect
5506 * to the current schedule?
5507 * That is, is the conditional validity constraint violated?
5509 * Additionally, mark all those adjacent condition dependences as local.
5510 * We also mark those adjacent condition dependences that were not marked
5511 * as local before, but just happened to be local already. This ensures
5512 * that they remain local if the schedule is recomputed.
5514 * We first collect domain and range of all violated conditional validity
5515 * dependences and then check if there are any adjacent non-local
5516 * condition dependences.
5518 static int has_violated_conditional_constraint(isl_ctx
*ctx
,
5519 struct isl_sched_graph
*graph
)
5523 isl_union_set
*source
, *sink
;
5525 source
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
5526 sink
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
5527 for (i
= 0; i
< graph
->n_edge
; ++i
) {
5528 isl_union_set
*uset
;
5529 isl_union_map
*umap
;
5532 if (!is_conditional_validity(&graph
->edge
[i
]))
5535 violated
= is_violated(graph
, i
);
5543 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_validity
);
5544 uset
= isl_union_map_domain(umap
);
5545 source
= isl_union_set_union(source
, uset
);
5546 source
= isl_union_set_coalesce(source
);
5548 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_validity
);
5549 uset
= isl_union_map_range(umap
);
5550 sink
= isl_union_set_union(sink
, uset
);
5551 sink
= isl_union_set_coalesce(sink
);
5555 any
= has_adjacent_true_conditions(graph
, source
, sink
);
5557 isl_union_set_free(source
);
5558 isl_union_set_free(sink
);
5561 isl_union_set_free(source
);
5562 isl_union_set_free(sink
);
5566 /* Examine the current band (the rows between graph->band_start and
5567 * graph->n_total_row), deciding whether to drop it or add it to "node"
5568 * and then continue with the computation of the next band, if any.
5569 * If "initialized" is set, then it may be assumed that compute_maxvar
5570 * has been called on the current band. Otherwise, call
5571 * compute_maxvar if and before carry_dependences gets called.
5573 * The caller keeps looking for a new row as long as
5574 * graph->n_row < graph->maxvar. If the latest attempt to find
5575 * such a row failed (i.e., we still have graph->n_row < graph->maxvar),
5577 * - split between SCCs and start over (assuming we found an interesting
5578 * pair of SCCs between which to split)
5579 * - continue with the next band (assuming the current band has at least
5581 * - if there is more than one SCC left, then split along all SCCs
5582 * - if outer coincidence needs to be enforced, then try to carry as many
5583 * validity or coincidence dependences as possible and
5584 * continue with the next band
5585 * - try to carry as many validity dependences as possible and
5586 * continue with the next band
5587 * In each case, we first insert a band node in the schedule tree
5588 * if any rows have been computed.
5590 * If the caller managed to complete the schedule and the current band
5591 * is empty, then finish off by topologically
5592 * sorting the statements based on the remaining dependences.
5593 * If, on the other hand, the current band has at least one row,
5594 * then continue with the next band. Note that this next band
5595 * will necessarily be empty, but the graph may still be split up
5596 * into weakly connected components before arriving back here.
5598 static __isl_give isl_schedule_node
*compute_schedule_finish_band(
5599 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
5607 empty
= graph
->n_total_row
== graph
->band_start
;
5608 if (graph
->n_row
< graph
->maxvar
) {
5611 ctx
= isl_schedule_node_get_ctx(node
);
5612 if (!ctx
->opt
->schedule_maximize_band_depth
&& !empty
)
5613 return compute_next_band(node
, graph
, 1);
5614 if (graph
->src_scc
>= 0)
5615 return compute_split_schedule(node
, graph
);
5617 return compute_next_band(node
, graph
, 1);
5619 return compute_component_schedule(node
, graph
, 1);
5620 if (!initialized
&& compute_maxvar(graph
) < 0)
5621 return isl_schedule_node_free(node
);
5622 if (isl_options_get_schedule_outer_coincidence(ctx
))
5623 return carry_coincidence(node
, graph
);
5624 return carry_dependences(node
, graph
);
5628 return compute_next_band(node
, graph
, 1);
5629 return sort_statements(node
, graph
, initialized
);
5632 /* Construct a band of schedule rows for a connected dependence graph.
5633 * The caller is responsible for determining the strongly connected
5634 * components and calling compute_maxvar first.
5636 * We try to find a sequence of as many schedule rows as possible that result
5637 * in non-negative dependence distances (independent of the previous rows
5638 * in the sequence, i.e., such that the sequence is tilable), with as
5639 * many of the initial rows as possible satisfying the coincidence constraints.
5640 * The computation stops if we can't find any more rows or if we have found
5641 * all the rows we wanted to find.
5643 * If ctx->opt->schedule_outer_coincidence is set, then we force the
5644 * outermost dimension to satisfy the coincidence constraints. If this
5645 * turns out to be impossible, we fall back on the general scheme above
5646 * and try to carry as many dependences as possible.
5648 * If "graph" contains both condition and conditional validity dependences,
5649 * then we need to check that that the conditional schedule constraint
5650 * is satisfied, i.e., there are no violated conditional validity dependences
5651 * that are adjacent to any non-local condition dependences.
5652 * If there are, then we mark all those adjacent condition dependences
5653 * as local and recompute the current band. Those dependences that
5654 * are marked local will then be forced to be local.
5655 * The initial computation is performed with no dependences marked as local.
5656 * If we are lucky, then there will be no violated conditional validity
5657 * dependences adjacent to any non-local condition dependences.
5658 * Otherwise, we mark some additional condition dependences as local and
5659 * recompute. We continue this process until there are no violations left or
5660 * until we are no longer able to compute a schedule.
5661 * Since there are only a finite number of dependences,
5662 * there will only be a finite number of iterations.
5664 static isl_stat
compute_schedule_wcc_band(isl_ctx
*ctx
,
5665 struct isl_sched_graph
*graph
)
5667 int has_coincidence
;
5668 int use_coincidence
;
5669 int force_coincidence
= 0;
5670 int check_conditional
;
5672 if (sort_sccs(graph
) < 0)
5673 return isl_stat_error
;
5675 clear_local_edges(graph
);
5676 check_conditional
= need_condition_check(graph
);
5677 has_coincidence
= has_any_coincidence(graph
);
5679 if (ctx
->opt
->schedule_outer_coincidence
)
5680 force_coincidence
= 1;
5682 use_coincidence
= has_coincidence
;
5683 while (graph
->n_row
< graph
->maxvar
) {
5688 graph
->src_scc
= -1;
5689 graph
->dst_scc
= -1;
5691 if (setup_lp(ctx
, graph
, use_coincidence
) < 0)
5692 return isl_stat_error
;
5693 sol
= solve_lp(ctx
, graph
);
5695 return isl_stat_error
;
5696 if (sol
->size
== 0) {
5697 int empty
= graph
->n_total_row
== graph
->band_start
;
5700 if (use_coincidence
&& (!force_coincidence
|| !empty
)) {
5701 use_coincidence
= 0;
5706 coincident
= !has_coincidence
|| use_coincidence
;
5707 if (update_schedule(graph
, sol
, coincident
) < 0)
5708 return isl_stat_error
;
5710 if (!check_conditional
)
5712 violated
= has_violated_conditional_constraint(ctx
, graph
);
5714 return isl_stat_error
;
5717 if (reset_band(graph
) < 0)
5718 return isl_stat_error
;
5719 use_coincidence
= has_coincidence
;
5725 /* Compute a schedule for a connected dependence graph by considering
5726 * the graph as a whole and return the updated schedule node.
5728 * The actual schedule rows of the current band are computed by
5729 * compute_schedule_wcc_band. compute_schedule_finish_band takes
5730 * care of integrating the band into "node" and continuing
5733 static __isl_give isl_schedule_node
*compute_schedule_wcc_whole(
5734 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
5741 ctx
= isl_schedule_node_get_ctx(node
);
5742 if (compute_schedule_wcc_band(ctx
, graph
) < 0)
5743 return isl_schedule_node_free(node
);
5745 return compute_schedule_finish_band(node
, graph
, 1);
5748 /* Clustering information used by compute_schedule_wcc_clustering.
5750 * "n" is the number of SCCs in the original dependence graph
5751 * "scc" is an array of "n" elements, each representing an SCC
5752 * of the original dependence graph. All entries in the same cluster
5753 * have the same number of schedule rows.
5754 * "scc_cluster" maps each SCC index to the cluster to which it belongs,
5755 * where each cluster is represented by the index of the first SCC
5756 * in the cluster. Initially, each SCC belongs to a cluster containing
5759 * "scc_in_merge" is used by merge_clusters_along_edge to keep
5760 * track of which SCCs need to be merged.
5762 * "cluster" contains the merged clusters of SCCs after the clustering
5765 * "scc_node" is a temporary data structure used inside copy_partial.
5766 * For each SCC, it keeps track of the number of nodes in the SCC
5767 * that have already been copied.
5769 struct isl_clustering
{
5771 struct isl_sched_graph
*scc
;
5772 struct isl_sched_graph
*cluster
;
5778 /* Initialize the clustering data structure "c" from "graph".
5780 * In particular, allocate memory, extract the SCCs from "graph"
5781 * into c->scc, initialize scc_cluster and construct
5782 * a band of schedule rows for each SCC.
5783 * Within each SCC, there is only one SCC by definition.
5784 * Each SCC initially belongs to a cluster containing only that SCC.
5786 static isl_stat
clustering_init(isl_ctx
*ctx
, struct isl_clustering
*c
,
5787 struct isl_sched_graph
*graph
)
5792 c
->scc
= isl_calloc_array(ctx
, struct isl_sched_graph
, c
->n
);
5793 c
->cluster
= isl_calloc_array(ctx
, struct isl_sched_graph
, c
->n
);
5794 c
->scc_cluster
= isl_calloc_array(ctx
, int, c
->n
);
5795 c
->scc_node
= isl_calloc_array(ctx
, int, c
->n
);
5796 c
->scc_in_merge
= isl_calloc_array(ctx
, int, c
->n
);
5797 if (!c
->scc
|| !c
->cluster
||
5798 !c
->scc_cluster
|| !c
->scc_node
|| !c
->scc_in_merge
)
5799 return isl_stat_error
;
5801 for (i
= 0; i
< c
->n
; ++i
) {
5802 if (extract_sub_graph(ctx
, graph
, &node_scc_exactly
,
5803 &edge_scc_exactly
, i
, &c
->scc
[i
]) < 0)
5804 return isl_stat_error
;
5806 if (compute_maxvar(&c
->scc
[i
]) < 0)
5807 return isl_stat_error
;
5808 if (compute_schedule_wcc_band(ctx
, &c
->scc
[i
]) < 0)
5809 return isl_stat_error
;
5810 c
->scc_cluster
[i
] = i
;
5816 /* Free all memory allocated for "c".
5818 static void clustering_free(isl_ctx
*ctx
, struct isl_clustering
*c
)
5823 for (i
= 0; i
< c
->n
; ++i
)
5824 graph_free(ctx
, &c
->scc
[i
]);
5827 for (i
= 0; i
< c
->n
; ++i
)
5828 graph_free(ctx
, &c
->cluster
[i
]);
5830 free(c
->scc_cluster
);
5832 free(c
->scc_in_merge
);
5835 /* Should we refrain from merging the cluster in "graph" with
5836 * any other cluster?
5837 * In particular, is its current schedule band empty and incomplete.
5839 static int bad_cluster(struct isl_sched_graph
*graph
)
5841 return graph
->n_row
< graph
->maxvar
&&
5842 graph
->n_total_row
== graph
->band_start
;
5845 /* Is "edge" a proximity edge with a non-empty dependence relation?
5847 static isl_bool
is_non_empty_proximity(struct isl_sched_edge
*edge
)
5849 if (!is_proximity(edge
))
5850 return isl_bool_false
;
5851 return isl_bool_not(isl_map_plain_is_empty(edge
->map
));
5854 /* Return the index of an edge in "graph" that can be used to merge
5855 * two clusters in "c".
5856 * Return graph->n_edge if no such edge can be found.
5857 * Return -1 on error.
5859 * In particular, return a proximity edge between two clusters
5860 * that is not marked "no_merge" and such that neither of the
5861 * two clusters has an incomplete, empty band.
5863 * If there are multiple such edges, then try and find the most
5864 * appropriate edge to use for merging. In particular, pick the edge
5865 * with the greatest weight. If there are multiple of those,
5866 * then pick one with the shortest distance between
5867 * the two cluster representatives.
5869 static int find_proximity(struct isl_sched_graph
*graph
,
5870 struct isl_clustering
*c
)
5872 int i
, best
= graph
->n_edge
, best_dist
, best_weight
;
5874 for (i
= 0; i
< graph
->n_edge
; ++i
) {
5875 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
5879 prox
= is_non_empty_proximity(edge
);
5886 if (bad_cluster(&c
->scc
[edge
->src
->scc
]) ||
5887 bad_cluster(&c
->scc
[edge
->dst
->scc
]))
5889 dist
= c
->scc_cluster
[edge
->dst
->scc
] -
5890 c
->scc_cluster
[edge
->src
->scc
];
5893 weight
= edge
->weight
;
5894 if (best
< graph
->n_edge
) {
5895 if (best_weight
> weight
)
5897 if (best_weight
== weight
&& best_dist
<= dist
)
5902 best_weight
= weight
;
5908 /* Internal data structure used in mark_merge_sccs.
5910 * "graph" is the dependence graph in which a strongly connected
5911 * component is constructed.
5912 * "scc_cluster" maps each SCC index to the cluster to which it belongs.
5913 * "src" and "dst" are the indices of the nodes that are being merged.
5915 struct isl_mark_merge_sccs_data
{
5916 struct isl_sched_graph
*graph
;
5922 /* Check whether the cluster containing node "i" depends on the cluster
5923 * containing node "j". If "i" and "j" belong to the same cluster,
5924 * then they are taken to depend on each other to ensure that
5925 * the resulting strongly connected component consists of complete
5926 * clusters. Furthermore, if "i" and "j" are the two nodes that
5927 * are being merged, then they are taken to depend on each other as well.
5928 * Otherwise, check if there is a (conditional) validity dependence
5929 * from node[j] to node[i], forcing node[i] to follow node[j].
5931 static isl_bool
cluster_follows(int i
, int j
, void *user
)
5933 struct isl_mark_merge_sccs_data
*data
= user
;
5934 struct isl_sched_graph
*graph
= data
->graph
;
5935 int *scc_cluster
= data
->scc_cluster
;
5937 if (data
->src
== i
&& data
->dst
== j
)
5938 return isl_bool_true
;
5939 if (data
->src
== j
&& data
->dst
== i
)
5940 return isl_bool_true
;
5941 if (scc_cluster
[graph
->node
[i
].scc
] == scc_cluster
[graph
->node
[j
].scc
])
5942 return isl_bool_true
;
5944 return graph_has_validity_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
5947 /* Mark all SCCs that belong to either of the two clusters in "c"
5948 * connected by the edge in "graph" with index "edge", or to any
5949 * of the intermediate clusters.
5950 * The marking is recorded in c->scc_in_merge.
5952 * The given edge has been selected for merging two clusters,
5953 * meaning that there is at least a proximity edge between the two nodes.
5954 * However, there may also be (indirect) validity dependences
5955 * between the two nodes. When merging the two clusters, all clusters
5956 * containing one or more of the intermediate nodes along the
5957 * indirect validity dependences need to be merged in as well.
5959 * First collect all such nodes by computing the strongly connected
5960 * component (SCC) containing the two nodes connected by the edge, where
5961 * the two nodes are considered to depend on each other to make
5962 * sure they end up in the same SCC. Similarly, each node is considered
5963 * to depend on every other node in the same cluster to ensure
5964 * that the SCC consists of complete clusters.
5966 * Then the original SCCs that contain any of these nodes are marked
5967 * in c->scc_in_merge.
5969 static isl_stat
mark_merge_sccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
5970 int edge
, struct isl_clustering
*c
)
5972 struct isl_mark_merge_sccs_data data
;
5973 struct isl_tarjan_graph
*g
;
5976 for (i
= 0; i
< c
->n
; ++i
)
5977 c
->scc_in_merge
[i
] = 0;
5980 data
.scc_cluster
= c
->scc_cluster
;
5981 data
.src
= graph
->edge
[edge
].src
- graph
->node
;
5982 data
.dst
= graph
->edge
[edge
].dst
- graph
->node
;
5984 g
= isl_tarjan_graph_component(ctx
, graph
->n
, data
.dst
,
5985 &cluster_follows
, &data
);
5991 isl_die(ctx
, isl_error_internal
,
5992 "expecting at least two nodes in component",
5994 if (g
->order
[--i
] != -1)
5995 isl_die(ctx
, isl_error_internal
,
5996 "expecting end of component marker", goto error
);
5998 for (--i
; i
>= 0 && g
->order
[i
] != -1; --i
) {
5999 int scc
= graph
->node
[g
->order
[i
]].scc
;
6000 c
->scc_in_merge
[scc
] = 1;
6003 isl_tarjan_graph_free(g
);
6006 isl_tarjan_graph_free(g
);
6007 return isl_stat_error
;
6010 /* Construct the identifier "cluster_i".
6012 static __isl_give isl_id
*cluster_id(isl_ctx
*ctx
, int i
)
6016 snprintf(name
, sizeof(name
), "cluster_%d", i
);
6017 return isl_id_alloc(ctx
, name
, NULL
);
6020 /* Construct the space of the cluster with index "i" containing
6021 * the strongly connected component "scc".
6023 * In particular, construct a space called cluster_i with dimension equal
6024 * to the number of schedule rows in the current band of "scc".
6026 static __isl_give isl_space
*cluster_space(struct isl_sched_graph
*scc
, int i
)
6032 nvar
= scc
->n_total_row
- scc
->band_start
;
6033 space
= isl_space_copy(scc
->node
[0].space
);
6034 space
= isl_space_params(space
);
6035 space
= isl_space_set_from_params(space
);
6036 space
= isl_space_add_dims(space
, isl_dim_set
, nvar
);
6037 id
= cluster_id(isl_space_get_ctx(space
), i
);
6038 space
= isl_space_set_tuple_id(space
, isl_dim_set
, id
);
6043 /* Collect the domain of the graph for merging clusters.
6045 * In particular, for each cluster with first SCC "i", construct
6046 * a set in the space called cluster_i with dimension equal
6047 * to the number of schedule rows in the current band of the cluster.
6049 static __isl_give isl_union_set
*collect_domain(isl_ctx
*ctx
,
6050 struct isl_sched_graph
*graph
, struct isl_clustering
*c
)
6054 isl_union_set
*domain
;
6056 space
= isl_space_params_alloc(ctx
, 0);
6057 domain
= isl_union_set_empty(space
);
6059 for (i
= 0; i
< graph
->scc
; ++i
) {
6062 if (!c
->scc_in_merge
[i
])
6064 if (c
->scc_cluster
[i
] != i
)
6066 space
= cluster_space(&c
->scc
[i
], i
);
6067 domain
= isl_union_set_add_set(domain
, isl_set_universe(space
));
6073 /* Construct a map from the original instances to the corresponding
6074 * cluster instance in the current bands of the clusters in "c".
6076 static __isl_give isl_union_map
*collect_cluster_map(isl_ctx
*ctx
,
6077 struct isl_sched_graph
*graph
, struct isl_clustering
*c
)
6081 isl_union_map
*cluster_map
;
6083 space
= isl_space_params_alloc(ctx
, 0);
6084 cluster_map
= isl_union_map_empty(space
);
6085 for (i
= 0; i
< graph
->scc
; ++i
) {
6089 if (!c
->scc_in_merge
[i
])
6092 id
= cluster_id(ctx
, c
->scc_cluster
[i
]);
6093 start
= c
->scc
[i
].band_start
;
6094 n
= c
->scc
[i
].n_total_row
- start
;
6095 for (j
= 0; j
< c
->scc
[i
].n
; ++j
) {
6098 struct isl_sched_node
*node
= &c
->scc
[i
].node
[j
];
6100 ma
= node_extract_partial_schedule_multi_aff(node
,
6102 ma
= isl_multi_aff_set_tuple_id(ma
, isl_dim_out
,
6104 map
= isl_map_from_multi_aff(ma
);
6105 cluster_map
= isl_union_map_add_map(cluster_map
, map
);
6113 /* Add "umap" to the schedule constraints "sc" of all types of "edge"
6114 * that are not isl_edge_condition or isl_edge_conditional_validity.
6116 static __isl_give isl_schedule_constraints
*add_non_conditional_constraints(
6117 struct isl_sched_edge
*edge
, __isl_keep isl_union_map
*umap
,
6118 __isl_take isl_schedule_constraints
*sc
)
6120 enum isl_edge_type t
;
6125 for (t
= isl_edge_first
; t
<= isl_edge_last
; ++t
) {
6126 if (t
== isl_edge_condition
||
6127 t
== isl_edge_conditional_validity
)
6129 if (!is_type(edge
, t
))
6131 sc
= isl_schedule_constraints_add(sc
, t
,
6132 isl_union_map_copy(umap
));
6138 /* Add schedule constraints of types isl_edge_condition and
6139 * isl_edge_conditional_validity to "sc" by applying "umap" to
6140 * the domains of the wrapped relations in domain and range
6141 * of the corresponding tagged constraints of "edge".
6143 static __isl_give isl_schedule_constraints
*add_conditional_constraints(
6144 struct isl_sched_edge
*edge
, __isl_keep isl_union_map
*umap
,
6145 __isl_take isl_schedule_constraints
*sc
)
6147 enum isl_edge_type t
;
6148 isl_union_map
*tagged
;
6150 for (t
= isl_edge_condition
; t
<= isl_edge_conditional_validity
; ++t
) {
6151 if (!is_type(edge
, t
))
6153 if (t
== isl_edge_condition
)
6154 tagged
= isl_union_map_copy(edge
->tagged_condition
);
6156 tagged
= isl_union_map_copy(edge
->tagged_validity
);
6157 tagged
= isl_union_map_zip(tagged
);
6158 tagged
= isl_union_map_apply_domain(tagged
,
6159 isl_union_map_copy(umap
));
6160 tagged
= isl_union_map_zip(tagged
);
6161 sc
= isl_schedule_constraints_add(sc
, t
, tagged
);
6169 /* Given a mapping "cluster_map" from the original instances to
6170 * the cluster instances, add schedule constraints on the clusters
6171 * to "sc" corresponding to the original constraints represented by "edge".
6173 * For non-tagged dependence constraints, the cluster constraints
6174 * are obtained by applying "cluster_map" to the edge->map.
6176 * For tagged dependence constraints, "cluster_map" needs to be applied
6177 * to the domains of the wrapped relations in domain and range
6178 * of the tagged dependence constraints. Pick out the mappings
6179 * from these domains from "cluster_map" and construct their product.
6180 * This mapping can then be applied to the pair of domains.
6182 static __isl_give isl_schedule_constraints
*collect_edge_constraints(
6183 struct isl_sched_edge
*edge
, __isl_keep isl_union_map
*cluster_map
,
6184 __isl_take isl_schedule_constraints
*sc
)
6186 isl_union_map
*umap
;
6188 isl_union_set
*uset
;
6189 isl_union_map
*umap1
, *umap2
;
6194 umap
= isl_union_map_from_map(isl_map_copy(edge
->map
));
6195 umap
= isl_union_map_apply_domain(umap
,
6196 isl_union_map_copy(cluster_map
));
6197 umap
= isl_union_map_apply_range(umap
,
6198 isl_union_map_copy(cluster_map
));
6199 sc
= add_non_conditional_constraints(edge
, umap
, sc
);
6200 isl_union_map_free(umap
);
6202 if (!sc
|| (!is_condition(edge
) && !is_conditional_validity(edge
)))
6205 space
= isl_space_domain(isl_map_get_space(edge
->map
));
6206 uset
= isl_union_set_from_set(isl_set_universe(space
));
6207 umap1
= isl_union_map_copy(cluster_map
);
6208 umap1
= isl_union_map_intersect_domain(umap1
, uset
);
6209 space
= isl_space_range(isl_map_get_space(edge
->map
));
6210 uset
= isl_union_set_from_set(isl_set_universe(space
));
6211 umap2
= isl_union_map_copy(cluster_map
);
6212 umap2
= isl_union_map_intersect_domain(umap2
, uset
);
6213 umap
= isl_union_map_product(umap1
, umap2
);
6215 sc
= add_conditional_constraints(edge
, umap
, sc
);
6217 isl_union_map_free(umap
);
6221 /* Given a mapping "cluster_map" from the original instances to
6222 * the cluster instances, add schedule constraints on the clusters
6223 * to "sc" corresponding to all edges in "graph" between nodes that
6224 * belong to SCCs that are marked for merging in "scc_in_merge".
6226 static __isl_give isl_schedule_constraints
*collect_constraints(
6227 struct isl_sched_graph
*graph
, int *scc_in_merge
,
6228 __isl_keep isl_union_map
*cluster_map
,
6229 __isl_take isl_schedule_constraints
*sc
)
6233 for (i
= 0; i
< graph
->n_edge
; ++i
) {
6234 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
6236 if (!scc_in_merge
[edge
->src
->scc
])
6238 if (!scc_in_merge
[edge
->dst
->scc
])
6240 sc
= collect_edge_constraints(edge
, cluster_map
, sc
);
6246 /* Construct a dependence graph for scheduling clusters with respect
6247 * to each other and store the result in "merge_graph".
6248 * In particular, the nodes of the graph correspond to the schedule
6249 * dimensions of the current bands of those clusters that have been
6250 * marked for merging in "c".
6252 * First construct an isl_schedule_constraints object for this domain
6253 * by transforming the edges in "graph" to the domain.
6254 * Then initialize a dependence graph for scheduling from these
6257 static isl_stat
init_merge_graph(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
6258 struct isl_clustering
*c
, struct isl_sched_graph
*merge_graph
)
6260 isl_union_set
*domain
;
6261 isl_union_map
*cluster_map
;
6262 isl_schedule_constraints
*sc
;
6265 domain
= collect_domain(ctx
, graph
, c
);
6266 sc
= isl_schedule_constraints_on_domain(domain
);
6268 return isl_stat_error
;
6269 cluster_map
= collect_cluster_map(ctx
, graph
, c
);
6270 sc
= collect_constraints(graph
, c
->scc_in_merge
, cluster_map
, sc
);
6271 isl_union_map_free(cluster_map
);
6273 r
= graph_init(merge_graph
, sc
);
6275 isl_schedule_constraints_free(sc
);
6280 /* Compute the maximal number of remaining schedule rows that still need
6281 * to be computed for the nodes that belong to clusters with the maximal
6282 * dimension for the current band (i.e., the band that is to be merged).
6283 * Only clusters that are about to be merged are considered.
6284 * "maxvar" is the maximal dimension for the current band.
6285 * "c" contains information about the clusters.
6287 * Return the maximal number of remaining schedule rows or -1 on error.
6289 static int compute_maxvar_max_slack(int maxvar
, struct isl_clustering
*c
)
6295 for (i
= 0; i
< c
->n
; ++i
) {
6297 struct isl_sched_graph
*scc
;
6299 if (!c
->scc_in_merge
[i
])
6302 nvar
= scc
->n_total_row
- scc
->band_start
;
6305 for (j
= 0; j
< scc
->n
; ++j
) {
6306 struct isl_sched_node
*node
= &scc
->node
[j
];
6309 if (node_update_vmap(node
) < 0)
6311 slack
= node
->nvar
- node
->rank
;
6312 if (slack
> max_slack
)
6320 /* If there are any clusters where the dimension of the current band
6321 * (i.e., the band that is to be merged) is smaller than "maxvar" and
6322 * if there are any nodes in such a cluster where the number
6323 * of remaining schedule rows that still need to be computed
6324 * is greater than "max_slack", then return the smallest current band
6325 * dimension of all these clusters. Otherwise return the original value
6326 * of "maxvar". Return -1 in case of any error.
6327 * Only clusters that are about to be merged are considered.
6328 * "c" contains information about the clusters.
6330 static int limit_maxvar_to_slack(int maxvar
, int max_slack
,
6331 struct isl_clustering
*c
)
6335 for (i
= 0; i
< c
->n
; ++i
) {
6337 struct isl_sched_graph
*scc
;
6339 if (!c
->scc_in_merge
[i
])
6342 nvar
= scc
->n_total_row
- scc
->band_start
;
6345 for (j
= 0; j
< scc
->n
; ++j
) {
6346 struct isl_sched_node
*node
= &scc
->node
[j
];
6349 if (node_update_vmap(node
) < 0)
6351 slack
= node
->nvar
- node
->rank
;
6352 if (slack
> max_slack
) {
6362 /* Adjust merge_graph->maxvar based on the number of remaining schedule rows
6363 * that still need to be computed. In particular, if there is a node
6364 * in a cluster where the dimension of the current band is smaller
6365 * than merge_graph->maxvar, but the number of remaining schedule rows
6366 * is greater than that of any node in a cluster with the maximal
6367 * dimension for the current band (i.e., merge_graph->maxvar),
6368 * then adjust merge_graph->maxvar to the (smallest) current band dimension
6369 * of those clusters. Without this adjustment, the total number of
6370 * schedule dimensions would be increased, resulting in a skewed view
6371 * of the number of coincident dimensions.
6372 * "c" contains information about the clusters.
6374 * If the maximize_band_depth option is set and merge_graph->maxvar is reduced,
6375 * then there is no point in attempting any merge since it will be rejected
6376 * anyway. Set merge_graph->maxvar to zero in such cases.
6378 static isl_stat
adjust_maxvar_to_slack(isl_ctx
*ctx
,
6379 struct isl_sched_graph
*merge_graph
, struct isl_clustering
*c
)
6381 int max_slack
, maxvar
;
6383 max_slack
= compute_maxvar_max_slack(merge_graph
->maxvar
, c
);
6385 return isl_stat_error
;
6386 maxvar
= limit_maxvar_to_slack(merge_graph
->maxvar
, max_slack
, c
);
6388 return isl_stat_error
;
6390 if (maxvar
< merge_graph
->maxvar
) {
6391 if (isl_options_get_schedule_maximize_band_depth(ctx
))
6392 merge_graph
->maxvar
= 0;
6394 merge_graph
->maxvar
= maxvar
;
6400 /* Return the number of coincident dimensions in the current band of "graph",
6401 * where the nodes of "graph" are assumed to be scheduled by a single band.
6403 static int get_n_coincident(struct isl_sched_graph
*graph
)
6407 for (i
= graph
->band_start
; i
< graph
->n_total_row
; ++i
)
6408 if (!graph
->node
[0].coincident
[i
])
6411 return i
- graph
->band_start
;
6414 /* Should the clusters be merged based on the cluster schedule
6415 * in the current (and only) band of "merge_graph", given that
6416 * coincidence should be maximized?
6418 * If the number of coincident schedule dimensions in the merged band
6419 * would be less than the maximal number of coincident schedule dimensions
6420 * in any of the merged clusters, then the clusters should not be merged.
6422 static isl_bool
ok_to_merge_coincident(struct isl_clustering
*c
,
6423 struct isl_sched_graph
*merge_graph
)
6430 for (i
= 0; i
< c
->n
; ++i
) {
6431 if (!c
->scc_in_merge
[i
])
6433 n_coincident
= get_n_coincident(&c
->scc
[i
]);
6434 if (n_coincident
> max_coincident
)
6435 max_coincident
= n_coincident
;
6438 n_coincident
= get_n_coincident(merge_graph
);
6440 return n_coincident
>= max_coincident
;
6443 /* Return the transformation on "node" expressed by the current (and only)
6444 * band of "merge_graph" applied to the clusters in "c".
6446 * First find the representation of "node" in its SCC in "c" and
6447 * extract the transformation expressed by the current band.
6448 * Then extract the transformation applied by "merge_graph"
6449 * to the cluster to which this SCC belongs.
6450 * Combine the two to obtain the complete transformation on the node.
6452 * Note that the range of the first transformation is an anonymous space,
6453 * while the domain of the second is named "cluster_X". The range
6454 * of the former therefore needs to be adjusted before the two
6457 static __isl_give isl_map
*extract_node_transformation(isl_ctx
*ctx
,
6458 struct isl_sched_node
*node
, struct isl_clustering
*c
,
6459 struct isl_sched_graph
*merge_graph
)
6461 struct isl_sched_node
*scc_node
, *cluster_node
;
6465 isl_multi_aff
*ma
, *ma2
;
6467 scc_node
= graph_find_node(ctx
, &c
->scc
[node
->scc
], node
->space
);
6468 if (scc_node
&& !is_node(&c
->scc
[node
->scc
], scc_node
))
6469 isl_die(ctx
, isl_error_internal
, "unable to find node",
6471 start
= c
->scc
[node
->scc
].band_start
;
6472 n
= c
->scc
[node
->scc
].n_total_row
- start
;
6473 ma
= node_extract_partial_schedule_multi_aff(scc_node
, start
, n
);
6474 space
= cluster_space(&c
->scc
[node
->scc
], c
->scc_cluster
[node
->scc
]);
6475 cluster_node
= graph_find_node(ctx
, merge_graph
, space
);
6476 if (cluster_node
&& !is_node(merge_graph
, cluster_node
))
6477 isl_die(ctx
, isl_error_internal
, "unable to find cluster",
6478 space
= isl_space_free(space
));
6479 id
= isl_space_get_tuple_id(space
, isl_dim_set
);
6480 ma
= isl_multi_aff_set_tuple_id(ma
, isl_dim_out
, id
);
6481 isl_space_free(space
);
6482 n
= merge_graph
->n_total_row
;
6483 ma2
= node_extract_partial_schedule_multi_aff(cluster_node
, 0, n
);
6484 ma
= isl_multi_aff_pullback_multi_aff(ma2
, ma
);
6486 return isl_map_from_multi_aff(ma
);
6489 /* Give a set of distances "set", are they bounded by a small constant
6490 * in direction "pos"?
6491 * In practice, check if they are bounded by 2 by checking that there
6492 * are no elements with a value greater than or equal to 3 or
6493 * smaller than or equal to -3.
6495 static isl_bool
distance_is_bounded(__isl_keep isl_set
*set
, int pos
)
6501 return isl_bool_error
;
6503 test
= isl_set_copy(set
);
6504 test
= isl_set_lower_bound_si(test
, isl_dim_set
, pos
, 3);
6505 bounded
= isl_set_is_empty(test
);
6508 if (bounded
< 0 || !bounded
)
6511 test
= isl_set_copy(set
);
6512 test
= isl_set_upper_bound_si(test
, isl_dim_set
, pos
, -3);
6513 bounded
= isl_set_is_empty(test
);
6519 /* Does the set "set" have a fixed (but possible parametric) value
6520 * at dimension "pos"?
6522 static isl_bool
has_single_value(__isl_keep isl_set
*set
, int pos
)
6527 n
= isl_set_dim(set
, isl_dim_set
);
6529 return isl_bool_error
;
6530 set
= isl_set_copy(set
);
6531 set
= isl_set_project_out(set
, isl_dim_set
, pos
+ 1, n
- (pos
+ 1));
6532 set
= isl_set_project_out(set
, isl_dim_set
, 0, pos
);
6533 single
= isl_set_is_singleton(set
);
6539 /* Does "map" have a fixed (but possible parametric) value
6540 * at dimension "pos" of either its domain or its range?
6542 static isl_bool
has_singular_src_or_dst(__isl_keep isl_map
*map
, int pos
)
6547 set
= isl_map_domain(isl_map_copy(map
));
6548 single
= has_single_value(set
, pos
);
6551 if (single
< 0 || single
)
6554 set
= isl_map_range(isl_map_copy(map
));
6555 single
= has_single_value(set
, pos
);
6561 /* Does the edge "edge" from "graph" have bounded dependence distances
6562 * in the merged graph "merge_graph" of a selection of clusters in "c"?
6564 * Extract the complete transformations of the source and destination
6565 * nodes of the edge, apply them to the edge constraints and
6566 * compute the differences. Finally, check if these differences are bounded
6567 * in each direction.
6569 * If the dimension of the band is greater than the number of
6570 * dimensions that can be expected to be optimized by the edge
6571 * (based on its weight), then also allow the differences to be unbounded
6572 * in the remaining dimensions, but only if either the source or
6573 * the destination has a fixed value in that direction.
6574 * This allows a statement that produces values that are used by
6575 * several instances of another statement to be merged with that
6577 * However, merging such clusters will introduce an inherently
6578 * large proximity distance inside the merged cluster, meaning
6579 * that proximity distances will no longer be optimized in
6580 * subsequent merges. These merges are therefore only allowed
6581 * after all other possible merges have been tried.
6582 * The first time such a merge is encountered, the weight of the edge
6583 * is replaced by a negative weight. The second time (i.e., after
6584 * all merges over edges with a non-negative weight have been tried),
6585 * the merge is allowed.
6587 static isl_bool
has_bounded_distances(isl_ctx
*ctx
, struct isl_sched_edge
*edge
,
6588 struct isl_sched_graph
*graph
, struct isl_clustering
*c
,
6589 struct isl_sched_graph
*merge_graph
)
6597 map
= isl_map_copy(edge
->map
);
6598 t
= extract_node_transformation(ctx
, edge
->src
, c
, merge_graph
);
6599 map
= isl_map_apply_domain(map
, t
);
6600 t
= extract_node_transformation(ctx
, edge
->dst
, c
, merge_graph
);
6601 map
= isl_map_apply_range(map
, t
);
6602 dist
= isl_map_deltas(isl_map_copy(map
));
6604 bounded
= isl_bool_true
;
6605 n
= isl_set_dim(dist
, isl_dim_set
);
6608 n_slack
= n
- edge
->weight
;
6609 if (edge
->weight
< 0)
6610 n_slack
-= graph
->max_weight
+ 1;
6611 for (i
= 0; i
< n
; ++i
) {
6612 isl_bool bounded_i
, singular_i
;
6614 bounded_i
= distance_is_bounded(dist
, i
);
6619 if (edge
->weight
>= 0)
6620 bounded
= isl_bool_false
;
6624 singular_i
= has_singular_src_or_dst(map
, i
);
6629 bounded
= isl_bool_false
;
6632 if (!bounded
&& i
>= n
&& edge
->weight
>= 0)
6633 edge
->weight
-= graph
->max_weight
+ 1;
6641 return isl_bool_error
;
6644 /* Should the clusters be merged based on the cluster schedule
6645 * in the current (and only) band of "merge_graph"?
6646 * "graph" is the original dependence graph, while "c" records
6647 * which SCCs are involved in the latest merge.
6649 * In particular, is there at least one proximity constraint
6650 * that is optimized by the merge?
6652 * A proximity constraint is considered to be optimized
6653 * if the dependence distances are small.
6655 static isl_bool
ok_to_merge_proximity(isl_ctx
*ctx
,
6656 struct isl_sched_graph
*graph
, struct isl_clustering
*c
,
6657 struct isl_sched_graph
*merge_graph
)
6661 for (i
= 0; i
< graph
->n_edge
; ++i
) {
6662 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
6665 if (!is_proximity(edge
))
6667 if (!c
->scc_in_merge
[edge
->src
->scc
])
6669 if (!c
->scc_in_merge
[edge
->dst
->scc
])
6671 if (c
->scc_cluster
[edge
->dst
->scc
] ==
6672 c
->scc_cluster
[edge
->src
->scc
])
6674 bounded
= has_bounded_distances(ctx
, edge
, graph
, c
,
6676 if (bounded
< 0 || bounded
)
6680 return isl_bool_false
;
6683 /* Should the clusters be merged based on the cluster schedule
6684 * in the current (and only) band of "merge_graph"?
6685 * "graph" is the original dependence graph, while "c" records
6686 * which SCCs are involved in the latest merge.
6688 * If the current band is empty, then the clusters should not be merged.
6690 * If the band depth should be maximized and the merge schedule
6691 * is incomplete (meaning that the dimension of some of the schedule
6692 * bands in the original schedule will be reduced), then the clusters
6693 * should not be merged.
6695 * If the schedule_maximize_coincidence option is set, then check that
6696 * the number of coincident schedule dimensions is not reduced.
6698 * Finally, only allow the merge if at least one proximity
6699 * constraint is optimized.
6701 static isl_bool
ok_to_merge(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
6702 struct isl_clustering
*c
, struct isl_sched_graph
*merge_graph
)
6704 if (merge_graph
->n_total_row
== merge_graph
->band_start
)
6705 return isl_bool_false
;
6707 if (isl_options_get_schedule_maximize_band_depth(ctx
) &&
6708 merge_graph
->n_total_row
< merge_graph
->maxvar
)
6709 return isl_bool_false
;
6711 if (isl_options_get_schedule_maximize_coincidence(ctx
)) {
6714 ok
= ok_to_merge_coincident(c
, merge_graph
);
6719 return ok_to_merge_proximity(ctx
, graph
, c
, merge_graph
);
6722 /* Apply the schedule in "t_node" to the "n" rows starting at "first"
6723 * of the schedule in "node" and return the result.
6725 * That is, essentially compute
6727 * T * N(first:first+n-1)
6729 * taking into account the constant term and the parameter coefficients
6732 static __isl_give isl_mat
*node_transformation(isl_ctx
*ctx
,
6733 struct isl_sched_node
*t_node
, struct isl_sched_node
*node
,
6738 int n_row
, n_col
, n_param
, n_var
;
6740 n_param
= node
->nparam
;
6742 n_row
= isl_mat_rows(t_node
->sched
);
6743 n_col
= isl_mat_cols(node
->sched
);
6744 t
= isl_mat_alloc(ctx
, n_row
, n_col
);
6747 for (i
= 0; i
< n_row
; ++i
) {
6748 isl_seq_cpy(t
->row
[i
], t_node
->sched
->row
[i
], 1 + n_param
);
6749 isl_seq_clr(t
->row
[i
] + 1 + n_param
, n_var
);
6750 for (j
= 0; j
< n
; ++j
)
6751 isl_seq_addmul(t
->row
[i
],
6752 t_node
->sched
->row
[i
][1 + n_param
+ j
],
6753 node
->sched
->row
[first
+ j
],
6754 1 + n_param
+ n_var
);
6759 /* Apply the cluster schedule in "t_node" to the current band
6760 * schedule of the nodes in "graph".
6762 * In particular, replace the rows starting at band_start
6763 * by the result of applying the cluster schedule in "t_node"
6764 * to the original rows.
6766 * The coincidence of the schedule is determined by the coincidence
6767 * of the cluster schedule.
6769 static isl_stat
transform(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
6770 struct isl_sched_node
*t_node
)
6776 start
= graph
->band_start
;
6777 n
= graph
->n_total_row
- start
;
6779 n_new
= isl_mat_rows(t_node
->sched
);
6780 for (i
= 0; i
< graph
->n
; ++i
) {
6781 struct isl_sched_node
*node
= &graph
->node
[i
];
6784 t
= node_transformation(ctx
, t_node
, node
, start
, n
);
6785 node
->sched
= isl_mat_drop_rows(node
->sched
, start
, n
);
6786 node
->sched
= isl_mat_concat(node
->sched
, t
);
6787 node
->sched_map
= isl_map_free(node
->sched_map
);
6789 return isl_stat_error
;
6790 for (j
= 0; j
< n_new
; ++j
)
6791 node
->coincident
[start
+ j
] = t_node
->coincident
[j
];
6793 graph
->n_total_row
-= n
;
6795 graph
->n_total_row
+= n_new
;
6796 graph
->n_row
+= n_new
;
6801 /* Merge the clusters marked for merging in "c" into a single
6802 * cluster using the cluster schedule in the current band of "merge_graph".
6803 * The representative SCC for the new cluster is the SCC with
6804 * the smallest index.
6806 * The current band schedule of each SCC in the new cluster is obtained
6807 * by applying the schedule of the corresponding original cluster
6808 * to the original band schedule.
6809 * All SCCs in the new cluster have the same number of schedule rows.
6811 static isl_stat
merge(isl_ctx
*ctx
, struct isl_clustering
*c
,
6812 struct isl_sched_graph
*merge_graph
)
6818 for (i
= 0; i
< c
->n
; ++i
) {
6819 struct isl_sched_node
*node
;
6821 if (!c
->scc_in_merge
[i
])
6825 space
= cluster_space(&c
->scc
[i
], c
->scc_cluster
[i
]);
6826 node
= graph_find_node(ctx
, merge_graph
, space
);
6827 isl_space_free(space
);
6829 return isl_stat_error
;
6830 if (!is_node(merge_graph
, node
))
6831 isl_die(ctx
, isl_error_internal
,
6832 "unable to find cluster",
6833 return isl_stat_error
);
6834 if (transform(ctx
, &c
->scc
[i
], node
) < 0)
6835 return isl_stat_error
;
6836 c
->scc_cluster
[i
] = cluster
;
6842 /* Try and merge the clusters of SCCs marked in c->scc_in_merge
6843 * by scheduling the current cluster bands with respect to each other.
6845 * Construct a dependence graph with a space for each cluster and
6846 * with the coordinates of each space corresponding to the schedule
6847 * dimensions of the current band of that cluster.
6848 * Construct a cluster schedule in this cluster dependence graph and
6849 * apply it to the current cluster bands if it is applicable
6850 * according to ok_to_merge.
6852 * If the number of remaining schedule dimensions in a cluster
6853 * with a non-maximal current schedule dimension is greater than
6854 * the number of remaining schedule dimensions in clusters
6855 * with a maximal current schedule dimension, then restrict
6856 * the number of rows to be computed in the cluster schedule
6857 * to the minimal such non-maximal current schedule dimension.
6858 * Do this by adjusting merge_graph.maxvar.
6860 * Return isl_bool_true if the clusters have effectively been merged
6861 * into a single cluster.
6863 * Note that since the standard scheduling algorithm minimizes the maximal
6864 * distance over proximity constraints, the proximity constraints between
6865 * the merged clusters may not be optimized any further than what is
6866 * sufficient to bring the distances within the limits of the internal
6867 * proximity constraints inside the individual clusters.
6868 * It may therefore make sense to perform an additional translation step
6869 * to bring the clusters closer to each other, while maintaining
6870 * the linear part of the merging schedule found using the standard
6871 * scheduling algorithm.
6873 static isl_bool
try_merge(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
6874 struct isl_clustering
*c
)
6876 struct isl_sched_graph merge_graph
= { 0 };
6879 if (init_merge_graph(ctx
, graph
, c
, &merge_graph
) < 0)
6882 if (compute_maxvar(&merge_graph
) < 0)
6884 if (adjust_maxvar_to_slack(ctx
, &merge_graph
,c
) < 0)
6886 if (compute_schedule_wcc_band(ctx
, &merge_graph
) < 0)
6888 merged
= ok_to_merge(ctx
, graph
, c
, &merge_graph
);
6889 if (merged
&& merge(ctx
, c
, &merge_graph
) < 0)
6892 graph_free(ctx
, &merge_graph
);
6895 graph_free(ctx
, &merge_graph
);
6896 return isl_bool_error
;
6899 /* Is there any edge marked "no_merge" between two SCCs that are
6900 * about to be merged (i.e., that are set in "scc_in_merge")?
6901 * "merge_edge" is the proximity edge along which the clusters of SCCs
6902 * are going to be merged.
6904 * If there is any edge between two SCCs with a negative weight,
6905 * while the weight of "merge_edge" is non-negative, then this
6906 * means that the edge was postponed. "merge_edge" should then
6907 * also be postponed since merging along the edge with negative weight should
6908 * be postponed until all edges with non-negative weight have been tried.
6909 * Replace the weight of "merge_edge" by a negative weight as well and
6910 * tell the caller not to attempt a merge.
6912 static int any_no_merge(struct isl_sched_graph
*graph
, int *scc_in_merge
,
6913 struct isl_sched_edge
*merge_edge
)
6917 for (i
= 0; i
< graph
->n_edge
; ++i
) {
6918 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
6920 if (!scc_in_merge
[edge
->src
->scc
])
6922 if (!scc_in_merge
[edge
->dst
->scc
])
6926 if (merge_edge
->weight
>= 0 && edge
->weight
< 0) {
6927 merge_edge
->weight
-= graph
->max_weight
+ 1;
6935 /* Merge the two clusters in "c" connected by the edge in "graph"
6936 * with index "edge" into a single cluster.
6937 * If it turns out to be impossible to merge these two clusters,
6938 * then mark the edge as "no_merge" such that it will not be
6941 * First mark all SCCs that need to be merged. This includes the SCCs
6942 * in the two clusters, but it may also include the SCCs
6943 * of intermediate clusters.
6944 * If there is already a no_merge edge between any pair of such SCCs,
6945 * then simply mark the current edge as no_merge as well.
6946 * Likewise, if any of those edges was postponed by has_bounded_distances,
6947 * then postpone the current edge as well.
6948 * Otherwise, try and merge the clusters and mark "edge" as "no_merge"
6949 * if the clusters did not end up getting merged, unless the non-merge
6950 * is due to the fact that the edge was postponed. This postponement
6951 * can be recognized by a change in weight (from non-negative to negative).
6953 static isl_stat
merge_clusters_along_edge(isl_ctx
*ctx
,
6954 struct isl_sched_graph
*graph
, int edge
, struct isl_clustering
*c
)
6957 int edge_weight
= graph
->edge
[edge
].weight
;
6959 if (mark_merge_sccs(ctx
, graph
, edge
, c
) < 0)
6960 return isl_stat_error
;
6962 if (any_no_merge(graph
, c
->scc_in_merge
, &graph
->edge
[edge
]))
6963 merged
= isl_bool_false
;
6965 merged
= try_merge(ctx
, graph
, c
);
6967 return isl_stat_error
;
6968 if (!merged
&& edge_weight
== graph
->edge
[edge
].weight
)
6969 graph
->edge
[edge
].no_merge
= 1;
6974 /* Does "node" belong to the cluster identified by "cluster"?
6976 static int node_cluster_exactly(struct isl_sched_node
*node
, int cluster
)
6978 return node
->cluster
== cluster
;
6981 /* Does "edge" connect two nodes belonging to the cluster
6982 * identified by "cluster"?
6984 static int edge_cluster_exactly(struct isl_sched_edge
*edge
, int cluster
)
6986 return edge
->src
->cluster
== cluster
&& edge
->dst
->cluster
== cluster
;
6989 /* Swap the schedule of "node1" and "node2".
6990 * Both nodes have been derived from the same node in a common parent graph.
6991 * Since the "coincident" field is shared with that node
6992 * in the parent graph, there is no need to also swap this field.
6994 static void swap_sched(struct isl_sched_node
*node1
,
6995 struct isl_sched_node
*node2
)
7000 sched
= node1
->sched
;
7001 node1
->sched
= node2
->sched
;
7002 node2
->sched
= sched
;
7004 sched_map
= node1
->sched_map
;
7005 node1
->sched_map
= node2
->sched_map
;
7006 node2
->sched_map
= sched_map
;
7009 /* Copy the current band schedule from the SCCs that form the cluster
7010 * with index "pos" to the actual cluster at position "pos".
7011 * By construction, the index of the first SCC that belongs to the cluster
7014 * The order of the nodes inside both the SCCs and the cluster
7015 * is assumed to be same as the order in the original "graph".
7017 * Since the SCC graphs will no longer be used after this function,
7018 * the schedules are actually swapped rather than copied.
7020 static isl_stat
copy_partial(struct isl_sched_graph
*graph
,
7021 struct isl_clustering
*c
, int pos
)
7025 c
->cluster
[pos
].n_total_row
= c
->scc
[pos
].n_total_row
;
7026 c
->cluster
[pos
].n_row
= c
->scc
[pos
].n_row
;
7027 c
->cluster
[pos
].maxvar
= c
->scc
[pos
].maxvar
;
7029 for (i
= 0; i
< graph
->n
; ++i
) {
7033 if (graph
->node
[i
].cluster
!= pos
)
7035 s
= graph
->node
[i
].scc
;
7036 k
= c
->scc_node
[s
]++;
7037 swap_sched(&c
->cluster
[pos
].node
[j
], &c
->scc
[s
].node
[k
]);
7038 if (c
->scc
[s
].maxvar
> c
->cluster
[pos
].maxvar
)
7039 c
->cluster
[pos
].maxvar
= c
->scc
[s
].maxvar
;
7046 /* Is there a (conditional) validity dependence from node[j] to node[i],
7047 * forcing node[i] to follow node[j] or do the nodes belong to the same
7050 static isl_bool
node_follows_strong_or_same_cluster(int i
, int j
, void *user
)
7052 struct isl_sched_graph
*graph
= user
;
7054 if (graph
->node
[i
].cluster
== graph
->node
[j
].cluster
)
7055 return isl_bool_true
;
7056 return graph_has_validity_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
7059 /* Extract the merged clusters of SCCs in "graph", sort them, and
7060 * store them in c->clusters. Update c->scc_cluster accordingly.
7062 * First keep track of the cluster containing the SCC to which a node
7063 * belongs in the node itself.
7064 * Then extract the clusters into c->clusters, copying the current
7065 * band schedule from the SCCs that belong to the cluster.
7066 * Do this only once per cluster.
7068 * Finally, topologically sort the clusters and update c->scc_cluster
7069 * to match the new scc numbering. While the SCCs were originally
7070 * sorted already, some SCCs that depend on some other SCCs may
7071 * have been merged with SCCs that appear before these other SCCs.
7072 * A reordering may therefore be required.
7074 static isl_stat
extract_clusters(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
7075 struct isl_clustering
*c
)
7079 for (i
= 0; i
< graph
->n
; ++i
)
7080 graph
->node
[i
].cluster
= c
->scc_cluster
[graph
->node
[i
].scc
];
7082 for (i
= 0; i
< graph
->scc
; ++i
) {
7083 if (c
->scc_cluster
[i
] != i
)
7085 if (extract_sub_graph(ctx
, graph
, &node_cluster_exactly
,
7086 &edge_cluster_exactly
, i
, &c
->cluster
[i
]) < 0)
7087 return isl_stat_error
;
7088 c
->cluster
[i
].src_scc
= -1;
7089 c
->cluster
[i
].dst_scc
= -1;
7090 if (copy_partial(graph
, c
, i
) < 0)
7091 return isl_stat_error
;
7094 if (detect_ccs(ctx
, graph
, &node_follows_strong_or_same_cluster
) < 0)
7095 return isl_stat_error
;
7096 for (i
= 0; i
< graph
->n
; ++i
)
7097 c
->scc_cluster
[graph
->node
[i
].scc
] = graph
->node
[i
].cluster
;
7102 /* Compute weights on the proximity edges of "graph" that can
7103 * be used by find_proximity to find the most appropriate
7104 * proximity edge to use to merge two clusters in "c".
7105 * The weights are also used by has_bounded_distances to determine
7106 * whether the merge should be allowed.
7107 * Store the maximum of the computed weights in graph->max_weight.
7109 * The computed weight is a measure for the number of remaining schedule
7110 * dimensions that can still be completely aligned.
7111 * In particular, compute the number of equalities between
7112 * input dimensions and output dimensions in the proximity constraints.
7113 * The directions that are already handled by outer schedule bands
7114 * are projected out prior to determining this number.
7116 * Edges that will never be considered by find_proximity are ignored.
7118 static isl_stat
compute_weights(struct isl_sched_graph
*graph
,
7119 struct isl_clustering
*c
)
7123 graph
->max_weight
= 0;
7125 for (i
= 0; i
< graph
->n_edge
; ++i
) {
7126 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
7127 struct isl_sched_node
*src
= edge
->src
;
7128 struct isl_sched_node
*dst
= edge
->dst
;
7129 isl_basic_map
*hull
;
7131 isl_size n_in
, n_out
;
7133 prox
= is_non_empty_proximity(edge
);
7135 return isl_stat_error
;
7138 if (bad_cluster(&c
->scc
[edge
->src
->scc
]) ||
7139 bad_cluster(&c
->scc
[edge
->dst
->scc
]))
7141 if (c
->scc_cluster
[edge
->dst
->scc
] ==
7142 c
->scc_cluster
[edge
->src
->scc
])
7145 hull
= isl_map_affine_hull(isl_map_copy(edge
->map
));
7146 hull
= isl_basic_map_transform_dims(hull
, isl_dim_in
, 0,
7147 isl_mat_copy(src
->vmap
));
7148 hull
= isl_basic_map_transform_dims(hull
, isl_dim_out
, 0,
7149 isl_mat_copy(dst
->vmap
));
7150 hull
= isl_basic_map_project_out(hull
,
7151 isl_dim_in
, 0, src
->rank
);
7152 hull
= isl_basic_map_project_out(hull
,
7153 isl_dim_out
, 0, dst
->rank
);
7154 hull
= isl_basic_map_remove_divs(hull
);
7155 n_in
= isl_basic_map_dim(hull
, isl_dim_in
);
7156 n_out
= isl_basic_map_dim(hull
, isl_dim_out
);
7157 if (n_in
< 0 || n_out
< 0)
7158 hull
= isl_basic_map_free(hull
);
7159 hull
= isl_basic_map_drop_constraints_not_involving_dims(hull
,
7160 isl_dim_in
, 0, n_in
);
7161 hull
= isl_basic_map_drop_constraints_not_involving_dims(hull
,
7162 isl_dim_out
, 0, n_out
);
7164 return isl_stat_error
;
7165 edge
->weight
= isl_basic_map_n_equality(hull
);
7166 isl_basic_map_free(hull
);
7168 if (edge
->weight
> graph
->max_weight
)
7169 graph
->max_weight
= edge
->weight
;
7175 /* Call compute_schedule_finish_band on each of the clusters in "c"
7176 * in their topological order. This order is determined by the scc
7177 * fields of the nodes in "graph".
7178 * Combine the results in a sequence expressing the topological order.
7180 * If there is only one cluster left, then there is no need to introduce
7181 * a sequence node. Also, in this case, the cluster necessarily contains
7182 * the SCC at position 0 in the original graph and is therefore also
7183 * stored in the first cluster of "c".
7185 static __isl_give isl_schedule_node
*finish_bands_clustering(
7186 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
7187 struct isl_clustering
*c
)
7191 isl_union_set_list
*filters
;
7193 if (graph
->scc
== 1)
7194 return compute_schedule_finish_band(node
, &c
->cluster
[0], 0);
7196 ctx
= isl_schedule_node_get_ctx(node
);
7198 filters
= extract_sccs(ctx
, graph
);
7199 node
= isl_schedule_node_insert_sequence(node
, filters
);
7201 for (i
= 0; i
< graph
->scc
; ++i
) {
7202 int j
= c
->scc_cluster
[i
];
7203 node
= isl_schedule_node_child(node
, i
);
7204 node
= isl_schedule_node_child(node
, 0);
7205 node
= compute_schedule_finish_band(node
, &c
->cluster
[j
], 0);
7206 node
= isl_schedule_node_parent(node
);
7207 node
= isl_schedule_node_parent(node
);
7213 /* Compute a schedule for a connected dependence graph by first considering
7214 * each strongly connected component (SCC) in the graph separately and then
7215 * incrementally combining them into clusters.
7216 * Return the updated schedule node.
7218 * Initially, each cluster consists of a single SCC, each with its
7219 * own band schedule. The algorithm then tries to merge pairs
7220 * of clusters along a proximity edge until no more suitable
7221 * proximity edges can be found. During this merging, the schedule
7222 * is maintained in the individual SCCs.
7223 * After the merging is completed, the full resulting clusters
7224 * are extracted and in finish_bands_clustering,
7225 * compute_schedule_finish_band is called on each of them to integrate
7226 * the band into "node" and to continue the computation.
7228 * compute_weights initializes the weights that are used by find_proximity.
7230 static __isl_give isl_schedule_node
*compute_schedule_wcc_clustering(
7231 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
7234 struct isl_clustering c
;
7237 ctx
= isl_schedule_node_get_ctx(node
);
7239 if (clustering_init(ctx
, &c
, graph
) < 0)
7242 if (compute_weights(graph
, &c
) < 0)
7246 i
= find_proximity(graph
, &c
);
7249 if (i
>= graph
->n_edge
)
7251 if (merge_clusters_along_edge(ctx
, graph
, i
, &c
) < 0)
7255 if (extract_clusters(ctx
, graph
, &c
) < 0)
7258 node
= finish_bands_clustering(node
, graph
, &c
);
7260 clustering_free(ctx
, &c
);
7263 clustering_free(ctx
, &c
);
7264 return isl_schedule_node_free(node
);
7267 /* Compute a schedule for a connected dependence graph and return
7268 * the updated schedule node.
7270 * If Feautrier's algorithm is selected, we first recursively try to satisfy
7271 * as many validity dependences as possible. When all validity dependences
7272 * are satisfied we extend the schedule to a full-dimensional schedule.
7274 * Call compute_schedule_wcc_whole or compute_schedule_wcc_clustering
7275 * depending on whether the user has selected the option to try and
7276 * compute a schedule for the entire (weakly connected) component first.
7277 * If there is only a single strongly connected component (SCC), then
7278 * there is no point in trying to combine SCCs
7279 * in compute_schedule_wcc_clustering, so compute_schedule_wcc_whole
7280 * is called instead.
7282 static __isl_give isl_schedule_node
*compute_schedule_wcc(
7283 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
7290 ctx
= isl_schedule_node_get_ctx(node
);
7291 if (detect_sccs(ctx
, graph
) < 0)
7292 return isl_schedule_node_free(node
);
7294 if (compute_maxvar(graph
) < 0)
7295 return isl_schedule_node_free(node
);
7297 if (need_feautrier_step(ctx
, graph
))
7298 return compute_schedule_wcc_feautrier(node
, graph
);
7300 if (graph
->scc
<= 1 || isl_options_get_schedule_whole_component(ctx
))
7301 return compute_schedule_wcc_whole(node
, graph
);
7303 return compute_schedule_wcc_clustering(node
, graph
);
7306 /* Compute a schedule for each group of nodes identified by node->scc
7307 * separately and then combine them in a sequence node (or as set node
7308 * if graph->weak is set) inserted at position "node" of the schedule tree.
7309 * Return the updated schedule node.
7311 * If "wcc" is set then each of the groups belongs to a single
7312 * weakly connected component in the dependence graph so that
7313 * there is no need for compute_sub_schedule to look for weakly
7314 * connected components.
7316 * If a set node would be introduced and if the number of components
7317 * is equal to the number of nodes, then check if the schedule
7318 * is already complete. If so, a redundant set node would be introduced
7319 * (without any further descendants) stating that the statements
7320 * can be executed in arbitrary order, which is also expressed
7321 * by the absence of any node. Refrain from inserting any nodes
7322 * in this case and simply return.
7324 static __isl_give isl_schedule_node
*compute_component_schedule(
7325 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
7330 isl_union_set_list
*filters
;
7335 if (graph
->weak
&& graph
->scc
== graph
->n
) {
7336 if (compute_maxvar(graph
) < 0)
7337 return isl_schedule_node_free(node
);
7338 if (graph
->n_row
>= graph
->maxvar
)
7342 ctx
= isl_schedule_node_get_ctx(node
);
7343 filters
= extract_sccs(ctx
, graph
);
7345 node
= isl_schedule_node_insert_set(node
, filters
);
7347 node
= isl_schedule_node_insert_sequence(node
, filters
);
7349 for (component
= 0; component
< graph
->scc
; ++component
) {
7350 node
= isl_schedule_node_child(node
, component
);
7351 node
= isl_schedule_node_child(node
, 0);
7352 node
= compute_sub_schedule(node
, ctx
, graph
,
7354 &edge_scc_exactly
, component
, wcc
);
7355 node
= isl_schedule_node_parent(node
);
7356 node
= isl_schedule_node_parent(node
);
7362 /* Compute a schedule for the given dependence graph and insert it at "node".
7363 * Return the updated schedule node.
7365 * We first check if the graph is connected (through validity and conditional
7366 * validity dependences) and, if not, compute a schedule
7367 * for each component separately.
7368 * If the schedule_serialize_sccs option is set, then we check for strongly
7369 * connected components instead and compute a separate schedule for
7370 * each such strongly connected component.
7372 static __isl_give isl_schedule_node
*compute_schedule(isl_schedule_node
*node
,
7373 struct isl_sched_graph
*graph
)
7380 ctx
= isl_schedule_node_get_ctx(node
);
7381 if (isl_options_get_schedule_serialize_sccs(ctx
)) {
7382 if (detect_sccs(ctx
, graph
) < 0)
7383 return isl_schedule_node_free(node
);
7385 if (detect_wccs(ctx
, graph
) < 0)
7386 return isl_schedule_node_free(node
);
7390 return compute_component_schedule(node
, graph
, 1);
7392 return compute_schedule_wcc(node
, graph
);
7395 /* Compute a schedule on sc->domain that respects the given schedule
7398 * In particular, the schedule respects all the validity dependences.
7399 * If the default isl scheduling algorithm is used, it tries to minimize
7400 * the dependence distances over the proximity dependences.
7401 * If Feautrier's scheduling algorithm is used, the proximity dependence
7402 * distances are only minimized during the extension to a full-dimensional
7405 * If there are any condition and conditional validity dependences,
7406 * then the conditional validity dependences may be violated inside
7407 * a tilable band, provided they have no adjacent non-local
7408 * condition dependences.
7410 __isl_give isl_schedule
*isl_schedule_constraints_compute_schedule(
7411 __isl_take isl_schedule_constraints
*sc
)
7413 isl_ctx
*ctx
= isl_schedule_constraints_get_ctx(sc
);
7414 struct isl_sched_graph graph
= { 0 };
7415 isl_schedule
*sched
;
7416 isl_schedule_node
*node
;
7417 isl_union_set
*domain
;
7419 sc
= isl_schedule_constraints_align_params(sc
);
7421 domain
= isl_schedule_constraints_get_domain(sc
);
7422 if (isl_union_set_n_set(domain
) == 0) {
7423 isl_schedule_constraints_free(sc
);
7424 return isl_schedule_from_domain(domain
);
7427 if (graph_init(&graph
, sc
) < 0)
7428 domain
= isl_union_set_free(domain
);
7430 node
= isl_schedule_node_from_domain(domain
);
7431 node
= isl_schedule_node_child(node
, 0);
7433 node
= compute_schedule(node
, &graph
);
7434 sched
= isl_schedule_node_get_schedule(node
);
7435 isl_schedule_node_free(node
);
7437 graph_free(ctx
, &graph
);
7438 isl_schedule_constraints_free(sc
);
7443 /* Compute a schedule for the given union of domains that respects
7444 * all the validity dependences and minimizes
7445 * the dependence distances over the proximity dependences.
7447 * This function is kept for backward compatibility.
7449 __isl_give isl_schedule
*isl_union_set_compute_schedule(
7450 __isl_take isl_union_set
*domain
,
7451 __isl_take isl_union_map
*validity
,
7452 __isl_take isl_union_map
*proximity
)
7454 isl_schedule_constraints
*sc
;
7456 sc
= isl_schedule_constraints_on_domain(domain
);
7457 sc
= isl_schedule_constraints_set_validity(sc
, validity
);
7458 sc
= isl_schedule_constraints_set_proximity(sc
, proximity
);
7460 return isl_schedule_constraints_compute_schedule(sc
);