2 * Copyright 2011 INRIA Saclay
3 * Copyright 2012-2014 Ecole Normale Superieure
4 * Copyright 2015-2016 Sven Verdoolaege
5 * Copyright 2016 INRIA Paris
6 * Copyright 2017 Sven Verdoolaege
8 * Use of this software is governed by the MIT license
10 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
11 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
13 * and Ecole Normale Superieure, 45 rue d'Ulm, 75230 Paris, France
14 * and Centre de Recherche Inria de Paris, 2 rue Simone Iff - Voie DQ12,
15 * CS 42112, 75589 Paris Cedex 12, France
18 #include <isl_ctx_private.h>
19 #include <isl_map_private.h>
20 #include <isl_space_private.h>
21 #include <isl_aff_private.h>
23 #include <isl/constraint.h>
24 #include <isl/schedule.h>
25 #include <isl_schedule_constraints.h>
26 #include <isl/schedule_node.h>
27 #include <isl_mat_private.h>
28 #include <isl_vec_private.h>
30 #include <isl_union_set_private.h>
33 #include <isl_dim_map.h>
34 #include <isl/map_to_basic_set.h>
36 #include <isl_options_private.h>
37 #include <isl_tarjan.h>
38 #include <isl_morph.h>
40 #include <isl_val_private.h>
43 * The scheduling algorithm implemented in this file was inspired by
44 * Bondhugula et al., "Automatic Transformations for Communication-Minimized
45 * Parallelization and Locality Optimization in the Polyhedral Model".
49 /* Internal information about a node that is used during the construction
51 * space represents the original space in which the domain lives;
52 * that is, the space is not affected by compression
53 * sched is a matrix representation of the schedule being constructed
54 * for this node; if compressed is set, then this schedule is
55 * defined over the compressed domain space
56 * sched_map is an isl_map representation of the same (partial) schedule
57 * sched_map may be NULL; if compressed is set, then this map
58 * is defined over the uncompressed domain space
59 * rank is the number of linearly independent rows in the linear part
61 * the rows of "vmap" represent a change of basis for the node
62 * variables; the first rank rows span the linear part of
63 * the schedule rows; the remaining rows are linearly independent
64 * the rows of "indep" represent linear combinations of the schedule
65 * coefficients that are non-zero when the schedule coefficients are
66 * linearly independent of previously computed schedule rows.
67 * start is the first variable in the LP problem in the sequences that
68 * represents the schedule coefficients of this node
69 * nvar is the dimension of the domain
70 * nparam is the number of parameters or 0 if we are not constructing
71 * a parametric schedule
73 * If compressed is set, then hull represents the constraints
74 * that were used to derive the compression, while compress and
75 * decompress map the original space to the compressed space and
78 * scc is the index of SCC (or WCC) this node belongs to
80 * "cluster" is only used inside extract_clusters and identifies
81 * the cluster of SCCs that the node belongs to.
83 * coincident contains a boolean for each of the rows of the schedule,
84 * indicating whether the corresponding scheduling dimension satisfies
85 * the coincidence constraints in the sense that the corresponding
86 * dependence distances are zero.
88 * If the schedule_treat_coalescing option is set, then
89 * "sizes" contains the sizes of the (compressed) instance set
90 * in each direction. If there is no fixed size in a given direction,
91 * then the corresponding size value is set to infinity.
92 * If the schedule_treat_coalescing option or the schedule_max_coefficient
93 * option is set, then "max" contains the maximal values for
94 * schedule coefficients of the (compressed) variables. If no bound
95 * needs to be imposed on a particular variable, then the corresponding
97 * If not NULL, then "bounds" contains a non-parametric set
98 * in the compressed space that is bounded by the size in each direction.
100 struct isl_sched_node
{
104 isl_multi_aff
*compress
;
105 isl_multi_aff
*decompress
;
120 isl_multi_val
*sizes
;
121 isl_basic_set
*bounds
;
125 static int node_has_tuples(const void *entry
, const void *val
)
127 struct isl_sched_node
*node
= (struct isl_sched_node
*)entry
;
128 isl_space
*space
= (isl_space
*) val
;
130 return isl_space_has_equal_tuples(node
->space
, space
);
133 static int node_scc_exactly(struct isl_sched_node
*node
, int scc
)
135 return node
->scc
== scc
;
138 static int node_scc_at_most(struct isl_sched_node
*node
, int scc
)
140 return node
->scc
<= scc
;
143 static int node_scc_at_least(struct isl_sched_node
*node
, int scc
)
145 return node
->scc
>= scc
;
148 /* An edge in the dependence graph. An edge may be used to
149 * ensure validity of the generated schedule, to minimize the dependence
152 * map is the dependence relation, with i -> j in the map if j depends on i
153 * tagged_condition and tagged_validity contain the union of all tagged
154 * condition or conditional validity dependence relations that
155 * specialize the dependence relation "map"; that is,
156 * if (i -> a) -> (j -> b) is an element of "tagged_condition"
157 * or "tagged_validity", then i -> j is an element of "map".
158 * If these fields are NULL, then they represent the empty relation.
159 * src is the source node
160 * dst is the sink node
162 * types is a bit vector containing the types of this edge.
163 * validity is set if the edge is used to ensure correctness
164 * coincidence is used to enforce zero dependence distances
165 * proximity is set if the edge is used to minimize dependence distances
166 * condition is set if the edge represents a condition
167 * for a conditional validity schedule constraint
168 * local can only be set for condition edges and indicates that
169 * the dependence distance over the edge should be zero
170 * conditional_validity is set if the edge is used to conditionally
173 * For validity edges, start and end mark the sequence of inequality
174 * constraints in the LP problem that encode the validity constraint
175 * corresponding to this edge.
177 * During clustering, an edge may be marked "no_merge" if it should
178 * not be used to merge clusters.
179 * The weight is also only used during clustering and it is
180 * an indication of how many schedule dimensions on either side
181 * of the schedule constraints can be aligned.
182 * If the weight is negative, then this means that this edge was postponed
183 * by has_bounded_distances or any_no_merge. The original weight can
184 * be retrieved by adding 1 + graph->max_weight, with "graph"
185 * the graph containing this edge.
187 struct isl_sched_edge
{
189 isl_union_map
*tagged_condition
;
190 isl_union_map
*tagged_validity
;
192 struct isl_sched_node
*src
;
193 struct isl_sched_node
*dst
;
204 /* Is "edge" marked as being of type "type"?
206 static int is_type(struct isl_sched_edge
*edge
, enum isl_edge_type type
)
208 return ISL_FL_ISSET(edge
->types
, 1 << type
);
211 /* Mark "edge" as being of type "type".
213 static void set_type(struct isl_sched_edge
*edge
, enum isl_edge_type type
)
215 ISL_FL_SET(edge
->types
, 1 << type
);
218 /* No longer mark "edge" as being of type "type"?
220 static void clear_type(struct isl_sched_edge
*edge
, enum isl_edge_type type
)
222 ISL_FL_CLR(edge
->types
, 1 << type
);
225 /* Is "edge" marked as a validity edge?
227 static int is_validity(struct isl_sched_edge
*edge
)
229 return is_type(edge
, isl_edge_validity
);
232 /* Mark "edge" as a validity edge.
234 static void set_validity(struct isl_sched_edge
*edge
)
236 set_type(edge
, isl_edge_validity
);
239 /* Is "edge" marked as a proximity edge?
241 static int is_proximity(struct isl_sched_edge
*edge
)
243 return is_type(edge
, isl_edge_proximity
);
246 /* Is "edge" marked as a local edge?
248 static int is_local(struct isl_sched_edge
*edge
)
250 return is_type(edge
, isl_edge_local
);
253 /* Mark "edge" as a local edge.
255 static void set_local(struct isl_sched_edge
*edge
)
257 set_type(edge
, isl_edge_local
);
260 /* No longer mark "edge" as a local edge.
262 static void clear_local(struct isl_sched_edge
*edge
)
264 clear_type(edge
, isl_edge_local
);
267 /* Is "edge" marked as a coincidence edge?
269 static int is_coincidence(struct isl_sched_edge
*edge
)
271 return is_type(edge
, isl_edge_coincidence
);
274 /* Is "edge" marked as a condition edge?
276 static int is_condition(struct isl_sched_edge
*edge
)
278 return is_type(edge
, isl_edge_condition
);
281 /* Is "edge" marked as a conditional validity edge?
283 static int is_conditional_validity(struct isl_sched_edge
*edge
)
285 return is_type(edge
, isl_edge_conditional_validity
);
288 /* Internal information about the dependence graph used during
289 * the construction of the schedule.
291 * intra_hmap is a cache, mapping dependence relations to their dual,
292 * for dependences from a node to itself, possibly without
293 * coefficients for the parameters
294 * intra_hmap_param is a cache, mapping dependence relations to their dual,
295 * for dependences from a node to itself, including coefficients
297 * inter_hmap is a cache, mapping dependence relations to their dual,
298 * for dependences between distinct nodes
299 * if compression is involved then the key for these maps
300 * is the original, uncompressed dependence relation, while
301 * the value is the dual of the compressed dependence relation.
303 * n is the number of nodes
304 * node is the list of nodes
305 * maxvar is the maximal number of variables over all nodes
306 * max_row is the allocated number of rows in the schedule
307 * n_row is the current (maximal) number of linearly independent
308 * rows in the node schedules
309 * n_total_row is the current number of rows in the node schedules
310 * band_start is the starting row in the node schedules of the current band
311 * root is set to the the original dependence graph from which this graph
312 * is derived through splitting. If this graph is not the result of
313 * splitting, then the root field points to the graph itself.
315 * sorted contains a list of node indices sorted according to the
316 * SCC to which a node belongs
318 * n_edge is the number of edges
319 * edge is the list of edges
320 * max_edge contains the maximal number of edges of each type;
321 * in particular, it contains the number of edges in the inital graph.
322 * edge_table contains pointers into the edge array, hashed on the source
323 * and sink spaces; there is one such table for each type;
324 * a given edge may be referenced from more than one table
325 * if the corresponding relation appears in more than one of the
326 * sets of dependences; however, for each type there is only
327 * a single edge between a given pair of source and sink space
328 * in the entire graph
330 * node_table contains pointers into the node array, hashed on the space tuples
332 * region contains a list of variable sequences that should be non-trivial
334 * lp contains the (I)LP problem used to obtain new schedule rows
336 * src_scc and dst_scc are the source and sink SCCs of an edge with
337 * conflicting constraints
339 * scc represents the number of components
340 * weak is set if the components are weakly connected
342 * max_weight is used during clustering and represents the maximal
343 * weight of the relevant proximity edges.
345 struct isl_sched_graph
{
346 isl_map_to_basic_set
*intra_hmap
;
347 isl_map_to_basic_set
*intra_hmap_param
;
348 isl_map_to_basic_set
*inter_hmap
;
350 struct isl_sched_node
*node
;
361 struct isl_sched_graph
*root
;
363 struct isl_sched_edge
*edge
;
365 int max_edge
[isl_edge_last
+ 1];
366 struct isl_hash_table
*edge_table
[isl_edge_last
+ 1];
368 struct isl_hash_table
*node_table
;
369 struct isl_trivial_region
*region
;
382 /* Initialize node_table based on the list of nodes.
384 static int graph_init_table(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
388 graph
->node_table
= isl_hash_table_alloc(ctx
, graph
->n
);
389 if (!graph
->node_table
)
392 for (i
= 0; i
< graph
->n
; ++i
) {
393 struct isl_hash_table_entry
*entry
;
396 hash
= isl_space_get_tuple_hash(graph
->node
[i
].space
);
397 entry
= isl_hash_table_find(ctx
, graph
->node_table
, hash
,
399 graph
->node
[i
].space
, 1);
402 entry
->data
= &graph
->node
[i
];
408 /* Return a pointer to the node that lives within the given space,
409 * or NULL if there is no such node.
411 static struct isl_sched_node
*graph_find_node(isl_ctx
*ctx
,
412 struct isl_sched_graph
*graph
, __isl_keep isl_space
*space
)
414 struct isl_hash_table_entry
*entry
;
417 hash
= isl_space_get_tuple_hash(space
);
418 entry
= isl_hash_table_find(ctx
, graph
->node_table
, hash
,
419 &node_has_tuples
, space
, 0);
421 return entry
? entry
->data
: NULL
;
424 /* Is "node" a node in "graph"?
426 static int is_node(struct isl_sched_graph
*graph
,
427 struct isl_sched_node
*node
)
429 return node
&& node
>= &graph
->node
[0] && node
< &graph
->node
[graph
->n
];
432 static int edge_has_src_and_dst(const void *entry
, const void *val
)
434 const struct isl_sched_edge
*edge
= entry
;
435 const struct isl_sched_edge
*temp
= val
;
437 return edge
->src
== temp
->src
&& edge
->dst
== temp
->dst
;
440 /* Add the given edge to graph->edge_table[type].
442 static isl_stat
graph_edge_table_add(isl_ctx
*ctx
,
443 struct isl_sched_graph
*graph
, enum isl_edge_type type
,
444 struct isl_sched_edge
*edge
)
446 struct isl_hash_table_entry
*entry
;
449 hash
= isl_hash_init();
450 hash
= isl_hash_builtin(hash
, edge
->src
);
451 hash
= isl_hash_builtin(hash
, edge
->dst
);
452 entry
= isl_hash_table_find(ctx
, graph
->edge_table
[type
], hash
,
453 &edge_has_src_and_dst
, edge
, 1);
455 return isl_stat_error
;
461 /* Allocate the edge_tables based on the maximal number of edges of
464 static int graph_init_edge_tables(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
468 for (i
= 0; i
<= isl_edge_last
; ++i
) {
469 graph
->edge_table
[i
] = isl_hash_table_alloc(ctx
,
471 if (!graph
->edge_table
[i
])
478 /* If graph->edge_table[type] contains an edge from the given source
479 * to the given destination, then return the hash table entry of this edge.
480 * Otherwise, return NULL.
482 static struct isl_hash_table_entry
*graph_find_edge_entry(
483 struct isl_sched_graph
*graph
,
484 enum isl_edge_type type
,
485 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
487 isl_ctx
*ctx
= isl_space_get_ctx(src
->space
);
489 struct isl_sched_edge temp
= { .src
= src
, .dst
= dst
};
491 hash
= isl_hash_init();
492 hash
= isl_hash_builtin(hash
, temp
.src
);
493 hash
= isl_hash_builtin(hash
, temp
.dst
);
494 return isl_hash_table_find(ctx
, graph
->edge_table
[type
], hash
,
495 &edge_has_src_and_dst
, &temp
, 0);
499 /* If graph->edge_table[type] contains an edge from the given source
500 * to the given destination, then return this edge.
501 * Otherwise, return NULL.
503 static struct isl_sched_edge
*graph_find_edge(struct isl_sched_graph
*graph
,
504 enum isl_edge_type type
,
505 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
507 struct isl_hash_table_entry
*entry
;
509 entry
= graph_find_edge_entry(graph
, type
, src
, dst
);
516 /* Check whether the dependence graph has an edge of the given type
517 * between the given two nodes.
519 static isl_bool
graph_has_edge(struct isl_sched_graph
*graph
,
520 enum isl_edge_type type
,
521 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
523 struct isl_sched_edge
*edge
;
526 edge
= graph_find_edge(graph
, type
, src
, dst
);
530 empty
= isl_map_plain_is_empty(edge
->map
);
532 return isl_bool_error
;
537 /* Look for any edge with the same src, dst and map fields as "model".
539 * Return the matching edge if one can be found.
540 * Return "model" if no matching edge is found.
541 * Return NULL on error.
543 static struct isl_sched_edge
*graph_find_matching_edge(
544 struct isl_sched_graph
*graph
, struct isl_sched_edge
*model
)
546 enum isl_edge_type i
;
547 struct isl_sched_edge
*edge
;
549 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
552 edge
= graph_find_edge(graph
, i
, model
->src
, model
->dst
);
555 is_equal
= isl_map_plain_is_equal(model
->map
, edge
->map
);
565 /* Remove the given edge from all the edge_tables that refer to it.
567 static void graph_remove_edge(struct isl_sched_graph
*graph
,
568 struct isl_sched_edge
*edge
)
570 isl_ctx
*ctx
= isl_map_get_ctx(edge
->map
);
571 enum isl_edge_type i
;
573 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
574 struct isl_hash_table_entry
*entry
;
576 entry
= graph_find_edge_entry(graph
, i
, edge
->src
, edge
->dst
);
579 if (entry
->data
!= edge
)
581 isl_hash_table_remove(ctx
, graph
->edge_table
[i
], entry
);
585 /* Check whether the dependence graph has any edge
586 * between the given two nodes.
588 static isl_bool
graph_has_any_edge(struct isl_sched_graph
*graph
,
589 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
591 enum isl_edge_type i
;
594 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
595 r
= graph_has_edge(graph
, i
, src
, dst
);
603 /* Check whether the dependence graph has a validity edge
604 * between the given two nodes.
606 * Conditional validity edges are essentially validity edges that
607 * can be ignored if the corresponding condition edges are iteration private.
608 * Here, we are only checking for the presence of validity
609 * edges, so we need to consider the conditional validity edges too.
610 * In particular, this function is used during the detection
611 * of strongly connected components and we cannot ignore
612 * conditional validity edges during this detection.
614 static isl_bool
graph_has_validity_edge(struct isl_sched_graph
*graph
,
615 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
619 r
= graph_has_edge(graph
, isl_edge_validity
, src
, dst
);
623 return graph_has_edge(graph
, isl_edge_conditional_validity
, src
, dst
);
626 static int graph_alloc(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
627 int n_node
, int n_edge
)
632 graph
->n_edge
= n_edge
;
633 graph
->node
= isl_calloc_array(ctx
, struct isl_sched_node
, graph
->n
);
634 graph
->sorted
= isl_calloc_array(ctx
, int, graph
->n
);
635 graph
->region
= isl_alloc_array(ctx
,
636 struct isl_trivial_region
, graph
->n
);
637 graph
->edge
= isl_calloc_array(ctx
,
638 struct isl_sched_edge
, graph
->n_edge
);
640 graph
->intra_hmap
= isl_map_to_basic_set_alloc(ctx
, 2 * n_edge
);
641 graph
->intra_hmap_param
= isl_map_to_basic_set_alloc(ctx
, 2 * n_edge
);
642 graph
->inter_hmap
= isl_map_to_basic_set_alloc(ctx
, 2 * n_edge
);
644 if (!graph
->node
|| !graph
->region
|| (graph
->n_edge
&& !graph
->edge
) ||
648 for(i
= 0; i
< graph
->n
; ++i
)
649 graph
->sorted
[i
] = i
;
654 static void graph_free(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
658 isl_map_to_basic_set_free(graph
->intra_hmap
);
659 isl_map_to_basic_set_free(graph
->intra_hmap_param
);
660 isl_map_to_basic_set_free(graph
->inter_hmap
);
663 for (i
= 0; i
< graph
->n
; ++i
) {
664 isl_space_free(graph
->node
[i
].space
);
665 isl_set_free(graph
->node
[i
].hull
);
666 isl_multi_aff_free(graph
->node
[i
].compress
);
667 isl_multi_aff_free(graph
->node
[i
].decompress
);
668 isl_mat_free(graph
->node
[i
].sched
);
669 isl_map_free(graph
->node
[i
].sched_map
);
670 isl_mat_free(graph
->node
[i
].indep
);
671 isl_mat_free(graph
->node
[i
].vmap
);
672 if (graph
->root
== graph
)
673 free(graph
->node
[i
].coincident
);
674 isl_multi_val_free(graph
->node
[i
].sizes
);
675 isl_basic_set_free(graph
->node
[i
].bounds
);
676 isl_vec_free(graph
->node
[i
].max
);
681 for (i
= 0; i
< graph
->n_edge
; ++i
) {
682 isl_map_free(graph
->edge
[i
].map
);
683 isl_union_map_free(graph
->edge
[i
].tagged_condition
);
684 isl_union_map_free(graph
->edge
[i
].tagged_validity
);
688 for (i
= 0; i
<= isl_edge_last
; ++i
)
689 isl_hash_table_free(ctx
, graph
->edge_table
[i
]);
690 isl_hash_table_free(ctx
, graph
->node_table
);
691 isl_basic_set_free(graph
->lp
);
694 /* For each "set" on which this function is called, increment
695 * graph->n by one and update graph->maxvar.
697 static isl_stat
init_n_maxvar(__isl_take isl_set
*set
, void *user
)
699 struct isl_sched_graph
*graph
= user
;
700 int nvar
= isl_set_dim(set
, isl_dim_set
);
703 if (nvar
> graph
->maxvar
)
704 graph
->maxvar
= nvar
;
711 /* Compute the number of rows that should be allocated for the schedule.
712 * In particular, we need one row for each variable or one row
713 * for each basic map in the dependences.
714 * Note that it is practically impossible to exhaust both
715 * the number of dependences and the number of variables.
717 static isl_stat
compute_max_row(struct isl_sched_graph
*graph
,
718 __isl_keep isl_schedule_constraints
*sc
)
722 isl_union_set
*domain
;
726 domain
= isl_schedule_constraints_get_domain(sc
);
727 r
= isl_union_set_foreach_set(domain
, &init_n_maxvar
, graph
);
728 isl_union_set_free(domain
);
730 return isl_stat_error
;
731 n_edge
= isl_schedule_constraints_n_basic_map(sc
);
733 return isl_stat_error
;
734 graph
->max_row
= n_edge
+ graph
->maxvar
;
739 /* Does "bset" have any defining equalities for its set variables?
741 static isl_bool
has_any_defining_equality(__isl_keep isl_basic_set
*bset
)
746 return isl_bool_error
;
748 n
= isl_basic_set_dim(bset
, isl_dim_set
);
749 for (i
= 0; i
< n
; ++i
) {
752 has
= isl_basic_set_has_defining_equality(bset
, isl_dim_set
, i
,
758 return isl_bool_false
;
761 /* Set the entries of node->max to the value of the schedule_max_coefficient
764 static isl_stat
set_max_coefficient(isl_ctx
*ctx
, struct isl_sched_node
*node
)
768 max
= isl_options_get_schedule_max_coefficient(ctx
);
772 node
->max
= isl_vec_alloc(ctx
, node
->nvar
);
773 node
->max
= isl_vec_set_si(node
->max
, max
);
775 return isl_stat_error
;
780 /* Set the entries of node->max to the minimum of the schedule_max_coefficient
781 * option (if set) and half of the minimum of the sizes in the other
782 * dimensions. Round up when computing the half such that
783 * if the minimum of the sizes is one, half of the size is taken to be one
785 * If the global minimum is unbounded (i.e., if both
786 * the schedule_max_coefficient is not set and the sizes in the other
787 * dimensions are unbounded), then store a negative value.
788 * If the schedule coefficient is close to the size of the instance set
789 * in another dimension, then the schedule may represent a loop
790 * coalescing transformation (especially if the coefficient
791 * in that other dimension is one). Forcing the coefficient to be
792 * smaller than or equal to half the minimal size should avoid this
795 static isl_stat
compute_max_coefficient(isl_ctx
*ctx
,
796 struct isl_sched_node
*node
)
802 max
= isl_options_get_schedule_max_coefficient(ctx
);
803 v
= isl_vec_alloc(ctx
, node
->nvar
);
805 return isl_stat_error
;
807 for (i
= 0; i
< node
->nvar
; ++i
) {
808 isl_int_set_si(v
->el
[i
], max
);
809 isl_int_mul_si(v
->el
[i
], v
->el
[i
], 2);
812 for (i
= 0; i
< node
->nvar
; ++i
) {
815 size
= isl_multi_val_get_val(node
->sizes
, i
);
818 if (!isl_val_is_int(size
)) {
822 for (j
= 0; j
< node
->nvar
; ++j
) {
825 if (isl_int_is_neg(v
->el
[j
]) ||
826 isl_int_gt(v
->el
[j
], size
->n
))
827 isl_int_set(v
->el
[j
], size
->n
);
832 for (i
= 0; i
< node
->nvar
; ++i
)
833 isl_int_cdiv_q_ui(v
->el
[i
], v
->el
[i
], 2);
839 return isl_stat_error
;
842 /* Compute and return the size of "set" in dimension "dim".
843 * The size is taken to be the difference in values for that variable
844 * for fixed values of the other variables.
845 * In particular, the variable is first isolated from the other variables
846 * in the range of a map
848 * [i_0, ..., i_dim-1, i_dim+1, ...] -> [i_dim]
850 * and then duplicated
852 * [i_0, ..., i_dim-1, i_dim+1, ...] -> [[i_dim] -> [i_dim']]
854 * The shared variables are then projected out and the maximal value
855 * of i_dim' - i_dim is computed.
857 static __isl_give isl_val
*compute_size(__isl_take isl_set
*set
, int dim
)
864 map
= isl_set_project_onto_map(set
, isl_dim_set
, dim
, 1);
865 map
= isl_map_project_out(map
, isl_dim_in
, dim
, 1);
866 map
= isl_map_range_product(map
, isl_map_copy(map
));
867 map
= isl_set_unwrap(isl_map_range(map
));
868 set
= isl_map_deltas(map
);
869 ls
= isl_local_space_from_space(isl_set_get_space(set
));
870 obj
= isl_aff_var_on_domain(ls
, isl_dim_set
, 0);
871 v
= isl_set_max_val(set
, obj
);
878 /* Compute the size of the instance set "set" of "node", after compression,
879 * as well as bounds on the corresponding coefficients, if needed.
881 * The sizes are needed when the schedule_treat_coalescing option is set.
882 * The bounds are needed when the schedule_treat_coalescing option or
883 * the schedule_max_coefficient option is set.
885 * If the schedule_treat_coalescing option is not set, then at most
886 * the bounds need to be set and this is done in set_max_coefficient.
887 * Otherwise, compress the domain if needed, compute the size
888 * in each direction and store the results in node->size.
889 * Finally, set the bounds on the coefficients based on the sizes
890 * and the schedule_max_coefficient option in compute_max_coefficient.
892 static isl_stat
compute_sizes_and_max(isl_ctx
*ctx
, struct isl_sched_node
*node
,
893 __isl_take isl_set
*set
)
898 if (!isl_options_get_schedule_treat_coalescing(ctx
)) {
900 return set_max_coefficient(ctx
, node
);
903 if (node
->compressed
)
904 set
= isl_set_preimage_multi_aff(set
,
905 isl_multi_aff_copy(node
->decompress
));
906 mv
= isl_multi_val_zero(isl_set_get_space(set
));
907 n
= isl_set_dim(set
, isl_dim_set
);
908 for (j
= 0; j
< n
; ++j
) {
911 v
= compute_size(isl_set_copy(set
), j
);
912 mv
= isl_multi_val_set_val(mv
, j
, v
);
917 return isl_stat_error
;
918 return compute_max_coefficient(ctx
, node
);
921 /* Add a new node to the graph representing the given instance set.
922 * "nvar" is the (possibly compressed) number of variables and
923 * may be smaller than then number of set variables in "set"
924 * if "compressed" is set.
925 * If "compressed" is set, then "hull" represents the constraints
926 * that were used to derive the compression, while "compress" and
927 * "decompress" map the original space to the compressed space and
929 * If "compressed" is not set, then "hull", "compress" and "decompress"
932 * Compute the size of the instance set and bounds on the coefficients,
935 static isl_stat
add_node(struct isl_sched_graph
*graph
,
936 __isl_take isl_set
*set
, int nvar
, int compressed
,
937 __isl_take isl_set
*hull
, __isl_take isl_multi_aff
*compress
,
938 __isl_take isl_multi_aff
*decompress
)
945 struct isl_sched_node
*node
;
948 return isl_stat_error
;
950 ctx
= isl_set_get_ctx(set
);
951 nparam
= isl_set_dim(set
, isl_dim_param
);
952 if (!ctx
->opt
->schedule_parametric
)
954 sched
= isl_mat_alloc(ctx
, 0, 1 + nparam
+ nvar
);
955 node
= &graph
->node
[graph
->n
];
957 space
= isl_set_get_space(set
);
960 node
->nparam
= nparam
;
962 node
->sched_map
= NULL
;
963 coincident
= isl_calloc_array(ctx
, int, graph
->max_row
);
964 node
->coincident
= coincident
;
965 node
->compressed
= compressed
;
967 node
->compress
= compress
;
968 node
->decompress
= decompress
;
969 if (compute_sizes_and_max(ctx
, node
, set
) < 0)
970 return isl_stat_error
;
972 if (!space
|| !sched
|| (graph
->max_row
&& !coincident
))
973 return isl_stat_error
;
974 if (compressed
&& (!hull
|| !compress
|| !decompress
))
975 return isl_stat_error
;
980 /* Construct an identifier for node "node", which will represent "set".
981 * The name of the identifier is either "compressed" or
982 * "compressed_<name>", with <name> the name of the space of "set".
983 * The user pointer of the identifier points to "node".
985 static __isl_give isl_id
*construct_compressed_id(__isl_keep isl_set
*set
,
986 struct isl_sched_node
*node
)
995 has_name
= isl_set_has_tuple_name(set
);
999 ctx
= isl_set_get_ctx(set
);
1001 return isl_id_alloc(ctx
, "compressed", node
);
1003 p
= isl_printer_to_str(ctx
);
1004 name
= isl_set_get_tuple_name(set
);
1005 p
= isl_printer_print_str(p
, "compressed_");
1006 p
= isl_printer_print_str(p
, name
);
1007 id_name
= isl_printer_get_str(p
);
1008 isl_printer_free(p
);
1010 id
= isl_id_alloc(ctx
, id_name
, node
);
1016 /* Add a new node to the graph representing the given set.
1018 * If any of the set variables is defined by an equality, then
1019 * we perform variable compression such that we can perform
1020 * the scheduling on the compressed domain.
1021 * In this case, an identifier is used that references the new node
1022 * such that each compressed space is unique and
1023 * such that the node can be recovered from the compressed space.
1025 static isl_stat
extract_node(__isl_take isl_set
*set
, void *user
)
1028 isl_bool has_equality
;
1030 isl_basic_set
*hull
;
1033 isl_multi_aff
*compress
, *decompress
;
1034 struct isl_sched_graph
*graph
= user
;
1036 hull
= isl_set_affine_hull(isl_set_copy(set
));
1037 hull
= isl_basic_set_remove_divs(hull
);
1038 nvar
= isl_set_dim(set
, isl_dim_set
);
1039 has_equality
= has_any_defining_equality(hull
);
1041 if (has_equality
< 0)
1043 if (!has_equality
) {
1044 isl_basic_set_free(hull
);
1045 return add_node(graph
, set
, nvar
, 0, NULL
, NULL
, NULL
);
1048 id
= construct_compressed_id(set
, &graph
->node
[graph
->n
]);
1049 morph
= isl_basic_set_variable_compression_with_id(hull
,
1052 nvar
= isl_morph_ran_dim(morph
, isl_dim_set
);
1053 compress
= isl_morph_get_var_multi_aff(morph
);
1054 morph
= isl_morph_inverse(morph
);
1055 decompress
= isl_morph_get_var_multi_aff(morph
);
1056 isl_morph_free(morph
);
1058 hull_set
= isl_set_from_basic_set(hull
);
1059 return add_node(graph
, set
, nvar
, 1, hull_set
, compress
, decompress
);
1061 isl_basic_set_free(hull
);
1063 return isl_stat_error
;
1066 struct isl_extract_edge_data
{
1067 enum isl_edge_type type
;
1068 struct isl_sched_graph
*graph
;
1071 /* Merge edge2 into edge1, freeing the contents of edge2.
1072 * Return 0 on success and -1 on failure.
1074 * edge1 and edge2 are assumed to have the same value for the map field.
1076 static int merge_edge(struct isl_sched_edge
*edge1
,
1077 struct isl_sched_edge
*edge2
)
1079 edge1
->types
|= edge2
->types
;
1080 isl_map_free(edge2
->map
);
1082 if (is_condition(edge2
)) {
1083 if (!edge1
->tagged_condition
)
1084 edge1
->tagged_condition
= edge2
->tagged_condition
;
1086 edge1
->tagged_condition
=
1087 isl_union_map_union(edge1
->tagged_condition
,
1088 edge2
->tagged_condition
);
1091 if (is_conditional_validity(edge2
)) {
1092 if (!edge1
->tagged_validity
)
1093 edge1
->tagged_validity
= edge2
->tagged_validity
;
1095 edge1
->tagged_validity
=
1096 isl_union_map_union(edge1
->tagged_validity
,
1097 edge2
->tagged_validity
);
1100 if (is_condition(edge2
) && !edge1
->tagged_condition
)
1102 if (is_conditional_validity(edge2
) && !edge1
->tagged_validity
)
1108 /* Insert dummy tags in domain and range of "map".
1110 * In particular, if "map" is of the form
1116 * [A -> dummy_tag] -> [B -> dummy_tag]
1118 * where the dummy_tags are identical and equal to any dummy tags
1119 * introduced by any other call to this function.
1121 static __isl_give isl_map
*insert_dummy_tags(__isl_take isl_map
*map
)
1127 isl_set
*domain
, *range
;
1129 ctx
= isl_map_get_ctx(map
);
1131 id
= isl_id_alloc(ctx
, NULL
, &dummy
);
1132 space
= isl_space_params(isl_map_get_space(map
));
1133 space
= isl_space_set_from_params(space
);
1134 space
= isl_space_set_tuple_id(space
, isl_dim_set
, id
);
1135 space
= isl_space_map_from_set(space
);
1137 domain
= isl_map_wrap(map
);
1138 range
= isl_map_wrap(isl_map_universe(space
));
1139 map
= isl_map_from_domain_and_range(domain
, range
);
1140 map
= isl_map_zip(map
);
1145 /* Given that at least one of "src" or "dst" is compressed, return
1146 * a map between the spaces of these nodes restricted to the affine
1147 * hull that was used in the compression.
1149 static __isl_give isl_map
*extract_hull(struct isl_sched_node
*src
,
1150 struct isl_sched_node
*dst
)
1154 if (src
->compressed
)
1155 dom
= isl_set_copy(src
->hull
);
1157 dom
= isl_set_universe(isl_space_copy(src
->space
));
1158 if (dst
->compressed
)
1159 ran
= isl_set_copy(dst
->hull
);
1161 ran
= isl_set_universe(isl_space_copy(dst
->space
));
1163 return isl_map_from_domain_and_range(dom
, ran
);
1166 /* Intersect the domains of the nested relations in domain and range
1167 * of "tagged" with "map".
1169 static __isl_give isl_map
*map_intersect_domains(__isl_take isl_map
*tagged
,
1170 __isl_keep isl_map
*map
)
1174 tagged
= isl_map_zip(tagged
);
1175 set
= isl_map_wrap(isl_map_copy(map
));
1176 tagged
= isl_map_intersect_domain(tagged
, set
);
1177 tagged
= isl_map_zip(tagged
);
1181 /* Return a pointer to the node that lives in the domain space of "map"
1182 * or NULL if there is no such node.
1184 static struct isl_sched_node
*find_domain_node(isl_ctx
*ctx
,
1185 struct isl_sched_graph
*graph
, __isl_keep isl_map
*map
)
1187 struct isl_sched_node
*node
;
1190 space
= isl_space_domain(isl_map_get_space(map
));
1191 node
= graph_find_node(ctx
, graph
, space
);
1192 isl_space_free(space
);
1197 /* Return a pointer to the node that lives in the range space of "map"
1198 * or NULL if there is no such node.
1200 static struct isl_sched_node
*find_range_node(isl_ctx
*ctx
,
1201 struct isl_sched_graph
*graph
, __isl_keep isl_map
*map
)
1203 struct isl_sched_node
*node
;
1206 space
= isl_space_range(isl_map_get_space(map
));
1207 node
= graph_find_node(ctx
, graph
, space
);
1208 isl_space_free(space
);
1213 /* Add a new edge to the graph based on the given map
1214 * and add it to data->graph->edge_table[data->type].
1215 * If a dependence relation of a given type happens to be identical
1216 * to one of the dependence relations of a type that was added before,
1217 * then we don't create a new edge, but instead mark the original edge
1218 * as also representing a dependence of the current type.
1220 * Edges of type isl_edge_condition or isl_edge_conditional_validity
1221 * may be specified as "tagged" dependence relations. That is, "map"
1222 * may contain elements (i -> a) -> (j -> b), where i -> j denotes
1223 * the dependence on iterations and a and b are tags.
1224 * edge->map is set to the relation containing the elements i -> j,
1225 * while edge->tagged_condition and edge->tagged_validity contain
1226 * the union of all the "map" relations
1227 * for which extract_edge is called that result in the same edge->map.
1229 * If the source or the destination node is compressed, then
1230 * intersect both "map" and "tagged" with the constraints that
1231 * were used to construct the compression.
1232 * This ensures that there are no schedule constraints defined
1233 * outside of these domains, while the scheduler no longer has
1234 * any control over those outside parts.
1236 static isl_stat
extract_edge(__isl_take isl_map
*map
, void *user
)
1238 isl_ctx
*ctx
= isl_map_get_ctx(map
);
1239 struct isl_extract_edge_data
*data
= user
;
1240 struct isl_sched_graph
*graph
= data
->graph
;
1241 struct isl_sched_node
*src
, *dst
;
1242 struct isl_sched_edge
*edge
;
1243 isl_map
*tagged
= NULL
;
1245 if (data
->type
== isl_edge_condition
||
1246 data
->type
== isl_edge_conditional_validity
) {
1247 if (isl_map_can_zip(map
)) {
1248 tagged
= isl_map_copy(map
);
1249 map
= isl_set_unwrap(isl_map_domain(isl_map_zip(map
)));
1251 tagged
= insert_dummy_tags(isl_map_copy(map
));
1255 src
= find_domain_node(ctx
, graph
, map
);
1256 dst
= find_range_node(ctx
, graph
, map
);
1260 isl_map_free(tagged
);
1264 if (src
->compressed
|| dst
->compressed
) {
1266 hull
= extract_hull(src
, dst
);
1268 tagged
= map_intersect_domains(tagged
, hull
);
1269 map
= isl_map_intersect(map
, hull
);
1272 graph
->edge
[graph
->n_edge
].src
= src
;
1273 graph
->edge
[graph
->n_edge
].dst
= dst
;
1274 graph
->edge
[graph
->n_edge
].map
= map
;
1275 graph
->edge
[graph
->n_edge
].types
= 0;
1276 graph
->edge
[graph
->n_edge
].tagged_condition
= NULL
;
1277 graph
->edge
[graph
->n_edge
].tagged_validity
= NULL
;
1278 set_type(&graph
->edge
[graph
->n_edge
], data
->type
);
1279 if (data
->type
== isl_edge_condition
)
1280 graph
->edge
[graph
->n_edge
].tagged_condition
=
1281 isl_union_map_from_map(tagged
);
1282 if (data
->type
== isl_edge_conditional_validity
)
1283 graph
->edge
[graph
->n_edge
].tagged_validity
=
1284 isl_union_map_from_map(tagged
);
1286 edge
= graph_find_matching_edge(graph
, &graph
->edge
[graph
->n_edge
]);
1289 return isl_stat_error
;
1291 if (edge
== &graph
->edge
[graph
->n_edge
])
1292 return graph_edge_table_add(ctx
, graph
, data
->type
,
1293 &graph
->edge
[graph
->n_edge
++]);
1295 if (merge_edge(edge
, &graph
->edge
[graph
->n_edge
]) < 0)
1298 return graph_edge_table_add(ctx
, graph
, data
->type
, edge
);
1301 /* Initialize the schedule graph "graph" from the schedule constraints "sc".
1303 * The context is included in the domain before the nodes of
1304 * the graphs are extracted in order to be able to exploit
1305 * any possible additional equalities.
1306 * Note that this intersection is only performed locally here.
1308 static isl_stat
graph_init(struct isl_sched_graph
*graph
,
1309 __isl_keep isl_schedule_constraints
*sc
)
1312 isl_union_set
*domain
;
1314 struct isl_extract_edge_data data
;
1315 enum isl_edge_type i
;
1319 return isl_stat_error
;
1321 ctx
= isl_schedule_constraints_get_ctx(sc
);
1323 domain
= isl_schedule_constraints_get_domain(sc
);
1324 graph
->n
= isl_union_set_n_set(domain
);
1325 isl_union_set_free(domain
);
1327 if (graph_alloc(ctx
, graph
, graph
->n
,
1328 isl_schedule_constraints_n_map(sc
)) < 0)
1329 return isl_stat_error
;
1331 if (compute_max_row(graph
, sc
) < 0)
1332 return isl_stat_error
;
1333 graph
->root
= graph
;
1335 domain
= isl_schedule_constraints_get_domain(sc
);
1336 domain
= isl_union_set_intersect_params(domain
,
1337 isl_schedule_constraints_get_context(sc
));
1338 r
= isl_union_set_foreach_set(domain
, &extract_node
, graph
);
1339 isl_union_set_free(domain
);
1341 return isl_stat_error
;
1342 if (graph_init_table(ctx
, graph
) < 0)
1343 return isl_stat_error
;
1344 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
1345 c
= isl_schedule_constraints_get(sc
, i
);
1346 graph
->max_edge
[i
] = isl_union_map_n_map(c
);
1347 isl_union_map_free(c
);
1349 return isl_stat_error
;
1351 if (graph_init_edge_tables(ctx
, graph
) < 0)
1352 return isl_stat_error
;
1355 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
1359 c
= isl_schedule_constraints_get(sc
, i
);
1360 r
= isl_union_map_foreach_map(c
, &extract_edge
, &data
);
1361 isl_union_map_free(c
);
1363 return isl_stat_error
;
1369 /* Check whether there is any dependence from node[j] to node[i]
1370 * or from node[i] to node[j].
1372 static isl_bool
node_follows_weak(int i
, int j
, void *user
)
1375 struct isl_sched_graph
*graph
= user
;
1377 f
= graph_has_any_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
1380 return graph_has_any_edge(graph
, &graph
->node
[i
], &graph
->node
[j
]);
1383 /* Check whether there is a (conditional) validity dependence from node[j]
1384 * to node[i], forcing node[i] to follow node[j].
1386 static isl_bool
node_follows_strong(int i
, int j
, void *user
)
1388 struct isl_sched_graph
*graph
= user
;
1390 return graph_has_validity_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
1393 /* Use Tarjan's algorithm for computing the strongly connected components
1394 * in the dependence graph only considering those edges defined by "follows".
1396 static int detect_ccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
1397 isl_bool (*follows
)(int i
, int j
, void *user
))
1400 struct isl_tarjan_graph
*g
= NULL
;
1402 g
= isl_tarjan_graph_init(ctx
, graph
->n
, follows
, graph
);
1410 while (g
->order
[i
] != -1) {
1411 graph
->node
[g
->order
[i
]].scc
= graph
->scc
;
1419 isl_tarjan_graph_free(g
);
1424 /* Apply Tarjan's algorithm to detect the strongly connected components
1425 * in the dependence graph.
1426 * Only consider the (conditional) validity dependences and clear "weak".
1428 static int detect_sccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
1431 return detect_ccs(ctx
, graph
, &node_follows_strong
);
1434 /* Apply Tarjan's algorithm to detect the (weakly) connected components
1435 * in the dependence graph.
1436 * Consider all dependences and set "weak".
1438 static int detect_wccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
1441 return detect_ccs(ctx
, graph
, &node_follows_weak
);
1444 static int cmp_scc(const void *a
, const void *b
, void *data
)
1446 struct isl_sched_graph
*graph
= data
;
1450 return graph
->node
[*i1
].scc
- graph
->node
[*i2
].scc
;
1453 /* Sort the elements of graph->sorted according to the corresponding SCCs.
1455 static int sort_sccs(struct isl_sched_graph
*graph
)
1457 return isl_sort(graph
->sorted
, graph
->n
, sizeof(int), &cmp_scc
, graph
);
1460 /* Return a non-parametric set in the compressed space of "node" that is
1461 * bounded by the size in each direction
1463 * { [x] : -S_i <= x_i <= S_i }
1465 * If S_i is infinity in direction i, then there are no constraints
1466 * in that direction.
1468 * Cache the result in node->bounds.
1470 static __isl_give isl_basic_set
*get_size_bounds(struct isl_sched_node
*node
)
1473 isl_basic_set
*bounds
;
1478 return isl_basic_set_copy(node
->bounds
);
1480 if (node
->compressed
)
1481 space
= isl_multi_aff_get_domain_space(node
->decompress
);
1483 space
= isl_space_copy(node
->space
);
1484 nparam
= isl_space_dim(space
, isl_dim_param
);
1485 space
= isl_space_drop_dims(space
, isl_dim_param
, 0, nparam
);
1486 bounds
= isl_basic_set_universe(space
);
1488 for (i
= 0; i
< node
->nvar
; ++i
) {
1491 size
= isl_multi_val_get_val(node
->sizes
, i
);
1493 return isl_basic_set_free(bounds
);
1494 if (!isl_val_is_int(size
)) {
1498 bounds
= isl_basic_set_upper_bound_val(bounds
, isl_dim_set
, i
,
1499 isl_val_copy(size
));
1500 bounds
= isl_basic_set_lower_bound_val(bounds
, isl_dim_set
, i
,
1504 node
->bounds
= isl_basic_set_copy(bounds
);
1508 /* Drop some constraints from "delta" that could be exploited
1509 * to construct loop coalescing schedules.
1510 * In particular, drop those constraint that bound the difference
1511 * to the size of the domain.
1512 * First project out the parameters to improve the effectiveness.
1514 static __isl_give isl_set
*drop_coalescing_constraints(
1515 __isl_take isl_set
*delta
, struct isl_sched_node
*node
)
1518 isl_basic_set
*bounds
;
1520 bounds
= get_size_bounds(node
);
1522 nparam
= isl_set_dim(delta
, isl_dim_param
);
1523 delta
= isl_set_project_out(delta
, isl_dim_param
, 0, nparam
);
1524 delta
= isl_set_remove_divs(delta
);
1525 delta
= isl_set_plain_gist_basic_set(delta
, bounds
);
1529 /* Given a dependence relation R from "node" to itself,
1530 * construct the set of coefficients of valid constraints for elements
1531 * in that dependence relation.
1532 * In particular, the result contains tuples of coefficients
1533 * c_0, c_n, c_x such that
1535 * c_0 + c_n n + c_x y - c_x x >= 0 for each (x,y) in R
1539 * c_0 + c_n n + c_x d >= 0 for each d in delta R = { y - x | (x,y) in R }
1541 * We choose here to compute the dual of delta R.
1542 * Alternatively, we could have computed the dual of R, resulting
1543 * in a set of tuples c_0, c_n, c_x, c_y, and then
1544 * plugged in (c_0, c_n, c_x, -c_x).
1546 * If "need_param" is set, then the resulting coefficients effectively
1547 * include coefficients for the parameters c_n. Otherwise, they may
1548 * have been projected out already.
1549 * Since the constraints may be different for these two cases,
1550 * they are stored in separate caches.
1551 * In particular, if no parameter coefficients are required and
1552 * the schedule_treat_coalescing option is set, then the parameters
1553 * are projected out and some constraints that could be exploited
1554 * to construct coalescing schedules are removed before the dual
1557 * If "node" has been compressed, then the dependence relation
1558 * is also compressed before the set of coefficients is computed.
1560 static __isl_give isl_basic_set
*intra_coefficients(
1561 struct isl_sched_graph
*graph
, struct isl_sched_node
*node
,
1562 __isl_take isl_map
*map
, int need_param
)
1567 isl_basic_set
*coef
;
1568 isl_maybe_isl_basic_set m
;
1569 isl_map_to_basic_set
**hmap
= &graph
->intra_hmap
;
1575 ctx
= isl_map_get_ctx(map
);
1576 treat
= !need_param
&& isl_options_get_schedule_treat_coalescing(ctx
);
1578 hmap
= &graph
->intra_hmap_param
;
1579 m
= isl_map_to_basic_set_try_get(*hmap
, map
);
1580 if (m
.valid
< 0 || m
.valid
) {
1585 key
= isl_map_copy(map
);
1586 if (node
->compressed
) {
1587 map
= isl_map_preimage_domain_multi_aff(map
,
1588 isl_multi_aff_copy(node
->decompress
));
1589 map
= isl_map_preimage_range_multi_aff(map
,
1590 isl_multi_aff_copy(node
->decompress
));
1592 delta
= isl_map_deltas(map
);
1594 delta
= drop_coalescing_constraints(delta
, node
);
1595 delta
= isl_set_remove_divs(delta
);
1596 coef
= isl_set_coefficients(delta
);
1597 *hmap
= isl_map_to_basic_set_set(*hmap
, key
, isl_basic_set_copy(coef
));
1602 /* Given a dependence relation R, construct the set of coefficients
1603 * of valid constraints for elements in that dependence relation.
1604 * In particular, the result contains tuples of coefficients
1605 * c_0, c_n, c_x, c_y such that
1607 * c_0 + c_n n + c_x x + c_y y >= 0 for each (x,y) in R
1609 * If the source or destination nodes of "edge" have been compressed,
1610 * then the dependence relation is also compressed before
1611 * the set of coefficients is computed.
1613 static __isl_give isl_basic_set
*inter_coefficients(
1614 struct isl_sched_graph
*graph
, struct isl_sched_edge
*edge
,
1615 __isl_take isl_map
*map
)
1619 isl_basic_set
*coef
;
1620 isl_maybe_isl_basic_set m
;
1622 m
= isl_map_to_basic_set_try_get(graph
->inter_hmap
, map
);
1623 if (m
.valid
< 0 || m
.valid
) {
1628 key
= isl_map_copy(map
);
1629 if (edge
->src
->compressed
)
1630 map
= isl_map_preimage_domain_multi_aff(map
,
1631 isl_multi_aff_copy(edge
->src
->decompress
));
1632 if (edge
->dst
->compressed
)
1633 map
= isl_map_preimage_range_multi_aff(map
,
1634 isl_multi_aff_copy(edge
->dst
->decompress
));
1635 set
= isl_map_wrap(isl_map_remove_divs(map
));
1636 coef
= isl_set_coefficients(set
);
1637 graph
->inter_hmap
= isl_map_to_basic_set_set(graph
->inter_hmap
, key
,
1638 isl_basic_set_copy(coef
));
1643 /* Return the position of the coefficients of the variables in
1644 * the coefficients constraints "coef".
1646 * The space of "coef" is of the form
1648 * { coefficients[[cst, params] -> S] }
1650 * Return the position of S.
1652 static int coef_var_offset(__isl_keep isl_basic_set
*coef
)
1657 space
= isl_space_unwrap(isl_basic_set_get_space(coef
));
1658 offset
= isl_space_dim(space
, isl_dim_in
);
1659 isl_space_free(space
);
1664 /* Return the offset of the coefficient of the constant term of "node"
1667 * Within each node, the coefficients have the following order:
1668 * - positive and negative parts of c_i_x
1669 * - c_i_n (if parametric)
1672 static int node_cst_coef_offset(struct isl_sched_node
*node
)
1674 return node
->start
+ 2 * node
->nvar
+ node
->nparam
;
1677 /* Return the offset of the coefficients of the parameters of "node"
1680 * Within each node, the coefficients have the following order:
1681 * - positive and negative parts of c_i_x
1682 * - c_i_n (if parametric)
1685 static int node_par_coef_offset(struct isl_sched_node
*node
)
1687 return node
->start
+ 2 * node
->nvar
;
1690 /* Return the offset of the coefficients of the variables of "node"
1693 * Within each node, the coefficients have the following order:
1694 * - positive and negative parts of c_i_x
1695 * - c_i_n (if parametric)
1698 static int node_var_coef_offset(struct isl_sched_node
*node
)
1703 /* Return the position of the pair of variables encoding
1704 * coefficient "i" of "node".
1706 * The order of these variable pairs is the opposite of
1707 * that of the coefficients, with 2 variables per coefficient.
1709 static int node_var_coef_pos(struct isl_sched_node
*node
, int i
)
1711 return node_var_coef_offset(node
) + 2 * (node
->nvar
- 1 - i
);
1714 /* Construct an isl_dim_map for mapping constraints on coefficients
1715 * for "node" to the corresponding positions in graph->lp.
1716 * "offset" is the offset of the coefficients for the variables
1717 * in the input constraints.
1718 * "s" is the sign of the mapping.
1720 * The input constraints are given in terms of the coefficients
1721 * (c_0, c_x) or (c_0, c_n, c_x).
1722 * The mapping produced by this function essentially plugs in
1723 * (0, c_i_x^+ - c_i_x^-) if s = 1 and
1724 * (0, -c_i_x^+ + c_i_x^-) if s = -1 or
1725 * (0, 0, c_i_x^+ - c_i_x^-) if s = 1 and
1726 * (0, 0, -c_i_x^+ + c_i_x^-) if s = -1.
1727 * In graph->lp, the c_i_x^- appear before their c_i_x^+ counterpart.
1728 * Furthermore, the order of these pairs is the opposite of that
1729 * of the corresponding coefficients.
1731 * The caller can extend the mapping to also map the other coefficients
1732 * (and therefore not plug in 0).
1734 static __isl_give isl_dim_map
*intra_dim_map(isl_ctx
*ctx
,
1735 struct isl_sched_graph
*graph
, struct isl_sched_node
*node
,
1740 isl_dim_map
*dim_map
;
1745 total
= isl_basic_set_total_dim(graph
->lp
);
1746 pos
= node_var_coef_pos(node
, 0);
1747 dim_map
= isl_dim_map_alloc(ctx
, total
);
1748 isl_dim_map_range(dim_map
, pos
, -2, offset
, 1, node
->nvar
, -s
);
1749 isl_dim_map_range(dim_map
, pos
+ 1, -2, offset
, 1, node
->nvar
, s
);
1754 /* Construct an isl_dim_map for mapping constraints on coefficients
1755 * for "src" (node i) and "dst" (node j) to the corresponding positions
1757 * "offset" is the offset of the coefficients for the variables of "src"
1758 * in the input constraints.
1759 * "s" is the sign of the mapping.
1761 * The input constraints are given in terms of the coefficients
1762 * (c_0, c_n, c_x, c_y).
1763 * The mapping produced by this function essentially plugs in
1764 * (c_j_0 - c_i_0, c_j_n - c_i_n,
1765 * -(c_i_x^+ - c_i_x^-), c_j_x^+ - c_j_x^-) if s = 1 and
1766 * (-c_j_0 + c_i_0, -c_j_n + c_i_n,
1767 * c_i_x^+ - c_i_x^-, -(c_j_x^+ - c_j_x^-)) if s = -1.
1768 * In graph->lp, the c_*^- appear before their c_*^+ counterpart.
1769 * Furthermore, the order of these pairs is the opposite of that
1770 * of the corresponding coefficients.
1772 * The caller can further extend the mapping.
1774 static __isl_give isl_dim_map
*inter_dim_map(isl_ctx
*ctx
,
1775 struct isl_sched_graph
*graph
, struct isl_sched_node
*src
,
1776 struct isl_sched_node
*dst
, int offset
, int s
)
1780 isl_dim_map
*dim_map
;
1785 total
= isl_basic_set_total_dim(graph
->lp
);
1786 dim_map
= isl_dim_map_alloc(ctx
, total
);
1788 pos
= node_cst_coef_offset(dst
);
1789 isl_dim_map_range(dim_map
, pos
, 0, 0, 0, 1, s
);
1790 pos
= node_par_coef_offset(dst
);
1791 isl_dim_map_range(dim_map
, pos
, 1, 1, 1, dst
->nparam
, s
);
1792 pos
= node_var_coef_pos(dst
, 0);
1793 isl_dim_map_range(dim_map
, pos
, -2, offset
+ src
->nvar
, 1,
1795 isl_dim_map_range(dim_map
, pos
+ 1, -2, offset
+ src
->nvar
, 1,
1798 pos
= node_cst_coef_offset(src
);
1799 isl_dim_map_range(dim_map
, pos
, 0, 0, 0, 1, -s
);
1800 pos
= node_par_coef_offset(src
);
1801 isl_dim_map_range(dim_map
, pos
, 1, 1, 1, src
->nparam
, -s
);
1802 pos
= node_var_coef_pos(src
, 0);
1803 isl_dim_map_range(dim_map
, pos
, -2, offset
, 1, src
->nvar
, s
);
1804 isl_dim_map_range(dim_map
, pos
+ 1, -2, offset
, 1, src
->nvar
, -s
);
1809 /* Add the constraints from "src" to "dst" using "dim_map",
1810 * after making sure there is enough room in "dst" for the extra constraints.
1812 static __isl_give isl_basic_set
*add_constraints_dim_map(
1813 __isl_take isl_basic_set
*dst
, __isl_take isl_basic_set
*src
,
1814 __isl_take isl_dim_map
*dim_map
)
1818 n_eq
= isl_basic_set_n_equality(src
);
1819 n_ineq
= isl_basic_set_n_inequality(src
);
1820 dst
= isl_basic_set_extend_constraints(dst
, n_eq
, n_ineq
);
1821 dst
= isl_basic_set_add_constraints_dim_map(dst
, src
, dim_map
);
1825 /* Add constraints to graph->lp that force validity for the given
1826 * dependence from a node i to itself.
1827 * That is, add constraints that enforce
1829 * (c_i_0 + c_i_n n + c_i_x y) - (c_i_0 + c_i_n n + c_i_x x)
1830 * = c_i_x (y - x) >= 0
1832 * for each (x,y) in R.
1833 * We obtain general constraints on coefficients (c_0, c_x)
1834 * of valid constraints for (y - x) and then plug in (0, c_i_x^+ - c_i_x^-),
1835 * where c_i_x = c_i_x^+ - c_i_x^-, with c_i_x^+ and c_i_x^- non-negative.
1836 * In graph->lp, the c_i_x^- appear before their c_i_x^+ counterpart.
1837 * Note that the result of intra_coefficients may also contain
1838 * parameter coefficients c_n, in which case 0 is plugged in for them as well.
1840 static isl_stat
add_intra_validity_constraints(struct isl_sched_graph
*graph
,
1841 struct isl_sched_edge
*edge
)
1844 isl_map
*map
= isl_map_copy(edge
->map
);
1845 isl_ctx
*ctx
= isl_map_get_ctx(map
);
1846 isl_dim_map
*dim_map
;
1847 isl_basic_set
*coef
;
1848 struct isl_sched_node
*node
= edge
->src
;
1850 coef
= intra_coefficients(graph
, node
, map
, 0);
1852 offset
= coef_var_offset(coef
);
1855 return isl_stat_error
;
1857 dim_map
= intra_dim_map(ctx
, graph
, node
, offset
, 1);
1858 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
1863 /* Add constraints to graph->lp that force validity for the given
1864 * dependence from node i to node j.
1865 * That is, add constraints that enforce
1867 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) >= 0
1869 * for each (x,y) in R.
1870 * We obtain general constraints on coefficients (c_0, c_n, c_x, c_y)
1871 * of valid constraints for R and then plug in
1872 * (c_j_0 - c_i_0, c_j_n - c_i_n, -(c_i_x^+ - c_i_x^-), c_j_x^+ - c_j_x^-),
1873 * where c_* = c_*^+ - c_*^-, with c_*^+ and c_*^- non-negative.
1874 * In graph->lp, the c_*^- appear before their c_*^+ counterpart.
1876 static isl_stat
add_inter_validity_constraints(struct isl_sched_graph
*graph
,
1877 struct isl_sched_edge
*edge
)
1882 isl_dim_map
*dim_map
;
1883 isl_basic_set
*coef
;
1884 struct isl_sched_node
*src
= edge
->src
;
1885 struct isl_sched_node
*dst
= edge
->dst
;
1888 return isl_stat_error
;
1890 map
= isl_map_copy(edge
->map
);
1891 ctx
= isl_map_get_ctx(map
);
1892 coef
= inter_coefficients(graph
, edge
, map
);
1894 offset
= coef_var_offset(coef
);
1897 return isl_stat_error
;
1899 dim_map
= inter_dim_map(ctx
, graph
, src
, dst
, offset
, 1);
1901 edge
->start
= graph
->lp
->n_ineq
;
1902 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
1904 return isl_stat_error
;
1905 edge
->end
= graph
->lp
->n_ineq
;
1910 /* Add constraints to graph->lp that bound the dependence distance for the given
1911 * dependence from a node i to itself.
1912 * If s = 1, we add the constraint
1914 * c_i_x (y - x) <= m_0 + m_n n
1918 * -c_i_x (y - x) + m_0 + m_n n >= 0
1920 * for each (x,y) in R.
1921 * If s = -1, we add the constraint
1923 * -c_i_x (y - x) <= m_0 + m_n n
1927 * c_i_x (y - x) + m_0 + m_n n >= 0
1929 * for each (x,y) in R.
1930 * We obtain general constraints on coefficients (c_0, c_n, c_x)
1931 * of valid constraints for (y - x) and then plug in (m_0, m_n, -s * c_i_x),
1932 * with each coefficient (except m_0) represented as a pair of non-negative
1936 * If "local" is set, then we add constraints
1938 * c_i_x (y - x) <= 0
1942 * -c_i_x (y - x) <= 0
1944 * instead, forcing the dependence distance to be (less than or) equal to 0.
1945 * That is, we plug in (0, 0, -s * c_i_x),
1946 * intra_coefficients is not required to have c_n in its result when
1947 * "local" is set. If they are missing, then (0, -s * c_i_x) is plugged in.
1948 * Note that dependences marked local are treated as validity constraints
1949 * by add_all_validity_constraints and therefore also have
1950 * their distances bounded by 0 from below.
1952 static isl_stat
add_intra_proximity_constraints(struct isl_sched_graph
*graph
,
1953 struct isl_sched_edge
*edge
, int s
, int local
)
1957 isl_map
*map
= isl_map_copy(edge
->map
);
1958 isl_ctx
*ctx
= isl_map_get_ctx(map
);
1959 isl_dim_map
*dim_map
;
1960 isl_basic_set
*coef
;
1961 struct isl_sched_node
*node
= edge
->src
;
1963 coef
= intra_coefficients(graph
, node
, map
, !local
);
1965 offset
= coef_var_offset(coef
);
1968 return isl_stat_error
;
1970 nparam
= isl_space_dim(node
->space
, isl_dim_param
);
1971 dim_map
= intra_dim_map(ctx
, graph
, node
, offset
, -s
);
1974 isl_dim_map_range(dim_map
, 1, 0, 0, 0, 1, 1);
1975 isl_dim_map_range(dim_map
, 4, 2, 1, 1, nparam
, -1);
1976 isl_dim_map_range(dim_map
, 5, 2, 1, 1, nparam
, 1);
1978 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
1983 /* Add constraints to graph->lp that bound the dependence distance for the given
1984 * dependence from node i to node j.
1985 * If s = 1, we add the constraint
1987 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x)
1992 * -(c_j_0 + c_j_n n + c_j_x y) + (c_i_0 + c_i_n n + c_i_x x) +
1995 * for each (x,y) in R.
1996 * If s = -1, we add the constraint
1998 * -((c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x))
2003 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) +
2006 * for each (x,y) in R.
2007 * We obtain general constraints on coefficients (c_0, c_n, c_x, c_y)
2008 * of valid constraints for R and then plug in
2009 * (m_0 - s*c_j_0 + s*c_i_0, m_n - s*c_j_n + s*c_i_n,
2010 * s*c_i_x, -s*c_j_x)
2011 * with each coefficient (except m_0, c_*_0 and c_*_n)
2012 * represented as a pair of non-negative coefficients.
2015 * If "local" is set (and s = 1), then we add constraints
2017 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) <= 0
2021 * -((c_j_0 + c_j_n n + c_j_x y) + (c_i_0 + c_i_n n + c_i_x x)) >= 0
2023 * instead, forcing the dependence distance to be (less than or) equal to 0.
2024 * That is, we plug in
2025 * (-s*c_j_0 + s*c_i_0, -s*c_j_n + s*c_i_n, s*c_i_x, -s*c_j_x).
2026 * Note that dependences marked local are treated as validity constraints
2027 * by add_all_validity_constraints and therefore also have
2028 * their distances bounded by 0 from below.
2030 static isl_stat
add_inter_proximity_constraints(struct isl_sched_graph
*graph
,
2031 struct isl_sched_edge
*edge
, int s
, int local
)
2035 isl_map
*map
= isl_map_copy(edge
->map
);
2036 isl_ctx
*ctx
= isl_map_get_ctx(map
);
2037 isl_dim_map
*dim_map
;
2038 isl_basic_set
*coef
;
2039 struct isl_sched_node
*src
= edge
->src
;
2040 struct isl_sched_node
*dst
= edge
->dst
;
2042 coef
= inter_coefficients(graph
, edge
, map
);
2044 offset
= coef_var_offset(coef
);
2047 return isl_stat_error
;
2049 nparam
= isl_space_dim(src
->space
, isl_dim_param
);
2050 dim_map
= inter_dim_map(ctx
, graph
, src
, dst
, offset
, -s
);
2053 isl_dim_map_range(dim_map
, 1, 0, 0, 0, 1, 1);
2054 isl_dim_map_range(dim_map
, 4, 2, 1, 1, nparam
, -1);
2055 isl_dim_map_range(dim_map
, 5, 2, 1, 1, nparam
, 1);
2058 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
2063 /* Should the distance over "edge" be forced to zero?
2064 * That is, is it marked as a local edge?
2065 * If "use_coincidence" is set, then coincidence edges are treated
2068 static int force_zero(struct isl_sched_edge
*edge
, int use_coincidence
)
2070 return is_local(edge
) || (use_coincidence
&& is_coincidence(edge
));
2073 /* Add all validity constraints to graph->lp.
2075 * An edge that is forced to be local needs to have its dependence
2076 * distances equal to zero. We take care of bounding them by 0 from below
2077 * here. add_all_proximity_constraints takes care of bounding them by 0
2080 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2081 * Otherwise, we ignore them.
2083 static int add_all_validity_constraints(struct isl_sched_graph
*graph
,
2084 int use_coincidence
)
2088 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2089 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
2092 zero
= force_zero(edge
, use_coincidence
);
2093 if (!is_validity(edge
) && !zero
)
2095 if (edge
->src
!= edge
->dst
)
2097 if (add_intra_validity_constraints(graph
, edge
) < 0)
2101 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2102 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
2105 zero
= force_zero(edge
, use_coincidence
);
2106 if (!is_validity(edge
) && !zero
)
2108 if (edge
->src
== edge
->dst
)
2110 if (add_inter_validity_constraints(graph
, edge
) < 0)
2117 /* Add constraints to graph->lp that bound the dependence distance
2118 * for all dependence relations.
2119 * If a given proximity dependence is identical to a validity
2120 * dependence, then the dependence distance is already bounded
2121 * from below (by zero), so we only need to bound the distance
2122 * from above. (This includes the case of "local" dependences
2123 * which are treated as validity dependence by add_all_validity_constraints.)
2124 * Otherwise, we need to bound the distance both from above and from below.
2126 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2127 * Otherwise, we ignore them.
2129 static int add_all_proximity_constraints(struct isl_sched_graph
*graph
,
2130 int use_coincidence
)
2134 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2135 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
2138 zero
= force_zero(edge
, use_coincidence
);
2139 if (!is_proximity(edge
) && !zero
)
2141 if (edge
->src
== edge
->dst
&&
2142 add_intra_proximity_constraints(graph
, edge
, 1, zero
) < 0)
2144 if (edge
->src
!= edge
->dst
&&
2145 add_inter_proximity_constraints(graph
, edge
, 1, zero
) < 0)
2147 if (is_validity(edge
) || zero
)
2149 if (edge
->src
== edge
->dst
&&
2150 add_intra_proximity_constraints(graph
, edge
, -1, 0) < 0)
2152 if (edge
->src
!= edge
->dst
&&
2153 add_inter_proximity_constraints(graph
, edge
, -1, 0) < 0)
2160 /* Normalize the rows of "indep" such that all rows are lexicographically
2161 * positive and such that each row contains as many final zeros as possible,
2162 * given the choice for the previous rows.
2163 * Do this by performing elementary row operations.
2165 static __isl_give isl_mat
*normalize_independent(__isl_take isl_mat
*indep
)
2167 indep
= isl_mat_reverse_gauss(indep
);
2168 indep
= isl_mat_lexnonneg_rows(indep
);
2172 /* Compute a basis for the rows in the linear part of the schedule
2173 * and extend this basis to a full basis. The remaining rows
2174 * can then be used to force linear independence from the rows
2177 * In particular, given the schedule rows S, we compute
2182 * with H the Hermite normal form of S. That is, all but the
2183 * first rank columns of H are zero and so each row in S is
2184 * a linear combination of the first rank rows of Q.
2185 * The matrix Q can be used as a variable transformation
2186 * that isolates the directions of S in the first rank rows.
2187 * Transposing S U = H yields
2191 * with all but the first rank rows of H^T zero.
2192 * The last rows of U^T are therefore linear combinations
2193 * of schedule coefficients that are all zero on schedule
2194 * coefficients that are linearly dependent on the rows of S.
2195 * At least one of these combinations is non-zero on
2196 * linearly independent schedule coefficients.
2197 * The rows are normalized to involve as few of the last
2198 * coefficients as possible and to have a positive initial value.
2200 static int node_update_vmap(struct isl_sched_node
*node
)
2203 int n_row
= isl_mat_rows(node
->sched
);
2205 H
= isl_mat_sub_alloc(node
->sched
, 0, n_row
,
2206 1 + node
->nparam
, node
->nvar
);
2208 H
= isl_mat_left_hermite(H
, 0, &U
, &Q
);
2209 isl_mat_free(node
->indep
);
2210 isl_mat_free(node
->vmap
);
2212 node
->indep
= isl_mat_transpose(U
);
2213 node
->rank
= isl_mat_initial_non_zero_cols(H
);
2214 node
->indep
= isl_mat_drop_rows(node
->indep
, 0, node
->rank
);
2215 node
->indep
= normalize_independent(node
->indep
);
2218 if (!node
->indep
|| !node
->vmap
|| node
->rank
< 0)
2223 /* Is "edge" marked as a validity or a conditional validity edge?
2225 static int is_any_validity(struct isl_sched_edge
*edge
)
2227 return is_validity(edge
) || is_conditional_validity(edge
);
2230 /* How many times should we count the constraints in "edge"?
2232 * We count as follows
2233 * validity -> 1 (>= 0)
2234 * validity+proximity -> 2 (>= 0 and upper bound)
2235 * proximity -> 2 (lower and upper bound)
2236 * local(+any) -> 2 (>= 0 and <= 0)
2238 * If an edge is only marked conditional_validity then it counts
2239 * as zero since it is only checked afterwards.
2241 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2242 * Otherwise, we ignore them.
2244 static int edge_multiplicity(struct isl_sched_edge
*edge
, int use_coincidence
)
2246 if (is_proximity(edge
) || force_zero(edge
, use_coincidence
))
2248 if (is_validity(edge
))
2253 /* How many times should the constraints in "edge" be counted
2254 * as a parametric intra-node constraint?
2256 * Only proximity edges that are not forced zero need
2257 * coefficient constraints that include coefficients for parameters.
2258 * If the edge is also a validity edge, then only
2259 * an upper bound is introduced. Otherwise, both lower and upper bounds
2262 static int parametric_intra_edge_multiplicity(struct isl_sched_edge
*edge
,
2263 int use_coincidence
)
2265 if (edge
->src
!= edge
->dst
)
2267 if (!is_proximity(edge
))
2269 if (force_zero(edge
, use_coincidence
))
2271 if (is_validity(edge
))
2277 /* Add "f" times the number of equality and inequality constraints of "bset"
2278 * to "n_eq" and "n_ineq" and free "bset".
2280 static isl_stat
update_count(__isl_take isl_basic_set
*bset
,
2281 int f
, int *n_eq
, int *n_ineq
)
2284 return isl_stat_error
;
2286 *n_eq
+= isl_basic_set_n_equality(bset
);
2287 *n_ineq
+= isl_basic_set_n_inequality(bset
);
2288 isl_basic_set_free(bset
);
2293 /* Count the number of equality and inequality constraints
2294 * that will be added for the given map.
2296 * The edges that require parameter coefficients are counted separately.
2298 * "use_coincidence" is set if we should take into account coincidence edges.
2300 static isl_stat
count_map_constraints(struct isl_sched_graph
*graph
,
2301 struct isl_sched_edge
*edge
, __isl_take isl_map
*map
,
2302 int *n_eq
, int *n_ineq
, int use_coincidence
)
2305 isl_basic_set
*coef
;
2306 int f
= edge_multiplicity(edge
, use_coincidence
);
2307 int fp
= parametric_intra_edge_multiplicity(edge
, use_coincidence
);
2314 if (edge
->src
!= edge
->dst
) {
2315 coef
= inter_coefficients(graph
, edge
, map
);
2316 return update_count(coef
, f
, n_eq
, n_ineq
);
2320 copy
= isl_map_copy(map
);
2321 coef
= intra_coefficients(graph
, edge
->src
, copy
, 1);
2322 if (update_count(coef
, fp
, n_eq
, n_ineq
) < 0)
2327 copy
= isl_map_copy(map
);
2328 coef
= intra_coefficients(graph
, edge
->src
, copy
, 0);
2329 if (update_count(coef
, f
- fp
, n_eq
, n_ineq
) < 0)
2337 return isl_stat_error
;
2340 /* Count the number of equality and inequality constraints
2341 * that will be added to the main lp problem.
2342 * We count as follows
2343 * validity -> 1 (>= 0)
2344 * validity+proximity -> 2 (>= 0 and upper bound)
2345 * proximity -> 2 (lower and upper bound)
2346 * local(+any) -> 2 (>= 0 and <= 0)
2348 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2349 * Otherwise, we ignore them.
2351 static int count_constraints(struct isl_sched_graph
*graph
,
2352 int *n_eq
, int *n_ineq
, int use_coincidence
)
2356 *n_eq
= *n_ineq
= 0;
2357 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2358 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
2359 isl_map
*map
= isl_map_copy(edge
->map
);
2361 if (count_map_constraints(graph
, edge
, map
, n_eq
, n_ineq
,
2362 use_coincidence
) < 0)
2369 /* Count the number of constraints that will be added by
2370 * add_bound_constant_constraints to bound the values of the constant terms
2371 * and increment *n_eq and *n_ineq accordingly.
2373 * In practice, add_bound_constant_constraints only adds inequalities.
2375 static isl_stat
count_bound_constant_constraints(isl_ctx
*ctx
,
2376 struct isl_sched_graph
*graph
, int *n_eq
, int *n_ineq
)
2378 if (isl_options_get_schedule_max_constant_term(ctx
) == -1)
2381 *n_ineq
+= graph
->n
;
2386 /* Add constraints to bound the values of the constant terms in the schedule,
2387 * if requested by the user.
2389 * The maximal value of the constant terms is defined by the option
2390 * "schedule_max_constant_term".
2392 static isl_stat
add_bound_constant_constraints(isl_ctx
*ctx
,
2393 struct isl_sched_graph
*graph
)
2399 max
= isl_options_get_schedule_max_constant_term(ctx
);
2403 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2405 for (i
= 0; i
< graph
->n
; ++i
) {
2406 struct isl_sched_node
*node
= &graph
->node
[i
];
2409 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2411 return isl_stat_error
;
2412 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
2413 pos
= node_cst_coef_offset(node
);
2414 isl_int_set_si(graph
->lp
->ineq
[k
][1 + pos
], -1);
2415 isl_int_set_si(graph
->lp
->ineq
[k
][0], max
);
2421 /* Count the number of constraints that will be added by
2422 * add_bound_coefficient_constraints and increment *n_eq and *n_ineq
2425 * In practice, add_bound_coefficient_constraints only adds inequalities.
2427 static int count_bound_coefficient_constraints(isl_ctx
*ctx
,
2428 struct isl_sched_graph
*graph
, int *n_eq
, int *n_ineq
)
2432 if (isl_options_get_schedule_max_coefficient(ctx
) == -1 &&
2433 !isl_options_get_schedule_treat_coalescing(ctx
))
2436 for (i
= 0; i
< graph
->n
; ++i
)
2437 *n_ineq
+= graph
->node
[i
].nparam
+ 2 * graph
->node
[i
].nvar
;
2442 /* Add constraints to graph->lp that bound the values of
2443 * the parameter schedule coefficients of "node" to "max" and
2444 * the variable schedule coefficients to the corresponding entry
2446 * In either case, a negative value means that no bound needs to be imposed.
2448 * For parameter coefficients, this amounts to adding a constraint
2456 * The variables coefficients are, however, not represented directly.
2457 * Instead, the variable coefficients c_x are written as differences
2458 * c_x = c_x^+ - c_x^-.
2461 * -max_i <= c_x_i <= max_i
2465 * -max_i <= c_x_i^+ - c_x_i^- <= max_i
2469 * -(c_x_i^+ - c_x_i^-) + max_i >= 0
2470 * c_x_i^+ - c_x_i^- + max_i >= 0
2472 static isl_stat
node_add_coefficient_constraints(isl_ctx
*ctx
,
2473 struct isl_sched_graph
*graph
, struct isl_sched_node
*node
, int max
)
2479 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2481 for (j
= 0; j
< node
->nparam
; ++j
) {
2487 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2489 return isl_stat_error
;
2490 dim
= 1 + node_par_coef_offset(node
) + j
;
2491 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
2492 isl_int_set_si(graph
->lp
->ineq
[k
][dim
], -1);
2493 isl_int_set_si(graph
->lp
->ineq
[k
][0], max
);
2496 ineq
= isl_vec_alloc(ctx
, 1 + total
);
2497 ineq
= isl_vec_clr(ineq
);
2499 return isl_stat_error
;
2500 for (i
= 0; i
< node
->nvar
; ++i
) {
2501 int pos
= 1 + node_var_coef_pos(node
, i
);
2503 if (isl_int_is_neg(node
->max
->el
[i
]))
2506 isl_int_set_si(ineq
->el
[pos
], 1);
2507 isl_int_set_si(ineq
->el
[pos
+ 1], -1);
2508 isl_int_set(ineq
->el
[0], node
->max
->el
[i
]);
2510 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2513 isl_seq_cpy(graph
->lp
->ineq
[k
], ineq
->el
, 1 + total
);
2515 isl_seq_neg(ineq
->el
+ pos
, ineq
->el
+ pos
, 2);
2516 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2519 isl_seq_cpy(graph
->lp
->ineq
[k
], ineq
->el
, 1 + total
);
2521 isl_seq_clr(ineq
->el
+ pos
, 2);
2528 return isl_stat_error
;
2531 /* Add constraints that bound the values of the variable and parameter
2532 * coefficients of the schedule.
2534 * The maximal value of the coefficients is defined by the option
2535 * 'schedule_max_coefficient' and the entries in node->max.
2536 * These latter entries are only set if either the schedule_max_coefficient
2537 * option or the schedule_treat_coalescing option is set.
2539 static isl_stat
add_bound_coefficient_constraints(isl_ctx
*ctx
,
2540 struct isl_sched_graph
*graph
)
2545 max
= isl_options_get_schedule_max_coefficient(ctx
);
2547 if (max
== -1 && !isl_options_get_schedule_treat_coalescing(ctx
))
2550 for (i
= 0; i
< graph
->n
; ++i
) {
2551 struct isl_sched_node
*node
= &graph
->node
[i
];
2553 if (node_add_coefficient_constraints(ctx
, graph
, node
, max
) < 0)
2554 return isl_stat_error
;
2560 /* Add a constraint to graph->lp that equates the value at position
2561 * "sum_pos" to the sum of the "n" values starting at "first".
2563 static isl_stat
add_sum_constraint(struct isl_sched_graph
*graph
,
2564 int sum_pos
, int first
, int n
)
2569 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2571 k
= isl_basic_set_alloc_equality(graph
->lp
);
2573 return isl_stat_error
;
2574 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2575 isl_int_set_si(graph
->lp
->eq
[k
][1 + sum_pos
], -1);
2576 for (i
= 0; i
< n
; ++i
)
2577 isl_int_set_si(graph
->lp
->eq
[k
][1 + first
+ i
], 1);
2582 /* Add a constraint to graph->lp that equates the value at position
2583 * "sum_pos" to the sum of the parameter coefficients of all nodes.
2585 static isl_stat
add_param_sum_constraint(struct isl_sched_graph
*graph
,
2591 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2593 k
= isl_basic_set_alloc_equality(graph
->lp
);
2595 return isl_stat_error
;
2596 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2597 isl_int_set_si(graph
->lp
->eq
[k
][1 + sum_pos
], -1);
2598 for (i
= 0; i
< graph
->n
; ++i
) {
2599 int pos
= 1 + node_par_coef_offset(&graph
->node
[i
]);
2601 for (j
= 0; j
< graph
->node
[i
].nparam
; ++j
)
2602 isl_int_set_si(graph
->lp
->eq
[k
][pos
+ j
], 1);
2608 /* Add a constraint to graph->lp that equates the value at position
2609 * "sum_pos" to the sum of the variable coefficients of all nodes.
2611 static isl_stat
add_var_sum_constraint(struct isl_sched_graph
*graph
,
2617 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2619 k
= isl_basic_set_alloc_equality(graph
->lp
);
2621 return isl_stat_error
;
2622 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2623 isl_int_set_si(graph
->lp
->eq
[k
][1 + sum_pos
], -1);
2624 for (i
= 0; i
< graph
->n
; ++i
) {
2625 struct isl_sched_node
*node
= &graph
->node
[i
];
2626 int pos
= 1 + node_var_coef_offset(node
);
2628 for (j
= 0; j
< 2 * node
->nvar
; ++j
)
2629 isl_int_set_si(graph
->lp
->eq
[k
][pos
+ j
], 1);
2635 /* Construct an ILP problem for finding schedule coefficients
2636 * that result in non-negative, but small dependence distances
2637 * over all dependences.
2638 * In particular, the dependence distances over proximity edges
2639 * are bounded by m_0 + m_n n and we compute schedule coefficients
2640 * with small values (preferably zero) of m_n and m_0.
2642 * All variables of the ILP are non-negative. The actual coefficients
2643 * may be negative, so each coefficient is represented as the difference
2644 * of two non-negative variables. The negative part always appears
2645 * immediately before the positive part.
2646 * Other than that, the variables have the following order
2648 * - sum of positive and negative parts of m_n coefficients
2650 * - sum of all c_n coefficients
2651 * (unconstrained when computing non-parametric schedules)
2652 * - sum of positive and negative parts of all c_x coefficients
2653 * - positive and negative parts of m_n coefficients
2655 * - positive and negative parts of c_i_x, in opposite order
2656 * - c_i_n (if parametric)
2659 * The constraints are those from the edges plus two or three equalities
2660 * to express the sums.
2662 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2663 * Otherwise, we ignore them.
2665 static isl_stat
setup_lp(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
2666 int use_coincidence
)
2676 parametric
= ctx
->opt
->schedule_parametric
;
2677 nparam
= isl_space_dim(graph
->node
[0].space
, isl_dim_param
);
2679 total
= param_pos
+ 2 * nparam
;
2680 for (i
= 0; i
< graph
->n
; ++i
) {
2681 struct isl_sched_node
*node
= &graph
->node
[graph
->sorted
[i
]];
2682 if (node_update_vmap(node
) < 0)
2683 return isl_stat_error
;
2684 node
->start
= total
;
2685 total
+= 1 + node
->nparam
+ 2 * node
->nvar
;
2688 if (count_constraints(graph
, &n_eq
, &n_ineq
, use_coincidence
) < 0)
2689 return isl_stat_error
;
2690 if (count_bound_constant_constraints(ctx
, graph
, &n_eq
, &n_ineq
) < 0)
2691 return isl_stat_error
;
2692 if (count_bound_coefficient_constraints(ctx
, graph
, &n_eq
, &n_ineq
) < 0)
2693 return isl_stat_error
;
2695 space
= isl_space_set_alloc(ctx
, 0, total
);
2696 isl_basic_set_free(graph
->lp
);
2697 n_eq
+= 2 + parametric
;
2699 graph
->lp
= isl_basic_set_alloc_space(space
, 0, n_eq
, n_ineq
);
2701 if (add_sum_constraint(graph
, 0, param_pos
, 2 * nparam
) < 0)
2702 return isl_stat_error
;
2703 if (parametric
&& add_param_sum_constraint(graph
, 2) < 0)
2704 return isl_stat_error
;
2705 if (add_var_sum_constraint(graph
, 3) < 0)
2706 return isl_stat_error
;
2707 if (add_bound_constant_constraints(ctx
, graph
) < 0)
2708 return isl_stat_error
;
2709 if (add_bound_coefficient_constraints(ctx
, graph
) < 0)
2710 return isl_stat_error
;
2711 if (add_all_validity_constraints(graph
, use_coincidence
) < 0)
2712 return isl_stat_error
;
2713 if (add_all_proximity_constraints(graph
, use_coincidence
) < 0)
2714 return isl_stat_error
;
2719 /* Analyze the conflicting constraint found by
2720 * isl_tab_basic_set_non_trivial_lexmin. If it corresponds to the validity
2721 * constraint of one of the edges between distinct nodes, living, moreover
2722 * in distinct SCCs, then record the source and sink SCC as this may
2723 * be a good place to cut between SCCs.
2725 static int check_conflict(int con
, void *user
)
2728 struct isl_sched_graph
*graph
= user
;
2730 if (graph
->src_scc
>= 0)
2733 con
-= graph
->lp
->n_eq
;
2735 if (con
>= graph
->lp
->n_ineq
)
2738 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2739 if (!is_validity(&graph
->edge
[i
]))
2741 if (graph
->edge
[i
].src
== graph
->edge
[i
].dst
)
2743 if (graph
->edge
[i
].src
->scc
== graph
->edge
[i
].dst
->scc
)
2745 if (graph
->edge
[i
].start
> con
)
2747 if (graph
->edge
[i
].end
<= con
)
2749 graph
->src_scc
= graph
->edge
[i
].src
->scc
;
2750 graph
->dst_scc
= graph
->edge
[i
].dst
->scc
;
2756 /* Check whether the next schedule row of the given node needs to be
2757 * non-trivial. Lower-dimensional domains may have some trivial rows,
2758 * but as soon as the number of remaining required non-trivial rows
2759 * is as large as the number or remaining rows to be computed,
2760 * all remaining rows need to be non-trivial.
2762 static int needs_row(struct isl_sched_graph
*graph
, struct isl_sched_node
*node
)
2764 return node
->nvar
- node
->rank
>= graph
->maxvar
- graph
->n_row
;
2767 /* Construct a non-triviality region with triviality directions
2768 * corresponding to the rows of "indep".
2769 * The rows of "indep" are expressed in terms of the schedule coefficients c_i,
2770 * while the triviality directions are expressed in terms of
2771 * pairs of non-negative variables c^+_i - c^-_i, with c^-_i appearing
2772 * before c^+_i. Furthermore,
2773 * the pairs of non-negative variables representing the coefficients
2774 * are stored in the opposite order.
2776 static __isl_give isl_mat
*construct_trivial(__isl_keep isl_mat
*indep
)
2785 ctx
= isl_mat_get_ctx(indep
);
2786 n
= isl_mat_rows(indep
);
2787 n_var
= isl_mat_cols(indep
);
2788 mat
= isl_mat_alloc(ctx
, n
, 2 * n_var
);
2791 for (i
= 0; i
< n
; ++i
) {
2792 for (j
= 0; j
< n_var
; ++j
) {
2793 int nj
= n_var
- 1 - j
;
2794 isl_int_neg(mat
->row
[i
][2 * nj
], indep
->row
[i
][j
]);
2795 isl_int_set(mat
->row
[i
][2 * nj
+ 1], indep
->row
[i
][j
]);
2802 /* Solve the ILP problem constructed in setup_lp.
2803 * For each node such that all the remaining rows of its schedule
2804 * need to be non-trivial, we construct a non-triviality region.
2805 * This region imposes that the next row is independent of previous rows.
2806 * In particular, the non-triviality region enforces that at least
2807 * one of the linear combinations in the rows of node->indep is non-zero.
2809 static __isl_give isl_vec
*solve_lp(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2815 for (i
= 0; i
< graph
->n
; ++i
) {
2816 struct isl_sched_node
*node
= &graph
->node
[i
];
2819 graph
->region
[i
].pos
= node_var_coef_offset(node
);
2820 if (needs_row(graph
, node
))
2821 trivial
= construct_trivial(node
->indep
);
2823 trivial
= isl_mat_zero(ctx
, 0, 0);
2824 graph
->region
[i
].trivial
= trivial
;
2826 lp
= isl_basic_set_copy(graph
->lp
);
2827 sol
= isl_tab_basic_set_non_trivial_lexmin(lp
, 2, graph
->n
,
2828 graph
->region
, &check_conflict
, graph
);
2829 for (i
= 0; i
< graph
->n
; ++i
)
2830 isl_mat_free(graph
->region
[i
].trivial
);
2834 /* Extract the coefficients for the variables of "node" from "sol".
2836 * Each schedule coefficient c_i_x is represented as the difference
2837 * between two non-negative variables c_i_x^+ - c_i_x^-.
2838 * The c_i_x^- appear before their c_i_x^+ counterpart.
2839 * Furthermore, the order of these pairs is the opposite of that
2840 * of the corresponding coefficients.
2842 * Return c_i_x = c_i_x^+ - c_i_x^-
2844 static __isl_give isl_vec
*extract_var_coef(struct isl_sched_node
*node
,
2845 __isl_keep isl_vec
*sol
)
2853 csol
= isl_vec_alloc(isl_vec_get_ctx(sol
), node
->nvar
);
2857 pos
= 1 + node_var_coef_offset(node
);
2858 for (i
= 0; i
< node
->nvar
; ++i
)
2859 isl_int_sub(csol
->el
[node
->nvar
- 1 - i
],
2860 sol
->el
[pos
+ 2 * i
+ 1], sol
->el
[pos
+ 2 * i
]);
2865 /* Update the schedules of all nodes based on the given solution
2866 * of the LP problem.
2867 * The new row is added to the current band.
2868 * All possibly negative coefficients are encoded as a difference
2869 * of two non-negative variables, so we need to perform the subtraction
2872 * If coincident is set, then the caller guarantees that the new
2873 * row satisfies the coincidence constraints.
2875 static int update_schedule(struct isl_sched_graph
*graph
,
2876 __isl_take isl_vec
*sol
, int coincident
)
2879 isl_vec
*csol
= NULL
;
2884 isl_die(sol
->ctx
, isl_error_internal
,
2885 "no solution found", goto error
);
2886 if (graph
->n_total_row
>= graph
->max_row
)
2887 isl_die(sol
->ctx
, isl_error_internal
,
2888 "too many schedule rows", goto error
);
2890 for (i
= 0; i
< graph
->n
; ++i
) {
2891 struct isl_sched_node
*node
= &graph
->node
[i
];
2893 int row
= isl_mat_rows(node
->sched
);
2896 csol
= extract_var_coef(node
, sol
);
2900 isl_map_free(node
->sched_map
);
2901 node
->sched_map
= NULL
;
2902 node
->sched
= isl_mat_add_rows(node
->sched
, 1);
2905 pos
= node_cst_coef_offset(node
);
2906 node
->sched
= isl_mat_set_element(node
->sched
,
2907 row
, 0, sol
->el
[1 + pos
]);
2908 pos
= node_par_coef_offset(node
);
2909 for (j
= 0; j
< node
->nparam
; ++j
)
2910 node
->sched
= isl_mat_set_element(node
->sched
,
2911 row
, 1 + j
, sol
->el
[1 + pos
+ j
]);
2912 for (j
= 0; j
< node
->nvar
; ++j
)
2913 node
->sched
= isl_mat_set_element(node
->sched
,
2914 row
, 1 + node
->nparam
+ j
, csol
->el
[j
]);
2915 node
->coincident
[graph
->n_total_row
] = coincident
;
2921 graph
->n_total_row
++;
2930 /* Convert row "row" of node->sched into an isl_aff living in "ls"
2931 * and return this isl_aff.
2933 static __isl_give isl_aff
*extract_schedule_row(__isl_take isl_local_space
*ls
,
2934 struct isl_sched_node
*node
, int row
)
2942 aff
= isl_aff_zero_on_domain(ls
);
2943 isl_mat_get_element(node
->sched
, row
, 0, &v
);
2944 aff
= isl_aff_set_constant(aff
, v
);
2945 for (j
= 0; j
< node
->nparam
; ++j
) {
2946 isl_mat_get_element(node
->sched
, row
, 1 + j
, &v
);
2947 aff
= isl_aff_set_coefficient(aff
, isl_dim_param
, j
, v
);
2949 for (j
= 0; j
< node
->nvar
; ++j
) {
2950 isl_mat_get_element(node
->sched
, row
, 1 + node
->nparam
+ j
, &v
);
2951 aff
= isl_aff_set_coefficient(aff
, isl_dim_in
, j
, v
);
2959 /* Convert the "n" rows starting at "first" of node->sched into a multi_aff
2960 * and return this multi_aff.
2962 * The result is defined over the uncompressed node domain.
2964 static __isl_give isl_multi_aff
*node_extract_partial_schedule_multi_aff(
2965 struct isl_sched_node
*node
, int first
, int n
)
2969 isl_local_space
*ls
;
2976 nrow
= isl_mat_rows(node
->sched
);
2977 if (node
->compressed
)
2978 space
= isl_multi_aff_get_domain_space(node
->decompress
);
2980 space
= isl_space_copy(node
->space
);
2981 ls
= isl_local_space_from_space(isl_space_copy(space
));
2982 space
= isl_space_from_domain(space
);
2983 space
= isl_space_add_dims(space
, isl_dim_out
, n
);
2984 ma
= isl_multi_aff_zero(space
);
2986 for (i
= first
; i
< first
+ n
; ++i
) {
2987 aff
= extract_schedule_row(isl_local_space_copy(ls
), node
, i
);
2988 ma
= isl_multi_aff_set_aff(ma
, i
- first
, aff
);
2991 isl_local_space_free(ls
);
2993 if (node
->compressed
)
2994 ma
= isl_multi_aff_pullback_multi_aff(ma
,
2995 isl_multi_aff_copy(node
->compress
));
3000 /* Convert node->sched into a multi_aff and return this multi_aff.
3002 * The result is defined over the uncompressed node domain.
3004 static __isl_give isl_multi_aff
*node_extract_schedule_multi_aff(
3005 struct isl_sched_node
*node
)
3009 nrow
= isl_mat_rows(node
->sched
);
3010 return node_extract_partial_schedule_multi_aff(node
, 0, nrow
);
3013 /* Convert node->sched into a map and return this map.
3015 * The result is cached in node->sched_map, which needs to be released
3016 * whenever node->sched is updated.
3017 * It is defined over the uncompressed node domain.
3019 static __isl_give isl_map
*node_extract_schedule(struct isl_sched_node
*node
)
3021 if (!node
->sched_map
) {
3024 ma
= node_extract_schedule_multi_aff(node
);
3025 node
->sched_map
= isl_map_from_multi_aff(ma
);
3028 return isl_map_copy(node
->sched_map
);
3031 /* Construct a map that can be used to update a dependence relation
3032 * based on the current schedule.
3033 * That is, construct a map expressing that source and sink
3034 * are executed within the same iteration of the current schedule.
3035 * This map can then be intersected with the dependence relation.
3036 * This is not the most efficient way, but this shouldn't be a critical
3039 static __isl_give isl_map
*specializer(struct isl_sched_node
*src
,
3040 struct isl_sched_node
*dst
)
3042 isl_map
*src_sched
, *dst_sched
;
3044 src_sched
= node_extract_schedule(src
);
3045 dst_sched
= node_extract_schedule(dst
);
3046 return isl_map_apply_range(src_sched
, isl_map_reverse(dst_sched
));
3049 /* Intersect the domains of the nested relations in domain and range
3050 * of "umap" with "map".
3052 static __isl_give isl_union_map
*intersect_domains(
3053 __isl_take isl_union_map
*umap
, __isl_keep isl_map
*map
)
3055 isl_union_set
*uset
;
3057 umap
= isl_union_map_zip(umap
);
3058 uset
= isl_union_set_from_set(isl_map_wrap(isl_map_copy(map
)));
3059 umap
= isl_union_map_intersect_domain(umap
, uset
);
3060 umap
= isl_union_map_zip(umap
);
3064 /* Update the dependence relation of the given edge based
3065 * on the current schedule.
3066 * If the dependence is carried completely by the current schedule, then
3067 * it is removed from the edge_tables. It is kept in the list of edges
3068 * as otherwise all edge_tables would have to be recomputed.
3070 static int update_edge(struct isl_sched_graph
*graph
,
3071 struct isl_sched_edge
*edge
)
3076 id
= specializer(edge
->src
, edge
->dst
);
3077 edge
->map
= isl_map_intersect(edge
->map
, isl_map_copy(id
));
3081 if (edge
->tagged_condition
) {
3082 edge
->tagged_condition
=
3083 intersect_domains(edge
->tagged_condition
, id
);
3084 if (!edge
->tagged_condition
)
3087 if (edge
->tagged_validity
) {
3088 edge
->tagged_validity
=
3089 intersect_domains(edge
->tagged_validity
, id
);
3090 if (!edge
->tagged_validity
)
3094 empty
= isl_map_plain_is_empty(edge
->map
);
3098 graph_remove_edge(graph
, edge
);
3107 /* Does the domain of "umap" intersect "uset"?
3109 static int domain_intersects(__isl_keep isl_union_map
*umap
,
3110 __isl_keep isl_union_set
*uset
)
3114 umap
= isl_union_map_copy(umap
);
3115 umap
= isl_union_map_intersect_domain(umap
, isl_union_set_copy(uset
));
3116 empty
= isl_union_map_is_empty(umap
);
3117 isl_union_map_free(umap
);
3119 return empty
< 0 ? -1 : !empty
;
3122 /* Does the range of "umap" intersect "uset"?
3124 static int range_intersects(__isl_keep isl_union_map
*umap
,
3125 __isl_keep isl_union_set
*uset
)
3129 umap
= isl_union_map_copy(umap
);
3130 umap
= isl_union_map_intersect_range(umap
, isl_union_set_copy(uset
));
3131 empty
= isl_union_map_is_empty(umap
);
3132 isl_union_map_free(umap
);
3134 return empty
< 0 ? -1 : !empty
;
3137 /* Are the condition dependences of "edge" local with respect to
3138 * the current schedule?
3140 * That is, are domain and range of the condition dependences mapped
3141 * to the same point?
3143 * In other words, is the condition false?
3145 static int is_condition_false(struct isl_sched_edge
*edge
)
3147 isl_union_map
*umap
;
3148 isl_map
*map
, *sched
, *test
;
3151 empty
= isl_union_map_is_empty(edge
->tagged_condition
);
3152 if (empty
< 0 || empty
)
3155 umap
= isl_union_map_copy(edge
->tagged_condition
);
3156 umap
= isl_union_map_zip(umap
);
3157 umap
= isl_union_set_unwrap(isl_union_map_domain(umap
));
3158 map
= isl_map_from_union_map(umap
);
3160 sched
= node_extract_schedule(edge
->src
);
3161 map
= isl_map_apply_domain(map
, sched
);
3162 sched
= node_extract_schedule(edge
->dst
);
3163 map
= isl_map_apply_range(map
, sched
);
3165 test
= isl_map_identity(isl_map_get_space(map
));
3166 local
= isl_map_is_subset(map
, test
);
3173 /* For each conditional validity constraint that is adjacent
3174 * to a condition with domain in condition_source or range in condition_sink,
3175 * turn it into an unconditional validity constraint.
3177 static int unconditionalize_adjacent_validity(struct isl_sched_graph
*graph
,
3178 __isl_take isl_union_set
*condition_source
,
3179 __isl_take isl_union_set
*condition_sink
)
3183 condition_source
= isl_union_set_coalesce(condition_source
);
3184 condition_sink
= isl_union_set_coalesce(condition_sink
);
3186 for (i
= 0; i
< graph
->n_edge
; ++i
) {
3188 isl_union_map
*validity
;
3190 if (!is_conditional_validity(&graph
->edge
[i
]))
3192 if (is_validity(&graph
->edge
[i
]))
3195 validity
= graph
->edge
[i
].tagged_validity
;
3196 adjacent
= domain_intersects(validity
, condition_sink
);
3197 if (adjacent
>= 0 && !adjacent
)
3198 adjacent
= range_intersects(validity
, condition_source
);
3204 set_validity(&graph
->edge
[i
]);
3207 isl_union_set_free(condition_source
);
3208 isl_union_set_free(condition_sink
);
3211 isl_union_set_free(condition_source
);
3212 isl_union_set_free(condition_sink
);
3216 /* Update the dependence relations of all edges based on the current schedule
3217 * and enforce conditional validity constraints that are adjacent
3218 * to satisfied condition constraints.
3220 * First check if any of the condition constraints are satisfied
3221 * (i.e., not local to the outer schedule) and keep track of
3222 * their domain and range.
3223 * Then update all dependence relations (which removes the non-local
3225 * Finally, if any condition constraints turned out to be satisfied,
3226 * then turn all adjacent conditional validity constraints into
3227 * unconditional validity constraints.
3229 static int update_edges(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
3233 isl_union_set
*source
, *sink
;
3235 source
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
3236 sink
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
3237 for (i
= 0; i
< graph
->n_edge
; ++i
) {
3239 isl_union_set
*uset
;
3240 isl_union_map
*umap
;
3242 if (!is_condition(&graph
->edge
[i
]))
3244 if (is_local(&graph
->edge
[i
]))
3246 local
= is_condition_false(&graph
->edge
[i
]);
3254 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_condition
);
3255 uset
= isl_union_map_domain(umap
);
3256 source
= isl_union_set_union(source
, uset
);
3258 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_condition
);
3259 uset
= isl_union_map_range(umap
);
3260 sink
= isl_union_set_union(sink
, uset
);
3263 for (i
= graph
->n_edge
- 1; i
>= 0; --i
) {
3264 if (update_edge(graph
, &graph
->edge
[i
]) < 0)
3269 return unconditionalize_adjacent_validity(graph
, source
, sink
);
3271 isl_union_set_free(source
);
3272 isl_union_set_free(sink
);
3275 isl_union_set_free(source
);
3276 isl_union_set_free(sink
);
3280 static void next_band(struct isl_sched_graph
*graph
)
3282 graph
->band_start
= graph
->n_total_row
;
3285 /* Return the union of the universe domains of the nodes in "graph"
3286 * that satisfy "pred".
3288 static __isl_give isl_union_set
*isl_sched_graph_domain(isl_ctx
*ctx
,
3289 struct isl_sched_graph
*graph
,
3290 int (*pred
)(struct isl_sched_node
*node
, int data
), int data
)
3296 for (i
= 0; i
< graph
->n
; ++i
)
3297 if (pred(&graph
->node
[i
], data
))
3301 isl_die(ctx
, isl_error_internal
,
3302 "empty component", return NULL
);
3304 set
= isl_set_universe(isl_space_copy(graph
->node
[i
].space
));
3305 dom
= isl_union_set_from_set(set
);
3307 for (i
= i
+ 1; i
< graph
->n
; ++i
) {
3308 if (!pred(&graph
->node
[i
], data
))
3310 set
= isl_set_universe(isl_space_copy(graph
->node
[i
].space
));
3311 dom
= isl_union_set_union(dom
, isl_union_set_from_set(set
));
3317 /* Return a list of unions of universe domains, where each element
3318 * in the list corresponds to an SCC (or WCC) indexed by node->scc.
3320 static __isl_give isl_union_set_list
*extract_sccs(isl_ctx
*ctx
,
3321 struct isl_sched_graph
*graph
)
3324 isl_union_set_list
*filters
;
3326 filters
= isl_union_set_list_alloc(ctx
, graph
->scc
);
3327 for (i
= 0; i
< graph
->scc
; ++i
) {
3330 dom
= isl_sched_graph_domain(ctx
, graph
, &node_scc_exactly
, i
);
3331 filters
= isl_union_set_list_add(filters
, dom
);
3337 /* Return a list of two unions of universe domains, one for the SCCs up
3338 * to and including graph->src_scc and another for the other SCCs.
3340 static __isl_give isl_union_set_list
*extract_split(isl_ctx
*ctx
,
3341 struct isl_sched_graph
*graph
)
3344 isl_union_set_list
*filters
;
3346 filters
= isl_union_set_list_alloc(ctx
, 2);
3347 dom
= isl_sched_graph_domain(ctx
, graph
,
3348 &node_scc_at_most
, graph
->src_scc
);
3349 filters
= isl_union_set_list_add(filters
, dom
);
3350 dom
= isl_sched_graph_domain(ctx
, graph
,
3351 &node_scc_at_least
, graph
->src_scc
+ 1);
3352 filters
= isl_union_set_list_add(filters
, dom
);
3357 /* Copy nodes that satisfy node_pred from the src dependence graph
3358 * to the dst dependence graph.
3360 static int copy_nodes(struct isl_sched_graph
*dst
, struct isl_sched_graph
*src
,
3361 int (*node_pred
)(struct isl_sched_node
*node
, int data
), int data
)
3366 for (i
= 0; i
< src
->n
; ++i
) {
3369 if (!node_pred(&src
->node
[i
], data
))
3373 dst
->node
[j
].space
= isl_space_copy(src
->node
[i
].space
);
3374 dst
->node
[j
].compressed
= src
->node
[i
].compressed
;
3375 dst
->node
[j
].hull
= isl_set_copy(src
->node
[i
].hull
);
3376 dst
->node
[j
].compress
=
3377 isl_multi_aff_copy(src
->node
[i
].compress
);
3378 dst
->node
[j
].decompress
=
3379 isl_multi_aff_copy(src
->node
[i
].decompress
);
3380 dst
->node
[j
].nvar
= src
->node
[i
].nvar
;
3381 dst
->node
[j
].nparam
= src
->node
[i
].nparam
;
3382 dst
->node
[j
].sched
= isl_mat_copy(src
->node
[i
].sched
);
3383 dst
->node
[j
].sched_map
= isl_map_copy(src
->node
[i
].sched_map
);
3384 dst
->node
[j
].coincident
= src
->node
[i
].coincident
;
3385 dst
->node
[j
].sizes
= isl_multi_val_copy(src
->node
[i
].sizes
);
3386 dst
->node
[j
].bounds
= isl_basic_set_copy(src
->node
[i
].bounds
);
3387 dst
->node
[j
].max
= isl_vec_copy(src
->node
[i
].max
);
3390 if (!dst
->node
[j
].space
|| !dst
->node
[j
].sched
)
3392 if (dst
->node
[j
].compressed
&&
3393 (!dst
->node
[j
].hull
|| !dst
->node
[j
].compress
||
3394 !dst
->node
[j
].decompress
))
3401 /* Copy non-empty edges that satisfy edge_pred from the src dependence graph
3402 * to the dst dependence graph.
3403 * If the source or destination node of the edge is not in the destination
3404 * graph, then it must be a backward proximity edge and it should simply
3407 static int copy_edges(isl_ctx
*ctx
, struct isl_sched_graph
*dst
,
3408 struct isl_sched_graph
*src
,
3409 int (*edge_pred
)(struct isl_sched_edge
*edge
, int data
), int data
)
3412 enum isl_edge_type t
;
3415 for (i
= 0; i
< src
->n_edge
; ++i
) {
3416 struct isl_sched_edge
*edge
= &src
->edge
[i
];
3418 isl_union_map
*tagged_condition
;
3419 isl_union_map
*tagged_validity
;
3420 struct isl_sched_node
*dst_src
, *dst_dst
;
3422 if (!edge_pred(edge
, data
))
3425 if (isl_map_plain_is_empty(edge
->map
))
3428 dst_src
= graph_find_node(ctx
, dst
, edge
->src
->space
);
3429 dst_dst
= graph_find_node(ctx
, dst
, edge
->dst
->space
);
3430 if (!dst_src
|| !dst_dst
) {
3431 if (is_validity(edge
) || is_conditional_validity(edge
))
3432 isl_die(ctx
, isl_error_internal
,
3433 "backward (conditional) validity edge",
3438 map
= isl_map_copy(edge
->map
);
3439 tagged_condition
= isl_union_map_copy(edge
->tagged_condition
);
3440 tagged_validity
= isl_union_map_copy(edge
->tagged_validity
);
3442 dst
->edge
[dst
->n_edge
].src
= dst_src
;
3443 dst
->edge
[dst
->n_edge
].dst
= dst_dst
;
3444 dst
->edge
[dst
->n_edge
].map
= map
;
3445 dst
->edge
[dst
->n_edge
].tagged_condition
= tagged_condition
;
3446 dst
->edge
[dst
->n_edge
].tagged_validity
= tagged_validity
;
3447 dst
->edge
[dst
->n_edge
].types
= edge
->types
;
3450 if (edge
->tagged_condition
&& !tagged_condition
)
3452 if (edge
->tagged_validity
&& !tagged_validity
)
3455 for (t
= isl_edge_first
; t
<= isl_edge_last
; ++t
) {
3457 graph_find_edge(src
, t
, edge
->src
, edge
->dst
))
3459 if (graph_edge_table_add(ctx
, dst
, t
,
3460 &dst
->edge
[dst
->n_edge
- 1]) < 0)
3468 /* Compute the maximal number of variables over all nodes.
3469 * This is the maximal number of linearly independent schedule
3470 * rows that we need to compute.
3471 * Just in case we end up in a part of the dependence graph
3472 * with only lower-dimensional domains, we make sure we will
3473 * compute the required amount of extra linearly independent rows.
3475 static int compute_maxvar(struct isl_sched_graph
*graph
)
3480 for (i
= 0; i
< graph
->n
; ++i
) {
3481 struct isl_sched_node
*node
= &graph
->node
[i
];
3484 if (node_update_vmap(node
) < 0)
3486 nvar
= node
->nvar
+ graph
->n_row
- node
->rank
;
3487 if (nvar
> graph
->maxvar
)
3488 graph
->maxvar
= nvar
;
3494 /* Extract the subgraph of "graph" that consists of the node satisfying
3495 * "node_pred" and the edges satisfying "edge_pred" and store
3496 * the result in "sub".
3498 static int extract_sub_graph(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
3499 int (*node_pred
)(struct isl_sched_node
*node
, int data
),
3500 int (*edge_pred
)(struct isl_sched_edge
*edge
, int data
),
3501 int data
, struct isl_sched_graph
*sub
)
3503 int i
, n
= 0, n_edge
= 0;
3506 for (i
= 0; i
< graph
->n
; ++i
)
3507 if (node_pred(&graph
->node
[i
], data
))
3509 for (i
= 0; i
< graph
->n_edge
; ++i
)
3510 if (edge_pred(&graph
->edge
[i
], data
))
3512 if (graph_alloc(ctx
, sub
, n
, n_edge
) < 0)
3514 sub
->root
= graph
->root
;
3515 if (copy_nodes(sub
, graph
, node_pred
, data
) < 0)
3517 if (graph_init_table(ctx
, sub
) < 0)
3519 for (t
= 0; t
<= isl_edge_last
; ++t
)
3520 sub
->max_edge
[t
] = graph
->max_edge
[t
];
3521 if (graph_init_edge_tables(ctx
, sub
) < 0)
3523 if (copy_edges(ctx
, sub
, graph
, edge_pred
, data
) < 0)
3525 sub
->n_row
= graph
->n_row
;
3526 sub
->max_row
= graph
->max_row
;
3527 sub
->n_total_row
= graph
->n_total_row
;
3528 sub
->band_start
= graph
->band_start
;
3533 static __isl_give isl_schedule_node
*compute_schedule(isl_schedule_node
*node
,
3534 struct isl_sched_graph
*graph
);
3535 static __isl_give isl_schedule_node
*compute_schedule_wcc(
3536 isl_schedule_node
*node
, struct isl_sched_graph
*graph
);
3538 /* Compute a schedule for a subgraph of "graph". In particular, for
3539 * the graph composed of nodes that satisfy node_pred and edges that
3540 * that satisfy edge_pred.
3541 * If the subgraph is known to consist of a single component, then wcc should
3542 * be set and then we call compute_schedule_wcc on the constructed subgraph.
3543 * Otherwise, we call compute_schedule, which will check whether the subgraph
3546 * The schedule is inserted at "node" and the updated schedule node
3549 static __isl_give isl_schedule_node
*compute_sub_schedule(
3550 __isl_take isl_schedule_node
*node
, isl_ctx
*ctx
,
3551 struct isl_sched_graph
*graph
,
3552 int (*node_pred
)(struct isl_sched_node
*node
, int data
),
3553 int (*edge_pred
)(struct isl_sched_edge
*edge
, int data
),
3556 struct isl_sched_graph split
= { 0 };
3558 if (extract_sub_graph(ctx
, graph
, node_pred
, edge_pred
, data
,
3563 node
= compute_schedule_wcc(node
, &split
);
3565 node
= compute_schedule(node
, &split
);
3567 graph_free(ctx
, &split
);
3570 graph_free(ctx
, &split
);
3571 return isl_schedule_node_free(node
);
3574 static int edge_scc_exactly(struct isl_sched_edge
*edge
, int scc
)
3576 return edge
->src
->scc
== scc
&& edge
->dst
->scc
== scc
;
3579 static int edge_dst_scc_at_most(struct isl_sched_edge
*edge
, int scc
)
3581 return edge
->dst
->scc
<= scc
;
3584 static int edge_src_scc_at_least(struct isl_sched_edge
*edge
, int scc
)
3586 return edge
->src
->scc
>= scc
;
3589 /* Reset the current band by dropping all its schedule rows.
3591 static int reset_band(struct isl_sched_graph
*graph
)
3596 drop
= graph
->n_total_row
- graph
->band_start
;
3597 graph
->n_total_row
-= drop
;
3598 graph
->n_row
-= drop
;
3600 for (i
= 0; i
< graph
->n
; ++i
) {
3601 struct isl_sched_node
*node
= &graph
->node
[i
];
3603 isl_map_free(node
->sched_map
);
3604 node
->sched_map
= NULL
;
3606 node
->sched
= isl_mat_drop_rows(node
->sched
,
3607 graph
->band_start
, drop
);
3616 /* Split the current graph into two parts and compute a schedule for each
3617 * part individually. In particular, one part consists of all SCCs up
3618 * to and including graph->src_scc, while the other part contains the other
3619 * SCCs. The split is enforced by a sequence node inserted at position "node"
3620 * in the schedule tree. Return the updated schedule node.
3621 * If either of these two parts consists of a sequence, then it is spliced
3622 * into the sequence containing the two parts.
3624 * The current band is reset. It would be possible to reuse
3625 * the previously computed rows as the first rows in the next
3626 * band, but recomputing them may result in better rows as we are looking
3627 * at a smaller part of the dependence graph.
3629 static __isl_give isl_schedule_node
*compute_split_schedule(
3630 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
3634 isl_union_set_list
*filters
;
3639 if (reset_band(graph
) < 0)
3640 return isl_schedule_node_free(node
);
3644 ctx
= isl_schedule_node_get_ctx(node
);
3645 filters
= extract_split(ctx
, graph
);
3646 node
= isl_schedule_node_insert_sequence(node
, filters
);
3647 node
= isl_schedule_node_child(node
, 1);
3648 node
= isl_schedule_node_child(node
, 0);
3650 node
= compute_sub_schedule(node
, ctx
, graph
,
3651 &node_scc_at_least
, &edge_src_scc_at_least
,
3652 graph
->src_scc
+ 1, 0);
3653 is_seq
= isl_schedule_node_get_type(node
) == isl_schedule_node_sequence
;
3654 node
= isl_schedule_node_parent(node
);
3655 node
= isl_schedule_node_parent(node
);
3657 node
= isl_schedule_node_sequence_splice_child(node
, 1);
3658 node
= isl_schedule_node_child(node
, 0);
3659 node
= isl_schedule_node_child(node
, 0);
3660 node
= compute_sub_schedule(node
, ctx
, graph
,
3661 &node_scc_at_most
, &edge_dst_scc_at_most
,
3663 is_seq
= isl_schedule_node_get_type(node
) == isl_schedule_node_sequence
;
3664 node
= isl_schedule_node_parent(node
);
3665 node
= isl_schedule_node_parent(node
);
3667 node
= isl_schedule_node_sequence_splice_child(node
, 0);
3672 /* Insert a band node at position "node" in the schedule tree corresponding
3673 * to the current band in "graph". Mark the band node permutable
3674 * if "permutable" is set.
3675 * The partial schedules and the coincidence property are extracted
3676 * from the graph nodes.
3677 * Return the updated schedule node.
3679 static __isl_give isl_schedule_node
*insert_current_band(
3680 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
3686 isl_multi_pw_aff
*mpa
;
3687 isl_multi_union_pw_aff
*mupa
;
3693 isl_die(isl_schedule_node_get_ctx(node
), isl_error_internal
,
3694 "graph should have at least one node",
3695 return isl_schedule_node_free(node
));
3697 start
= graph
->band_start
;
3698 end
= graph
->n_total_row
;
3701 ma
= node_extract_partial_schedule_multi_aff(&graph
->node
[0], start
, n
);
3702 mpa
= isl_multi_pw_aff_from_multi_aff(ma
);
3703 mupa
= isl_multi_union_pw_aff_from_multi_pw_aff(mpa
);
3705 for (i
= 1; i
< graph
->n
; ++i
) {
3706 isl_multi_union_pw_aff
*mupa_i
;
3708 ma
= node_extract_partial_schedule_multi_aff(&graph
->node
[i
],
3710 mpa
= isl_multi_pw_aff_from_multi_aff(ma
);
3711 mupa_i
= isl_multi_union_pw_aff_from_multi_pw_aff(mpa
);
3712 mupa
= isl_multi_union_pw_aff_union_add(mupa
, mupa_i
);
3714 node
= isl_schedule_node_insert_partial_schedule(node
, mupa
);
3716 for (i
= 0; i
< n
; ++i
)
3717 node
= isl_schedule_node_band_member_set_coincident(node
, i
,
3718 graph
->node
[0].coincident
[start
+ i
]);
3719 node
= isl_schedule_node_band_set_permutable(node
, permutable
);
3724 /* Update the dependence relations based on the current schedule,
3725 * add the current band to "node" and then continue with the computation
3727 * Return the updated schedule node.
3729 static __isl_give isl_schedule_node
*compute_next_band(
3730 __isl_take isl_schedule_node
*node
,
3731 struct isl_sched_graph
*graph
, int permutable
)
3738 ctx
= isl_schedule_node_get_ctx(node
);
3739 if (update_edges(ctx
, graph
) < 0)
3740 return isl_schedule_node_free(node
);
3741 node
= insert_current_band(node
, graph
, permutable
);
3744 node
= isl_schedule_node_child(node
, 0);
3745 node
= compute_schedule(node
, graph
);
3746 node
= isl_schedule_node_parent(node
);
3751 /* Add the constraints "coef" derived from an edge from "node" to itself
3752 * to graph->lp in order to respect the dependences and to try and carry them.
3753 * "pos" is the sequence number of the edge that needs to be carried.
3754 * "coef" represents general constraints on coefficients (c_0, c_x)
3755 * of valid constraints for (y - x) with x and y instances of the node.
3757 * The constraints added to graph->lp need to enforce
3759 * (c_j_0 + c_j_x y) - (c_j_0 + c_j_x x)
3760 * = c_j_x (y - x) >= e_i
3762 * for each (x,y) in the dependence relation of the edge.
3763 * That is, (-e_i, c_j_x) needs to be plugged in for (c_0, c_x),
3764 * taking into account that each coefficient in c_j_x is represented
3765 * as a pair of non-negative coefficients.
3767 static isl_stat
add_intra_constraints(struct isl_sched_graph
*graph
,
3768 struct isl_sched_node
*node
, __isl_take isl_basic_set
*coef
, int pos
)
3772 isl_dim_map
*dim_map
;
3775 return isl_stat_error
;
3777 ctx
= isl_basic_set_get_ctx(coef
);
3778 offset
= coef_var_offset(coef
);
3779 dim_map
= intra_dim_map(ctx
, graph
, node
, offset
, 1);
3780 isl_dim_map_range(dim_map
, 3 + pos
, 0, 0, 0, 1, -1);
3781 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
3786 /* Add the constraints "coef" derived from an edge from "src" to "dst"
3787 * to graph->lp in order to respect the dependences and to try and carry them.
3788 * "pos" is the sequence number of the edge that needs to be carried or
3789 * -1 if no attempt should be made to carry the dependences.
3790 * "coef" represents general constraints on coefficients (c_0, c_n, c_x, c_y)
3791 * of valid constraints for (x, y) with x and y instances of "src" and "dst".
3793 * The constraints added to graph->lp need to enforce
3795 * (c_k_0 + c_k_n n + c_k_x y) - (c_j_0 + c_j_n n + c_j_x x) >= e_i
3797 * for each (x,y) in the dependence relation of the edge or
3799 * (c_k_0 + c_k_n n + c_k_x y) - (c_j_0 + c_j_n n + c_j_x x) >= 0
3803 * (-e_i + c_k_0 - c_j_0, c_k_n - c_j_n, -c_j_x, c_k_x)
3805 * (c_k_0 - c_j_0, c_k_n - c_j_n, -c_j_x, c_k_x)
3806 * needs to be plugged in for (c_0, c_n, c_x, c_y),
3807 * taking into account that each coefficient in c_j_x and c_k_x is represented
3808 * as a pair of non-negative coefficients.
3810 static isl_stat
add_inter_constraints(struct isl_sched_graph
*graph
,
3811 struct isl_sched_node
*src
, struct isl_sched_node
*dst
,
3812 __isl_take isl_basic_set
*coef
, int pos
)
3816 isl_dim_map
*dim_map
;
3819 return isl_stat_error
;
3821 ctx
= isl_basic_set_get_ctx(coef
);
3822 offset
= coef_var_offset(coef
);
3823 dim_map
= inter_dim_map(ctx
, graph
, src
, dst
, offset
, 1);
3825 isl_dim_map_range(dim_map
, 3 + pos
, 0, 0, 0, 1, -1);
3826 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
3831 /* Data structure for keeping track of the data needed
3832 * to exploit non-trivial lineality spaces.
3834 * "any_non_trivial" is true if there are any non-trivial lineality spaces.
3835 * If "any_non_trivial" is not true, then "equivalent" and "mask" may be NULL.
3836 * "equivalent" connects instances to other instances on the same line(s).
3837 * "mask" contains the domain spaces of "equivalent".
3838 * Any instance set not in "mask" does not have a non-trivial lineality space.
3840 struct isl_exploit_lineality_data
{
3841 isl_bool any_non_trivial
;
3842 isl_union_map
*equivalent
;
3843 isl_union_set
*mask
;
3846 /* Data structure collecting information used during the construction
3847 * of an LP for carrying dependences.
3849 * "intra" is a sequence of coefficient constraints for intra-node edges.
3850 * "inter" is a sequence of coefficient constraints for inter-node edges.
3851 * "lineality" contains data used to exploit non-trivial lineality spaces.
3854 isl_basic_set_list
*intra
;
3855 isl_basic_set_list
*inter
;
3856 struct isl_exploit_lineality_data lineality
;
3859 /* Free all the data stored in "carry".
3861 static void isl_carry_clear(struct isl_carry
*carry
)
3863 isl_basic_set_list_free(carry
->intra
);
3864 isl_basic_set_list_free(carry
->inter
);
3865 isl_union_map_free(carry
->lineality
.equivalent
);
3866 isl_union_set_free(carry
->lineality
.mask
);
3869 /* Return a pointer to the node in "graph" that lives in "space".
3870 * If the requested node has been compressed, then "space"
3871 * corresponds to the compressed space.
3873 * First try and see if "space" is the space of an uncompressed node.
3874 * If so, return that node.
3875 * Otherwise, "space" was constructed by construct_compressed_id and
3876 * contains a user pointer pointing to the node in the tuple id.
3877 * However, this node belongs to the original dependence graph.
3878 * If "graph" is a subgraph of this original dependence graph,
3879 * then the node with the same space still needs to be looked up
3880 * in the current graph.
3882 static struct isl_sched_node
*graph_find_compressed_node(isl_ctx
*ctx
,
3883 struct isl_sched_graph
*graph
, __isl_keep isl_space
*space
)
3886 struct isl_sched_node
*node
;
3891 node
= graph_find_node(ctx
, graph
, space
);
3895 id
= isl_space_get_tuple_id(space
, isl_dim_set
);
3896 node
= isl_id_get_user(id
);
3902 if (!is_node(graph
->root
, node
))
3903 isl_die(ctx
, isl_error_internal
,
3904 "space points to invalid node", return NULL
);
3905 if (graph
!= graph
->root
)
3906 node
= graph_find_node(ctx
, graph
, node
->space
);
3911 /* Internal data structure for add_all_constraints.
3913 * "graph" is the schedule constraint graph for which an LP problem
3914 * is being constructed.
3915 * "carry_inter" indicates whether inter-node edges should be carried.
3916 * "pos" is the position of the next edge that needs to be carried.
3918 struct isl_add_all_constraints_data
{
3920 struct isl_sched_graph
*graph
;
3925 /* Add the constraints "coef" derived from an edge from a node to itself
3926 * to data->graph->lp in order to respect the dependences and
3927 * to try and carry them.
3929 * The space of "coef" is of the form
3931 * coefficients[[c_cst] -> S[c_x]]
3933 * with S[c_x] the (compressed) space of the node.
3934 * Extract the node from the space and call add_intra_constraints.
3936 static isl_stat
lp_add_intra(__isl_take isl_basic_set
*coef
, void *user
)
3938 struct isl_add_all_constraints_data
*data
= user
;
3940 struct isl_sched_node
*node
;
3942 space
= isl_basic_set_get_space(coef
);
3943 space
= isl_space_range(isl_space_unwrap(space
));
3944 node
= graph_find_compressed_node(data
->ctx
, data
->graph
, space
);
3945 isl_space_free(space
);
3946 return add_intra_constraints(data
->graph
, node
, coef
, data
->pos
++);
3949 /* Add the constraints "coef" derived from an edge from a node j
3950 * to a node k to data->graph->lp in order to respect the dependences and
3951 * to try and carry them (provided data->carry_inter is set).
3953 * The space of "coef" is of the form
3955 * coefficients[[c_cst, c_n] -> [S_j[c_x] -> S_k[c_y]]]
3957 * with S_j[c_x] and S_k[c_y] the (compressed) spaces of the nodes.
3958 * Extract the nodes from the space and call add_inter_constraints.
3960 static isl_stat
lp_add_inter(__isl_take isl_basic_set
*coef
, void *user
)
3962 struct isl_add_all_constraints_data
*data
= user
;
3963 isl_space
*space
, *dom
;
3964 struct isl_sched_node
*src
, *dst
;
3967 space
= isl_basic_set_get_space(coef
);
3968 space
= isl_space_unwrap(isl_space_range(isl_space_unwrap(space
)));
3969 dom
= isl_space_domain(isl_space_copy(space
));
3970 src
= graph_find_compressed_node(data
->ctx
, data
->graph
, dom
);
3971 isl_space_free(dom
);
3972 space
= isl_space_range(space
);
3973 dst
= graph_find_compressed_node(data
->ctx
, data
->graph
, space
);
3974 isl_space_free(space
);
3976 pos
= data
->carry_inter
? data
->pos
++ : -1;
3977 return add_inter_constraints(data
->graph
, src
, dst
, coef
, pos
);
3980 /* Add constraints to graph->lp that force all (conditional) validity
3981 * dependences to be respected and attempt to carry them.
3982 * "intra" is the sequence of coefficient constraints for intra-node edges.
3983 * "inter" is the sequence of coefficient constraints for inter-node edges.
3984 * "carry_inter" indicates whether inter-node edges should be carried or
3987 static isl_stat
add_all_constraints(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
3988 __isl_keep isl_basic_set_list
*intra
,
3989 __isl_keep isl_basic_set_list
*inter
, int carry_inter
)
3991 struct isl_add_all_constraints_data data
= { ctx
, graph
, carry_inter
};
3994 if (isl_basic_set_list_foreach(intra
, &lp_add_intra
, &data
) < 0)
3995 return isl_stat_error
;
3996 if (isl_basic_set_list_foreach(inter
, &lp_add_inter
, &data
) < 0)
3997 return isl_stat_error
;
4001 /* Internal data structure for count_all_constraints
4002 * for keeping track of the number of equality and inequality constraints.
4004 struct isl_sched_count
{
4009 /* Add the number of equality and inequality constraints of "bset"
4010 * to data->n_eq and data->n_ineq.
4012 static isl_stat
bset_update_count(__isl_take isl_basic_set
*bset
, void *user
)
4014 struct isl_sched_count
*data
= user
;
4016 return update_count(bset
, 1, &data
->n_eq
, &data
->n_ineq
);
4019 /* Count the number of equality and inequality constraints
4020 * that will be added to the carry_lp problem.
4021 * We count each edge exactly once.
4022 * "intra" is the sequence of coefficient constraints for intra-node edges.
4023 * "inter" is the sequence of coefficient constraints for inter-node edges.
4025 static isl_stat
count_all_constraints(__isl_keep isl_basic_set_list
*intra
,
4026 __isl_keep isl_basic_set_list
*inter
, int *n_eq
, int *n_ineq
)
4028 struct isl_sched_count data
;
4030 data
.n_eq
= data
.n_ineq
= 0;
4031 if (isl_basic_set_list_foreach(inter
, &bset_update_count
, &data
) < 0)
4032 return isl_stat_error
;
4033 if (isl_basic_set_list_foreach(intra
, &bset_update_count
, &data
) < 0)
4034 return isl_stat_error
;
4037 *n_ineq
= data
.n_ineq
;
4042 /* Construct an LP problem for finding schedule coefficients
4043 * such that the schedule carries as many validity dependences as possible.
4044 * In particular, for each dependence i, we bound the dependence distance
4045 * from below by e_i, with 0 <= e_i <= 1 and then maximize the sum
4046 * of all e_i's. Dependences with e_i = 0 in the solution are simply
4047 * respected, while those with e_i > 0 (in practice e_i = 1) are carried.
4048 * "intra" is the sequence of coefficient constraints for intra-node edges.
4049 * "inter" is the sequence of coefficient constraints for inter-node edges.
4050 * "n_edge" is the total number of edges.
4051 * "carry_inter" indicates whether inter-node edges should be carried or
4052 * only respected. That is, if "carry_inter" is not set, then
4053 * no e_i variables are introduced for the inter-node edges.
4055 * All variables of the LP are non-negative. The actual coefficients
4056 * may be negative, so each coefficient is represented as the difference
4057 * of two non-negative variables. The negative part always appears
4058 * immediately before the positive part.
4059 * Other than that, the variables have the following order
4061 * - sum of (1 - e_i) over all edges
4062 * - sum of all c_n coefficients
4063 * (unconstrained when computing non-parametric schedules)
4064 * - sum of positive and negative parts of all c_x coefficients
4068 * - positive and negative parts of c_i_x, in opposite order
4069 * - c_i_n (if parametric)
4072 * The constraints are those from the (validity) edges plus three equalities
4073 * to express the sums and n_edge inequalities to express e_i <= 1.
4075 static isl_stat
setup_carry_lp(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
4076 int n_edge
, __isl_keep isl_basic_set_list
*intra
,
4077 __isl_keep isl_basic_set_list
*inter
, int carry_inter
)
4086 for (i
= 0; i
< graph
->n
; ++i
) {
4087 struct isl_sched_node
*node
= &graph
->node
[graph
->sorted
[i
]];
4088 node
->start
= total
;
4089 total
+= 1 + node
->nparam
+ 2 * node
->nvar
;
4092 if (count_all_constraints(intra
, inter
, &n_eq
, &n_ineq
) < 0)
4093 return isl_stat_error
;
4095 dim
= isl_space_set_alloc(ctx
, 0, total
);
4096 isl_basic_set_free(graph
->lp
);
4099 graph
->lp
= isl_basic_set_alloc_space(dim
, 0, n_eq
, n_ineq
);
4100 graph
->lp
= isl_basic_set_set_rational(graph
->lp
);
4102 k
= isl_basic_set_alloc_equality(graph
->lp
);
4104 return isl_stat_error
;
4105 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
4106 isl_int_set_si(graph
->lp
->eq
[k
][0], -n_edge
);
4107 isl_int_set_si(graph
->lp
->eq
[k
][1], 1);
4108 for (i
= 0; i
< n_edge
; ++i
)
4109 isl_int_set_si(graph
->lp
->eq
[k
][4 + i
], 1);
4111 if (add_param_sum_constraint(graph
, 1) < 0)
4112 return isl_stat_error
;
4113 if (add_var_sum_constraint(graph
, 2) < 0)
4114 return isl_stat_error
;
4116 for (i
= 0; i
< n_edge
; ++i
) {
4117 k
= isl_basic_set_alloc_inequality(graph
->lp
);
4119 return isl_stat_error
;
4120 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
4121 isl_int_set_si(graph
->lp
->ineq
[k
][4 + i
], -1);
4122 isl_int_set_si(graph
->lp
->ineq
[k
][0], 1);
4125 if (add_all_constraints(ctx
, graph
, intra
, inter
, carry_inter
) < 0)
4126 return isl_stat_error
;
4131 static __isl_give isl_schedule_node
*compute_component_schedule(
4132 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
4135 /* If the schedule_split_scaled option is set and if the linear
4136 * parts of the scheduling rows for all nodes in the graphs have
4137 * a non-trivial common divisor, then remove this
4138 * common divisor from the linear part.
4139 * Otherwise, insert a band node directly and continue with
4140 * the construction of the schedule.
4142 * If a non-trivial common divisor is found, then
4143 * the linear part is reduced and the remainder is ignored.
4144 * The pieces of the graph that are assigned different remainders
4145 * form (groups of) strongly connected components within
4146 * the scaled down band. If needed, they can therefore
4147 * be ordered along this remainder in a sequence node.
4148 * However, this ordering is not enforced here in order to allow
4149 * the scheduler to combine some of the strongly connected components.
4151 static __isl_give isl_schedule_node
*split_scaled(
4152 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
4162 ctx
= isl_schedule_node_get_ctx(node
);
4163 if (!ctx
->opt
->schedule_split_scaled
)
4164 return compute_next_band(node
, graph
, 0);
4166 return compute_next_band(node
, graph
, 0);
4169 isl_int_init(gcd_i
);
4171 isl_int_set_si(gcd
, 0);
4173 row
= isl_mat_rows(graph
->node
[0].sched
) - 1;
4175 for (i
= 0; i
< graph
->n
; ++i
) {
4176 struct isl_sched_node
*node
= &graph
->node
[i
];
4177 int cols
= isl_mat_cols(node
->sched
);
4179 isl_seq_gcd(node
->sched
->row
[row
] + 1, cols
- 1, &gcd_i
);
4180 isl_int_gcd(gcd
, gcd
, gcd_i
);
4183 isl_int_clear(gcd_i
);
4185 if (isl_int_cmp_si(gcd
, 1) <= 0) {
4187 return compute_next_band(node
, graph
, 0);
4190 for (i
= 0; i
< graph
->n
; ++i
) {
4191 struct isl_sched_node
*node
= &graph
->node
[i
];
4193 isl_int_fdiv_q(node
->sched
->row
[row
][0],
4194 node
->sched
->row
[row
][0], gcd
);
4195 isl_int_mul(node
->sched
->row
[row
][0],
4196 node
->sched
->row
[row
][0], gcd
);
4197 node
->sched
= isl_mat_scale_down_row(node
->sched
, row
, gcd
);
4204 return compute_next_band(node
, graph
, 0);
4207 return isl_schedule_node_free(node
);
4210 /* Is the schedule row "sol" trivial on node "node"?
4211 * That is, is the solution zero on the dimensions linearly independent of
4212 * the previously found solutions?
4213 * Return 1 if the solution is trivial, 0 if it is not and -1 on error.
4215 * Each coefficient is represented as the difference between
4216 * two non-negative values in "sol".
4217 * We construct the schedule row s and check if it is linearly
4218 * independent of previously computed schedule rows
4219 * by computing T s, with T the linear combinations that are zero
4220 * on linearly dependent schedule rows.
4221 * If the result consists of all zeros, then the solution is trivial.
4223 static int is_trivial(struct isl_sched_node
*node
, __isl_keep isl_vec
*sol
)
4230 if (node
->nvar
== node
->rank
)
4233 node_sol
= extract_var_coef(node
, sol
);
4234 node_sol
= isl_mat_vec_product(isl_mat_copy(node
->indep
), node_sol
);
4238 trivial
= isl_seq_first_non_zero(node_sol
->el
,
4239 node
->nvar
- node
->rank
) == -1;
4241 isl_vec_free(node_sol
);
4246 /* Is the schedule row "sol" trivial on any node where it should
4248 * Return 1 if any solution is trivial, 0 if they are not and -1 on error.
4250 static int is_any_trivial(struct isl_sched_graph
*graph
,
4251 __isl_keep isl_vec
*sol
)
4255 for (i
= 0; i
< graph
->n
; ++i
) {
4256 struct isl_sched_node
*node
= &graph
->node
[i
];
4259 if (!needs_row(graph
, node
))
4261 trivial
= is_trivial(node
, sol
);
4262 if (trivial
< 0 || trivial
)
4269 /* Does the schedule represented by "sol" perform loop coalescing on "node"?
4270 * If so, return the position of the coalesced dimension.
4271 * Otherwise, return node->nvar or -1 on error.
4273 * In particular, look for pairs of coefficients c_i and c_j such that
4274 * |c_j/c_i| > ceil(size_i/2), i.e., |c_j| > |c_i * ceil(size_i/2)|.
4275 * If any such pair is found, then return i.
4276 * If size_i is infinity, then no check on c_i needs to be performed.
4278 static int find_node_coalescing(struct isl_sched_node
*node
,
4279 __isl_keep isl_vec
*sol
)
4285 if (node
->nvar
<= 1)
4288 csol
= extract_var_coef(node
, sol
);
4292 for (i
= 0; i
< node
->nvar
; ++i
) {
4295 if (isl_int_is_zero(csol
->el
[i
]))
4297 v
= isl_multi_val_get_val(node
->sizes
, i
);
4300 if (!isl_val_is_int(v
)) {
4304 v
= isl_val_div_ui(v
, 2);
4305 v
= isl_val_ceil(v
);
4308 isl_int_mul(max
, v
->n
, csol
->el
[i
]);
4311 for (j
= 0; j
< node
->nvar
; ++j
) {
4314 if (isl_int_abs_gt(csol
->el
[j
], max
))
4330 /* Force the schedule coefficient at position "pos" of "node" to be zero
4332 * The coefficient is encoded as the difference between two non-negative
4333 * variables. Force these two variables to have the same value.
4335 static __isl_give isl_tab_lexmin
*zero_out_node_coef(
4336 __isl_take isl_tab_lexmin
*tl
, struct isl_sched_node
*node
, int pos
)
4342 ctx
= isl_space_get_ctx(node
->space
);
4343 dim
= isl_tab_lexmin_dim(tl
);
4345 return isl_tab_lexmin_free(tl
);
4346 eq
= isl_vec_alloc(ctx
, 1 + dim
);
4347 eq
= isl_vec_clr(eq
);
4349 return isl_tab_lexmin_free(tl
);
4351 pos
= 1 + node_var_coef_pos(node
, pos
);
4352 isl_int_set_si(eq
->el
[pos
], 1);
4353 isl_int_set_si(eq
->el
[pos
+ 1], -1);
4354 tl
= isl_tab_lexmin_add_eq(tl
, eq
->el
);
4360 /* Return the lexicographically smallest rational point in the basic set
4361 * from which "tl" was constructed, double checking that this input set
4364 static __isl_give isl_vec
*non_empty_solution(__isl_keep isl_tab_lexmin
*tl
)
4368 sol
= isl_tab_lexmin_get_solution(tl
);
4372 isl_die(isl_vec_get_ctx(sol
), isl_error_internal
,
4373 "error in schedule construction",
4374 return isl_vec_free(sol
));
4378 /* Does the solution "sol" of the LP problem constructed by setup_carry_lp
4379 * carry any of the "n_edge" groups of dependences?
4380 * The value in the first position is the sum of (1 - e_i) over all "n_edge"
4381 * edges, with 0 <= e_i <= 1 equal to 1 when the dependences represented
4382 * by the edge are carried by the solution.
4383 * If the sum of the (1 - e_i) is smaller than "n_edge" then at least
4384 * one of those is carried.
4386 * Note that despite the fact that the problem is solved using a rational
4387 * solver, the solution is guaranteed to be integral.
4388 * Specifically, the dependence distance lower bounds e_i (and therefore
4389 * also their sum) are integers. See Lemma 5 of [1].
4391 * Any potential denominator of the sum is cleared by this function.
4392 * The denominator is not relevant for any of the other elements
4395 * [1] P. Feautrier, Some Efficient Solutions to the Affine Scheduling
4396 * Problem, Part II: Multi-Dimensional Time.
4397 * In Intl. Journal of Parallel Programming, 1992.
4399 static int carries_dependences(__isl_keep isl_vec
*sol
, int n_edge
)
4401 isl_int_divexact(sol
->el
[1], sol
->el
[1], sol
->el
[0]);
4402 isl_int_set_si(sol
->el
[0], 1);
4403 return isl_int_cmp_si(sol
->el
[1], n_edge
) < 0;
4406 /* Return the lexicographically smallest rational point in "lp",
4407 * assuming that all variables are non-negative and performing some
4408 * additional sanity checks.
4409 * If "want_integral" is set, then compute the lexicographically smallest
4410 * integer point instead.
4411 * In particular, "lp" should not be empty by construction.
4412 * Double check that this is the case.
4413 * If dependences are not carried for any of the "n_edge" edges,
4414 * then return an empty vector.
4416 * If the schedule_treat_coalescing option is set and
4417 * if the computed schedule performs loop coalescing on a given node,
4418 * i.e., if it is of the form
4420 * c_i i + c_j j + ...
4422 * with |c_j/c_i| >= size_i, then force the coefficient c_i to be zero
4423 * to cut out this solution. Repeat this process until no more loop
4424 * coalescing occurs or until no more dependences can be carried.
4425 * In the latter case, revert to the previously computed solution.
4427 * If the caller requests an integral solution and if coalescing should
4428 * be treated, then perform the coalescing treatment first as
4429 * an integral solution computed before coalescing treatment
4430 * would carry the same number of edges and would therefore probably
4431 * also be coalescing.
4433 * To allow the coalescing treatment to be performed first,
4434 * the initial solution is allowed to be rational and it is only
4435 * cut out (if needed) in the next iteration, if no coalescing measures
4438 static __isl_give isl_vec
*non_neg_lexmin(struct isl_sched_graph
*graph
,
4439 __isl_take isl_basic_set
*lp
, int n_edge
, int want_integral
)
4444 isl_vec
*sol
, *prev
= NULL
;
4445 int treat_coalescing
;
4449 ctx
= isl_basic_set_get_ctx(lp
);
4450 treat_coalescing
= isl_options_get_schedule_treat_coalescing(ctx
);
4451 tl
= isl_tab_lexmin_from_basic_set(lp
);
4458 tl
= isl_tab_lexmin_cut_to_integer(tl
);
4459 sol
= non_empty_solution(tl
);
4463 integral
= isl_int_is_one(sol
->el
[0]);
4464 if (!carries_dependences(sol
, n_edge
)) {
4466 prev
= isl_vec_alloc(ctx
, 0);
4471 prev
= isl_vec_free(prev
);
4472 cut
= want_integral
&& !integral
;
4475 if (!treat_coalescing
)
4477 for (i
= 0; i
< graph
->n
; ++i
) {
4478 struct isl_sched_node
*node
= &graph
->node
[i
];
4480 pos
= find_node_coalescing(node
, sol
);
4483 if (pos
< node
->nvar
)
4488 tl
= zero_out_node_coef(tl
, &graph
->node
[i
], pos
);
4493 isl_tab_lexmin_free(tl
);
4497 isl_tab_lexmin_free(tl
);
4503 /* If "edge" is an edge from a node to itself, then add the corresponding
4504 * dependence relation to "umap".
4505 * If "node" has been compressed, then the dependence relation
4506 * is also compressed first.
4508 static __isl_give isl_union_map
*add_intra(__isl_take isl_union_map
*umap
,
4509 struct isl_sched_edge
*edge
)
4512 struct isl_sched_node
*node
= edge
->src
;
4514 if (edge
->src
!= edge
->dst
)
4517 map
= isl_map_copy(edge
->map
);
4518 if (node
->compressed
) {
4519 map
= isl_map_preimage_domain_multi_aff(map
,
4520 isl_multi_aff_copy(node
->decompress
));
4521 map
= isl_map_preimage_range_multi_aff(map
,
4522 isl_multi_aff_copy(node
->decompress
));
4524 umap
= isl_union_map_add_map(umap
, map
);
4528 /* If "edge" is an edge from a node to another node, then add the corresponding
4529 * dependence relation to "umap".
4530 * If the source or destination nodes of "edge" have been compressed,
4531 * then the dependence relation is also compressed first.
4533 static __isl_give isl_union_map
*add_inter(__isl_take isl_union_map
*umap
,
4534 struct isl_sched_edge
*edge
)
4538 if (edge
->src
== edge
->dst
)
4541 map
= isl_map_copy(edge
->map
);
4542 if (edge
->src
->compressed
)
4543 map
= isl_map_preimage_domain_multi_aff(map
,
4544 isl_multi_aff_copy(edge
->src
->decompress
));
4545 if (edge
->dst
->compressed
)
4546 map
= isl_map_preimage_range_multi_aff(map
,
4547 isl_multi_aff_copy(edge
->dst
->decompress
));
4548 umap
= isl_union_map_add_map(umap
, map
);
4552 /* Internal data structure used by union_drop_coalescing_constraints
4553 * to collect bounds on all relevant statements.
4555 * "graph" is the schedule constraint graph for which an LP problem
4556 * is being constructed.
4557 * "bounds" collects the bounds.
4559 struct isl_collect_bounds_data
{
4561 struct isl_sched_graph
*graph
;
4562 isl_union_set
*bounds
;
4565 /* Add the size bounds for the node with instance deltas in "set"
4568 static isl_stat
collect_bounds(__isl_take isl_set
*set
, void *user
)
4570 struct isl_collect_bounds_data
*data
= user
;
4571 struct isl_sched_node
*node
;
4575 space
= isl_set_get_space(set
);
4578 node
= graph_find_compressed_node(data
->ctx
, data
->graph
, space
);
4579 isl_space_free(space
);
4581 bounds
= isl_set_from_basic_set(get_size_bounds(node
));
4582 data
->bounds
= isl_union_set_add_set(data
->bounds
, bounds
);
4587 /* Drop some constraints from "delta" that could be exploited
4588 * to construct loop coalescing schedules.
4589 * In particular, drop those constraint that bound the difference
4590 * to the size of the domain.
4591 * Do this for each set/node in "delta" separately.
4592 * The parameters are assumed to have been projected out by the caller.
4594 static __isl_give isl_union_set
*union_drop_coalescing_constraints(isl_ctx
*ctx
,
4595 struct isl_sched_graph
*graph
, __isl_take isl_union_set
*delta
)
4597 struct isl_collect_bounds_data data
= { ctx
, graph
};
4599 data
.bounds
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
4600 if (isl_union_set_foreach_set(delta
, &collect_bounds
, &data
) < 0)
4601 data
.bounds
= isl_union_set_free(data
.bounds
);
4602 delta
= isl_union_set_plain_gist(delta
, data
.bounds
);
4607 /* Given a non-trivial lineality space "lineality", add the corresponding
4608 * universe set to data->mask and add a map from elements to
4609 * other elements along the lines in "lineality" to data->equivalent.
4610 * If this is the first time this function gets called
4611 * (data->any_non_trivial is still false), then set data->any_non_trivial and
4612 * initialize data->mask and data->equivalent.
4614 * In particular, if the lineality space is defined by equality constraints
4618 * then construct an affine mapping
4622 * and compute the equivalence relation of having the same image under f:
4624 * { x -> x' : E x = E x' }
4626 static isl_stat
add_non_trivial_lineality(__isl_take isl_basic_set
*lineality
,
4627 struct isl_exploit_lineality_data
*data
)
4633 isl_multi_pw_aff
*mpa
;
4638 return isl_stat_error
;
4639 if (isl_basic_set_dim(lineality
, isl_dim_div
) != 0)
4640 isl_die(isl_basic_set_get_ctx(lineality
), isl_error_internal
,
4641 "local variables not allowed", goto error
);
4643 space
= isl_basic_set_get_space(lineality
);
4644 if (!data
->any_non_trivial
) {
4645 data
->equivalent
= isl_union_map_empty(isl_space_copy(space
));
4646 data
->mask
= isl_union_set_empty(isl_space_copy(space
));
4648 data
->any_non_trivial
= isl_bool_true
;
4650 univ
= isl_set_universe(isl_space_copy(space
));
4651 data
->mask
= isl_union_set_add_set(data
->mask
, univ
);
4653 eq
= isl_basic_set_extract_equalities(lineality
);
4654 n
= isl_mat_rows(eq
);
4655 eq
= isl_mat_insert_zero_rows(eq
, 0, 1);
4656 eq
= isl_mat_set_element_si(eq
, 0, 0, 1);
4657 space
= isl_space_from_domain(space
);
4658 space
= isl_space_add_dims(space
, isl_dim_out
, n
);
4659 ma
= isl_multi_aff_from_aff_mat(space
, eq
);
4660 mpa
= isl_multi_pw_aff_from_multi_aff(ma
);
4661 map
= isl_multi_pw_aff_eq_map(mpa
, isl_multi_pw_aff_copy(mpa
));
4662 data
->equivalent
= isl_union_map_add_map(data
->equivalent
, map
);
4664 isl_basic_set_free(lineality
);
4667 isl_basic_set_free(lineality
);
4668 return isl_stat_error
;
4671 /* Check if the lineality space "set" is non-trivial (i.e., is not just
4672 * the origin or, in other words, satisfies a number of equality constraints
4673 * that is smaller than the dimension of the set).
4674 * If so, extend data->mask and data->equivalent accordingly.
4676 * The input should not have any local variables already, but
4677 * isl_set_remove_divs is called to make sure it does not.
4679 static isl_stat
add_lineality(__isl_take isl_set
*set
, void *user
)
4681 struct isl_exploit_lineality_data
*data
= user
;
4682 isl_basic_set
*hull
;
4685 set
= isl_set_remove_divs(set
);
4686 hull
= isl_set_unshifted_simple_hull(set
);
4687 dim
= isl_basic_set_dim(hull
, isl_dim_set
);
4688 n_eq
= isl_basic_set_n_equality(hull
);
4690 return isl_stat_error
;
4692 return add_non_trivial_lineality(hull
, data
);
4693 isl_basic_set_free(hull
);
4697 /* Check if the difference set on intra-node schedule constraints "intra"
4698 * has any non-trivial lineality space.
4699 * If so, then extend the difference set to a difference set
4700 * on equivalent elements. That is, if "intra" is
4702 * { y - x : (x,y) \in V }
4704 * and elements are equivalent if they have the same image under f,
4707 * { y' - x' : (x,y) \in V and f(x) = f(x') and f(y) = f(y') }
4709 * or, since f is linear,
4711 * { y' - x' : (x,y) \in V and f(y - x) = f(y' - x') }
4713 * The results of the search for non-trivial lineality spaces is stored
4716 static __isl_give isl_union_set
*exploit_intra_lineality(
4717 __isl_take isl_union_set
*intra
,
4718 struct isl_exploit_lineality_data
*data
)
4720 isl_union_set
*lineality
;
4721 isl_union_set
*uset
;
4723 data
->any_non_trivial
= isl_bool_false
;
4724 lineality
= isl_union_set_copy(intra
);
4725 lineality
= isl_union_set_combined_lineality_space(lineality
);
4726 if (isl_union_set_foreach_set(lineality
, &add_lineality
, data
) < 0)
4727 data
->any_non_trivial
= isl_bool_error
;
4728 isl_union_set_free(lineality
);
4730 if (data
->any_non_trivial
< 0)
4731 return isl_union_set_free(intra
);
4732 if (!data
->any_non_trivial
)
4735 uset
= isl_union_set_copy(intra
);
4736 intra
= isl_union_set_subtract(intra
, isl_union_set_copy(data
->mask
));
4737 uset
= isl_union_set_apply(uset
, isl_union_map_copy(data
->equivalent
));
4738 intra
= isl_union_set_union(intra
, uset
);
4740 intra
= isl_union_set_remove_divs(intra
);
4745 /* If the difference set on intra-node schedule constraints was found to have
4746 * any non-trivial lineality space by exploit_intra_lineality,
4747 * as recorded in "data", then extend the inter-node
4748 * schedule constraints "inter" to schedule constraints on equivalent elements.
4749 * That is, if "inter" is V and
4750 * elements are equivalent if they have the same image under f, then return
4752 * { (x', y') : (x,y) \in V and f(x) = f(x') and f(y) = f(y') }
4754 static __isl_give isl_union_map
*exploit_inter_lineality(
4755 __isl_take isl_union_map
*inter
,
4756 struct isl_exploit_lineality_data
*data
)
4758 isl_union_map
*umap
;
4760 if (data
->any_non_trivial
< 0)
4761 return isl_union_map_free(inter
);
4762 if (!data
->any_non_trivial
)
4765 umap
= isl_union_map_copy(inter
);
4766 inter
= isl_union_map_subtract_range(inter
,
4767 isl_union_set_copy(data
->mask
));
4768 umap
= isl_union_map_apply_range(umap
,
4769 isl_union_map_copy(data
->equivalent
));
4770 inter
= isl_union_map_union(inter
, umap
);
4771 umap
= isl_union_map_copy(inter
);
4772 inter
= isl_union_map_subtract_domain(inter
,
4773 isl_union_set_copy(data
->mask
));
4774 umap
= isl_union_map_apply_range(isl_union_map_copy(data
->equivalent
),
4776 inter
= isl_union_map_union(inter
, umap
);
4778 inter
= isl_union_map_remove_divs(inter
);
4783 /* For each (conditional) validity edge in "graph",
4784 * add the corresponding dependence relation using "add"
4785 * to a collection of dependence relations and return the result.
4786 * If "coincidence" is set, then coincidence edges are considered as well.
4788 static __isl_give isl_union_map
*collect_validity(struct isl_sched_graph
*graph
,
4789 __isl_give isl_union_map
*(*add
)(__isl_take isl_union_map
*umap
,
4790 struct isl_sched_edge
*edge
), int coincidence
)
4794 isl_union_map
*umap
;
4796 space
= isl_space_copy(graph
->node
[0].space
);
4797 umap
= isl_union_map_empty(space
);
4799 for (i
= 0; i
< graph
->n_edge
; ++i
) {
4800 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
4802 if (!is_any_validity(edge
) &&
4803 (!coincidence
|| !is_coincidence(edge
)))
4806 umap
= add(umap
, edge
);
4812 /* Project out all parameters from "uset" and return the result.
4814 static __isl_give isl_union_set
*union_set_drop_parameters(
4815 __isl_take isl_union_set
*uset
)
4819 nparam
= isl_union_set_dim(uset
, isl_dim_param
);
4820 return isl_union_set_project_out(uset
, isl_dim_param
, 0, nparam
);
4823 /* For each dependence relation on a (conditional) validity edge
4824 * from a node to itself,
4825 * construct the set of coefficients of valid constraints for elements
4826 * in that dependence relation and collect the results.
4827 * If "coincidence" is set, then coincidence edges are considered as well.
4829 * In particular, for each dependence relation R, constraints
4830 * on coefficients (c_0, c_x) are constructed such that
4832 * c_0 + c_x d >= 0 for each d in delta R = { y - x | (x,y) in R }
4834 * If the schedule_treat_coalescing option is set, then some constraints
4835 * that could be exploited to construct coalescing schedules
4836 * are removed before the dual is computed, but after the parameters
4837 * have been projected out.
4838 * The entire computation is essentially the same as that performed
4839 * by intra_coefficients, except that it operates on multiple
4840 * edges together and that the parameters are always projected out.
4842 * Additionally, exploit any non-trivial lineality space
4843 * in the difference set after removing coalescing constraints and
4844 * store the results of the non-trivial lineality space detection in "data".
4845 * The procedure is currently run unconditionally, but it is unlikely
4846 * to find any non-trivial lineality spaces if no coalescing constraints
4847 * have been removed.
4849 * Note that if a dependence relation is a union of basic maps,
4850 * then each basic map needs to be treated individually as it may only
4851 * be possible to carry the dependences expressed by some of those
4852 * basic maps and not all of them.
4853 * The collected validity constraints are therefore not coalesced and
4854 * it is assumed that they are not coalesced automatically.
4855 * Duplicate basic maps can be removed, however.
4856 * In particular, if the same basic map appears as a disjunct
4857 * in multiple edges, then it only needs to be carried once.
4859 static __isl_give isl_basic_set_list
*collect_intra_validity(isl_ctx
*ctx
,
4860 struct isl_sched_graph
*graph
, int coincidence
,
4861 struct isl_exploit_lineality_data
*data
)
4863 isl_union_map
*intra
;
4864 isl_union_set
*delta
;
4865 isl_basic_set_list
*list
;
4867 intra
= collect_validity(graph
, &add_intra
, coincidence
);
4868 delta
= isl_union_map_deltas(intra
);
4869 delta
= union_set_drop_parameters(delta
);
4870 delta
= isl_union_set_remove_divs(delta
);
4871 if (isl_options_get_schedule_treat_coalescing(ctx
))
4872 delta
= union_drop_coalescing_constraints(ctx
, graph
, delta
);
4873 delta
= exploit_intra_lineality(delta
, data
);
4874 list
= isl_union_set_get_basic_set_list(delta
);
4875 isl_union_set_free(delta
);
4877 return isl_basic_set_list_coefficients(list
);
4880 /* For each dependence relation on a (conditional) validity edge
4881 * from a node to some other node,
4882 * construct the set of coefficients of valid constraints for elements
4883 * in that dependence relation and collect the results.
4884 * If "coincidence" is set, then coincidence edges are considered as well.
4886 * In particular, for each dependence relation R, constraints
4887 * on coefficients (c_0, c_n, c_x, c_y) are constructed such that
4889 * c_0 + c_n n + c_x x + c_y y >= 0 for each (x,y) in R
4891 * This computation is essentially the same as that performed
4892 * by inter_coefficients, except that it operates on multiple
4895 * Additionally, exploit any non-trivial lineality space
4896 * that may have been discovered by collect_intra_validity
4897 * (as stored in "data").
4899 * Note that if a dependence relation is a union of basic maps,
4900 * then each basic map needs to be treated individually as it may only
4901 * be possible to carry the dependences expressed by some of those
4902 * basic maps and not all of them.
4903 * The collected validity constraints are therefore not coalesced and
4904 * it is assumed that they are not coalesced automatically.
4905 * Duplicate basic maps can be removed, however.
4906 * In particular, if the same basic map appears as a disjunct
4907 * in multiple edges, then it only needs to be carried once.
4909 static __isl_give isl_basic_set_list
*collect_inter_validity(
4910 struct isl_sched_graph
*graph
, int coincidence
,
4911 struct isl_exploit_lineality_data
*data
)
4913 isl_union_map
*inter
;
4914 isl_union_set
*wrap
;
4915 isl_basic_set_list
*list
;
4917 inter
= collect_validity(graph
, &add_inter
, coincidence
);
4918 inter
= exploit_inter_lineality(inter
, data
);
4919 inter
= isl_union_map_remove_divs(inter
);
4920 wrap
= isl_union_map_wrap(inter
);
4921 list
= isl_union_set_get_basic_set_list(wrap
);
4922 isl_union_set_free(wrap
);
4923 return isl_basic_set_list_coefficients(list
);
4926 /* Construct an LP problem for finding schedule coefficients
4927 * such that the schedule carries as many of the "n_edge" groups of
4928 * dependences as possible based on the corresponding coefficient
4929 * constraints and return the lexicographically smallest non-trivial solution.
4930 * "intra" is the sequence of coefficient constraints for intra-node edges.
4931 * "inter" is the sequence of coefficient constraints for inter-node edges.
4932 * If "want_integral" is set, then compute an integral solution
4933 * for the coefficients rather than using the numerators
4934 * of a rational solution.
4935 * "carry_inter" indicates whether inter-node edges should be carried or
4938 * If none of the "n_edge" groups can be carried
4939 * then return an empty vector.
4941 static __isl_give isl_vec
*compute_carrying_sol_coef(isl_ctx
*ctx
,
4942 struct isl_sched_graph
*graph
, int n_edge
,
4943 __isl_keep isl_basic_set_list
*intra
,
4944 __isl_keep isl_basic_set_list
*inter
, int want_integral
,
4949 if (setup_carry_lp(ctx
, graph
, n_edge
, intra
, inter
, carry_inter
) < 0)
4952 lp
= isl_basic_set_copy(graph
->lp
);
4953 return non_neg_lexmin(graph
, lp
, n_edge
, want_integral
);
4956 /* Construct an LP problem for finding schedule coefficients
4957 * such that the schedule carries as many of the validity dependences
4959 * return the lexicographically smallest non-trivial solution.
4960 * If "fallback" is set, then the carrying is performed as a fallback
4961 * for the Pluto-like scheduler.
4962 * If "coincidence" is set, then try and carry coincidence edges as well.
4964 * The variable "n_edge" stores the number of groups that should be carried.
4965 * If none of the "n_edge" groups can be carried
4966 * then return an empty vector.
4967 * If, moreover, "n_edge" is zero, then the LP problem does not even
4968 * need to be constructed.
4970 * If a fallback solution is being computed, then compute an integral solution
4971 * for the coefficients rather than using the numerators
4972 * of a rational solution.
4974 * If a fallback solution is being computed, if there are any intra-node
4975 * dependences, and if requested by the user, then first try
4976 * to only carry those intra-node dependences.
4977 * If this fails to carry any dependences, then try again
4978 * with the inter-node dependences included.
4980 static __isl_give isl_vec
*compute_carrying_sol(isl_ctx
*ctx
,
4981 struct isl_sched_graph
*graph
, int fallback
, int coincidence
)
4983 int n_intra
, n_inter
;
4985 struct isl_carry carry
= { 0 };
4988 carry
.intra
= collect_intra_validity(ctx
, graph
, coincidence
,
4990 carry
.inter
= collect_inter_validity(graph
, coincidence
,
4992 if (!carry
.intra
|| !carry
.inter
)
4994 n_intra
= isl_basic_set_list_n_basic_set(carry
.intra
);
4995 n_inter
= isl_basic_set_list_n_basic_set(carry
.inter
);
4997 if (fallback
&& n_intra
> 0 &&
4998 isl_options_get_schedule_carry_self_first(ctx
)) {
4999 sol
= compute_carrying_sol_coef(ctx
, graph
, n_intra
,
5000 carry
.intra
, carry
.inter
, fallback
, 0);
5001 if (!sol
|| sol
->size
!= 0 || n_inter
== 0) {
5002 isl_carry_clear(&carry
);
5008 n_edge
= n_intra
+ n_inter
;
5010 isl_carry_clear(&carry
);
5011 return isl_vec_alloc(ctx
, 0);
5014 sol
= compute_carrying_sol_coef(ctx
, graph
, n_edge
,
5015 carry
.intra
, carry
.inter
, fallback
, 1);
5016 isl_carry_clear(&carry
);
5019 isl_carry_clear(&carry
);
5023 /* Construct a schedule row for each node such that as many validity dependences
5024 * as possible are carried and then continue with the next band.
5025 * If "fallback" is set, then the carrying is performed as a fallback
5026 * for the Pluto-like scheduler.
5027 * If "coincidence" is set, then try and carry coincidence edges as well.
5029 * If there are no validity dependences, then no dependence can be carried and
5030 * the procedure is guaranteed to fail. If there is more than one component,
5031 * then try computing a schedule on each component separately
5032 * to prevent or at least postpone this failure.
5034 * If a schedule row is computed, then check that dependences are carried
5035 * for at least one of the edges.
5037 * If the computed schedule row turns out to be trivial on one or
5038 * more nodes where it should not be trivial, then we throw it away
5039 * and try again on each component separately.
5041 * If there is only one component, then we accept the schedule row anyway,
5042 * but we do not consider it as a complete row and therefore do not
5043 * increment graph->n_row. Note that the ranks of the nodes that
5044 * do get a non-trivial schedule part will get updated regardless and
5045 * graph->maxvar is computed based on these ranks. The test for
5046 * whether more schedule rows are required in compute_schedule_wcc
5047 * is therefore not affected.
5049 * Insert a band corresponding to the schedule row at position "node"
5050 * of the schedule tree and continue with the construction of the schedule.
5051 * This insertion and the continued construction is performed by split_scaled
5052 * after optionally checking for non-trivial common divisors.
5054 static __isl_give isl_schedule_node
*carry(__isl_take isl_schedule_node
*node
,
5055 struct isl_sched_graph
*graph
, int fallback
, int coincidence
)
5064 ctx
= isl_schedule_node_get_ctx(node
);
5065 sol
= compute_carrying_sol(ctx
, graph
, fallback
, coincidence
);
5067 return isl_schedule_node_free(node
);
5068 if (sol
->size
== 0) {
5071 return compute_component_schedule(node
, graph
, 1);
5072 isl_die(ctx
, isl_error_unknown
, "unable to carry dependences",
5073 return isl_schedule_node_free(node
));
5076 trivial
= is_any_trivial(graph
, sol
);
5078 sol
= isl_vec_free(sol
);
5079 } else if (trivial
&& graph
->scc
> 1) {
5081 return compute_component_schedule(node
, graph
, 1);
5084 if (update_schedule(graph
, sol
, 0) < 0)
5085 return isl_schedule_node_free(node
);
5089 return split_scaled(node
, graph
);
5092 /* Construct a schedule row for each node such that as many validity dependences
5093 * as possible are carried and then continue with the next band.
5094 * Do so as a fallback for the Pluto-like scheduler.
5095 * If "coincidence" is set, then try and carry coincidence edges as well.
5097 static __isl_give isl_schedule_node
*carry_fallback(
5098 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
5101 return carry(node
, graph
, 1, coincidence
);
5104 /* Construct a schedule row for each node such that as many validity dependences
5105 * as possible are carried and then continue with the next band.
5106 * Do so for the case where the Feautrier scheduler was selected
5109 static __isl_give isl_schedule_node
*carry_feautrier(
5110 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
5112 return carry(node
, graph
, 0, 0);
5115 /* Construct a schedule row for each node such that as many validity dependences
5116 * as possible are carried and then continue with the next band.
5117 * Do so as a fallback for the Pluto-like scheduler.
5119 static __isl_give isl_schedule_node
*carry_dependences(
5120 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
5122 return carry_fallback(node
, graph
, 0);
5125 /* Construct a schedule row for each node such that as many validity or
5126 * coincidence dependences as possible are carried and
5127 * then continue with the next band.
5128 * Do so as a fallback for the Pluto-like scheduler.
5130 static __isl_give isl_schedule_node
*carry_coincidence(
5131 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
5133 return carry_fallback(node
, graph
, 1);
5136 /* Topologically sort statements mapped to the same schedule iteration
5137 * and add insert a sequence node in front of "node"
5138 * corresponding to this order.
5139 * If "initialized" is set, then it may be assumed that compute_maxvar
5140 * has been called on the current band. Otherwise, call
5141 * compute_maxvar if and before carry_dependences gets called.
5143 * If it turns out to be impossible to sort the statements apart,
5144 * because different dependences impose different orderings
5145 * on the statements, then we extend the schedule such that
5146 * it carries at least one more dependence.
5148 static __isl_give isl_schedule_node
*sort_statements(
5149 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
5153 isl_union_set_list
*filters
;
5158 ctx
= isl_schedule_node_get_ctx(node
);
5160 isl_die(ctx
, isl_error_internal
,
5161 "graph should have at least one node",
5162 return isl_schedule_node_free(node
));
5167 if (update_edges(ctx
, graph
) < 0)
5168 return isl_schedule_node_free(node
);
5170 if (graph
->n_edge
== 0)
5173 if (detect_sccs(ctx
, graph
) < 0)
5174 return isl_schedule_node_free(node
);
5177 if (graph
->scc
< graph
->n
) {
5178 if (!initialized
&& compute_maxvar(graph
) < 0)
5179 return isl_schedule_node_free(node
);
5180 return carry_dependences(node
, graph
);
5183 filters
= extract_sccs(ctx
, graph
);
5184 node
= isl_schedule_node_insert_sequence(node
, filters
);
5189 /* Are there any (non-empty) (conditional) validity edges in the graph?
5191 static int has_validity_edges(struct isl_sched_graph
*graph
)
5195 for (i
= 0; i
< graph
->n_edge
; ++i
) {
5198 empty
= isl_map_plain_is_empty(graph
->edge
[i
].map
);
5203 if (is_any_validity(&graph
->edge
[i
]))
5210 /* Should we apply a Feautrier step?
5211 * That is, did the user request the Feautrier algorithm and are
5212 * there any validity dependences (left)?
5214 static int need_feautrier_step(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
5216 if (ctx
->opt
->schedule_algorithm
!= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
)
5219 return has_validity_edges(graph
);
5222 /* Compute a schedule for a connected dependence graph using Feautrier's
5223 * multi-dimensional scheduling algorithm and return the updated schedule node.
5225 * The original algorithm is described in [1].
5226 * The main idea is to minimize the number of scheduling dimensions, by
5227 * trying to satisfy as many dependences as possible per scheduling dimension.
5229 * [1] P. Feautrier, Some Efficient Solutions to the Affine Scheduling
5230 * Problem, Part II: Multi-Dimensional Time.
5231 * In Intl. Journal of Parallel Programming, 1992.
5233 static __isl_give isl_schedule_node
*compute_schedule_wcc_feautrier(
5234 isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
5236 return carry_feautrier(node
, graph
);
5239 /* Turn off the "local" bit on all (condition) edges.
5241 static void clear_local_edges(struct isl_sched_graph
*graph
)
5245 for (i
= 0; i
< graph
->n_edge
; ++i
)
5246 if (is_condition(&graph
->edge
[i
]))
5247 clear_local(&graph
->edge
[i
]);
5250 /* Does "graph" have both condition and conditional validity edges?
5252 static int need_condition_check(struct isl_sched_graph
*graph
)
5255 int any_condition
= 0;
5256 int any_conditional_validity
= 0;
5258 for (i
= 0; i
< graph
->n_edge
; ++i
) {
5259 if (is_condition(&graph
->edge
[i
]))
5261 if (is_conditional_validity(&graph
->edge
[i
]))
5262 any_conditional_validity
= 1;
5265 return any_condition
&& any_conditional_validity
;
5268 /* Does "graph" contain any coincidence edge?
5270 static int has_any_coincidence(struct isl_sched_graph
*graph
)
5274 for (i
= 0; i
< graph
->n_edge
; ++i
)
5275 if (is_coincidence(&graph
->edge
[i
]))
5281 /* Extract the final schedule row as a map with the iteration domain
5282 * of "node" as domain.
5284 static __isl_give isl_map
*final_row(struct isl_sched_node
*node
)
5289 row
= isl_mat_rows(node
->sched
) - 1;
5290 ma
= node_extract_partial_schedule_multi_aff(node
, row
, 1);
5291 return isl_map_from_multi_aff(ma
);
5294 /* Is the conditional validity dependence in the edge with index "edge_index"
5295 * violated by the latest (i.e., final) row of the schedule?
5296 * That is, is i scheduled after j
5297 * for any conditional validity dependence i -> j?
5299 static int is_violated(struct isl_sched_graph
*graph
, int edge_index
)
5301 isl_map
*src_sched
, *dst_sched
, *map
;
5302 struct isl_sched_edge
*edge
= &graph
->edge
[edge_index
];
5305 src_sched
= final_row(edge
->src
);
5306 dst_sched
= final_row(edge
->dst
);
5307 map
= isl_map_copy(edge
->map
);
5308 map
= isl_map_apply_domain(map
, src_sched
);
5309 map
= isl_map_apply_range(map
, dst_sched
);
5310 map
= isl_map_order_gt(map
, isl_dim_in
, 0, isl_dim_out
, 0);
5311 empty
= isl_map_is_empty(map
);
5320 /* Does "graph" have any satisfied condition edges that
5321 * are adjacent to the conditional validity constraint with
5322 * domain "conditional_source" and range "conditional_sink"?
5324 * A satisfied condition is one that is not local.
5325 * If a condition was forced to be local already (i.e., marked as local)
5326 * then there is no need to check if it is in fact local.
5328 * Additionally, mark all adjacent condition edges found as local.
5330 static int has_adjacent_true_conditions(struct isl_sched_graph
*graph
,
5331 __isl_keep isl_union_set
*conditional_source
,
5332 __isl_keep isl_union_set
*conditional_sink
)
5337 for (i
= 0; i
< graph
->n_edge
; ++i
) {
5338 int adjacent
, local
;
5339 isl_union_map
*condition
;
5341 if (!is_condition(&graph
->edge
[i
]))
5343 if (is_local(&graph
->edge
[i
]))
5346 condition
= graph
->edge
[i
].tagged_condition
;
5347 adjacent
= domain_intersects(condition
, conditional_sink
);
5348 if (adjacent
>= 0 && !adjacent
)
5349 adjacent
= range_intersects(condition
,
5350 conditional_source
);
5356 set_local(&graph
->edge
[i
]);
5358 local
= is_condition_false(&graph
->edge
[i
]);
5368 /* Are there any violated conditional validity dependences with
5369 * adjacent condition dependences that are not local with respect
5370 * to the current schedule?
5371 * That is, is the conditional validity constraint violated?
5373 * Additionally, mark all those adjacent condition dependences as local.
5374 * We also mark those adjacent condition dependences that were not marked
5375 * as local before, but just happened to be local already. This ensures
5376 * that they remain local if the schedule is recomputed.
5378 * We first collect domain and range of all violated conditional validity
5379 * dependences and then check if there are any adjacent non-local
5380 * condition dependences.
5382 static int has_violated_conditional_constraint(isl_ctx
*ctx
,
5383 struct isl_sched_graph
*graph
)
5387 isl_union_set
*source
, *sink
;
5389 source
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
5390 sink
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
5391 for (i
= 0; i
< graph
->n_edge
; ++i
) {
5392 isl_union_set
*uset
;
5393 isl_union_map
*umap
;
5396 if (!is_conditional_validity(&graph
->edge
[i
]))
5399 violated
= is_violated(graph
, i
);
5407 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_validity
);
5408 uset
= isl_union_map_domain(umap
);
5409 source
= isl_union_set_union(source
, uset
);
5410 source
= isl_union_set_coalesce(source
);
5412 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_validity
);
5413 uset
= isl_union_map_range(umap
);
5414 sink
= isl_union_set_union(sink
, uset
);
5415 sink
= isl_union_set_coalesce(sink
);
5419 any
= has_adjacent_true_conditions(graph
, source
, sink
);
5421 isl_union_set_free(source
);
5422 isl_union_set_free(sink
);
5425 isl_union_set_free(source
);
5426 isl_union_set_free(sink
);
5430 /* Examine the current band (the rows between graph->band_start and
5431 * graph->n_total_row), deciding whether to drop it or add it to "node"
5432 * and then continue with the computation of the next band, if any.
5433 * If "initialized" is set, then it may be assumed that compute_maxvar
5434 * has been called on the current band. Otherwise, call
5435 * compute_maxvar if and before carry_dependences gets called.
5437 * The caller keeps looking for a new row as long as
5438 * graph->n_row < graph->maxvar. If the latest attempt to find
5439 * such a row failed (i.e., we still have graph->n_row < graph->maxvar),
5441 * - split between SCCs and start over (assuming we found an interesting
5442 * pair of SCCs between which to split)
5443 * - continue with the next band (assuming the current band has at least
5445 * - if there is more than one SCC left, then split along all SCCs
5446 * - if outer coincidence needs to be enforced, then try to carry as many
5447 * validity or coincidence dependences as possible and
5448 * continue with the next band
5449 * - try to carry as many validity dependences as possible and
5450 * continue with the next band
5451 * In each case, we first insert a band node in the schedule tree
5452 * if any rows have been computed.
5454 * If the caller managed to complete the schedule, we insert a band node
5455 * (if any schedule rows were computed) and we finish off by topologically
5456 * sorting the statements based on the remaining dependences.
5458 static __isl_give isl_schedule_node
*compute_schedule_finish_band(
5459 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
5467 if (graph
->n_row
< graph
->maxvar
) {
5469 int empty
= graph
->n_total_row
== graph
->band_start
;
5471 ctx
= isl_schedule_node_get_ctx(node
);
5472 if (!ctx
->opt
->schedule_maximize_band_depth
&& !empty
)
5473 return compute_next_band(node
, graph
, 1);
5474 if (graph
->src_scc
>= 0)
5475 return compute_split_schedule(node
, graph
);
5477 return compute_next_band(node
, graph
, 1);
5479 return compute_component_schedule(node
, graph
, 1);
5480 if (!initialized
&& compute_maxvar(graph
) < 0)
5481 return isl_schedule_node_free(node
);
5482 if (isl_options_get_schedule_outer_coincidence(ctx
))
5483 return carry_coincidence(node
, graph
);
5484 return carry_dependences(node
, graph
);
5487 insert
= graph
->n_total_row
> graph
->band_start
;
5489 node
= insert_current_band(node
, graph
, 1);
5490 node
= isl_schedule_node_child(node
, 0);
5492 node
= sort_statements(node
, graph
, initialized
);
5494 node
= isl_schedule_node_parent(node
);
5499 /* Construct a band of schedule rows for a connected dependence graph.
5500 * The caller is responsible for determining the strongly connected
5501 * components and calling compute_maxvar first.
5503 * We try to find a sequence of as many schedule rows as possible that result
5504 * in non-negative dependence distances (independent of the previous rows
5505 * in the sequence, i.e., such that the sequence is tilable), with as
5506 * many of the initial rows as possible satisfying the coincidence constraints.
5507 * The computation stops if we can't find any more rows or if we have found
5508 * all the rows we wanted to find.
5510 * If ctx->opt->schedule_outer_coincidence is set, then we force the
5511 * outermost dimension to satisfy the coincidence constraints. If this
5512 * turns out to be impossible, we fall back on the general scheme above
5513 * and try to carry as many dependences as possible.
5515 * If "graph" contains both condition and conditional validity dependences,
5516 * then we need to check that that the conditional schedule constraint
5517 * is satisfied, i.e., there are no violated conditional validity dependences
5518 * that are adjacent to any non-local condition dependences.
5519 * If there are, then we mark all those adjacent condition dependences
5520 * as local and recompute the current band. Those dependences that
5521 * are marked local will then be forced to be local.
5522 * The initial computation is performed with no dependences marked as local.
5523 * If we are lucky, then there will be no violated conditional validity
5524 * dependences adjacent to any non-local condition dependences.
5525 * Otherwise, we mark some additional condition dependences as local and
5526 * recompute. We continue this process until there are no violations left or
5527 * until we are no longer able to compute a schedule.
5528 * Since there are only a finite number of dependences,
5529 * there will only be a finite number of iterations.
5531 static isl_stat
compute_schedule_wcc_band(isl_ctx
*ctx
,
5532 struct isl_sched_graph
*graph
)
5534 int has_coincidence
;
5535 int use_coincidence
;
5536 int force_coincidence
= 0;
5537 int check_conditional
;
5539 if (sort_sccs(graph
) < 0)
5540 return isl_stat_error
;
5542 clear_local_edges(graph
);
5543 check_conditional
= need_condition_check(graph
);
5544 has_coincidence
= has_any_coincidence(graph
);
5546 if (ctx
->opt
->schedule_outer_coincidence
)
5547 force_coincidence
= 1;
5549 use_coincidence
= has_coincidence
;
5550 while (graph
->n_row
< graph
->maxvar
) {
5555 graph
->src_scc
= -1;
5556 graph
->dst_scc
= -1;
5558 if (setup_lp(ctx
, graph
, use_coincidence
) < 0)
5559 return isl_stat_error
;
5560 sol
= solve_lp(ctx
, graph
);
5562 return isl_stat_error
;
5563 if (sol
->size
== 0) {
5564 int empty
= graph
->n_total_row
== graph
->band_start
;
5567 if (use_coincidence
&& (!force_coincidence
|| !empty
)) {
5568 use_coincidence
= 0;
5573 coincident
= !has_coincidence
|| use_coincidence
;
5574 if (update_schedule(graph
, sol
, coincident
) < 0)
5575 return isl_stat_error
;
5577 if (!check_conditional
)
5579 violated
= has_violated_conditional_constraint(ctx
, graph
);
5581 return isl_stat_error
;
5584 if (reset_band(graph
) < 0)
5585 return isl_stat_error
;
5586 use_coincidence
= has_coincidence
;
5592 /* Compute a schedule for a connected dependence graph by considering
5593 * the graph as a whole and return the updated schedule node.
5595 * The actual schedule rows of the current band are computed by
5596 * compute_schedule_wcc_band. compute_schedule_finish_band takes
5597 * care of integrating the band into "node" and continuing
5600 static __isl_give isl_schedule_node
*compute_schedule_wcc_whole(
5601 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
5608 ctx
= isl_schedule_node_get_ctx(node
);
5609 if (compute_schedule_wcc_band(ctx
, graph
) < 0)
5610 return isl_schedule_node_free(node
);
5612 return compute_schedule_finish_band(node
, graph
, 1);
5615 /* Clustering information used by compute_schedule_wcc_clustering.
5617 * "n" is the number of SCCs in the original dependence graph
5618 * "scc" is an array of "n" elements, each representing an SCC
5619 * of the original dependence graph. All entries in the same cluster
5620 * have the same number of schedule rows.
5621 * "scc_cluster" maps each SCC index to the cluster to which it belongs,
5622 * where each cluster is represented by the index of the first SCC
5623 * in the cluster. Initially, each SCC belongs to a cluster containing
5626 * "scc_in_merge" is used by merge_clusters_along_edge to keep
5627 * track of which SCCs need to be merged.
5629 * "cluster" contains the merged clusters of SCCs after the clustering
5632 * "scc_node" is a temporary data structure used inside copy_partial.
5633 * For each SCC, it keeps track of the number of nodes in the SCC
5634 * that have already been copied.
5636 struct isl_clustering
{
5638 struct isl_sched_graph
*scc
;
5639 struct isl_sched_graph
*cluster
;
5645 /* Initialize the clustering data structure "c" from "graph".
5647 * In particular, allocate memory, extract the SCCs from "graph"
5648 * into c->scc, initialize scc_cluster and construct
5649 * a band of schedule rows for each SCC.
5650 * Within each SCC, there is only one SCC by definition.
5651 * Each SCC initially belongs to a cluster containing only that SCC.
5653 static isl_stat
clustering_init(isl_ctx
*ctx
, struct isl_clustering
*c
,
5654 struct isl_sched_graph
*graph
)
5659 c
->scc
= isl_calloc_array(ctx
, struct isl_sched_graph
, c
->n
);
5660 c
->cluster
= isl_calloc_array(ctx
, struct isl_sched_graph
, c
->n
);
5661 c
->scc_cluster
= isl_calloc_array(ctx
, int, c
->n
);
5662 c
->scc_node
= isl_calloc_array(ctx
, int, c
->n
);
5663 c
->scc_in_merge
= isl_calloc_array(ctx
, int, c
->n
);
5664 if (!c
->scc
|| !c
->cluster
||
5665 !c
->scc_cluster
|| !c
->scc_node
|| !c
->scc_in_merge
)
5666 return isl_stat_error
;
5668 for (i
= 0; i
< c
->n
; ++i
) {
5669 if (extract_sub_graph(ctx
, graph
, &node_scc_exactly
,
5670 &edge_scc_exactly
, i
, &c
->scc
[i
]) < 0)
5671 return isl_stat_error
;
5673 if (compute_maxvar(&c
->scc
[i
]) < 0)
5674 return isl_stat_error
;
5675 if (compute_schedule_wcc_band(ctx
, &c
->scc
[i
]) < 0)
5676 return isl_stat_error
;
5677 c
->scc_cluster
[i
] = i
;
5683 /* Free all memory allocated for "c".
5685 static void clustering_free(isl_ctx
*ctx
, struct isl_clustering
*c
)
5690 for (i
= 0; i
< c
->n
; ++i
)
5691 graph_free(ctx
, &c
->scc
[i
]);
5694 for (i
= 0; i
< c
->n
; ++i
)
5695 graph_free(ctx
, &c
->cluster
[i
]);
5697 free(c
->scc_cluster
);
5699 free(c
->scc_in_merge
);
5702 /* Should we refrain from merging the cluster in "graph" with
5703 * any other cluster?
5704 * In particular, is its current schedule band empty and incomplete.
5706 static int bad_cluster(struct isl_sched_graph
*graph
)
5708 return graph
->n_row
< graph
->maxvar
&&
5709 graph
->n_total_row
== graph
->band_start
;
5712 /* Is "edge" a proximity edge with a non-empty dependence relation?
5714 static isl_bool
is_non_empty_proximity(struct isl_sched_edge
*edge
)
5716 if (!is_proximity(edge
))
5717 return isl_bool_false
;
5718 return isl_bool_not(isl_map_plain_is_empty(edge
->map
));
5721 /* Return the index of an edge in "graph" that can be used to merge
5722 * two clusters in "c".
5723 * Return graph->n_edge if no such edge can be found.
5724 * Return -1 on error.
5726 * In particular, return a proximity edge between two clusters
5727 * that is not marked "no_merge" and such that neither of the
5728 * two clusters has an incomplete, empty band.
5730 * If there are multiple such edges, then try and find the most
5731 * appropriate edge to use for merging. In particular, pick the edge
5732 * with the greatest weight. If there are multiple of those,
5733 * then pick one with the shortest distance between
5734 * the two cluster representatives.
5736 static int find_proximity(struct isl_sched_graph
*graph
,
5737 struct isl_clustering
*c
)
5739 int i
, best
= graph
->n_edge
, best_dist
, best_weight
;
5741 for (i
= 0; i
< graph
->n_edge
; ++i
) {
5742 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
5746 prox
= is_non_empty_proximity(edge
);
5753 if (bad_cluster(&c
->scc
[edge
->src
->scc
]) ||
5754 bad_cluster(&c
->scc
[edge
->dst
->scc
]))
5756 dist
= c
->scc_cluster
[edge
->dst
->scc
] -
5757 c
->scc_cluster
[edge
->src
->scc
];
5760 weight
= edge
->weight
;
5761 if (best
< graph
->n_edge
) {
5762 if (best_weight
> weight
)
5764 if (best_weight
== weight
&& best_dist
<= dist
)
5769 best_weight
= weight
;
5775 /* Internal data structure used in mark_merge_sccs.
5777 * "graph" is the dependence graph in which a strongly connected
5778 * component is constructed.
5779 * "scc_cluster" maps each SCC index to the cluster to which it belongs.
5780 * "src" and "dst" are the indices of the nodes that are being merged.
5782 struct isl_mark_merge_sccs_data
{
5783 struct isl_sched_graph
*graph
;
5789 /* Check whether the cluster containing node "i" depends on the cluster
5790 * containing node "j". If "i" and "j" belong to the same cluster,
5791 * then they are taken to depend on each other to ensure that
5792 * the resulting strongly connected component consists of complete
5793 * clusters. Furthermore, if "i" and "j" are the two nodes that
5794 * are being merged, then they are taken to depend on each other as well.
5795 * Otherwise, check if there is a (conditional) validity dependence
5796 * from node[j] to node[i], forcing node[i] to follow node[j].
5798 static isl_bool
cluster_follows(int i
, int j
, void *user
)
5800 struct isl_mark_merge_sccs_data
*data
= user
;
5801 struct isl_sched_graph
*graph
= data
->graph
;
5802 int *scc_cluster
= data
->scc_cluster
;
5804 if (data
->src
== i
&& data
->dst
== j
)
5805 return isl_bool_true
;
5806 if (data
->src
== j
&& data
->dst
== i
)
5807 return isl_bool_true
;
5808 if (scc_cluster
[graph
->node
[i
].scc
] == scc_cluster
[graph
->node
[j
].scc
])
5809 return isl_bool_true
;
5811 return graph_has_validity_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
5814 /* Mark all SCCs that belong to either of the two clusters in "c"
5815 * connected by the edge in "graph" with index "edge", or to any
5816 * of the intermediate clusters.
5817 * The marking is recorded in c->scc_in_merge.
5819 * The given edge has been selected for merging two clusters,
5820 * meaning that there is at least a proximity edge between the two nodes.
5821 * However, there may also be (indirect) validity dependences
5822 * between the two nodes. When merging the two clusters, all clusters
5823 * containing one or more of the intermediate nodes along the
5824 * indirect validity dependences need to be merged in as well.
5826 * First collect all such nodes by computing the strongly connected
5827 * component (SCC) containing the two nodes connected by the edge, where
5828 * the two nodes are considered to depend on each other to make
5829 * sure they end up in the same SCC. Similarly, each node is considered
5830 * to depend on every other node in the same cluster to ensure
5831 * that the SCC consists of complete clusters.
5833 * Then the original SCCs that contain any of these nodes are marked
5834 * in c->scc_in_merge.
5836 static isl_stat
mark_merge_sccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
5837 int edge
, struct isl_clustering
*c
)
5839 struct isl_mark_merge_sccs_data data
;
5840 struct isl_tarjan_graph
*g
;
5843 for (i
= 0; i
< c
->n
; ++i
)
5844 c
->scc_in_merge
[i
] = 0;
5847 data
.scc_cluster
= c
->scc_cluster
;
5848 data
.src
= graph
->edge
[edge
].src
- graph
->node
;
5849 data
.dst
= graph
->edge
[edge
].dst
- graph
->node
;
5851 g
= isl_tarjan_graph_component(ctx
, graph
->n
, data
.dst
,
5852 &cluster_follows
, &data
);
5858 isl_die(ctx
, isl_error_internal
,
5859 "expecting at least two nodes in component",
5861 if (g
->order
[--i
] != -1)
5862 isl_die(ctx
, isl_error_internal
,
5863 "expecting end of component marker", goto error
);
5865 for (--i
; i
>= 0 && g
->order
[i
] != -1; --i
) {
5866 int scc
= graph
->node
[g
->order
[i
]].scc
;
5867 c
->scc_in_merge
[scc
] = 1;
5870 isl_tarjan_graph_free(g
);
5873 isl_tarjan_graph_free(g
);
5874 return isl_stat_error
;
5877 /* Construct the identifier "cluster_i".
5879 static __isl_give isl_id
*cluster_id(isl_ctx
*ctx
, int i
)
5883 snprintf(name
, sizeof(name
), "cluster_%d", i
);
5884 return isl_id_alloc(ctx
, name
, NULL
);
5887 /* Construct the space of the cluster with index "i" containing
5888 * the strongly connected component "scc".
5890 * In particular, construct a space called cluster_i with dimension equal
5891 * to the number of schedule rows in the current band of "scc".
5893 static __isl_give isl_space
*cluster_space(struct isl_sched_graph
*scc
, int i
)
5899 nvar
= scc
->n_total_row
- scc
->band_start
;
5900 space
= isl_space_copy(scc
->node
[0].space
);
5901 space
= isl_space_params(space
);
5902 space
= isl_space_set_from_params(space
);
5903 space
= isl_space_add_dims(space
, isl_dim_set
, nvar
);
5904 id
= cluster_id(isl_space_get_ctx(space
), i
);
5905 space
= isl_space_set_tuple_id(space
, isl_dim_set
, id
);
5910 /* Collect the domain of the graph for merging clusters.
5912 * In particular, for each cluster with first SCC "i", construct
5913 * a set in the space called cluster_i with dimension equal
5914 * to the number of schedule rows in the current band of the cluster.
5916 static __isl_give isl_union_set
*collect_domain(isl_ctx
*ctx
,
5917 struct isl_sched_graph
*graph
, struct isl_clustering
*c
)
5921 isl_union_set
*domain
;
5923 space
= isl_space_params_alloc(ctx
, 0);
5924 domain
= isl_union_set_empty(space
);
5926 for (i
= 0; i
< graph
->scc
; ++i
) {
5929 if (!c
->scc_in_merge
[i
])
5931 if (c
->scc_cluster
[i
] != i
)
5933 space
= cluster_space(&c
->scc
[i
], i
);
5934 domain
= isl_union_set_add_set(domain
, isl_set_universe(space
));
5940 /* Construct a map from the original instances to the corresponding
5941 * cluster instance in the current bands of the clusters in "c".
5943 static __isl_give isl_union_map
*collect_cluster_map(isl_ctx
*ctx
,
5944 struct isl_sched_graph
*graph
, struct isl_clustering
*c
)
5948 isl_union_map
*cluster_map
;
5950 space
= isl_space_params_alloc(ctx
, 0);
5951 cluster_map
= isl_union_map_empty(space
);
5952 for (i
= 0; i
< graph
->scc
; ++i
) {
5956 if (!c
->scc_in_merge
[i
])
5959 id
= cluster_id(ctx
, c
->scc_cluster
[i
]);
5960 start
= c
->scc
[i
].band_start
;
5961 n
= c
->scc
[i
].n_total_row
- start
;
5962 for (j
= 0; j
< c
->scc
[i
].n
; ++j
) {
5965 struct isl_sched_node
*node
= &c
->scc
[i
].node
[j
];
5967 ma
= node_extract_partial_schedule_multi_aff(node
,
5969 ma
= isl_multi_aff_set_tuple_id(ma
, isl_dim_out
,
5971 map
= isl_map_from_multi_aff(ma
);
5972 cluster_map
= isl_union_map_add_map(cluster_map
, map
);
5980 /* Add "umap" to the schedule constraints "sc" of all types of "edge"
5981 * that are not isl_edge_condition or isl_edge_conditional_validity.
5983 static __isl_give isl_schedule_constraints
*add_non_conditional_constraints(
5984 struct isl_sched_edge
*edge
, __isl_keep isl_union_map
*umap
,
5985 __isl_take isl_schedule_constraints
*sc
)
5987 enum isl_edge_type t
;
5992 for (t
= isl_edge_first
; t
<= isl_edge_last
; ++t
) {
5993 if (t
== isl_edge_condition
||
5994 t
== isl_edge_conditional_validity
)
5996 if (!is_type(edge
, t
))
5998 sc
= isl_schedule_constraints_add(sc
, t
,
5999 isl_union_map_copy(umap
));
6005 /* Add schedule constraints of types isl_edge_condition and
6006 * isl_edge_conditional_validity to "sc" by applying "umap" to
6007 * the domains of the wrapped relations in domain and range
6008 * of the corresponding tagged constraints of "edge".
6010 static __isl_give isl_schedule_constraints
*add_conditional_constraints(
6011 struct isl_sched_edge
*edge
, __isl_keep isl_union_map
*umap
,
6012 __isl_take isl_schedule_constraints
*sc
)
6014 enum isl_edge_type t
;
6015 isl_union_map
*tagged
;
6017 for (t
= isl_edge_condition
; t
<= isl_edge_conditional_validity
; ++t
) {
6018 if (!is_type(edge
, t
))
6020 if (t
== isl_edge_condition
)
6021 tagged
= isl_union_map_copy(edge
->tagged_condition
);
6023 tagged
= isl_union_map_copy(edge
->tagged_validity
);
6024 tagged
= isl_union_map_zip(tagged
);
6025 tagged
= isl_union_map_apply_domain(tagged
,
6026 isl_union_map_copy(umap
));
6027 tagged
= isl_union_map_zip(tagged
);
6028 sc
= isl_schedule_constraints_add(sc
, t
, tagged
);
6036 /* Given a mapping "cluster_map" from the original instances to
6037 * the cluster instances, add schedule constraints on the clusters
6038 * to "sc" corresponding to the original constraints represented by "edge".
6040 * For non-tagged dependence constraints, the cluster constraints
6041 * are obtained by applying "cluster_map" to the edge->map.
6043 * For tagged dependence constraints, "cluster_map" needs to be applied
6044 * to the domains of the wrapped relations in domain and range
6045 * of the tagged dependence constraints. Pick out the mappings
6046 * from these domains from "cluster_map" and construct their product.
6047 * This mapping can then be applied to the pair of domains.
6049 static __isl_give isl_schedule_constraints
*collect_edge_constraints(
6050 struct isl_sched_edge
*edge
, __isl_keep isl_union_map
*cluster_map
,
6051 __isl_take isl_schedule_constraints
*sc
)
6053 isl_union_map
*umap
;
6055 isl_union_set
*uset
;
6056 isl_union_map
*umap1
, *umap2
;
6061 umap
= isl_union_map_from_map(isl_map_copy(edge
->map
));
6062 umap
= isl_union_map_apply_domain(umap
,
6063 isl_union_map_copy(cluster_map
));
6064 umap
= isl_union_map_apply_range(umap
,
6065 isl_union_map_copy(cluster_map
));
6066 sc
= add_non_conditional_constraints(edge
, umap
, sc
);
6067 isl_union_map_free(umap
);
6069 if (!sc
|| (!is_condition(edge
) && !is_conditional_validity(edge
)))
6072 space
= isl_space_domain(isl_map_get_space(edge
->map
));
6073 uset
= isl_union_set_from_set(isl_set_universe(space
));
6074 umap1
= isl_union_map_copy(cluster_map
);
6075 umap1
= isl_union_map_intersect_domain(umap1
, uset
);
6076 space
= isl_space_range(isl_map_get_space(edge
->map
));
6077 uset
= isl_union_set_from_set(isl_set_universe(space
));
6078 umap2
= isl_union_map_copy(cluster_map
);
6079 umap2
= isl_union_map_intersect_domain(umap2
, uset
);
6080 umap
= isl_union_map_product(umap1
, umap2
);
6082 sc
= add_conditional_constraints(edge
, umap
, sc
);
6084 isl_union_map_free(umap
);
6088 /* Given a mapping "cluster_map" from the original instances to
6089 * the cluster instances, add schedule constraints on the clusters
6090 * to "sc" corresponding to all edges in "graph" between nodes that
6091 * belong to SCCs that are marked for merging in "scc_in_merge".
6093 static __isl_give isl_schedule_constraints
*collect_constraints(
6094 struct isl_sched_graph
*graph
, int *scc_in_merge
,
6095 __isl_keep isl_union_map
*cluster_map
,
6096 __isl_take isl_schedule_constraints
*sc
)
6100 for (i
= 0; i
< graph
->n_edge
; ++i
) {
6101 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
6103 if (!scc_in_merge
[edge
->src
->scc
])
6105 if (!scc_in_merge
[edge
->dst
->scc
])
6107 sc
= collect_edge_constraints(edge
, cluster_map
, sc
);
6113 /* Construct a dependence graph for scheduling clusters with respect
6114 * to each other and store the result in "merge_graph".
6115 * In particular, the nodes of the graph correspond to the schedule
6116 * dimensions of the current bands of those clusters that have been
6117 * marked for merging in "c".
6119 * First construct an isl_schedule_constraints object for this domain
6120 * by transforming the edges in "graph" to the domain.
6121 * Then initialize a dependence graph for scheduling from these
6124 static isl_stat
init_merge_graph(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
6125 struct isl_clustering
*c
, struct isl_sched_graph
*merge_graph
)
6127 isl_union_set
*domain
;
6128 isl_union_map
*cluster_map
;
6129 isl_schedule_constraints
*sc
;
6132 domain
= collect_domain(ctx
, graph
, c
);
6133 sc
= isl_schedule_constraints_on_domain(domain
);
6135 return isl_stat_error
;
6136 cluster_map
= collect_cluster_map(ctx
, graph
, c
);
6137 sc
= collect_constraints(graph
, c
->scc_in_merge
, cluster_map
, sc
);
6138 isl_union_map_free(cluster_map
);
6140 r
= graph_init(merge_graph
, sc
);
6142 isl_schedule_constraints_free(sc
);
6147 /* Compute the maximal number of remaining schedule rows that still need
6148 * to be computed for the nodes that belong to clusters with the maximal
6149 * dimension for the current band (i.e., the band that is to be merged).
6150 * Only clusters that are about to be merged are considered.
6151 * "maxvar" is the maximal dimension for the current band.
6152 * "c" contains information about the clusters.
6154 * Return the maximal number of remaining schedule rows or -1 on error.
6156 static int compute_maxvar_max_slack(int maxvar
, struct isl_clustering
*c
)
6162 for (i
= 0; i
< c
->n
; ++i
) {
6164 struct isl_sched_graph
*scc
;
6166 if (!c
->scc_in_merge
[i
])
6169 nvar
= scc
->n_total_row
- scc
->band_start
;
6172 for (j
= 0; j
< scc
->n
; ++j
) {
6173 struct isl_sched_node
*node
= &scc
->node
[j
];
6176 if (node_update_vmap(node
) < 0)
6178 slack
= node
->nvar
- node
->rank
;
6179 if (slack
> max_slack
)
6187 /* If there are any clusters where the dimension of the current band
6188 * (i.e., the band that is to be merged) is smaller than "maxvar" and
6189 * if there are any nodes in such a cluster where the number
6190 * of remaining schedule rows that still need to be computed
6191 * is greater than "max_slack", then return the smallest current band
6192 * dimension of all these clusters. Otherwise return the original value
6193 * of "maxvar". Return -1 in case of any error.
6194 * Only clusters that are about to be merged are considered.
6195 * "c" contains information about the clusters.
6197 static int limit_maxvar_to_slack(int maxvar
, int max_slack
,
6198 struct isl_clustering
*c
)
6202 for (i
= 0; i
< c
->n
; ++i
) {
6204 struct isl_sched_graph
*scc
;
6206 if (!c
->scc_in_merge
[i
])
6209 nvar
= scc
->n_total_row
- scc
->band_start
;
6212 for (j
= 0; j
< scc
->n
; ++j
) {
6213 struct isl_sched_node
*node
= &scc
->node
[j
];
6216 if (node_update_vmap(node
) < 0)
6218 slack
= node
->nvar
- node
->rank
;
6219 if (slack
> max_slack
) {
6229 /* Adjust merge_graph->maxvar based on the number of remaining schedule rows
6230 * that still need to be computed. In particular, if there is a node
6231 * in a cluster where the dimension of the current band is smaller
6232 * than merge_graph->maxvar, but the number of remaining schedule rows
6233 * is greater than that of any node in a cluster with the maximal
6234 * dimension for the current band (i.e., merge_graph->maxvar),
6235 * then adjust merge_graph->maxvar to the (smallest) current band dimension
6236 * of those clusters. Without this adjustment, the total number of
6237 * schedule dimensions would be increased, resulting in a skewed view
6238 * of the number of coincident dimensions.
6239 * "c" contains information about the clusters.
6241 * If the maximize_band_depth option is set and merge_graph->maxvar is reduced,
6242 * then there is no point in attempting any merge since it will be rejected
6243 * anyway. Set merge_graph->maxvar to zero in such cases.
6245 static isl_stat
adjust_maxvar_to_slack(isl_ctx
*ctx
,
6246 struct isl_sched_graph
*merge_graph
, struct isl_clustering
*c
)
6248 int max_slack
, maxvar
;
6250 max_slack
= compute_maxvar_max_slack(merge_graph
->maxvar
, c
);
6252 return isl_stat_error
;
6253 maxvar
= limit_maxvar_to_slack(merge_graph
->maxvar
, max_slack
, c
);
6255 return isl_stat_error
;
6257 if (maxvar
< merge_graph
->maxvar
) {
6258 if (isl_options_get_schedule_maximize_band_depth(ctx
))
6259 merge_graph
->maxvar
= 0;
6261 merge_graph
->maxvar
= maxvar
;
6267 /* Return the number of coincident dimensions in the current band of "graph",
6268 * where the nodes of "graph" are assumed to be scheduled by a single band.
6270 static int get_n_coincident(struct isl_sched_graph
*graph
)
6274 for (i
= graph
->band_start
; i
< graph
->n_total_row
; ++i
)
6275 if (!graph
->node
[0].coincident
[i
])
6278 return i
- graph
->band_start
;
6281 /* Should the clusters be merged based on the cluster schedule
6282 * in the current (and only) band of "merge_graph", given that
6283 * coincidence should be maximized?
6285 * If the number of coincident schedule dimensions in the merged band
6286 * would be less than the maximal number of coincident schedule dimensions
6287 * in any of the merged clusters, then the clusters should not be merged.
6289 static isl_bool
ok_to_merge_coincident(struct isl_clustering
*c
,
6290 struct isl_sched_graph
*merge_graph
)
6297 for (i
= 0; i
< c
->n
; ++i
) {
6298 if (!c
->scc_in_merge
[i
])
6300 n_coincident
= get_n_coincident(&c
->scc
[i
]);
6301 if (n_coincident
> max_coincident
)
6302 max_coincident
= n_coincident
;
6305 n_coincident
= get_n_coincident(merge_graph
);
6307 return n_coincident
>= max_coincident
;
6310 /* Return the transformation on "node" expressed by the current (and only)
6311 * band of "merge_graph" applied to the clusters in "c".
6313 * First find the representation of "node" in its SCC in "c" and
6314 * extract the transformation expressed by the current band.
6315 * Then extract the transformation applied by "merge_graph"
6316 * to the cluster to which this SCC belongs.
6317 * Combine the two to obtain the complete transformation on the node.
6319 * Note that the range of the first transformation is an anonymous space,
6320 * while the domain of the second is named "cluster_X". The range
6321 * of the former therefore needs to be adjusted before the two
6324 static __isl_give isl_map
*extract_node_transformation(isl_ctx
*ctx
,
6325 struct isl_sched_node
*node
, struct isl_clustering
*c
,
6326 struct isl_sched_graph
*merge_graph
)
6328 struct isl_sched_node
*scc_node
, *cluster_node
;
6332 isl_multi_aff
*ma
, *ma2
;
6334 scc_node
= graph_find_node(ctx
, &c
->scc
[node
->scc
], node
->space
);
6335 start
= c
->scc
[node
->scc
].band_start
;
6336 n
= c
->scc
[node
->scc
].n_total_row
- start
;
6337 ma
= node_extract_partial_schedule_multi_aff(scc_node
, start
, n
);
6338 space
= cluster_space(&c
->scc
[node
->scc
], c
->scc_cluster
[node
->scc
]);
6339 cluster_node
= graph_find_node(ctx
, merge_graph
, space
);
6340 if (space
&& !cluster_node
)
6341 isl_die(ctx
, isl_error_internal
, "unable to find cluster",
6342 space
= isl_space_free(space
));
6343 id
= isl_space_get_tuple_id(space
, isl_dim_set
);
6344 ma
= isl_multi_aff_set_tuple_id(ma
, isl_dim_out
, id
);
6345 isl_space_free(space
);
6346 n
= merge_graph
->n_total_row
;
6347 ma2
= node_extract_partial_schedule_multi_aff(cluster_node
, 0, n
);
6348 ma
= isl_multi_aff_pullback_multi_aff(ma2
, ma
);
6350 return isl_map_from_multi_aff(ma
);
6353 /* Give a set of distances "set", are they bounded by a small constant
6354 * in direction "pos"?
6355 * In practice, check if they are bounded by 2 by checking that there
6356 * are no elements with a value greater than or equal to 3 or
6357 * smaller than or equal to -3.
6359 static isl_bool
distance_is_bounded(__isl_keep isl_set
*set
, int pos
)
6365 return isl_bool_error
;
6367 test
= isl_set_copy(set
);
6368 test
= isl_set_lower_bound_si(test
, isl_dim_set
, pos
, 3);
6369 bounded
= isl_set_is_empty(test
);
6372 if (bounded
< 0 || !bounded
)
6375 test
= isl_set_copy(set
);
6376 test
= isl_set_upper_bound_si(test
, isl_dim_set
, pos
, -3);
6377 bounded
= isl_set_is_empty(test
);
6383 /* Does the set "set" have a fixed (but possible parametric) value
6384 * at dimension "pos"?
6386 static isl_bool
has_single_value(__isl_keep isl_set
*set
, int pos
)
6392 return isl_bool_error
;
6393 set
= isl_set_copy(set
);
6394 n
= isl_set_dim(set
, isl_dim_set
);
6395 set
= isl_set_project_out(set
, isl_dim_set
, pos
+ 1, n
- (pos
+ 1));
6396 set
= isl_set_project_out(set
, isl_dim_set
, 0, pos
);
6397 single
= isl_set_is_singleton(set
);
6403 /* Does "map" have a fixed (but possible parametric) value
6404 * at dimension "pos" of either its domain or its range?
6406 static isl_bool
has_singular_src_or_dst(__isl_keep isl_map
*map
, int pos
)
6411 set
= isl_map_domain(isl_map_copy(map
));
6412 single
= has_single_value(set
, pos
);
6415 if (single
< 0 || single
)
6418 set
= isl_map_range(isl_map_copy(map
));
6419 single
= has_single_value(set
, pos
);
6425 /* Does the edge "edge" from "graph" have bounded dependence distances
6426 * in the merged graph "merge_graph" of a selection of clusters in "c"?
6428 * Extract the complete transformations of the source and destination
6429 * nodes of the edge, apply them to the edge constraints and
6430 * compute the differences. Finally, check if these differences are bounded
6431 * in each direction.
6433 * If the dimension of the band is greater than the number of
6434 * dimensions that can be expected to be optimized by the edge
6435 * (based on its weight), then also allow the differences to be unbounded
6436 * in the remaining dimensions, but only if either the source or
6437 * the destination has a fixed value in that direction.
6438 * This allows a statement that produces values that are used by
6439 * several instances of another statement to be merged with that
6441 * However, merging such clusters will introduce an inherently
6442 * large proximity distance inside the merged cluster, meaning
6443 * that proximity distances will no longer be optimized in
6444 * subsequent merges. These merges are therefore only allowed
6445 * after all other possible merges have been tried.
6446 * The first time such a merge is encountered, the weight of the edge
6447 * is replaced by a negative weight. The second time (i.e., after
6448 * all merges over edges with a non-negative weight have been tried),
6449 * the merge is allowed.
6451 static isl_bool
has_bounded_distances(isl_ctx
*ctx
, struct isl_sched_edge
*edge
,
6452 struct isl_sched_graph
*graph
, struct isl_clustering
*c
,
6453 struct isl_sched_graph
*merge_graph
)
6460 map
= isl_map_copy(edge
->map
);
6461 t
= extract_node_transformation(ctx
, edge
->src
, c
, merge_graph
);
6462 map
= isl_map_apply_domain(map
, t
);
6463 t
= extract_node_transformation(ctx
, edge
->dst
, c
, merge_graph
);
6464 map
= isl_map_apply_range(map
, t
);
6465 dist
= isl_map_deltas(isl_map_copy(map
));
6467 bounded
= isl_bool_true
;
6468 n
= isl_set_dim(dist
, isl_dim_set
);
6469 n_slack
= n
- edge
->weight
;
6470 if (edge
->weight
< 0)
6471 n_slack
-= graph
->max_weight
+ 1;
6472 for (i
= 0; i
< n
; ++i
) {
6473 isl_bool bounded_i
, singular_i
;
6475 bounded_i
= distance_is_bounded(dist
, i
);
6480 if (edge
->weight
>= 0)
6481 bounded
= isl_bool_false
;
6485 singular_i
= has_singular_src_or_dst(map
, i
);
6490 bounded
= isl_bool_false
;
6493 if (!bounded
&& i
>= n
&& edge
->weight
>= 0)
6494 edge
->weight
-= graph
->max_weight
+ 1;
6502 return isl_bool_error
;
6505 /* Should the clusters be merged based on the cluster schedule
6506 * in the current (and only) band of "merge_graph"?
6507 * "graph" is the original dependence graph, while "c" records
6508 * which SCCs are involved in the latest merge.
6510 * In particular, is there at least one proximity constraint
6511 * that is optimized by the merge?
6513 * A proximity constraint is considered to be optimized
6514 * if the dependence distances are small.
6516 static isl_bool
ok_to_merge_proximity(isl_ctx
*ctx
,
6517 struct isl_sched_graph
*graph
, struct isl_clustering
*c
,
6518 struct isl_sched_graph
*merge_graph
)
6522 for (i
= 0; i
< graph
->n_edge
; ++i
) {
6523 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
6526 if (!is_proximity(edge
))
6528 if (!c
->scc_in_merge
[edge
->src
->scc
])
6530 if (!c
->scc_in_merge
[edge
->dst
->scc
])
6532 if (c
->scc_cluster
[edge
->dst
->scc
] ==
6533 c
->scc_cluster
[edge
->src
->scc
])
6535 bounded
= has_bounded_distances(ctx
, edge
, graph
, c
,
6537 if (bounded
< 0 || bounded
)
6541 return isl_bool_false
;
6544 /* Should the clusters be merged based on the cluster schedule
6545 * in the current (and only) band of "merge_graph"?
6546 * "graph" is the original dependence graph, while "c" records
6547 * which SCCs are involved in the latest merge.
6549 * If the current band is empty, then the clusters should not be merged.
6551 * If the band depth should be maximized and the merge schedule
6552 * is incomplete (meaning that the dimension of some of the schedule
6553 * bands in the original schedule will be reduced), then the clusters
6554 * should not be merged.
6556 * If the schedule_maximize_coincidence option is set, then check that
6557 * the number of coincident schedule dimensions is not reduced.
6559 * Finally, only allow the merge if at least one proximity
6560 * constraint is optimized.
6562 static isl_bool
ok_to_merge(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
6563 struct isl_clustering
*c
, struct isl_sched_graph
*merge_graph
)
6565 if (merge_graph
->n_total_row
== merge_graph
->band_start
)
6566 return isl_bool_false
;
6568 if (isl_options_get_schedule_maximize_band_depth(ctx
) &&
6569 merge_graph
->n_total_row
< merge_graph
->maxvar
)
6570 return isl_bool_false
;
6572 if (isl_options_get_schedule_maximize_coincidence(ctx
)) {
6575 ok
= ok_to_merge_coincident(c
, merge_graph
);
6580 return ok_to_merge_proximity(ctx
, graph
, c
, merge_graph
);
6583 /* Apply the schedule in "t_node" to the "n" rows starting at "first"
6584 * of the schedule in "node" and return the result.
6586 * That is, essentially compute
6588 * T * N(first:first+n-1)
6590 * taking into account the constant term and the parameter coefficients
6593 static __isl_give isl_mat
*node_transformation(isl_ctx
*ctx
,
6594 struct isl_sched_node
*t_node
, struct isl_sched_node
*node
,
6599 int n_row
, n_col
, n_param
, n_var
;
6601 n_param
= node
->nparam
;
6603 n_row
= isl_mat_rows(t_node
->sched
);
6604 n_col
= isl_mat_cols(node
->sched
);
6605 t
= isl_mat_alloc(ctx
, n_row
, n_col
);
6608 for (i
= 0; i
< n_row
; ++i
) {
6609 isl_seq_cpy(t
->row
[i
], t_node
->sched
->row
[i
], 1 + n_param
);
6610 isl_seq_clr(t
->row
[i
] + 1 + n_param
, n_var
);
6611 for (j
= 0; j
< n
; ++j
)
6612 isl_seq_addmul(t
->row
[i
],
6613 t_node
->sched
->row
[i
][1 + n_param
+ j
],
6614 node
->sched
->row
[first
+ j
],
6615 1 + n_param
+ n_var
);
6620 /* Apply the cluster schedule in "t_node" to the current band
6621 * schedule of the nodes in "graph".
6623 * In particular, replace the rows starting at band_start
6624 * by the result of applying the cluster schedule in "t_node"
6625 * to the original rows.
6627 * The coincidence of the schedule is determined by the coincidence
6628 * of the cluster schedule.
6630 static isl_stat
transform(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
6631 struct isl_sched_node
*t_node
)
6637 start
= graph
->band_start
;
6638 n
= graph
->n_total_row
- start
;
6640 n_new
= isl_mat_rows(t_node
->sched
);
6641 for (i
= 0; i
< graph
->n
; ++i
) {
6642 struct isl_sched_node
*node
= &graph
->node
[i
];
6645 t
= node_transformation(ctx
, t_node
, node
, start
, n
);
6646 node
->sched
= isl_mat_drop_rows(node
->sched
, start
, n
);
6647 node
->sched
= isl_mat_concat(node
->sched
, t
);
6648 node
->sched_map
= isl_map_free(node
->sched_map
);
6650 return isl_stat_error
;
6651 for (j
= 0; j
< n_new
; ++j
)
6652 node
->coincident
[start
+ j
] = t_node
->coincident
[j
];
6654 graph
->n_total_row
-= n
;
6656 graph
->n_total_row
+= n_new
;
6657 graph
->n_row
+= n_new
;
6662 /* Merge the clusters marked for merging in "c" into a single
6663 * cluster using the cluster schedule in the current band of "merge_graph".
6664 * The representative SCC for the new cluster is the SCC with
6665 * the smallest index.
6667 * The current band schedule of each SCC in the new cluster is obtained
6668 * by applying the schedule of the corresponding original cluster
6669 * to the original band schedule.
6670 * All SCCs in the new cluster have the same number of schedule rows.
6672 static isl_stat
merge(isl_ctx
*ctx
, struct isl_clustering
*c
,
6673 struct isl_sched_graph
*merge_graph
)
6679 for (i
= 0; i
< c
->n
; ++i
) {
6680 struct isl_sched_node
*node
;
6682 if (!c
->scc_in_merge
[i
])
6686 space
= cluster_space(&c
->scc
[i
], c
->scc_cluster
[i
]);
6688 return isl_stat_error
;
6689 node
= graph_find_node(ctx
, merge_graph
, space
);
6690 isl_space_free(space
);
6692 isl_die(ctx
, isl_error_internal
,
6693 "unable to find cluster",
6694 return isl_stat_error
);
6695 if (transform(ctx
, &c
->scc
[i
], node
) < 0)
6696 return isl_stat_error
;
6697 c
->scc_cluster
[i
] = cluster
;
6703 /* Try and merge the clusters of SCCs marked in c->scc_in_merge
6704 * by scheduling the current cluster bands with respect to each other.
6706 * Construct a dependence graph with a space for each cluster and
6707 * with the coordinates of each space corresponding to the schedule
6708 * dimensions of the current band of that cluster.
6709 * Construct a cluster schedule in this cluster dependence graph and
6710 * apply it to the current cluster bands if it is applicable
6711 * according to ok_to_merge.
6713 * If the number of remaining schedule dimensions in a cluster
6714 * with a non-maximal current schedule dimension is greater than
6715 * the number of remaining schedule dimensions in clusters
6716 * with a maximal current schedule dimension, then restrict
6717 * the number of rows to be computed in the cluster schedule
6718 * to the minimal such non-maximal current schedule dimension.
6719 * Do this by adjusting merge_graph.maxvar.
6721 * Return isl_bool_true if the clusters have effectively been merged
6722 * into a single cluster.
6724 * Note that since the standard scheduling algorithm minimizes the maximal
6725 * distance over proximity constraints, the proximity constraints between
6726 * the merged clusters may not be optimized any further than what is
6727 * sufficient to bring the distances within the limits of the internal
6728 * proximity constraints inside the individual clusters.
6729 * It may therefore make sense to perform an additional translation step
6730 * to bring the clusters closer to each other, while maintaining
6731 * the linear part of the merging schedule found using the standard
6732 * scheduling algorithm.
6734 static isl_bool
try_merge(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
6735 struct isl_clustering
*c
)
6737 struct isl_sched_graph merge_graph
= { 0 };
6740 if (init_merge_graph(ctx
, graph
, c
, &merge_graph
) < 0)
6743 if (compute_maxvar(&merge_graph
) < 0)
6745 if (adjust_maxvar_to_slack(ctx
, &merge_graph
,c
) < 0)
6747 if (compute_schedule_wcc_band(ctx
, &merge_graph
) < 0)
6749 merged
= ok_to_merge(ctx
, graph
, c
, &merge_graph
);
6750 if (merged
&& merge(ctx
, c
, &merge_graph
) < 0)
6753 graph_free(ctx
, &merge_graph
);
6756 graph_free(ctx
, &merge_graph
);
6757 return isl_bool_error
;
6760 /* Is there any edge marked "no_merge" between two SCCs that are
6761 * about to be merged (i.e., that are set in "scc_in_merge")?
6762 * "merge_edge" is the proximity edge along which the clusters of SCCs
6763 * are going to be merged.
6765 * If there is any edge between two SCCs with a negative weight,
6766 * while the weight of "merge_edge" is non-negative, then this
6767 * means that the edge was postponed. "merge_edge" should then
6768 * also be postponed since merging along the edge with negative weight should
6769 * be postponed until all edges with non-negative weight have been tried.
6770 * Replace the weight of "merge_edge" by a negative weight as well and
6771 * tell the caller not to attempt a merge.
6773 static int any_no_merge(struct isl_sched_graph
*graph
, int *scc_in_merge
,
6774 struct isl_sched_edge
*merge_edge
)
6778 for (i
= 0; i
< graph
->n_edge
; ++i
) {
6779 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
6781 if (!scc_in_merge
[edge
->src
->scc
])
6783 if (!scc_in_merge
[edge
->dst
->scc
])
6787 if (merge_edge
->weight
>= 0 && edge
->weight
< 0) {
6788 merge_edge
->weight
-= graph
->max_weight
+ 1;
6796 /* Merge the two clusters in "c" connected by the edge in "graph"
6797 * with index "edge" into a single cluster.
6798 * If it turns out to be impossible to merge these two clusters,
6799 * then mark the edge as "no_merge" such that it will not be
6802 * First mark all SCCs that need to be merged. This includes the SCCs
6803 * in the two clusters, but it may also include the SCCs
6804 * of intermediate clusters.
6805 * If there is already a no_merge edge between any pair of such SCCs,
6806 * then simply mark the current edge as no_merge as well.
6807 * Likewise, if any of those edges was postponed by has_bounded_distances,
6808 * then postpone the current edge as well.
6809 * Otherwise, try and merge the clusters and mark "edge" as "no_merge"
6810 * if the clusters did not end up getting merged, unless the non-merge
6811 * is due to the fact that the edge was postponed. This postponement
6812 * can be recognized by a change in weight (from non-negative to negative).
6814 static isl_stat
merge_clusters_along_edge(isl_ctx
*ctx
,
6815 struct isl_sched_graph
*graph
, int edge
, struct isl_clustering
*c
)
6818 int edge_weight
= graph
->edge
[edge
].weight
;
6820 if (mark_merge_sccs(ctx
, graph
, edge
, c
) < 0)
6821 return isl_stat_error
;
6823 if (any_no_merge(graph
, c
->scc_in_merge
, &graph
->edge
[edge
]))
6824 merged
= isl_bool_false
;
6826 merged
= try_merge(ctx
, graph
, c
);
6828 return isl_stat_error
;
6829 if (!merged
&& edge_weight
== graph
->edge
[edge
].weight
)
6830 graph
->edge
[edge
].no_merge
= 1;
6835 /* Does "node" belong to the cluster identified by "cluster"?
6837 static int node_cluster_exactly(struct isl_sched_node
*node
, int cluster
)
6839 return node
->cluster
== cluster
;
6842 /* Does "edge" connect two nodes belonging to the cluster
6843 * identified by "cluster"?
6845 static int edge_cluster_exactly(struct isl_sched_edge
*edge
, int cluster
)
6847 return edge
->src
->cluster
== cluster
&& edge
->dst
->cluster
== cluster
;
6850 /* Swap the schedule of "node1" and "node2".
6851 * Both nodes have been derived from the same node in a common parent graph.
6852 * Since the "coincident" field is shared with that node
6853 * in the parent graph, there is no need to also swap this field.
6855 static void swap_sched(struct isl_sched_node
*node1
,
6856 struct isl_sched_node
*node2
)
6861 sched
= node1
->sched
;
6862 node1
->sched
= node2
->sched
;
6863 node2
->sched
= sched
;
6865 sched_map
= node1
->sched_map
;
6866 node1
->sched_map
= node2
->sched_map
;
6867 node2
->sched_map
= sched_map
;
6870 /* Copy the current band schedule from the SCCs that form the cluster
6871 * with index "pos" to the actual cluster at position "pos".
6872 * By construction, the index of the first SCC that belongs to the cluster
6875 * The order of the nodes inside both the SCCs and the cluster
6876 * is assumed to be same as the order in the original "graph".
6878 * Since the SCC graphs will no longer be used after this function,
6879 * the schedules are actually swapped rather than copied.
6881 static isl_stat
copy_partial(struct isl_sched_graph
*graph
,
6882 struct isl_clustering
*c
, int pos
)
6886 c
->cluster
[pos
].n_total_row
= c
->scc
[pos
].n_total_row
;
6887 c
->cluster
[pos
].n_row
= c
->scc
[pos
].n_row
;
6888 c
->cluster
[pos
].maxvar
= c
->scc
[pos
].maxvar
;
6890 for (i
= 0; i
< graph
->n
; ++i
) {
6894 if (graph
->node
[i
].cluster
!= pos
)
6896 s
= graph
->node
[i
].scc
;
6897 k
= c
->scc_node
[s
]++;
6898 swap_sched(&c
->cluster
[pos
].node
[j
], &c
->scc
[s
].node
[k
]);
6899 if (c
->scc
[s
].maxvar
> c
->cluster
[pos
].maxvar
)
6900 c
->cluster
[pos
].maxvar
= c
->scc
[s
].maxvar
;
6907 /* Is there a (conditional) validity dependence from node[j] to node[i],
6908 * forcing node[i] to follow node[j] or do the nodes belong to the same
6911 static isl_bool
node_follows_strong_or_same_cluster(int i
, int j
, void *user
)
6913 struct isl_sched_graph
*graph
= user
;
6915 if (graph
->node
[i
].cluster
== graph
->node
[j
].cluster
)
6916 return isl_bool_true
;
6917 return graph_has_validity_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
6920 /* Extract the merged clusters of SCCs in "graph", sort them, and
6921 * store them in c->clusters. Update c->scc_cluster accordingly.
6923 * First keep track of the cluster containing the SCC to which a node
6924 * belongs in the node itself.
6925 * Then extract the clusters into c->clusters, copying the current
6926 * band schedule from the SCCs that belong to the cluster.
6927 * Do this only once per cluster.
6929 * Finally, topologically sort the clusters and update c->scc_cluster
6930 * to match the new scc numbering. While the SCCs were originally
6931 * sorted already, some SCCs that depend on some other SCCs may
6932 * have been merged with SCCs that appear before these other SCCs.
6933 * A reordering may therefore be required.
6935 static isl_stat
extract_clusters(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
6936 struct isl_clustering
*c
)
6940 for (i
= 0; i
< graph
->n
; ++i
)
6941 graph
->node
[i
].cluster
= c
->scc_cluster
[graph
->node
[i
].scc
];
6943 for (i
= 0; i
< graph
->scc
; ++i
) {
6944 if (c
->scc_cluster
[i
] != i
)
6946 if (extract_sub_graph(ctx
, graph
, &node_cluster_exactly
,
6947 &edge_cluster_exactly
, i
, &c
->cluster
[i
]) < 0)
6948 return isl_stat_error
;
6949 c
->cluster
[i
].src_scc
= -1;
6950 c
->cluster
[i
].dst_scc
= -1;
6951 if (copy_partial(graph
, c
, i
) < 0)
6952 return isl_stat_error
;
6955 if (detect_ccs(ctx
, graph
, &node_follows_strong_or_same_cluster
) < 0)
6956 return isl_stat_error
;
6957 for (i
= 0; i
< graph
->n
; ++i
)
6958 c
->scc_cluster
[graph
->node
[i
].scc
] = graph
->node
[i
].cluster
;
6963 /* Compute weights on the proximity edges of "graph" that can
6964 * be used by find_proximity to find the most appropriate
6965 * proximity edge to use to merge two clusters in "c".
6966 * The weights are also used by has_bounded_distances to determine
6967 * whether the merge should be allowed.
6968 * Store the maximum of the computed weights in graph->max_weight.
6970 * The computed weight is a measure for the number of remaining schedule
6971 * dimensions that can still be completely aligned.
6972 * In particular, compute the number of equalities between
6973 * input dimensions and output dimensions in the proximity constraints.
6974 * The directions that are already handled by outer schedule bands
6975 * are projected out prior to determining this number.
6977 * Edges that will never be considered by find_proximity are ignored.
6979 static isl_stat
compute_weights(struct isl_sched_graph
*graph
,
6980 struct isl_clustering
*c
)
6984 graph
->max_weight
= 0;
6986 for (i
= 0; i
< graph
->n_edge
; ++i
) {
6987 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
6988 struct isl_sched_node
*src
= edge
->src
;
6989 struct isl_sched_node
*dst
= edge
->dst
;
6990 isl_basic_map
*hull
;
6994 prox
= is_non_empty_proximity(edge
);
6996 return isl_stat_error
;
6999 if (bad_cluster(&c
->scc
[edge
->src
->scc
]) ||
7000 bad_cluster(&c
->scc
[edge
->dst
->scc
]))
7002 if (c
->scc_cluster
[edge
->dst
->scc
] ==
7003 c
->scc_cluster
[edge
->src
->scc
])
7006 hull
= isl_map_affine_hull(isl_map_copy(edge
->map
));
7007 hull
= isl_basic_map_transform_dims(hull
, isl_dim_in
, 0,
7008 isl_mat_copy(src
->vmap
));
7009 hull
= isl_basic_map_transform_dims(hull
, isl_dim_out
, 0,
7010 isl_mat_copy(dst
->vmap
));
7011 hull
= isl_basic_map_project_out(hull
,
7012 isl_dim_in
, 0, src
->rank
);
7013 hull
= isl_basic_map_project_out(hull
,
7014 isl_dim_out
, 0, dst
->rank
);
7015 hull
= isl_basic_map_remove_divs(hull
);
7016 n_in
= isl_basic_map_dim(hull
, isl_dim_in
);
7017 n_out
= isl_basic_map_dim(hull
, isl_dim_out
);
7018 hull
= isl_basic_map_drop_constraints_not_involving_dims(hull
,
7019 isl_dim_in
, 0, n_in
);
7020 hull
= isl_basic_map_drop_constraints_not_involving_dims(hull
,
7021 isl_dim_out
, 0, n_out
);
7023 return isl_stat_error
;
7024 edge
->weight
= isl_basic_map_n_equality(hull
);
7025 isl_basic_map_free(hull
);
7027 if (edge
->weight
> graph
->max_weight
)
7028 graph
->max_weight
= edge
->weight
;
7034 /* Call compute_schedule_finish_band on each of the clusters in "c"
7035 * in their topological order. This order is determined by the scc
7036 * fields of the nodes in "graph".
7037 * Combine the results in a sequence expressing the topological order.
7039 * If there is only one cluster left, then there is no need to introduce
7040 * a sequence node. Also, in this case, the cluster necessarily contains
7041 * the SCC at position 0 in the original graph and is therefore also
7042 * stored in the first cluster of "c".
7044 static __isl_give isl_schedule_node
*finish_bands_clustering(
7045 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
7046 struct isl_clustering
*c
)
7050 isl_union_set_list
*filters
;
7052 if (graph
->scc
== 1)
7053 return compute_schedule_finish_band(node
, &c
->cluster
[0], 0);
7055 ctx
= isl_schedule_node_get_ctx(node
);
7057 filters
= extract_sccs(ctx
, graph
);
7058 node
= isl_schedule_node_insert_sequence(node
, filters
);
7060 for (i
= 0; i
< graph
->scc
; ++i
) {
7061 int j
= c
->scc_cluster
[i
];
7062 node
= isl_schedule_node_child(node
, i
);
7063 node
= isl_schedule_node_child(node
, 0);
7064 node
= compute_schedule_finish_band(node
, &c
->cluster
[j
], 0);
7065 node
= isl_schedule_node_parent(node
);
7066 node
= isl_schedule_node_parent(node
);
7072 /* Compute a schedule for a connected dependence graph by first considering
7073 * each strongly connected component (SCC) in the graph separately and then
7074 * incrementally combining them into clusters.
7075 * Return the updated schedule node.
7077 * Initially, each cluster consists of a single SCC, each with its
7078 * own band schedule. The algorithm then tries to merge pairs
7079 * of clusters along a proximity edge until no more suitable
7080 * proximity edges can be found. During this merging, the schedule
7081 * is maintained in the individual SCCs.
7082 * After the merging is completed, the full resulting clusters
7083 * are extracted and in finish_bands_clustering,
7084 * compute_schedule_finish_band is called on each of them to integrate
7085 * the band into "node" and to continue the computation.
7087 * compute_weights initializes the weights that are used by find_proximity.
7089 static __isl_give isl_schedule_node
*compute_schedule_wcc_clustering(
7090 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
7093 struct isl_clustering c
;
7096 ctx
= isl_schedule_node_get_ctx(node
);
7098 if (clustering_init(ctx
, &c
, graph
) < 0)
7101 if (compute_weights(graph
, &c
) < 0)
7105 i
= find_proximity(graph
, &c
);
7108 if (i
>= graph
->n_edge
)
7110 if (merge_clusters_along_edge(ctx
, graph
, i
, &c
) < 0)
7114 if (extract_clusters(ctx
, graph
, &c
) < 0)
7117 node
= finish_bands_clustering(node
, graph
, &c
);
7119 clustering_free(ctx
, &c
);
7122 clustering_free(ctx
, &c
);
7123 return isl_schedule_node_free(node
);
7126 /* Compute a schedule for a connected dependence graph and return
7127 * the updated schedule node.
7129 * If Feautrier's algorithm is selected, we first recursively try to satisfy
7130 * as many validity dependences as possible. When all validity dependences
7131 * are satisfied we extend the schedule to a full-dimensional schedule.
7133 * Call compute_schedule_wcc_whole or compute_schedule_wcc_clustering
7134 * depending on whether the user has selected the option to try and
7135 * compute a schedule for the entire (weakly connected) component first.
7136 * If there is only a single strongly connected component (SCC), then
7137 * there is no point in trying to combine SCCs
7138 * in compute_schedule_wcc_clustering, so compute_schedule_wcc_whole
7139 * is called instead.
7141 static __isl_give isl_schedule_node
*compute_schedule_wcc(
7142 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
7149 ctx
= isl_schedule_node_get_ctx(node
);
7150 if (detect_sccs(ctx
, graph
) < 0)
7151 return isl_schedule_node_free(node
);
7153 if (compute_maxvar(graph
) < 0)
7154 return isl_schedule_node_free(node
);
7156 if (need_feautrier_step(ctx
, graph
))
7157 return compute_schedule_wcc_feautrier(node
, graph
);
7159 if (graph
->scc
<= 1 || isl_options_get_schedule_whole_component(ctx
))
7160 return compute_schedule_wcc_whole(node
, graph
);
7162 return compute_schedule_wcc_clustering(node
, graph
);
7165 /* Compute a schedule for each group of nodes identified by node->scc
7166 * separately and then combine them in a sequence node (or as set node
7167 * if graph->weak is set) inserted at position "node" of the schedule tree.
7168 * Return the updated schedule node.
7170 * If "wcc" is set then each of the groups belongs to a single
7171 * weakly connected component in the dependence graph so that
7172 * there is no need for compute_sub_schedule to look for weakly
7173 * connected components.
7175 static __isl_give isl_schedule_node
*compute_component_schedule(
7176 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
7181 isl_union_set_list
*filters
;
7185 ctx
= isl_schedule_node_get_ctx(node
);
7187 filters
= extract_sccs(ctx
, graph
);
7189 node
= isl_schedule_node_insert_set(node
, filters
);
7191 node
= isl_schedule_node_insert_sequence(node
, filters
);
7193 for (component
= 0; component
< graph
->scc
; ++component
) {
7194 node
= isl_schedule_node_child(node
, component
);
7195 node
= isl_schedule_node_child(node
, 0);
7196 node
= compute_sub_schedule(node
, ctx
, graph
,
7198 &edge_scc_exactly
, component
, wcc
);
7199 node
= isl_schedule_node_parent(node
);
7200 node
= isl_schedule_node_parent(node
);
7206 /* Compute a schedule for the given dependence graph and insert it at "node".
7207 * Return the updated schedule node.
7209 * We first check if the graph is connected (through validity and conditional
7210 * validity dependences) and, if not, compute a schedule
7211 * for each component separately.
7212 * If the schedule_serialize_sccs option is set, then we check for strongly
7213 * connected components instead and compute a separate schedule for
7214 * each such strongly connected component.
7216 static __isl_give isl_schedule_node
*compute_schedule(isl_schedule_node
*node
,
7217 struct isl_sched_graph
*graph
)
7224 ctx
= isl_schedule_node_get_ctx(node
);
7225 if (isl_options_get_schedule_serialize_sccs(ctx
)) {
7226 if (detect_sccs(ctx
, graph
) < 0)
7227 return isl_schedule_node_free(node
);
7229 if (detect_wccs(ctx
, graph
) < 0)
7230 return isl_schedule_node_free(node
);
7234 return compute_component_schedule(node
, graph
, 1);
7236 return compute_schedule_wcc(node
, graph
);
7239 /* Compute a schedule on sc->domain that respects the given schedule
7242 * In particular, the schedule respects all the validity dependences.
7243 * If the default isl scheduling algorithm is used, it tries to minimize
7244 * the dependence distances over the proximity dependences.
7245 * If Feautrier's scheduling algorithm is used, the proximity dependence
7246 * distances are only minimized during the extension to a full-dimensional
7249 * If there are any condition and conditional validity dependences,
7250 * then the conditional validity dependences may be violated inside
7251 * a tilable band, provided they have no adjacent non-local
7252 * condition dependences.
7254 __isl_give isl_schedule
*isl_schedule_constraints_compute_schedule(
7255 __isl_take isl_schedule_constraints
*sc
)
7257 isl_ctx
*ctx
= isl_schedule_constraints_get_ctx(sc
);
7258 struct isl_sched_graph graph
= { 0 };
7259 isl_schedule
*sched
;
7260 isl_schedule_node
*node
;
7261 isl_union_set
*domain
;
7263 sc
= isl_schedule_constraints_align_params(sc
);
7265 domain
= isl_schedule_constraints_get_domain(sc
);
7266 if (isl_union_set_n_set(domain
) == 0) {
7267 isl_schedule_constraints_free(sc
);
7268 return isl_schedule_from_domain(domain
);
7271 if (graph_init(&graph
, sc
) < 0)
7272 domain
= isl_union_set_free(domain
);
7274 node
= isl_schedule_node_from_domain(domain
);
7275 node
= isl_schedule_node_child(node
, 0);
7277 node
= compute_schedule(node
, &graph
);
7278 sched
= isl_schedule_node_get_schedule(node
);
7279 isl_schedule_node_free(node
);
7281 graph_free(ctx
, &graph
);
7282 isl_schedule_constraints_free(sc
);
7287 /* Compute a schedule for the given union of domains that respects
7288 * all the validity dependences and minimizes
7289 * the dependence distances over the proximity dependences.
7291 * This function is kept for backward compatibility.
7293 __isl_give isl_schedule
*isl_union_set_compute_schedule(
7294 __isl_take isl_union_set
*domain
,
7295 __isl_take isl_union_map
*validity
,
7296 __isl_take isl_union_map
*proximity
)
7298 isl_schedule_constraints
*sc
;
7300 sc
= isl_schedule_constraints_on_domain(domain
);
7301 sc
= isl_schedule_constraints_set_validity(sc
, validity
);
7302 sc
= isl_schedule_constraints_set_proximity(sc
, proximity
);
7304 return isl_schedule_constraints_compute_schedule(sc
);