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.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
98 struct isl_sched_node
{
102 isl_multi_aff
*compress
;
103 isl_multi_aff
*decompress
;
118 isl_multi_val
*sizes
;
122 static int node_has_tuples(const void *entry
, const void *val
)
124 struct isl_sched_node
*node
= (struct isl_sched_node
*)entry
;
125 isl_space
*space
= (isl_space
*) val
;
127 return isl_space_has_equal_tuples(node
->space
, space
);
130 static int node_scc_exactly(struct isl_sched_node
*node
, int scc
)
132 return node
->scc
== scc
;
135 static int node_scc_at_most(struct isl_sched_node
*node
, int scc
)
137 return node
->scc
<= scc
;
140 static int node_scc_at_least(struct isl_sched_node
*node
, int scc
)
142 return node
->scc
>= scc
;
145 /* An edge in the dependence graph. An edge may be used to
146 * ensure validity of the generated schedule, to minimize the dependence
149 * map is the dependence relation, with i -> j in the map if j depends on i
150 * tagged_condition and tagged_validity contain the union of all tagged
151 * condition or conditional validity dependence relations that
152 * specialize the dependence relation "map"; that is,
153 * if (i -> a) -> (j -> b) is an element of "tagged_condition"
154 * or "tagged_validity", then i -> j is an element of "map".
155 * If these fields are NULL, then they represent the empty relation.
156 * src is the source node
157 * dst is the sink node
159 * types is a bit vector containing the types of this edge.
160 * validity is set if the edge is used to ensure correctness
161 * coincidence is used to enforce zero dependence distances
162 * proximity is set if the edge is used to minimize dependence distances
163 * condition is set if the edge represents a condition
164 * for a conditional validity schedule constraint
165 * local can only be set for condition edges and indicates that
166 * the dependence distance over the edge should be zero
167 * conditional_validity is set if the edge is used to conditionally
170 * For validity edges, start and end mark the sequence of inequality
171 * constraints in the LP problem that encode the validity constraint
172 * corresponding to this edge.
174 * During clustering, an edge may be marked "no_merge" if it should
175 * not be used to merge clusters.
176 * The weight is also only used during clustering and it is
177 * an indication of how many schedule dimensions on either side
178 * of the schedule constraints can be aligned.
179 * If the weight is negative, then this means that this edge was postponed
180 * by has_bounded_distances or any_no_merge. The original weight can
181 * be retrieved by adding 1 + graph->max_weight, with "graph"
182 * the graph containing this edge.
184 struct isl_sched_edge
{
186 isl_union_map
*tagged_condition
;
187 isl_union_map
*tagged_validity
;
189 struct isl_sched_node
*src
;
190 struct isl_sched_node
*dst
;
201 /* Is "edge" marked as being of type "type"?
203 static int is_type(struct isl_sched_edge
*edge
, enum isl_edge_type type
)
205 return ISL_FL_ISSET(edge
->types
, 1 << type
);
208 /* Mark "edge" as being of type "type".
210 static void set_type(struct isl_sched_edge
*edge
, enum isl_edge_type type
)
212 ISL_FL_SET(edge
->types
, 1 << type
);
215 /* No longer mark "edge" as being of type "type"?
217 static void clear_type(struct isl_sched_edge
*edge
, enum isl_edge_type type
)
219 ISL_FL_CLR(edge
->types
, 1 << type
);
222 /* Is "edge" marked as a validity edge?
224 static int is_validity(struct isl_sched_edge
*edge
)
226 return is_type(edge
, isl_edge_validity
);
229 /* Mark "edge" as a validity edge.
231 static void set_validity(struct isl_sched_edge
*edge
)
233 set_type(edge
, isl_edge_validity
);
236 /* Is "edge" marked as a proximity edge?
238 static int is_proximity(struct isl_sched_edge
*edge
)
240 return is_type(edge
, isl_edge_proximity
);
243 /* Is "edge" marked as a local edge?
245 static int is_local(struct isl_sched_edge
*edge
)
247 return is_type(edge
, isl_edge_local
);
250 /* Mark "edge" as a local edge.
252 static void set_local(struct isl_sched_edge
*edge
)
254 set_type(edge
, isl_edge_local
);
257 /* No longer mark "edge" as a local edge.
259 static void clear_local(struct isl_sched_edge
*edge
)
261 clear_type(edge
, isl_edge_local
);
264 /* Is "edge" marked as a coincidence edge?
266 static int is_coincidence(struct isl_sched_edge
*edge
)
268 return is_type(edge
, isl_edge_coincidence
);
271 /* Is "edge" marked as a condition edge?
273 static int is_condition(struct isl_sched_edge
*edge
)
275 return is_type(edge
, isl_edge_condition
);
278 /* Is "edge" marked as a conditional validity edge?
280 static int is_conditional_validity(struct isl_sched_edge
*edge
)
282 return is_type(edge
, isl_edge_conditional_validity
);
285 /* Internal information about the dependence graph used during
286 * the construction of the schedule.
288 * intra_hmap is a cache, mapping dependence relations to their dual,
289 * for dependences from a node to itself
290 * inter_hmap is a cache, mapping dependence relations to their dual,
291 * for dependences between distinct nodes
292 * if compression is involved then the key for these maps
293 * is the original, uncompressed dependence relation, while
294 * the value is the dual of the compressed dependence relation.
296 * n is the number of nodes
297 * node is the list of nodes
298 * maxvar is the maximal number of variables over all nodes
299 * max_row is the allocated number of rows in the schedule
300 * n_row is the current (maximal) number of linearly independent
301 * rows in the node schedules
302 * n_total_row is the current number of rows in the node schedules
303 * band_start is the starting row in the node schedules of the current band
304 * root is set if this graph is the original dependence graph,
305 * without any splitting
307 * sorted contains a list of node indices sorted according to the
308 * SCC to which a node belongs
310 * n_edge is the number of edges
311 * edge is the list of edges
312 * max_edge contains the maximal number of edges of each type;
313 * in particular, it contains the number of edges in the inital graph.
314 * edge_table contains pointers into the edge array, hashed on the source
315 * and sink spaces; there is one such table for each type;
316 * a given edge may be referenced from more than one table
317 * if the corresponding relation appears in more than one of the
318 * sets of dependences; however, for each type there is only
319 * a single edge between a given pair of source and sink space
320 * in the entire graph
322 * node_table contains pointers into the node array, hashed on the space tuples
324 * region contains a list of variable sequences that should be non-trivial
326 * lp contains the (I)LP problem used to obtain new schedule rows
328 * src_scc and dst_scc are the source and sink SCCs of an edge with
329 * conflicting constraints
331 * scc represents the number of components
332 * weak is set if the components are weakly connected
334 * max_weight is used during clustering and represents the maximal
335 * weight of the relevant proximity edges.
337 struct isl_sched_graph
{
338 isl_map_to_basic_set
*intra_hmap
;
339 isl_map_to_basic_set
*inter_hmap
;
341 struct isl_sched_node
*node
;
354 struct isl_sched_edge
*edge
;
356 int max_edge
[isl_edge_last
+ 1];
357 struct isl_hash_table
*edge_table
[isl_edge_last
+ 1];
359 struct isl_hash_table
*node_table
;
360 struct isl_trivial_region
*region
;
373 /* Initialize node_table based on the list of nodes.
375 static int graph_init_table(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
379 graph
->node_table
= isl_hash_table_alloc(ctx
, graph
->n
);
380 if (!graph
->node_table
)
383 for (i
= 0; i
< graph
->n
; ++i
) {
384 struct isl_hash_table_entry
*entry
;
387 hash
= isl_space_get_tuple_hash(graph
->node
[i
].space
);
388 entry
= isl_hash_table_find(ctx
, graph
->node_table
, hash
,
390 graph
->node
[i
].space
, 1);
393 entry
->data
= &graph
->node
[i
];
399 /* Return a pointer to the node that lives within the given space,
400 * or NULL if there is no such node.
402 static struct isl_sched_node
*graph_find_node(isl_ctx
*ctx
,
403 struct isl_sched_graph
*graph
, __isl_keep isl_space
*space
)
405 struct isl_hash_table_entry
*entry
;
408 hash
= isl_space_get_tuple_hash(space
);
409 entry
= isl_hash_table_find(ctx
, graph
->node_table
, hash
,
410 &node_has_tuples
, space
, 0);
412 return entry
? entry
->data
: NULL
;
415 static int edge_has_src_and_dst(const void *entry
, const void *val
)
417 const struct isl_sched_edge
*edge
= entry
;
418 const struct isl_sched_edge
*temp
= val
;
420 return edge
->src
== temp
->src
&& edge
->dst
== temp
->dst
;
423 /* Add the given edge to graph->edge_table[type].
425 static isl_stat
graph_edge_table_add(isl_ctx
*ctx
,
426 struct isl_sched_graph
*graph
, enum isl_edge_type type
,
427 struct isl_sched_edge
*edge
)
429 struct isl_hash_table_entry
*entry
;
432 hash
= isl_hash_init();
433 hash
= isl_hash_builtin(hash
, edge
->src
);
434 hash
= isl_hash_builtin(hash
, edge
->dst
);
435 entry
= isl_hash_table_find(ctx
, graph
->edge_table
[type
], hash
,
436 &edge_has_src_and_dst
, edge
, 1);
438 return isl_stat_error
;
444 /* Allocate the edge_tables based on the maximal number of edges of
447 static int graph_init_edge_tables(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
451 for (i
= 0; i
<= isl_edge_last
; ++i
) {
452 graph
->edge_table
[i
] = isl_hash_table_alloc(ctx
,
454 if (!graph
->edge_table
[i
])
461 /* If graph->edge_table[type] contains an edge from the given source
462 * to the given destination, then return the hash table entry of this edge.
463 * Otherwise, return NULL.
465 static struct isl_hash_table_entry
*graph_find_edge_entry(
466 struct isl_sched_graph
*graph
,
467 enum isl_edge_type type
,
468 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
470 isl_ctx
*ctx
= isl_space_get_ctx(src
->space
);
472 struct isl_sched_edge temp
= { .src
= src
, .dst
= dst
};
474 hash
= isl_hash_init();
475 hash
= isl_hash_builtin(hash
, temp
.src
);
476 hash
= isl_hash_builtin(hash
, temp
.dst
);
477 return isl_hash_table_find(ctx
, graph
->edge_table
[type
], hash
,
478 &edge_has_src_and_dst
, &temp
, 0);
482 /* If graph->edge_table[type] contains an edge from the given source
483 * to the given destination, then return this edge.
484 * Otherwise, return NULL.
486 static struct isl_sched_edge
*graph_find_edge(struct isl_sched_graph
*graph
,
487 enum isl_edge_type type
,
488 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
490 struct isl_hash_table_entry
*entry
;
492 entry
= graph_find_edge_entry(graph
, type
, src
, dst
);
499 /* Check whether the dependence graph has an edge of the given type
500 * between the given two nodes.
502 static isl_bool
graph_has_edge(struct isl_sched_graph
*graph
,
503 enum isl_edge_type type
,
504 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
506 struct isl_sched_edge
*edge
;
509 edge
= graph_find_edge(graph
, type
, src
, dst
);
513 empty
= isl_map_plain_is_empty(edge
->map
);
515 return isl_bool_error
;
520 /* Look for any edge with the same src, dst and map fields as "model".
522 * Return the matching edge if one can be found.
523 * Return "model" if no matching edge is found.
524 * Return NULL on error.
526 static struct isl_sched_edge
*graph_find_matching_edge(
527 struct isl_sched_graph
*graph
, struct isl_sched_edge
*model
)
529 enum isl_edge_type i
;
530 struct isl_sched_edge
*edge
;
532 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
535 edge
= graph_find_edge(graph
, i
, model
->src
, model
->dst
);
538 is_equal
= isl_map_plain_is_equal(model
->map
, edge
->map
);
548 /* Remove the given edge from all the edge_tables that refer to it.
550 static void graph_remove_edge(struct isl_sched_graph
*graph
,
551 struct isl_sched_edge
*edge
)
553 isl_ctx
*ctx
= isl_map_get_ctx(edge
->map
);
554 enum isl_edge_type i
;
556 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
557 struct isl_hash_table_entry
*entry
;
559 entry
= graph_find_edge_entry(graph
, i
, edge
->src
, edge
->dst
);
562 if (entry
->data
!= edge
)
564 isl_hash_table_remove(ctx
, graph
->edge_table
[i
], entry
);
568 /* Check whether the dependence graph has any edge
569 * between the given two nodes.
571 static isl_bool
graph_has_any_edge(struct isl_sched_graph
*graph
,
572 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
574 enum isl_edge_type i
;
577 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
578 r
= graph_has_edge(graph
, i
, src
, dst
);
586 /* Check whether the dependence graph has a validity edge
587 * between the given two nodes.
589 * Conditional validity edges are essentially validity edges that
590 * can be ignored if the corresponding condition edges are iteration private.
591 * Here, we are only checking for the presence of validity
592 * edges, so we need to consider the conditional validity edges too.
593 * In particular, this function is used during the detection
594 * of strongly connected components and we cannot ignore
595 * conditional validity edges during this detection.
597 static isl_bool
graph_has_validity_edge(struct isl_sched_graph
*graph
,
598 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
602 r
= graph_has_edge(graph
, isl_edge_validity
, src
, dst
);
606 return graph_has_edge(graph
, isl_edge_conditional_validity
, src
, dst
);
609 static int graph_alloc(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
610 int n_node
, int n_edge
)
615 graph
->n_edge
= n_edge
;
616 graph
->node
= isl_calloc_array(ctx
, struct isl_sched_node
, graph
->n
);
617 graph
->sorted
= isl_calloc_array(ctx
, int, graph
->n
);
618 graph
->region
= isl_alloc_array(ctx
,
619 struct isl_trivial_region
, graph
->n
);
620 graph
->edge
= isl_calloc_array(ctx
,
621 struct isl_sched_edge
, graph
->n_edge
);
623 graph
->intra_hmap
= isl_map_to_basic_set_alloc(ctx
, 2 * n_edge
);
624 graph
->inter_hmap
= isl_map_to_basic_set_alloc(ctx
, 2 * n_edge
);
626 if (!graph
->node
|| !graph
->region
|| (graph
->n_edge
&& !graph
->edge
) ||
630 for(i
= 0; i
< graph
->n
; ++i
)
631 graph
->sorted
[i
] = i
;
636 static void graph_free(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
640 isl_map_to_basic_set_free(graph
->intra_hmap
);
641 isl_map_to_basic_set_free(graph
->inter_hmap
);
644 for (i
= 0; i
< graph
->n
; ++i
) {
645 isl_space_free(graph
->node
[i
].space
);
646 isl_set_free(graph
->node
[i
].hull
);
647 isl_multi_aff_free(graph
->node
[i
].compress
);
648 isl_multi_aff_free(graph
->node
[i
].decompress
);
649 isl_mat_free(graph
->node
[i
].sched
);
650 isl_map_free(graph
->node
[i
].sched_map
);
651 isl_mat_free(graph
->node
[i
].indep
);
652 isl_mat_free(graph
->node
[i
].vmap
);
654 free(graph
->node
[i
].coincident
);
655 isl_multi_val_free(graph
->node
[i
].sizes
);
656 isl_vec_free(graph
->node
[i
].max
);
661 for (i
= 0; i
< graph
->n_edge
; ++i
) {
662 isl_map_free(graph
->edge
[i
].map
);
663 isl_union_map_free(graph
->edge
[i
].tagged_condition
);
664 isl_union_map_free(graph
->edge
[i
].tagged_validity
);
668 for (i
= 0; i
<= isl_edge_last
; ++i
)
669 isl_hash_table_free(ctx
, graph
->edge_table
[i
]);
670 isl_hash_table_free(ctx
, graph
->node_table
);
671 isl_basic_set_free(graph
->lp
);
674 /* For each "set" on which this function is called, increment
675 * graph->n by one and update graph->maxvar.
677 static isl_stat
init_n_maxvar(__isl_take isl_set
*set
, void *user
)
679 struct isl_sched_graph
*graph
= user
;
680 int nvar
= isl_set_dim(set
, isl_dim_set
);
683 if (nvar
> graph
->maxvar
)
684 graph
->maxvar
= nvar
;
691 /* Compute the number of rows that should be allocated for the schedule.
692 * In particular, we need one row for each variable or one row
693 * for each basic map in the dependences.
694 * Note that it is practically impossible to exhaust both
695 * the number of dependences and the number of variables.
697 static isl_stat
compute_max_row(struct isl_sched_graph
*graph
,
698 __isl_keep isl_schedule_constraints
*sc
)
702 isl_union_set
*domain
;
706 domain
= isl_schedule_constraints_get_domain(sc
);
707 r
= isl_union_set_foreach_set(domain
, &init_n_maxvar
, graph
);
708 isl_union_set_free(domain
);
710 return isl_stat_error
;
711 n_edge
= isl_schedule_constraints_n_basic_map(sc
);
713 return isl_stat_error
;
714 graph
->max_row
= n_edge
+ graph
->maxvar
;
719 /* Does "bset" have any defining equalities for its set variables?
721 static isl_bool
has_any_defining_equality(__isl_keep isl_basic_set
*bset
)
726 return isl_bool_error
;
728 n
= isl_basic_set_dim(bset
, isl_dim_set
);
729 for (i
= 0; i
< n
; ++i
) {
732 has
= isl_basic_set_has_defining_equality(bset
, isl_dim_set
, i
,
738 return isl_bool_false
;
741 /* Set the entries of node->max to the value of the schedule_max_coefficient
744 static isl_stat
set_max_coefficient(isl_ctx
*ctx
, struct isl_sched_node
*node
)
748 max
= isl_options_get_schedule_max_coefficient(ctx
);
752 node
->max
= isl_vec_alloc(ctx
, node
->nvar
);
753 node
->max
= isl_vec_set_si(node
->max
, max
);
755 return isl_stat_error
;
760 /* Set the entries of node->max to the minimum of the schedule_max_coefficient
761 * option (if set) and half of the minimum of the sizes in the other
762 * dimensions. Round up when computing the half such that
763 * if the minimum of the sizes is one, half of the size is taken to be one
765 * If the global minimum is unbounded (i.e., if both
766 * the schedule_max_coefficient is not set and the sizes in the other
767 * dimensions are unbounded), then store a negative value.
768 * If the schedule coefficient is close to the size of the instance set
769 * in another dimension, then the schedule may represent a loop
770 * coalescing transformation (especially if the coefficient
771 * in that other dimension is one). Forcing the coefficient to be
772 * smaller than or equal to half the minimal size should avoid this
775 static isl_stat
compute_max_coefficient(isl_ctx
*ctx
,
776 struct isl_sched_node
*node
)
782 max
= isl_options_get_schedule_max_coefficient(ctx
);
783 v
= isl_vec_alloc(ctx
, node
->nvar
);
785 return isl_stat_error
;
787 for (i
= 0; i
< node
->nvar
; ++i
) {
788 isl_int_set_si(v
->el
[i
], max
);
789 isl_int_mul_si(v
->el
[i
], v
->el
[i
], 2);
792 for (i
= 0; i
< node
->nvar
; ++i
) {
795 size
= isl_multi_val_get_val(node
->sizes
, i
);
798 if (!isl_val_is_int(size
)) {
802 for (j
= 0; j
< node
->nvar
; ++j
) {
805 if (isl_int_is_neg(v
->el
[j
]) ||
806 isl_int_gt(v
->el
[j
], size
->n
))
807 isl_int_set(v
->el
[j
], size
->n
);
812 for (i
= 0; i
< node
->nvar
; ++i
)
813 isl_int_cdiv_q_ui(v
->el
[i
], v
->el
[i
], 2);
819 return isl_stat_error
;
822 /* Compute and return the size of "set" in dimension "dim".
823 * The size is taken to be the difference in values for that variable
824 * for fixed values of the other variables.
825 * In particular, the variable is first isolated from the other variables
826 * in the range of a map
828 * [i_0, ..., i_dim-1, i_dim+1, ...] -> [i_dim]
830 * and then duplicated
832 * [i_0, ..., i_dim-1, i_dim+1, ...] -> [[i_dim] -> [i_dim']]
834 * The shared variables are then projected out and the maximal value
835 * of i_dim' - i_dim is computed.
837 static __isl_give isl_val
*compute_size(__isl_take isl_set
*set
, int dim
)
844 map
= isl_set_project_onto_map(set
, isl_dim_set
, dim
, 1);
845 map
= isl_map_project_out(map
, isl_dim_in
, dim
, 1);
846 map
= isl_map_range_product(map
, isl_map_copy(map
));
847 map
= isl_set_unwrap(isl_map_range(map
));
848 set
= isl_map_deltas(map
);
849 ls
= isl_local_space_from_space(isl_set_get_space(set
));
850 obj
= isl_aff_var_on_domain(ls
, isl_dim_set
, 0);
851 v
= isl_set_max_val(set
, obj
);
858 /* Compute the size of the instance set "set" of "node", after compression,
859 * as well as bounds on the corresponding coefficients, if needed.
861 * The sizes are needed when the schedule_treat_coalescing option is set.
862 * The bounds are needed when the schedule_treat_coalescing option or
863 * the schedule_max_coefficient option is set.
865 * If the schedule_treat_coalescing option is not set, then at most
866 * the bounds need to be set and this is done in set_max_coefficient.
867 * Otherwise, compress the domain if needed, compute the size
868 * in each direction and store the results in node->size.
869 * Finally, set the bounds on the coefficients based on the sizes
870 * and the schedule_max_coefficient option in compute_max_coefficient.
872 static isl_stat
compute_sizes_and_max(isl_ctx
*ctx
, struct isl_sched_node
*node
,
873 __isl_take isl_set
*set
)
878 if (!isl_options_get_schedule_treat_coalescing(ctx
)) {
880 return set_max_coefficient(ctx
, node
);
883 if (node
->compressed
)
884 set
= isl_set_preimage_multi_aff(set
,
885 isl_multi_aff_copy(node
->decompress
));
886 mv
= isl_multi_val_zero(isl_set_get_space(set
));
887 n
= isl_set_dim(set
, isl_dim_set
);
888 for (j
= 0; j
< n
; ++j
) {
891 v
= compute_size(isl_set_copy(set
), j
);
892 mv
= isl_multi_val_set_val(mv
, j
, v
);
897 return isl_stat_error
;
898 return compute_max_coefficient(ctx
, node
);
901 /* Add a new node to the graph representing the given instance set.
902 * "nvar" is the (possibly compressed) number of variables and
903 * may be smaller than then number of set variables in "set"
904 * if "compressed" is set.
905 * If "compressed" is set, then "hull" represents the constraints
906 * that were used to derive the compression, while "compress" and
907 * "decompress" map the original space to the compressed space and
909 * If "compressed" is not set, then "hull", "compress" and "decompress"
912 * Compute the size of the instance set and bounds on the coefficients,
915 static isl_stat
add_node(struct isl_sched_graph
*graph
,
916 __isl_take isl_set
*set
, int nvar
, int compressed
,
917 __isl_take isl_set
*hull
, __isl_take isl_multi_aff
*compress
,
918 __isl_take isl_multi_aff
*decompress
)
925 struct isl_sched_node
*node
;
928 return isl_stat_error
;
930 ctx
= isl_set_get_ctx(set
);
931 nparam
= isl_set_dim(set
, isl_dim_param
);
932 if (!ctx
->opt
->schedule_parametric
)
934 sched
= isl_mat_alloc(ctx
, 0, 1 + nparam
+ nvar
);
935 node
= &graph
->node
[graph
->n
];
937 space
= isl_set_get_space(set
);
940 node
->nparam
= nparam
;
942 node
->sched_map
= NULL
;
943 coincident
= isl_calloc_array(ctx
, int, graph
->max_row
);
944 node
->coincident
= coincident
;
945 node
->compressed
= compressed
;
947 node
->compress
= compress
;
948 node
->decompress
= decompress
;
949 if (compute_sizes_and_max(ctx
, node
, set
) < 0)
950 return isl_stat_error
;
952 if (!space
|| !sched
|| (graph
->max_row
&& !coincident
))
953 return isl_stat_error
;
954 if (compressed
&& (!hull
|| !compress
|| !decompress
))
955 return isl_stat_error
;
960 /* Construct an identifier for node "node", which will represent "set".
961 * The name of the identifier is either "compressed" or
962 * "compressed_<name>", with <name> the name of the space of "set".
963 * The user pointer of the identifier points to "node".
965 static __isl_give isl_id
*construct_compressed_id(__isl_keep isl_set
*set
,
966 struct isl_sched_node
*node
)
975 has_name
= isl_set_has_tuple_name(set
);
979 ctx
= isl_set_get_ctx(set
);
981 return isl_id_alloc(ctx
, "compressed", node
);
983 p
= isl_printer_to_str(ctx
);
984 name
= isl_set_get_tuple_name(set
);
985 p
= isl_printer_print_str(p
, "compressed_");
986 p
= isl_printer_print_str(p
, name
);
987 id_name
= isl_printer_get_str(p
);
990 id
= isl_id_alloc(ctx
, id_name
, node
);
996 /* Add a new node to the graph representing the given set.
998 * If any of the set variables is defined by an equality, then
999 * we perform variable compression such that we can perform
1000 * the scheduling on the compressed domain.
1001 * In this case, an identifier is used that references the new node
1002 * such that each compressed space is unique and
1003 * such that the node can be recovered from the compressed space.
1005 static isl_stat
extract_node(__isl_take isl_set
*set
, void *user
)
1008 isl_bool has_equality
;
1010 isl_basic_set
*hull
;
1013 isl_multi_aff
*compress
, *decompress
;
1014 struct isl_sched_graph
*graph
= user
;
1016 hull
= isl_set_affine_hull(isl_set_copy(set
));
1017 hull
= isl_basic_set_remove_divs(hull
);
1018 nvar
= isl_set_dim(set
, isl_dim_set
);
1019 has_equality
= has_any_defining_equality(hull
);
1021 if (has_equality
< 0)
1023 if (!has_equality
) {
1024 isl_basic_set_free(hull
);
1025 return add_node(graph
, set
, nvar
, 0, NULL
, NULL
, NULL
);
1028 id
= construct_compressed_id(set
, &graph
->node
[graph
->n
]);
1029 morph
= isl_basic_set_variable_compression_with_id(hull
,
1032 nvar
= isl_morph_ran_dim(morph
, isl_dim_set
);
1033 compress
= isl_morph_get_var_multi_aff(morph
);
1034 morph
= isl_morph_inverse(morph
);
1035 decompress
= isl_morph_get_var_multi_aff(morph
);
1036 isl_morph_free(morph
);
1038 hull_set
= isl_set_from_basic_set(hull
);
1039 return add_node(graph
, set
, nvar
, 1, hull_set
, compress
, decompress
);
1041 isl_basic_set_free(hull
);
1043 return isl_stat_error
;
1046 struct isl_extract_edge_data
{
1047 enum isl_edge_type type
;
1048 struct isl_sched_graph
*graph
;
1051 /* Merge edge2 into edge1, freeing the contents of edge2.
1052 * Return 0 on success and -1 on failure.
1054 * edge1 and edge2 are assumed to have the same value for the map field.
1056 static int merge_edge(struct isl_sched_edge
*edge1
,
1057 struct isl_sched_edge
*edge2
)
1059 edge1
->types
|= edge2
->types
;
1060 isl_map_free(edge2
->map
);
1062 if (is_condition(edge2
)) {
1063 if (!edge1
->tagged_condition
)
1064 edge1
->tagged_condition
= edge2
->tagged_condition
;
1066 edge1
->tagged_condition
=
1067 isl_union_map_union(edge1
->tagged_condition
,
1068 edge2
->tagged_condition
);
1071 if (is_conditional_validity(edge2
)) {
1072 if (!edge1
->tagged_validity
)
1073 edge1
->tagged_validity
= edge2
->tagged_validity
;
1075 edge1
->tagged_validity
=
1076 isl_union_map_union(edge1
->tagged_validity
,
1077 edge2
->tagged_validity
);
1080 if (is_condition(edge2
) && !edge1
->tagged_condition
)
1082 if (is_conditional_validity(edge2
) && !edge1
->tagged_validity
)
1088 /* Insert dummy tags in domain and range of "map".
1090 * In particular, if "map" is of the form
1096 * [A -> dummy_tag] -> [B -> dummy_tag]
1098 * where the dummy_tags are identical and equal to any dummy tags
1099 * introduced by any other call to this function.
1101 static __isl_give isl_map
*insert_dummy_tags(__isl_take isl_map
*map
)
1107 isl_set
*domain
, *range
;
1109 ctx
= isl_map_get_ctx(map
);
1111 id
= isl_id_alloc(ctx
, NULL
, &dummy
);
1112 space
= isl_space_params(isl_map_get_space(map
));
1113 space
= isl_space_set_from_params(space
);
1114 space
= isl_space_set_tuple_id(space
, isl_dim_set
, id
);
1115 space
= isl_space_map_from_set(space
);
1117 domain
= isl_map_wrap(map
);
1118 range
= isl_map_wrap(isl_map_universe(space
));
1119 map
= isl_map_from_domain_and_range(domain
, range
);
1120 map
= isl_map_zip(map
);
1125 /* Given that at least one of "src" or "dst" is compressed, return
1126 * a map between the spaces of these nodes restricted to the affine
1127 * hull that was used in the compression.
1129 static __isl_give isl_map
*extract_hull(struct isl_sched_node
*src
,
1130 struct isl_sched_node
*dst
)
1134 if (src
->compressed
)
1135 dom
= isl_set_copy(src
->hull
);
1137 dom
= isl_set_universe(isl_space_copy(src
->space
));
1138 if (dst
->compressed
)
1139 ran
= isl_set_copy(dst
->hull
);
1141 ran
= isl_set_universe(isl_space_copy(dst
->space
));
1143 return isl_map_from_domain_and_range(dom
, ran
);
1146 /* Intersect the domains of the nested relations in domain and range
1147 * of "tagged" with "map".
1149 static __isl_give isl_map
*map_intersect_domains(__isl_take isl_map
*tagged
,
1150 __isl_keep isl_map
*map
)
1154 tagged
= isl_map_zip(tagged
);
1155 set
= isl_map_wrap(isl_map_copy(map
));
1156 tagged
= isl_map_intersect_domain(tagged
, set
);
1157 tagged
= isl_map_zip(tagged
);
1161 /* Return a pointer to the node that lives in the domain space of "map"
1162 * or NULL if there is no such node.
1164 static struct isl_sched_node
*find_domain_node(isl_ctx
*ctx
,
1165 struct isl_sched_graph
*graph
, __isl_keep isl_map
*map
)
1167 struct isl_sched_node
*node
;
1170 space
= isl_space_domain(isl_map_get_space(map
));
1171 node
= graph_find_node(ctx
, graph
, space
);
1172 isl_space_free(space
);
1177 /* Return a pointer to the node that lives in the range space of "map"
1178 * or NULL if there is no such node.
1180 static struct isl_sched_node
*find_range_node(isl_ctx
*ctx
,
1181 struct isl_sched_graph
*graph
, __isl_keep isl_map
*map
)
1183 struct isl_sched_node
*node
;
1186 space
= isl_space_range(isl_map_get_space(map
));
1187 node
= graph_find_node(ctx
, graph
, space
);
1188 isl_space_free(space
);
1193 /* Add a new edge to the graph based on the given map
1194 * and add it to data->graph->edge_table[data->type].
1195 * If a dependence relation of a given type happens to be identical
1196 * to one of the dependence relations of a type that was added before,
1197 * then we don't create a new edge, but instead mark the original edge
1198 * as also representing a dependence of the current type.
1200 * Edges of type isl_edge_condition or isl_edge_conditional_validity
1201 * may be specified as "tagged" dependence relations. That is, "map"
1202 * may contain elements (i -> a) -> (j -> b), where i -> j denotes
1203 * the dependence on iterations and a and b are tags.
1204 * edge->map is set to the relation containing the elements i -> j,
1205 * while edge->tagged_condition and edge->tagged_validity contain
1206 * the union of all the "map" relations
1207 * for which extract_edge is called that result in the same edge->map.
1209 * If the source or the destination node is compressed, then
1210 * intersect both "map" and "tagged" with the constraints that
1211 * were used to construct the compression.
1212 * This ensures that there are no schedule constraints defined
1213 * outside of these domains, while the scheduler no longer has
1214 * any control over those outside parts.
1216 static isl_stat
extract_edge(__isl_take isl_map
*map
, void *user
)
1218 isl_ctx
*ctx
= isl_map_get_ctx(map
);
1219 struct isl_extract_edge_data
*data
= user
;
1220 struct isl_sched_graph
*graph
= data
->graph
;
1221 struct isl_sched_node
*src
, *dst
;
1222 struct isl_sched_edge
*edge
;
1223 isl_map
*tagged
= NULL
;
1225 if (data
->type
== isl_edge_condition
||
1226 data
->type
== isl_edge_conditional_validity
) {
1227 if (isl_map_can_zip(map
)) {
1228 tagged
= isl_map_copy(map
);
1229 map
= isl_set_unwrap(isl_map_domain(isl_map_zip(map
)));
1231 tagged
= insert_dummy_tags(isl_map_copy(map
));
1235 src
= find_domain_node(ctx
, graph
, map
);
1236 dst
= find_range_node(ctx
, graph
, map
);
1240 isl_map_free(tagged
);
1244 if (src
->compressed
|| dst
->compressed
) {
1246 hull
= extract_hull(src
, dst
);
1248 tagged
= map_intersect_domains(tagged
, hull
);
1249 map
= isl_map_intersect(map
, hull
);
1252 graph
->edge
[graph
->n_edge
].src
= src
;
1253 graph
->edge
[graph
->n_edge
].dst
= dst
;
1254 graph
->edge
[graph
->n_edge
].map
= map
;
1255 graph
->edge
[graph
->n_edge
].types
= 0;
1256 graph
->edge
[graph
->n_edge
].tagged_condition
= NULL
;
1257 graph
->edge
[graph
->n_edge
].tagged_validity
= NULL
;
1258 set_type(&graph
->edge
[graph
->n_edge
], data
->type
);
1259 if (data
->type
== isl_edge_condition
)
1260 graph
->edge
[graph
->n_edge
].tagged_condition
=
1261 isl_union_map_from_map(tagged
);
1262 if (data
->type
== isl_edge_conditional_validity
)
1263 graph
->edge
[graph
->n_edge
].tagged_validity
=
1264 isl_union_map_from_map(tagged
);
1266 edge
= graph_find_matching_edge(graph
, &graph
->edge
[graph
->n_edge
]);
1269 return isl_stat_error
;
1271 if (edge
== &graph
->edge
[graph
->n_edge
])
1272 return graph_edge_table_add(ctx
, graph
, data
->type
,
1273 &graph
->edge
[graph
->n_edge
++]);
1275 if (merge_edge(edge
, &graph
->edge
[graph
->n_edge
]) < 0)
1278 return graph_edge_table_add(ctx
, graph
, data
->type
, edge
);
1281 /* Initialize the schedule graph "graph" from the schedule constraints "sc".
1283 * The context is included in the domain before the nodes of
1284 * the graphs are extracted in order to be able to exploit
1285 * any possible additional equalities.
1286 * Note that this intersection is only performed locally here.
1288 static isl_stat
graph_init(struct isl_sched_graph
*graph
,
1289 __isl_keep isl_schedule_constraints
*sc
)
1292 isl_union_set
*domain
;
1294 struct isl_extract_edge_data data
;
1295 enum isl_edge_type i
;
1299 return isl_stat_error
;
1301 ctx
= isl_schedule_constraints_get_ctx(sc
);
1303 domain
= isl_schedule_constraints_get_domain(sc
);
1304 graph
->n
= isl_union_set_n_set(domain
);
1305 isl_union_set_free(domain
);
1307 if (graph_alloc(ctx
, graph
, graph
->n
,
1308 isl_schedule_constraints_n_map(sc
)) < 0)
1309 return isl_stat_error
;
1311 if (compute_max_row(graph
, sc
) < 0)
1312 return isl_stat_error
;
1315 domain
= isl_schedule_constraints_get_domain(sc
);
1316 domain
= isl_union_set_intersect_params(domain
,
1317 isl_schedule_constraints_get_context(sc
));
1318 r
= isl_union_set_foreach_set(domain
, &extract_node
, graph
);
1319 isl_union_set_free(domain
);
1321 return isl_stat_error
;
1322 if (graph_init_table(ctx
, graph
) < 0)
1323 return isl_stat_error
;
1324 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
1325 c
= isl_schedule_constraints_get(sc
, i
);
1326 graph
->max_edge
[i
] = isl_union_map_n_map(c
);
1327 isl_union_map_free(c
);
1329 return isl_stat_error
;
1331 if (graph_init_edge_tables(ctx
, graph
) < 0)
1332 return isl_stat_error
;
1335 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
1339 c
= isl_schedule_constraints_get(sc
, i
);
1340 r
= isl_union_map_foreach_map(c
, &extract_edge
, &data
);
1341 isl_union_map_free(c
);
1343 return isl_stat_error
;
1349 /* Check whether there is any dependence from node[j] to node[i]
1350 * or from node[i] to node[j].
1352 static isl_bool
node_follows_weak(int i
, int j
, void *user
)
1355 struct isl_sched_graph
*graph
= user
;
1357 f
= graph_has_any_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
1360 return graph_has_any_edge(graph
, &graph
->node
[i
], &graph
->node
[j
]);
1363 /* Check whether there is a (conditional) validity dependence from node[j]
1364 * to node[i], forcing node[i] to follow node[j].
1366 static isl_bool
node_follows_strong(int i
, int j
, void *user
)
1368 struct isl_sched_graph
*graph
= user
;
1370 return graph_has_validity_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
1373 /* Use Tarjan's algorithm for computing the strongly connected components
1374 * in the dependence graph only considering those edges defined by "follows".
1376 static int detect_ccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
1377 isl_bool (*follows
)(int i
, int j
, void *user
))
1380 struct isl_tarjan_graph
*g
= NULL
;
1382 g
= isl_tarjan_graph_init(ctx
, graph
->n
, follows
, graph
);
1390 while (g
->order
[i
] != -1) {
1391 graph
->node
[g
->order
[i
]].scc
= graph
->scc
;
1399 isl_tarjan_graph_free(g
);
1404 /* Apply Tarjan's algorithm to detect the strongly connected components
1405 * in the dependence graph.
1406 * Only consider the (conditional) validity dependences and clear "weak".
1408 static int detect_sccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
1411 return detect_ccs(ctx
, graph
, &node_follows_strong
);
1414 /* Apply Tarjan's algorithm to detect the (weakly) connected components
1415 * in the dependence graph.
1416 * Consider all dependences and set "weak".
1418 static int detect_wccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
1421 return detect_ccs(ctx
, graph
, &node_follows_weak
);
1424 static int cmp_scc(const void *a
, const void *b
, void *data
)
1426 struct isl_sched_graph
*graph
= data
;
1430 return graph
->node
[*i1
].scc
- graph
->node
[*i2
].scc
;
1433 /* Sort the elements of graph->sorted according to the corresponding SCCs.
1435 static int sort_sccs(struct isl_sched_graph
*graph
)
1437 return isl_sort(graph
->sorted
, graph
->n
, sizeof(int), &cmp_scc
, graph
);
1440 /* Given a dependence relation R from "node" to itself,
1441 * construct the set of coefficients of valid constraints for elements
1442 * in that dependence relation.
1443 * In particular, the result contains tuples of coefficients
1444 * c_0, c_n, c_x such that
1446 * c_0 + c_n n + c_x y - c_x x >= 0 for each (x,y) in R
1450 * c_0 + c_n n + c_x d >= 0 for each d in delta R = { y - x | (x,y) in R }
1452 * We choose here to compute the dual of delta R.
1453 * Alternatively, we could have computed the dual of R, resulting
1454 * in a set of tuples c_0, c_n, c_x, c_y, and then
1455 * plugged in (c_0, c_n, c_x, -c_x).
1457 * If "node" has been compressed, then the dependence relation
1458 * is also compressed before the set of coefficients is computed.
1460 static __isl_give isl_basic_set
*intra_coefficients(
1461 struct isl_sched_graph
*graph
, struct isl_sched_node
*node
,
1462 __isl_take isl_map
*map
)
1466 isl_basic_set
*coef
;
1467 isl_maybe_isl_basic_set m
;
1469 m
= isl_map_to_basic_set_try_get(graph
->intra_hmap
, map
);
1470 if (m
.valid
< 0 || m
.valid
) {
1475 key
= isl_map_copy(map
);
1476 if (node
->compressed
) {
1477 map
= isl_map_preimage_domain_multi_aff(map
,
1478 isl_multi_aff_copy(node
->decompress
));
1479 map
= isl_map_preimage_range_multi_aff(map
,
1480 isl_multi_aff_copy(node
->decompress
));
1482 delta
= isl_set_remove_divs(isl_map_deltas(map
));
1483 coef
= isl_set_coefficients(delta
);
1484 graph
->intra_hmap
= isl_map_to_basic_set_set(graph
->intra_hmap
, key
,
1485 isl_basic_set_copy(coef
));
1490 /* Given a dependence relation R, construct the set of coefficients
1491 * of valid constraints for elements in that dependence relation.
1492 * In particular, the result contains tuples of coefficients
1493 * c_0, c_n, c_x, c_y such that
1495 * c_0 + c_n n + c_x x + c_y y >= 0 for each (x,y) in R
1497 * If the source or destination nodes of "edge" have been compressed,
1498 * then the dependence relation is also compressed before
1499 * the set of coefficients is computed.
1501 static __isl_give isl_basic_set
*inter_coefficients(
1502 struct isl_sched_graph
*graph
, struct isl_sched_edge
*edge
,
1503 __isl_take isl_map
*map
)
1507 isl_basic_set
*coef
;
1508 isl_maybe_isl_basic_set m
;
1510 m
= isl_map_to_basic_set_try_get(graph
->inter_hmap
, map
);
1511 if (m
.valid
< 0 || m
.valid
) {
1516 key
= isl_map_copy(map
);
1517 if (edge
->src
->compressed
)
1518 map
= isl_map_preimage_domain_multi_aff(map
,
1519 isl_multi_aff_copy(edge
->src
->decompress
));
1520 if (edge
->dst
->compressed
)
1521 map
= isl_map_preimage_range_multi_aff(map
,
1522 isl_multi_aff_copy(edge
->dst
->decompress
));
1523 set
= isl_map_wrap(isl_map_remove_divs(map
));
1524 coef
= isl_set_coefficients(set
);
1525 graph
->inter_hmap
= isl_map_to_basic_set_set(graph
->inter_hmap
, key
,
1526 isl_basic_set_copy(coef
));
1531 /* Return the position of the coefficients of the variables in
1532 * the coefficients constraints "coef".
1534 * The space of "coef" is of the form
1536 * { coefficients[[cst, params] -> S] }
1538 * Return the position of S.
1540 static int coef_var_offset(__isl_keep isl_basic_set
*coef
)
1545 space
= isl_space_unwrap(isl_basic_set_get_space(coef
));
1546 offset
= isl_space_dim(space
, isl_dim_in
);
1547 isl_space_free(space
);
1552 /* Return the offset of the coefficient of the constant term of "node"
1555 * Within each node, the coefficients have the following order:
1556 * - positive and negative parts of c_i_x
1557 * - c_i_n (if parametric)
1560 static int node_cst_coef_offset(struct isl_sched_node
*node
)
1562 return node
->start
+ 2 * node
->nvar
+ node
->nparam
;
1565 /* Return the offset of the coefficients of the parameters of "node"
1568 * Within each node, the coefficients have the following order:
1569 * - positive and negative parts of c_i_x
1570 * - c_i_n (if parametric)
1573 static int node_par_coef_offset(struct isl_sched_node
*node
)
1575 return node
->start
+ 2 * node
->nvar
;
1578 /* Return the offset of the coefficients of the variables of "node"
1581 * Within each node, the coefficients have the following order:
1582 * - positive and negative parts of c_i_x
1583 * - c_i_n (if parametric)
1586 static int node_var_coef_offset(struct isl_sched_node
*node
)
1591 /* Return the position of the pair of variables encoding
1592 * coefficient "i" of "node".
1594 * The order of these variable pairs is the opposite of
1595 * that of the coefficients, with 2 variables per coefficient.
1597 static int node_var_coef_pos(struct isl_sched_node
*node
, int i
)
1599 return node_var_coef_offset(node
) + 2 * (node
->nvar
- 1 - i
);
1602 /* Construct an isl_dim_map for mapping constraints on coefficients
1603 * for "node" to the corresponding positions in graph->lp.
1604 * "offset" is the offset of the coefficients for the variables
1605 * in the input constraints.
1606 * "s" is the sign of the mapping.
1608 * The input constraints are given in terms of the coefficients (c_0, c_n, c_x).
1609 * The mapping produced by this function essentially plugs in
1610 * (0, 0, c_i_x^+ - c_i_x^-) if s = 1 and
1611 * (0, 0, -c_i_x^+ + c_i_x^-) if s = -1.
1612 * In graph->lp, the c_i_x^- appear before their c_i_x^+ counterpart.
1613 * Furthermore, the order of these pairs is the opposite of that
1614 * of the corresponding coefficients.
1616 * The caller can extend the mapping to also map the other coefficients
1617 * (and therefore not plug in 0).
1619 static __isl_give isl_dim_map
*intra_dim_map(isl_ctx
*ctx
,
1620 struct isl_sched_graph
*graph
, struct isl_sched_node
*node
,
1625 isl_dim_map
*dim_map
;
1630 total
= isl_basic_set_total_dim(graph
->lp
);
1631 pos
= node_var_coef_pos(node
, 0);
1632 dim_map
= isl_dim_map_alloc(ctx
, total
);
1633 isl_dim_map_range(dim_map
, pos
, -2, offset
, 1, node
->nvar
, -s
);
1634 isl_dim_map_range(dim_map
, pos
+ 1, -2, offset
, 1, node
->nvar
, s
);
1639 /* Construct an isl_dim_map for mapping constraints on coefficients
1640 * for "src" (node i) and "dst" (node j) to the corresponding positions
1642 * "offset" is the offset of the coefficients for the variables of "src"
1643 * in the input constraints.
1644 * "s" is the sign of the mapping.
1646 * The input constraints are given in terms of the coefficients
1647 * (c_0, c_n, c_x, c_y).
1648 * The mapping produced by this function essentially plugs in
1649 * (c_j_0 - c_i_0, c_j_n - c_i_n,
1650 * -(c_i_x^+ - c_i_x^-), c_j_x^+ - c_j_x^-) if s = 1 and
1651 * (-c_j_0 + c_i_0, -c_j_n + c_i_n,
1652 * c_i_x^+ - c_i_x^-, -(c_j_x^+ - c_j_x^-)) if s = -1.
1653 * In graph->lp, the c_*^- appear before their c_*^+ counterpart.
1654 * Furthermore, the order of these pairs is the opposite of that
1655 * of the corresponding coefficients.
1657 * The caller can further extend the mapping.
1659 static __isl_give isl_dim_map
*inter_dim_map(isl_ctx
*ctx
,
1660 struct isl_sched_graph
*graph
, struct isl_sched_node
*src
,
1661 struct isl_sched_node
*dst
, int offset
, int s
)
1665 isl_dim_map
*dim_map
;
1670 total
= isl_basic_set_total_dim(graph
->lp
);
1671 dim_map
= isl_dim_map_alloc(ctx
, total
);
1673 pos
= node_cst_coef_offset(dst
);
1674 isl_dim_map_range(dim_map
, pos
, 0, 0, 0, 1, s
);
1675 pos
= node_par_coef_offset(dst
);
1676 isl_dim_map_range(dim_map
, pos
, 1, 1, 1, dst
->nparam
, s
);
1677 pos
= node_var_coef_pos(dst
, 0);
1678 isl_dim_map_range(dim_map
, pos
, -2, offset
+ src
->nvar
, 1,
1680 isl_dim_map_range(dim_map
, pos
+ 1, -2, offset
+ src
->nvar
, 1,
1683 pos
= node_cst_coef_offset(src
);
1684 isl_dim_map_range(dim_map
, pos
, 0, 0, 0, 1, -s
);
1685 pos
= node_par_coef_offset(src
);
1686 isl_dim_map_range(dim_map
, pos
, 1, 1, 1, src
->nparam
, -s
);
1687 pos
= node_var_coef_pos(src
, 0);
1688 isl_dim_map_range(dim_map
, pos
, -2, offset
, 1, src
->nvar
, s
);
1689 isl_dim_map_range(dim_map
, pos
+ 1, -2, offset
, 1, src
->nvar
, -s
);
1694 /* Add the constraints from "src" to "dst" using "dim_map",
1695 * after making sure there is enough room in "dst" for the extra constraints.
1697 static __isl_give isl_basic_set
*add_constraints_dim_map(
1698 __isl_take isl_basic_set
*dst
, __isl_take isl_basic_set
*src
,
1699 __isl_take isl_dim_map
*dim_map
)
1703 n_eq
= isl_basic_set_n_equality(src
);
1704 n_ineq
= isl_basic_set_n_inequality(src
);
1705 dst
= isl_basic_set_extend_constraints(dst
, n_eq
, n_ineq
);
1706 dst
= isl_basic_set_add_constraints_dim_map(dst
, src
, dim_map
);
1710 /* Add constraints to graph->lp that force validity for the given
1711 * dependence from a node i to itself.
1712 * That is, add constraints that enforce
1714 * (c_i_0 + c_i_n n + c_i_x y) - (c_i_0 + c_i_n n + c_i_x x)
1715 * = c_i_x (y - x) >= 0
1717 * for each (x,y) in R.
1718 * We obtain general constraints on coefficients (c_0, c_n, c_x)
1719 * of valid constraints for (y - x) and then plug in (0, 0, c_i_x^+ - c_i_x^-),
1720 * where c_i_x = c_i_x^+ - c_i_x^-, with c_i_x^+ and c_i_x^- non-negative.
1721 * In graph->lp, the c_i_x^- appear before their c_i_x^+ counterpart.
1723 static isl_stat
add_intra_validity_constraints(struct isl_sched_graph
*graph
,
1724 struct isl_sched_edge
*edge
)
1727 isl_map
*map
= isl_map_copy(edge
->map
);
1728 isl_ctx
*ctx
= isl_map_get_ctx(map
);
1729 isl_dim_map
*dim_map
;
1730 isl_basic_set
*coef
;
1731 struct isl_sched_node
*node
= edge
->src
;
1733 coef
= intra_coefficients(graph
, node
, map
);
1735 offset
= coef_var_offset(coef
);
1738 return isl_stat_error
;
1740 dim_map
= intra_dim_map(ctx
, graph
, node
, offset
, 1);
1741 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
1746 /* Add constraints to graph->lp that force validity for the given
1747 * dependence from node i to node j.
1748 * That is, add constraints that enforce
1750 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) >= 0
1752 * for each (x,y) in R.
1753 * We obtain general constraints on coefficients (c_0, c_n, c_x, c_y)
1754 * of valid constraints for R and then plug in
1755 * (c_j_0 - c_i_0, c_j_n - c_i_n, -(c_i_x^+ - c_i_x^-), c_j_x^+ - c_j_x^-),
1756 * where c_* = c_*^+ - c_*^-, with c_*^+ and c_*^- non-negative.
1757 * In graph->lp, the c_*^- appear before their c_*^+ counterpart.
1759 static isl_stat
add_inter_validity_constraints(struct isl_sched_graph
*graph
,
1760 struct isl_sched_edge
*edge
)
1765 isl_dim_map
*dim_map
;
1766 isl_basic_set
*coef
;
1767 struct isl_sched_node
*src
= edge
->src
;
1768 struct isl_sched_node
*dst
= edge
->dst
;
1771 return isl_stat_error
;
1773 map
= isl_map_copy(edge
->map
);
1774 ctx
= isl_map_get_ctx(map
);
1775 coef
= inter_coefficients(graph
, edge
, map
);
1777 offset
= coef_var_offset(coef
);
1780 return isl_stat_error
;
1782 dim_map
= inter_dim_map(ctx
, graph
, src
, dst
, offset
, 1);
1784 edge
->start
= graph
->lp
->n_ineq
;
1785 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
1787 return isl_stat_error
;
1788 edge
->end
= graph
->lp
->n_ineq
;
1793 /* Add constraints to graph->lp that bound the dependence distance for the given
1794 * dependence from a node i to itself.
1795 * If s = 1, we add the constraint
1797 * c_i_x (y - x) <= m_0 + m_n n
1801 * -c_i_x (y - x) + m_0 + m_n n >= 0
1803 * for each (x,y) in R.
1804 * If s = -1, we add the constraint
1806 * -c_i_x (y - x) <= m_0 + m_n n
1810 * c_i_x (y - x) + m_0 + m_n n >= 0
1812 * for each (x,y) in R.
1813 * We obtain general constraints on coefficients (c_0, c_n, c_x)
1814 * of valid constraints for (y - x) and then plug in (m_0, m_n, -s * c_i_x),
1815 * with each coefficient (except m_0) represented as a pair of non-negative
1819 * If "local" is set, then we add constraints
1821 * c_i_x (y - x) <= 0
1825 * -c_i_x (y - x) <= 0
1827 * instead, forcing the dependence distance to be (less than or) equal to 0.
1828 * That is, we plug in (0, 0, -s * c_i_x),
1829 * Note that dependences marked local are treated as validity constraints
1830 * by add_all_validity_constraints and therefore also have
1831 * their distances bounded by 0 from below.
1833 static isl_stat
add_intra_proximity_constraints(struct isl_sched_graph
*graph
,
1834 struct isl_sched_edge
*edge
, int s
, int local
)
1838 isl_map
*map
= isl_map_copy(edge
->map
);
1839 isl_ctx
*ctx
= isl_map_get_ctx(map
);
1840 isl_dim_map
*dim_map
;
1841 isl_basic_set
*coef
;
1842 struct isl_sched_node
*node
= edge
->src
;
1844 coef
= intra_coefficients(graph
, node
, map
);
1846 offset
= coef_var_offset(coef
);
1849 return isl_stat_error
;
1851 nparam
= isl_space_dim(node
->space
, isl_dim_param
);
1852 dim_map
= intra_dim_map(ctx
, graph
, node
, offset
, -s
);
1855 isl_dim_map_range(dim_map
, 1, 0, 0, 0, 1, 1);
1856 isl_dim_map_range(dim_map
, 4, 2, 1, 1, nparam
, -1);
1857 isl_dim_map_range(dim_map
, 5, 2, 1, 1, nparam
, 1);
1859 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
1864 /* Add constraints to graph->lp that bound the dependence distance for the given
1865 * dependence from node i to node j.
1866 * If s = 1, we add the constraint
1868 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x)
1873 * -(c_j_0 + c_j_n n + c_j_x y) + (c_i_0 + c_i_n n + c_i_x x) +
1876 * for each (x,y) in R.
1877 * If s = -1, we add the constraint
1879 * -((c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x))
1884 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) +
1887 * for each (x,y) in R.
1888 * We obtain general constraints on coefficients (c_0, c_n, c_x, c_y)
1889 * of valid constraints for R and then plug in
1890 * (m_0 - s*c_j_0 + s*c_i_0, m_n - s*c_j_n + s*c_i_n,
1891 * s*c_i_x, -s*c_j_x)
1892 * with each coefficient (except m_0, c_*_0 and c_*_n)
1893 * represented as a pair of non-negative coefficients.
1896 * If "local" is set (and s = 1), then we add constraints
1898 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) <= 0
1902 * -((c_j_0 + c_j_n n + c_j_x y) + (c_i_0 + c_i_n n + c_i_x x)) >= 0
1904 * instead, forcing the dependence distance to be (less than or) equal to 0.
1905 * That is, we plug in
1906 * (-s*c_j_0 + s*c_i_0, -s*c_j_n + s*c_i_n, s*c_i_x, -s*c_j_x).
1907 * Note that dependences marked local are treated as validity constraints
1908 * by add_all_validity_constraints and therefore also have
1909 * their distances bounded by 0 from below.
1911 static isl_stat
add_inter_proximity_constraints(struct isl_sched_graph
*graph
,
1912 struct isl_sched_edge
*edge
, int s
, int local
)
1916 isl_map
*map
= isl_map_copy(edge
->map
);
1917 isl_ctx
*ctx
= isl_map_get_ctx(map
);
1918 isl_dim_map
*dim_map
;
1919 isl_basic_set
*coef
;
1920 struct isl_sched_node
*src
= edge
->src
;
1921 struct isl_sched_node
*dst
= edge
->dst
;
1923 coef
= inter_coefficients(graph
, edge
, map
);
1925 offset
= coef_var_offset(coef
);
1928 return isl_stat_error
;
1930 nparam
= isl_space_dim(src
->space
, isl_dim_param
);
1931 dim_map
= inter_dim_map(ctx
, graph
, src
, dst
, offset
, -s
);
1934 isl_dim_map_range(dim_map
, 1, 0, 0, 0, 1, 1);
1935 isl_dim_map_range(dim_map
, 4, 2, 1, 1, nparam
, -1);
1936 isl_dim_map_range(dim_map
, 5, 2, 1, 1, nparam
, 1);
1939 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
1944 /* Add all validity constraints to graph->lp.
1946 * An edge that is forced to be local needs to have its dependence
1947 * distances equal to zero. We take care of bounding them by 0 from below
1948 * here. add_all_proximity_constraints takes care of bounding them by 0
1951 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
1952 * Otherwise, we ignore them.
1954 static int add_all_validity_constraints(struct isl_sched_graph
*graph
,
1955 int use_coincidence
)
1959 for (i
= 0; i
< graph
->n_edge
; ++i
) {
1960 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
1963 local
= is_local(edge
) ||
1964 (is_coincidence(edge
) && use_coincidence
);
1965 if (!is_validity(edge
) && !local
)
1967 if (edge
->src
!= edge
->dst
)
1969 if (add_intra_validity_constraints(graph
, edge
) < 0)
1973 for (i
= 0; i
< graph
->n_edge
; ++i
) {
1974 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
1977 local
= is_local(edge
) ||
1978 (is_coincidence(edge
) && use_coincidence
);
1979 if (!is_validity(edge
) && !local
)
1981 if (edge
->src
== edge
->dst
)
1983 if (add_inter_validity_constraints(graph
, edge
) < 0)
1990 /* Add constraints to graph->lp that bound the dependence distance
1991 * for all dependence relations.
1992 * If a given proximity dependence is identical to a validity
1993 * dependence, then the dependence distance is already bounded
1994 * from below (by zero), so we only need to bound the distance
1995 * from above. (This includes the case of "local" dependences
1996 * which are treated as validity dependence by add_all_validity_constraints.)
1997 * Otherwise, we need to bound the distance both from above and from below.
1999 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2000 * Otherwise, we ignore them.
2002 static int add_all_proximity_constraints(struct isl_sched_graph
*graph
,
2003 int use_coincidence
)
2007 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2008 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
2011 local
= is_local(edge
) ||
2012 (is_coincidence(edge
) && use_coincidence
);
2013 if (!is_proximity(edge
) && !local
)
2015 if (edge
->src
== edge
->dst
&&
2016 add_intra_proximity_constraints(graph
, edge
, 1, local
) < 0)
2018 if (edge
->src
!= edge
->dst
&&
2019 add_inter_proximity_constraints(graph
, edge
, 1, local
) < 0)
2021 if (is_validity(edge
) || local
)
2023 if (edge
->src
== edge
->dst
&&
2024 add_intra_proximity_constraints(graph
, edge
, -1, 0) < 0)
2026 if (edge
->src
!= edge
->dst
&&
2027 add_inter_proximity_constraints(graph
, edge
, -1, 0) < 0)
2034 /* Normalize the rows of "indep" such that all rows are lexicographically
2035 * positive and such that each row contains as many final zeros as possible,
2036 * given the choice for the previous rows.
2037 * Do this by performing elementary row operations.
2039 static __isl_give isl_mat
*normalize_independent(__isl_take isl_mat
*indep
)
2041 indep
= isl_mat_reverse_gauss(indep
);
2042 indep
= isl_mat_lexnonneg_rows(indep
);
2046 /* Compute a basis for the rows in the linear part of the schedule
2047 * and extend this basis to a full basis. The remaining rows
2048 * can then be used to force linear independence from the rows
2051 * In particular, given the schedule rows S, we compute
2056 * with H the Hermite normal form of S. That is, all but the
2057 * first rank columns of H are zero and so each row in S is
2058 * a linear combination of the first rank rows of Q.
2059 * The matrix Q can be used as a variable transformation
2060 * that isolates the directions of S in the first rank rows.
2061 * Transposing S U = H yields
2065 * with all but the first rank rows of H^T zero.
2066 * The last rows of U^T are therefore linear combinations
2067 * of schedule coefficients that are all zero on schedule
2068 * coefficients that are linearly dependent on the rows of S.
2069 * At least one of these combinations is non-zero on
2070 * linearly independent schedule coefficients.
2071 * The rows are normalized to involve as few of the last
2072 * coefficients as possible and to have a positive initial value.
2074 static int node_update_vmap(struct isl_sched_node
*node
)
2077 int n_row
= isl_mat_rows(node
->sched
);
2079 H
= isl_mat_sub_alloc(node
->sched
, 0, n_row
,
2080 1 + node
->nparam
, node
->nvar
);
2082 H
= isl_mat_left_hermite(H
, 0, &U
, &Q
);
2083 isl_mat_free(node
->indep
);
2084 isl_mat_free(node
->vmap
);
2086 node
->indep
= isl_mat_transpose(U
);
2087 node
->rank
= isl_mat_initial_non_zero_cols(H
);
2088 node
->indep
= isl_mat_drop_rows(node
->indep
, 0, node
->rank
);
2089 node
->indep
= normalize_independent(node
->indep
);
2092 if (!node
->indep
|| !node
->vmap
|| node
->rank
< 0)
2097 /* Is "edge" marked as a validity or a conditional validity edge?
2099 static int is_any_validity(struct isl_sched_edge
*edge
)
2101 return is_validity(edge
) || is_conditional_validity(edge
);
2104 /* How many times should we count the constraints in "edge"?
2106 * We count as follows
2107 * validity -> 1 (>= 0)
2108 * validity+proximity -> 2 (>= 0 and upper bound)
2109 * proximity -> 2 (lower and upper bound)
2110 * local(+any) -> 2 (>= 0 and <= 0)
2112 * If an edge is only marked conditional_validity then it counts
2113 * as zero since it is only checked afterwards.
2115 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2116 * Otherwise, we ignore them.
2118 static int edge_multiplicity(struct isl_sched_edge
*edge
, int use_coincidence
)
2120 if (is_proximity(edge
) || is_local(edge
))
2122 if (use_coincidence
&& is_coincidence(edge
))
2124 if (is_validity(edge
))
2129 /* Count the number of equality and inequality constraints
2130 * that will be added for the given map.
2132 * "use_coincidence" is set if we should take into account coincidence edges.
2134 static isl_stat
count_map_constraints(struct isl_sched_graph
*graph
,
2135 struct isl_sched_edge
*edge
, __isl_take isl_map
*map
,
2136 int *n_eq
, int *n_ineq
, int use_coincidence
)
2138 isl_basic_set
*coef
;
2139 int f
= edge_multiplicity(edge
, use_coincidence
);
2146 if (edge
->src
== edge
->dst
)
2147 coef
= intra_coefficients(graph
, edge
->src
, map
);
2149 coef
= inter_coefficients(graph
, edge
, map
);
2151 return isl_stat_error
;
2152 *n_eq
+= f
* isl_basic_set_n_equality(coef
);
2153 *n_ineq
+= f
* isl_basic_set_n_inequality(coef
);
2154 isl_basic_set_free(coef
);
2159 /* Count the number of equality and inequality constraints
2160 * that will be added to the main lp problem.
2161 * We count as follows
2162 * validity -> 1 (>= 0)
2163 * validity+proximity -> 2 (>= 0 and upper bound)
2164 * proximity -> 2 (lower and upper bound)
2165 * local(+any) -> 2 (>= 0 and <= 0)
2167 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2168 * Otherwise, we ignore them.
2170 static int count_constraints(struct isl_sched_graph
*graph
,
2171 int *n_eq
, int *n_ineq
, int use_coincidence
)
2175 *n_eq
= *n_ineq
= 0;
2176 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2177 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
2178 isl_map
*map
= isl_map_copy(edge
->map
);
2180 if (count_map_constraints(graph
, edge
, map
, n_eq
, n_ineq
,
2181 use_coincidence
) < 0)
2188 /* Count the number of constraints that will be added by
2189 * add_bound_constant_constraints to bound the values of the constant terms
2190 * and increment *n_eq and *n_ineq accordingly.
2192 * In practice, add_bound_constant_constraints only adds inequalities.
2194 static isl_stat
count_bound_constant_constraints(isl_ctx
*ctx
,
2195 struct isl_sched_graph
*graph
, int *n_eq
, int *n_ineq
)
2197 if (isl_options_get_schedule_max_constant_term(ctx
) == -1)
2200 *n_ineq
+= graph
->n
;
2205 /* Add constraints to bound the values of the constant terms in the schedule,
2206 * if requested by the user.
2208 * The maximal value of the constant terms is defined by the option
2209 * "schedule_max_constant_term".
2211 static isl_stat
add_bound_constant_constraints(isl_ctx
*ctx
,
2212 struct isl_sched_graph
*graph
)
2218 max
= isl_options_get_schedule_max_constant_term(ctx
);
2222 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2224 for (i
= 0; i
< graph
->n
; ++i
) {
2225 struct isl_sched_node
*node
= &graph
->node
[i
];
2228 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2230 return isl_stat_error
;
2231 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
2232 pos
= node_cst_coef_offset(node
);
2233 isl_int_set_si(graph
->lp
->ineq
[k
][1 + pos
], -1);
2234 isl_int_set_si(graph
->lp
->ineq
[k
][0], max
);
2240 /* Count the number of constraints that will be added by
2241 * add_bound_coefficient_constraints and increment *n_eq and *n_ineq
2244 * In practice, add_bound_coefficient_constraints only adds inequalities.
2246 static int count_bound_coefficient_constraints(isl_ctx
*ctx
,
2247 struct isl_sched_graph
*graph
, int *n_eq
, int *n_ineq
)
2251 if (isl_options_get_schedule_max_coefficient(ctx
) == -1 &&
2252 !isl_options_get_schedule_treat_coalescing(ctx
))
2255 for (i
= 0; i
< graph
->n
; ++i
)
2256 *n_ineq
+= graph
->node
[i
].nparam
+ 2 * graph
->node
[i
].nvar
;
2261 /* Add constraints to graph->lp that bound the values of
2262 * the parameter schedule coefficients of "node" to "max" and
2263 * the variable schedule coefficients to the corresponding entry
2265 * In either case, a negative value means that no bound needs to be imposed.
2267 * For parameter coefficients, this amounts to adding a constraint
2275 * The variables coefficients are, however, not represented directly.
2276 * Instead, the variable coefficients c_x are written as differences
2277 * c_x = c_x^+ - c_x^-.
2280 * -max_i <= c_x_i <= max_i
2284 * -max_i <= c_x_i^+ - c_x_i^- <= max_i
2288 * -(c_x_i^+ - c_x_i^-) + max_i >= 0
2289 * c_x_i^+ - c_x_i^- + max_i >= 0
2291 static isl_stat
node_add_coefficient_constraints(isl_ctx
*ctx
,
2292 struct isl_sched_graph
*graph
, struct isl_sched_node
*node
, int max
)
2298 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2300 for (j
= 0; j
< node
->nparam
; ++j
) {
2306 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2308 return isl_stat_error
;
2309 dim
= 1 + node_par_coef_offset(node
) + j
;
2310 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
2311 isl_int_set_si(graph
->lp
->ineq
[k
][dim
], -1);
2312 isl_int_set_si(graph
->lp
->ineq
[k
][0], max
);
2315 ineq
= isl_vec_alloc(ctx
, 1 + total
);
2316 ineq
= isl_vec_clr(ineq
);
2318 return isl_stat_error
;
2319 for (i
= 0; i
< node
->nvar
; ++i
) {
2320 int pos
= 1 + node_var_coef_pos(node
, i
);
2322 if (isl_int_is_neg(node
->max
->el
[i
]))
2325 isl_int_set_si(ineq
->el
[pos
], 1);
2326 isl_int_set_si(ineq
->el
[pos
+ 1], -1);
2327 isl_int_set(ineq
->el
[0], node
->max
->el
[i
]);
2329 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2332 isl_seq_cpy(graph
->lp
->ineq
[k
], ineq
->el
, 1 + total
);
2334 isl_seq_neg(ineq
->el
+ pos
, ineq
->el
+ pos
+ 2 * i
, 2);
2335 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2338 isl_seq_cpy(graph
->lp
->ineq
[k
], ineq
->el
, 1 + total
);
2345 return isl_stat_error
;
2348 /* Add constraints that bound the values of the variable and parameter
2349 * coefficients of the schedule.
2351 * The maximal value of the coefficients is defined by the option
2352 * 'schedule_max_coefficient' and the entries in node->max.
2353 * These latter entries are only set if either the schedule_max_coefficient
2354 * option or the schedule_treat_coalescing option is set.
2356 static isl_stat
add_bound_coefficient_constraints(isl_ctx
*ctx
,
2357 struct isl_sched_graph
*graph
)
2362 max
= isl_options_get_schedule_max_coefficient(ctx
);
2364 if (max
== -1 && !isl_options_get_schedule_treat_coalescing(ctx
))
2367 for (i
= 0; i
< graph
->n
; ++i
) {
2368 struct isl_sched_node
*node
= &graph
->node
[i
];
2370 if (node_add_coefficient_constraints(ctx
, graph
, node
, max
) < 0)
2371 return isl_stat_error
;
2377 /* Add a constraint to graph->lp that equates the value at position
2378 * "sum_pos" to the sum of the "n" values starting at "first".
2380 static isl_stat
add_sum_constraint(struct isl_sched_graph
*graph
,
2381 int sum_pos
, int first
, int n
)
2386 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2388 k
= isl_basic_set_alloc_equality(graph
->lp
);
2390 return isl_stat_error
;
2391 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2392 isl_int_set_si(graph
->lp
->eq
[k
][1 + sum_pos
], -1);
2393 for (i
= 0; i
< n
; ++i
)
2394 isl_int_set_si(graph
->lp
->eq
[k
][1 + first
+ i
], 1);
2399 /* Add a constraint to graph->lp that equates the value at position
2400 * "sum_pos" to the sum of the parameter coefficients of all nodes.
2402 static isl_stat
add_param_sum_constraint(struct isl_sched_graph
*graph
,
2408 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2410 k
= isl_basic_set_alloc_equality(graph
->lp
);
2412 return isl_stat_error
;
2413 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2414 isl_int_set_si(graph
->lp
->eq
[k
][1 + sum_pos
], -1);
2415 for (i
= 0; i
< graph
->n
; ++i
) {
2416 int pos
= 1 + node_par_coef_offset(&graph
->node
[i
]);
2418 for (j
= 0; j
< graph
->node
[i
].nparam
; ++j
)
2419 isl_int_set_si(graph
->lp
->eq
[k
][pos
+ j
], 1);
2425 /* Add a constraint to graph->lp that equates the value at position
2426 * "sum_pos" to the sum of the variable coefficients of all nodes.
2428 static isl_stat
add_var_sum_constraint(struct isl_sched_graph
*graph
,
2434 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2436 k
= isl_basic_set_alloc_equality(graph
->lp
);
2438 return isl_stat_error
;
2439 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2440 isl_int_set_si(graph
->lp
->eq
[k
][1 + sum_pos
], -1);
2441 for (i
= 0; i
< graph
->n
; ++i
) {
2442 struct isl_sched_node
*node
= &graph
->node
[i
];
2443 int pos
= 1 + node_var_coef_offset(node
);
2445 for (j
= 0; j
< 2 * node
->nvar
; ++j
)
2446 isl_int_set_si(graph
->lp
->eq
[k
][pos
+ j
], 1);
2452 /* Construct an ILP problem for finding schedule coefficients
2453 * that result in non-negative, but small dependence distances
2454 * over all dependences.
2455 * In particular, the dependence distances over proximity edges
2456 * are bounded by m_0 + m_n n and we compute schedule coefficients
2457 * with small values (preferably zero) of m_n and m_0.
2459 * All variables of the ILP are non-negative. The actual coefficients
2460 * may be negative, so each coefficient is represented as the difference
2461 * of two non-negative variables. The negative part always appears
2462 * immediately before the positive part.
2463 * Other than that, the variables have the following order
2465 * - sum of positive and negative parts of m_n coefficients
2467 * - sum of all c_n coefficients
2468 * (unconstrained when computing non-parametric schedules)
2469 * - sum of positive and negative parts of all c_x coefficients
2470 * - positive and negative parts of m_n coefficients
2472 * - positive and negative parts of c_i_x, in opposite order
2473 * - c_i_n (if parametric)
2476 * The constraints are those from the edges plus two or three equalities
2477 * to express the sums.
2479 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2480 * Otherwise, we ignore them.
2482 static isl_stat
setup_lp(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
2483 int use_coincidence
)
2493 parametric
= ctx
->opt
->schedule_parametric
;
2494 nparam
= isl_space_dim(graph
->node
[0].space
, isl_dim_param
);
2496 total
= param_pos
+ 2 * nparam
;
2497 for (i
= 0; i
< graph
->n
; ++i
) {
2498 struct isl_sched_node
*node
= &graph
->node
[graph
->sorted
[i
]];
2499 if (node_update_vmap(node
) < 0)
2500 return isl_stat_error
;
2501 node
->start
= total
;
2502 total
+= 1 + node
->nparam
+ 2 * node
->nvar
;
2505 if (count_constraints(graph
, &n_eq
, &n_ineq
, use_coincidence
) < 0)
2506 return isl_stat_error
;
2507 if (count_bound_constant_constraints(ctx
, graph
, &n_eq
, &n_ineq
) < 0)
2508 return isl_stat_error
;
2509 if (count_bound_coefficient_constraints(ctx
, graph
, &n_eq
, &n_ineq
) < 0)
2510 return isl_stat_error
;
2512 space
= isl_space_set_alloc(ctx
, 0, total
);
2513 isl_basic_set_free(graph
->lp
);
2514 n_eq
+= 2 + parametric
;
2516 graph
->lp
= isl_basic_set_alloc_space(space
, 0, n_eq
, n_ineq
);
2518 if (add_sum_constraint(graph
, 0, param_pos
, 2 * nparam
) < 0)
2519 return isl_stat_error
;
2520 if (parametric
&& add_param_sum_constraint(graph
, 2) < 0)
2521 return isl_stat_error
;
2522 if (add_var_sum_constraint(graph
, 3) < 0)
2523 return isl_stat_error
;
2524 if (add_bound_constant_constraints(ctx
, graph
) < 0)
2525 return isl_stat_error
;
2526 if (add_bound_coefficient_constraints(ctx
, graph
) < 0)
2527 return isl_stat_error
;
2528 if (add_all_validity_constraints(graph
, use_coincidence
) < 0)
2529 return isl_stat_error
;
2530 if (add_all_proximity_constraints(graph
, use_coincidence
) < 0)
2531 return isl_stat_error
;
2536 /* Analyze the conflicting constraint found by
2537 * isl_tab_basic_set_non_trivial_lexmin. If it corresponds to the validity
2538 * constraint of one of the edges between distinct nodes, living, moreover
2539 * in distinct SCCs, then record the source and sink SCC as this may
2540 * be a good place to cut between SCCs.
2542 static int check_conflict(int con
, void *user
)
2545 struct isl_sched_graph
*graph
= user
;
2547 if (graph
->src_scc
>= 0)
2550 con
-= graph
->lp
->n_eq
;
2552 if (con
>= graph
->lp
->n_ineq
)
2555 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2556 if (!is_validity(&graph
->edge
[i
]))
2558 if (graph
->edge
[i
].src
== graph
->edge
[i
].dst
)
2560 if (graph
->edge
[i
].src
->scc
== graph
->edge
[i
].dst
->scc
)
2562 if (graph
->edge
[i
].start
> con
)
2564 if (graph
->edge
[i
].end
<= con
)
2566 graph
->src_scc
= graph
->edge
[i
].src
->scc
;
2567 graph
->dst_scc
= graph
->edge
[i
].dst
->scc
;
2573 /* Check whether the next schedule row of the given node needs to be
2574 * non-trivial. Lower-dimensional domains may have some trivial rows,
2575 * but as soon as the number of remaining required non-trivial rows
2576 * is as large as the number or remaining rows to be computed,
2577 * all remaining rows need to be non-trivial.
2579 static int needs_row(struct isl_sched_graph
*graph
, struct isl_sched_node
*node
)
2581 return node
->nvar
- node
->rank
>= graph
->maxvar
- graph
->n_row
;
2584 /* Construct a non-triviality region with triviality directions
2585 * corresponding to the rows of "indep".
2586 * The rows of "indep" are expressed in terms of the schedule coefficients c_i,
2587 * while the triviality directions are expressed in terms of
2588 * pairs of non-negative variables c^+_i - c^-_i, with c^-_i appearing
2589 * before c^+_i. Furthermore,
2590 * the pairs of non-negative variables representing the coefficients
2591 * are stored in the opposite order.
2593 static __isl_give isl_mat
*construct_trivial(__isl_keep isl_mat
*indep
)
2602 ctx
= isl_mat_get_ctx(indep
);
2603 n
= isl_mat_rows(indep
);
2604 n_var
= isl_mat_cols(indep
);
2605 mat
= isl_mat_alloc(ctx
, n
, 2 * n_var
);
2608 for (i
= 0; i
< n
; ++i
) {
2609 for (j
= 0; j
< n_var
; ++j
) {
2610 int nj
= n_var
- 1 - j
;
2611 isl_int_neg(mat
->row
[i
][2 * nj
], indep
->row
[i
][j
]);
2612 isl_int_set(mat
->row
[i
][2 * nj
+ 1], indep
->row
[i
][j
]);
2619 /* Solve the ILP problem constructed in setup_lp.
2620 * For each node such that all the remaining rows of its schedule
2621 * need to be non-trivial, we construct a non-triviality region.
2622 * This region imposes that the next row is independent of previous rows.
2623 * In particular, the non-triviality region enforces that at least
2624 * one of the linear combinations in the rows of node->indep is non-zero.
2626 static __isl_give isl_vec
*solve_lp(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2632 for (i
= 0; i
< graph
->n
; ++i
) {
2633 struct isl_sched_node
*node
= &graph
->node
[i
];
2636 graph
->region
[i
].pos
= node_var_coef_offset(node
);
2637 if (needs_row(graph
, node
))
2638 trivial
= construct_trivial(node
->indep
);
2640 trivial
= isl_mat_zero(ctx
, 0, 0);
2641 graph
->region
[i
].trivial
= trivial
;
2643 lp
= isl_basic_set_copy(graph
->lp
);
2644 sol
= isl_tab_basic_set_non_trivial_lexmin(lp
, 2, graph
->n
,
2645 graph
->region
, &check_conflict
, graph
);
2646 for (i
= 0; i
< graph
->n
; ++i
)
2647 isl_mat_free(graph
->region
[i
].trivial
);
2651 /* Extract the coefficients for the variables of "node" from "sol".
2653 * Each schedule coefficient c_i_x is represented as the difference
2654 * between two non-negative variables c_i_x^+ - c_i_x^-.
2655 * The c_i_x^- appear before their c_i_x^+ counterpart.
2656 * Furthermore, the order of these pairs is the opposite of that
2657 * of the corresponding coefficients.
2659 * Return c_i_x = c_i_x^+ - c_i_x^-
2661 static __isl_give isl_vec
*extract_var_coef(struct isl_sched_node
*node
,
2662 __isl_keep isl_vec
*sol
)
2670 csol
= isl_vec_alloc(isl_vec_get_ctx(sol
), node
->nvar
);
2674 pos
= 1 + node_var_coef_offset(node
);
2675 for (i
= 0; i
< node
->nvar
; ++i
)
2676 isl_int_sub(csol
->el
[node
->nvar
- 1 - i
],
2677 sol
->el
[pos
+ 2 * i
+ 1], sol
->el
[pos
+ 2 * i
]);
2682 /* Update the schedules of all nodes based on the given solution
2683 * of the LP problem.
2684 * The new row is added to the current band.
2685 * All possibly negative coefficients are encoded as a difference
2686 * of two non-negative variables, so we need to perform the subtraction
2689 * If coincident is set, then the caller guarantees that the new
2690 * row satisfies the coincidence constraints.
2692 static int update_schedule(struct isl_sched_graph
*graph
,
2693 __isl_take isl_vec
*sol
, int coincident
)
2696 isl_vec
*csol
= NULL
;
2701 isl_die(sol
->ctx
, isl_error_internal
,
2702 "no solution found", goto error
);
2703 if (graph
->n_total_row
>= graph
->max_row
)
2704 isl_die(sol
->ctx
, isl_error_internal
,
2705 "too many schedule rows", goto error
);
2707 for (i
= 0; i
< graph
->n
; ++i
) {
2708 struct isl_sched_node
*node
= &graph
->node
[i
];
2710 int row
= isl_mat_rows(node
->sched
);
2713 csol
= extract_var_coef(node
, sol
);
2717 isl_map_free(node
->sched_map
);
2718 node
->sched_map
= NULL
;
2719 node
->sched
= isl_mat_add_rows(node
->sched
, 1);
2722 pos
= node_cst_coef_offset(node
);
2723 node
->sched
= isl_mat_set_element(node
->sched
,
2724 row
, 0, sol
->el
[1 + pos
]);
2725 pos
= node_par_coef_offset(node
);
2726 for (j
= 0; j
< node
->nparam
; ++j
)
2727 node
->sched
= isl_mat_set_element(node
->sched
,
2728 row
, 1 + j
, sol
->el
[1 + pos
+ j
]);
2729 for (j
= 0; j
< node
->nvar
; ++j
)
2730 node
->sched
= isl_mat_set_element(node
->sched
,
2731 row
, 1 + node
->nparam
+ j
, csol
->el
[j
]);
2732 node
->coincident
[graph
->n_total_row
] = coincident
;
2738 graph
->n_total_row
++;
2747 /* Convert row "row" of node->sched into an isl_aff living in "ls"
2748 * and return this isl_aff.
2750 static __isl_give isl_aff
*extract_schedule_row(__isl_take isl_local_space
*ls
,
2751 struct isl_sched_node
*node
, int row
)
2759 aff
= isl_aff_zero_on_domain(ls
);
2760 isl_mat_get_element(node
->sched
, row
, 0, &v
);
2761 aff
= isl_aff_set_constant(aff
, v
);
2762 for (j
= 0; j
< node
->nparam
; ++j
) {
2763 isl_mat_get_element(node
->sched
, row
, 1 + j
, &v
);
2764 aff
= isl_aff_set_coefficient(aff
, isl_dim_param
, j
, v
);
2766 for (j
= 0; j
< node
->nvar
; ++j
) {
2767 isl_mat_get_element(node
->sched
, row
, 1 + node
->nparam
+ j
, &v
);
2768 aff
= isl_aff_set_coefficient(aff
, isl_dim_in
, j
, v
);
2776 /* Convert the "n" rows starting at "first" of node->sched into a multi_aff
2777 * and return this multi_aff.
2779 * The result is defined over the uncompressed node domain.
2781 static __isl_give isl_multi_aff
*node_extract_partial_schedule_multi_aff(
2782 struct isl_sched_node
*node
, int first
, int n
)
2786 isl_local_space
*ls
;
2793 nrow
= isl_mat_rows(node
->sched
);
2794 if (node
->compressed
)
2795 space
= isl_multi_aff_get_domain_space(node
->decompress
);
2797 space
= isl_space_copy(node
->space
);
2798 ls
= isl_local_space_from_space(isl_space_copy(space
));
2799 space
= isl_space_from_domain(space
);
2800 space
= isl_space_add_dims(space
, isl_dim_out
, n
);
2801 ma
= isl_multi_aff_zero(space
);
2803 for (i
= first
; i
< first
+ n
; ++i
) {
2804 aff
= extract_schedule_row(isl_local_space_copy(ls
), node
, i
);
2805 ma
= isl_multi_aff_set_aff(ma
, i
- first
, aff
);
2808 isl_local_space_free(ls
);
2810 if (node
->compressed
)
2811 ma
= isl_multi_aff_pullback_multi_aff(ma
,
2812 isl_multi_aff_copy(node
->compress
));
2817 /* Convert node->sched into a multi_aff and return this multi_aff.
2819 * The result is defined over the uncompressed node domain.
2821 static __isl_give isl_multi_aff
*node_extract_schedule_multi_aff(
2822 struct isl_sched_node
*node
)
2826 nrow
= isl_mat_rows(node
->sched
);
2827 return node_extract_partial_schedule_multi_aff(node
, 0, nrow
);
2830 /* Convert node->sched into a map and return this map.
2832 * The result is cached in node->sched_map, which needs to be released
2833 * whenever node->sched is updated.
2834 * It is defined over the uncompressed node domain.
2836 static __isl_give isl_map
*node_extract_schedule(struct isl_sched_node
*node
)
2838 if (!node
->sched_map
) {
2841 ma
= node_extract_schedule_multi_aff(node
);
2842 node
->sched_map
= isl_map_from_multi_aff(ma
);
2845 return isl_map_copy(node
->sched_map
);
2848 /* Construct a map that can be used to update a dependence relation
2849 * based on the current schedule.
2850 * That is, construct a map expressing that source and sink
2851 * are executed within the same iteration of the current schedule.
2852 * This map can then be intersected with the dependence relation.
2853 * This is not the most efficient way, but this shouldn't be a critical
2856 static __isl_give isl_map
*specializer(struct isl_sched_node
*src
,
2857 struct isl_sched_node
*dst
)
2859 isl_map
*src_sched
, *dst_sched
;
2861 src_sched
= node_extract_schedule(src
);
2862 dst_sched
= node_extract_schedule(dst
);
2863 return isl_map_apply_range(src_sched
, isl_map_reverse(dst_sched
));
2866 /* Intersect the domains of the nested relations in domain and range
2867 * of "umap" with "map".
2869 static __isl_give isl_union_map
*intersect_domains(
2870 __isl_take isl_union_map
*umap
, __isl_keep isl_map
*map
)
2872 isl_union_set
*uset
;
2874 umap
= isl_union_map_zip(umap
);
2875 uset
= isl_union_set_from_set(isl_map_wrap(isl_map_copy(map
)));
2876 umap
= isl_union_map_intersect_domain(umap
, uset
);
2877 umap
= isl_union_map_zip(umap
);
2881 /* Update the dependence relation of the given edge based
2882 * on the current schedule.
2883 * If the dependence is carried completely by the current schedule, then
2884 * it is removed from the edge_tables. It is kept in the list of edges
2885 * as otherwise all edge_tables would have to be recomputed.
2887 static int update_edge(struct isl_sched_graph
*graph
,
2888 struct isl_sched_edge
*edge
)
2893 id
= specializer(edge
->src
, edge
->dst
);
2894 edge
->map
= isl_map_intersect(edge
->map
, isl_map_copy(id
));
2898 if (edge
->tagged_condition
) {
2899 edge
->tagged_condition
=
2900 intersect_domains(edge
->tagged_condition
, id
);
2901 if (!edge
->tagged_condition
)
2904 if (edge
->tagged_validity
) {
2905 edge
->tagged_validity
=
2906 intersect_domains(edge
->tagged_validity
, id
);
2907 if (!edge
->tagged_validity
)
2911 empty
= isl_map_plain_is_empty(edge
->map
);
2915 graph_remove_edge(graph
, edge
);
2924 /* Does the domain of "umap" intersect "uset"?
2926 static int domain_intersects(__isl_keep isl_union_map
*umap
,
2927 __isl_keep isl_union_set
*uset
)
2931 umap
= isl_union_map_copy(umap
);
2932 umap
= isl_union_map_intersect_domain(umap
, isl_union_set_copy(uset
));
2933 empty
= isl_union_map_is_empty(umap
);
2934 isl_union_map_free(umap
);
2936 return empty
< 0 ? -1 : !empty
;
2939 /* Does the range of "umap" intersect "uset"?
2941 static int range_intersects(__isl_keep isl_union_map
*umap
,
2942 __isl_keep isl_union_set
*uset
)
2946 umap
= isl_union_map_copy(umap
);
2947 umap
= isl_union_map_intersect_range(umap
, isl_union_set_copy(uset
));
2948 empty
= isl_union_map_is_empty(umap
);
2949 isl_union_map_free(umap
);
2951 return empty
< 0 ? -1 : !empty
;
2954 /* Are the condition dependences of "edge" local with respect to
2955 * the current schedule?
2957 * That is, are domain and range of the condition dependences mapped
2958 * to the same point?
2960 * In other words, is the condition false?
2962 static int is_condition_false(struct isl_sched_edge
*edge
)
2964 isl_union_map
*umap
;
2965 isl_map
*map
, *sched
, *test
;
2968 empty
= isl_union_map_is_empty(edge
->tagged_condition
);
2969 if (empty
< 0 || empty
)
2972 umap
= isl_union_map_copy(edge
->tagged_condition
);
2973 umap
= isl_union_map_zip(umap
);
2974 umap
= isl_union_set_unwrap(isl_union_map_domain(umap
));
2975 map
= isl_map_from_union_map(umap
);
2977 sched
= node_extract_schedule(edge
->src
);
2978 map
= isl_map_apply_domain(map
, sched
);
2979 sched
= node_extract_schedule(edge
->dst
);
2980 map
= isl_map_apply_range(map
, sched
);
2982 test
= isl_map_identity(isl_map_get_space(map
));
2983 local
= isl_map_is_subset(map
, test
);
2990 /* For each conditional validity constraint that is adjacent
2991 * to a condition with domain in condition_source or range in condition_sink,
2992 * turn it into an unconditional validity constraint.
2994 static int unconditionalize_adjacent_validity(struct isl_sched_graph
*graph
,
2995 __isl_take isl_union_set
*condition_source
,
2996 __isl_take isl_union_set
*condition_sink
)
3000 condition_source
= isl_union_set_coalesce(condition_source
);
3001 condition_sink
= isl_union_set_coalesce(condition_sink
);
3003 for (i
= 0; i
< graph
->n_edge
; ++i
) {
3005 isl_union_map
*validity
;
3007 if (!is_conditional_validity(&graph
->edge
[i
]))
3009 if (is_validity(&graph
->edge
[i
]))
3012 validity
= graph
->edge
[i
].tagged_validity
;
3013 adjacent
= domain_intersects(validity
, condition_sink
);
3014 if (adjacent
>= 0 && !adjacent
)
3015 adjacent
= range_intersects(validity
, condition_source
);
3021 set_validity(&graph
->edge
[i
]);
3024 isl_union_set_free(condition_source
);
3025 isl_union_set_free(condition_sink
);
3028 isl_union_set_free(condition_source
);
3029 isl_union_set_free(condition_sink
);
3033 /* Update the dependence relations of all edges based on the current schedule
3034 * and enforce conditional validity constraints that are adjacent
3035 * to satisfied condition constraints.
3037 * First check if any of the condition constraints are satisfied
3038 * (i.e., not local to the outer schedule) and keep track of
3039 * their domain and range.
3040 * Then update all dependence relations (which removes the non-local
3042 * Finally, if any condition constraints turned out to be satisfied,
3043 * then turn all adjacent conditional validity constraints into
3044 * unconditional validity constraints.
3046 static int update_edges(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
3050 isl_union_set
*source
, *sink
;
3052 source
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
3053 sink
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
3054 for (i
= 0; i
< graph
->n_edge
; ++i
) {
3056 isl_union_set
*uset
;
3057 isl_union_map
*umap
;
3059 if (!is_condition(&graph
->edge
[i
]))
3061 if (is_local(&graph
->edge
[i
]))
3063 local
= is_condition_false(&graph
->edge
[i
]);
3071 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_condition
);
3072 uset
= isl_union_map_domain(umap
);
3073 source
= isl_union_set_union(source
, uset
);
3075 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_condition
);
3076 uset
= isl_union_map_range(umap
);
3077 sink
= isl_union_set_union(sink
, uset
);
3080 for (i
= graph
->n_edge
- 1; i
>= 0; --i
) {
3081 if (update_edge(graph
, &graph
->edge
[i
]) < 0)
3086 return unconditionalize_adjacent_validity(graph
, source
, sink
);
3088 isl_union_set_free(source
);
3089 isl_union_set_free(sink
);
3092 isl_union_set_free(source
);
3093 isl_union_set_free(sink
);
3097 static void next_band(struct isl_sched_graph
*graph
)
3099 graph
->band_start
= graph
->n_total_row
;
3102 /* Return the union of the universe domains of the nodes in "graph"
3103 * that satisfy "pred".
3105 static __isl_give isl_union_set
*isl_sched_graph_domain(isl_ctx
*ctx
,
3106 struct isl_sched_graph
*graph
,
3107 int (*pred
)(struct isl_sched_node
*node
, int data
), int data
)
3113 for (i
= 0; i
< graph
->n
; ++i
)
3114 if (pred(&graph
->node
[i
], data
))
3118 isl_die(ctx
, isl_error_internal
,
3119 "empty component", return NULL
);
3121 set
= isl_set_universe(isl_space_copy(graph
->node
[i
].space
));
3122 dom
= isl_union_set_from_set(set
);
3124 for (i
= i
+ 1; i
< graph
->n
; ++i
) {
3125 if (!pred(&graph
->node
[i
], data
))
3127 set
= isl_set_universe(isl_space_copy(graph
->node
[i
].space
));
3128 dom
= isl_union_set_union(dom
, isl_union_set_from_set(set
));
3134 /* Return a list of unions of universe domains, where each element
3135 * in the list corresponds to an SCC (or WCC) indexed by node->scc.
3137 static __isl_give isl_union_set_list
*extract_sccs(isl_ctx
*ctx
,
3138 struct isl_sched_graph
*graph
)
3141 isl_union_set_list
*filters
;
3143 filters
= isl_union_set_list_alloc(ctx
, graph
->scc
);
3144 for (i
= 0; i
< graph
->scc
; ++i
) {
3147 dom
= isl_sched_graph_domain(ctx
, graph
, &node_scc_exactly
, i
);
3148 filters
= isl_union_set_list_add(filters
, dom
);
3154 /* Return a list of two unions of universe domains, one for the SCCs up
3155 * to and including graph->src_scc and another for the other SCCs.
3157 static __isl_give isl_union_set_list
*extract_split(isl_ctx
*ctx
,
3158 struct isl_sched_graph
*graph
)
3161 isl_union_set_list
*filters
;
3163 filters
= isl_union_set_list_alloc(ctx
, 2);
3164 dom
= isl_sched_graph_domain(ctx
, graph
,
3165 &node_scc_at_most
, graph
->src_scc
);
3166 filters
= isl_union_set_list_add(filters
, dom
);
3167 dom
= isl_sched_graph_domain(ctx
, graph
,
3168 &node_scc_at_least
, graph
->src_scc
+ 1);
3169 filters
= isl_union_set_list_add(filters
, dom
);
3174 /* Copy nodes that satisfy node_pred from the src dependence graph
3175 * to the dst dependence graph.
3177 static int copy_nodes(struct isl_sched_graph
*dst
, struct isl_sched_graph
*src
,
3178 int (*node_pred
)(struct isl_sched_node
*node
, int data
), int data
)
3183 for (i
= 0; i
< src
->n
; ++i
) {
3186 if (!node_pred(&src
->node
[i
], data
))
3190 dst
->node
[j
].space
= isl_space_copy(src
->node
[i
].space
);
3191 dst
->node
[j
].compressed
= src
->node
[i
].compressed
;
3192 dst
->node
[j
].hull
= isl_set_copy(src
->node
[i
].hull
);
3193 dst
->node
[j
].compress
=
3194 isl_multi_aff_copy(src
->node
[i
].compress
);
3195 dst
->node
[j
].decompress
=
3196 isl_multi_aff_copy(src
->node
[i
].decompress
);
3197 dst
->node
[j
].nvar
= src
->node
[i
].nvar
;
3198 dst
->node
[j
].nparam
= src
->node
[i
].nparam
;
3199 dst
->node
[j
].sched
= isl_mat_copy(src
->node
[i
].sched
);
3200 dst
->node
[j
].sched_map
= isl_map_copy(src
->node
[i
].sched_map
);
3201 dst
->node
[j
].coincident
= src
->node
[i
].coincident
;
3202 dst
->node
[j
].sizes
= isl_multi_val_copy(src
->node
[i
].sizes
);
3203 dst
->node
[j
].max
= isl_vec_copy(src
->node
[i
].max
);
3206 if (!dst
->node
[j
].space
|| !dst
->node
[j
].sched
)
3208 if (dst
->node
[j
].compressed
&&
3209 (!dst
->node
[j
].hull
|| !dst
->node
[j
].compress
||
3210 !dst
->node
[j
].decompress
))
3217 /* Copy non-empty edges that satisfy edge_pred from the src dependence graph
3218 * to the dst dependence graph.
3219 * If the source or destination node of the edge is not in the destination
3220 * graph, then it must be a backward proximity edge and it should simply
3223 static int copy_edges(isl_ctx
*ctx
, struct isl_sched_graph
*dst
,
3224 struct isl_sched_graph
*src
,
3225 int (*edge_pred
)(struct isl_sched_edge
*edge
, int data
), int data
)
3228 enum isl_edge_type t
;
3231 for (i
= 0; i
< src
->n_edge
; ++i
) {
3232 struct isl_sched_edge
*edge
= &src
->edge
[i
];
3234 isl_union_map
*tagged_condition
;
3235 isl_union_map
*tagged_validity
;
3236 struct isl_sched_node
*dst_src
, *dst_dst
;
3238 if (!edge_pred(edge
, data
))
3241 if (isl_map_plain_is_empty(edge
->map
))
3244 dst_src
= graph_find_node(ctx
, dst
, edge
->src
->space
);
3245 dst_dst
= graph_find_node(ctx
, dst
, edge
->dst
->space
);
3246 if (!dst_src
|| !dst_dst
) {
3247 if (is_validity(edge
) || is_conditional_validity(edge
))
3248 isl_die(ctx
, isl_error_internal
,
3249 "backward (conditional) validity edge",
3254 map
= isl_map_copy(edge
->map
);
3255 tagged_condition
= isl_union_map_copy(edge
->tagged_condition
);
3256 tagged_validity
= isl_union_map_copy(edge
->tagged_validity
);
3258 dst
->edge
[dst
->n_edge
].src
= dst_src
;
3259 dst
->edge
[dst
->n_edge
].dst
= dst_dst
;
3260 dst
->edge
[dst
->n_edge
].map
= map
;
3261 dst
->edge
[dst
->n_edge
].tagged_condition
= tagged_condition
;
3262 dst
->edge
[dst
->n_edge
].tagged_validity
= tagged_validity
;
3263 dst
->edge
[dst
->n_edge
].types
= edge
->types
;
3266 if (edge
->tagged_condition
&& !tagged_condition
)
3268 if (edge
->tagged_validity
&& !tagged_validity
)
3271 for (t
= isl_edge_first
; t
<= isl_edge_last
; ++t
) {
3273 graph_find_edge(src
, t
, edge
->src
, edge
->dst
))
3275 if (graph_edge_table_add(ctx
, dst
, t
,
3276 &dst
->edge
[dst
->n_edge
- 1]) < 0)
3284 /* Compute the maximal number of variables over all nodes.
3285 * This is the maximal number of linearly independent schedule
3286 * rows that we need to compute.
3287 * Just in case we end up in a part of the dependence graph
3288 * with only lower-dimensional domains, we make sure we will
3289 * compute the required amount of extra linearly independent rows.
3291 static int compute_maxvar(struct isl_sched_graph
*graph
)
3296 for (i
= 0; i
< graph
->n
; ++i
) {
3297 struct isl_sched_node
*node
= &graph
->node
[i
];
3300 if (node_update_vmap(node
) < 0)
3302 nvar
= node
->nvar
+ graph
->n_row
- node
->rank
;
3303 if (nvar
> graph
->maxvar
)
3304 graph
->maxvar
= nvar
;
3310 /* Extract the subgraph of "graph" that consists of the node satisfying
3311 * "node_pred" and the edges satisfying "edge_pred" and store
3312 * the result in "sub".
3314 static int extract_sub_graph(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
3315 int (*node_pred
)(struct isl_sched_node
*node
, int data
),
3316 int (*edge_pred
)(struct isl_sched_edge
*edge
, int data
),
3317 int data
, struct isl_sched_graph
*sub
)
3319 int i
, n
= 0, n_edge
= 0;
3322 for (i
= 0; i
< graph
->n
; ++i
)
3323 if (node_pred(&graph
->node
[i
], data
))
3325 for (i
= 0; i
< graph
->n_edge
; ++i
)
3326 if (edge_pred(&graph
->edge
[i
], data
))
3328 if (graph_alloc(ctx
, sub
, n
, n_edge
) < 0)
3330 if (copy_nodes(sub
, graph
, node_pred
, data
) < 0)
3332 if (graph_init_table(ctx
, sub
) < 0)
3334 for (t
= 0; t
<= isl_edge_last
; ++t
)
3335 sub
->max_edge
[t
] = graph
->max_edge
[t
];
3336 if (graph_init_edge_tables(ctx
, sub
) < 0)
3338 if (copy_edges(ctx
, sub
, graph
, edge_pred
, data
) < 0)
3340 sub
->n_row
= graph
->n_row
;
3341 sub
->max_row
= graph
->max_row
;
3342 sub
->n_total_row
= graph
->n_total_row
;
3343 sub
->band_start
= graph
->band_start
;
3348 static __isl_give isl_schedule_node
*compute_schedule(isl_schedule_node
*node
,
3349 struct isl_sched_graph
*graph
);
3350 static __isl_give isl_schedule_node
*compute_schedule_wcc(
3351 isl_schedule_node
*node
, struct isl_sched_graph
*graph
);
3353 /* Compute a schedule for a subgraph of "graph". In particular, for
3354 * the graph composed of nodes that satisfy node_pred and edges that
3355 * that satisfy edge_pred.
3356 * If the subgraph is known to consist of a single component, then wcc should
3357 * be set and then we call compute_schedule_wcc on the constructed subgraph.
3358 * Otherwise, we call compute_schedule, which will check whether the subgraph
3361 * The schedule is inserted at "node" and the updated schedule node
3364 static __isl_give isl_schedule_node
*compute_sub_schedule(
3365 __isl_take isl_schedule_node
*node
, isl_ctx
*ctx
,
3366 struct isl_sched_graph
*graph
,
3367 int (*node_pred
)(struct isl_sched_node
*node
, int data
),
3368 int (*edge_pred
)(struct isl_sched_edge
*edge
, int data
),
3371 struct isl_sched_graph split
= { 0 };
3373 if (extract_sub_graph(ctx
, graph
, node_pred
, edge_pred
, data
,
3378 node
= compute_schedule_wcc(node
, &split
);
3380 node
= compute_schedule(node
, &split
);
3382 graph_free(ctx
, &split
);
3385 graph_free(ctx
, &split
);
3386 return isl_schedule_node_free(node
);
3389 static int edge_scc_exactly(struct isl_sched_edge
*edge
, int scc
)
3391 return edge
->src
->scc
== scc
&& edge
->dst
->scc
== scc
;
3394 static int edge_dst_scc_at_most(struct isl_sched_edge
*edge
, int scc
)
3396 return edge
->dst
->scc
<= scc
;
3399 static int edge_src_scc_at_least(struct isl_sched_edge
*edge
, int scc
)
3401 return edge
->src
->scc
>= scc
;
3404 /* Reset the current band by dropping all its schedule rows.
3406 static int reset_band(struct isl_sched_graph
*graph
)
3411 drop
= graph
->n_total_row
- graph
->band_start
;
3412 graph
->n_total_row
-= drop
;
3413 graph
->n_row
-= drop
;
3415 for (i
= 0; i
< graph
->n
; ++i
) {
3416 struct isl_sched_node
*node
= &graph
->node
[i
];
3418 isl_map_free(node
->sched_map
);
3419 node
->sched_map
= NULL
;
3421 node
->sched
= isl_mat_drop_rows(node
->sched
,
3422 graph
->band_start
, drop
);
3431 /* Split the current graph into two parts and compute a schedule for each
3432 * part individually. In particular, one part consists of all SCCs up
3433 * to and including graph->src_scc, while the other part contains the other
3434 * SCCs. The split is enforced by a sequence node inserted at position "node"
3435 * in the schedule tree. Return the updated schedule node.
3436 * If either of these two parts consists of a sequence, then it is spliced
3437 * into the sequence containing the two parts.
3439 * The current band is reset. It would be possible to reuse
3440 * the previously computed rows as the first rows in the next
3441 * band, but recomputing them may result in better rows as we are looking
3442 * at a smaller part of the dependence graph.
3444 static __isl_give isl_schedule_node
*compute_split_schedule(
3445 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
3449 isl_union_set_list
*filters
;
3454 if (reset_band(graph
) < 0)
3455 return isl_schedule_node_free(node
);
3459 ctx
= isl_schedule_node_get_ctx(node
);
3460 filters
= extract_split(ctx
, graph
);
3461 node
= isl_schedule_node_insert_sequence(node
, filters
);
3462 node
= isl_schedule_node_child(node
, 1);
3463 node
= isl_schedule_node_child(node
, 0);
3465 node
= compute_sub_schedule(node
, ctx
, graph
,
3466 &node_scc_at_least
, &edge_src_scc_at_least
,
3467 graph
->src_scc
+ 1, 0);
3468 is_seq
= isl_schedule_node_get_type(node
) == isl_schedule_node_sequence
;
3469 node
= isl_schedule_node_parent(node
);
3470 node
= isl_schedule_node_parent(node
);
3472 node
= isl_schedule_node_sequence_splice_child(node
, 1);
3473 node
= isl_schedule_node_child(node
, 0);
3474 node
= isl_schedule_node_child(node
, 0);
3475 node
= compute_sub_schedule(node
, ctx
, graph
,
3476 &node_scc_at_most
, &edge_dst_scc_at_most
,
3478 is_seq
= isl_schedule_node_get_type(node
) == isl_schedule_node_sequence
;
3479 node
= isl_schedule_node_parent(node
);
3480 node
= isl_schedule_node_parent(node
);
3482 node
= isl_schedule_node_sequence_splice_child(node
, 0);
3487 /* Insert a band node at position "node" in the schedule tree corresponding
3488 * to the current band in "graph". Mark the band node permutable
3489 * if "permutable" is set.
3490 * The partial schedules and the coincidence property are extracted
3491 * from the graph nodes.
3492 * Return the updated schedule node.
3494 static __isl_give isl_schedule_node
*insert_current_band(
3495 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
3501 isl_multi_pw_aff
*mpa
;
3502 isl_multi_union_pw_aff
*mupa
;
3508 isl_die(isl_schedule_node_get_ctx(node
), isl_error_internal
,
3509 "graph should have at least one node",
3510 return isl_schedule_node_free(node
));
3512 start
= graph
->band_start
;
3513 end
= graph
->n_total_row
;
3516 ma
= node_extract_partial_schedule_multi_aff(&graph
->node
[0], start
, n
);
3517 mpa
= isl_multi_pw_aff_from_multi_aff(ma
);
3518 mupa
= isl_multi_union_pw_aff_from_multi_pw_aff(mpa
);
3520 for (i
= 1; i
< graph
->n
; ++i
) {
3521 isl_multi_union_pw_aff
*mupa_i
;
3523 ma
= node_extract_partial_schedule_multi_aff(&graph
->node
[i
],
3525 mpa
= isl_multi_pw_aff_from_multi_aff(ma
);
3526 mupa_i
= isl_multi_union_pw_aff_from_multi_pw_aff(mpa
);
3527 mupa
= isl_multi_union_pw_aff_union_add(mupa
, mupa_i
);
3529 node
= isl_schedule_node_insert_partial_schedule(node
, mupa
);
3531 for (i
= 0; i
< n
; ++i
)
3532 node
= isl_schedule_node_band_member_set_coincident(node
, i
,
3533 graph
->node
[0].coincident
[start
+ i
]);
3534 node
= isl_schedule_node_band_set_permutable(node
, permutable
);
3539 /* Update the dependence relations based on the current schedule,
3540 * add the current band to "node" and then continue with the computation
3542 * Return the updated schedule node.
3544 static __isl_give isl_schedule_node
*compute_next_band(
3545 __isl_take isl_schedule_node
*node
,
3546 struct isl_sched_graph
*graph
, int permutable
)
3553 ctx
= isl_schedule_node_get_ctx(node
);
3554 if (update_edges(ctx
, graph
) < 0)
3555 return isl_schedule_node_free(node
);
3556 node
= insert_current_band(node
, graph
, permutable
);
3559 node
= isl_schedule_node_child(node
, 0);
3560 node
= compute_schedule(node
, graph
);
3561 node
= isl_schedule_node_parent(node
);
3566 /* Add the constraints "coef" derived from an edge from "node" to itself
3567 * to graph->lp in order to respect the dependences and to try and carry them.
3568 * "pos" is the sequence number of the edge that needs to be carried.
3569 * "coef" represents general constraints on coefficients (c_0, c_n, c_x)
3570 * of valid constraints for (y - x) with x and y instances of the node.
3572 * The constraints added to graph->lp need to enforce
3574 * (c_j_0 + c_j_n n + c_j_x y) - (c_j_0 + c_j_n n + c_j_x x)
3575 * = c_j_x (y - x) >= e_i
3577 * for each (x,y) in the dependence relation of the edge.
3578 * That is, (-e_i, 0, c_j_x) needs to be plugged in for (c_0, c_n, c_x),
3579 * taking into account that each coefficient in c_j_x is represented
3580 * as a pair of non-negative coefficients.
3582 static isl_stat
add_intra_constraints(struct isl_sched_graph
*graph
,
3583 struct isl_sched_node
*node
, __isl_take isl_basic_set
*coef
, int pos
)
3587 isl_dim_map
*dim_map
;
3590 return isl_stat_error
;
3592 ctx
= isl_basic_set_get_ctx(coef
);
3593 offset
= coef_var_offset(coef
);
3594 dim_map
= intra_dim_map(ctx
, graph
, node
, offset
, 1);
3595 isl_dim_map_range(dim_map
, 3 + pos
, 0, 0, 0, 1, -1);
3596 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
3601 /* Add the constraints "coef" derived from an edge from "src" to "dst"
3602 * to graph->lp in order to respect the dependences and to try and carry them.
3603 * "pos" is the sequence number of the edge that needs to be carried.
3604 * "coef" represents general constraints on coefficients (c_0, c_n, c_x, c_y)
3605 * of valid constraints for (x, y) with x and y instances of "src" and "dst".
3607 * The constraints added to graph->lp need to enforce
3609 * (c_k_0 + c_k_n n + c_k_x y) - (c_j_0 + c_j_n n + c_j_x x) >= e_i
3611 * for each (x,y) in the dependence relation of the edge.
3613 * (-e_i + c_k_0 - c_j_0, c_k_n - c_j_n, -c_j_x, c_k_x)
3614 * needs to be plugged in for (c_0, c_n, c_x, c_y),
3615 * taking into account that each coefficient in c_j_x and c_k_x is represented
3616 * as a pair of non-negative coefficients.
3618 static isl_stat
add_inter_constraints(struct isl_sched_graph
*graph
,
3619 struct isl_sched_node
*src
, struct isl_sched_node
*dst
,
3620 __isl_take isl_basic_set
*coef
, int pos
)
3624 isl_dim_map
*dim_map
;
3627 return isl_stat_error
;
3629 ctx
= isl_basic_set_get_ctx(coef
);
3630 offset
= coef_var_offset(coef
);
3631 dim_map
= inter_dim_map(ctx
, graph
, src
, dst
, offset
, 1);
3632 isl_dim_map_range(dim_map
, 3 + pos
, 0, 0, 0, 1, -1);
3633 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
3638 /* Data structure collecting information used during the construction
3639 * of an LP for carrying dependences.
3641 * "intra" is a sequence of coefficient constraints for intra-node edges.
3642 * "inter" is a sequence of coefficient constraints for inter-node edges.
3645 isl_basic_set_list
*intra
;
3646 isl_basic_set_list
*inter
;
3649 /* Free all the data stored in "carry".
3651 static void isl_carry_clear(struct isl_carry
*carry
)
3653 isl_basic_set_list_free(carry
->intra
);
3654 isl_basic_set_list_free(carry
->inter
);
3657 /* Return a pointer to the node in "graph" that lives in "space".
3658 * If the requested node has been compressed, then "space"
3659 * corresponds to the compressed space.
3661 * First try and see if "space" is the space of an uncompressed node.
3662 * If so, return that node.
3663 * Otherwise, "space" was constructed by construct_compressed_id and
3664 * contains a user pointer pointing to the node in the tuple id.
3666 static struct isl_sched_node
*graph_find_compressed_node(isl_ctx
*ctx
,
3667 struct isl_sched_graph
*graph
, __isl_keep isl_space
*space
)
3670 struct isl_sched_node
*node
;
3675 node
= graph_find_node(ctx
, graph
, space
);
3679 id
= isl_space_get_tuple_id(space
, isl_dim_set
);
3680 node
= isl_id_get_user(id
);
3686 if (!(node
>= &graph
->node
[0] && node
< &graph
->node
[graph
->n
]))
3687 isl_die(ctx
, isl_error_internal
,
3688 "space points to invalid node", return NULL
);
3693 /* Internal data structure for add_all_constraints.
3695 * "graph" is the schedule constraint graph for which an LP problem
3696 * is being constructed.
3697 * "pos" is the position of the next edge that needs to be carried.
3699 struct isl_add_all_constraints_data
{
3701 struct isl_sched_graph
*graph
;
3705 /* Add the constraints "coef" derived from an edge from a node to itself
3706 * to data->graph->lp in order to respect the dependences and
3707 * to try and carry them.
3709 * The space of "coef" is of the form
3711 * coefficients[[c_cst, c_n] -> S[c_x]]
3713 * with S[c_x] the (compressed) space of the node.
3714 * Extract the node from the space and call add_intra_constraints.
3716 static isl_stat
lp_add_intra(__isl_take isl_basic_set
*coef
, void *user
)
3718 struct isl_add_all_constraints_data
*data
= user
;
3720 struct isl_sched_node
*node
;
3722 space
= isl_basic_set_get_space(coef
);
3723 space
= isl_space_range(isl_space_unwrap(space
));
3724 node
= graph_find_compressed_node(data
->ctx
, data
->graph
, space
);
3725 isl_space_free(space
);
3726 return add_intra_constraints(data
->graph
, node
, coef
, data
->pos
++);
3729 /* Add the constraints "coef" derived from an edge from a node j
3730 * to a node k to data->graph->lp in order to respect the dependences and
3731 * to try and carry them.
3733 * The space of "coef" is of the form
3735 * coefficients[[c_cst, c_n] -> [S_j[c_x] -> S_k[c_y]]]
3737 * with S_j[c_x] and S_k[c_y] the (compressed) spaces of the nodes.
3738 * Extract the nodes from the space and call add_inter_constraints.
3740 static isl_stat
lp_add_inter(__isl_take isl_basic_set
*coef
, void *user
)
3742 struct isl_add_all_constraints_data
*data
= user
;
3743 isl_space
*space
, *dom
;
3744 struct isl_sched_node
*src
, *dst
;
3746 space
= isl_basic_set_get_space(coef
);
3747 space
= isl_space_unwrap(isl_space_range(isl_space_unwrap(space
)));
3748 dom
= isl_space_domain(isl_space_copy(space
));
3749 src
= graph_find_compressed_node(data
->ctx
, data
->graph
, dom
);
3750 isl_space_free(dom
);
3751 space
= isl_space_range(space
);
3752 dst
= graph_find_compressed_node(data
->ctx
, data
->graph
, space
);
3753 isl_space_free(space
);
3755 return add_inter_constraints(data
->graph
, src
, dst
, coef
, data
->pos
++);
3758 /* Add constraints to graph->lp that force all (conditional) validity
3759 * dependences to be respected and attempt to carry them.
3760 * "intra" is the sequence of coefficient constraints for intra-node edges.
3761 * "inter" is the sequence of coefficient constraints for inter-node edges.
3763 static isl_stat
add_all_constraints(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
3764 __isl_keep isl_basic_set_list
*intra
,
3765 __isl_keep isl_basic_set_list
*inter
)
3767 struct isl_add_all_constraints_data data
= { ctx
, graph
};
3770 if (isl_basic_set_list_foreach(intra
, &lp_add_intra
, &data
) < 0)
3771 return isl_stat_error
;
3772 if (isl_basic_set_list_foreach(inter
, &lp_add_inter
, &data
) < 0)
3773 return isl_stat_error
;
3777 /* Internal data structure for count_all_constraints
3778 * for keeping track of the number of equality and inequality constraints.
3780 struct isl_sched_count
{
3785 /* Add the number of equality and inequality constraints of "bset"
3786 * to data->n_eq and data->n_ineq.
3788 static isl_stat
bset_update_count(__isl_take isl_basic_set
*bset
, void *user
)
3790 struct isl_sched_count
*data
= user
;
3792 data
->n_eq
+= isl_basic_set_n_equality(bset
);
3793 data
->n_ineq
+= isl_basic_set_n_inequality(bset
);
3794 isl_basic_set_free(bset
);
3799 /* Count the number of equality and inequality constraints
3800 * that will be added to the carry_lp problem.
3801 * We count each edge exactly once.
3802 * "intra" is the sequence of coefficient constraints for intra-node edges.
3803 * "inter" is the sequence of coefficient constraints for inter-node edges.
3805 static isl_stat
count_all_constraints(__isl_keep isl_basic_set_list
*intra
,
3806 __isl_keep isl_basic_set_list
*inter
, int *n_eq
, int *n_ineq
)
3808 struct isl_sched_count data
;
3810 data
.n_eq
= data
.n_ineq
= 0;
3811 if (isl_basic_set_list_foreach(inter
, &bset_update_count
, &data
) < 0)
3812 return isl_stat_error
;
3813 if (isl_basic_set_list_foreach(intra
, &bset_update_count
, &data
) < 0)
3814 return isl_stat_error
;
3817 *n_ineq
= data
.n_ineq
;
3822 /* Construct an LP problem for finding schedule coefficients
3823 * such that the schedule carries as many validity dependences as possible.
3824 * In particular, for each dependence i, we bound the dependence distance
3825 * from below by e_i, with 0 <= e_i <= 1 and then maximize the sum
3826 * of all e_i's. Dependences with e_i = 0 in the solution are simply
3827 * respected, while those with e_i > 0 (in practice e_i = 1) are carried.
3828 * "intra" is the sequence of coefficient constraints for intra-node edges.
3829 * "inter" is the sequence of coefficient constraints for inter-node edges.
3830 * "n_edge" is the total number of edges.
3832 * All variables of the LP are non-negative. The actual coefficients
3833 * may be negative, so each coefficient is represented as the difference
3834 * of two non-negative variables. The negative part always appears
3835 * immediately before the positive part.
3836 * Other than that, the variables have the following order
3838 * - sum of (1 - e_i) over all edges
3839 * - sum of all c_n coefficients
3840 * (unconstrained when computing non-parametric schedules)
3841 * - sum of positive and negative parts of all c_x coefficients
3845 * - positive and negative parts of c_i_x, in opposite order
3846 * - c_i_n (if parametric)
3849 * The constraints are those from the (validity) edges plus three equalities
3850 * to express the sums and n_edge inequalities to express e_i <= 1.
3852 static isl_stat
setup_carry_lp(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
3853 int n_edge
, __isl_keep isl_basic_set_list
*intra
,
3854 __isl_keep isl_basic_set_list
*inter
)
3863 for (i
= 0; i
< graph
->n
; ++i
) {
3864 struct isl_sched_node
*node
= &graph
->node
[graph
->sorted
[i
]];
3865 node
->start
= total
;
3866 total
+= 1 + node
->nparam
+ 2 * node
->nvar
;
3869 if (count_all_constraints(intra
, inter
, &n_eq
, &n_ineq
) < 0)
3870 return isl_stat_error
;
3872 dim
= isl_space_set_alloc(ctx
, 0, total
);
3873 isl_basic_set_free(graph
->lp
);
3876 graph
->lp
= isl_basic_set_alloc_space(dim
, 0, n_eq
, n_ineq
);
3877 graph
->lp
= isl_basic_set_set_rational(graph
->lp
);
3879 k
= isl_basic_set_alloc_equality(graph
->lp
);
3881 return isl_stat_error
;
3882 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
3883 isl_int_set_si(graph
->lp
->eq
[k
][0], -n_edge
);
3884 isl_int_set_si(graph
->lp
->eq
[k
][1], 1);
3885 for (i
= 0; i
< n_edge
; ++i
)
3886 isl_int_set_si(graph
->lp
->eq
[k
][4 + i
], 1);
3888 if (add_param_sum_constraint(graph
, 1) < 0)
3889 return isl_stat_error
;
3890 if (add_var_sum_constraint(graph
, 2) < 0)
3891 return isl_stat_error
;
3893 for (i
= 0; i
< n_edge
; ++i
) {
3894 k
= isl_basic_set_alloc_inequality(graph
->lp
);
3896 return isl_stat_error
;
3897 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
3898 isl_int_set_si(graph
->lp
->ineq
[k
][4 + i
], -1);
3899 isl_int_set_si(graph
->lp
->ineq
[k
][0], 1);
3902 if (add_all_constraints(ctx
, graph
, intra
, inter
) < 0)
3903 return isl_stat_error
;
3908 static __isl_give isl_schedule_node
*compute_component_schedule(
3909 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
3912 /* If the schedule_split_scaled option is set and if the linear
3913 * parts of the scheduling rows for all nodes in the graphs have
3914 * a non-trivial common divisor, then remove this
3915 * common divisor from the linear part.
3916 * Otherwise, insert a band node directly and continue with
3917 * the construction of the schedule.
3919 * If a non-trivial common divisor is found, then
3920 * the linear part is reduced and the remainder is ignored.
3921 * The pieces of the graph that are assigned different remainders
3922 * form (groups of) strongly connected components within
3923 * the scaled down band. If needed, they can therefore
3924 * be ordered along this remainder in a sequence node.
3925 * However, this ordering is not enforced here in order to allow
3926 * the scheduler to combine some of the strongly connected components.
3928 static __isl_give isl_schedule_node
*split_scaled(
3929 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
3939 ctx
= isl_schedule_node_get_ctx(node
);
3940 if (!ctx
->opt
->schedule_split_scaled
)
3941 return compute_next_band(node
, graph
, 0);
3943 return compute_next_band(node
, graph
, 0);
3946 isl_int_init(gcd_i
);
3948 isl_int_set_si(gcd
, 0);
3950 row
= isl_mat_rows(graph
->node
[0].sched
) - 1;
3952 for (i
= 0; i
< graph
->n
; ++i
) {
3953 struct isl_sched_node
*node
= &graph
->node
[i
];
3954 int cols
= isl_mat_cols(node
->sched
);
3956 isl_seq_gcd(node
->sched
->row
[row
] + 1, cols
- 1, &gcd_i
);
3957 isl_int_gcd(gcd
, gcd
, gcd_i
);
3960 isl_int_clear(gcd_i
);
3962 if (isl_int_cmp_si(gcd
, 1) <= 0) {
3964 return compute_next_band(node
, graph
, 0);
3967 for (i
= 0; i
< graph
->n
; ++i
) {
3968 struct isl_sched_node
*node
= &graph
->node
[i
];
3970 isl_int_fdiv_q(node
->sched
->row
[row
][0],
3971 node
->sched
->row
[row
][0], gcd
);
3972 isl_int_mul(node
->sched
->row
[row
][0],
3973 node
->sched
->row
[row
][0], gcd
);
3974 node
->sched
= isl_mat_scale_down_row(node
->sched
, row
, gcd
);
3981 return compute_next_band(node
, graph
, 0);
3984 return isl_schedule_node_free(node
);
3987 /* Is the schedule row "sol" trivial on node "node"?
3988 * That is, is the solution zero on the dimensions linearly independent of
3989 * the previously found solutions?
3990 * Return 1 if the solution is trivial, 0 if it is not and -1 on error.
3992 * Each coefficient is represented as the difference between
3993 * two non-negative values in "sol".
3994 * We construct the schedule row s and check if it is linearly
3995 * independent of previously computed schedule rows
3996 * by computing T s, with T the linear combinations that are zero
3997 * on linearly dependent schedule rows.
3998 * If the result consists of all zeros, then the solution is trivial.
4000 static int is_trivial(struct isl_sched_node
*node
, __isl_keep isl_vec
*sol
)
4007 if (node
->nvar
== node
->rank
)
4010 node_sol
= extract_var_coef(node
, sol
);
4011 node_sol
= isl_mat_vec_product(isl_mat_copy(node
->indep
), node_sol
);
4015 trivial
= isl_seq_first_non_zero(node_sol
->el
,
4016 node
->nvar
- node
->rank
) == -1;
4018 isl_vec_free(node_sol
);
4023 /* Is the schedule row "sol" trivial on any node where it should
4025 * Return 1 if any solution is trivial, 0 if they are not and -1 on error.
4027 static int is_any_trivial(struct isl_sched_graph
*graph
,
4028 __isl_keep isl_vec
*sol
)
4032 for (i
= 0; i
< graph
->n
; ++i
) {
4033 struct isl_sched_node
*node
= &graph
->node
[i
];
4036 if (!needs_row(graph
, node
))
4038 trivial
= is_trivial(node
, sol
);
4039 if (trivial
< 0 || trivial
)
4046 /* Does the schedule represented by "sol" perform loop coalescing on "node"?
4047 * If so, return the position of the coalesced dimension.
4048 * Otherwise, return node->nvar or -1 on error.
4050 * In particular, look for pairs of coefficients c_i and c_j such that
4051 * |c_j/c_i| > ceil(size_i/2), i.e., |c_j| > |c_i * ceil(size_i/2)|.
4052 * If any such pair is found, then return i.
4053 * If size_i is infinity, then no check on c_i needs to be performed.
4055 static int find_node_coalescing(struct isl_sched_node
*node
,
4056 __isl_keep isl_vec
*sol
)
4062 if (node
->nvar
<= 1)
4065 csol
= extract_var_coef(node
, sol
);
4069 for (i
= 0; i
< node
->nvar
; ++i
) {
4072 if (isl_int_is_zero(csol
->el
[i
]))
4074 v
= isl_multi_val_get_val(node
->sizes
, i
);
4077 if (!isl_val_is_int(v
)) {
4081 v
= isl_val_div_ui(v
, 2);
4082 v
= isl_val_ceil(v
);
4085 isl_int_mul(max
, v
->n
, csol
->el
[i
]);
4088 for (j
= 0; j
< node
->nvar
; ++j
) {
4091 if (isl_int_abs_gt(csol
->el
[j
], max
))
4107 /* Force the schedule coefficient at position "pos" of "node" to be zero
4109 * The coefficient is encoded as the difference between two non-negative
4110 * variables. Force these two variables to have the same value.
4112 static __isl_give isl_tab_lexmin
*zero_out_node_coef(
4113 __isl_take isl_tab_lexmin
*tl
, struct isl_sched_node
*node
, int pos
)
4119 ctx
= isl_space_get_ctx(node
->space
);
4120 dim
= isl_tab_lexmin_dim(tl
);
4122 return isl_tab_lexmin_free(tl
);
4123 eq
= isl_vec_alloc(ctx
, 1 + dim
);
4124 eq
= isl_vec_clr(eq
);
4126 return isl_tab_lexmin_free(tl
);
4128 pos
= 1 + node_var_coef_pos(node
, pos
);
4129 isl_int_set_si(eq
->el
[pos
], 1);
4130 isl_int_set_si(eq
->el
[pos
+ 1], -1);
4131 tl
= isl_tab_lexmin_add_eq(tl
, eq
->el
);
4137 /* Return the lexicographically smallest rational point in the basic set
4138 * from which "tl" was constructed, double checking that this input set
4141 static __isl_give isl_vec
*non_empty_solution(__isl_keep isl_tab_lexmin
*tl
)
4145 sol
= isl_tab_lexmin_get_solution(tl
);
4149 isl_die(isl_vec_get_ctx(sol
), isl_error_internal
,
4150 "error in schedule construction",
4151 return isl_vec_free(sol
));
4155 /* Does the solution "sol" of the LP problem constructed by setup_carry_lp
4156 * carry any of the "n_edge" groups of dependences?
4157 * The value in the first position is the sum of (1 - e_i) over all "n_edge"
4158 * edges, with 0 <= e_i <= 1 equal to 1 when the dependences represented
4159 * by the edge are carried by the solution.
4160 * If the sum of the (1 - e_i) is smaller than "n_edge" then at least
4161 * one of those is carried.
4163 * Note that despite the fact that the problem is solved using a rational
4164 * solver, the solution is guaranteed to be integral.
4165 * Specifically, the dependence distance lower bounds e_i (and therefore
4166 * also their sum) are integers. See Lemma 5 of [1].
4168 * Any potential denominator of the sum is cleared by this function.
4169 * The denominator is not relevant for any of the other elements
4172 * [1] P. Feautrier, Some Efficient Solutions to the Affine Scheduling
4173 * Problem, Part II: Multi-Dimensional Time.
4174 * In Intl. Journal of Parallel Programming, 1992.
4176 static int carries_dependences(__isl_keep isl_vec
*sol
, int n_edge
)
4178 isl_int_divexact(sol
->el
[1], sol
->el
[1], sol
->el
[0]);
4179 isl_int_set_si(sol
->el
[0], 1);
4180 return isl_int_cmp_si(sol
->el
[1], n_edge
) < 0;
4183 /* Return the lexicographically smallest rational point in "lp",
4184 * assuming that all variables are non-negative and performing some
4185 * additional sanity checks.
4186 * If "want_integral" is set, then compute the lexicographically smallest
4187 * integer point instead.
4188 * In particular, "lp" should not be empty by construction.
4189 * Double check that this is the case.
4190 * If dependences are not carried for any of the "n_edge" edges,
4191 * then return an empty vector.
4193 * If the schedule_treat_coalescing option is set and
4194 * if the computed schedule performs loop coalescing on a given node,
4195 * i.e., if it is of the form
4197 * c_i i + c_j j + ...
4199 * with |c_j/c_i| >= size_i, then force the coefficient c_i to be zero
4200 * to cut out this solution. Repeat this process until no more loop
4201 * coalescing occurs or until no more dependences can be carried.
4202 * In the latter case, revert to the previously computed solution.
4204 * If the caller requests an integral solution and if coalescing should
4205 * be treated, then perform the coalescing treatment first as
4206 * an integral solution computed before coalescing treatment
4207 * would carry the same number of edges and would therefore probably
4208 * also be coalescing.
4210 * To allow the coalescing treatment to be performed first,
4211 * the initial solution is allowed to be rational and it is only
4212 * cut out (if needed) in the next iteration, if no coalescing measures
4215 static __isl_give isl_vec
*non_neg_lexmin(struct isl_sched_graph
*graph
,
4216 __isl_take isl_basic_set
*lp
, int n_edge
, int want_integral
)
4221 isl_vec
*sol
, *prev
= NULL
;
4222 int treat_coalescing
;
4226 ctx
= isl_basic_set_get_ctx(lp
);
4227 treat_coalescing
= isl_options_get_schedule_treat_coalescing(ctx
);
4228 tl
= isl_tab_lexmin_from_basic_set(lp
);
4235 tl
= isl_tab_lexmin_cut_to_integer(tl
);
4236 sol
= non_empty_solution(tl
);
4240 integral
= isl_int_is_one(sol
->el
[0]);
4241 if (!carries_dependences(sol
, n_edge
)) {
4243 prev
= isl_vec_alloc(ctx
, 0);
4248 prev
= isl_vec_free(prev
);
4249 cut
= want_integral
&& !integral
;
4252 if (!treat_coalescing
)
4254 for (i
= 0; i
< graph
->n
; ++i
) {
4255 struct isl_sched_node
*node
= &graph
->node
[i
];
4257 pos
= find_node_coalescing(node
, sol
);
4260 if (pos
< node
->nvar
)
4265 tl
= zero_out_node_coef(tl
, &graph
->node
[i
], pos
);
4270 isl_tab_lexmin_free(tl
);
4274 isl_tab_lexmin_free(tl
);
4280 /* If "edge" is an edge from a node to itself, then add the corresponding
4281 * dependence relation to "umap".
4282 * If "node" has been compressed, then the dependence relation
4283 * is also compressed first.
4285 static __isl_give isl_union_map
*add_intra(__isl_take isl_union_map
*umap
,
4286 struct isl_sched_edge
*edge
)
4289 struct isl_sched_node
*node
= edge
->src
;
4291 if (edge
->src
!= edge
->dst
)
4294 map
= isl_map_copy(edge
->map
);
4295 if (node
->compressed
) {
4296 map
= isl_map_preimage_domain_multi_aff(map
,
4297 isl_multi_aff_copy(node
->decompress
));
4298 map
= isl_map_preimage_range_multi_aff(map
,
4299 isl_multi_aff_copy(node
->decompress
));
4301 umap
= isl_union_map_add_map(umap
, map
);
4305 /* If "edge" is an edge from a node to another node, then add the corresponding
4306 * dependence relation to "umap".
4307 * If the source or destination nodes of "edge" have been compressed,
4308 * then the dependence relation is also compressed first.
4310 static __isl_give isl_union_map
*add_inter(__isl_take isl_union_map
*umap
,
4311 struct isl_sched_edge
*edge
)
4315 if (edge
->src
== edge
->dst
)
4318 map
= isl_map_copy(edge
->map
);
4319 if (edge
->src
->compressed
)
4320 map
= isl_map_preimage_domain_multi_aff(map
,
4321 isl_multi_aff_copy(edge
->src
->decompress
));
4322 if (edge
->dst
->compressed
)
4323 map
= isl_map_preimage_range_multi_aff(map
,
4324 isl_multi_aff_copy(edge
->dst
->decompress
));
4325 umap
= isl_union_map_add_map(umap
, map
);
4329 /* For each (conditional) validity edge in "graph",
4330 * add the corresponding dependence relation using "add"
4331 * to a collection of dependence relations and return the result.
4332 * If "coincidence" is set, then coincidence edges are considered as well.
4334 static __isl_give isl_union_map
*collect_validity(struct isl_sched_graph
*graph
,
4335 __isl_give isl_union_map
*(*add
)(__isl_take isl_union_map
*umap
,
4336 struct isl_sched_edge
*edge
), int coincidence
)
4340 isl_union_map
*umap
;
4342 space
= isl_space_copy(graph
->node
[0].space
);
4343 umap
= isl_union_map_empty(space
);
4345 for (i
= 0; i
< graph
->n_edge
; ++i
) {
4346 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
4348 if (!is_any_validity(edge
) &&
4349 (!coincidence
|| !is_coincidence(edge
)))
4352 umap
= add(umap
, edge
);
4358 /* For each dependence relation on a (conditional) validity edge
4359 * from a node to itself,
4360 * construct the set of coefficients of valid constraints for elements
4361 * in that dependence relation and collect the results.
4362 * If "coincidence" is set, then coincidence edges are considered as well.
4364 * In particular, for each dependence relation R, constraints
4365 * on coefficients (c_0, c_n, c_x) are constructed such that
4367 * c_0 + c_n n + c_x d >= 0 for each d in delta R = { y - x | (x,y) in R }
4369 * This computation is essentially the same as that performed
4370 * by intra_coefficients, except that it operates on multiple
4373 * Note that if a dependence relation is a union of basic maps,
4374 * then each basic map needs to be treated individually as it may only
4375 * be possible to carry the dependences expressed by some of those
4376 * basic maps and not all of them.
4377 * The collected validity constraints are therefore not coalesced and
4378 * it is assumed that they are not coalesced automatically.
4379 * Duplicate basic maps can be removed, however.
4380 * In particular, if the same basic map appears as a disjunct
4381 * in multiple edges, then it only needs to be carried once.
4383 static __isl_give isl_basic_set_list
*collect_intra_validity(
4384 struct isl_sched_graph
*graph
, int coincidence
)
4386 isl_union_map
*intra
;
4387 isl_union_set
*delta
;
4388 isl_basic_set_list
*list
;
4390 intra
= collect_validity(graph
, &add_intra
, coincidence
);
4391 delta
= isl_union_map_deltas(intra
);
4392 delta
= isl_union_set_remove_divs(delta
);
4393 list
= isl_union_set_get_basic_set_list(delta
);
4394 isl_union_set_free(delta
);
4396 return isl_basic_set_list_coefficients(list
);
4399 /* For each dependence relation on a (conditional) validity edge
4400 * from a node to some other node,
4401 * construct the set of coefficients of valid constraints for elements
4402 * in that dependence relation and collect the results.
4403 * If "coincidence" is set, then coincidence edges are considered as well.
4405 * In particular, for each dependence relation R, constraints
4406 * on coefficients (c_0, c_n, c_x, c_y) are constructed such that
4408 * c_0 + c_n n + c_x x + c_y y >= 0 for each (x,y) in R
4410 * This computation is essentially the same as that performed
4411 * by inter_coefficients, except that it operates on multiple
4414 * Note that if a dependence relation is a union of basic maps,
4415 * then each basic map needs to be treated individually as it may only
4416 * be possible to carry the dependences expressed by some of those
4417 * basic maps and not all of them.
4418 * The collected validity constraints are therefore not coalesced and
4419 * it is assumed that they are not coalesced automatically.
4420 * Duplicate basic maps can be removed, however.
4421 * In particular, if the same basic map appears as a disjunct
4422 * in multiple edges, then it only needs to be carried once.
4424 static __isl_give isl_basic_set_list
*collect_inter_validity(
4425 struct isl_sched_graph
*graph
, int coincidence
)
4427 isl_union_map
*inter
;
4428 isl_union_set
*wrap
;
4429 isl_basic_set_list
*list
;
4431 inter
= collect_validity(graph
, &add_inter
, coincidence
);
4432 inter
= isl_union_map_remove_divs(inter
);
4433 wrap
= isl_union_map_wrap(inter
);
4434 list
= isl_union_set_get_basic_set_list(wrap
);
4435 isl_union_set_free(wrap
);
4436 return isl_basic_set_list_coefficients(list
);
4439 /* Construct an LP problem for finding schedule coefficients
4440 * such that the schedule carries as many of the "n_edge" groups of
4441 * dependences as possible based on the corresponding coefficient
4442 * constraints and return the lexicographically smallest non-trivial solution.
4443 * "intra" is the sequence of coefficient constraints for intra-node edges.
4444 * "inter" is the sequence of coefficient constraints for inter-node edges.
4445 * If "want_integral" is set, then compute an integral solution
4446 * for the coefficients rather than using the numerators
4447 * of a rational solution.
4449 * If none of the "n_edge" groups can be carried
4450 * then return an empty vector.
4452 static __isl_give isl_vec
*compute_carrying_sol_coef(isl_ctx
*ctx
,
4453 struct isl_sched_graph
*graph
, int n_edge
,
4454 __isl_keep isl_basic_set_list
*intra
,
4455 __isl_keep isl_basic_set_list
*inter
, int want_integral
)
4459 if (setup_carry_lp(ctx
, graph
, n_edge
, intra
, inter
) < 0)
4462 lp
= isl_basic_set_copy(graph
->lp
);
4463 return non_neg_lexmin(graph
, lp
, n_edge
, want_integral
);
4466 /* Construct an LP problem for finding schedule coefficients
4467 * such that the schedule carries as many of the validity dependences
4469 * return the lexicographically smallest non-trivial solution.
4470 * If "fallback" is set, then the carrying is performed as a fallback
4471 * for the Pluto-like scheduler.
4472 * If "coincidence" is set, then try and carry coincidence edges as well.
4474 * The variable "n_edge" stores the number of groups that should be carried.
4475 * If none of the "n_edge" groups can be carried
4476 * then return an empty vector.
4477 * If, moreover, "n_edge" is zero, then the LP problem does not even
4478 * need to be constructed.
4480 * If a fallback solution is being computed, then compute an integral solution
4481 * for the coefficients rather than using the numerators
4482 * of a rational solution.
4484 static __isl_give isl_vec
*compute_carrying_sol(isl_ctx
*ctx
,
4485 struct isl_sched_graph
*graph
, int fallback
, int coincidence
)
4487 int n_intra
, n_inter
;
4489 struct isl_carry carry
= { 0 };
4492 carry
.intra
= collect_intra_validity(graph
, coincidence
);
4493 carry
.inter
= collect_inter_validity(graph
, coincidence
);
4494 if (!carry
.intra
|| !carry
.inter
)
4496 n_intra
= isl_basic_set_list_n_basic_set(carry
.intra
);
4497 n_inter
= isl_basic_set_list_n_basic_set(carry
.inter
);
4498 n_edge
= n_intra
+ n_inter
;
4500 isl_carry_clear(&carry
);
4501 return isl_vec_alloc(ctx
, 0);
4504 sol
= compute_carrying_sol_coef(ctx
, graph
, n_edge
,
4505 carry
.intra
, carry
.inter
, fallback
);
4506 isl_carry_clear(&carry
);
4509 isl_carry_clear(&carry
);
4513 /* Construct a schedule row for each node such that as many validity dependences
4514 * as possible are carried and then continue with the next band.
4515 * If "fallback" is set, then the carrying is performed as a fallback
4516 * for the Pluto-like scheduler.
4517 * If "coincidence" is set, then try and carry coincidence edges as well.
4519 * If there are no validity dependences, then no dependence can be carried and
4520 * the procedure is guaranteed to fail. If there is more than one component,
4521 * then try computing a schedule on each component separately
4522 * to prevent or at least postpone this failure.
4524 * If a schedule row is computed, then check that dependences are carried
4525 * for at least one of the edges.
4527 * If the computed schedule row turns out to be trivial on one or
4528 * more nodes where it should not be trivial, then we throw it away
4529 * and try again on each component separately.
4531 * If there is only one component, then we accept the schedule row anyway,
4532 * but we do not consider it as a complete row and therefore do not
4533 * increment graph->n_row. Note that the ranks of the nodes that
4534 * do get a non-trivial schedule part will get updated regardless and
4535 * graph->maxvar is computed based on these ranks. The test for
4536 * whether more schedule rows are required in compute_schedule_wcc
4537 * is therefore not affected.
4539 * Insert a band corresponding to the schedule row at position "node"
4540 * of the schedule tree and continue with the construction of the schedule.
4541 * This insertion and the continued construction is performed by split_scaled
4542 * after optionally checking for non-trivial common divisors.
4544 static __isl_give isl_schedule_node
*carry(__isl_take isl_schedule_node
*node
,
4545 struct isl_sched_graph
*graph
, int fallback
, int coincidence
)
4554 ctx
= isl_schedule_node_get_ctx(node
);
4555 sol
= compute_carrying_sol(ctx
, graph
, fallback
, coincidence
);
4557 return isl_schedule_node_free(node
);
4558 if (sol
->size
== 0) {
4561 return compute_component_schedule(node
, graph
, 1);
4562 isl_die(ctx
, isl_error_unknown
, "unable to carry dependences",
4563 return isl_schedule_node_free(node
));
4566 trivial
= is_any_trivial(graph
, sol
);
4568 sol
= isl_vec_free(sol
);
4569 } else if (trivial
&& graph
->scc
> 1) {
4571 return compute_component_schedule(node
, graph
, 1);
4574 if (update_schedule(graph
, sol
, 0) < 0)
4575 return isl_schedule_node_free(node
);
4579 return split_scaled(node
, graph
);
4582 /* Construct a schedule row for each node such that as many validity dependences
4583 * as possible are carried and then continue with the next band.
4584 * Do so as a fallback for the Pluto-like scheduler.
4585 * If "coincidence" is set, then try and carry coincidence edges as well.
4587 static __isl_give isl_schedule_node
*carry_fallback(
4588 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
4591 return carry(node
, graph
, 1, coincidence
);
4594 /* Construct a schedule row for each node such that as many validity dependences
4595 * as possible are carried and then continue with the next band.
4596 * Do so for the case where the Feautrier scheduler was selected
4599 static __isl_give isl_schedule_node
*carry_feautrier(
4600 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
4602 return carry(node
, graph
, 0, 0);
4605 /* Construct a schedule row for each node such that as many validity dependences
4606 * as possible are carried and then continue with the next band.
4607 * Do so as a fallback for the Pluto-like scheduler.
4609 static __isl_give isl_schedule_node
*carry_dependences(
4610 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
4612 return carry_fallback(node
, graph
, 0);
4615 /* Construct a schedule row for each node such that as many validity or
4616 * coincidence dependences as possible are carried and
4617 * then continue with the next band.
4618 * Do so as a fallback for the Pluto-like scheduler.
4620 static __isl_give isl_schedule_node
*carry_coincidence(
4621 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
4623 return carry_fallback(node
, graph
, 1);
4626 /* Topologically sort statements mapped to the same schedule iteration
4627 * and add insert a sequence node in front of "node"
4628 * corresponding to this order.
4629 * If "initialized" is set, then it may be assumed that compute_maxvar
4630 * has been called on the current band. Otherwise, call
4631 * compute_maxvar if and before carry_dependences gets called.
4633 * If it turns out to be impossible to sort the statements apart,
4634 * because different dependences impose different orderings
4635 * on the statements, then we extend the schedule such that
4636 * it carries at least one more dependence.
4638 static __isl_give isl_schedule_node
*sort_statements(
4639 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
4643 isl_union_set_list
*filters
;
4648 ctx
= isl_schedule_node_get_ctx(node
);
4650 isl_die(ctx
, isl_error_internal
,
4651 "graph should have at least one node",
4652 return isl_schedule_node_free(node
));
4657 if (update_edges(ctx
, graph
) < 0)
4658 return isl_schedule_node_free(node
);
4660 if (graph
->n_edge
== 0)
4663 if (detect_sccs(ctx
, graph
) < 0)
4664 return isl_schedule_node_free(node
);
4667 if (graph
->scc
< graph
->n
) {
4668 if (!initialized
&& compute_maxvar(graph
) < 0)
4669 return isl_schedule_node_free(node
);
4670 return carry_dependences(node
, graph
);
4673 filters
= extract_sccs(ctx
, graph
);
4674 node
= isl_schedule_node_insert_sequence(node
, filters
);
4679 /* Are there any (non-empty) (conditional) validity edges in the graph?
4681 static int has_validity_edges(struct isl_sched_graph
*graph
)
4685 for (i
= 0; i
< graph
->n_edge
; ++i
) {
4688 empty
= isl_map_plain_is_empty(graph
->edge
[i
].map
);
4693 if (is_any_validity(&graph
->edge
[i
]))
4700 /* Should we apply a Feautrier step?
4701 * That is, did the user request the Feautrier algorithm and are
4702 * there any validity dependences (left)?
4704 static int need_feautrier_step(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
4706 if (ctx
->opt
->schedule_algorithm
!= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
)
4709 return has_validity_edges(graph
);
4712 /* Compute a schedule for a connected dependence graph using Feautrier's
4713 * multi-dimensional scheduling algorithm and return the updated schedule node.
4715 * The original algorithm is described in [1].
4716 * The main idea is to minimize the number of scheduling dimensions, by
4717 * trying to satisfy as many dependences as possible per scheduling dimension.
4719 * [1] P. Feautrier, Some Efficient Solutions to the Affine Scheduling
4720 * Problem, Part II: Multi-Dimensional Time.
4721 * In Intl. Journal of Parallel Programming, 1992.
4723 static __isl_give isl_schedule_node
*compute_schedule_wcc_feautrier(
4724 isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
4726 return carry_feautrier(node
, graph
);
4729 /* Turn off the "local" bit on all (condition) edges.
4731 static void clear_local_edges(struct isl_sched_graph
*graph
)
4735 for (i
= 0; i
< graph
->n_edge
; ++i
)
4736 if (is_condition(&graph
->edge
[i
]))
4737 clear_local(&graph
->edge
[i
]);
4740 /* Does "graph" have both condition and conditional validity edges?
4742 static int need_condition_check(struct isl_sched_graph
*graph
)
4745 int any_condition
= 0;
4746 int any_conditional_validity
= 0;
4748 for (i
= 0; i
< graph
->n_edge
; ++i
) {
4749 if (is_condition(&graph
->edge
[i
]))
4751 if (is_conditional_validity(&graph
->edge
[i
]))
4752 any_conditional_validity
= 1;
4755 return any_condition
&& any_conditional_validity
;
4758 /* Does "graph" contain any coincidence edge?
4760 static int has_any_coincidence(struct isl_sched_graph
*graph
)
4764 for (i
= 0; i
< graph
->n_edge
; ++i
)
4765 if (is_coincidence(&graph
->edge
[i
]))
4771 /* Extract the final schedule row as a map with the iteration domain
4772 * of "node" as domain.
4774 static __isl_give isl_map
*final_row(struct isl_sched_node
*node
)
4779 row
= isl_mat_rows(node
->sched
) - 1;
4780 ma
= node_extract_partial_schedule_multi_aff(node
, row
, 1);
4781 return isl_map_from_multi_aff(ma
);
4784 /* Is the conditional validity dependence in the edge with index "edge_index"
4785 * violated by the latest (i.e., final) row of the schedule?
4786 * That is, is i scheduled after j
4787 * for any conditional validity dependence i -> j?
4789 static int is_violated(struct isl_sched_graph
*graph
, int edge_index
)
4791 isl_map
*src_sched
, *dst_sched
, *map
;
4792 struct isl_sched_edge
*edge
= &graph
->edge
[edge_index
];
4795 src_sched
= final_row(edge
->src
);
4796 dst_sched
= final_row(edge
->dst
);
4797 map
= isl_map_copy(edge
->map
);
4798 map
= isl_map_apply_domain(map
, src_sched
);
4799 map
= isl_map_apply_range(map
, dst_sched
);
4800 map
= isl_map_order_gt(map
, isl_dim_in
, 0, isl_dim_out
, 0);
4801 empty
= isl_map_is_empty(map
);
4810 /* Does "graph" have any satisfied condition edges that
4811 * are adjacent to the conditional validity constraint with
4812 * domain "conditional_source" and range "conditional_sink"?
4814 * A satisfied condition is one that is not local.
4815 * If a condition was forced to be local already (i.e., marked as local)
4816 * then there is no need to check if it is in fact local.
4818 * Additionally, mark all adjacent condition edges found as local.
4820 static int has_adjacent_true_conditions(struct isl_sched_graph
*graph
,
4821 __isl_keep isl_union_set
*conditional_source
,
4822 __isl_keep isl_union_set
*conditional_sink
)
4827 for (i
= 0; i
< graph
->n_edge
; ++i
) {
4828 int adjacent
, local
;
4829 isl_union_map
*condition
;
4831 if (!is_condition(&graph
->edge
[i
]))
4833 if (is_local(&graph
->edge
[i
]))
4836 condition
= graph
->edge
[i
].tagged_condition
;
4837 adjacent
= domain_intersects(condition
, conditional_sink
);
4838 if (adjacent
>= 0 && !adjacent
)
4839 adjacent
= range_intersects(condition
,
4840 conditional_source
);
4846 set_local(&graph
->edge
[i
]);
4848 local
= is_condition_false(&graph
->edge
[i
]);
4858 /* Are there any violated conditional validity dependences with
4859 * adjacent condition dependences that are not local with respect
4860 * to the current schedule?
4861 * That is, is the conditional validity constraint violated?
4863 * Additionally, mark all those adjacent condition dependences as local.
4864 * We also mark those adjacent condition dependences that were not marked
4865 * as local before, but just happened to be local already. This ensures
4866 * that they remain local if the schedule is recomputed.
4868 * We first collect domain and range of all violated conditional validity
4869 * dependences and then check if there are any adjacent non-local
4870 * condition dependences.
4872 static int has_violated_conditional_constraint(isl_ctx
*ctx
,
4873 struct isl_sched_graph
*graph
)
4877 isl_union_set
*source
, *sink
;
4879 source
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
4880 sink
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
4881 for (i
= 0; i
< graph
->n_edge
; ++i
) {
4882 isl_union_set
*uset
;
4883 isl_union_map
*umap
;
4886 if (!is_conditional_validity(&graph
->edge
[i
]))
4889 violated
= is_violated(graph
, i
);
4897 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_validity
);
4898 uset
= isl_union_map_domain(umap
);
4899 source
= isl_union_set_union(source
, uset
);
4900 source
= isl_union_set_coalesce(source
);
4902 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_validity
);
4903 uset
= isl_union_map_range(umap
);
4904 sink
= isl_union_set_union(sink
, uset
);
4905 sink
= isl_union_set_coalesce(sink
);
4909 any
= has_adjacent_true_conditions(graph
, source
, sink
);
4911 isl_union_set_free(source
);
4912 isl_union_set_free(sink
);
4915 isl_union_set_free(source
);
4916 isl_union_set_free(sink
);
4920 /* Examine the current band (the rows between graph->band_start and
4921 * graph->n_total_row), deciding whether to drop it or add it to "node"
4922 * and then continue with the computation of the next band, if any.
4923 * If "initialized" is set, then it may be assumed that compute_maxvar
4924 * has been called on the current band. Otherwise, call
4925 * compute_maxvar if and before carry_dependences gets called.
4927 * The caller keeps looking for a new row as long as
4928 * graph->n_row < graph->maxvar. If the latest attempt to find
4929 * such a row failed (i.e., we still have graph->n_row < graph->maxvar),
4931 * - split between SCCs and start over (assuming we found an interesting
4932 * pair of SCCs between which to split)
4933 * - continue with the next band (assuming the current band has at least
4935 * - if there is more than one SCC left, then split along all SCCs
4936 * - if outer coincidence needs to be enforced, then try to carry as many
4937 * validity or coincidence dependences as possible and
4938 * continue with the next band
4939 * - try to carry as many validity dependences as possible and
4940 * continue with the next band
4941 * In each case, we first insert a band node in the schedule tree
4942 * if any rows have been computed.
4944 * If the caller managed to complete the schedule, we insert a band node
4945 * (if any schedule rows were computed) and we finish off by topologically
4946 * sorting the statements based on the remaining dependences.
4948 static __isl_give isl_schedule_node
*compute_schedule_finish_band(
4949 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
4957 if (graph
->n_row
< graph
->maxvar
) {
4959 int empty
= graph
->n_total_row
== graph
->band_start
;
4961 ctx
= isl_schedule_node_get_ctx(node
);
4962 if (!ctx
->opt
->schedule_maximize_band_depth
&& !empty
)
4963 return compute_next_band(node
, graph
, 1);
4964 if (graph
->src_scc
>= 0)
4965 return compute_split_schedule(node
, graph
);
4967 return compute_next_band(node
, graph
, 1);
4969 return compute_component_schedule(node
, graph
, 1);
4970 if (!initialized
&& compute_maxvar(graph
) < 0)
4971 return isl_schedule_node_free(node
);
4972 if (isl_options_get_schedule_outer_coincidence(ctx
))
4973 return carry_coincidence(node
, graph
);
4974 return carry_dependences(node
, graph
);
4977 insert
= graph
->n_total_row
> graph
->band_start
;
4979 node
= insert_current_band(node
, graph
, 1);
4980 node
= isl_schedule_node_child(node
, 0);
4982 node
= sort_statements(node
, graph
, initialized
);
4984 node
= isl_schedule_node_parent(node
);
4989 /* Construct a band of schedule rows for a connected dependence graph.
4990 * The caller is responsible for determining the strongly connected
4991 * components and calling compute_maxvar first.
4993 * We try to find a sequence of as many schedule rows as possible that result
4994 * in non-negative dependence distances (independent of the previous rows
4995 * in the sequence, i.e., such that the sequence is tilable), with as
4996 * many of the initial rows as possible satisfying the coincidence constraints.
4997 * The computation stops if we can't find any more rows or if we have found
4998 * all the rows we wanted to find.
5000 * If ctx->opt->schedule_outer_coincidence is set, then we force the
5001 * outermost dimension to satisfy the coincidence constraints. If this
5002 * turns out to be impossible, we fall back on the general scheme above
5003 * and try to carry as many dependences as possible.
5005 * If "graph" contains both condition and conditional validity dependences,
5006 * then we need to check that that the conditional schedule constraint
5007 * is satisfied, i.e., there are no violated conditional validity dependences
5008 * that are adjacent to any non-local condition dependences.
5009 * If there are, then we mark all those adjacent condition dependences
5010 * as local and recompute the current band. Those dependences that
5011 * are marked local will then be forced to be local.
5012 * The initial computation is performed with no dependences marked as local.
5013 * If we are lucky, then there will be no violated conditional validity
5014 * dependences adjacent to any non-local condition dependences.
5015 * Otherwise, we mark some additional condition dependences as local and
5016 * recompute. We continue this process until there are no violations left or
5017 * until we are no longer able to compute a schedule.
5018 * Since there are only a finite number of dependences,
5019 * there will only be a finite number of iterations.
5021 static isl_stat
compute_schedule_wcc_band(isl_ctx
*ctx
,
5022 struct isl_sched_graph
*graph
)
5024 int has_coincidence
;
5025 int use_coincidence
;
5026 int force_coincidence
= 0;
5027 int check_conditional
;
5029 if (sort_sccs(graph
) < 0)
5030 return isl_stat_error
;
5032 clear_local_edges(graph
);
5033 check_conditional
= need_condition_check(graph
);
5034 has_coincidence
= has_any_coincidence(graph
);
5036 if (ctx
->opt
->schedule_outer_coincidence
)
5037 force_coincidence
= 1;
5039 use_coincidence
= has_coincidence
;
5040 while (graph
->n_row
< graph
->maxvar
) {
5045 graph
->src_scc
= -1;
5046 graph
->dst_scc
= -1;
5048 if (setup_lp(ctx
, graph
, use_coincidence
) < 0)
5049 return isl_stat_error
;
5050 sol
= solve_lp(ctx
, graph
);
5052 return isl_stat_error
;
5053 if (sol
->size
== 0) {
5054 int empty
= graph
->n_total_row
== graph
->band_start
;
5057 if (use_coincidence
&& (!force_coincidence
|| !empty
)) {
5058 use_coincidence
= 0;
5063 coincident
= !has_coincidence
|| use_coincidence
;
5064 if (update_schedule(graph
, sol
, coincident
) < 0)
5065 return isl_stat_error
;
5067 if (!check_conditional
)
5069 violated
= has_violated_conditional_constraint(ctx
, graph
);
5071 return isl_stat_error
;
5074 if (reset_band(graph
) < 0)
5075 return isl_stat_error
;
5076 use_coincidence
= has_coincidence
;
5082 /* Compute a schedule for a connected dependence graph by considering
5083 * the graph as a whole and return the updated schedule node.
5085 * The actual schedule rows of the current band are computed by
5086 * compute_schedule_wcc_band. compute_schedule_finish_band takes
5087 * care of integrating the band into "node" and continuing
5090 static __isl_give isl_schedule_node
*compute_schedule_wcc_whole(
5091 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
5098 ctx
= isl_schedule_node_get_ctx(node
);
5099 if (compute_schedule_wcc_band(ctx
, graph
) < 0)
5100 return isl_schedule_node_free(node
);
5102 return compute_schedule_finish_band(node
, graph
, 1);
5105 /* Clustering information used by compute_schedule_wcc_clustering.
5107 * "n" is the number of SCCs in the original dependence graph
5108 * "scc" is an array of "n" elements, each representing an SCC
5109 * of the original dependence graph. All entries in the same cluster
5110 * have the same number of schedule rows.
5111 * "scc_cluster" maps each SCC index to the cluster to which it belongs,
5112 * where each cluster is represented by the index of the first SCC
5113 * in the cluster. Initially, each SCC belongs to a cluster containing
5116 * "scc_in_merge" is used by merge_clusters_along_edge to keep
5117 * track of which SCCs need to be merged.
5119 * "cluster" contains the merged clusters of SCCs after the clustering
5122 * "scc_node" is a temporary data structure used inside copy_partial.
5123 * For each SCC, it keeps track of the number of nodes in the SCC
5124 * that have already been copied.
5126 struct isl_clustering
{
5128 struct isl_sched_graph
*scc
;
5129 struct isl_sched_graph
*cluster
;
5135 /* Initialize the clustering data structure "c" from "graph".
5137 * In particular, allocate memory, extract the SCCs from "graph"
5138 * into c->scc, initialize scc_cluster and construct
5139 * a band of schedule rows for each SCC.
5140 * Within each SCC, there is only one SCC by definition.
5141 * Each SCC initially belongs to a cluster containing only that SCC.
5143 static isl_stat
clustering_init(isl_ctx
*ctx
, struct isl_clustering
*c
,
5144 struct isl_sched_graph
*graph
)
5149 c
->scc
= isl_calloc_array(ctx
, struct isl_sched_graph
, c
->n
);
5150 c
->cluster
= isl_calloc_array(ctx
, struct isl_sched_graph
, c
->n
);
5151 c
->scc_cluster
= isl_calloc_array(ctx
, int, c
->n
);
5152 c
->scc_node
= isl_calloc_array(ctx
, int, c
->n
);
5153 c
->scc_in_merge
= isl_calloc_array(ctx
, int, c
->n
);
5154 if (!c
->scc
|| !c
->cluster
||
5155 !c
->scc_cluster
|| !c
->scc_node
|| !c
->scc_in_merge
)
5156 return isl_stat_error
;
5158 for (i
= 0; i
< c
->n
; ++i
) {
5159 if (extract_sub_graph(ctx
, graph
, &node_scc_exactly
,
5160 &edge_scc_exactly
, i
, &c
->scc
[i
]) < 0)
5161 return isl_stat_error
;
5163 if (compute_maxvar(&c
->scc
[i
]) < 0)
5164 return isl_stat_error
;
5165 if (compute_schedule_wcc_band(ctx
, &c
->scc
[i
]) < 0)
5166 return isl_stat_error
;
5167 c
->scc_cluster
[i
] = i
;
5173 /* Free all memory allocated for "c".
5175 static void clustering_free(isl_ctx
*ctx
, struct isl_clustering
*c
)
5180 for (i
= 0; i
< c
->n
; ++i
)
5181 graph_free(ctx
, &c
->scc
[i
]);
5184 for (i
= 0; i
< c
->n
; ++i
)
5185 graph_free(ctx
, &c
->cluster
[i
]);
5187 free(c
->scc_cluster
);
5189 free(c
->scc_in_merge
);
5192 /* Should we refrain from merging the cluster in "graph" with
5193 * any other cluster?
5194 * In particular, is its current schedule band empty and incomplete.
5196 static int bad_cluster(struct isl_sched_graph
*graph
)
5198 return graph
->n_row
< graph
->maxvar
&&
5199 graph
->n_total_row
== graph
->band_start
;
5202 /* Is "edge" a proximity edge with a non-empty dependence relation?
5204 static isl_bool
is_non_empty_proximity(struct isl_sched_edge
*edge
)
5206 if (!is_proximity(edge
))
5207 return isl_bool_false
;
5208 return isl_bool_not(isl_map_plain_is_empty(edge
->map
));
5211 /* Return the index of an edge in "graph" that can be used to merge
5212 * two clusters in "c".
5213 * Return graph->n_edge if no such edge can be found.
5214 * Return -1 on error.
5216 * In particular, return a proximity edge between two clusters
5217 * that is not marked "no_merge" and such that neither of the
5218 * two clusters has an incomplete, empty band.
5220 * If there are multiple such edges, then try and find the most
5221 * appropriate edge to use for merging. In particular, pick the edge
5222 * with the greatest weight. If there are multiple of those,
5223 * then pick one with the shortest distance between
5224 * the two cluster representatives.
5226 static int find_proximity(struct isl_sched_graph
*graph
,
5227 struct isl_clustering
*c
)
5229 int i
, best
= graph
->n_edge
, best_dist
, best_weight
;
5231 for (i
= 0; i
< graph
->n_edge
; ++i
) {
5232 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
5236 prox
= is_non_empty_proximity(edge
);
5243 if (bad_cluster(&c
->scc
[edge
->src
->scc
]) ||
5244 bad_cluster(&c
->scc
[edge
->dst
->scc
]))
5246 dist
= c
->scc_cluster
[edge
->dst
->scc
] -
5247 c
->scc_cluster
[edge
->src
->scc
];
5250 weight
= edge
->weight
;
5251 if (best
< graph
->n_edge
) {
5252 if (best_weight
> weight
)
5254 if (best_weight
== weight
&& best_dist
<= dist
)
5259 best_weight
= weight
;
5265 /* Internal data structure used in mark_merge_sccs.
5267 * "graph" is the dependence graph in which a strongly connected
5268 * component is constructed.
5269 * "scc_cluster" maps each SCC index to the cluster to which it belongs.
5270 * "src" and "dst" are the indices of the nodes that are being merged.
5272 struct isl_mark_merge_sccs_data
{
5273 struct isl_sched_graph
*graph
;
5279 /* Check whether the cluster containing node "i" depends on the cluster
5280 * containing node "j". If "i" and "j" belong to the same cluster,
5281 * then they are taken to depend on each other to ensure that
5282 * the resulting strongly connected component consists of complete
5283 * clusters. Furthermore, if "i" and "j" are the two nodes that
5284 * are being merged, then they are taken to depend on each other as well.
5285 * Otherwise, check if there is a (conditional) validity dependence
5286 * from node[j] to node[i], forcing node[i] to follow node[j].
5288 static isl_bool
cluster_follows(int i
, int j
, void *user
)
5290 struct isl_mark_merge_sccs_data
*data
= user
;
5291 struct isl_sched_graph
*graph
= data
->graph
;
5292 int *scc_cluster
= data
->scc_cluster
;
5294 if (data
->src
== i
&& data
->dst
== j
)
5295 return isl_bool_true
;
5296 if (data
->src
== j
&& data
->dst
== i
)
5297 return isl_bool_true
;
5298 if (scc_cluster
[graph
->node
[i
].scc
] == scc_cluster
[graph
->node
[j
].scc
])
5299 return isl_bool_true
;
5301 return graph_has_validity_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
5304 /* Mark all SCCs that belong to either of the two clusters in "c"
5305 * connected by the edge in "graph" with index "edge", or to any
5306 * of the intermediate clusters.
5307 * The marking is recorded in c->scc_in_merge.
5309 * The given edge has been selected for merging two clusters,
5310 * meaning that there is at least a proximity edge between the two nodes.
5311 * However, there may also be (indirect) validity dependences
5312 * between the two nodes. When merging the two clusters, all clusters
5313 * containing one or more of the intermediate nodes along the
5314 * indirect validity dependences need to be merged in as well.
5316 * First collect all such nodes by computing the strongly connected
5317 * component (SCC) containing the two nodes connected by the edge, where
5318 * the two nodes are considered to depend on each other to make
5319 * sure they end up in the same SCC. Similarly, each node is considered
5320 * to depend on every other node in the same cluster to ensure
5321 * that the SCC consists of complete clusters.
5323 * Then the original SCCs that contain any of these nodes are marked
5324 * in c->scc_in_merge.
5326 static isl_stat
mark_merge_sccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
5327 int edge
, struct isl_clustering
*c
)
5329 struct isl_mark_merge_sccs_data data
;
5330 struct isl_tarjan_graph
*g
;
5333 for (i
= 0; i
< c
->n
; ++i
)
5334 c
->scc_in_merge
[i
] = 0;
5337 data
.scc_cluster
= c
->scc_cluster
;
5338 data
.src
= graph
->edge
[edge
].src
- graph
->node
;
5339 data
.dst
= graph
->edge
[edge
].dst
- graph
->node
;
5341 g
= isl_tarjan_graph_component(ctx
, graph
->n
, data
.dst
,
5342 &cluster_follows
, &data
);
5348 isl_die(ctx
, isl_error_internal
,
5349 "expecting at least two nodes in component",
5351 if (g
->order
[--i
] != -1)
5352 isl_die(ctx
, isl_error_internal
,
5353 "expecting end of component marker", goto error
);
5355 for (--i
; i
>= 0 && g
->order
[i
] != -1; --i
) {
5356 int scc
= graph
->node
[g
->order
[i
]].scc
;
5357 c
->scc_in_merge
[scc
] = 1;
5360 isl_tarjan_graph_free(g
);
5363 isl_tarjan_graph_free(g
);
5364 return isl_stat_error
;
5367 /* Construct the identifier "cluster_i".
5369 static __isl_give isl_id
*cluster_id(isl_ctx
*ctx
, int i
)
5373 snprintf(name
, sizeof(name
), "cluster_%d", i
);
5374 return isl_id_alloc(ctx
, name
, NULL
);
5377 /* Construct the space of the cluster with index "i" containing
5378 * the strongly connected component "scc".
5380 * In particular, construct a space called cluster_i with dimension equal
5381 * to the number of schedule rows in the current band of "scc".
5383 static __isl_give isl_space
*cluster_space(struct isl_sched_graph
*scc
, int i
)
5389 nvar
= scc
->n_total_row
- scc
->band_start
;
5390 space
= isl_space_copy(scc
->node
[0].space
);
5391 space
= isl_space_params(space
);
5392 space
= isl_space_set_from_params(space
);
5393 space
= isl_space_add_dims(space
, isl_dim_set
, nvar
);
5394 id
= cluster_id(isl_space_get_ctx(space
), i
);
5395 space
= isl_space_set_tuple_id(space
, isl_dim_set
, id
);
5400 /* Collect the domain of the graph for merging clusters.
5402 * In particular, for each cluster with first SCC "i", construct
5403 * a set in the space called cluster_i with dimension equal
5404 * to the number of schedule rows in the current band of the cluster.
5406 static __isl_give isl_union_set
*collect_domain(isl_ctx
*ctx
,
5407 struct isl_sched_graph
*graph
, struct isl_clustering
*c
)
5411 isl_union_set
*domain
;
5413 space
= isl_space_params_alloc(ctx
, 0);
5414 domain
= isl_union_set_empty(space
);
5416 for (i
= 0; i
< graph
->scc
; ++i
) {
5419 if (!c
->scc_in_merge
[i
])
5421 if (c
->scc_cluster
[i
] != i
)
5423 space
= cluster_space(&c
->scc
[i
], i
);
5424 domain
= isl_union_set_add_set(domain
, isl_set_universe(space
));
5430 /* Construct a map from the original instances to the corresponding
5431 * cluster instance in the current bands of the clusters in "c".
5433 static __isl_give isl_union_map
*collect_cluster_map(isl_ctx
*ctx
,
5434 struct isl_sched_graph
*graph
, struct isl_clustering
*c
)
5438 isl_union_map
*cluster_map
;
5440 space
= isl_space_params_alloc(ctx
, 0);
5441 cluster_map
= isl_union_map_empty(space
);
5442 for (i
= 0; i
< graph
->scc
; ++i
) {
5446 if (!c
->scc_in_merge
[i
])
5449 id
= cluster_id(ctx
, c
->scc_cluster
[i
]);
5450 start
= c
->scc
[i
].band_start
;
5451 n
= c
->scc
[i
].n_total_row
- start
;
5452 for (j
= 0; j
< c
->scc
[i
].n
; ++j
) {
5455 struct isl_sched_node
*node
= &c
->scc
[i
].node
[j
];
5457 ma
= node_extract_partial_schedule_multi_aff(node
,
5459 ma
= isl_multi_aff_set_tuple_id(ma
, isl_dim_out
,
5461 map
= isl_map_from_multi_aff(ma
);
5462 cluster_map
= isl_union_map_add_map(cluster_map
, map
);
5470 /* Add "umap" to the schedule constraints "sc" of all types of "edge"
5471 * that are not isl_edge_condition or isl_edge_conditional_validity.
5473 static __isl_give isl_schedule_constraints
*add_non_conditional_constraints(
5474 struct isl_sched_edge
*edge
, __isl_keep isl_union_map
*umap
,
5475 __isl_take isl_schedule_constraints
*sc
)
5477 enum isl_edge_type t
;
5482 for (t
= isl_edge_first
; t
<= isl_edge_last
; ++t
) {
5483 if (t
== isl_edge_condition
||
5484 t
== isl_edge_conditional_validity
)
5486 if (!is_type(edge
, t
))
5488 sc
= isl_schedule_constraints_add(sc
, t
,
5489 isl_union_map_copy(umap
));
5495 /* Add schedule constraints of types isl_edge_condition and
5496 * isl_edge_conditional_validity to "sc" by applying "umap" to
5497 * the domains of the wrapped relations in domain and range
5498 * of the corresponding tagged constraints of "edge".
5500 static __isl_give isl_schedule_constraints
*add_conditional_constraints(
5501 struct isl_sched_edge
*edge
, __isl_keep isl_union_map
*umap
,
5502 __isl_take isl_schedule_constraints
*sc
)
5504 enum isl_edge_type t
;
5505 isl_union_map
*tagged
;
5507 for (t
= isl_edge_condition
; t
<= isl_edge_conditional_validity
; ++t
) {
5508 if (!is_type(edge
, t
))
5510 if (t
== isl_edge_condition
)
5511 tagged
= isl_union_map_copy(edge
->tagged_condition
);
5513 tagged
= isl_union_map_copy(edge
->tagged_validity
);
5514 tagged
= isl_union_map_zip(tagged
);
5515 tagged
= isl_union_map_apply_domain(tagged
,
5516 isl_union_map_copy(umap
));
5517 tagged
= isl_union_map_zip(tagged
);
5518 sc
= isl_schedule_constraints_add(sc
, t
, tagged
);
5526 /* Given a mapping "cluster_map" from the original instances to
5527 * the cluster instances, add schedule constraints on the clusters
5528 * to "sc" corresponding to the original constraints represented by "edge".
5530 * For non-tagged dependence constraints, the cluster constraints
5531 * are obtained by applying "cluster_map" to the edge->map.
5533 * For tagged dependence constraints, "cluster_map" needs to be applied
5534 * to the domains of the wrapped relations in domain and range
5535 * of the tagged dependence constraints. Pick out the mappings
5536 * from these domains from "cluster_map" and construct their product.
5537 * This mapping can then be applied to the pair of domains.
5539 static __isl_give isl_schedule_constraints
*collect_edge_constraints(
5540 struct isl_sched_edge
*edge
, __isl_keep isl_union_map
*cluster_map
,
5541 __isl_take isl_schedule_constraints
*sc
)
5543 isl_union_map
*umap
;
5545 isl_union_set
*uset
;
5546 isl_union_map
*umap1
, *umap2
;
5551 umap
= isl_union_map_from_map(isl_map_copy(edge
->map
));
5552 umap
= isl_union_map_apply_domain(umap
,
5553 isl_union_map_copy(cluster_map
));
5554 umap
= isl_union_map_apply_range(umap
,
5555 isl_union_map_copy(cluster_map
));
5556 sc
= add_non_conditional_constraints(edge
, umap
, sc
);
5557 isl_union_map_free(umap
);
5559 if (!sc
|| (!is_condition(edge
) && !is_conditional_validity(edge
)))
5562 space
= isl_space_domain(isl_map_get_space(edge
->map
));
5563 uset
= isl_union_set_from_set(isl_set_universe(space
));
5564 umap1
= isl_union_map_copy(cluster_map
);
5565 umap1
= isl_union_map_intersect_domain(umap1
, uset
);
5566 space
= isl_space_range(isl_map_get_space(edge
->map
));
5567 uset
= isl_union_set_from_set(isl_set_universe(space
));
5568 umap2
= isl_union_map_copy(cluster_map
);
5569 umap2
= isl_union_map_intersect_domain(umap2
, uset
);
5570 umap
= isl_union_map_product(umap1
, umap2
);
5572 sc
= add_conditional_constraints(edge
, umap
, sc
);
5574 isl_union_map_free(umap
);
5578 /* Given a mapping "cluster_map" from the original instances to
5579 * the cluster instances, add schedule constraints on the clusters
5580 * to "sc" corresponding to all edges in "graph" between nodes that
5581 * belong to SCCs that are marked for merging in "scc_in_merge".
5583 static __isl_give isl_schedule_constraints
*collect_constraints(
5584 struct isl_sched_graph
*graph
, int *scc_in_merge
,
5585 __isl_keep isl_union_map
*cluster_map
,
5586 __isl_take isl_schedule_constraints
*sc
)
5590 for (i
= 0; i
< graph
->n_edge
; ++i
) {
5591 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
5593 if (!scc_in_merge
[edge
->src
->scc
])
5595 if (!scc_in_merge
[edge
->dst
->scc
])
5597 sc
= collect_edge_constraints(edge
, cluster_map
, sc
);
5603 /* Construct a dependence graph for scheduling clusters with respect
5604 * to each other and store the result in "merge_graph".
5605 * In particular, the nodes of the graph correspond to the schedule
5606 * dimensions of the current bands of those clusters that have been
5607 * marked for merging in "c".
5609 * First construct an isl_schedule_constraints object for this domain
5610 * by transforming the edges in "graph" to the domain.
5611 * Then initialize a dependence graph for scheduling from these
5614 static isl_stat
init_merge_graph(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
5615 struct isl_clustering
*c
, struct isl_sched_graph
*merge_graph
)
5617 isl_union_set
*domain
;
5618 isl_union_map
*cluster_map
;
5619 isl_schedule_constraints
*sc
;
5622 domain
= collect_domain(ctx
, graph
, c
);
5623 sc
= isl_schedule_constraints_on_domain(domain
);
5625 return isl_stat_error
;
5626 cluster_map
= collect_cluster_map(ctx
, graph
, c
);
5627 sc
= collect_constraints(graph
, c
->scc_in_merge
, cluster_map
, sc
);
5628 isl_union_map_free(cluster_map
);
5630 r
= graph_init(merge_graph
, sc
);
5632 isl_schedule_constraints_free(sc
);
5637 /* Compute the maximal number of remaining schedule rows that still need
5638 * to be computed for the nodes that belong to clusters with the maximal
5639 * dimension for the current band (i.e., the band that is to be merged).
5640 * Only clusters that are about to be merged are considered.
5641 * "maxvar" is the maximal dimension for the current band.
5642 * "c" contains information about the clusters.
5644 * Return the maximal number of remaining schedule rows or -1 on error.
5646 static int compute_maxvar_max_slack(int maxvar
, struct isl_clustering
*c
)
5652 for (i
= 0; i
< c
->n
; ++i
) {
5654 struct isl_sched_graph
*scc
;
5656 if (!c
->scc_in_merge
[i
])
5659 nvar
= scc
->n_total_row
- scc
->band_start
;
5662 for (j
= 0; j
< scc
->n
; ++j
) {
5663 struct isl_sched_node
*node
= &scc
->node
[j
];
5666 if (node_update_vmap(node
) < 0)
5668 slack
= node
->nvar
- node
->rank
;
5669 if (slack
> max_slack
)
5677 /* If there are any clusters where the dimension of the current band
5678 * (i.e., the band that is to be merged) is smaller than "maxvar" and
5679 * if there are any nodes in such a cluster where the number
5680 * of remaining schedule rows that still need to be computed
5681 * is greater than "max_slack", then return the smallest current band
5682 * dimension of all these clusters. Otherwise return the original value
5683 * of "maxvar". Return -1 in case of any error.
5684 * Only clusters that are about to be merged are considered.
5685 * "c" contains information about the clusters.
5687 static int limit_maxvar_to_slack(int maxvar
, int max_slack
,
5688 struct isl_clustering
*c
)
5692 for (i
= 0; i
< c
->n
; ++i
) {
5694 struct isl_sched_graph
*scc
;
5696 if (!c
->scc_in_merge
[i
])
5699 nvar
= scc
->n_total_row
- scc
->band_start
;
5702 for (j
= 0; j
< scc
->n
; ++j
) {
5703 struct isl_sched_node
*node
= &scc
->node
[j
];
5706 if (node_update_vmap(node
) < 0)
5708 slack
= node
->nvar
- node
->rank
;
5709 if (slack
> max_slack
) {
5719 /* Adjust merge_graph->maxvar based on the number of remaining schedule rows
5720 * that still need to be computed. In particular, if there is a node
5721 * in a cluster where the dimension of the current band is smaller
5722 * than merge_graph->maxvar, but the number of remaining schedule rows
5723 * is greater than that of any node in a cluster with the maximal
5724 * dimension for the current band (i.e., merge_graph->maxvar),
5725 * then adjust merge_graph->maxvar to the (smallest) current band dimension
5726 * of those clusters. Without this adjustment, the total number of
5727 * schedule dimensions would be increased, resulting in a skewed view
5728 * of the number of coincident dimensions.
5729 * "c" contains information about the clusters.
5731 * If the maximize_band_depth option is set and merge_graph->maxvar is reduced,
5732 * then there is no point in attempting any merge since it will be rejected
5733 * anyway. Set merge_graph->maxvar to zero in such cases.
5735 static isl_stat
adjust_maxvar_to_slack(isl_ctx
*ctx
,
5736 struct isl_sched_graph
*merge_graph
, struct isl_clustering
*c
)
5738 int max_slack
, maxvar
;
5740 max_slack
= compute_maxvar_max_slack(merge_graph
->maxvar
, c
);
5742 return isl_stat_error
;
5743 maxvar
= limit_maxvar_to_slack(merge_graph
->maxvar
, max_slack
, c
);
5745 return isl_stat_error
;
5747 if (maxvar
< merge_graph
->maxvar
) {
5748 if (isl_options_get_schedule_maximize_band_depth(ctx
))
5749 merge_graph
->maxvar
= 0;
5751 merge_graph
->maxvar
= maxvar
;
5757 /* Return the number of coincident dimensions in the current band of "graph",
5758 * where the nodes of "graph" are assumed to be scheduled by a single band.
5760 static int get_n_coincident(struct isl_sched_graph
*graph
)
5764 for (i
= graph
->band_start
; i
< graph
->n_total_row
; ++i
)
5765 if (!graph
->node
[0].coincident
[i
])
5768 return i
- graph
->band_start
;
5771 /* Should the clusters be merged based on the cluster schedule
5772 * in the current (and only) band of "merge_graph", given that
5773 * coincidence should be maximized?
5775 * If the number of coincident schedule dimensions in the merged band
5776 * would be less than the maximal number of coincident schedule dimensions
5777 * in any of the merged clusters, then the clusters should not be merged.
5779 static isl_bool
ok_to_merge_coincident(struct isl_clustering
*c
,
5780 struct isl_sched_graph
*merge_graph
)
5787 for (i
= 0; i
< c
->n
; ++i
) {
5788 if (!c
->scc_in_merge
[i
])
5790 n_coincident
= get_n_coincident(&c
->scc
[i
]);
5791 if (n_coincident
> max_coincident
)
5792 max_coincident
= n_coincident
;
5795 n_coincident
= get_n_coincident(merge_graph
);
5797 return n_coincident
>= max_coincident
;
5800 /* Return the transformation on "node" expressed by the current (and only)
5801 * band of "merge_graph" applied to the clusters in "c".
5803 * First find the representation of "node" in its SCC in "c" and
5804 * extract the transformation expressed by the current band.
5805 * Then extract the transformation applied by "merge_graph"
5806 * to the cluster to which this SCC belongs.
5807 * Combine the two to obtain the complete transformation on the node.
5809 * Note that the range of the first transformation is an anonymous space,
5810 * while the domain of the second is named "cluster_X". The range
5811 * of the former therefore needs to be adjusted before the two
5814 static __isl_give isl_map
*extract_node_transformation(isl_ctx
*ctx
,
5815 struct isl_sched_node
*node
, struct isl_clustering
*c
,
5816 struct isl_sched_graph
*merge_graph
)
5818 struct isl_sched_node
*scc_node
, *cluster_node
;
5822 isl_multi_aff
*ma
, *ma2
;
5824 scc_node
= graph_find_node(ctx
, &c
->scc
[node
->scc
], node
->space
);
5825 start
= c
->scc
[node
->scc
].band_start
;
5826 n
= c
->scc
[node
->scc
].n_total_row
- start
;
5827 ma
= node_extract_partial_schedule_multi_aff(scc_node
, start
, n
);
5828 space
= cluster_space(&c
->scc
[node
->scc
], c
->scc_cluster
[node
->scc
]);
5829 cluster_node
= graph_find_node(ctx
, merge_graph
, space
);
5830 if (space
&& !cluster_node
)
5831 isl_die(ctx
, isl_error_internal
, "unable to find cluster",
5832 space
= isl_space_free(space
));
5833 id
= isl_space_get_tuple_id(space
, isl_dim_set
);
5834 ma
= isl_multi_aff_set_tuple_id(ma
, isl_dim_out
, id
);
5835 isl_space_free(space
);
5836 n
= merge_graph
->n_total_row
;
5837 ma2
= node_extract_partial_schedule_multi_aff(cluster_node
, 0, n
);
5838 ma
= isl_multi_aff_pullback_multi_aff(ma2
, ma
);
5840 return isl_map_from_multi_aff(ma
);
5843 /* Give a set of distances "set", are they bounded by a small constant
5844 * in direction "pos"?
5845 * In practice, check if they are bounded by 2 by checking that there
5846 * are no elements with a value greater than or equal to 3 or
5847 * smaller than or equal to -3.
5849 static isl_bool
distance_is_bounded(__isl_keep isl_set
*set
, int pos
)
5855 return isl_bool_error
;
5857 test
= isl_set_copy(set
);
5858 test
= isl_set_lower_bound_si(test
, isl_dim_set
, pos
, 3);
5859 bounded
= isl_set_is_empty(test
);
5862 if (bounded
< 0 || !bounded
)
5865 test
= isl_set_copy(set
);
5866 test
= isl_set_upper_bound_si(test
, isl_dim_set
, pos
, -3);
5867 bounded
= isl_set_is_empty(test
);
5873 /* Does the set "set" have a fixed (but possible parametric) value
5874 * at dimension "pos"?
5876 static isl_bool
has_single_value(__isl_keep isl_set
*set
, int pos
)
5882 return isl_bool_error
;
5883 set
= isl_set_copy(set
);
5884 n
= isl_set_dim(set
, isl_dim_set
);
5885 set
= isl_set_project_out(set
, isl_dim_set
, pos
+ 1, n
- (pos
+ 1));
5886 set
= isl_set_project_out(set
, isl_dim_set
, 0, pos
);
5887 single
= isl_set_is_singleton(set
);
5893 /* Does "map" have a fixed (but possible parametric) value
5894 * at dimension "pos" of either its domain or its range?
5896 static isl_bool
has_singular_src_or_dst(__isl_keep isl_map
*map
, int pos
)
5901 set
= isl_map_domain(isl_map_copy(map
));
5902 single
= has_single_value(set
, pos
);
5905 if (single
< 0 || single
)
5908 set
= isl_map_range(isl_map_copy(map
));
5909 single
= has_single_value(set
, pos
);
5915 /* Does the edge "edge" from "graph" have bounded dependence distances
5916 * in the merged graph "merge_graph" of a selection of clusters in "c"?
5918 * Extract the complete transformations of the source and destination
5919 * nodes of the edge, apply them to the edge constraints and
5920 * compute the differences. Finally, check if these differences are bounded
5921 * in each direction.
5923 * If the dimension of the band is greater than the number of
5924 * dimensions that can be expected to be optimized by the edge
5925 * (based on its weight), then also allow the differences to be unbounded
5926 * in the remaining dimensions, but only if either the source or
5927 * the destination has a fixed value in that direction.
5928 * This allows a statement that produces values that are used by
5929 * several instances of another statement to be merged with that
5931 * However, merging such clusters will introduce an inherently
5932 * large proximity distance inside the merged cluster, meaning
5933 * that proximity distances will no longer be optimized in
5934 * subsequent merges. These merges are therefore only allowed
5935 * after all other possible merges have been tried.
5936 * The first time such a merge is encountered, the weight of the edge
5937 * is replaced by a negative weight. The second time (i.e., after
5938 * all merges over edges with a non-negative weight have been tried),
5939 * the merge is allowed.
5941 static isl_bool
has_bounded_distances(isl_ctx
*ctx
, struct isl_sched_edge
*edge
,
5942 struct isl_sched_graph
*graph
, struct isl_clustering
*c
,
5943 struct isl_sched_graph
*merge_graph
)
5950 map
= isl_map_copy(edge
->map
);
5951 t
= extract_node_transformation(ctx
, edge
->src
, c
, merge_graph
);
5952 map
= isl_map_apply_domain(map
, t
);
5953 t
= extract_node_transformation(ctx
, edge
->dst
, c
, merge_graph
);
5954 map
= isl_map_apply_range(map
, t
);
5955 dist
= isl_map_deltas(isl_map_copy(map
));
5957 bounded
= isl_bool_true
;
5958 n
= isl_set_dim(dist
, isl_dim_set
);
5959 n_slack
= n
- edge
->weight
;
5960 if (edge
->weight
< 0)
5961 n_slack
-= graph
->max_weight
+ 1;
5962 for (i
= 0; i
< n
; ++i
) {
5963 isl_bool bounded_i
, singular_i
;
5965 bounded_i
= distance_is_bounded(dist
, i
);
5970 if (edge
->weight
>= 0)
5971 bounded
= isl_bool_false
;
5975 singular_i
= has_singular_src_or_dst(map
, i
);
5980 bounded
= isl_bool_false
;
5983 if (!bounded
&& i
>= n
&& edge
->weight
>= 0)
5984 edge
->weight
-= graph
->max_weight
+ 1;
5992 return isl_bool_error
;
5995 /* Should the clusters be merged based on the cluster schedule
5996 * in the current (and only) band of "merge_graph"?
5997 * "graph" is the original dependence graph, while "c" records
5998 * which SCCs are involved in the latest merge.
6000 * In particular, is there at least one proximity constraint
6001 * that is optimized by the merge?
6003 * A proximity constraint is considered to be optimized
6004 * if the dependence distances are small.
6006 static isl_bool
ok_to_merge_proximity(isl_ctx
*ctx
,
6007 struct isl_sched_graph
*graph
, struct isl_clustering
*c
,
6008 struct isl_sched_graph
*merge_graph
)
6012 for (i
= 0; i
< graph
->n_edge
; ++i
) {
6013 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
6016 if (!is_proximity(edge
))
6018 if (!c
->scc_in_merge
[edge
->src
->scc
])
6020 if (!c
->scc_in_merge
[edge
->dst
->scc
])
6022 if (c
->scc_cluster
[edge
->dst
->scc
] ==
6023 c
->scc_cluster
[edge
->src
->scc
])
6025 bounded
= has_bounded_distances(ctx
, edge
, graph
, c
,
6027 if (bounded
< 0 || bounded
)
6031 return isl_bool_false
;
6034 /* Should the clusters be merged based on the cluster schedule
6035 * in the current (and only) band of "merge_graph"?
6036 * "graph" is the original dependence graph, while "c" records
6037 * which SCCs are involved in the latest merge.
6039 * If the current band is empty, then the clusters should not be merged.
6041 * If the band depth should be maximized and the merge schedule
6042 * is incomplete (meaning that the dimension of some of the schedule
6043 * bands in the original schedule will be reduced), then the clusters
6044 * should not be merged.
6046 * If the schedule_maximize_coincidence option is set, then check that
6047 * the number of coincident schedule dimensions is not reduced.
6049 * Finally, only allow the merge if at least one proximity
6050 * constraint is optimized.
6052 static isl_bool
ok_to_merge(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
6053 struct isl_clustering
*c
, struct isl_sched_graph
*merge_graph
)
6055 if (merge_graph
->n_total_row
== merge_graph
->band_start
)
6056 return isl_bool_false
;
6058 if (isl_options_get_schedule_maximize_band_depth(ctx
) &&
6059 merge_graph
->n_total_row
< merge_graph
->maxvar
)
6060 return isl_bool_false
;
6062 if (isl_options_get_schedule_maximize_coincidence(ctx
)) {
6065 ok
= ok_to_merge_coincident(c
, merge_graph
);
6070 return ok_to_merge_proximity(ctx
, graph
, c
, merge_graph
);
6073 /* Apply the schedule in "t_node" to the "n" rows starting at "first"
6074 * of the schedule in "node" and return the result.
6076 * That is, essentially compute
6078 * T * N(first:first+n-1)
6080 * taking into account the constant term and the parameter coefficients
6083 static __isl_give isl_mat
*node_transformation(isl_ctx
*ctx
,
6084 struct isl_sched_node
*t_node
, struct isl_sched_node
*node
,
6089 int n_row
, n_col
, n_param
, n_var
;
6091 n_param
= node
->nparam
;
6093 n_row
= isl_mat_rows(t_node
->sched
);
6094 n_col
= isl_mat_cols(node
->sched
);
6095 t
= isl_mat_alloc(ctx
, n_row
, n_col
);
6098 for (i
= 0; i
< n_row
; ++i
) {
6099 isl_seq_cpy(t
->row
[i
], t_node
->sched
->row
[i
], 1 + n_param
);
6100 isl_seq_clr(t
->row
[i
] + 1 + n_param
, n_var
);
6101 for (j
= 0; j
< n
; ++j
)
6102 isl_seq_addmul(t
->row
[i
],
6103 t_node
->sched
->row
[i
][1 + n_param
+ j
],
6104 node
->sched
->row
[first
+ j
],
6105 1 + n_param
+ n_var
);
6110 /* Apply the cluster schedule in "t_node" to the current band
6111 * schedule of the nodes in "graph".
6113 * In particular, replace the rows starting at band_start
6114 * by the result of applying the cluster schedule in "t_node"
6115 * to the original rows.
6117 * The coincidence of the schedule is determined by the coincidence
6118 * of the cluster schedule.
6120 static isl_stat
transform(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
6121 struct isl_sched_node
*t_node
)
6127 start
= graph
->band_start
;
6128 n
= graph
->n_total_row
- start
;
6130 n_new
= isl_mat_rows(t_node
->sched
);
6131 for (i
= 0; i
< graph
->n
; ++i
) {
6132 struct isl_sched_node
*node
= &graph
->node
[i
];
6135 t
= node_transformation(ctx
, t_node
, node
, start
, n
);
6136 node
->sched
= isl_mat_drop_rows(node
->sched
, start
, n
);
6137 node
->sched
= isl_mat_concat(node
->sched
, t
);
6138 node
->sched_map
= isl_map_free(node
->sched_map
);
6140 return isl_stat_error
;
6141 for (j
= 0; j
< n_new
; ++j
)
6142 node
->coincident
[start
+ j
] = t_node
->coincident
[j
];
6144 graph
->n_total_row
-= n
;
6146 graph
->n_total_row
+= n_new
;
6147 graph
->n_row
+= n_new
;
6152 /* Merge the clusters marked for merging in "c" into a single
6153 * cluster using the cluster schedule in the current band of "merge_graph".
6154 * The representative SCC for the new cluster is the SCC with
6155 * the smallest index.
6157 * The current band schedule of each SCC in the new cluster is obtained
6158 * by applying the schedule of the corresponding original cluster
6159 * to the original band schedule.
6160 * All SCCs in the new cluster have the same number of schedule rows.
6162 static isl_stat
merge(isl_ctx
*ctx
, struct isl_clustering
*c
,
6163 struct isl_sched_graph
*merge_graph
)
6169 for (i
= 0; i
< c
->n
; ++i
) {
6170 struct isl_sched_node
*node
;
6172 if (!c
->scc_in_merge
[i
])
6176 space
= cluster_space(&c
->scc
[i
], c
->scc_cluster
[i
]);
6178 return isl_stat_error
;
6179 node
= graph_find_node(ctx
, merge_graph
, space
);
6180 isl_space_free(space
);
6182 isl_die(ctx
, isl_error_internal
,
6183 "unable to find cluster",
6184 return isl_stat_error
);
6185 if (transform(ctx
, &c
->scc
[i
], node
) < 0)
6186 return isl_stat_error
;
6187 c
->scc_cluster
[i
] = cluster
;
6193 /* Try and merge the clusters of SCCs marked in c->scc_in_merge
6194 * by scheduling the current cluster bands with respect to each other.
6196 * Construct a dependence graph with a space for each cluster and
6197 * with the coordinates of each space corresponding to the schedule
6198 * dimensions of the current band of that cluster.
6199 * Construct a cluster schedule in this cluster dependence graph and
6200 * apply it to the current cluster bands if it is applicable
6201 * according to ok_to_merge.
6203 * If the number of remaining schedule dimensions in a cluster
6204 * with a non-maximal current schedule dimension is greater than
6205 * the number of remaining schedule dimensions in clusters
6206 * with a maximal current schedule dimension, then restrict
6207 * the number of rows to be computed in the cluster schedule
6208 * to the minimal such non-maximal current schedule dimension.
6209 * Do this by adjusting merge_graph.maxvar.
6211 * Return isl_bool_true if the clusters have effectively been merged
6212 * into a single cluster.
6214 * Note that since the standard scheduling algorithm minimizes the maximal
6215 * distance over proximity constraints, the proximity constraints between
6216 * the merged clusters may not be optimized any further than what is
6217 * sufficient to bring the distances within the limits of the internal
6218 * proximity constraints inside the individual clusters.
6219 * It may therefore make sense to perform an additional translation step
6220 * to bring the clusters closer to each other, while maintaining
6221 * the linear part of the merging schedule found using the standard
6222 * scheduling algorithm.
6224 static isl_bool
try_merge(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
6225 struct isl_clustering
*c
)
6227 struct isl_sched_graph merge_graph
= { 0 };
6230 if (init_merge_graph(ctx
, graph
, c
, &merge_graph
) < 0)
6233 if (compute_maxvar(&merge_graph
) < 0)
6235 if (adjust_maxvar_to_slack(ctx
, &merge_graph
,c
) < 0)
6237 if (compute_schedule_wcc_band(ctx
, &merge_graph
) < 0)
6239 merged
= ok_to_merge(ctx
, graph
, c
, &merge_graph
);
6240 if (merged
&& merge(ctx
, c
, &merge_graph
) < 0)
6243 graph_free(ctx
, &merge_graph
);
6246 graph_free(ctx
, &merge_graph
);
6247 return isl_bool_error
;
6250 /* Is there any edge marked "no_merge" between two SCCs that are
6251 * about to be merged (i.e., that are set in "scc_in_merge")?
6252 * "merge_edge" is the proximity edge along which the clusters of SCCs
6253 * are going to be merged.
6255 * If there is any edge between two SCCs with a negative weight,
6256 * while the weight of "merge_edge" is non-negative, then this
6257 * means that the edge was postponed. "merge_edge" should then
6258 * also be postponed since merging along the edge with negative weight should
6259 * be postponed until all edges with non-negative weight have been tried.
6260 * Replace the weight of "merge_edge" by a negative weight as well and
6261 * tell the caller not to attempt a merge.
6263 static int any_no_merge(struct isl_sched_graph
*graph
, int *scc_in_merge
,
6264 struct isl_sched_edge
*merge_edge
)
6268 for (i
= 0; i
< graph
->n_edge
; ++i
) {
6269 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
6271 if (!scc_in_merge
[edge
->src
->scc
])
6273 if (!scc_in_merge
[edge
->dst
->scc
])
6277 if (merge_edge
->weight
>= 0 && edge
->weight
< 0) {
6278 merge_edge
->weight
-= graph
->max_weight
+ 1;
6286 /* Merge the two clusters in "c" connected by the edge in "graph"
6287 * with index "edge" into a single cluster.
6288 * If it turns out to be impossible to merge these two clusters,
6289 * then mark the edge as "no_merge" such that it will not be
6292 * First mark all SCCs that need to be merged. This includes the SCCs
6293 * in the two clusters, but it may also include the SCCs
6294 * of intermediate clusters.
6295 * If there is already a no_merge edge between any pair of such SCCs,
6296 * then simply mark the current edge as no_merge as well.
6297 * Likewise, if any of those edges was postponed by has_bounded_distances,
6298 * then postpone the current edge as well.
6299 * Otherwise, try and merge the clusters and mark "edge" as "no_merge"
6300 * if the clusters did not end up getting merged, unless the non-merge
6301 * is due to the fact that the edge was postponed. This postponement
6302 * can be recognized by a change in weight (from non-negative to negative).
6304 static isl_stat
merge_clusters_along_edge(isl_ctx
*ctx
,
6305 struct isl_sched_graph
*graph
, int edge
, struct isl_clustering
*c
)
6308 int edge_weight
= graph
->edge
[edge
].weight
;
6310 if (mark_merge_sccs(ctx
, graph
, edge
, c
) < 0)
6311 return isl_stat_error
;
6313 if (any_no_merge(graph
, c
->scc_in_merge
, &graph
->edge
[edge
]))
6314 merged
= isl_bool_false
;
6316 merged
= try_merge(ctx
, graph
, c
);
6318 return isl_stat_error
;
6319 if (!merged
&& edge_weight
== graph
->edge
[edge
].weight
)
6320 graph
->edge
[edge
].no_merge
= 1;
6325 /* Does "node" belong to the cluster identified by "cluster"?
6327 static int node_cluster_exactly(struct isl_sched_node
*node
, int cluster
)
6329 return node
->cluster
== cluster
;
6332 /* Does "edge" connect two nodes belonging to the cluster
6333 * identified by "cluster"?
6335 static int edge_cluster_exactly(struct isl_sched_edge
*edge
, int cluster
)
6337 return edge
->src
->cluster
== cluster
&& edge
->dst
->cluster
== cluster
;
6340 /* Swap the schedule of "node1" and "node2".
6341 * Both nodes have been derived from the same node in a common parent graph.
6342 * Since the "coincident" field is shared with that node
6343 * in the parent graph, there is no need to also swap this field.
6345 static void swap_sched(struct isl_sched_node
*node1
,
6346 struct isl_sched_node
*node2
)
6351 sched
= node1
->sched
;
6352 node1
->sched
= node2
->sched
;
6353 node2
->sched
= sched
;
6355 sched_map
= node1
->sched_map
;
6356 node1
->sched_map
= node2
->sched_map
;
6357 node2
->sched_map
= sched_map
;
6360 /* Copy the current band schedule from the SCCs that form the cluster
6361 * with index "pos" to the actual cluster at position "pos".
6362 * By construction, the index of the first SCC that belongs to the cluster
6365 * The order of the nodes inside both the SCCs and the cluster
6366 * is assumed to be same as the order in the original "graph".
6368 * Since the SCC graphs will no longer be used after this function,
6369 * the schedules are actually swapped rather than copied.
6371 static isl_stat
copy_partial(struct isl_sched_graph
*graph
,
6372 struct isl_clustering
*c
, int pos
)
6376 c
->cluster
[pos
].n_total_row
= c
->scc
[pos
].n_total_row
;
6377 c
->cluster
[pos
].n_row
= c
->scc
[pos
].n_row
;
6378 c
->cluster
[pos
].maxvar
= c
->scc
[pos
].maxvar
;
6380 for (i
= 0; i
< graph
->n
; ++i
) {
6384 if (graph
->node
[i
].cluster
!= pos
)
6386 s
= graph
->node
[i
].scc
;
6387 k
= c
->scc_node
[s
]++;
6388 swap_sched(&c
->cluster
[pos
].node
[j
], &c
->scc
[s
].node
[k
]);
6389 if (c
->scc
[s
].maxvar
> c
->cluster
[pos
].maxvar
)
6390 c
->cluster
[pos
].maxvar
= c
->scc
[s
].maxvar
;
6397 /* Is there a (conditional) validity dependence from node[j] to node[i],
6398 * forcing node[i] to follow node[j] or do the nodes belong to the same
6401 static isl_bool
node_follows_strong_or_same_cluster(int i
, int j
, void *user
)
6403 struct isl_sched_graph
*graph
= user
;
6405 if (graph
->node
[i
].cluster
== graph
->node
[j
].cluster
)
6406 return isl_bool_true
;
6407 return graph_has_validity_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
6410 /* Extract the merged clusters of SCCs in "graph", sort them, and
6411 * store them in c->clusters. Update c->scc_cluster accordingly.
6413 * First keep track of the cluster containing the SCC to which a node
6414 * belongs in the node itself.
6415 * Then extract the clusters into c->clusters, copying the current
6416 * band schedule from the SCCs that belong to the cluster.
6417 * Do this only once per cluster.
6419 * Finally, topologically sort the clusters and update c->scc_cluster
6420 * to match the new scc numbering. While the SCCs were originally
6421 * sorted already, some SCCs that depend on some other SCCs may
6422 * have been merged with SCCs that appear before these other SCCs.
6423 * A reordering may therefore be required.
6425 static isl_stat
extract_clusters(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
6426 struct isl_clustering
*c
)
6430 for (i
= 0; i
< graph
->n
; ++i
)
6431 graph
->node
[i
].cluster
= c
->scc_cluster
[graph
->node
[i
].scc
];
6433 for (i
= 0; i
< graph
->scc
; ++i
) {
6434 if (c
->scc_cluster
[i
] != i
)
6436 if (extract_sub_graph(ctx
, graph
, &node_cluster_exactly
,
6437 &edge_cluster_exactly
, i
, &c
->cluster
[i
]) < 0)
6438 return isl_stat_error
;
6439 c
->cluster
[i
].src_scc
= -1;
6440 c
->cluster
[i
].dst_scc
= -1;
6441 if (copy_partial(graph
, c
, i
) < 0)
6442 return isl_stat_error
;
6445 if (detect_ccs(ctx
, graph
, &node_follows_strong_or_same_cluster
) < 0)
6446 return isl_stat_error
;
6447 for (i
= 0; i
< graph
->n
; ++i
)
6448 c
->scc_cluster
[graph
->node
[i
].scc
] = graph
->node
[i
].cluster
;
6453 /* Compute weights on the proximity edges of "graph" that can
6454 * be used by find_proximity to find the most appropriate
6455 * proximity edge to use to merge two clusters in "c".
6456 * The weights are also used by has_bounded_distances to determine
6457 * whether the merge should be allowed.
6458 * Store the maximum of the computed weights in graph->max_weight.
6460 * The computed weight is a measure for the number of remaining schedule
6461 * dimensions that can still be completely aligned.
6462 * In particular, compute the number of equalities between
6463 * input dimensions and output dimensions in the proximity constraints.
6464 * The directions that are already handled by outer schedule bands
6465 * are projected out prior to determining this number.
6467 * Edges that will never be considered by find_proximity are ignored.
6469 static isl_stat
compute_weights(struct isl_sched_graph
*graph
,
6470 struct isl_clustering
*c
)
6474 graph
->max_weight
= 0;
6476 for (i
= 0; i
< graph
->n_edge
; ++i
) {
6477 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
6478 struct isl_sched_node
*src
= edge
->src
;
6479 struct isl_sched_node
*dst
= edge
->dst
;
6480 isl_basic_map
*hull
;
6484 prox
= is_non_empty_proximity(edge
);
6486 return isl_stat_error
;
6489 if (bad_cluster(&c
->scc
[edge
->src
->scc
]) ||
6490 bad_cluster(&c
->scc
[edge
->dst
->scc
]))
6492 if (c
->scc_cluster
[edge
->dst
->scc
] ==
6493 c
->scc_cluster
[edge
->src
->scc
])
6496 hull
= isl_map_affine_hull(isl_map_copy(edge
->map
));
6497 hull
= isl_basic_map_transform_dims(hull
, isl_dim_in
, 0,
6498 isl_mat_copy(src
->vmap
));
6499 hull
= isl_basic_map_transform_dims(hull
, isl_dim_out
, 0,
6500 isl_mat_copy(dst
->vmap
));
6501 hull
= isl_basic_map_project_out(hull
,
6502 isl_dim_in
, 0, src
->rank
);
6503 hull
= isl_basic_map_project_out(hull
,
6504 isl_dim_out
, 0, dst
->rank
);
6505 hull
= isl_basic_map_remove_divs(hull
);
6506 n_in
= isl_basic_map_dim(hull
, isl_dim_in
);
6507 n_out
= isl_basic_map_dim(hull
, isl_dim_out
);
6508 hull
= isl_basic_map_drop_constraints_not_involving_dims(hull
,
6509 isl_dim_in
, 0, n_in
);
6510 hull
= isl_basic_map_drop_constraints_not_involving_dims(hull
,
6511 isl_dim_out
, 0, n_out
);
6513 return isl_stat_error
;
6514 edge
->weight
= isl_basic_map_n_equality(hull
);
6515 isl_basic_map_free(hull
);
6517 if (edge
->weight
> graph
->max_weight
)
6518 graph
->max_weight
= edge
->weight
;
6524 /* Call compute_schedule_finish_band on each of the clusters in "c"
6525 * in their topological order. This order is determined by the scc
6526 * fields of the nodes in "graph".
6527 * Combine the results in a sequence expressing the topological order.
6529 * If there is only one cluster left, then there is no need to introduce
6530 * a sequence node. Also, in this case, the cluster necessarily contains
6531 * the SCC at position 0 in the original graph and is therefore also
6532 * stored in the first cluster of "c".
6534 static __isl_give isl_schedule_node
*finish_bands_clustering(
6535 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
6536 struct isl_clustering
*c
)
6540 isl_union_set_list
*filters
;
6542 if (graph
->scc
== 1)
6543 return compute_schedule_finish_band(node
, &c
->cluster
[0], 0);
6545 ctx
= isl_schedule_node_get_ctx(node
);
6547 filters
= extract_sccs(ctx
, graph
);
6548 node
= isl_schedule_node_insert_sequence(node
, filters
);
6550 for (i
= 0; i
< graph
->scc
; ++i
) {
6551 int j
= c
->scc_cluster
[i
];
6552 node
= isl_schedule_node_child(node
, i
);
6553 node
= isl_schedule_node_child(node
, 0);
6554 node
= compute_schedule_finish_band(node
, &c
->cluster
[j
], 0);
6555 node
= isl_schedule_node_parent(node
);
6556 node
= isl_schedule_node_parent(node
);
6562 /* Compute a schedule for a connected dependence graph by first considering
6563 * each strongly connected component (SCC) in the graph separately and then
6564 * incrementally combining them into clusters.
6565 * Return the updated schedule node.
6567 * Initially, each cluster consists of a single SCC, each with its
6568 * own band schedule. The algorithm then tries to merge pairs
6569 * of clusters along a proximity edge until no more suitable
6570 * proximity edges can be found. During this merging, the schedule
6571 * is maintained in the individual SCCs.
6572 * After the merging is completed, the full resulting clusters
6573 * are extracted and in finish_bands_clustering,
6574 * compute_schedule_finish_band is called on each of them to integrate
6575 * the band into "node" and to continue the computation.
6577 * compute_weights initializes the weights that are used by find_proximity.
6579 static __isl_give isl_schedule_node
*compute_schedule_wcc_clustering(
6580 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
6583 struct isl_clustering c
;
6586 ctx
= isl_schedule_node_get_ctx(node
);
6588 if (clustering_init(ctx
, &c
, graph
) < 0)
6591 if (compute_weights(graph
, &c
) < 0)
6595 i
= find_proximity(graph
, &c
);
6598 if (i
>= graph
->n_edge
)
6600 if (merge_clusters_along_edge(ctx
, graph
, i
, &c
) < 0)
6604 if (extract_clusters(ctx
, graph
, &c
) < 0)
6607 node
= finish_bands_clustering(node
, graph
, &c
);
6609 clustering_free(ctx
, &c
);
6612 clustering_free(ctx
, &c
);
6613 return isl_schedule_node_free(node
);
6616 /* Compute a schedule for a connected dependence graph and return
6617 * the updated schedule node.
6619 * If Feautrier's algorithm is selected, we first recursively try to satisfy
6620 * as many validity dependences as possible. When all validity dependences
6621 * are satisfied we extend the schedule to a full-dimensional schedule.
6623 * Call compute_schedule_wcc_whole or compute_schedule_wcc_clustering
6624 * depending on whether the user has selected the option to try and
6625 * compute a schedule for the entire (weakly connected) component first.
6626 * If there is only a single strongly connected component (SCC), then
6627 * there is no point in trying to combine SCCs
6628 * in compute_schedule_wcc_clustering, so compute_schedule_wcc_whole
6629 * is called instead.
6631 static __isl_give isl_schedule_node
*compute_schedule_wcc(
6632 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
6639 ctx
= isl_schedule_node_get_ctx(node
);
6640 if (detect_sccs(ctx
, graph
) < 0)
6641 return isl_schedule_node_free(node
);
6643 if (compute_maxvar(graph
) < 0)
6644 return isl_schedule_node_free(node
);
6646 if (need_feautrier_step(ctx
, graph
))
6647 return compute_schedule_wcc_feautrier(node
, graph
);
6649 if (graph
->scc
<= 1 || isl_options_get_schedule_whole_component(ctx
))
6650 return compute_schedule_wcc_whole(node
, graph
);
6652 return compute_schedule_wcc_clustering(node
, graph
);
6655 /* Compute a schedule for each group of nodes identified by node->scc
6656 * separately and then combine them in a sequence node (or as set node
6657 * if graph->weak is set) inserted at position "node" of the schedule tree.
6658 * Return the updated schedule node.
6660 * If "wcc" is set then each of the groups belongs to a single
6661 * weakly connected component in the dependence graph so that
6662 * there is no need for compute_sub_schedule to look for weakly
6663 * connected components.
6665 static __isl_give isl_schedule_node
*compute_component_schedule(
6666 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
6671 isl_union_set_list
*filters
;
6675 ctx
= isl_schedule_node_get_ctx(node
);
6677 filters
= extract_sccs(ctx
, graph
);
6679 node
= isl_schedule_node_insert_set(node
, filters
);
6681 node
= isl_schedule_node_insert_sequence(node
, filters
);
6683 for (component
= 0; component
< graph
->scc
; ++component
) {
6684 node
= isl_schedule_node_child(node
, component
);
6685 node
= isl_schedule_node_child(node
, 0);
6686 node
= compute_sub_schedule(node
, ctx
, graph
,
6688 &edge_scc_exactly
, component
, wcc
);
6689 node
= isl_schedule_node_parent(node
);
6690 node
= isl_schedule_node_parent(node
);
6696 /* Compute a schedule for the given dependence graph and insert it at "node".
6697 * Return the updated schedule node.
6699 * We first check if the graph is connected (through validity and conditional
6700 * validity dependences) and, if not, compute a schedule
6701 * for each component separately.
6702 * If the schedule_serialize_sccs option is set, then we check for strongly
6703 * connected components instead and compute a separate schedule for
6704 * each such strongly connected component.
6706 static __isl_give isl_schedule_node
*compute_schedule(isl_schedule_node
*node
,
6707 struct isl_sched_graph
*graph
)
6714 ctx
= isl_schedule_node_get_ctx(node
);
6715 if (isl_options_get_schedule_serialize_sccs(ctx
)) {
6716 if (detect_sccs(ctx
, graph
) < 0)
6717 return isl_schedule_node_free(node
);
6719 if (detect_wccs(ctx
, graph
) < 0)
6720 return isl_schedule_node_free(node
);
6724 return compute_component_schedule(node
, graph
, 1);
6726 return compute_schedule_wcc(node
, graph
);
6729 /* Compute a schedule on sc->domain that respects the given schedule
6732 * In particular, the schedule respects all the validity dependences.
6733 * If the default isl scheduling algorithm is used, it tries to minimize
6734 * the dependence distances over the proximity dependences.
6735 * If Feautrier's scheduling algorithm is used, the proximity dependence
6736 * distances are only minimized during the extension to a full-dimensional
6739 * If there are any condition and conditional validity dependences,
6740 * then the conditional validity dependences may be violated inside
6741 * a tilable band, provided they have no adjacent non-local
6742 * condition dependences.
6744 __isl_give isl_schedule
*isl_schedule_constraints_compute_schedule(
6745 __isl_take isl_schedule_constraints
*sc
)
6747 isl_ctx
*ctx
= isl_schedule_constraints_get_ctx(sc
);
6748 struct isl_sched_graph graph
= { 0 };
6749 isl_schedule
*sched
;
6750 isl_schedule_node
*node
;
6751 isl_union_set
*domain
;
6753 sc
= isl_schedule_constraints_align_params(sc
);
6755 domain
= isl_schedule_constraints_get_domain(sc
);
6756 if (isl_union_set_n_set(domain
) == 0) {
6757 isl_schedule_constraints_free(sc
);
6758 return isl_schedule_from_domain(domain
);
6761 if (graph_init(&graph
, sc
) < 0)
6762 domain
= isl_union_set_free(domain
);
6764 node
= isl_schedule_node_from_domain(domain
);
6765 node
= isl_schedule_node_child(node
, 0);
6767 node
= compute_schedule(node
, &graph
);
6768 sched
= isl_schedule_node_get_schedule(node
);
6769 isl_schedule_node_free(node
);
6771 graph_free(ctx
, &graph
);
6772 isl_schedule_constraints_free(sc
);
6777 /* Compute a schedule for the given union of domains that respects
6778 * all the validity dependences and minimizes
6779 * the dependence distances over the proximity dependences.
6781 * This function is kept for backward compatibility.
6783 __isl_give isl_schedule
*isl_union_set_compute_schedule(
6784 __isl_take isl_union_set
*domain
,
6785 __isl_take isl_union_map
*validity
,
6786 __isl_take isl_union_map
*proximity
)
6788 isl_schedule_constraints
*sc
;
6790 sc
= isl_schedule_constraints_on_domain(domain
);
6791 sc
= isl_schedule_constraints_set_validity(sc
, validity
);
6792 sc
= isl_schedule_constraints_set_proximity(sc
, proximity
);
6794 return isl_schedule_constraints_compute_schedule(sc
);