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 columns of cmap represent a change of basis for the schedule
62 * coefficients; the first rank columns span the linear part of
64 * cinv is the inverse of cmap.
65 * ctrans is the transpose of cmap.
66 * start is the first variable in the LP problem in the sequences that
67 * represents the schedule coefficients of this node
68 * nvar is the dimension of the domain
69 * nparam is the number of parameters or 0 if we are not constructing
70 * a parametric schedule
72 * If compressed is set, then hull represents the constraints
73 * that were used to derive the compression, while compress and
74 * decompress map the original space to the compressed space and
77 * scc is the index of SCC (or WCC) this node belongs to
79 * "cluster" is only used inside extract_clusters and identifies
80 * the cluster of SCCs that the node belongs to.
82 * coincident contains a boolean for each of the rows of the schedule,
83 * indicating whether the corresponding scheduling dimension satisfies
84 * the coincidence constraints in the sense that the corresponding
85 * dependence distances are zero.
87 * If the schedule_treat_coalescing option is set, then
88 * "sizes" contains the sizes of the (compressed) instance set
89 * in each direction. If there is no fixed size in a given direction,
90 * then the corresponding size value is set to infinity.
91 * If the schedule_treat_coalescing option or the schedule_max_coefficient
92 * option is set, then "max" contains the maximal values for
93 * schedule coefficients of the (compressed) variables. If no bound
94 * needs to be imposed on a particular variable, then the corresponding
97 struct isl_sched_node
{
101 isl_multi_aff
*compress
;
102 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
].cmap
);
652 isl_mat_free(graph
->node
[i
].cinv
);
653 isl_mat_free(graph
->node
[i
].ctrans
);
655 free(graph
->node
[i
].coincident
);
656 isl_multi_val_free(graph
->node
[i
].sizes
);
657 isl_vec_free(graph
->node
[i
].max
);
662 for (i
= 0; i
< graph
->n_edge
; ++i
) {
663 isl_map_free(graph
->edge
[i
].map
);
664 isl_union_map_free(graph
->edge
[i
].tagged_condition
);
665 isl_union_map_free(graph
->edge
[i
].tagged_validity
);
669 for (i
= 0; i
<= isl_edge_last
; ++i
)
670 isl_hash_table_free(ctx
, graph
->edge_table
[i
]);
671 isl_hash_table_free(ctx
, graph
->node_table
);
672 isl_basic_set_free(graph
->lp
);
675 /* For each "set" on which this function is called, increment
676 * graph->n by one and update graph->maxvar.
678 static isl_stat
init_n_maxvar(__isl_take isl_set
*set
, void *user
)
680 struct isl_sched_graph
*graph
= user
;
681 int nvar
= isl_set_dim(set
, isl_dim_set
);
684 if (nvar
> graph
->maxvar
)
685 graph
->maxvar
= nvar
;
692 /* Compute the number of rows that should be allocated for the schedule.
693 * In particular, we need one row for each variable or one row
694 * for each basic map in the dependences.
695 * Note that it is practically impossible to exhaust both
696 * the number of dependences and the number of variables.
698 static isl_stat
compute_max_row(struct isl_sched_graph
*graph
,
699 __isl_keep isl_schedule_constraints
*sc
)
703 isl_union_set
*domain
;
707 domain
= isl_schedule_constraints_get_domain(sc
);
708 r
= isl_union_set_foreach_set(domain
, &init_n_maxvar
, graph
);
709 isl_union_set_free(domain
);
711 return isl_stat_error
;
712 n_edge
= isl_schedule_constraints_n_basic_map(sc
);
714 return isl_stat_error
;
715 graph
->max_row
= n_edge
+ graph
->maxvar
;
720 /* Does "bset" have any defining equalities for its set variables?
722 static isl_bool
has_any_defining_equality(__isl_keep isl_basic_set
*bset
)
727 return isl_bool_error
;
729 n
= isl_basic_set_dim(bset
, isl_dim_set
);
730 for (i
= 0; i
< n
; ++i
) {
733 has
= isl_basic_set_has_defining_equality(bset
, isl_dim_set
, i
,
739 return isl_bool_false
;
742 /* Set the entries of node->max to the value of the schedule_max_coefficient
745 static isl_stat
set_max_coefficient(isl_ctx
*ctx
, struct isl_sched_node
*node
)
749 max
= isl_options_get_schedule_max_coefficient(ctx
);
753 node
->max
= isl_vec_alloc(ctx
, node
->nvar
);
754 node
->max
= isl_vec_set_si(node
->max
, max
);
756 return isl_stat_error
;
761 /* Set the entries of node->max to the minimum of the schedule_max_coefficient
762 * option (if set) and half of the minimum of the sizes in the other
763 * dimensions. If the minimum of the sizes is one, half of the size
764 * is zero and this value is reset to 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_fdiv_q_ui(v
->el
[i
], v
->el
[i
], 2);
814 if (isl_int_is_zero(v
->el
[i
]))
815 isl_int_set_si(v
->el
[i
], 1);
822 return isl_stat_error
;
825 /* Compute and return the size of "set" in dimension "dim".
826 * The size is taken to be the difference in values for that variable
827 * for fixed values of the other variables.
828 * In particular, the variable is first isolated from the other variables
829 * in the range of a map
831 * [i_0, ..., i_dim-1, i_dim+1, ...] -> [i_dim]
833 * and then duplicated
835 * [i_0, ..., i_dim-1, i_dim+1, ...] -> [[i_dim] -> [i_dim']]
837 * The shared variables are then projected out and the maximal value
838 * of i_dim' - i_dim is computed.
840 static __isl_give isl_val
*compute_size(__isl_take isl_set
*set
, int dim
)
847 map
= isl_set_project_onto_map(set
, isl_dim_set
, dim
, 1);
848 map
= isl_map_project_out(map
, isl_dim_in
, dim
, 1);
849 map
= isl_map_range_product(map
, isl_map_copy(map
));
850 map
= isl_set_unwrap(isl_map_range(map
));
851 set
= isl_map_deltas(map
);
852 ls
= isl_local_space_from_space(isl_set_get_space(set
));
853 obj
= isl_aff_var_on_domain(ls
, isl_dim_set
, 0);
854 v
= isl_set_max_val(set
, obj
);
861 /* Compute the size of the instance set "set" of "node", after compression,
862 * as well as bounds on the corresponding coefficients, if needed.
864 * The sizes are needed when the schedule_treat_coalescing option is set.
865 * The bounds are needed when the schedule_treat_coalescing option or
866 * the schedule_max_coefficient option is set.
868 * If the schedule_treat_coalescing option is not set, then at most
869 * the bounds need to be set and this is done in set_max_coefficient.
870 * Otherwise, compress the domain if needed, compute the size
871 * in each direction and store the results in node->size.
872 * Finally, set the bounds on the coefficients based on the sizes
873 * and the schedule_max_coefficient option in compute_max_coefficient.
875 static isl_stat
compute_sizes_and_max(isl_ctx
*ctx
, struct isl_sched_node
*node
,
876 __isl_take isl_set
*set
)
881 if (!isl_options_get_schedule_treat_coalescing(ctx
)) {
883 return set_max_coefficient(ctx
, node
);
886 if (node
->compressed
)
887 set
= isl_set_preimage_multi_aff(set
,
888 isl_multi_aff_copy(node
->decompress
));
889 mv
= isl_multi_val_zero(isl_set_get_space(set
));
890 n
= isl_set_dim(set
, isl_dim_set
);
891 for (j
= 0; j
< n
; ++j
) {
894 v
= compute_size(isl_set_copy(set
), j
);
895 mv
= isl_multi_val_set_val(mv
, j
, v
);
900 return isl_stat_error
;
901 return compute_max_coefficient(ctx
, node
);
904 /* Add a new node to the graph representing the given instance set.
905 * "nvar" is the (possibly compressed) number of variables and
906 * may be smaller than then number of set variables in "set"
907 * if "compressed" is set.
908 * If "compressed" is set, then "hull" represents the constraints
909 * that were used to derive the compression, while "compress" and
910 * "decompress" map the original space to the compressed space and
912 * If "compressed" is not set, then "hull", "compress" and "decompress"
915 * Compute the size of the instance set and bounds on the coefficients,
918 static isl_stat
add_node(struct isl_sched_graph
*graph
,
919 __isl_take isl_set
*set
, int nvar
, int compressed
,
920 __isl_take isl_set
*hull
, __isl_take isl_multi_aff
*compress
,
921 __isl_take isl_multi_aff
*decompress
)
928 struct isl_sched_node
*node
;
931 return isl_stat_error
;
933 ctx
= isl_set_get_ctx(set
);
934 nparam
= isl_set_dim(set
, isl_dim_param
);
935 if (!ctx
->opt
->schedule_parametric
)
937 sched
= isl_mat_alloc(ctx
, 0, 1 + nparam
+ nvar
);
938 node
= &graph
->node
[graph
->n
];
940 space
= isl_set_get_space(set
);
943 node
->nparam
= nparam
;
945 node
->sched_map
= NULL
;
946 coincident
= isl_calloc_array(ctx
, int, graph
->max_row
);
947 node
->coincident
= coincident
;
948 node
->compressed
= compressed
;
950 node
->compress
= compress
;
951 node
->decompress
= decompress
;
952 if (compute_sizes_and_max(ctx
, node
, set
) < 0)
953 return isl_stat_error
;
955 if (!space
|| !sched
|| (graph
->max_row
&& !coincident
))
956 return isl_stat_error
;
957 if (compressed
&& (!hull
|| !compress
|| !decompress
))
958 return isl_stat_error
;
963 /* Construct an identifier for node "node", which will represent "set".
964 * The name of the identifier is either "compressed" or
965 * "compressed_<name>", with <name> the name of the space of "set".
966 * The user pointer of the identifier points to "node".
968 static __isl_give isl_id
*construct_compressed_id(__isl_keep isl_set
*set
,
969 struct isl_sched_node
*node
)
978 has_name
= isl_set_has_tuple_name(set
);
982 ctx
= isl_set_get_ctx(set
);
984 return isl_id_alloc(ctx
, "compressed", node
);
986 p
= isl_printer_to_str(ctx
);
987 name
= isl_set_get_tuple_name(set
);
988 p
= isl_printer_print_str(p
, "compressed_");
989 p
= isl_printer_print_str(p
, name
);
990 id_name
= isl_printer_get_str(p
);
993 id
= isl_id_alloc(ctx
, id_name
, node
);
999 /* Add a new node to the graph representing the given set.
1001 * If any of the set variables is defined by an equality, then
1002 * we perform variable compression such that we can perform
1003 * the scheduling on the compressed domain.
1004 * In this case, an identifier is used that references the new node
1005 * such that each compressed space is unique and
1006 * such that the node can be recovered from the compressed space.
1008 static isl_stat
extract_node(__isl_take isl_set
*set
, void *user
)
1011 isl_bool has_equality
;
1013 isl_basic_set
*hull
;
1016 isl_multi_aff
*compress
, *decompress
;
1017 struct isl_sched_graph
*graph
= user
;
1019 hull
= isl_set_affine_hull(isl_set_copy(set
));
1020 hull
= isl_basic_set_remove_divs(hull
);
1021 nvar
= isl_set_dim(set
, isl_dim_set
);
1022 has_equality
= has_any_defining_equality(hull
);
1024 if (has_equality
< 0)
1026 if (!has_equality
) {
1027 isl_basic_set_free(hull
);
1028 return add_node(graph
, set
, nvar
, 0, NULL
, NULL
, NULL
);
1031 id
= construct_compressed_id(set
, &graph
->node
[graph
->n
]);
1032 morph
= isl_basic_set_variable_compression_with_id(hull
,
1035 nvar
= isl_morph_ran_dim(morph
, isl_dim_set
);
1036 compress
= isl_morph_get_var_multi_aff(morph
);
1037 morph
= isl_morph_inverse(morph
);
1038 decompress
= isl_morph_get_var_multi_aff(morph
);
1039 isl_morph_free(morph
);
1041 hull_set
= isl_set_from_basic_set(hull
);
1042 return add_node(graph
, set
, nvar
, 1, hull_set
, compress
, decompress
);
1044 isl_basic_set_free(hull
);
1046 return isl_stat_error
;
1049 struct isl_extract_edge_data
{
1050 enum isl_edge_type type
;
1051 struct isl_sched_graph
*graph
;
1054 /* Merge edge2 into edge1, freeing the contents of edge2.
1055 * Return 0 on success and -1 on failure.
1057 * edge1 and edge2 are assumed to have the same value for the map field.
1059 static int merge_edge(struct isl_sched_edge
*edge1
,
1060 struct isl_sched_edge
*edge2
)
1062 edge1
->types
|= edge2
->types
;
1063 isl_map_free(edge2
->map
);
1065 if (is_condition(edge2
)) {
1066 if (!edge1
->tagged_condition
)
1067 edge1
->tagged_condition
= edge2
->tagged_condition
;
1069 edge1
->tagged_condition
=
1070 isl_union_map_union(edge1
->tagged_condition
,
1071 edge2
->tagged_condition
);
1074 if (is_conditional_validity(edge2
)) {
1075 if (!edge1
->tagged_validity
)
1076 edge1
->tagged_validity
= edge2
->tagged_validity
;
1078 edge1
->tagged_validity
=
1079 isl_union_map_union(edge1
->tagged_validity
,
1080 edge2
->tagged_validity
);
1083 if (is_condition(edge2
) && !edge1
->tagged_condition
)
1085 if (is_conditional_validity(edge2
) && !edge1
->tagged_validity
)
1091 /* Insert dummy tags in domain and range of "map".
1093 * In particular, if "map" is of the form
1099 * [A -> dummy_tag] -> [B -> dummy_tag]
1101 * where the dummy_tags are identical and equal to any dummy tags
1102 * introduced by any other call to this function.
1104 static __isl_give isl_map
*insert_dummy_tags(__isl_take isl_map
*map
)
1110 isl_set
*domain
, *range
;
1112 ctx
= isl_map_get_ctx(map
);
1114 id
= isl_id_alloc(ctx
, NULL
, &dummy
);
1115 space
= isl_space_params(isl_map_get_space(map
));
1116 space
= isl_space_set_from_params(space
);
1117 space
= isl_space_set_tuple_id(space
, isl_dim_set
, id
);
1118 space
= isl_space_map_from_set(space
);
1120 domain
= isl_map_wrap(map
);
1121 range
= isl_map_wrap(isl_map_universe(space
));
1122 map
= isl_map_from_domain_and_range(domain
, range
);
1123 map
= isl_map_zip(map
);
1128 /* Given that at least one of "src" or "dst" is compressed, return
1129 * a map between the spaces of these nodes restricted to the affine
1130 * hull that was used in the compression.
1132 static __isl_give isl_map
*extract_hull(struct isl_sched_node
*src
,
1133 struct isl_sched_node
*dst
)
1137 if (src
->compressed
)
1138 dom
= isl_set_copy(src
->hull
);
1140 dom
= isl_set_universe(isl_space_copy(src
->space
));
1141 if (dst
->compressed
)
1142 ran
= isl_set_copy(dst
->hull
);
1144 ran
= isl_set_universe(isl_space_copy(dst
->space
));
1146 return isl_map_from_domain_and_range(dom
, ran
);
1149 /* Intersect the domains of the nested relations in domain and range
1150 * of "tagged" with "map".
1152 static __isl_give isl_map
*map_intersect_domains(__isl_take isl_map
*tagged
,
1153 __isl_keep isl_map
*map
)
1157 tagged
= isl_map_zip(tagged
);
1158 set
= isl_map_wrap(isl_map_copy(map
));
1159 tagged
= isl_map_intersect_domain(tagged
, set
);
1160 tagged
= isl_map_zip(tagged
);
1164 /* Return a pointer to the node that lives in the domain space of "map"
1165 * or NULL if there is no such node.
1167 static struct isl_sched_node
*find_domain_node(isl_ctx
*ctx
,
1168 struct isl_sched_graph
*graph
, __isl_keep isl_map
*map
)
1170 struct isl_sched_node
*node
;
1173 space
= isl_space_domain(isl_map_get_space(map
));
1174 node
= graph_find_node(ctx
, graph
, space
);
1175 isl_space_free(space
);
1180 /* Return a pointer to the node that lives in the range space of "map"
1181 * or NULL if there is no such node.
1183 static struct isl_sched_node
*find_range_node(isl_ctx
*ctx
,
1184 struct isl_sched_graph
*graph
, __isl_keep isl_map
*map
)
1186 struct isl_sched_node
*node
;
1189 space
= isl_space_range(isl_map_get_space(map
));
1190 node
= graph_find_node(ctx
, graph
, space
);
1191 isl_space_free(space
);
1196 /* Add a new edge to the graph based on the given map
1197 * and add it to data->graph->edge_table[data->type].
1198 * If a dependence relation of a given type happens to be identical
1199 * to one of the dependence relations of a type that was added before,
1200 * then we don't create a new edge, but instead mark the original edge
1201 * as also representing a dependence of the current type.
1203 * Edges of type isl_edge_condition or isl_edge_conditional_validity
1204 * may be specified as "tagged" dependence relations. That is, "map"
1205 * may contain elements (i -> a) -> (j -> b), where i -> j denotes
1206 * the dependence on iterations and a and b are tags.
1207 * edge->map is set to the relation containing the elements i -> j,
1208 * while edge->tagged_condition and edge->tagged_validity contain
1209 * the union of all the "map" relations
1210 * for which extract_edge is called that result in the same edge->map.
1212 * If the source or the destination node is compressed, then
1213 * intersect both "map" and "tagged" with the constraints that
1214 * were used to construct the compression.
1215 * This ensures that there are no schedule constraints defined
1216 * outside of these domains, while the scheduler no longer has
1217 * any control over those outside parts.
1219 static isl_stat
extract_edge(__isl_take isl_map
*map
, void *user
)
1221 isl_ctx
*ctx
= isl_map_get_ctx(map
);
1222 struct isl_extract_edge_data
*data
= user
;
1223 struct isl_sched_graph
*graph
= data
->graph
;
1224 struct isl_sched_node
*src
, *dst
;
1225 struct isl_sched_edge
*edge
;
1226 isl_map
*tagged
= NULL
;
1228 if (data
->type
== isl_edge_condition
||
1229 data
->type
== isl_edge_conditional_validity
) {
1230 if (isl_map_can_zip(map
)) {
1231 tagged
= isl_map_copy(map
);
1232 map
= isl_set_unwrap(isl_map_domain(isl_map_zip(map
)));
1234 tagged
= insert_dummy_tags(isl_map_copy(map
));
1238 src
= find_domain_node(ctx
, graph
, map
);
1239 dst
= find_range_node(ctx
, graph
, map
);
1243 isl_map_free(tagged
);
1247 if (src
->compressed
|| dst
->compressed
) {
1249 hull
= extract_hull(src
, dst
);
1251 tagged
= map_intersect_domains(tagged
, hull
);
1252 map
= isl_map_intersect(map
, hull
);
1255 graph
->edge
[graph
->n_edge
].src
= src
;
1256 graph
->edge
[graph
->n_edge
].dst
= dst
;
1257 graph
->edge
[graph
->n_edge
].map
= map
;
1258 graph
->edge
[graph
->n_edge
].types
= 0;
1259 graph
->edge
[graph
->n_edge
].tagged_condition
= NULL
;
1260 graph
->edge
[graph
->n_edge
].tagged_validity
= NULL
;
1261 set_type(&graph
->edge
[graph
->n_edge
], data
->type
);
1262 if (data
->type
== isl_edge_condition
)
1263 graph
->edge
[graph
->n_edge
].tagged_condition
=
1264 isl_union_map_from_map(tagged
);
1265 if (data
->type
== isl_edge_conditional_validity
)
1266 graph
->edge
[graph
->n_edge
].tagged_validity
=
1267 isl_union_map_from_map(tagged
);
1269 edge
= graph_find_matching_edge(graph
, &graph
->edge
[graph
->n_edge
]);
1272 return isl_stat_error
;
1274 if (edge
== &graph
->edge
[graph
->n_edge
])
1275 return graph_edge_table_add(ctx
, graph
, data
->type
,
1276 &graph
->edge
[graph
->n_edge
++]);
1278 if (merge_edge(edge
, &graph
->edge
[graph
->n_edge
]) < 0)
1281 return graph_edge_table_add(ctx
, graph
, data
->type
, edge
);
1284 /* Initialize the schedule graph "graph" from the schedule constraints "sc".
1286 * The context is included in the domain before the nodes of
1287 * the graphs are extracted in order to be able to exploit
1288 * any possible additional equalities.
1289 * Note that this intersection is only performed locally here.
1291 static isl_stat
graph_init(struct isl_sched_graph
*graph
,
1292 __isl_keep isl_schedule_constraints
*sc
)
1295 isl_union_set
*domain
;
1297 struct isl_extract_edge_data data
;
1298 enum isl_edge_type i
;
1302 return isl_stat_error
;
1304 ctx
= isl_schedule_constraints_get_ctx(sc
);
1306 domain
= isl_schedule_constraints_get_domain(sc
);
1307 graph
->n
= isl_union_set_n_set(domain
);
1308 isl_union_set_free(domain
);
1310 if (graph_alloc(ctx
, graph
, graph
->n
,
1311 isl_schedule_constraints_n_map(sc
)) < 0)
1312 return isl_stat_error
;
1314 if (compute_max_row(graph
, sc
) < 0)
1315 return isl_stat_error
;
1318 domain
= isl_schedule_constraints_get_domain(sc
);
1319 domain
= isl_union_set_intersect_params(domain
,
1320 isl_schedule_constraints_get_context(sc
));
1321 r
= isl_union_set_foreach_set(domain
, &extract_node
, graph
);
1322 isl_union_set_free(domain
);
1324 return isl_stat_error
;
1325 if (graph_init_table(ctx
, graph
) < 0)
1326 return isl_stat_error
;
1327 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
1328 c
= isl_schedule_constraints_get(sc
, i
);
1329 graph
->max_edge
[i
] = isl_union_map_n_map(c
);
1330 isl_union_map_free(c
);
1332 return isl_stat_error
;
1334 if (graph_init_edge_tables(ctx
, graph
) < 0)
1335 return isl_stat_error
;
1338 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
1342 c
= isl_schedule_constraints_get(sc
, i
);
1343 r
= isl_union_map_foreach_map(c
, &extract_edge
, &data
);
1344 isl_union_map_free(c
);
1346 return isl_stat_error
;
1352 /* Check whether there is any dependence from node[j] to node[i]
1353 * or from node[i] to node[j].
1355 static isl_bool
node_follows_weak(int i
, int j
, void *user
)
1358 struct isl_sched_graph
*graph
= user
;
1360 f
= graph_has_any_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
1363 return graph_has_any_edge(graph
, &graph
->node
[i
], &graph
->node
[j
]);
1366 /* Check whether there is a (conditional) validity dependence from node[j]
1367 * to node[i], forcing node[i] to follow node[j].
1369 static isl_bool
node_follows_strong(int i
, int j
, void *user
)
1371 struct isl_sched_graph
*graph
= user
;
1373 return graph_has_validity_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
1376 /* Use Tarjan's algorithm for computing the strongly connected components
1377 * in the dependence graph only considering those edges defined by "follows".
1379 static int detect_ccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
1380 isl_bool (*follows
)(int i
, int j
, void *user
))
1383 struct isl_tarjan_graph
*g
= NULL
;
1385 g
= isl_tarjan_graph_init(ctx
, graph
->n
, follows
, graph
);
1393 while (g
->order
[i
] != -1) {
1394 graph
->node
[g
->order
[i
]].scc
= graph
->scc
;
1402 isl_tarjan_graph_free(g
);
1407 /* Apply Tarjan's algorithm to detect the strongly connected components
1408 * in the dependence graph.
1409 * Only consider the (conditional) validity dependences and clear "weak".
1411 static int detect_sccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
1414 return detect_ccs(ctx
, graph
, &node_follows_strong
);
1417 /* Apply Tarjan's algorithm to detect the (weakly) connected components
1418 * in the dependence graph.
1419 * Consider all dependences and set "weak".
1421 static int detect_wccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
1424 return detect_ccs(ctx
, graph
, &node_follows_weak
);
1427 static int cmp_scc(const void *a
, const void *b
, void *data
)
1429 struct isl_sched_graph
*graph
= data
;
1433 return graph
->node
[*i1
].scc
- graph
->node
[*i2
].scc
;
1436 /* Sort the elements of graph->sorted according to the corresponding SCCs.
1438 static int sort_sccs(struct isl_sched_graph
*graph
)
1440 return isl_sort(graph
->sorted
, graph
->n
, sizeof(int), &cmp_scc
, graph
);
1443 /* Given a dependence relation R from "node" to itself,
1444 * construct the set of coefficients of valid constraints for elements
1445 * in that dependence relation.
1446 * In particular, the result contains tuples of coefficients
1447 * c_0, c_n, c_x such that
1449 * c_0 + c_n n + c_x y - c_x x >= 0 for each (x,y) in R
1453 * c_0 + c_n n + c_x d >= 0 for each d in delta R = { y - x | (x,y) in R }
1455 * We choose here to compute the dual of delta R.
1456 * Alternatively, we could have computed the dual of R, resulting
1457 * in a set of tuples c_0, c_n, c_x, c_y, and then
1458 * plugged in (c_0, c_n, c_x, -c_x).
1460 * If "node" has been compressed, then the dependence relation
1461 * is also compressed before the set of coefficients is computed.
1463 static __isl_give isl_basic_set
*intra_coefficients(
1464 struct isl_sched_graph
*graph
, struct isl_sched_node
*node
,
1465 __isl_take isl_map
*map
)
1469 isl_basic_set
*coef
;
1470 isl_maybe_isl_basic_set m
;
1472 m
= isl_map_to_basic_set_try_get(graph
->intra_hmap
, map
);
1473 if (m
.valid
< 0 || m
.valid
) {
1478 key
= isl_map_copy(map
);
1479 if (node
->compressed
) {
1480 map
= isl_map_preimage_domain_multi_aff(map
,
1481 isl_multi_aff_copy(node
->decompress
));
1482 map
= isl_map_preimage_range_multi_aff(map
,
1483 isl_multi_aff_copy(node
->decompress
));
1485 delta
= isl_set_remove_divs(isl_map_deltas(map
));
1486 coef
= isl_set_coefficients(delta
);
1487 graph
->intra_hmap
= isl_map_to_basic_set_set(graph
->intra_hmap
, key
,
1488 isl_basic_set_copy(coef
));
1493 /* Given a dependence relation R, construct the set of coefficients
1494 * of valid constraints for elements in that dependence relation.
1495 * In particular, the result contains tuples of coefficients
1496 * c_0, c_n, c_x, c_y such that
1498 * c_0 + c_n n + c_x x + c_y y >= 0 for each (x,y) in R
1500 * If the source or destination nodes of "edge" have been compressed,
1501 * then the dependence relation is also compressed before
1502 * the set of coefficients is computed.
1504 static __isl_give isl_basic_set
*inter_coefficients(
1505 struct isl_sched_graph
*graph
, struct isl_sched_edge
*edge
,
1506 __isl_take isl_map
*map
)
1510 isl_basic_set
*coef
;
1511 isl_maybe_isl_basic_set m
;
1513 m
= isl_map_to_basic_set_try_get(graph
->inter_hmap
, map
);
1514 if (m
.valid
< 0 || m
.valid
) {
1519 key
= isl_map_copy(map
);
1520 if (edge
->src
->compressed
)
1521 map
= isl_map_preimage_domain_multi_aff(map
,
1522 isl_multi_aff_copy(edge
->src
->decompress
));
1523 if (edge
->dst
->compressed
)
1524 map
= isl_map_preimage_range_multi_aff(map
,
1525 isl_multi_aff_copy(edge
->dst
->decompress
));
1526 set
= isl_map_wrap(isl_map_remove_divs(map
));
1527 coef
= isl_set_coefficients(set
);
1528 graph
->inter_hmap
= isl_map_to_basic_set_set(graph
->inter_hmap
, key
,
1529 isl_basic_set_copy(coef
));
1534 /* Return the position of the coefficients of the variables in
1535 * the coefficients constraints "coef".
1537 * The space of "coef" is of the form
1539 * { coefficients[[cst, params] -> S] }
1541 * Return the position of S.
1543 static int coef_var_offset(__isl_keep isl_basic_set
*coef
)
1548 space
= isl_space_unwrap(isl_basic_set_get_space(coef
));
1549 offset
= isl_space_dim(space
, isl_dim_in
);
1550 isl_space_free(space
);
1555 /* Return the offset of the coefficients of the variables of "node"
1558 * Within each node, the coefficients have the following order:
1560 * - c_i_n (if parametric)
1561 * - positive and negative parts of c_i_x
1563 static int node_var_coef_offset(struct isl_sched_node
*node
)
1565 return node
->start
+ 1 + node
->nparam
;
1568 /* Return the position of the pair of variables encoding
1569 * coefficient "i" of "node".
1571 * The order of these variable pairs is the same as that of the coefficients,
1572 * with 2 variables per coefficient.
1574 static int node_var_coef_pos(struct isl_sched_node
*node
, int i
)
1576 return node_var_coef_offset(node
) + 2 * i
;
1579 /* Construct an isl_dim_map for mapping constraints on coefficients
1580 * for "node" to the corresponding positions in graph->lp.
1581 * "offset" is the offset of the coefficients for the variables
1582 * in the input constraints.
1583 * "s" is the sign of the mapping.
1585 * The input constraints are given in terms of the coefficients (c_0, c_n, c_x).
1586 * The mapping produced by this function essentially plugs in
1587 * (0, 0, c_i_x^+ - c_i_x^-) if s = 1 and
1588 * (0, 0, -c_i_x^+ + c_i_x^-) if s = -1.
1589 * In graph->lp, the c_i_x^- appear before their c_i_x^+ counterpart.
1591 * The caller can extend the mapping to also map the other coefficients
1592 * (and therefore not plug in 0).
1594 static __isl_give isl_dim_map
*intra_dim_map(isl_ctx
*ctx
,
1595 struct isl_sched_graph
*graph
, struct isl_sched_node
*node
,
1600 isl_dim_map
*dim_map
;
1605 total
= isl_basic_set_total_dim(graph
->lp
);
1606 pos
= node_var_coef_pos(node
, 0);
1607 dim_map
= isl_dim_map_alloc(ctx
, total
);
1608 isl_dim_map_range(dim_map
, pos
, 2, offset
, 1, node
->nvar
, -s
);
1609 isl_dim_map_range(dim_map
, pos
+ 1, 2, offset
, 1, node
->nvar
, s
);
1614 /* Construct an isl_dim_map for mapping constraints on coefficients
1615 * for "src" (node i) and "dst" (node j) to the corresponding positions
1617 * "offset" is the offset of the coefficients for the variables of "src"
1618 * in the input constraints.
1619 * "s" is the sign of the mapping.
1621 * The input constraints are given in terms of the coefficients
1622 * (c_0, c_n, c_x, c_y).
1623 * The mapping produced by this function essentially plugs in
1624 * (c_j_0 - c_i_0, c_j_n - c_i_n,
1625 * -(c_i_x^+ - c_i_x^-), c_j_x^+ - c_j_x^-) if s = 1 and
1626 * (-c_j_0 + c_i_0, -c_j_n + c_i_n,
1627 * c_i_x^+ - c_i_x^-, -(c_j_x^+ - c_j_x^-)) if s = -1.
1628 * In graph->lp, the c_*^- appear before their c_*^+ counterpart.
1630 * The caller can further extend the mapping.
1632 static __isl_give isl_dim_map
*inter_dim_map(isl_ctx
*ctx
,
1633 struct isl_sched_graph
*graph
, struct isl_sched_node
*src
,
1634 struct isl_sched_node
*dst
, int offset
, int s
)
1638 isl_dim_map
*dim_map
;
1643 total
= isl_basic_set_total_dim(graph
->lp
);
1644 dim_map
= isl_dim_map_alloc(ctx
, total
);
1646 isl_dim_map_range(dim_map
, dst
->start
, 0, 0, 0, 1, s
);
1647 isl_dim_map_range(dim_map
, dst
->start
+ 1, 1, 1, 1, dst
->nparam
, s
);
1648 pos
= node_var_coef_pos(dst
, 0);
1649 isl_dim_map_range(dim_map
, pos
, 2, offset
+ src
->nvar
, 1,
1651 isl_dim_map_range(dim_map
, pos
+ 1, 2, offset
+ src
->nvar
, 1,
1654 isl_dim_map_range(dim_map
, src
->start
, 0, 0, 0, 1, -s
);
1655 isl_dim_map_range(dim_map
, src
->start
+ 1, 1, 1, 1, src
->nparam
, -s
);
1656 pos
= node_var_coef_pos(src
, 0);
1657 isl_dim_map_range(dim_map
, pos
, 2, offset
, 1, src
->nvar
, s
);
1658 isl_dim_map_range(dim_map
, pos
+ 1, 2, offset
, 1, src
->nvar
, -s
);
1663 /* Add the constraints from "src" to "dst" using "dim_map",
1664 * after making sure there is enough room in "dst" for the extra constraints.
1666 static __isl_give isl_basic_set
*add_constraints_dim_map(
1667 __isl_take isl_basic_set
*dst
, __isl_take isl_basic_set
*src
,
1668 __isl_take isl_dim_map
*dim_map
)
1672 n_eq
= isl_basic_set_n_equality(src
);
1673 n_ineq
= isl_basic_set_n_inequality(src
);
1674 dst
= isl_basic_set_extend_constraints(dst
, n_eq
, n_ineq
);
1675 dst
= isl_basic_set_add_constraints_dim_map(dst
, src
, dim_map
);
1679 /* Add constraints to graph->lp that force validity for the given
1680 * dependence from a node i to itself.
1681 * That is, add constraints that enforce
1683 * (c_i_0 + c_i_n n + c_i_x y) - (c_i_0 + c_i_n n + c_i_x x)
1684 * = c_i_x (y - x) >= 0
1686 * for each (x,y) in R.
1687 * We obtain general constraints on coefficients (c_0, c_n, c_x)
1688 * of valid constraints for (y - x) and then plug in (0, 0, c_i_x^+ - c_i_x^-),
1689 * where c_i_x = c_i_x^+ - c_i_x^-, with c_i_x^+ and c_i_x^- non-negative.
1690 * In graph->lp, the c_i_x^- appear before their c_i_x^+ counterpart.
1692 * Actually, we do not construct constraints for the c_i_x themselves,
1693 * but for the coefficients of c_i_x written as a linear combination
1694 * of the columns in node->cmap.
1696 static isl_stat
add_intra_validity_constraints(struct isl_sched_graph
*graph
,
1697 struct isl_sched_edge
*edge
)
1700 isl_map
*map
= isl_map_copy(edge
->map
);
1701 isl_ctx
*ctx
= isl_map_get_ctx(map
);
1702 isl_dim_map
*dim_map
;
1703 isl_basic_set
*coef
;
1704 struct isl_sched_node
*node
= edge
->src
;
1706 coef
= intra_coefficients(graph
, node
, map
);
1708 offset
= coef_var_offset(coef
);
1710 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
1711 offset
, isl_mat_copy(node
->cmap
));
1713 return isl_stat_error
;
1715 dim_map
= intra_dim_map(ctx
, graph
, node
, offset
, 1);
1716 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
1721 /* Add constraints to graph->lp that force validity for the given
1722 * dependence from node i to node j.
1723 * That is, add constraints that enforce
1725 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) >= 0
1727 * for each (x,y) in R.
1728 * We obtain general constraints on coefficients (c_0, c_n, c_x, c_y)
1729 * of valid constraints for R and then plug in
1730 * (c_j_0 - c_i_0, c_j_n - c_i_n, -(c_i_x^+ - c_i_x^-), c_j_x^+ - c_j_x^-),
1731 * where c_* = c_*^+ - c_*^-, with c_*^+ and c_*^- non-negative.
1732 * In graph->lp, the c_*^- appear before their c_*^+ counterpart.
1734 * Actually, we do not construct constraints for the c_*_x themselves,
1735 * but for the coefficients of c_*_x written as a linear combination
1736 * of the columns in node->cmap.
1738 static isl_stat
add_inter_validity_constraints(struct isl_sched_graph
*graph
,
1739 struct isl_sched_edge
*edge
)
1744 isl_dim_map
*dim_map
;
1745 isl_basic_set
*coef
;
1746 struct isl_sched_node
*src
= edge
->src
;
1747 struct isl_sched_node
*dst
= edge
->dst
;
1750 return isl_stat_error
;
1752 map
= isl_map_copy(edge
->map
);
1753 ctx
= isl_map_get_ctx(map
);
1754 coef
= inter_coefficients(graph
, edge
, map
);
1756 offset
= coef_var_offset(coef
);
1758 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
1759 offset
, isl_mat_copy(src
->cmap
));
1760 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
1761 offset
+ src
->nvar
, isl_mat_copy(dst
->cmap
));
1763 return isl_stat_error
;
1765 dim_map
= inter_dim_map(ctx
, graph
, src
, dst
, offset
, 1);
1767 edge
->start
= graph
->lp
->n_ineq
;
1768 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
1770 return isl_stat_error
;
1771 edge
->end
= graph
->lp
->n_ineq
;
1776 /* Add constraints to graph->lp that bound the dependence distance for the given
1777 * dependence from a node i to itself.
1778 * If s = 1, we add the constraint
1780 * c_i_x (y - x) <= m_0 + m_n n
1784 * -c_i_x (y - x) + m_0 + m_n n >= 0
1786 * for each (x,y) in R.
1787 * If s = -1, we add the constraint
1789 * -c_i_x (y - x) <= m_0 + m_n n
1793 * c_i_x (y - x) + m_0 + m_n n >= 0
1795 * for each (x,y) in R.
1796 * We obtain general constraints on coefficients (c_0, c_n, c_x)
1797 * of valid constraints for (y - x) and then plug in (m_0, m_n, -s * c_i_x),
1798 * with each coefficient (except m_0) represented as a pair of non-negative
1801 * Actually, we do not construct constraints for the c_i_x themselves,
1802 * but for the coefficients of c_i_x written as a linear combination
1803 * of the columns in node->cmap.
1806 * If "local" is set, then we add constraints
1808 * c_i_x (y - x) <= 0
1812 * -c_i_x (y - x) <= 0
1814 * instead, forcing the dependence distance to be (less than or) equal to 0.
1815 * That is, we plug in (0, 0, -s * c_i_x),
1816 * Note that dependences marked local are treated as validity constraints
1817 * by add_all_validity_constraints and therefore also have
1818 * their distances bounded by 0 from below.
1820 static isl_stat
add_intra_proximity_constraints(struct isl_sched_graph
*graph
,
1821 struct isl_sched_edge
*edge
, int s
, int local
)
1825 isl_map
*map
= isl_map_copy(edge
->map
);
1826 isl_ctx
*ctx
= isl_map_get_ctx(map
);
1827 isl_dim_map
*dim_map
;
1828 isl_basic_set
*coef
;
1829 struct isl_sched_node
*node
= edge
->src
;
1831 coef
= intra_coefficients(graph
, node
, map
);
1833 offset
= coef_var_offset(coef
);
1835 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
1836 offset
, isl_mat_copy(node
->cmap
));
1838 return isl_stat_error
;
1840 nparam
= isl_space_dim(node
->space
, isl_dim_param
);
1841 dim_map
= intra_dim_map(ctx
, graph
, node
, offset
, -s
);
1844 isl_dim_map_range(dim_map
, 1, 0, 0, 0, 1, 1);
1845 isl_dim_map_range(dim_map
, 4, 2, 1, 1, nparam
, -1);
1846 isl_dim_map_range(dim_map
, 5, 2, 1, 1, nparam
, 1);
1848 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
1853 /* Add constraints to graph->lp that bound the dependence distance for the given
1854 * dependence from node i to node j.
1855 * If s = 1, we add the constraint
1857 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x)
1862 * -(c_j_0 + c_j_n n + c_j_x y) + (c_i_0 + c_i_n n + c_i_x x) +
1865 * for each (x,y) in R.
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 * We obtain general constraints on coefficients (c_0, c_n, c_x, c_y)
1878 * of valid constraints for R and then plug in
1879 * (m_0 - s*c_j_0 + s*c_i_0, m_n - s*c_j_n + s*c_i_n,
1880 * s*c_i_x, -s*c_j_x)
1881 * with each coefficient (except m_0, c_*_0 and c_*_n)
1882 * represented as a pair of non-negative coefficients.
1884 * Actually, we do not construct constraints for the c_*_x themselves,
1885 * but for the coefficients of c_*_x written as a linear combination
1886 * of the columns in node->cmap.
1889 * If "local" is set (and s = 1), then we add constraints
1891 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) <= 0
1895 * -((c_j_0 + c_j_n n + c_j_x y) + (c_i_0 + c_i_n n + c_i_x x)) >= 0
1897 * instead, forcing the dependence distance to be (less than or) equal to 0.
1898 * That is, we plug in
1899 * (-s*c_j_0 + s*c_i_0, -s*c_j_n + s*c_i_n, s*c_i_x, -s*c_j_x).
1900 * Note that dependences marked local are treated as validity constraints
1901 * by add_all_validity_constraints and therefore also have
1902 * their distances bounded by 0 from below.
1904 static isl_stat
add_inter_proximity_constraints(struct isl_sched_graph
*graph
,
1905 struct isl_sched_edge
*edge
, int s
, int local
)
1909 isl_map
*map
= isl_map_copy(edge
->map
);
1910 isl_ctx
*ctx
= isl_map_get_ctx(map
);
1911 isl_dim_map
*dim_map
;
1912 isl_basic_set
*coef
;
1913 struct isl_sched_node
*src
= edge
->src
;
1914 struct isl_sched_node
*dst
= edge
->dst
;
1916 coef
= inter_coefficients(graph
, edge
, map
);
1918 offset
= coef_var_offset(coef
);
1920 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
1921 offset
, isl_mat_copy(src
->cmap
));
1922 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
1923 offset
+ src
->nvar
, isl_mat_copy(dst
->cmap
));
1925 return isl_stat_error
;
1927 nparam
= isl_space_dim(src
->space
, isl_dim_param
);
1928 dim_map
= inter_dim_map(ctx
, graph
, src
, dst
, offset
, -s
);
1931 isl_dim_map_range(dim_map
, 1, 0, 0, 0, 1, 1);
1932 isl_dim_map_range(dim_map
, 4, 2, 1, 1, nparam
, -1);
1933 isl_dim_map_range(dim_map
, 5, 2, 1, 1, nparam
, 1);
1936 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
1941 /* Add all validity constraints to graph->lp.
1943 * An edge that is forced to be local needs to have its dependence
1944 * distances equal to zero. We take care of bounding them by 0 from below
1945 * here. add_all_proximity_constraints takes care of bounding them by 0
1948 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
1949 * Otherwise, we ignore them.
1951 static int add_all_validity_constraints(struct isl_sched_graph
*graph
,
1952 int use_coincidence
)
1956 for (i
= 0; i
< graph
->n_edge
; ++i
) {
1957 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
1960 local
= is_local(edge
) ||
1961 (is_coincidence(edge
) && use_coincidence
);
1962 if (!is_validity(edge
) && !local
)
1964 if (edge
->src
!= edge
->dst
)
1966 if (add_intra_validity_constraints(graph
, edge
) < 0)
1970 for (i
= 0; i
< graph
->n_edge
; ++i
) {
1971 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
1974 local
= is_local(edge
) ||
1975 (is_coincidence(edge
) && use_coincidence
);
1976 if (!is_validity(edge
) && !local
)
1978 if (edge
->src
== edge
->dst
)
1980 if (add_inter_validity_constraints(graph
, edge
) < 0)
1987 /* Add constraints to graph->lp that bound the dependence distance
1988 * for all dependence relations.
1989 * If a given proximity dependence is identical to a validity
1990 * dependence, then the dependence distance is already bounded
1991 * from below (by zero), so we only need to bound the distance
1992 * from above. (This includes the case of "local" dependences
1993 * which are treated as validity dependence by add_all_validity_constraints.)
1994 * Otherwise, we need to bound the distance both from above and from below.
1996 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
1997 * Otherwise, we ignore them.
1999 static int add_all_proximity_constraints(struct isl_sched_graph
*graph
,
2000 int use_coincidence
)
2004 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2005 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
2008 local
= is_local(edge
) ||
2009 (is_coincidence(edge
) && use_coincidence
);
2010 if (!is_proximity(edge
) && !local
)
2012 if (edge
->src
== edge
->dst
&&
2013 add_intra_proximity_constraints(graph
, edge
, 1, local
) < 0)
2015 if (edge
->src
!= edge
->dst
&&
2016 add_inter_proximity_constraints(graph
, edge
, 1, local
) < 0)
2018 if (is_validity(edge
) || local
)
2020 if (edge
->src
== edge
->dst
&&
2021 add_intra_proximity_constraints(graph
, edge
, -1, 0) < 0)
2023 if (edge
->src
!= edge
->dst
&&
2024 add_inter_proximity_constraints(graph
, edge
, -1, 0) < 0)
2031 /* Compute a basis for the rows in the linear part of the schedule
2032 * and extend this basis to a full basis. The remaining rows
2033 * can then be used to force linear independence from the rows
2036 * In particular, given the schedule rows S, we compute
2041 * with H the Hermite normal form of S. That is, all but the
2042 * first rank columns of H are zero and so each row in S is
2043 * a linear combination of the first rank rows of Q.
2044 * The matrix Q is then transposed because we will write the
2045 * coefficients of the next schedule row as a column vector s
2046 * and express this s as a linear combination s = Q c of the
2048 * Similarly, the matrix U is transposed such that we can
2049 * compute the coefficients c = U s from a schedule row s.
2051 static int node_update_cmap(struct isl_sched_node
*node
)
2054 int n_row
= isl_mat_rows(node
->sched
);
2056 H
= isl_mat_sub_alloc(node
->sched
, 0, n_row
,
2057 1 + node
->nparam
, node
->nvar
);
2059 H
= isl_mat_left_hermite(H
, 0, &U
, &Q
);
2060 isl_mat_free(node
->cmap
);
2061 isl_mat_free(node
->cinv
);
2062 isl_mat_free(node
->ctrans
);
2063 node
->ctrans
= isl_mat_copy(Q
);
2064 node
->cmap
= isl_mat_transpose(Q
);
2065 node
->cinv
= isl_mat_transpose(U
);
2066 node
->rank
= isl_mat_initial_non_zero_cols(H
);
2069 if (!node
->cmap
|| !node
->cinv
|| !node
->ctrans
|| node
->rank
< 0)
2074 /* Is "edge" marked as a validity or a conditional validity edge?
2076 static int is_any_validity(struct isl_sched_edge
*edge
)
2078 return is_validity(edge
) || is_conditional_validity(edge
);
2081 /* How many times should we count the constraints in "edge"?
2083 * We count as follows
2084 * validity -> 1 (>= 0)
2085 * validity+proximity -> 2 (>= 0 and upper bound)
2086 * proximity -> 2 (lower and upper bound)
2087 * local(+any) -> 2 (>= 0 and <= 0)
2089 * If an edge is only marked conditional_validity then it counts
2090 * as zero since it is only checked afterwards.
2092 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2093 * Otherwise, we ignore them.
2095 static int edge_multiplicity(struct isl_sched_edge
*edge
, int use_coincidence
)
2097 if (is_proximity(edge
) || is_local(edge
))
2099 if (use_coincidence
&& is_coincidence(edge
))
2101 if (is_validity(edge
))
2106 /* Count the number of equality and inequality constraints
2107 * that will be added for the given map.
2109 * "use_coincidence" is set if we should take into account coincidence edges.
2111 static isl_stat
count_map_constraints(struct isl_sched_graph
*graph
,
2112 struct isl_sched_edge
*edge
, __isl_take isl_map
*map
,
2113 int *n_eq
, int *n_ineq
, int use_coincidence
)
2115 isl_basic_set
*coef
;
2116 int f
= edge_multiplicity(edge
, use_coincidence
);
2123 if (edge
->src
== edge
->dst
)
2124 coef
= intra_coefficients(graph
, edge
->src
, map
);
2126 coef
= inter_coefficients(graph
, edge
, map
);
2128 return isl_stat_error
;
2129 *n_eq
+= f
* isl_basic_set_n_equality(coef
);
2130 *n_ineq
+= f
* isl_basic_set_n_inequality(coef
);
2131 isl_basic_set_free(coef
);
2136 /* Count the number of equality and inequality constraints
2137 * that will be added to the main lp problem.
2138 * We count as follows
2139 * validity -> 1 (>= 0)
2140 * validity+proximity -> 2 (>= 0 and upper bound)
2141 * proximity -> 2 (lower and upper bound)
2142 * local(+any) -> 2 (>= 0 and <= 0)
2144 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2145 * Otherwise, we ignore them.
2147 static int count_constraints(struct isl_sched_graph
*graph
,
2148 int *n_eq
, int *n_ineq
, int use_coincidence
)
2152 *n_eq
= *n_ineq
= 0;
2153 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2154 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
2155 isl_map
*map
= isl_map_copy(edge
->map
);
2157 if (count_map_constraints(graph
, edge
, map
, n_eq
, n_ineq
,
2158 use_coincidence
) < 0)
2165 /* Count the number of constraints that will be added by
2166 * add_bound_constant_constraints to bound the values of the constant terms
2167 * and increment *n_eq and *n_ineq accordingly.
2169 * In practice, add_bound_constant_constraints only adds inequalities.
2171 static isl_stat
count_bound_constant_constraints(isl_ctx
*ctx
,
2172 struct isl_sched_graph
*graph
, int *n_eq
, int *n_ineq
)
2174 if (isl_options_get_schedule_max_constant_term(ctx
) == -1)
2177 *n_ineq
+= graph
->n
;
2182 /* Add constraints to bound the values of the constant terms in the schedule,
2183 * if requested by the user.
2185 * The maximal value of the constant terms is defined by the option
2186 * "schedule_max_constant_term".
2188 * Within each node, the coefficients have the following order:
2190 * - c_i_n (if parametric)
2191 * - positive and negative parts of c_i_x
2193 static isl_stat
add_bound_constant_constraints(isl_ctx
*ctx
,
2194 struct isl_sched_graph
*graph
)
2200 max
= isl_options_get_schedule_max_constant_term(ctx
);
2204 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2206 for (i
= 0; i
< graph
->n
; ++i
) {
2207 struct isl_sched_node
*node
= &graph
->node
[i
];
2208 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2210 return isl_stat_error
;
2211 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
2212 isl_int_set_si(graph
->lp
->ineq
[k
][1 + node
->start
], -1);
2213 isl_int_set_si(graph
->lp
->ineq
[k
][0], max
);
2219 /* Count the number of constraints that will be added by
2220 * add_bound_coefficient_constraints and increment *n_eq and *n_ineq
2223 * In practice, add_bound_coefficient_constraints only adds inequalities.
2225 static int count_bound_coefficient_constraints(isl_ctx
*ctx
,
2226 struct isl_sched_graph
*graph
, int *n_eq
, int *n_ineq
)
2230 if (isl_options_get_schedule_max_coefficient(ctx
) == -1 &&
2231 !isl_options_get_schedule_treat_coalescing(ctx
))
2234 for (i
= 0; i
< graph
->n
; ++i
)
2235 *n_ineq
+= graph
->node
[i
].nparam
+ 2 * graph
->node
[i
].nvar
;
2240 /* Add constraints to graph->lp that bound the values of
2241 * the parameter schedule coefficients of "node" to "max" and
2242 * the variable schedule coefficients to the corresponding entry
2244 * In either case, a negative value means that no bound needs to be imposed.
2246 * For parameter coefficients, this amounts to adding a constraint
2254 * The variables coefficients are, however, not represented directly.
2255 * Instead, the variables coefficients c_x are written as a linear
2256 * combination c_x = cmap c_z of some other coefficients c_z,
2257 * which are in turn encoded as c_z = c_z^+ - c_z^-.
2258 * Let a_j be the elements of row i of node->cmap, then
2260 * -max_i <= c_x_i <= max_i
2264 * -max_i <= \sum_j a_j (c_z_j^+ - c_z_j^-) <= max_i
2268 * -\sum_j a_j (c_z_j^+ - c_z_j^-) + max_i >= 0
2269 * \sum_j a_j (c_z_j^+ - c_z_j^-) + max_i >= 0
2271 static isl_stat
node_add_coefficient_constraints(isl_ctx
*ctx
,
2272 struct isl_sched_graph
*graph
, struct isl_sched_node
*node
, int max
)
2278 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2280 for (j
= 0; j
< node
->nparam
; ++j
) {
2286 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2288 return isl_stat_error
;
2289 dim
= 1 + node
->start
+ 1 + j
;
2290 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
2291 isl_int_set_si(graph
->lp
->ineq
[k
][dim
], -1);
2292 isl_int_set_si(graph
->lp
->ineq
[k
][0], max
);
2295 ineq
= isl_vec_alloc(ctx
, 1 + total
);
2296 ineq
= isl_vec_clr(ineq
);
2298 return isl_stat_error
;
2299 for (i
= 0; i
< node
->nvar
; ++i
) {
2300 int pos
= 1 + node_var_coef_offset(node
);
2302 if (isl_int_is_neg(node
->max
->el
[i
]))
2305 for (j
= 0; j
< node
->nvar
; ++j
) {
2306 int pos_j
= 1 + node_var_coef_pos(node
, j
);
2308 isl_int_set(ineq
->el
[pos_j
], node
->cmap
->row
[i
][j
]);
2309 isl_int_neg(ineq
->el
[pos_j
], node
->cmap
->row
[i
][j
]);
2311 isl_int_set(ineq
->el
[0], node
->max
->el
[i
]);
2313 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2316 isl_seq_cpy(graph
->lp
->ineq
[k
], ineq
->el
, 1 + total
);
2318 isl_seq_neg(ineq
->el
+ pos
, ineq
->el
+ pos
, 2 * node
->nvar
);
2319 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2322 isl_seq_cpy(graph
->lp
->ineq
[k
], ineq
->el
, 1 + total
);
2329 return isl_stat_error
;
2332 /* Add constraints that bound the values of the variable and parameter
2333 * coefficients of the schedule.
2335 * The maximal value of the coefficients is defined by the option
2336 * 'schedule_max_coefficient' and the entries in node->max.
2337 * These latter entries are only set if either the schedule_max_coefficient
2338 * option or the schedule_treat_coalescing option is set.
2340 static isl_stat
add_bound_coefficient_constraints(isl_ctx
*ctx
,
2341 struct isl_sched_graph
*graph
)
2346 max
= isl_options_get_schedule_max_coefficient(ctx
);
2348 if (max
== -1 && !isl_options_get_schedule_treat_coalescing(ctx
))
2351 for (i
= 0; i
< graph
->n
; ++i
) {
2352 struct isl_sched_node
*node
= &graph
->node
[i
];
2354 if (node_add_coefficient_constraints(ctx
, graph
, node
, max
) < 0)
2355 return isl_stat_error
;
2361 /* Add a constraint to graph->lp that equates the value at position
2362 * "sum_pos" to the sum of the "n" values starting at "first".
2364 static isl_stat
add_sum_constraint(struct isl_sched_graph
*graph
,
2365 int sum_pos
, int first
, int n
)
2370 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2372 k
= isl_basic_set_alloc_equality(graph
->lp
);
2374 return isl_stat_error
;
2375 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2376 isl_int_set_si(graph
->lp
->eq
[k
][1 + sum_pos
], -1);
2377 for (i
= 0; i
< n
; ++i
)
2378 isl_int_set_si(graph
->lp
->eq
[k
][1 + first
+ i
], 1);
2383 /* Add a constraint to graph->lp that equates the value at position
2384 * "sum_pos" to the sum of the parameter coefficients of all nodes.
2386 * Within each node, the coefficients have the following order:
2388 * - c_i_n (if parametric)
2389 * - positive and negative parts of c_i_x
2391 static isl_stat
add_param_sum_constraint(struct isl_sched_graph
*graph
,
2397 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2399 k
= isl_basic_set_alloc_equality(graph
->lp
);
2401 return isl_stat_error
;
2402 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2403 isl_int_set_si(graph
->lp
->eq
[k
][1 + sum_pos
], -1);
2404 for (i
= 0; i
< graph
->n
; ++i
) {
2405 int pos
= 1 + graph
->node
[i
].start
+ 1;
2407 for (j
= 0; j
< graph
->node
[i
].nparam
; ++j
)
2408 isl_int_set_si(graph
->lp
->eq
[k
][pos
+ j
], 1);
2414 /* Add a constraint to graph->lp that equates the value at position
2415 * "sum_pos" to the sum of the variable coefficients of all nodes.
2417 * Within each node, the coefficients have the following order:
2419 * - c_i_n (if parametric)
2420 * - positive and negative parts of c_i_x
2422 static isl_stat
add_var_sum_constraint(struct isl_sched_graph
*graph
,
2428 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2430 k
= isl_basic_set_alloc_equality(graph
->lp
);
2432 return isl_stat_error
;
2433 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2434 isl_int_set_si(graph
->lp
->eq
[k
][1 + sum_pos
], -1);
2435 for (i
= 0; i
< graph
->n
; ++i
) {
2436 struct isl_sched_node
*node
= &graph
->node
[i
];
2437 int pos
= 1 + node_var_coef_offset(node
);
2439 for (j
= 0; j
< 2 * node
->nvar
; ++j
)
2440 isl_int_set_si(graph
->lp
->eq
[k
][pos
+ j
], 1);
2446 /* Construct an ILP problem for finding schedule coefficients
2447 * that result in non-negative, but small dependence distances
2448 * over all dependences.
2449 * In particular, the dependence distances over proximity edges
2450 * are bounded by m_0 + m_n n and we compute schedule coefficients
2451 * with small values (preferably zero) of m_n and m_0.
2453 * All variables of the ILP are non-negative. The actual coefficients
2454 * may be negative, so each coefficient is represented as the difference
2455 * of two non-negative variables. The negative part always appears
2456 * immediately before the positive part.
2457 * Other than that, the variables have the following order
2459 * - sum of positive and negative parts of m_n coefficients
2461 * - sum of all c_n coefficients
2462 * (unconstrained when computing non-parametric schedules)
2463 * - sum of positive and negative parts of all c_x coefficients
2464 * - positive and negative parts of m_n coefficients
2467 * - c_i_n (if parametric)
2468 * - positive and negative parts of c_i_x
2470 * The c_i_x are not represented directly, but through the columns of
2471 * node->cmap. That is, the computed values are for variable t_i_x
2472 * such that c_i_x = Q t_i_x with Q equal to node->cmap.
2474 * The constraints are those from the edges plus two or three equalities
2475 * to express the sums.
2477 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2478 * Otherwise, we ignore them.
2480 static isl_stat
setup_lp(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
2481 int use_coincidence
)
2491 parametric
= ctx
->opt
->schedule_parametric
;
2492 nparam
= isl_space_dim(graph
->node
[0].space
, isl_dim_param
);
2494 total
= param_pos
+ 2 * nparam
;
2495 for (i
= 0; i
< graph
->n
; ++i
) {
2496 struct isl_sched_node
*node
= &graph
->node
[graph
->sorted
[i
]];
2497 if (node_update_cmap(node
) < 0)
2498 return isl_stat_error
;
2499 node
->start
= total
;
2500 total
+= 1 + node
->nparam
+ 2 * node
->nvar
;
2503 if (count_constraints(graph
, &n_eq
, &n_ineq
, use_coincidence
) < 0)
2504 return isl_stat_error
;
2505 if (count_bound_constant_constraints(ctx
, graph
, &n_eq
, &n_ineq
) < 0)
2506 return isl_stat_error
;
2507 if (count_bound_coefficient_constraints(ctx
, graph
, &n_eq
, &n_ineq
) < 0)
2508 return isl_stat_error
;
2510 space
= isl_space_set_alloc(ctx
, 0, total
);
2511 isl_basic_set_free(graph
->lp
);
2512 n_eq
+= 2 + parametric
;
2514 graph
->lp
= isl_basic_set_alloc_space(space
, 0, n_eq
, n_ineq
);
2516 if (add_sum_constraint(graph
, 0, param_pos
, 2 * nparam
) < 0)
2517 return isl_stat_error
;
2518 if (parametric
&& add_param_sum_constraint(graph
, 2) < 0)
2519 return isl_stat_error
;
2520 if (add_var_sum_constraint(graph
, 3) < 0)
2521 return isl_stat_error
;
2522 if (add_bound_constant_constraints(ctx
, graph
) < 0)
2523 return isl_stat_error
;
2524 if (add_bound_coefficient_constraints(ctx
, graph
) < 0)
2525 return isl_stat_error
;
2526 if (add_all_validity_constraints(graph
, use_coincidence
) < 0)
2527 return isl_stat_error
;
2528 if (add_all_proximity_constraints(graph
, use_coincidence
) < 0)
2529 return isl_stat_error
;
2534 /* Analyze the conflicting constraint found by
2535 * isl_tab_basic_set_non_trivial_lexmin. If it corresponds to the validity
2536 * constraint of one of the edges between distinct nodes, living, moreover
2537 * in distinct SCCs, then record the source and sink SCC as this may
2538 * be a good place to cut between SCCs.
2540 static int check_conflict(int con
, void *user
)
2543 struct isl_sched_graph
*graph
= user
;
2545 if (graph
->src_scc
>= 0)
2548 con
-= graph
->lp
->n_eq
;
2550 if (con
>= graph
->lp
->n_ineq
)
2553 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2554 if (!is_validity(&graph
->edge
[i
]))
2556 if (graph
->edge
[i
].src
== graph
->edge
[i
].dst
)
2558 if (graph
->edge
[i
].src
->scc
== graph
->edge
[i
].dst
->scc
)
2560 if (graph
->edge
[i
].start
> con
)
2562 if (graph
->edge
[i
].end
<= con
)
2564 graph
->src_scc
= graph
->edge
[i
].src
->scc
;
2565 graph
->dst_scc
= graph
->edge
[i
].dst
->scc
;
2571 /* Check whether the next schedule row of the given node needs to be
2572 * non-trivial. Lower-dimensional domains may have some trivial rows,
2573 * but as soon as the number of remaining required non-trivial rows
2574 * is as large as the number or remaining rows to be computed,
2575 * all remaining rows need to be non-trivial.
2577 static int needs_row(struct isl_sched_graph
*graph
, struct isl_sched_node
*node
)
2579 return node
->nvar
- node
->rank
>= graph
->maxvar
- graph
->n_row
;
2582 /* Construct a non-triviality region with "n" directions
2583 * over "n_var" coefficients.
2584 * Each direction corresponds to a schedule coefficient,
2585 * where each schedule coefficient is encoded as the difference
2586 * of two non-negative variables, c^+_i - c^-_i
2587 * with c^-_i at position 2 * i and c^+_i at position 2 * i + 1.
2588 * The order of the directions is the same as that of the variables,
2589 * but if the number of variables is greater than the number of directions,
2590 * then the directions correspond to the last variables.
2592 static __isl_give isl_mat
*construct_trivial(isl_ctx
*ctx
, int n
, int n_var
)
2598 mat
= isl_mat_zero(ctx
, n
, 2 * n_var
);
2599 for (i
= 0; i
< n
; ++i
) {
2600 mat
= isl_mat_set_element_si(mat
, i
, 2 * (off
+ i
), -1);
2601 mat
= isl_mat_set_element_si(mat
, i
, 2 * (off
+ i
) + 1, 1);
2607 /* Solve the ILP problem constructed in setup_lp.
2608 * For each node such that all the remaining rows of its schedule
2609 * need to be non-trivial, we construct a non-triviality region.
2610 * This region imposes that the next row is independent of previous rows.
2611 * In particular the coefficients c_i_x are represented by t_i_x
2612 * variables with c_i_x = Q t_i_x and Q a unimodular matrix such that
2613 * its first columns span the rows of the previously computed part
2614 * of the schedule. The non-triviality region enforces that at least
2615 * one of the remaining components of t_i_x is non-zero, i.e.,
2616 * that the new schedule row depends on at least one of the remaining
2619 static __isl_give isl_vec
*solve_lp(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2625 for (i
= 0; i
< graph
->n
; ++i
) {
2626 struct isl_sched_node
*node
= &graph
->node
[i
];
2627 int skip
= node
->rank
;
2630 graph
->region
[i
].pos
= node_var_coef_offset(node
);
2631 if (needs_row(graph
, node
))
2632 trivial
= construct_trivial(ctx
, node
->nvar
- skip
,
2635 trivial
= isl_mat_zero(ctx
, 0, 0);
2636 graph
->region
[i
].trivial
= trivial
;
2638 lp
= isl_basic_set_copy(graph
->lp
);
2639 sol
= isl_tab_basic_set_non_trivial_lexmin(lp
, 2, graph
->n
,
2640 graph
->region
, &check_conflict
, graph
);
2641 for (i
= 0; i
< graph
->n
; ++i
)
2642 isl_mat_free(graph
->region
[i
].trivial
);
2646 /* Extract the coefficients for the variables of "node" from "sol".
2648 * Within each node, the coefficients have the following order:
2650 * - c_i_n (if parametric)
2651 * - positive and negative parts of c_i_x
2653 * The c_i_x^- appear before their c_i_x^+ counterpart.
2655 * Return c_i_x = c_i_x^+ - c_i_x^-
2657 static __isl_give isl_vec
*extract_var_coef(struct isl_sched_node
*node
,
2658 __isl_keep isl_vec
*sol
)
2666 csol
= isl_vec_alloc(isl_vec_get_ctx(sol
), node
->nvar
);
2670 pos
= 1 + node_var_coef_offset(node
);
2671 for (i
= 0; i
< node
->nvar
; ++i
)
2672 isl_int_sub(csol
->el
[i
],
2673 sol
->el
[pos
+ 2 * i
+ 1], sol
->el
[pos
+ 2 * i
]);
2678 /* Update the schedules of all nodes based on the given solution
2679 * of the LP problem.
2680 * The new row is added to the current band.
2681 * All possibly negative coefficients are encoded as a difference
2682 * of two non-negative variables, so we need to perform the subtraction
2683 * here. Moreover, if use_cmap is set, then the solution does
2684 * not refer to the actual coefficients c_i_x, but instead to variables
2685 * t_i_x such that c_i_x = Q t_i_x and Q is equal to node->cmap.
2686 * In this case, we then also need to perform this multiplication
2687 * to obtain the values of c_i_x.
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 use_cmap
, 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
];
2709 int pos
= node
->start
;
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 for (j
= 0; j
< 1 + node
->nparam
; ++j
)
2723 node
->sched
= isl_mat_set_element(node
->sched
,
2724 row
, j
, sol
->el
[1 + pos
+ j
]);
2726 csol
= isl_mat_vec_product(isl_mat_copy(node
->cmap
),
2730 for (j
= 0; j
< node
->nvar
; ++j
)
2731 node
->sched
= isl_mat_set_element(node
->sched
,
2732 row
, 1 + node
->nparam
+ j
, csol
->el
[j
]);
2733 node
->coincident
[graph
->n_total_row
] = coincident
;
2739 graph
->n_total_row
++;
2748 /* Convert row "row" of node->sched into an isl_aff living in "ls"
2749 * and return this isl_aff.
2751 static __isl_give isl_aff
*extract_schedule_row(__isl_take isl_local_space
*ls
,
2752 struct isl_sched_node
*node
, int row
)
2760 aff
= isl_aff_zero_on_domain(ls
);
2761 isl_mat_get_element(node
->sched
, row
, 0, &v
);
2762 aff
= isl_aff_set_constant(aff
, v
);
2763 for (j
= 0; j
< node
->nparam
; ++j
) {
2764 isl_mat_get_element(node
->sched
, row
, 1 + j
, &v
);
2765 aff
= isl_aff_set_coefficient(aff
, isl_dim_param
, j
, v
);
2767 for (j
= 0; j
< node
->nvar
; ++j
) {
2768 isl_mat_get_element(node
->sched
, row
, 1 + node
->nparam
+ j
, &v
);
2769 aff
= isl_aff_set_coefficient(aff
, isl_dim_in
, j
, v
);
2777 /* Convert the "n" rows starting at "first" of node->sched into a multi_aff
2778 * and return this multi_aff.
2780 * The result is defined over the uncompressed node domain.
2782 static __isl_give isl_multi_aff
*node_extract_partial_schedule_multi_aff(
2783 struct isl_sched_node
*node
, int first
, int n
)
2787 isl_local_space
*ls
;
2794 nrow
= isl_mat_rows(node
->sched
);
2795 if (node
->compressed
)
2796 space
= isl_multi_aff_get_domain_space(node
->decompress
);
2798 space
= isl_space_copy(node
->space
);
2799 ls
= isl_local_space_from_space(isl_space_copy(space
));
2800 space
= isl_space_from_domain(space
);
2801 space
= isl_space_add_dims(space
, isl_dim_out
, n
);
2802 ma
= isl_multi_aff_zero(space
);
2804 for (i
= first
; i
< first
+ n
; ++i
) {
2805 aff
= extract_schedule_row(isl_local_space_copy(ls
), node
, i
);
2806 ma
= isl_multi_aff_set_aff(ma
, i
- first
, aff
);
2809 isl_local_space_free(ls
);
2811 if (node
->compressed
)
2812 ma
= isl_multi_aff_pullback_multi_aff(ma
,
2813 isl_multi_aff_copy(node
->compress
));
2818 /* Convert node->sched into a multi_aff and return this multi_aff.
2820 * The result is defined over the uncompressed node domain.
2822 static __isl_give isl_multi_aff
*node_extract_schedule_multi_aff(
2823 struct isl_sched_node
*node
)
2827 nrow
= isl_mat_rows(node
->sched
);
2828 return node_extract_partial_schedule_multi_aff(node
, 0, nrow
);
2831 /* Convert node->sched into a map and return this map.
2833 * The result is cached in node->sched_map, which needs to be released
2834 * whenever node->sched is updated.
2835 * It is defined over the uncompressed node domain.
2837 static __isl_give isl_map
*node_extract_schedule(struct isl_sched_node
*node
)
2839 if (!node
->sched_map
) {
2842 ma
= node_extract_schedule_multi_aff(node
);
2843 node
->sched_map
= isl_map_from_multi_aff(ma
);
2846 return isl_map_copy(node
->sched_map
);
2849 /* Construct a map that can be used to update a dependence relation
2850 * based on the current schedule.
2851 * That is, construct a map expressing that source and sink
2852 * are executed within the same iteration of the current schedule.
2853 * This map can then be intersected with the dependence relation.
2854 * This is not the most efficient way, but this shouldn't be a critical
2857 static __isl_give isl_map
*specializer(struct isl_sched_node
*src
,
2858 struct isl_sched_node
*dst
)
2860 isl_map
*src_sched
, *dst_sched
;
2862 src_sched
= node_extract_schedule(src
);
2863 dst_sched
= node_extract_schedule(dst
);
2864 return isl_map_apply_range(src_sched
, isl_map_reverse(dst_sched
));
2867 /* Intersect the domains of the nested relations in domain and range
2868 * of "umap" with "map".
2870 static __isl_give isl_union_map
*intersect_domains(
2871 __isl_take isl_union_map
*umap
, __isl_keep isl_map
*map
)
2873 isl_union_set
*uset
;
2875 umap
= isl_union_map_zip(umap
);
2876 uset
= isl_union_set_from_set(isl_map_wrap(isl_map_copy(map
)));
2877 umap
= isl_union_map_intersect_domain(umap
, uset
);
2878 umap
= isl_union_map_zip(umap
);
2882 /* Update the dependence relation of the given edge based
2883 * on the current schedule.
2884 * If the dependence is carried completely by the current schedule, then
2885 * it is removed from the edge_tables. It is kept in the list of edges
2886 * as otherwise all edge_tables would have to be recomputed.
2888 static int update_edge(struct isl_sched_graph
*graph
,
2889 struct isl_sched_edge
*edge
)
2894 id
= specializer(edge
->src
, edge
->dst
);
2895 edge
->map
= isl_map_intersect(edge
->map
, isl_map_copy(id
));
2899 if (edge
->tagged_condition
) {
2900 edge
->tagged_condition
=
2901 intersect_domains(edge
->tagged_condition
, id
);
2902 if (!edge
->tagged_condition
)
2905 if (edge
->tagged_validity
) {
2906 edge
->tagged_validity
=
2907 intersect_domains(edge
->tagged_validity
, id
);
2908 if (!edge
->tagged_validity
)
2912 empty
= isl_map_plain_is_empty(edge
->map
);
2916 graph_remove_edge(graph
, edge
);
2925 /* Does the domain of "umap" intersect "uset"?
2927 static int domain_intersects(__isl_keep isl_union_map
*umap
,
2928 __isl_keep isl_union_set
*uset
)
2932 umap
= isl_union_map_copy(umap
);
2933 umap
= isl_union_map_intersect_domain(umap
, isl_union_set_copy(uset
));
2934 empty
= isl_union_map_is_empty(umap
);
2935 isl_union_map_free(umap
);
2937 return empty
< 0 ? -1 : !empty
;
2940 /* Does the range of "umap" intersect "uset"?
2942 static int range_intersects(__isl_keep isl_union_map
*umap
,
2943 __isl_keep isl_union_set
*uset
)
2947 umap
= isl_union_map_copy(umap
);
2948 umap
= isl_union_map_intersect_range(umap
, isl_union_set_copy(uset
));
2949 empty
= isl_union_map_is_empty(umap
);
2950 isl_union_map_free(umap
);
2952 return empty
< 0 ? -1 : !empty
;
2955 /* Are the condition dependences of "edge" local with respect to
2956 * the current schedule?
2958 * That is, are domain and range of the condition dependences mapped
2959 * to the same point?
2961 * In other words, is the condition false?
2963 static int is_condition_false(struct isl_sched_edge
*edge
)
2965 isl_union_map
*umap
;
2966 isl_map
*map
, *sched
, *test
;
2969 empty
= isl_union_map_is_empty(edge
->tagged_condition
);
2970 if (empty
< 0 || empty
)
2973 umap
= isl_union_map_copy(edge
->tagged_condition
);
2974 umap
= isl_union_map_zip(umap
);
2975 umap
= isl_union_set_unwrap(isl_union_map_domain(umap
));
2976 map
= isl_map_from_union_map(umap
);
2978 sched
= node_extract_schedule(edge
->src
);
2979 map
= isl_map_apply_domain(map
, sched
);
2980 sched
= node_extract_schedule(edge
->dst
);
2981 map
= isl_map_apply_range(map
, sched
);
2983 test
= isl_map_identity(isl_map_get_space(map
));
2984 local
= isl_map_is_subset(map
, test
);
2991 /* For each conditional validity constraint that is adjacent
2992 * to a condition with domain in condition_source or range in condition_sink,
2993 * turn it into an unconditional validity constraint.
2995 static int unconditionalize_adjacent_validity(struct isl_sched_graph
*graph
,
2996 __isl_take isl_union_set
*condition_source
,
2997 __isl_take isl_union_set
*condition_sink
)
3001 condition_source
= isl_union_set_coalesce(condition_source
);
3002 condition_sink
= isl_union_set_coalesce(condition_sink
);
3004 for (i
= 0; i
< graph
->n_edge
; ++i
) {
3006 isl_union_map
*validity
;
3008 if (!is_conditional_validity(&graph
->edge
[i
]))
3010 if (is_validity(&graph
->edge
[i
]))
3013 validity
= graph
->edge
[i
].tagged_validity
;
3014 adjacent
= domain_intersects(validity
, condition_sink
);
3015 if (adjacent
>= 0 && !adjacent
)
3016 adjacent
= range_intersects(validity
, condition_source
);
3022 set_validity(&graph
->edge
[i
]);
3025 isl_union_set_free(condition_source
);
3026 isl_union_set_free(condition_sink
);
3029 isl_union_set_free(condition_source
);
3030 isl_union_set_free(condition_sink
);
3034 /* Update the dependence relations of all edges based on the current schedule
3035 * and enforce conditional validity constraints that are adjacent
3036 * to satisfied condition constraints.
3038 * First check if any of the condition constraints are satisfied
3039 * (i.e., not local to the outer schedule) and keep track of
3040 * their domain and range.
3041 * Then update all dependence relations (which removes the non-local
3043 * Finally, if any condition constraints turned out to be satisfied,
3044 * then turn all adjacent conditional validity constraints into
3045 * unconditional validity constraints.
3047 static int update_edges(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
3051 isl_union_set
*source
, *sink
;
3053 source
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
3054 sink
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
3055 for (i
= 0; i
< graph
->n_edge
; ++i
) {
3057 isl_union_set
*uset
;
3058 isl_union_map
*umap
;
3060 if (!is_condition(&graph
->edge
[i
]))
3062 if (is_local(&graph
->edge
[i
]))
3064 local
= is_condition_false(&graph
->edge
[i
]);
3072 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_condition
);
3073 uset
= isl_union_map_domain(umap
);
3074 source
= isl_union_set_union(source
, uset
);
3076 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_condition
);
3077 uset
= isl_union_map_range(umap
);
3078 sink
= isl_union_set_union(sink
, uset
);
3081 for (i
= graph
->n_edge
- 1; i
>= 0; --i
) {
3082 if (update_edge(graph
, &graph
->edge
[i
]) < 0)
3087 return unconditionalize_adjacent_validity(graph
, source
, sink
);
3089 isl_union_set_free(source
);
3090 isl_union_set_free(sink
);
3093 isl_union_set_free(source
);
3094 isl_union_set_free(sink
);
3098 static void next_band(struct isl_sched_graph
*graph
)
3100 graph
->band_start
= graph
->n_total_row
;
3103 /* Return the union of the universe domains of the nodes in "graph"
3104 * that satisfy "pred".
3106 static __isl_give isl_union_set
*isl_sched_graph_domain(isl_ctx
*ctx
,
3107 struct isl_sched_graph
*graph
,
3108 int (*pred
)(struct isl_sched_node
*node
, int data
), int data
)
3114 for (i
= 0; i
< graph
->n
; ++i
)
3115 if (pred(&graph
->node
[i
], data
))
3119 isl_die(ctx
, isl_error_internal
,
3120 "empty component", return NULL
);
3122 set
= isl_set_universe(isl_space_copy(graph
->node
[i
].space
));
3123 dom
= isl_union_set_from_set(set
);
3125 for (i
= i
+ 1; i
< graph
->n
; ++i
) {
3126 if (!pred(&graph
->node
[i
], data
))
3128 set
= isl_set_universe(isl_space_copy(graph
->node
[i
].space
));
3129 dom
= isl_union_set_union(dom
, isl_union_set_from_set(set
));
3135 /* Return a list of unions of universe domains, where each element
3136 * in the list corresponds to an SCC (or WCC) indexed by node->scc.
3138 static __isl_give isl_union_set_list
*extract_sccs(isl_ctx
*ctx
,
3139 struct isl_sched_graph
*graph
)
3142 isl_union_set_list
*filters
;
3144 filters
= isl_union_set_list_alloc(ctx
, graph
->scc
);
3145 for (i
= 0; i
< graph
->scc
; ++i
) {
3148 dom
= isl_sched_graph_domain(ctx
, graph
, &node_scc_exactly
, i
);
3149 filters
= isl_union_set_list_add(filters
, dom
);
3155 /* Return a list of two unions of universe domains, one for the SCCs up
3156 * to and including graph->src_scc and another for the other SCCs.
3158 static __isl_give isl_union_set_list
*extract_split(isl_ctx
*ctx
,
3159 struct isl_sched_graph
*graph
)
3162 isl_union_set_list
*filters
;
3164 filters
= isl_union_set_list_alloc(ctx
, 2);
3165 dom
= isl_sched_graph_domain(ctx
, graph
,
3166 &node_scc_at_most
, graph
->src_scc
);
3167 filters
= isl_union_set_list_add(filters
, dom
);
3168 dom
= isl_sched_graph_domain(ctx
, graph
,
3169 &node_scc_at_least
, graph
->src_scc
+ 1);
3170 filters
= isl_union_set_list_add(filters
, dom
);
3175 /* Copy nodes that satisfy node_pred from the src dependence graph
3176 * to the dst dependence graph.
3178 static int copy_nodes(struct isl_sched_graph
*dst
, struct isl_sched_graph
*src
,
3179 int (*node_pred
)(struct isl_sched_node
*node
, int data
), int data
)
3184 for (i
= 0; i
< src
->n
; ++i
) {
3187 if (!node_pred(&src
->node
[i
], data
))
3191 dst
->node
[j
].space
= isl_space_copy(src
->node
[i
].space
);
3192 dst
->node
[j
].compressed
= src
->node
[i
].compressed
;
3193 dst
->node
[j
].hull
= isl_set_copy(src
->node
[i
].hull
);
3194 dst
->node
[j
].compress
=
3195 isl_multi_aff_copy(src
->node
[i
].compress
);
3196 dst
->node
[j
].decompress
=
3197 isl_multi_aff_copy(src
->node
[i
].decompress
);
3198 dst
->node
[j
].nvar
= src
->node
[i
].nvar
;
3199 dst
->node
[j
].nparam
= src
->node
[i
].nparam
;
3200 dst
->node
[j
].sched
= isl_mat_copy(src
->node
[i
].sched
);
3201 dst
->node
[j
].sched_map
= isl_map_copy(src
->node
[i
].sched_map
);
3202 dst
->node
[j
].coincident
= src
->node
[i
].coincident
;
3203 dst
->node
[j
].sizes
= isl_multi_val_copy(src
->node
[i
].sizes
);
3204 dst
->node
[j
].max
= isl_vec_copy(src
->node
[i
].max
);
3207 if (!dst
->node
[j
].space
|| !dst
->node
[j
].sched
)
3209 if (dst
->node
[j
].compressed
&&
3210 (!dst
->node
[j
].hull
|| !dst
->node
[j
].compress
||
3211 !dst
->node
[j
].decompress
))
3218 /* Copy non-empty edges that satisfy edge_pred from the src dependence graph
3219 * to the dst dependence graph.
3220 * If the source or destination node of the edge is not in the destination
3221 * graph, then it must be a backward proximity edge and it should simply
3224 static int copy_edges(isl_ctx
*ctx
, struct isl_sched_graph
*dst
,
3225 struct isl_sched_graph
*src
,
3226 int (*edge_pred
)(struct isl_sched_edge
*edge
, int data
), int data
)
3229 enum isl_edge_type t
;
3232 for (i
= 0; i
< src
->n_edge
; ++i
) {
3233 struct isl_sched_edge
*edge
= &src
->edge
[i
];
3235 isl_union_map
*tagged_condition
;
3236 isl_union_map
*tagged_validity
;
3237 struct isl_sched_node
*dst_src
, *dst_dst
;
3239 if (!edge_pred(edge
, data
))
3242 if (isl_map_plain_is_empty(edge
->map
))
3245 dst_src
= graph_find_node(ctx
, dst
, edge
->src
->space
);
3246 dst_dst
= graph_find_node(ctx
, dst
, edge
->dst
->space
);
3247 if (!dst_src
|| !dst_dst
) {
3248 if (is_validity(edge
) || is_conditional_validity(edge
))
3249 isl_die(ctx
, isl_error_internal
,
3250 "backward (conditional) validity edge",
3255 map
= isl_map_copy(edge
->map
);
3256 tagged_condition
= isl_union_map_copy(edge
->tagged_condition
);
3257 tagged_validity
= isl_union_map_copy(edge
->tagged_validity
);
3259 dst
->edge
[dst
->n_edge
].src
= dst_src
;
3260 dst
->edge
[dst
->n_edge
].dst
= dst_dst
;
3261 dst
->edge
[dst
->n_edge
].map
= map
;
3262 dst
->edge
[dst
->n_edge
].tagged_condition
= tagged_condition
;
3263 dst
->edge
[dst
->n_edge
].tagged_validity
= tagged_validity
;
3264 dst
->edge
[dst
->n_edge
].types
= edge
->types
;
3267 if (edge
->tagged_condition
&& !tagged_condition
)
3269 if (edge
->tagged_validity
&& !tagged_validity
)
3272 for (t
= isl_edge_first
; t
<= isl_edge_last
; ++t
) {
3274 graph_find_edge(src
, t
, edge
->src
, edge
->dst
))
3276 if (graph_edge_table_add(ctx
, dst
, t
,
3277 &dst
->edge
[dst
->n_edge
- 1]) < 0)
3285 /* Compute the maximal number of variables over all nodes.
3286 * This is the maximal number of linearly independent schedule
3287 * rows that we need to compute.
3288 * Just in case we end up in a part of the dependence graph
3289 * with only lower-dimensional domains, we make sure we will
3290 * compute the required amount of extra linearly independent rows.
3292 static int compute_maxvar(struct isl_sched_graph
*graph
)
3297 for (i
= 0; i
< graph
->n
; ++i
) {
3298 struct isl_sched_node
*node
= &graph
->node
[i
];
3301 if (node_update_cmap(node
) < 0)
3303 nvar
= node
->nvar
+ graph
->n_row
- node
->rank
;
3304 if (nvar
> graph
->maxvar
)
3305 graph
->maxvar
= nvar
;
3311 /* Extract the subgraph of "graph" that consists of the node satisfying
3312 * "node_pred" and the edges satisfying "edge_pred" and store
3313 * the result in "sub".
3315 static int extract_sub_graph(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
3316 int (*node_pred
)(struct isl_sched_node
*node
, int data
),
3317 int (*edge_pred
)(struct isl_sched_edge
*edge
, int data
),
3318 int data
, struct isl_sched_graph
*sub
)
3320 int i
, n
= 0, n_edge
= 0;
3323 for (i
= 0; i
< graph
->n
; ++i
)
3324 if (node_pred(&graph
->node
[i
], data
))
3326 for (i
= 0; i
< graph
->n_edge
; ++i
)
3327 if (edge_pred(&graph
->edge
[i
], data
))
3329 if (graph_alloc(ctx
, sub
, n
, n_edge
) < 0)
3331 if (copy_nodes(sub
, graph
, node_pred
, data
) < 0)
3333 if (graph_init_table(ctx
, sub
) < 0)
3335 for (t
= 0; t
<= isl_edge_last
; ++t
)
3336 sub
->max_edge
[t
] = graph
->max_edge
[t
];
3337 if (graph_init_edge_tables(ctx
, sub
) < 0)
3339 if (copy_edges(ctx
, sub
, graph
, edge_pred
, data
) < 0)
3341 sub
->n_row
= graph
->n_row
;
3342 sub
->max_row
= graph
->max_row
;
3343 sub
->n_total_row
= graph
->n_total_row
;
3344 sub
->band_start
= graph
->band_start
;
3349 static __isl_give isl_schedule_node
*compute_schedule(isl_schedule_node
*node
,
3350 struct isl_sched_graph
*graph
);
3351 static __isl_give isl_schedule_node
*compute_schedule_wcc(
3352 isl_schedule_node
*node
, struct isl_sched_graph
*graph
);
3354 /* Compute a schedule for a subgraph of "graph". In particular, for
3355 * the graph composed of nodes that satisfy node_pred and edges that
3356 * that satisfy edge_pred.
3357 * If the subgraph is known to consist of a single component, then wcc should
3358 * be set and then we call compute_schedule_wcc on the constructed subgraph.
3359 * Otherwise, we call compute_schedule, which will check whether the subgraph
3362 * The schedule is inserted at "node" and the updated schedule node
3365 static __isl_give isl_schedule_node
*compute_sub_schedule(
3366 __isl_take isl_schedule_node
*node
, isl_ctx
*ctx
,
3367 struct isl_sched_graph
*graph
,
3368 int (*node_pred
)(struct isl_sched_node
*node
, int data
),
3369 int (*edge_pred
)(struct isl_sched_edge
*edge
, int data
),
3372 struct isl_sched_graph split
= { 0 };
3374 if (extract_sub_graph(ctx
, graph
, node_pred
, edge_pred
, data
,
3379 node
= compute_schedule_wcc(node
, &split
);
3381 node
= compute_schedule(node
, &split
);
3383 graph_free(ctx
, &split
);
3386 graph_free(ctx
, &split
);
3387 return isl_schedule_node_free(node
);
3390 static int edge_scc_exactly(struct isl_sched_edge
*edge
, int scc
)
3392 return edge
->src
->scc
== scc
&& edge
->dst
->scc
== scc
;
3395 static int edge_dst_scc_at_most(struct isl_sched_edge
*edge
, int scc
)
3397 return edge
->dst
->scc
<= scc
;
3400 static int edge_src_scc_at_least(struct isl_sched_edge
*edge
, int scc
)
3402 return edge
->src
->scc
>= scc
;
3405 /* Reset the current band by dropping all its schedule rows.
3407 static int reset_band(struct isl_sched_graph
*graph
)
3412 drop
= graph
->n_total_row
- graph
->band_start
;
3413 graph
->n_total_row
-= drop
;
3414 graph
->n_row
-= drop
;
3416 for (i
= 0; i
< graph
->n
; ++i
) {
3417 struct isl_sched_node
*node
= &graph
->node
[i
];
3419 isl_map_free(node
->sched_map
);
3420 node
->sched_map
= NULL
;
3422 node
->sched
= isl_mat_drop_rows(node
->sched
,
3423 graph
->band_start
, drop
);
3432 /* Split the current graph into two parts and compute a schedule for each
3433 * part individually. In particular, one part consists of all SCCs up
3434 * to and including graph->src_scc, while the other part contains the other
3435 * SCCs. The split is enforced by a sequence node inserted at position "node"
3436 * in the schedule tree. Return the updated schedule node.
3437 * If either of these two parts consists of a sequence, then it is spliced
3438 * into the sequence containing the two parts.
3440 * The current band is reset. It would be possible to reuse
3441 * the previously computed rows as the first rows in the next
3442 * band, but recomputing them may result in better rows as we are looking
3443 * at a smaller part of the dependence graph.
3445 static __isl_give isl_schedule_node
*compute_split_schedule(
3446 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
3450 isl_union_set_list
*filters
;
3455 if (reset_band(graph
) < 0)
3456 return isl_schedule_node_free(node
);
3460 ctx
= isl_schedule_node_get_ctx(node
);
3461 filters
= extract_split(ctx
, graph
);
3462 node
= isl_schedule_node_insert_sequence(node
, filters
);
3463 node
= isl_schedule_node_child(node
, 1);
3464 node
= isl_schedule_node_child(node
, 0);
3466 node
= compute_sub_schedule(node
, ctx
, graph
,
3467 &node_scc_at_least
, &edge_src_scc_at_least
,
3468 graph
->src_scc
+ 1, 0);
3469 is_seq
= isl_schedule_node_get_type(node
) == isl_schedule_node_sequence
;
3470 node
= isl_schedule_node_parent(node
);
3471 node
= isl_schedule_node_parent(node
);
3473 node
= isl_schedule_node_sequence_splice_child(node
, 1);
3474 node
= isl_schedule_node_child(node
, 0);
3475 node
= isl_schedule_node_child(node
, 0);
3476 node
= compute_sub_schedule(node
, ctx
, graph
,
3477 &node_scc_at_most
, &edge_dst_scc_at_most
,
3479 is_seq
= isl_schedule_node_get_type(node
) == isl_schedule_node_sequence
;
3480 node
= isl_schedule_node_parent(node
);
3481 node
= isl_schedule_node_parent(node
);
3483 node
= isl_schedule_node_sequence_splice_child(node
, 0);
3488 /* Insert a band node at position "node" in the schedule tree corresponding
3489 * to the current band in "graph". Mark the band node permutable
3490 * if "permutable" is set.
3491 * The partial schedules and the coincidence property are extracted
3492 * from the graph nodes.
3493 * Return the updated schedule node.
3495 static __isl_give isl_schedule_node
*insert_current_band(
3496 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
3502 isl_multi_pw_aff
*mpa
;
3503 isl_multi_union_pw_aff
*mupa
;
3509 isl_die(isl_schedule_node_get_ctx(node
), isl_error_internal
,
3510 "graph should have at least one node",
3511 return isl_schedule_node_free(node
));
3513 start
= graph
->band_start
;
3514 end
= graph
->n_total_row
;
3517 ma
= node_extract_partial_schedule_multi_aff(&graph
->node
[0], start
, n
);
3518 mpa
= isl_multi_pw_aff_from_multi_aff(ma
);
3519 mupa
= isl_multi_union_pw_aff_from_multi_pw_aff(mpa
);
3521 for (i
= 1; i
< graph
->n
; ++i
) {
3522 isl_multi_union_pw_aff
*mupa_i
;
3524 ma
= node_extract_partial_schedule_multi_aff(&graph
->node
[i
],
3526 mpa
= isl_multi_pw_aff_from_multi_aff(ma
);
3527 mupa_i
= isl_multi_union_pw_aff_from_multi_pw_aff(mpa
);
3528 mupa
= isl_multi_union_pw_aff_union_add(mupa
, mupa_i
);
3530 node
= isl_schedule_node_insert_partial_schedule(node
, mupa
);
3532 for (i
= 0; i
< n
; ++i
)
3533 node
= isl_schedule_node_band_member_set_coincident(node
, i
,
3534 graph
->node
[0].coincident
[start
+ i
]);
3535 node
= isl_schedule_node_band_set_permutable(node
, permutable
);
3540 /* Update the dependence relations based on the current schedule,
3541 * add the current band to "node" and then continue with the computation
3543 * Return the updated schedule node.
3545 static __isl_give isl_schedule_node
*compute_next_band(
3546 __isl_take isl_schedule_node
*node
,
3547 struct isl_sched_graph
*graph
, int permutable
)
3554 ctx
= isl_schedule_node_get_ctx(node
);
3555 if (update_edges(ctx
, graph
) < 0)
3556 return isl_schedule_node_free(node
);
3557 node
= insert_current_band(node
, graph
, permutable
);
3560 node
= isl_schedule_node_child(node
, 0);
3561 node
= compute_schedule(node
, graph
);
3562 node
= isl_schedule_node_parent(node
);
3567 /* Add the constraints "coef" derived from an edge from "node" to itself
3568 * to graph->lp in order to respect the dependences and to try and carry them.
3569 * "pos" is the sequence number of the edge that needs to be carried.
3570 * "coef" represents general constraints on coefficients (c_0, c_n, c_x)
3571 * of valid constraints for (y - x) with x and y instances of the node.
3573 * The constraints added to graph->lp need to enforce
3575 * (c_j_0 + c_j_n n + c_j_x y) - (c_j_0 + c_j_n n + c_j_x x)
3576 * = c_j_x (y - x) >= e_i
3578 * for each (x,y) in the dependence relation of the edge.
3579 * That is, (-e_i, 0, c_j_x) needs to be plugged in for (c_0, c_n, c_x),
3580 * taking into account that each coefficient in c_j_x is represented
3581 * as a pair of non-negative coefficients.
3583 static isl_stat
add_intra_constraints(struct isl_sched_graph
*graph
,
3584 struct isl_sched_node
*node
, __isl_take isl_basic_set
*coef
, int pos
)
3588 isl_dim_map
*dim_map
;
3591 return isl_stat_error
;
3593 ctx
= isl_basic_set_get_ctx(coef
);
3594 offset
= coef_var_offset(coef
);
3595 dim_map
= intra_dim_map(ctx
, graph
, node
, offset
, 1);
3596 isl_dim_map_range(dim_map
, 3 + pos
, 0, 0, 0, 1, -1);
3597 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
3602 /* Add the constraints "coef" derived from an edge from "src" to "dst"
3603 * to graph->lp in order to respect the dependences and to try and carry them.
3604 * "pos" is the sequence number of the edge that needs to be carried.
3605 * "coef" represents general constraints on coefficients (c_0, c_n, c_x, c_y)
3606 * of valid constraints for (x, y) with x and y instances of "src" and "dst".
3608 * The constraints added to graph->lp need to enforce
3610 * (c_k_0 + c_k_n n + c_k_x y) - (c_j_0 + c_j_n n + c_j_x x) >= e_i
3612 * for each (x,y) in the dependence relation of the edge.
3614 * (-e_i + c_k_0 - c_j_0, c_k_n - c_j_n, -c_j_x, c_k_x)
3615 * needs to be plugged in for (c_0, c_n, c_x, c_y),
3616 * taking into account that each coefficient in c_j_x and c_k_x is represented
3617 * as a pair of non-negative coefficients.
3619 static isl_stat
add_inter_constraints(struct isl_sched_graph
*graph
,
3620 struct isl_sched_node
*src
, struct isl_sched_node
*dst
,
3621 __isl_take isl_basic_set
*coef
, int pos
)
3625 isl_dim_map
*dim_map
;
3628 return isl_stat_error
;
3630 ctx
= isl_basic_set_get_ctx(coef
);
3631 offset
= coef_var_offset(coef
);
3632 dim_map
= inter_dim_map(ctx
, graph
, src
, dst
, offset
, 1);
3633 isl_dim_map_range(dim_map
, 3 + pos
, 0, 0, 0, 1, -1);
3634 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
3639 /* Data structure collecting information used during the construction
3640 * of an LP for carrying dependences.
3642 * "intra" is a sequence of coefficient constraints for intra-node edges.
3643 * "inter" is a sequence of coefficient constraints for inter-node edges.
3646 isl_basic_set_list
*intra
;
3647 isl_basic_set_list
*inter
;
3650 /* Free all the data stored in "carry".
3652 static void isl_carry_clear(struct isl_carry
*carry
)
3654 isl_basic_set_list_free(carry
->intra
);
3655 isl_basic_set_list_free(carry
->inter
);
3658 /* Return a pointer to the node in "graph" that lives in "space".
3659 * If the requested node has been compressed, then "space"
3660 * corresponds to the compressed space.
3662 * First try and see if "space" is the space of an uncompressed node.
3663 * If so, return that node.
3664 * Otherwise, "space" was constructed by construct_compressed_id and
3665 * contains a user pointer pointing to the node in the tuple id.
3667 static struct isl_sched_node
*graph_find_compressed_node(isl_ctx
*ctx
,
3668 struct isl_sched_graph
*graph
, __isl_keep isl_space
*space
)
3671 struct isl_sched_node
*node
;
3676 node
= graph_find_node(ctx
, graph
, space
);
3680 id
= isl_space_get_tuple_id(space
, isl_dim_set
);
3681 node
= isl_id_get_user(id
);
3687 if (!(node
>= &graph
->node
[0] && node
< &graph
->node
[graph
->n
]))
3688 isl_die(ctx
, isl_error_internal
,
3689 "space points to invalid node", return NULL
);
3694 /* Internal data structure for add_all_constraints.
3696 * "graph" is the schedule constraint graph for which an LP problem
3697 * is being constructed.
3698 * "pos" is the position of the next edge that needs to be carried.
3700 struct isl_add_all_constraints_data
{
3702 struct isl_sched_graph
*graph
;
3706 /* Add the constraints "coef" derived from an edge from a node to itself
3707 * to data->graph->lp in order to respect the dependences and
3708 * to try and carry them.
3710 * The space of "coef" is of the form
3712 * coefficients[[c_cst, c_n] -> S[c_x]]
3714 * with S[c_x] the (compressed) space of the node.
3715 * Extract the node from the space and call add_intra_constraints.
3717 static isl_stat
lp_add_intra(__isl_take isl_basic_set
*coef
, void *user
)
3719 struct isl_add_all_constraints_data
*data
= user
;
3721 struct isl_sched_node
*node
;
3723 space
= isl_basic_set_get_space(coef
);
3724 space
= isl_space_range(isl_space_unwrap(space
));
3725 node
= graph_find_compressed_node(data
->ctx
, data
->graph
, space
);
3726 isl_space_free(space
);
3727 return add_intra_constraints(data
->graph
, node
, coef
, data
->pos
++);
3730 /* Add the constraints "coef" derived from an edge from a node j
3731 * to a node k to data->graph->lp in order to respect the dependences and
3732 * to try and carry them.
3734 * The space of "coef" is of the form
3736 * coefficients[[c_cst, c_n] -> [S_j[c_x] -> S_k[c_y]]]
3738 * with S_j[c_x] and S_k[c_y] the (compressed) spaces of the nodes.
3739 * Extract the nodes from the space and call add_inter_constraints.
3741 static isl_stat
lp_add_inter(__isl_take isl_basic_set
*coef
, void *user
)
3743 struct isl_add_all_constraints_data
*data
= user
;
3744 isl_space
*space
, *dom
;
3745 struct isl_sched_node
*src
, *dst
;
3747 space
= isl_basic_set_get_space(coef
);
3748 space
= isl_space_unwrap(isl_space_range(isl_space_unwrap(space
)));
3749 dom
= isl_space_domain(isl_space_copy(space
));
3750 src
= graph_find_compressed_node(data
->ctx
, data
->graph
, dom
);
3751 isl_space_free(dom
);
3752 space
= isl_space_range(space
);
3753 dst
= graph_find_compressed_node(data
->ctx
, data
->graph
, space
);
3754 isl_space_free(space
);
3756 return add_inter_constraints(data
->graph
, src
, dst
, coef
, data
->pos
++);
3759 /* Add constraints to graph->lp that force all (conditional) validity
3760 * dependences to be respected and attempt to carry them.
3761 * "intra" is the sequence of coefficient constraints for intra-node edges.
3762 * "inter" is the sequence of coefficient constraints for inter-node edges.
3764 static isl_stat
add_all_constraints(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
3765 __isl_keep isl_basic_set_list
*intra
,
3766 __isl_keep isl_basic_set_list
*inter
)
3768 struct isl_add_all_constraints_data data
= { ctx
, graph
};
3771 if (isl_basic_set_list_foreach(intra
, &lp_add_intra
, &data
) < 0)
3772 return isl_stat_error
;
3773 if (isl_basic_set_list_foreach(inter
, &lp_add_inter
, &data
) < 0)
3774 return isl_stat_error
;
3778 /* Internal data structure for count_all_constraints
3779 * for keeping track of the number of equality and inequality constraints.
3781 struct isl_sched_count
{
3786 /* Add the number of equality and inequality constraints of "bset"
3787 * to data->n_eq and data->n_ineq.
3789 static isl_stat
bset_update_count(__isl_take isl_basic_set
*bset
, void *user
)
3791 struct isl_sched_count
*data
= user
;
3793 data
->n_eq
+= isl_basic_set_n_equality(bset
);
3794 data
->n_ineq
+= isl_basic_set_n_inequality(bset
);
3795 isl_basic_set_free(bset
);
3800 /* Count the number of equality and inequality constraints
3801 * that will be added to the carry_lp problem.
3802 * We count each edge exactly once.
3803 * "intra" is the sequence of coefficient constraints for intra-node edges.
3804 * "inter" is the sequence of coefficient constraints for inter-node edges.
3806 static isl_stat
count_all_constraints(__isl_keep isl_basic_set_list
*intra
,
3807 __isl_keep isl_basic_set_list
*inter
, int *n_eq
, int *n_ineq
)
3809 struct isl_sched_count data
;
3811 data
.n_eq
= data
.n_ineq
= 0;
3812 if (isl_basic_set_list_foreach(inter
, &bset_update_count
, &data
) < 0)
3813 return isl_stat_error
;
3814 if (isl_basic_set_list_foreach(intra
, &bset_update_count
, &data
) < 0)
3815 return isl_stat_error
;
3818 *n_ineq
= data
.n_ineq
;
3823 /* Construct an LP problem for finding schedule coefficients
3824 * such that the schedule carries as many validity dependences as possible.
3825 * In particular, for each dependence i, we bound the dependence distance
3826 * from below by e_i, with 0 <= e_i <= 1 and then maximize the sum
3827 * of all e_i's. Dependences with e_i = 0 in the solution are simply
3828 * respected, while those with e_i > 0 (in practice e_i = 1) are carried.
3829 * "intra" is the sequence of coefficient constraints for intra-node edges.
3830 * "inter" is the sequence of coefficient constraints for inter-node edges.
3831 * "n_edge" is the total number of edges.
3833 * All variables of the LP are non-negative. The actual coefficients
3834 * may be negative, so each coefficient is represented as the difference
3835 * of two non-negative variables. The negative part always appears
3836 * immediately before the positive part.
3837 * Other than that, the variables have the following order
3839 * - sum of (1 - e_i) over all edges
3840 * - sum of all c_n coefficients
3841 * (unconstrained when computing non-parametric schedules)
3842 * - sum of positive and negative parts of all c_x coefficients
3847 * - c_i_n (if parametric)
3848 * - positive and negative parts of c_i_x
3850 * The constraints are those from the (validity) edges plus three equalities
3851 * to express the sums and n_edge inequalities to express e_i <= 1.
3853 static isl_stat
setup_carry_lp(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
3854 int n_edge
, __isl_keep isl_basic_set_list
*intra
,
3855 __isl_keep isl_basic_set_list
*inter
)
3864 for (i
= 0; i
< graph
->n
; ++i
) {
3865 struct isl_sched_node
*node
= &graph
->node
[graph
->sorted
[i
]];
3866 node
->start
= total
;
3867 total
+= 1 + node
->nparam
+ 2 * node
->nvar
;
3870 if (count_all_constraints(intra
, inter
, &n_eq
, &n_ineq
) < 0)
3871 return isl_stat_error
;
3873 dim
= isl_space_set_alloc(ctx
, 0, total
);
3874 isl_basic_set_free(graph
->lp
);
3877 graph
->lp
= isl_basic_set_alloc_space(dim
, 0, n_eq
, n_ineq
);
3878 graph
->lp
= isl_basic_set_set_rational(graph
->lp
);
3880 k
= isl_basic_set_alloc_equality(graph
->lp
);
3882 return isl_stat_error
;
3883 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
3884 isl_int_set_si(graph
->lp
->eq
[k
][0], -n_edge
);
3885 isl_int_set_si(graph
->lp
->eq
[k
][1], 1);
3886 for (i
= 0; i
< n_edge
; ++i
)
3887 isl_int_set_si(graph
->lp
->eq
[k
][4 + i
], 1);
3889 if (add_param_sum_constraint(graph
, 1) < 0)
3890 return isl_stat_error
;
3891 if (add_var_sum_constraint(graph
, 2) < 0)
3892 return isl_stat_error
;
3894 for (i
= 0; i
< n_edge
; ++i
) {
3895 k
= isl_basic_set_alloc_inequality(graph
->lp
);
3897 return isl_stat_error
;
3898 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
3899 isl_int_set_si(graph
->lp
->ineq
[k
][4 + i
], -1);
3900 isl_int_set_si(graph
->lp
->ineq
[k
][0], 1);
3903 if (add_all_constraints(ctx
, graph
, intra
, inter
) < 0)
3904 return isl_stat_error
;
3909 static __isl_give isl_schedule_node
*compute_component_schedule(
3910 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
3913 /* Comparison function for sorting the statements based on
3914 * the corresponding value in "r".
3916 static int smaller_value(const void *a
, const void *b
, void *data
)
3922 return isl_int_cmp(r
->el
[*i1
], r
->el
[*i2
]);
3925 /* If the schedule_split_scaled option is set and if the linear
3926 * parts of the scheduling rows for all nodes in the graphs have
3927 * a non-trivial common divisor, then split off the remainder of the
3928 * constant term modulo this common divisor from the linear part.
3929 * Otherwise, insert a band node directly and continue with
3930 * the construction of the schedule.
3932 * If a non-trivial common divisor is found, then
3933 * the linear part is reduced and the remainder is enforced
3934 * by a sequence node with the children placed in the order
3935 * of this remainder.
3936 * In particular, we assign an scc index based on the remainder and
3937 * then rely on compute_component_schedule to insert the sequence and
3938 * to continue the schedule construction on each part.
3940 static __isl_give isl_schedule_node
*split_scaled(
3941 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
3954 ctx
= isl_schedule_node_get_ctx(node
);
3955 if (!ctx
->opt
->schedule_split_scaled
)
3956 return compute_next_band(node
, graph
, 0);
3958 return compute_next_band(node
, graph
, 0);
3961 isl_int_init(gcd_i
);
3963 isl_int_set_si(gcd
, 0);
3965 row
= isl_mat_rows(graph
->node
[0].sched
) - 1;
3967 for (i
= 0; i
< graph
->n
; ++i
) {
3968 struct isl_sched_node
*node
= &graph
->node
[i
];
3969 int cols
= isl_mat_cols(node
->sched
);
3971 isl_seq_gcd(node
->sched
->row
[row
] + 1, cols
- 1, &gcd_i
);
3972 isl_int_gcd(gcd
, gcd
, gcd_i
);
3975 isl_int_clear(gcd_i
);
3977 if (isl_int_cmp_si(gcd
, 1) <= 0) {
3979 return compute_next_band(node
, graph
, 0);
3982 r
= isl_vec_alloc(ctx
, graph
->n
);
3983 order
= isl_calloc_array(ctx
, int, graph
->n
);
3987 for (i
= 0; i
< graph
->n
; ++i
) {
3988 struct isl_sched_node
*node
= &graph
->node
[i
];
3991 isl_int_fdiv_r(r
->el
[i
], node
->sched
->row
[row
][0], gcd
);
3992 isl_int_fdiv_q(node
->sched
->row
[row
][0],
3993 node
->sched
->row
[row
][0], gcd
);
3994 isl_int_mul(node
->sched
->row
[row
][0],
3995 node
->sched
->row
[row
][0], gcd
);
3996 node
->sched
= isl_mat_scale_down_row(node
->sched
, row
, gcd
);
4001 if (isl_sort(order
, graph
->n
, sizeof(order
[0]), &smaller_value
, r
) < 0)
4005 for (i
= 0; i
< graph
->n
; ++i
) {
4006 if (i
> 0 && isl_int_ne(r
->el
[order
[i
- 1]], r
->el
[order
[i
]]))
4008 graph
->node
[order
[i
]].scc
= scc
;
4017 if (update_edges(ctx
, graph
) < 0)
4018 return isl_schedule_node_free(node
);
4019 node
= insert_current_band(node
, graph
, 0);
4022 node
= isl_schedule_node_child(node
, 0);
4023 node
= compute_component_schedule(node
, graph
, 0);
4024 node
= isl_schedule_node_parent(node
);
4031 return isl_schedule_node_free(node
);
4034 /* Is the schedule row "sol" trivial on node "node"?
4035 * That is, is the solution zero on the dimensions linearly independent of
4036 * the previously found solutions?
4037 * Return 1 if the solution is trivial, 0 if it is not and -1 on error.
4039 * Each coefficient is represented as the difference between
4040 * two non-negative values in "sol". "sol" has been computed
4041 * in terms of the original iterators (i.e., without use of cmap).
4042 * We construct the schedule row s and write it as a linear
4043 * combination of (linear combinations of) previously computed schedule rows.
4044 * s = Q c or c = U s.
4045 * If the final entries of c are all zero, then the solution is trivial.
4047 static int is_trivial(struct isl_sched_node
*node
, __isl_keep isl_vec
*sol
)
4054 if (node
->nvar
== node
->rank
)
4057 node_sol
= extract_var_coef(node
, sol
);
4058 node_sol
= isl_mat_vec_product(isl_mat_copy(node
->cinv
), node_sol
);
4062 trivial
= isl_seq_first_non_zero(node_sol
->el
+ node
->rank
,
4063 node
->nvar
- node
->rank
) == -1;
4065 isl_vec_free(node_sol
);
4070 /* Is the schedule row "sol" trivial on any node where it should
4072 * "sol" has been computed in terms of the original iterators
4073 * (i.e., without use of cmap).
4074 * Return 1 if any solution is trivial, 0 if they are not and -1 on error.
4076 static int is_any_trivial(struct isl_sched_graph
*graph
,
4077 __isl_keep isl_vec
*sol
)
4081 for (i
= 0; i
< graph
->n
; ++i
) {
4082 struct isl_sched_node
*node
= &graph
->node
[i
];
4085 if (!needs_row(graph
, node
))
4087 trivial
= is_trivial(node
, sol
);
4088 if (trivial
< 0 || trivial
)
4095 /* Does the schedule represented by "sol" perform loop coalescing on "node"?
4096 * If so, return the position of the coalesced dimension.
4097 * Otherwise, return node->nvar or -1 on error.
4099 * In particular, look for pairs of coefficients c_i and c_j such that
4100 * |c_j/c_i| >= size_i, i.e., |c_j| >= |c_i * size_i|.
4101 * If any such pair is found, then return i.
4102 * If size_i is infinity, then no check on c_i needs to be performed.
4104 static int find_node_coalescing(struct isl_sched_node
*node
,
4105 __isl_keep isl_vec
*sol
)
4111 if (node
->nvar
<= 1)
4114 csol
= extract_var_coef(node
, sol
);
4118 for (i
= 0; i
< node
->nvar
; ++i
) {
4121 if (isl_int_is_zero(csol
->el
[i
]))
4123 v
= isl_multi_val_get_val(node
->sizes
, i
);
4126 if (!isl_val_is_int(v
)) {
4130 isl_int_mul(max
, v
->n
, csol
->el
[i
]);
4133 for (j
= 0; j
< node
->nvar
; ++j
) {
4136 if (isl_int_abs_ge(csol
->el
[j
], max
))
4152 /* Force the schedule coefficient at position "pos" of "node" to be zero
4154 * The coefficient is encoded as the difference between two non-negative
4155 * variables. Force these two variables to have the same value.
4157 static __isl_give isl_tab_lexmin
*zero_out_node_coef(
4158 __isl_take isl_tab_lexmin
*tl
, struct isl_sched_node
*node
, int pos
)
4164 ctx
= isl_space_get_ctx(node
->space
);
4165 dim
= isl_tab_lexmin_dim(tl
);
4167 return isl_tab_lexmin_free(tl
);
4168 eq
= isl_vec_alloc(ctx
, 1 + dim
);
4169 eq
= isl_vec_clr(eq
);
4171 return isl_tab_lexmin_free(tl
);
4173 pos
= 1 + node_var_coef_pos(node
, pos
);
4174 isl_int_set_si(eq
->el
[pos
], 1);
4175 isl_int_set_si(eq
->el
[pos
+ 1], -1);
4176 tl
= isl_tab_lexmin_add_eq(tl
, eq
->el
);
4182 /* Return the lexicographically smallest rational point in the basic set
4183 * from which "tl" was constructed, double checking that this input set
4186 static __isl_give isl_vec
*non_empty_solution(__isl_keep isl_tab_lexmin
*tl
)
4190 sol
= isl_tab_lexmin_get_solution(tl
);
4194 isl_die(isl_vec_get_ctx(sol
), isl_error_internal
,
4195 "error in schedule construction",
4196 return isl_vec_free(sol
));
4200 /* Does the solution "sol" of the LP problem constructed by setup_carry_lp
4201 * carry any of the "n_edge" groups of dependences?
4202 * The value in the first position is the sum of (1 - e_i) over all "n_edge"
4203 * edges, with 0 <= e_i <= 1 equal to 1 when the dependences represented
4204 * by the edge are carried by the solution.
4205 * If the sum of the (1 - e_i) is smaller than "n_edge" then at least
4206 * one of those is carried.
4208 * Note that despite the fact that the problem is solved using a rational
4209 * solver, the solution is guaranteed to be integral.
4210 * Specifically, the dependence distance lower bounds e_i (and therefore
4211 * also their sum) are integers. See Lemma 5 of [1].
4213 * Any potential denominator of the sum is cleared by this function.
4214 * The denominator is not relevant for any of the other elements
4217 * [1] P. Feautrier, Some Efficient Solutions to the Affine Scheduling
4218 * Problem, Part II: Multi-Dimensional Time.
4219 * In Intl. Journal of Parallel Programming, 1992.
4221 static int carries_dependences(__isl_keep isl_vec
*sol
, int n_edge
)
4223 isl_int_divexact(sol
->el
[1], sol
->el
[1], sol
->el
[0]);
4224 isl_int_set_si(sol
->el
[0], 1);
4225 return isl_int_cmp_si(sol
->el
[1], n_edge
) < 0;
4228 /* Return the lexicographically smallest rational point in "lp",
4229 * assuming that all variables are non-negative and performing some
4230 * additional sanity checks.
4231 * If "want_integral" is set, then compute the lexicographically smallest
4232 * integer point instead.
4233 * In particular, "lp" should not be empty by construction.
4234 * Double check that this is the case.
4235 * If dependences are not carried for any of the "n_edge" edges,
4236 * then return an empty vector.
4238 * If the schedule_treat_coalescing option is set and
4239 * if the computed schedule performs loop coalescing on a given node,
4240 * i.e., if it is of the form
4242 * c_i i + c_j j + ...
4244 * with |c_j/c_i| >= size_i, then force the coefficient c_i to be zero
4245 * to cut out this solution. Repeat this process until no more loop
4246 * coalescing occurs or until no more dependences can be carried.
4247 * In the latter case, revert to the previously computed solution.
4249 * If the caller requests an integral solution and if coalescing should
4250 * be treated, then perform the coalescing treatment first as
4251 * an integral solution computed before coalescing treatment
4252 * would carry the same number of edges and would therefore probably
4253 * also be coalescing.
4255 * To allow the coalescing treatment to be performed first,
4256 * the initial solution is allowed to be rational and it is only
4257 * cut out (if needed) in the next iteration, if no coalescing measures
4260 static __isl_give isl_vec
*non_neg_lexmin(struct isl_sched_graph
*graph
,
4261 __isl_take isl_basic_set
*lp
, int n_edge
, int want_integral
)
4266 isl_vec
*sol
, *prev
= NULL
;
4267 int treat_coalescing
;
4271 ctx
= isl_basic_set_get_ctx(lp
);
4272 treat_coalescing
= isl_options_get_schedule_treat_coalescing(ctx
);
4273 tl
= isl_tab_lexmin_from_basic_set(lp
);
4280 tl
= isl_tab_lexmin_cut_to_integer(tl
);
4281 sol
= non_empty_solution(tl
);
4285 integral
= isl_int_is_one(sol
->el
[0]);
4286 if (!carries_dependences(sol
, n_edge
)) {
4288 prev
= isl_vec_alloc(ctx
, 0);
4293 prev
= isl_vec_free(prev
);
4294 cut
= want_integral
&& !integral
;
4297 if (!treat_coalescing
)
4299 for (i
= 0; i
< graph
->n
; ++i
) {
4300 struct isl_sched_node
*node
= &graph
->node
[i
];
4302 pos
= find_node_coalescing(node
, sol
);
4305 if (pos
< node
->nvar
)
4310 tl
= zero_out_node_coef(tl
, &graph
->node
[i
], pos
);
4315 isl_tab_lexmin_free(tl
);
4319 isl_tab_lexmin_free(tl
);
4325 /* If "edge" is an edge from a node to itself, then add the corresponding
4326 * dependence relation to "umap".
4327 * If "node" has been compressed, then the dependence relation
4328 * is also compressed first.
4330 static __isl_give isl_union_map
*add_intra(__isl_take isl_union_map
*umap
,
4331 struct isl_sched_edge
*edge
)
4334 struct isl_sched_node
*node
= edge
->src
;
4336 if (edge
->src
!= edge
->dst
)
4339 map
= isl_map_copy(edge
->map
);
4340 if (node
->compressed
) {
4341 map
= isl_map_preimage_domain_multi_aff(map
,
4342 isl_multi_aff_copy(node
->decompress
));
4343 map
= isl_map_preimage_range_multi_aff(map
,
4344 isl_multi_aff_copy(node
->decompress
));
4346 umap
= isl_union_map_add_map(umap
, map
);
4350 /* If "edge" is an edge from a node to another node, then add the corresponding
4351 * dependence relation to "umap".
4352 * If the source or destination nodes of "edge" have been compressed,
4353 * then the dependence relation is also compressed first.
4355 static __isl_give isl_union_map
*add_inter(__isl_take isl_union_map
*umap
,
4356 struct isl_sched_edge
*edge
)
4360 if (edge
->src
== edge
->dst
)
4363 map
= isl_map_copy(edge
->map
);
4364 if (edge
->src
->compressed
)
4365 map
= isl_map_preimage_domain_multi_aff(map
,
4366 isl_multi_aff_copy(edge
->src
->decompress
));
4367 if (edge
->dst
->compressed
)
4368 map
= isl_map_preimage_range_multi_aff(map
,
4369 isl_multi_aff_copy(edge
->dst
->decompress
));
4370 umap
= isl_union_map_add_map(umap
, map
);
4374 /* For each (conditional) validity edge in "graph",
4375 * add the corresponding dependence relation using "add"
4376 * to a collection of dependence relations and return the result.
4377 * If "coincidence" is set, then coincidence edges are considered as well.
4379 static __isl_give isl_union_map
*collect_validity(struct isl_sched_graph
*graph
,
4380 __isl_give isl_union_map
*(*add
)(__isl_take isl_union_map
*umap
,
4381 struct isl_sched_edge
*edge
), int coincidence
)
4385 isl_union_map
*umap
;
4387 space
= isl_space_copy(graph
->node
[0].space
);
4388 umap
= isl_union_map_empty(space
);
4390 for (i
= 0; i
< graph
->n_edge
; ++i
) {
4391 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
4393 if (!is_any_validity(edge
) &&
4394 (!coincidence
|| !is_coincidence(edge
)))
4397 umap
= add(umap
, edge
);
4403 /* For each dependence relation on a (conditional) validity edge
4404 * from a node to itself,
4405 * construct the set of coefficients of valid constraints for elements
4406 * in that dependence relation and collect the results.
4407 * If "coincidence" is set, then coincidence edges are considered as well.
4409 * In particular, for each dependence relation R, constraints
4410 * on coefficients (c_0, c_n, c_x) are constructed such that
4412 * c_0 + c_n n + c_x d >= 0 for each d in delta R = { y - x | (x,y) in R }
4414 * This computation is essentially the same as that performed
4415 * by intra_coefficients, except that it operates on multiple
4418 * Note that if a dependence relation is a union of basic maps,
4419 * then each basic map needs to be treated individually as it may only
4420 * be possible to carry the dependences expressed by some of those
4421 * basic maps and not all of them.
4422 * The collected validity constraints are therefore not coalesced and
4423 * it is assumed that they are not coalesced automatically.
4424 * Duplicate basic maps can be removed, however.
4425 * In particular, if the same basic map appears as a disjunct
4426 * in multiple edges, then it only needs to be carried once.
4428 static __isl_give isl_basic_set_list
*collect_intra_validity(
4429 struct isl_sched_graph
*graph
, int coincidence
)
4431 isl_union_map
*intra
;
4432 isl_union_set
*delta
;
4433 isl_basic_set_list
*list
;
4435 intra
= collect_validity(graph
, &add_intra
, coincidence
);
4436 delta
= isl_union_map_deltas(intra
);
4437 delta
= isl_union_set_remove_divs(delta
);
4438 list
= isl_union_set_get_basic_set_list(delta
);
4439 isl_union_set_free(delta
);
4441 return isl_basic_set_list_coefficients(list
);
4444 /* For each dependence relation on a (conditional) validity edge
4445 * from a node to some other node,
4446 * construct the set of coefficients of valid constraints for elements
4447 * in that dependence relation and collect the results.
4448 * If "coincidence" is set, then coincidence edges are considered as well.
4450 * In particular, for each dependence relation R, constraints
4451 * on coefficients (c_0, c_n, c_x, c_y) are constructed such that
4453 * c_0 + c_n n + c_x x + c_y y >= 0 for each (x,y) in R
4455 * This computation is essentially the same as that performed
4456 * by inter_coefficients, except that it operates on multiple
4459 * Note that if a dependence relation is a union of basic maps,
4460 * then each basic map needs to be treated individually as it may only
4461 * be possible to carry the dependences expressed by some of those
4462 * basic maps and not all of them.
4463 * The collected validity constraints are therefore not coalesced and
4464 * it is assumed that they are not coalesced automatically.
4465 * Duplicate basic maps can be removed, however.
4466 * In particular, if the same basic map appears as a disjunct
4467 * in multiple edges, then it only needs to be carried once.
4469 static __isl_give isl_basic_set_list
*collect_inter_validity(
4470 struct isl_sched_graph
*graph
, int coincidence
)
4472 isl_union_map
*inter
;
4473 isl_union_set
*wrap
;
4474 isl_basic_set_list
*list
;
4476 inter
= collect_validity(graph
, &add_inter
, coincidence
);
4477 inter
= isl_union_map_remove_divs(inter
);
4478 wrap
= isl_union_map_wrap(inter
);
4479 list
= isl_union_set_get_basic_set_list(wrap
);
4480 isl_union_set_free(wrap
);
4481 return isl_basic_set_list_coefficients(list
);
4484 /* Construct an LP problem for finding schedule coefficients
4485 * such that the schedule carries as many of the validity dependences
4487 * return the lexicographically smallest non-trivial solution.
4488 * If "fallback" is set, then the carrying is performed as a fallback
4489 * for the Pluto-like scheduler.
4490 * If "coincidence" is set, then try and carry coincidence edges as well.
4492 * The variable "n_edge" stores the number of groups that should be carried.
4493 * If none of the "n_edge" groups can be carried
4494 * then return an empty vector.
4495 * If, moreover, "n_edge" is zero, then the LP problem does not even
4496 * need to be constructed.
4498 * If a fallback solution is being computed, then compute an integral solution
4499 * for the coefficients rather than using the numerators
4500 * of a rational solution.
4502 static __isl_give isl_vec
*compute_carrying_sol(isl_ctx
*ctx
,
4503 struct isl_sched_graph
*graph
, int fallback
, int coincidence
)
4505 int n_intra
, n_inter
;
4508 struct isl_carry carry
= { 0 };
4510 carry
.intra
= collect_intra_validity(graph
, coincidence
);
4511 carry
.inter
= collect_inter_validity(graph
, coincidence
);
4512 if (!carry
.intra
|| !carry
.inter
)
4514 n_intra
= isl_basic_set_list_n_basic_set(carry
.intra
);
4515 n_inter
= isl_basic_set_list_n_basic_set(carry
.inter
);
4516 n_edge
= n_intra
+ n_inter
;
4518 isl_carry_clear(&carry
);
4519 return isl_vec_alloc(ctx
, 0);
4522 if (setup_carry_lp(ctx
, graph
, n_edge
, carry
.intra
, carry
.inter
) < 0)
4525 isl_carry_clear(&carry
);
4526 lp
= isl_basic_set_copy(graph
->lp
);
4527 return non_neg_lexmin(graph
, lp
, n_edge
, fallback
);
4529 isl_carry_clear(&carry
);
4533 /* Construct a schedule row for each node such that as many validity dependences
4534 * as possible are carried and then continue with the next band.
4535 * If "fallback" is set, then the carrying is performed as a fallback
4536 * for the Pluto-like scheduler.
4537 * If "coincidence" is set, then try and carry coincidence edges as well.
4539 * If there are no validity dependences, then no dependence can be carried and
4540 * the procedure is guaranteed to fail. If there is more than one component,
4541 * then try computing a schedule on each component separately
4542 * to prevent or at least postpone this failure.
4544 * If a schedule row is computed, then check that dependences are carried
4545 * for at least one of the edges.
4547 * If the computed schedule row turns out to be trivial on one or
4548 * more nodes where it should not be trivial, then we throw it away
4549 * and try again on each component separately.
4551 * If there is only one component, then we accept the schedule row anyway,
4552 * but we do not consider it as a complete row and therefore do not
4553 * increment graph->n_row. Note that the ranks of the nodes that
4554 * do get a non-trivial schedule part will get updated regardless and
4555 * graph->maxvar is computed based on these ranks. The test for
4556 * whether more schedule rows are required in compute_schedule_wcc
4557 * is therefore not affected.
4559 * Insert a band corresponding to the schedule row at position "node"
4560 * of the schedule tree and continue with the construction of the schedule.
4561 * This insertion and the continued construction is performed by split_scaled
4562 * after optionally checking for non-trivial common divisors.
4564 static __isl_give isl_schedule_node
*carry(__isl_take isl_schedule_node
*node
,
4565 struct isl_sched_graph
*graph
, int fallback
, int coincidence
)
4574 ctx
= isl_schedule_node_get_ctx(node
);
4575 sol
= compute_carrying_sol(ctx
, graph
, fallback
, coincidence
);
4577 return isl_schedule_node_free(node
);
4578 if (sol
->size
== 0) {
4581 return compute_component_schedule(node
, graph
, 1);
4582 isl_die(ctx
, isl_error_unknown
, "unable to carry dependences",
4583 return isl_schedule_node_free(node
));
4586 trivial
= is_any_trivial(graph
, sol
);
4588 sol
= isl_vec_free(sol
);
4589 } else if (trivial
&& graph
->scc
> 1) {
4591 return compute_component_schedule(node
, graph
, 1);
4594 if (update_schedule(graph
, sol
, 0, 0) < 0)
4595 return isl_schedule_node_free(node
);
4599 return split_scaled(node
, graph
);
4602 /* Construct a schedule row for each node such that as many validity dependences
4603 * as possible are carried and then continue with the next band.
4604 * Do so as a fallback for the Pluto-like scheduler.
4605 * If "coincidence" is set, then try and carry coincidence edges as well.
4607 static __isl_give isl_schedule_node
*carry_fallback(
4608 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
4611 return carry(node
, graph
, 1, coincidence
);
4614 /* Construct a schedule row for each node such that as many validity dependences
4615 * as possible are carried and then continue with the next band.
4616 * Do so for the case where the Feautrier scheduler was selected
4619 static __isl_give isl_schedule_node
*carry_feautrier(
4620 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
4622 return carry(node
, graph
, 0, 0);
4625 /* Construct a schedule row for each node such that as many validity dependences
4626 * as possible are carried and then continue with the next band.
4627 * Do so as a fallback for the Pluto-like scheduler.
4629 static __isl_give isl_schedule_node
*carry_dependences(
4630 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
4632 return carry_fallback(node
, graph
, 0);
4635 /* Construct a schedule row for each node such that as many validity or
4636 * coincidence dependences as possible are carried and
4637 * then continue with the next band.
4638 * Do so as a fallback for the Pluto-like scheduler.
4640 static __isl_give isl_schedule_node
*carry_coincidence(
4641 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
4643 return carry_fallback(node
, graph
, 1);
4646 /* Topologically sort statements mapped to the same schedule iteration
4647 * and add insert a sequence node in front of "node"
4648 * corresponding to this order.
4649 * If "initialized" is set, then it may be assumed that compute_maxvar
4650 * has been called on the current band. Otherwise, call
4651 * compute_maxvar if and before carry_dependences gets called.
4653 * If it turns out to be impossible to sort the statements apart,
4654 * because different dependences impose different orderings
4655 * on the statements, then we extend the schedule such that
4656 * it carries at least one more dependence.
4658 static __isl_give isl_schedule_node
*sort_statements(
4659 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
4663 isl_union_set_list
*filters
;
4668 ctx
= isl_schedule_node_get_ctx(node
);
4670 isl_die(ctx
, isl_error_internal
,
4671 "graph should have at least one node",
4672 return isl_schedule_node_free(node
));
4677 if (update_edges(ctx
, graph
) < 0)
4678 return isl_schedule_node_free(node
);
4680 if (graph
->n_edge
== 0)
4683 if (detect_sccs(ctx
, graph
) < 0)
4684 return isl_schedule_node_free(node
);
4687 if (graph
->scc
< graph
->n
) {
4688 if (!initialized
&& compute_maxvar(graph
) < 0)
4689 return isl_schedule_node_free(node
);
4690 return carry_dependences(node
, graph
);
4693 filters
= extract_sccs(ctx
, graph
);
4694 node
= isl_schedule_node_insert_sequence(node
, filters
);
4699 /* Are there any (non-empty) (conditional) validity edges in the graph?
4701 static int has_validity_edges(struct isl_sched_graph
*graph
)
4705 for (i
= 0; i
< graph
->n_edge
; ++i
) {
4708 empty
= isl_map_plain_is_empty(graph
->edge
[i
].map
);
4713 if (is_any_validity(&graph
->edge
[i
]))
4720 /* Should we apply a Feautrier step?
4721 * That is, did the user request the Feautrier algorithm and are
4722 * there any validity dependences (left)?
4724 static int need_feautrier_step(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
4726 if (ctx
->opt
->schedule_algorithm
!= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
)
4729 return has_validity_edges(graph
);
4732 /* Compute a schedule for a connected dependence graph using Feautrier's
4733 * multi-dimensional scheduling algorithm and return the updated schedule node.
4735 * The original algorithm is described in [1].
4736 * The main idea is to minimize the number of scheduling dimensions, by
4737 * trying to satisfy as many dependences as possible per scheduling dimension.
4739 * [1] P. Feautrier, Some Efficient Solutions to the Affine Scheduling
4740 * Problem, Part II: Multi-Dimensional Time.
4741 * In Intl. Journal of Parallel Programming, 1992.
4743 static __isl_give isl_schedule_node
*compute_schedule_wcc_feautrier(
4744 isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
4746 return carry_feautrier(node
, graph
);
4749 /* Turn off the "local" bit on all (condition) edges.
4751 static void clear_local_edges(struct isl_sched_graph
*graph
)
4755 for (i
= 0; i
< graph
->n_edge
; ++i
)
4756 if (is_condition(&graph
->edge
[i
]))
4757 clear_local(&graph
->edge
[i
]);
4760 /* Does "graph" have both condition and conditional validity edges?
4762 static int need_condition_check(struct isl_sched_graph
*graph
)
4765 int any_condition
= 0;
4766 int any_conditional_validity
= 0;
4768 for (i
= 0; i
< graph
->n_edge
; ++i
) {
4769 if (is_condition(&graph
->edge
[i
]))
4771 if (is_conditional_validity(&graph
->edge
[i
]))
4772 any_conditional_validity
= 1;
4775 return any_condition
&& any_conditional_validity
;
4778 /* Does "graph" contain any coincidence edge?
4780 static int has_any_coincidence(struct isl_sched_graph
*graph
)
4784 for (i
= 0; i
< graph
->n_edge
; ++i
)
4785 if (is_coincidence(&graph
->edge
[i
]))
4791 /* Extract the final schedule row as a map with the iteration domain
4792 * of "node" as domain.
4794 static __isl_give isl_map
*final_row(struct isl_sched_node
*node
)
4799 row
= isl_mat_rows(node
->sched
) - 1;
4800 ma
= node_extract_partial_schedule_multi_aff(node
, row
, 1);
4801 return isl_map_from_multi_aff(ma
);
4804 /* Is the conditional validity dependence in the edge with index "edge_index"
4805 * violated by the latest (i.e., final) row of the schedule?
4806 * That is, is i scheduled after j
4807 * for any conditional validity dependence i -> j?
4809 static int is_violated(struct isl_sched_graph
*graph
, int edge_index
)
4811 isl_map
*src_sched
, *dst_sched
, *map
;
4812 struct isl_sched_edge
*edge
= &graph
->edge
[edge_index
];
4815 src_sched
= final_row(edge
->src
);
4816 dst_sched
= final_row(edge
->dst
);
4817 map
= isl_map_copy(edge
->map
);
4818 map
= isl_map_apply_domain(map
, src_sched
);
4819 map
= isl_map_apply_range(map
, dst_sched
);
4820 map
= isl_map_order_gt(map
, isl_dim_in
, 0, isl_dim_out
, 0);
4821 empty
= isl_map_is_empty(map
);
4830 /* Does "graph" have any satisfied condition edges that
4831 * are adjacent to the conditional validity constraint with
4832 * domain "conditional_source" and range "conditional_sink"?
4834 * A satisfied condition is one that is not local.
4835 * If a condition was forced to be local already (i.e., marked as local)
4836 * then there is no need to check if it is in fact local.
4838 * Additionally, mark all adjacent condition edges found as local.
4840 static int has_adjacent_true_conditions(struct isl_sched_graph
*graph
,
4841 __isl_keep isl_union_set
*conditional_source
,
4842 __isl_keep isl_union_set
*conditional_sink
)
4847 for (i
= 0; i
< graph
->n_edge
; ++i
) {
4848 int adjacent
, local
;
4849 isl_union_map
*condition
;
4851 if (!is_condition(&graph
->edge
[i
]))
4853 if (is_local(&graph
->edge
[i
]))
4856 condition
= graph
->edge
[i
].tagged_condition
;
4857 adjacent
= domain_intersects(condition
, conditional_sink
);
4858 if (adjacent
>= 0 && !adjacent
)
4859 adjacent
= range_intersects(condition
,
4860 conditional_source
);
4866 set_local(&graph
->edge
[i
]);
4868 local
= is_condition_false(&graph
->edge
[i
]);
4878 /* Are there any violated conditional validity dependences with
4879 * adjacent condition dependences that are not local with respect
4880 * to the current schedule?
4881 * That is, is the conditional validity constraint violated?
4883 * Additionally, mark all those adjacent condition dependences as local.
4884 * We also mark those adjacent condition dependences that were not marked
4885 * as local before, but just happened to be local already. This ensures
4886 * that they remain local if the schedule is recomputed.
4888 * We first collect domain and range of all violated conditional validity
4889 * dependences and then check if there are any adjacent non-local
4890 * condition dependences.
4892 static int has_violated_conditional_constraint(isl_ctx
*ctx
,
4893 struct isl_sched_graph
*graph
)
4897 isl_union_set
*source
, *sink
;
4899 source
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
4900 sink
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
4901 for (i
= 0; i
< graph
->n_edge
; ++i
) {
4902 isl_union_set
*uset
;
4903 isl_union_map
*umap
;
4906 if (!is_conditional_validity(&graph
->edge
[i
]))
4909 violated
= is_violated(graph
, i
);
4917 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_validity
);
4918 uset
= isl_union_map_domain(umap
);
4919 source
= isl_union_set_union(source
, uset
);
4920 source
= isl_union_set_coalesce(source
);
4922 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_validity
);
4923 uset
= isl_union_map_range(umap
);
4924 sink
= isl_union_set_union(sink
, uset
);
4925 sink
= isl_union_set_coalesce(sink
);
4929 any
= has_adjacent_true_conditions(graph
, source
, sink
);
4931 isl_union_set_free(source
);
4932 isl_union_set_free(sink
);
4935 isl_union_set_free(source
);
4936 isl_union_set_free(sink
);
4940 /* Examine the current band (the rows between graph->band_start and
4941 * graph->n_total_row), deciding whether to drop it or add it to "node"
4942 * and then continue with the computation of the next band, if any.
4943 * If "initialized" is set, then it may be assumed that compute_maxvar
4944 * has been called on the current band. Otherwise, call
4945 * compute_maxvar if and before carry_dependences gets called.
4947 * The caller keeps looking for a new row as long as
4948 * graph->n_row < graph->maxvar. If the latest attempt to find
4949 * such a row failed (i.e., we still have graph->n_row < graph->maxvar),
4951 * - split between SCCs and start over (assuming we found an interesting
4952 * pair of SCCs between which to split)
4953 * - continue with the next band (assuming the current band has at least
4955 * - if outer coincidence needs to be enforced, then try to carry as many
4956 * validity or coincidence dependences as possible and
4957 * continue with the next band
4958 * - try to carry as many validity dependences as possible and
4959 * continue with the next band
4960 * In each case, we first insert a band node in the schedule tree
4961 * if any rows have been computed.
4963 * If the caller managed to complete the schedule, we insert a band node
4964 * (if any schedule rows were computed) and we finish off by topologically
4965 * sorting the statements based on the remaining dependences.
4967 static __isl_give isl_schedule_node
*compute_schedule_finish_band(
4968 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
4976 if (graph
->n_row
< graph
->maxvar
) {
4978 int empty
= graph
->n_total_row
== graph
->band_start
;
4980 ctx
= isl_schedule_node_get_ctx(node
);
4981 if (!ctx
->opt
->schedule_maximize_band_depth
&& !empty
)
4982 return compute_next_band(node
, graph
, 1);
4983 if (graph
->src_scc
>= 0)
4984 return compute_split_schedule(node
, graph
);
4986 return compute_next_band(node
, graph
, 1);
4987 if (!initialized
&& compute_maxvar(graph
) < 0)
4988 return isl_schedule_node_free(node
);
4989 if (isl_options_get_schedule_outer_coincidence(ctx
))
4990 return carry_coincidence(node
, graph
);
4991 return carry_dependences(node
, graph
);
4994 insert
= graph
->n_total_row
> graph
->band_start
;
4996 node
= insert_current_band(node
, graph
, 1);
4997 node
= isl_schedule_node_child(node
, 0);
4999 node
= sort_statements(node
, graph
, initialized
);
5001 node
= isl_schedule_node_parent(node
);
5006 /* Construct a band of schedule rows for a connected dependence graph.
5007 * The caller is responsible for determining the strongly connected
5008 * components and calling compute_maxvar first.
5010 * We try to find a sequence of as many schedule rows as possible that result
5011 * in non-negative dependence distances (independent of the previous rows
5012 * in the sequence, i.e., such that the sequence is tilable), with as
5013 * many of the initial rows as possible satisfying the coincidence constraints.
5014 * The computation stops if we can't find any more rows or if we have found
5015 * all the rows we wanted to find.
5017 * If ctx->opt->schedule_outer_coincidence is set, then we force the
5018 * outermost dimension to satisfy the coincidence constraints. If this
5019 * turns out to be impossible, we fall back on the general scheme above
5020 * and try to carry as many dependences as possible.
5022 * If "graph" contains both condition and conditional validity dependences,
5023 * then we need to check that that the conditional schedule constraint
5024 * is satisfied, i.e., there are no violated conditional validity dependences
5025 * that are adjacent to any non-local condition dependences.
5026 * If there are, then we mark all those adjacent condition dependences
5027 * as local and recompute the current band. Those dependences that
5028 * are marked local will then be forced to be local.
5029 * The initial computation is performed with no dependences marked as local.
5030 * If we are lucky, then there will be no violated conditional validity
5031 * dependences adjacent to any non-local condition dependences.
5032 * Otherwise, we mark some additional condition dependences as local and
5033 * recompute. We continue this process until there are no violations left or
5034 * until we are no longer able to compute a schedule.
5035 * Since there are only a finite number of dependences,
5036 * there will only be a finite number of iterations.
5038 static isl_stat
compute_schedule_wcc_band(isl_ctx
*ctx
,
5039 struct isl_sched_graph
*graph
)
5041 int has_coincidence
;
5042 int use_coincidence
;
5043 int force_coincidence
= 0;
5044 int check_conditional
;
5046 if (sort_sccs(graph
) < 0)
5047 return isl_stat_error
;
5049 clear_local_edges(graph
);
5050 check_conditional
= need_condition_check(graph
);
5051 has_coincidence
= has_any_coincidence(graph
);
5053 if (ctx
->opt
->schedule_outer_coincidence
)
5054 force_coincidence
= 1;
5056 use_coincidence
= has_coincidence
;
5057 while (graph
->n_row
< graph
->maxvar
) {
5062 graph
->src_scc
= -1;
5063 graph
->dst_scc
= -1;
5065 if (setup_lp(ctx
, graph
, use_coincidence
) < 0)
5066 return isl_stat_error
;
5067 sol
= solve_lp(ctx
, graph
);
5069 return isl_stat_error
;
5070 if (sol
->size
== 0) {
5071 int empty
= graph
->n_total_row
== graph
->band_start
;
5074 if (use_coincidence
&& (!force_coincidence
|| !empty
)) {
5075 use_coincidence
= 0;
5080 coincident
= !has_coincidence
|| use_coincidence
;
5081 if (update_schedule(graph
, sol
, 1, coincident
) < 0)
5082 return isl_stat_error
;
5084 if (!check_conditional
)
5086 violated
= has_violated_conditional_constraint(ctx
, graph
);
5088 return isl_stat_error
;
5091 if (reset_band(graph
) < 0)
5092 return isl_stat_error
;
5093 use_coincidence
= has_coincidence
;
5099 /* Compute a schedule for a connected dependence graph by considering
5100 * the graph as a whole and return the updated schedule node.
5102 * The actual schedule rows of the current band are computed by
5103 * compute_schedule_wcc_band. compute_schedule_finish_band takes
5104 * care of integrating the band into "node" and continuing
5107 static __isl_give isl_schedule_node
*compute_schedule_wcc_whole(
5108 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
5115 ctx
= isl_schedule_node_get_ctx(node
);
5116 if (compute_schedule_wcc_band(ctx
, graph
) < 0)
5117 return isl_schedule_node_free(node
);
5119 return compute_schedule_finish_band(node
, graph
, 1);
5122 /* Clustering information used by compute_schedule_wcc_clustering.
5124 * "n" is the number of SCCs in the original dependence graph
5125 * "scc" is an array of "n" elements, each representing an SCC
5126 * of the original dependence graph. All entries in the same cluster
5127 * have the same number of schedule rows.
5128 * "scc_cluster" maps each SCC index to the cluster to which it belongs,
5129 * where each cluster is represented by the index of the first SCC
5130 * in the cluster. Initially, each SCC belongs to a cluster containing
5133 * "scc_in_merge" is used by merge_clusters_along_edge to keep
5134 * track of which SCCs need to be merged.
5136 * "cluster" contains the merged clusters of SCCs after the clustering
5139 * "scc_node" is a temporary data structure used inside copy_partial.
5140 * For each SCC, it keeps track of the number of nodes in the SCC
5141 * that have already been copied.
5143 struct isl_clustering
{
5145 struct isl_sched_graph
*scc
;
5146 struct isl_sched_graph
*cluster
;
5152 /* Initialize the clustering data structure "c" from "graph".
5154 * In particular, allocate memory, extract the SCCs from "graph"
5155 * into c->scc, initialize scc_cluster and construct
5156 * a band of schedule rows for each SCC.
5157 * Within each SCC, there is only one SCC by definition.
5158 * Each SCC initially belongs to a cluster containing only that SCC.
5160 static isl_stat
clustering_init(isl_ctx
*ctx
, struct isl_clustering
*c
,
5161 struct isl_sched_graph
*graph
)
5166 c
->scc
= isl_calloc_array(ctx
, struct isl_sched_graph
, c
->n
);
5167 c
->cluster
= isl_calloc_array(ctx
, struct isl_sched_graph
, c
->n
);
5168 c
->scc_cluster
= isl_calloc_array(ctx
, int, c
->n
);
5169 c
->scc_node
= isl_calloc_array(ctx
, int, c
->n
);
5170 c
->scc_in_merge
= isl_calloc_array(ctx
, int, c
->n
);
5171 if (!c
->scc
|| !c
->cluster
||
5172 !c
->scc_cluster
|| !c
->scc_node
|| !c
->scc_in_merge
)
5173 return isl_stat_error
;
5175 for (i
= 0; i
< c
->n
; ++i
) {
5176 if (extract_sub_graph(ctx
, graph
, &node_scc_exactly
,
5177 &edge_scc_exactly
, i
, &c
->scc
[i
]) < 0)
5178 return isl_stat_error
;
5180 if (compute_maxvar(&c
->scc
[i
]) < 0)
5181 return isl_stat_error
;
5182 if (compute_schedule_wcc_band(ctx
, &c
->scc
[i
]) < 0)
5183 return isl_stat_error
;
5184 c
->scc_cluster
[i
] = i
;
5190 /* Free all memory allocated for "c".
5192 static void clustering_free(isl_ctx
*ctx
, struct isl_clustering
*c
)
5197 for (i
= 0; i
< c
->n
; ++i
)
5198 graph_free(ctx
, &c
->scc
[i
]);
5201 for (i
= 0; i
< c
->n
; ++i
)
5202 graph_free(ctx
, &c
->cluster
[i
]);
5204 free(c
->scc_cluster
);
5206 free(c
->scc_in_merge
);
5209 /* Should we refrain from merging the cluster in "graph" with
5210 * any other cluster?
5211 * In particular, is its current schedule band empty and incomplete.
5213 static int bad_cluster(struct isl_sched_graph
*graph
)
5215 return graph
->n_row
< graph
->maxvar
&&
5216 graph
->n_total_row
== graph
->band_start
;
5219 /* Is "edge" a proximity edge with a non-empty dependence relation?
5221 static isl_bool
is_non_empty_proximity(struct isl_sched_edge
*edge
)
5223 if (!is_proximity(edge
))
5224 return isl_bool_false
;
5225 return isl_bool_not(isl_map_plain_is_empty(edge
->map
));
5228 /* Return the index of an edge in "graph" that can be used to merge
5229 * two clusters in "c".
5230 * Return graph->n_edge if no such edge can be found.
5231 * Return -1 on error.
5233 * In particular, return a proximity edge between two clusters
5234 * that is not marked "no_merge" and such that neither of the
5235 * two clusters has an incomplete, empty band.
5237 * If there are multiple such edges, then try and find the most
5238 * appropriate edge to use for merging. In particular, pick the edge
5239 * with the greatest weight. If there are multiple of those,
5240 * then pick one with the shortest distance between
5241 * the two cluster representatives.
5243 static int find_proximity(struct isl_sched_graph
*graph
,
5244 struct isl_clustering
*c
)
5246 int i
, best
= graph
->n_edge
, best_dist
, best_weight
;
5248 for (i
= 0; i
< graph
->n_edge
; ++i
) {
5249 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
5253 prox
= is_non_empty_proximity(edge
);
5260 if (bad_cluster(&c
->scc
[edge
->src
->scc
]) ||
5261 bad_cluster(&c
->scc
[edge
->dst
->scc
]))
5263 dist
= c
->scc_cluster
[edge
->dst
->scc
] -
5264 c
->scc_cluster
[edge
->src
->scc
];
5267 weight
= edge
->weight
;
5268 if (best
< graph
->n_edge
) {
5269 if (best_weight
> weight
)
5271 if (best_weight
== weight
&& best_dist
<= dist
)
5276 best_weight
= weight
;
5282 /* Internal data structure used in mark_merge_sccs.
5284 * "graph" is the dependence graph in which a strongly connected
5285 * component is constructed.
5286 * "scc_cluster" maps each SCC index to the cluster to which it belongs.
5287 * "src" and "dst" are the indices of the nodes that are being merged.
5289 struct isl_mark_merge_sccs_data
{
5290 struct isl_sched_graph
*graph
;
5296 /* Check whether the cluster containing node "i" depends on the cluster
5297 * containing node "j". If "i" and "j" belong to the same cluster,
5298 * then they are taken to depend on each other to ensure that
5299 * the resulting strongly connected component consists of complete
5300 * clusters. Furthermore, if "i" and "j" are the two nodes that
5301 * are being merged, then they are taken to depend on each other as well.
5302 * Otherwise, check if there is a (conditional) validity dependence
5303 * from node[j] to node[i], forcing node[i] to follow node[j].
5305 static isl_bool
cluster_follows(int i
, int j
, void *user
)
5307 struct isl_mark_merge_sccs_data
*data
= user
;
5308 struct isl_sched_graph
*graph
= data
->graph
;
5309 int *scc_cluster
= data
->scc_cluster
;
5311 if (data
->src
== i
&& data
->dst
== j
)
5312 return isl_bool_true
;
5313 if (data
->src
== j
&& data
->dst
== i
)
5314 return isl_bool_true
;
5315 if (scc_cluster
[graph
->node
[i
].scc
] == scc_cluster
[graph
->node
[j
].scc
])
5316 return isl_bool_true
;
5318 return graph_has_validity_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
5321 /* Mark all SCCs that belong to either of the two clusters in "c"
5322 * connected by the edge in "graph" with index "edge", or to any
5323 * of the intermediate clusters.
5324 * The marking is recorded in c->scc_in_merge.
5326 * The given edge has been selected for merging two clusters,
5327 * meaning that there is at least a proximity edge between the two nodes.
5328 * However, there may also be (indirect) validity dependences
5329 * between the two nodes. When merging the two clusters, all clusters
5330 * containing one or more of the intermediate nodes along the
5331 * indirect validity dependences need to be merged in as well.
5333 * First collect all such nodes by computing the strongly connected
5334 * component (SCC) containing the two nodes connected by the edge, where
5335 * the two nodes are considered to depend on each other to make
5336 * sure they end up in the same SCC. Similarly, each node is considered
5337 * to depend on every other node in the same cluster to ensure
5338 * that the SCC consists of complete clusters.
5340 * Then the original SCCs that contain any of these nodes are marked
5341 * in c->scc_in_merge.
5343 static isl_stat
mark_merge_sccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
5344 int edge
, struct isl_clustering
*c
)
5346 struct isl_mark_merge_sccs_data data
;
5347 struct isl_tarjan_graph
*g
;
5350 for (i
= 0; i
< c
->n
; ++i
)
5351 c
->scc_in_merge
[i
] = 0;
5354 data
.scc_cluster
= c
->scc_cluster
;
5355 data
.src
= graph
->edge
[edge
].src
- graph
->node
;
5356 data
.dst
= graph
->edge
[edge
].dst
- graph
->node
;
5358 g
= isl_tarjan_graph_component(ctx
, graph
->n
, data
.dst
,
5359 &cluster_follows
, &data
);
5365 isl_die(ctx
, isl_error_internal
,
5366 "expecting at least two nodes in component",
5368 if (g
->order
[--i
] != -1)
5369 isl_die(ctx
, isl_error_internal
,
5370 "expecting end of component marker", goto error
);
5372 for (--i
; i
>= 0 && g
->order
[i
] != -1; --i
) {
5373 int scc
= graph
->node
[g
->order
[i
]].scc
;
5374 c
->scc_in_merge
[scc
] = 1;
5377 isl_tarjan_graph_free(g
);
5380 isl_tarjan_graph_free(g
);
5381 return isl_stat_error
;
5384 /* Construct the identifier "cluster_i".
5386 static __isl_give isl_id
*cluster_id(isl_ctx
*ctx
, int i
)
5390 snprintf(name
, sizeof(name
), "cluster_%d", i
);
5391 return isl_id_alloc(ctx
, name
, NULL
);
5394 /* Construct the space of the cluster with index "i" containing
5395 * the strongly connected component "scc".
5397 * In particular, construct a space called cluster_i with dimension equal
5398 * to the number of schedule rows in the current band of "scc".
5400 static __isl_give isl_space
*cluster_space(struct isl_sched_graph
*scc
, int i
)
5406 nvar
= scc
->n_total_row
- scc
->band_start
;
5407 space
= isl_space_copy(scc
->node
[0].space
);
5408 space
= isl_space_params(space
);
5409 space
= isl_space_set_from_params(space
);
5410 space
= isl_space_add_dims(space
, isl_dim_set
, nvar
);
5411 id
= cluster_id(isl_space_get_ctx(space
), i
);
5412 space
= isl_space_set_tuple_id(space
, isl_dim_set
, id
);
5417 /* Collect the domain of the graph for merging clusters.
5419 * In particular, for each cluster with first SCC "i", construct
5420 * a set in the space called cluster_i with dimension equal
5421 * to the number of schedule rows in the current band of the cluster.
5423 static __isl_give isl_union_set
*collect_domain(isl_ctx
*ctx
,
5424 struct isl_sched_graph
*graph
, struct isl_clustering
*c
)
5428 isl_union_set
*domain
;
5430 space
= isl_space_params_alloc(ctx
, 0);
5431 domain
= isl_union_set_empty(space
);
5433 for (i
= 0; i
< graph
->scc
; ++i
) {
5436 if (!c
->scc_in_merge
[i
])
5438 if (c
->scc_cluster
[i
] != i
)
5440 space
= cluster_space(&c
->scc
[i
], i
);
5441 domain
= isl_union_set_add_set(domain
, isl_set_universe(space
));
5447 /* Construct a map from the original instances to the corresponding
5448 * cluster instance in the current bands of the clusters in "c".
5450 static __isl_give isl_union_map
*collect_cluster_map(isl_ctx
*ctx
,
5451 struct isl_sched_graph
*graph
, struct isl_clustering
*c
)
5455 isl_union_map
*cluster_map
;
5457 space
= isl_space_params_alloc(ctx
, 0);
5458 cluster_map
= isl_union_map_empty(space
);
5459 for (i
= 0; i
< graph
->scc
; ++i
) {
5463 if (!c
->scc_in_merge
[i
])
5466 id
= cluster_id(ctx
, c
->scc_cluster
[i
]);
5467 start
= c
->scc
[i
].band_start
;
5468 n
= c
->scc
[i
].n_total_row
- start
;
5469 for (j
= 0; j
< c
->scc
[i
].n
; ++j
) {
5472 struct isl_sched_node
*node
= &c
->scc
[i
].node
[j
];
5474 ma
= node_extract_partial_schedule_multi_aff(node
,
5476 ma
= isl_multi_aff_set_tuple_id(ma
, isl_dim_out
,
5478 map
= isl_map_from_multi_aff(ma
);
5479 cluster_map
= isl_union_map_add_map(cluster_map
, map
);
5487 /* Add "umap" to the schedule constraints "sc" of all types of "edge"
5488 * that are not isl_edge_condition or isl_edge_conditional_validity.
5490 static __isl_give isl_schedule_constraints
*add_non_conditional_constraints(
5491 struct isl_sched_edge
*edge
, __isl_keep isl_union_map
*umap
,
5492 __isl_take isl_schedule_constraints
*sc
)
5494 enum isl_edge_type t
;
5499 for (t
= isl_edge_first
; t
<= isl_edge_last
; ++t
) {
5500 if (t
== isl_edge_condition
||
5501 t
== isl_edge_conditional_validity
)
5503 if (!is_type(edge
, t
))
5505 sc
= isl_schedule_constraints_add(sc
, t
,
5506 isl_union_map_copy(umap
));
5512 /* Add schedule constraints of types isl_edge_condition and
5513 * isl_edge_conditional_validity to "sc" by applying "umap" to
5514 * the domains of the wrapped relations in domain and range
5515 * of the corresponding tagged constraints of "edge".
5517 static __isl_give isl_schedule_constraints
*add_conditional_constraints(
5518 struct isl_sched_edge
*edge
, __isl_keep isl_union_map
*umap
,
5519 __isl_take isl_schedule_constraints
*sc
)
5521 enum isl_edge_type t
;
5522 isl_union_map
*tagged
;
5524 for (t
= isl_edge_condition
; t
<= isl_edge_conditional_validity
; ++t
) {
5525 if (!is_type(edge
, t
))
5527 if (t
== isl_edge_condition
)
5528 tagged
= isl_union_map_copy(edge
->tagged_condition
);
5530 tagged
= isl_union_map_copy(edge
->tagged_validity
);
5531 tagged
= isl_union_map_zip(tagged
);
5532 tagged
= isl_union_map_apply_domain(tagged
,
5533 isl_union_map_copy(umap
));
5534 tagged
= isl_union_map_zip(tagged
);
5535 sc
= isl_schedule_constraints_add(sc
, t
, tagged
);
5543 /* Given a mapping "cluster_map" from the original instances to
5544 * the cluster instances, add schedule constraints on the clusters
5545 * to "sc" corresponding to the original constraints represented by "edge".
5547 * For non-tagged dependence constraints, the cluster constraints
5548 * are obtained by applying "cluster_map" to the edge->map.
5550 * For tagged dependence constraints, "cluster_map" needs to be applied
5551 * to the domains of the wrapped relations in domain and range
5552 * of the tagged dependence constraints. Pick out the mappings
5553 * from these domains from "cluster_map" and construct their product.
5554 * This mapping can then be applied to the pair of domains.
5556 static __isl_give isl_schedule_constraints
*collect_edge_constraints(
5557 struct isl_sched_edge
*edge
, __isl_keep isl_union_map
*cluster_map
,
5558 __isl_take isl_schedule_constraints
*sc
)
5560 isl_union_map
*umap
;
5562 isl_union_set
*uset
;
5563 isl_union_map
*umap1
, *umap2
;
5568 umap
= isl_union_map_from_map(isl_map_copy(edge
->map
));
5569 umap
= isl_union_map_apply_domain(umap
,
5570 isl_union_map_copy(cluster_map
));
5571 umap
= isl_union_map_apply_range(umap
,
5572 isl_union_map_copy(cluster_map
));
5573 sc
= add_non_conditional_constraints(edge
, umap
, sc
);
5574 isl_union_map_free(umap
);
5576 if (!sc
|| (!is_condition(edge
) && !is_conditional_validity(edge
)))
5579 space
= isl_space_domain(isl_map_get_space(edge
->map
));
5580 uset
= isl_union_set_from_set(isl_set_universe(space
));
5581 umap1
= isl_union_map_copy(cluster_map
);
5582 umap1
= isl_union_map_intersect_domain(umap1
, uset
);
5583 space
= isl_space_range(isl_map_get_space(edge
->map
));
5584 uset
= isl_union_set_from_set(isl_set_universe(space
));
5585 umap2
= isl_union_map_copy(cluster_map
);
5586 umap2
= isl_union_map_intersect_domain(umap2
, uset
);
5587 umap
= isl_union_map_product(umap1
, umap2
);
5589 sc
= add_conditional_constraints(edge
, umap
, sc
);
5591 isl_union_map_free(umap
);
5595 /* Given a mapping "cluster_map" from the original instances to
5596 * the cluster instances, add schedule constraints on the clusters
5597 * to "sc" corresponding to all edges in "graph" between nodes that
5598 * belong to SCCs that are marked for merging in "scc_in_merge".
5600 static __isl_give isl_schedule_constraints
*collect_constraints(
5601 struct isl_sched_graph
*graph
, int *scc_in_merge
,
5602 __isl_keep isl_union_map
*cluster_map
,
5603 __isl_take isl_schedule_constraints
*sc
)
5607 for (i
= 0; i
< graph
->n_edge
; ++i
) {
5608 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
5610 if (!scc_in_merge
[edge
->src
->scc
])
5612 if (!scc_in_merge
[edge
->dst
->scc
])
5614 sc
= collect_edge_constraints(edge
, cluster_map
, sc
);
5620 /* Construct a dependence graph for scheduling clusters with respect
5621 * to each other and store the result in "merge_graph".
5622 * In particular, the nodes of the graph correspond to the schedule
5623 * dimensions of the current bands of those clusters that have been
5624 * marked for merging in "c".
5626 * First construct an isl_schedule_constraints object for this domain
5627 * by transforming the edges in "graph" to the domain.
5628 * Then initialize a dependence graph for scheduling from these
5631 static isl_stat
init_merge_graph(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
5632 struct isl_clustering
*c
, struct isl_sched_graph
*merge_graph
)
5634 isl_union_set
*domain
;
5635 isl_union_map
*cluster_map
;
5636 isl_schedule_constraints
*sc
;
5639 domain
= collect_domain(ctx
, graph
, c
);
5640 sc
= isl_schedule_constraints_on_domain(domain
);
5642 return isl_stat_error
;
5643 cluster_map
= collect_cluster_map(ctx
, graph
, c
);
5644 sc
= collect_constraints(graph
, c
->scc_in_merge
, cluster_map
, sc
);
5645 isl_union_map_free(cluster_map
);
5647 r
= graph_init(merge_graph
, sc
);
5649 isl_schedule_constraints_free(sc
);
5654 /* Compute the maximal number of remaining schedule rows that still need
5655 * to be computed for the nodes that belong to clusters with the maximal
5656 * dimension for the current band (i.e., the band that is to be merged).
5657 * Only clusters that are about to be merged are considered.
5658 * "maxvar" is the maximal dimension for the current band.
5659 * "c" contains information about the clusters.
5661 * Return the maximal number of remaining schedule rows or -1 on error.
5663 static int compute_maxvar_max_slack(int maxvar
, struct isl_clustering
*c
)
5669 for (i
= 0; i
< c
->n
; ++i
) {
5671 struct isl_sched_graph
*scc
;
5673 if (!c
->scc_in_merge
[i
])
5676 nvar
= scc
->n_total_row
- scc
->band_start
;
5679 for (j
= 0; j
< scc
->n
; ++j
) {
5680 struct isl_sched_node
*node
= &scc
->node
[j
];
5683 if (node_update_cmap(node
) < 0)
5685 slack
= node
->nvar
- node
->rank
;
5686 if (slack
> max_slack
)
5694 /* If there are any clusters where the dimension of the current band
5695 * (i.e., the band that is to be merged) is smaller than "maxvar" and
5696 * if there are any nodes in such a cluster where the number
5697 * of remaining schedule rows that still need to be computed
5698 * is greater than "max_slack", then return the smallest current band
5699 * dimension of all these clusters. Otherwise return the original value
5700 * of "maxvar". Return -1 in case of any error.
5701 * Only clusters that are about to be merged are considered.
5702 * "c" contains information about the clusters.
5704 static int limit_maxvar_to_slack(int maxvar
, int max_slack
,
5705 struct isl_clustering
*c
)
5709 for (i
= 0; i
< c
->n
; ++i
) {
5711 struct isl_sched_graph
*scc
;
5713 if (!c
->scc_in_merge
[i
])
5716 nvar
= scc
->n_total_row
- scc
->band_start
;
5719 for (j
= 0; j
< scc
->n
; ++j
) {
5720 struct isl_sched_node
*node
= &scc
->node
[j
];
5723 if (node_update_cmap(node
) < 0)
5725 slack
= node
->nvar
- node
->rank
;
5726 if (slack
> max_slack
) {
5736 /* Adjust merge_graph->maxvar based on the number of remaining schedule rows
5737 * that still need to be computed. In particular, if there is a node
5738 * in a cluster where the dimension of the current band is smaller
5739 * than merge_graph->maxvar, but the number of remaining schedule rows
5740 * is greater than that of any node in a cluster with the maximal
5741 * dimension for the current band (i.e., merge_graph->maxvar),
5742 * then adjust merge_graph->maxvar to the (smallest) current band dimension
5743 * of those clusters. Without this adjustment, the total number of
5744 * schedule dimensions would be increased, resulting in a skewed view
5745 * of the number of coincident dimensions.
5746 * "c" contains information about the clusters.
5748 * If the maximize_band_depth option is set and merge_graph->maxvar is reduced,
5749 * then there is no point in attempting any merge since it will be rejected
5750 * anyway. Set merge_graph->maxvar to zero in such cases.
5752 static isl_stat
adjust_maxvar_to_slack(isl_ctx
*ctx
,
5753 struct isl_sched_graph
*merge_graph
, struct isl_clustering
*c
)
5755 int max_slack
, maxvar
;
5757 max_slack
= compute_maxvar_max_slack(merge_graph
->maxvar
, c
);
5759 return isl_stat_error
;
5760 maxvar
= limit_maxvar_to_slack(merge_graph
->maxvar
, max_slack
, c
);
5762 return isl_stat_error
;
5764 if (maxvar
< merge_graph
->maxvar
) {
5765 if (isl_options_get_schedule_maximize_band_depth(ctx
))
5766 merge_graph
->maxvar
= 0;
5768 merge_graph
->maxvar
= maxvar
;
5774 /* Return the number of coincident dimensions in the current band of "graph",
5775 * where the nodes of "graph" are assumed to be scheduled by a single band.
5777 static int get_n_coincident(struct isl_sched_graph
*graph
)
5781 for (i
= graph
->band_start
; i
< graph
->n_total_row
; ++i
)
5782 if (!graph
->node
[0].coincident
[i
])
5785 return i
- graph
->band_start
;
5788 /* Should the clusters be merged based on the cluster schedule
5789 * in the current (and only) band of "merge_graph", given that
5790 * coincidence should be maximized?
5792 * If the number of coincident schedule dimensions in the merged band
5793 * would be less than the maximal number of coincident schedule dimensions
5794 * in any of the merged clusters, then the clusters should not be merged.
5796 static isl_bool
ok_to_merge_coincident(struct isl_clustering
*c
,
5797 struct isl_sched_graph
*merge_graph
)
5804 for (i
= 0; i
< c
->n
; ++i
) {
5805 if (!c
->scc_in_merge
[i
])
5807 n_coincident
= get_n_coincident(&c
->scc
[i
]);
5808 if (n_coincident
> max_coincident
)
5809 max_coincident
= n_coincident
;
5812 n_coincident
= get_n_coincident(merge_graph
);
5814 return n_coincident
>= max_coincident
;
5817 /* Return the transformation on "node" expressed by the current (and only)
5818 * band of "merge_graph" applied to the clusters in "c".
5820 * First find the representation of "node" in its SCC in "c" and
5821 * extract the transformation expressed by the current band.
5822 * Then extract the transformation applied by "merge_graph"
5823 * to the cluster to which this SCC belongs.
5824 * Combine the two to obtain the complete transformation on the node.
5826 * Note that the range of the first transformation is an anonymous space,
5827 * while the domain of the second is named "cluster_X". The range
5828 * of the former therefore needs to be adjusted before the two
5831 static __isl_give isl_map
*extract_node_transformation(isl_ctx
*ctx
,
5832 struct isl_sched_node
*node
, struct isl_clustering
*c
,
5833 struct isl_sched_graph
*merge_graph
)
5835 struct isl_sched_node
*scc_node
, *cluster_node
;
5839 isl_multi_aff
*ma
, *ma2
;
5841 scc_node
= graph_find_node(ctx
, &c
->scc
[node
->scc
], node
->space
);
5842 start
= c
->scc
[node
->scc
].band_start
;
5843 n
= c
->scc
[node
->scc
].n_total_row
- start
;
5844 ma
= node_extract_partial_schedule_multi_aff(scc_node
, start
, n
);
5845 space
= cluster_space(&c
->scc
[node
->scc
], c
->scc_cluster
[node
->scc
]);
5846 cluster_node
= graph_find_node(ctx
, merge_graph
, space
);
5847 if (space
&& !cluster_node
)
5848 isl_die(ctx
, isl_error_internal
, "unable to find cluster",
5849 space
= isl_space_free(space
));
5850 id
= isl_space_get_tuple_id(space
, isl_dim_set
);
5851 ma
= isl_multi_aff_set_tuple_id(ma
, isl_dim_out
, id
);
5852 isl_space_free(space
);
5853 n
= merge_graph
->n_total_row
;
5854 ma2
= node_extract_partial_schedule_multi_aff(cluster_node
, 0, n
);
5855 ma
= isl_multi_aff_pullback_multi_aff(ma2
, ma
);
5857 return isl_map_from_multi_aff(ma
);
5860 /* Give a set of distances "set", are they bounded by a small constant
5861 * in direction "pos"?
5862 * In practice, check if they are bounded by 2 by checking that there
5863 * are no elements with a value greater than or equal to 3 or
5864 * smaller than or equal to -3.
5866 static isl_bool
distance_is_bounded(__isl_keep isl_set
*set
, int pos
)
5872 return isl_bool_error
;
5874 test
= isl_set_copy(set
);
5875 test
= isl_set_lower_bound_si(test
, isl_dim_set
, pos
, 3);
5876 bounded
= isl_set_is_empty(test
);
5879 if (bounded
< 0 || !bounded
)
5882 test
= isl_set_copy(set
);
5883 test
= isl_set_upper_bound_si(test
, isl_dim_set
, pos
, -3);
5884 bounded
= isl_set_is_empty(test
);
5890 /* Does the set "set" have a fixed (but possible parametric) value
5891 * at dimension "pos"?
5893 static isl_bool
has_single_value(__isl_keep isl_set
*set
, int pos
)
5899 return isl_bool_error
;
5900 set
= isl_set_copy(set
);
5901 n
= isl_set_dim(set
, isl_dim_set
);
5902 set
= isl_set_project_out(set
, isl_dim_set
, pos
+ 1, n
- (pos
+ 1));
5903 set
= isl_set_project_out(set
, isl_dim_set
, 0, pos
);
5904 single
= isl_set_is_singleton(set
);
5910 /* Does "map" have a fixed (but possible parametric) value
5911 * at dimension "pos" of either its domain or its range?
5913 static isl_bool
has_singular_src_or_dst(__isl_keep isl_map
*map
, int pos
)
5918 set
= isl_map_domain(isl_map_copy(map
));
5919 single
= has_single_value(set
, pos
);
5922 if (single
< 0 || single
)
5925 set
= isl_map_range(isl_map_copy(map
));
5926 single
= has_single_value(set
, pos
);
5932 /* Does the edge "edge" from "graph" have bounded dependence distances
5933 * in the merged graph "merge_graph" of a selection of clusters in "c"?
5935 * Extract the complete transformations of the source and destination
5936 * nodes of the edge, apply them to the edge constraints and
5937 * compute the differences. Finally, check if these differences are bounded
5938 * in each direction.
5940 * If the dimension of the band is greater than the number of
5941 * dimensions that can be expected to be optimized by the edge
5942 * (based on its weight), then also allow the differences to be unbounded
5943 * in the remaining dimensions, but only if either the source or
5944 * the destination has a fixed value in that direction.
5945 * This allows a statement that produces values that are used by
5946 * several instances of another statement to be merged with that
5948 * However, merging such clusters will introduce an inherently
5949 * large proximity distance inside the merged cluster, meaning
5950 * that proximity distances will no longer be optimized in
5951 * subsequent merges. These merges are therefore only allowed
5952 * after all other possible merges have been tried.
5953 * The first time such a merge is encountered, the weight of the edge
5954 * is replaced by a negative weight. The second time (i.e., after
5955 * all merges over edges with a non-negative weight have been tried),
5956 * the merge is allowed.
5958 static isl_bool
has_bounded_distances(isl_ctx
*ctx
, struct isl_sched_edge
*edge
,
5959 struct isl_sched_graph
*graph
, struct isl_clustering
*c
,
5960 struct isl_sched_graph
*merge_graph
)
5967 map
= isl_map_copy(edge
->map
);
5968 t
= extract_node_transformation(ctx
, edge
->src
, c
, merge_graph
);
5969 map
= isl_map_apply_domain(map
, t
);
5970 t
= extract_node_transformation(ctx
, edge
->dst
, c
, merge_graph
);
5971 map
= isl_map_apply_range(map
, t
);
5972 dist
= isl_map_deltas(isl_map_copy(map
));
5974 bounded
= isl_bool_true
;
5975 n
= isl_set_dim(dist
, isl_dim_set
);
5976 n_slack
= n
- edge
->weight
;
5977 if (edge
->weight
< 0)
5978 n_slack
-= graph
->max_weight
+ 1;
5979 for (i
= 0; i
< n
; ++i
) {
5980 isl_bool bounded_i
, singular_i
;
5982 bounded_i
= distance_is_bounded(dist
, i
);
5987 if (edge
->weight
>= 0)
5988 bounded
= isl_bool_false
;
5992 singular_i
= has_singular_src_or_dst(map
, i
);
5997 bounded
= isl_bool_false
;
6000 if (!bounded
&& i
>= n
&& edge
->weight
>= 0)
6001 edge
->weight
-= graph
->max_weight
+ 1;
6009 return isl_bool_error
;
6012 /* Should the clusters be merged based on the cluster schedule
6013 * in the current (and only) band of "merge_graph"?
6014 * "graph" is the original dependence graph, while "c" records
6015 * which SCCs are involved in the latest merge.
6017 * In particular, is there at least one proximity constraint
6018 * that is optimized by the merge?
6020 * A proximity constraint is considered to be optimized
6021 * if the dependence distances are small.
6023 static isl_bool
ok_to_merge_proximity(isl_ctx
*ctx
,
6024 struct isl_sched_graph
*graph
, struct isl_clustering
*c
,
6025 struct isl_sched_graph
*merge_graph
)
6029 for (i
= 0; i
< graph
->n_edge
; ++i
) {
6030 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
6033 if (!is_proximity(edge
))
6035 if (!c
->scc_in_merge
[edge
->src
->scc
])
6037 if (!c
->scc_in_merge
[edge
->dst
->scc
])
6039 if (c
->scc_cluster
[edge
->dst
->scc
] ==
6040 c
->scc_cluster
[edge
->src
->scc
])
6042 bounded
= has_bounded_distances(ctx
, edge
, graph
, c
,
6044 if (bounded
< 0 || bounded
)
6048 return isl_bool_false
;
6051 /* Should the clusters be merged based on the cluster schedule
6052 * in the current (and only) band of "merge_graph"?
6053 * "graph" is the original dependence graph, while "c" records
6054 * which SCCs are involved in the latest merge.
6056 * If the current band is empty, then the clusters should not be merged.
6058 * If the band depth should be maximized and the merge schedule
6059 * is incomplete (meaning that the dimension of some of the schedule
6060 * bands in the original schedule will be reduced), then the clusters
6061 * should not be merged.
6063 * If the schedule_maximize_coincidence option is set, then check that
6064 * the number of coincident schedule dimensions is not reduced.
6066 * Finally, only allow the merge if at least one proximity
6067 * constraint is optimized.
6069 static isl_bool
ok_to_merge(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
6070 struct isl_clustering
*c
, struct isl_sched_graph
*merge_graph
)
6072 if (merge_graph
->n_total_row
== merge_graph
->band_start
)
6073 return isl_bool_false
;
6075 if (isl_options_get_schedule_maximize_band_depth(ctx
) &&
6076 merge_graph
->n_total_row
< merge_graph
->maxvar
)
6077 return isl_bool_false
;
6079 if (isl_options_get_schedule_maximize_coincidence(ctx
)) {
6082 ok
= ok_to_merge_coincident(c
, merge_graph
);
6087 return ok_to_merge_proximity(ctx
, graph
, c
, merge_graph
);
6090 /* Apply the schedule in "t_node" to the "n" rows starting at "first"
6091 * of the schedule in "node" and return the result.
6093 * That is, essentially compute
6095 * T * N(first:first+n-1)
6097 * taking into account the constant term and the parameter coefficients
6100 static __isl_give isl_mat
*node_transformation(isl_ctx
*ctx
,
6101 struct isl_sched_node
*t_node
, struct isl_sched_node
*node
,
6106 int n_row
, n_col
, n_param
, n_var
;
6108 n_param
= node
->nparam
;
6110 n_row
= isl_mat_rows(t_node
->sched
);
6111 n_col
= isl_mat_cols(node
->sched
);
6112 t
= isl_mat_alloc(ctx
, n_row
, n_col
);
6115 for (i
= 0; i
< n_row
; ++i
) {
6116 isl_seq_cpy(t
->row
[i
], t_node
->sched
->row
[i
], 1 + n_param
);
6117 isl_seq_clr(t
->row
[i
] + 1 + n_param
, n_var
);
6118 for (j
= 0; j
< n
; ++j
)
6119 isl_seq_addmul(t
->row
[i
],
6120 t_node
->sched
->row
[i
][1 + n_param
+ j
],
6121 node
->sched
->row
[first
+ j
],
6122 1 + n_param
+ n_var
);
6127 /* Apply the cluster schedule in "t_node" to the current band
6128 * schedule of the nodes in "graph".
6130 * In particular, replace the rows starting at band_start
6131 * by the result of applying the cluster schedule in "t_node"
6132 * to the original rows.
6134 * The coincidence of the schedule is determined by the coincidence
6135 * of the cluster schedule.
6137 static isl_stat
transform(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
6138 struct isl_sched_node
*t_node
)
6144 start
= graph
->band_start
;
6145 n
= graph
->n_total_row
- start
;
6147 n_new
= isl_mat_rows(t_node
->sched
);
6148 for (i
= 0; i
< graph
->n
; ++i
) {
6149 struct isl_sched_node
*node
= &graph
->node
[i
];
6152 t
= node_transformation(ctx
, t_node
, node
, start
, n
);
6153 node
->sched
= isl_mat_drop_rows(node
->sched
, start
, n
);
6154 node
->sched
= isl_mat_concat(node
->sched
, t
);
6155 node
->sched_map
= isl_map_free(node
->sched_map
);
6157 return isl_stat_error
;
6158 for (j
= 0; j
< n_new
; ++j
)
6159 node
->coincident
[start
+ j
] = t_node
->coincident
[j
];
6161 graph
->n_total_row
-= n
;
6163 graph
->n_total_row
+= n_new
;
6164 graph
->n_row
+= n_new
;
6169 /* Merge the clusters marked for merging in "c" into a single
6170 * cluster using the cluster schedule in the current band of "merge_graph".
6171 * The representative SCC for the new cluster is the SCC with
6172 * the smallest index.
6174 * The current band schedule of each SCC in the new cluster is obtained
6175 * by applying the schedule of the corresponding original cluster
6176 * to the original band schedule.
6177 * All SCCs in the new cluster have the same number of schedule rows.
6179 static isl_stat
merge(isl_ctx
*ctx
, struct isl_clustering
*c
,
6180 struct isl_sched_graph
*merge_graph
)
6186 for (i
= 0; i
< c
->n
; ++i
) {
6187 struct isl_sched_node
*node
;
6189 if (!c
->scc_in_merge
[i
])
6193 space
= cluster_space(&c
->scc
[i
], c
->scc_cluster
[i
]);
6195 return isl_stat_error
;
6196 node
= graph_find_node(ctx
, merge_graph
, space
);
6197 isl_space_free(space
);
6199 isl_die(ctx
, isl_error_internal
,
6200 "unable to find cluster",
6201 return isl_stat_error
);
6202 if (transform(ctx
, &c
->scc
[i
], node
) < 0)
6203 return isl_stat_error
;
6204 c
->scc_cluster
[i
] = cluster
;
6210 /* Try and merge the clusters of SCCs marked in c->scc_in_merge
6211 * by scheduling the current cluster bands with respect to each other.
6213 * Construct a dependence graph with a space for each cluster and
6214 * with the coordinates of each space corresponding to the schedule
6215 * dimensions of the current band of that cluster.
6216 * Construct a cluster schedule in this cluster dependence graph and
6217 * apply it to the current cluster bands if it is applicable
6218 * according to ok_to_merge.
6220 * If the number of remaining schedule dimensions in a cluster
6221 * with a non-maximal current schedule dimension is greater than
6222 * the number of remaining schedule dimensions in clusters
6223 * with a maximal current schedule dimension, then restrict
6224 * the number of rows to be computed in the cluster schedule
6225 * to the minimal such non-maximal current schedule dimension.
6226 * Do this by adjusting merge_graph.maxvar.
6228 * Return isl_bool_true if the clusters have effectively been merged
6229 * into a single cluster.
6231 * Note that since the standard scheduling algorithm minimizes the maximal
6232 * distance over proximity constraints, the proximity constraints between
6233 * the merged clusters may not be optimized any further than what is
6234 * sufficient to bring the distances within the limits of the internal
6235 * proximity constraints inside the individual clusters.
6236 * It may therefore make sense to perform an additional translation step
6237 * to bring the clusters closer to each other, while maintaining
6238 * the linear part of the merging schedule found using the standard
6239 * scheduling algorithm.
6241 static isl_bool
try_merge(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
6242 struct isl_clustering
*c
)
6244 struct isl_sched_graph merge_graph
= { 0 };
6247 if (init_merge_graph(ctx
, graph
, c
, &merge_graph
) < 0)
6250 if (compute_maxvar(&merge_graph
) < 0)
6252 if (adjust_maxvar_to_slack(ctx
, &merge_graph
,c
) < 0)
6254 if (compute_schedule_wcc_band(ctx
, &merge_graph
) < 0)
6256 merged
= ok_to_merge(ctx
, graph
, c
, &merge_graph
);
6257 if (merged
&& merge(ctx
, c
, &merge_graph
) < 0)
6260 graph_free(ctx
, &merge_graph
);
6263 graph_free(ctx
, &merge_graph
);
6264 return isl_bool_error
;
6267 /* Is there any edge marked "no_merge" between two SCCs that are
6268 * about to be merged (i.e., that are set in "scc_in_merge")?
6269 * "merge_edge" is the proximity edge along which the clusters of SCCs
6270 * are going to be merged.
6272 * If there is any edge between two SCCs with a negative weight,
6273 * while the weight of "merge_edge" is non-negative, then this
6274 * means that the edge was postponed. "merge_edge" should then
6275 * also be postponed since merging along the edge with negative weight should
6276 * be postponed until all edges with non-negative weight have been tried.
6277 * Replace the weight of "merge_edge" by a negative weight as well and
6278 * tell the caller not to attempt a merge.
6280 static int any_no_merge(struct isl_sched_graph
*graph
, int *scc_in_merge
,
6281 struct isl_sched_edge
*merge_edge
)
6285 for (i
= 0; i
< graph
->n_edge
; ++i
) {
6286 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
6288 if (!scc_in_merge
[edge
->src
->scc
])
6290 if (!scc_in_merge
[edge
->dst
->scc
])
6294 if (merge_edge
->weight
>= 0 && edge
->weight
< 0) {
6295 merge_edge
->weight
-= graph
->max_weight
+ 1;
6303 /* Merge the two clusters in "c" connected by the edge in "graph"
6304 * with index "edge" into a single cluster.
6305 * If it turns out to be impossible to merge these two clusters,
6306 * then mark the edge as "no_merge" such that it will not be
6309 * First mark all SCCs that need to be merged. This includes the SCCs
6310 * in the two clusters, but it may also include the SCCs
6311 * of intermediate clusters.
6312 * If there is already a no_merge edge between any pair of such SCCs,
6313 * then simply mark the current edge as no_merge as well.
6314 * Likewise, if any of those edges was postponed by has_bounded_distances,
6315 * then postpone the current edge as well.
6316 * Otherwise, try and merge the clusters and mark "edge" as "no_merge"
6317 * if the clusters did not end up getting merged, unless the non-merge
6318 * is due to the fact that the edge was postponed. This postponement
6319 * can be recognized by a change in weight (from non-negative to negative).
6321 static isl_stat
merge_clusters_along_edge(isl_ctx
*ctx
,
6322 struct isl_sched_graph
*graph
, int edge
, struct isl_clustering
*c
)
6325 int edge_weight
= graph
->edge
[edge
].weight
;
6327 if (mark_merge_sccs(ctx
, graph
, edge
, c
) < 0)
6328 return isl_stat_error
;
6330 if (any_no_merge(graph
, c
->scc_in_merge
, &graph
->edge
[edge
]))
6331 merged
= isl_bool_false
;
6333 merged
= try_merge(ctx
, graph
, c
);
6335 return isl_stat_error
;
6336 if (!merged
&& edge_weight
== graph
->edge
[edge
].weight
)
6337 graph
->edge
[edge
].no_merge
= 1;
6342 /* Does "node" belong to the cluster identified by "cluster"?
6344 static int node_cluster_exactly(struct isl_sched_node
*node
, int cluster
)
6346 return node
->cluster
== cluster
;
6349 /* Does "edge" connect two nodes belonging to the cluster
6350 * identified by "cluster"?
6352 static int edge_cluster_exactly(struct isl_sched_edge
*edge
, int cluster
)
6354 return edge
->src
->cluster
== cluster
&& edge
->dst
->cluster
== cluster
;
6357 /* Swap the schedule of "node1" and "node2".
6358 * Both nodes have been derived from the same node in a common parent graph.
6359 * Since the "coincident" field is shared with that node
6360 * in the parent graph, there is no need to also swap this field.
6362 static void swap_sched(struct isl_sched_node
*node1
,
6363 struct isl_sched_node
*node2
)
6368 sched
= node1
->sched
;
6369 node1
->sched
= node2
->sched
;
6370 node2
->sched
= sched
;
6372 sched_map
= node1
->sched_map
;
6373 node1
->sched_map
= node2
->sched_map
;
6374 node2
->sched_map
= sched_map
;
6377 /* Copy the current band schedule from the SCCs that form the cluster
6378 * with index "pos" to the actual cluster at position "pos".
6379 * By construction, the index of the first SCC that belongs to the cluster
6382 * The order of the nodes inside both the SCCs and the cluster
6383 * is assumed to be same as the order in the original "graph".
6385 * Since the SCC graphs will no longer be used after this function,
6386 * the schedules are actually swapped rather than copied.
6388 static isl_stat
copy_partial(struct isl_sched_graph
*graph
,
6389 struct isl_clustering
*c
, int pos
)
6393 c
->cluster
[pos
].n_total_row
= c
->scc
[pos
].n_total_row
;
6394 c
->cluster
[pos
].n_row
= c
->scc
[pos
].n_row
;
6395 c
->cluster
[pos
].maxvar
= c
->scc
[pos
].maxvar
;
6397 for (i
= 0; i
< graph
->n
; ++i
) {
6401 if (graph
->node
[i
].cluster
!= pos
)
6403 s
= graph
->node
[i
].scc
;
6404 k
= c
->scc_node
[s
]++;
6405 swap_sched(&c
->cluster
[pos
].node
[j
], &c
->scc
[s
].node
[k
]);
6406 if (c
->scc
[s
].maxvar
> c
->cluster
[pos
].maxvar
)
6407 c
->cluster
[pos
].maxvar
= c
->scc
[s
].maxvar
;
6414 /* Is there a (conditional) validity dependence from node[j] to node[i],
6415 * forcing node[i] to follow node[j] or do the nodes belong to the same
6418 static isl_bool
node_follows_strong_or_same_cluster(int i
, int j
, void *user
)
6420 struct isl_sched_graph
*graph
= user
;
6422 if (graph
->node
[i
].cluster
== graph
->node
[j
].cluster
)
6423 return isl_bool_true
;
6424 return graph_has_validity_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
6427 /* Extract the merged clusters of SCCs in "graph", sort them, and
6428 * store them in c->clusters. Update c->scc_cluster accordingly.
6430 * First keep track of the cluster containing the SCC to which a node
6431 * belongs in the node itself.
6432 * Then extract the clusters into c->clusters, copying the current
6433 * band schedule from the SCCs that belong to the cluster.
6434 * Do this only once per cluster.
6436 * Finally, topologically sort the clusters and update c->scc_cluster
6437 * to match the new scc numbering. While the SCCs were originally
6438 * sorted already, some SCCs that depend on some other SCCs may
6439 * have been merged with SCCs that appear before these other SCCs.
6440 * A reordering may therefore be required.
6442 static isl_stat
extract_clusters(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
6443 struct isl_clustering
*c
)
6447 for (i
= 0; i
< graph
->n
; ++i
)
6448 graph
->node
[i
].cluster
= c
->scc_cluster
[graph
->node
[i
].scc
];
6450 for (i
= 0; i
< graph
->scc
; ++i
) {
6451 if (c
->scc_cluster
[i
] != i
)
6453 if (extract_sub_graph(ctx
, graph
, &node_cluster_exactly
,
6454 &edge_cluster_exactly
, i
, &c
->cluster
[i
]) < 0)
6455 return isl_stat_error
;
6456 c
->cluster
[i
].src_scc
= -1;
6457 c
->cluster
[i
].dst_scc
= -1;
6458 if (copy_partial(graph
, c
, i
) < 0)
6459 return isl_stat_error
;
6462 if (detect_ccs(ctx
, graph
, &node_follows_strong_or_same_cluster
) < 0)
6463 return isl_stat_error
;
6464 for (i
= 0; i
< graph
->n
; ++i
)
6465 c
->scc_cluster
[graph
->node
[i
].scc
] = graph
->node
[i
].cluster
;
6470 /* Compute weights on the proximity edges of "graph" that can
6471 * be used by find_proximity to find the most appropriate
6472 * proximity edge to use to merge two clusters in "c".
6473 * The weights are also used by has_bounded_distances to determine
6474 * whether the merge should be allowed.
6475 * Store the maximum of the computed weights in graph->max_weight.
6477 * The computed weight is a measure for the number of remaining schedule
6478 * dimensions that can still be completely aligned.
6479 * In particular, compute the number of equalities between
6480 * input dimensions and output dimensions in the proximity constraints.
6481 * The directions that are already handled by outer schedule bands
6482 * are projected out prior to determining this number.
6484 * Edges that will never be considered by find_proximity are ignored.
6486 static isl_stat
compute_weights(struct isl_sched_graph
*graph
,
6487 struct isl_clustering
*c
)
6491 graph
->max_weight
= 0;
6493 for (i
= 0; i
< graph
->n_edge
; ++i
) {
6494 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
6495 struct isl_sched_node
*src
= edge
->src
;
6496 struct isl_sched_node
*dst
= edge
->dst
;
6497 isl_basic_map
*hull
;
6501 prox
= is_non_empty_proximity(edge
);
6503 return isl_stat_error
;
6506 if (bad_cluster(&c
->scc
[edge
->src
->scc
]) ||
6507 bad_cluster(&c
->scc
[edge
->dst
->scc
]))
6509 if (c
->scc_cluster
[edge
->dst
->scc
] ==
6510 c
->scc_cluster
[edge
->src
->scc
])
6513 hull
= isl_map_affine_hull(isl_map_copy(edge
->map
));
6514 hull
= isl_basic_map_transform_dims(hull
, isl_dim_in
, 0,
6515 isl_mat_copy(src
->ctrans
));
6516 hull
= isl_basic_map_transform_dims(hull
, isl_dim_out
, 0,
6517 isl_mat_copy(dst
->ctrans
));
6518 hull
= isl_basic_map_project_out(hull
,
6519 isl_dim_in
, 0, src
->rank
);
6520 hull
= isl_basic_map_project_out(hull
,
6521 isl_dim_out
, 0, dst
->rank
);
6522 hull
= isl_basic_map_remove_divs(hull
);
6523 n_in
= isl_basic_map_dim(hull
, isl_dim_in
);
6524 n_out
= isl_basic_map_dim(hull
, isl_dim_out
);
6525 hull
= isl_basic_map_drop_constraints_not_involving_dims(hull
,
6526 isl_dim_in
, 0, n_in
);
6527 hull
= isl_basic_map_drop_constraints_not_involving_dims(hull
,
6528 isl_dim_out
, 0, n_out
);
6530 return isl_stat_error
;
6531 edge
->weight
= isl_basic_map_n_equality(hull
);
6532 isl_basic_map_free(hull
);
6534 if (edge
->weight
> graph
->max_weight
)
6535 graph
->max_weight
= edge
->weight
;
6541 /* Call compute_schedule_finish_band on each of the clusters in "c"
6542 * in their topological order. This order is determined by the scc
6543 * fields of the nodes in "graph".
6544 * Combine the results in a sequence expressing the topological order.
6546 * If there is only one cluster left, then there is no need to introduce
6547 * a sequence node. Also, in this case, the cluster necessarily contains
6548 * the SCC at position 0 in the original graph and is therefore also
6549 * stored in the first cluster of "c".
6551 static __isl_give isl_schedule_node
*finish_bands_clustering(
6552 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
6553 struct isl_clustering
*c
)
6557 isl_union_set_list
*filters
;
6559 if (graph
->scc
== 1)
6560 return compute_schedule_finish_band(node
, &c
->cluster
[0], 0);
6562 ctx
= isl_schedule_node_get_ctx(node
);
6564 filters
= extract_sccs(ctx
, graph
);
6565 node
= isl_schedule_node_insert_sequence(node
, filters
);
6567 for (i
= 0; i
< graph
->scc
; ++i
) {
6568 int j
= c
->scc_cluster
[i
];
6569 node
= isl_schedule_node_child(node
, i
);
6570 node
= isl_schedule_node_child(node
, 0);
6571 node
= compute_schedule_finish_band(node
, &c
->cluster
[j
], 0);
6572 node
= isl_schedule_node_parent(node
);
6573 node
= isl_schedule_node_parent(node
);
6579 /* Compute a schedule for a connected dependence graph by first considering
6580 * each strongly connected component (SCC) in the graph separately and then
6581 * incrementally combining them into clusters.
6582 * Return the updated schedule node.
6584 * Initially, each cluster consists of a single SCC, each with its
6585 * own band schedule. The algorithm then tries to merge pairs
6586 * of clusters along a proximity edge until no more suitable
6587 * proximity edges can be found. During this merging, the schedule
6588 * is maintained in the individual SCCs.
6589 * After the merging is completed, the full resulting clusters
6590 * are extracted and in finish_bands_clustering,
6591 * compute_schedule_finish_band is called on each of them to integrate
6592 * the band into "node" and to continue the computation.
6594 * compute_weights initializes the weights that are used by find_proximity.
6596 static __isl_give isl_schedule_node
*compute_schedule_wcc_clustering(
6597 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
6600 struct isl_clustering c
;
6603 ctx
= isl_schedule_node_get_ctx(node
);
6605 if (clustering_init(ctx
, &c
, graph
) < 0)
6608 if (compute_weights(graph
, &c
) < 0)
6612 i
= find_proximity(graph
, &c
);
6615 if (i
>= graph
->n_edge
)
6617 if (merge_clusters_along_edge(ctx
, graph
, i
, &c
) < 0)
6621 if (extract_clusters(ctx
, graph
, &c
) < 0)
6624 node
= finish_bands_clustering(node
, graph
, &c
);
6626 clustering_free(ctx
, &c
);
6629 clustering_free(ctx
, &c
);
6630 return isl_schedule_node_free(node
);
6633 /* Compute a schedule for a connected dependence graph and return
6634 * the updated schedule node.
6636 * If Feautrier's algorithm is selected, we first recursively try to satisfy
6637 * as many validity dependences as possible. When all validity dependences
6638 * are satisfied we extend the schedule to a full-dimensional schedule.
6640 * Call compute_schedule_wcc_whole or compute_schedule_wcc_clustering
6641 * depending on whether the user has selected the option to try and
6642 * compute a schedule for the entire (weakly connected) component first.
6643 * If there is only a single strongly connected component (SCC), then
6644 * there is no point in trying to combine SCCs
6645 * in compute_schedule_wcc_clustering, so compute_schedule_wcc_whole
6646 * is called instead.
6648 static __isl_give isl_schedule_node
*compute_schedule_wcc(
6649 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
6656 ctx
= isl_schedule_node_get_ctx(node
);
6657 if (detect_sccs(ctx
, graph
) < 0)
6658 return isl_schedule_node_free(node
);
6660 if (compute_maxvar(graph
) < 0)
6661 return isl_schedule_node_free(node
);
6663 if (need_feautrier_step(ctx
, graph
))
6664 return compute_schedule_wcc_feautrier(node
, graph
);
6666 if (graph
->scc
<= 1 || isl_options_get_schedule_whole_component(ctx
))
6667 return compute_schedule_wcc_whole(node
, graph
);
6669 return compute_schedule_wcc_clustering(node
, graph
);
6672 /* Compute a schedule for each group of nodes identified by node->scc
6673 * separately and then combine them in a sequence node (or as set node
6674 * if graph->weak is set) inserted at position "node" of the schedule tree.
6675 * Return the updated schedule node.
6677 * If "wcc" is set then each of the groups belongs to a single
6678 * weakly connected component in the dependence graph so that
6679 * there is no need for compute_sub_schedule to look for weakly
6680 * connected components.
6682 static __isl_give isl_schedule_node
*compute_component_schedule(
6683 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
6688 isl_union_set_list
*filters
;
6692 ctx
= isl_schedule_node_get_ctx(node
);
6694 filters
= extract_sccs(ctx
, graph
);
6696 node
= isl_schedule_node_insert_set(node
, filters
);
6698 node
= isl_schedule_node_insert_sequence(node
, filters
);
6700 for (component
= 0; component
< graph
->scc
; ++component
) {
6701 node
= isl_schedule_node_child(node
, component
);
6702 node
= isl_schedule_node_child(node
, 0);
6703 node
= compute_sub_schedule(node
, ctx
, graph
,
6705 &edge_scc_exactly
, component
, wcc
);
6706 node
= isl_schedule_node_parent(node
);
6707 node
= isl_schedule_node_parent(node
);
6713 /* Compute a schedule for the given dependence graph and insert it at "node".
6714 * Return the updated schedule node.
6716 * We first check if the graph is connected (through validity and conditional
6717 * validity dependences) and, if not, compute a schedule
6718 * for each component separately.
6719 * If the schedule_serialize_sccs option is set, then we check for strongly
6720 * connected components instead and compute a separate schedule for
6721 * each such strongly connected component.
6723 static __isl_give isl_schedule_node
*compute_schedule(isl_schedule_node
*node
,
6724 struct isl_sched_graph
*graph
)
6731 ctx
= isl_schedule_node_get_ctx(node
);
6732 if (isl_options_get_schedule_serialize_sccs(ctx
)) {
6733 if (detect_sccs(ctx
, graph
) < 0)
6734 return isl_schedule_node_free(node
);
6736 if (detect_wccs(ctx
, graph
) < 0)
6737 return isl_schedule_node_free(node
);
6741 return compute_component_schedule(node
, graph
, 1);
6743 return compute_schedule_wcc(node
, graph
);
6746 /* Compute a schedule on sc->domain that respects the given schedule
6749 * In particular, the schedule respects all the validity dependences.
6750 * If the default isl scheduling algorithm is used, it tries to minimize
6751 * the dependence distances over the proximity dependences.
6752 * If Feautrier's scheduling algorithm is used, the proximity dependence
6753 * distances are only minimized during the extension to a full-dimensional
6756 * If there are any condition and conditional validity dependences,
6757 * then the conditional validity dependences may be violated inside
6758 * a tilable band, provided they have no adjacent non-local
6759 * condition dependences.
6761 __isl_give isl_schedule
*isl_schedule_constraints_compute_schedule(
6762 __isl_take isl_schedule_constraints
*sc
)
6764 isl_ctx
*ctx
= isl_schedule_constraints_get_ctx(sc
);
6765 struct isl_sched_graph graph
= { 0 };
6766 isl_schedule
*sched
;
6767 isl_schedule_node
*node
;
6768 isl_union_set
*domain
;
6770 sc
= isl_schedule_constraints_align_params(sc
);
6772 domain
= isl_schedule_constraints_get_domain(sc
);
6773 if (isl_union_set_n_set(domain
) == 0) {
6774 isl_schedule_constraints_free(sc
);
6775 return isl_schedule_from_domain(domain
);
6778 if (graph_init(&graph
, sc
) < 0)
6779 domain
= isl_union_set_free(domain
);
6781 node
= isl_schedule_node_from_domain(domain
);
6782 node
= isl_schedule_node_child(node
, 0);
6784 node
= compute_schedule(node
, &graph
);
6785 sched
= isl_schedule_node_get_schedule(node
);
6786 isl_schedule_node_free(node
);
6788 graph_free(ctx
, &graph
);
6789 isl_schedule_constraints_free(sc
);
6794 /* Compute a schedule for the given union of domains that respects
6795 * all the validity dependences and minimizes
6796 * the dependence distances over the proximity dependences.
6798 * This function is kept for backward compatibility.
6800 __isl_give isl_schedule
*isl_union_set_compute_schedule(
6801 __isl_take isl_union_set
*domain
,
6802 __isl_take isl_union_map
*validity
,
6803 __isl_take isl_union_map
*proximity
)
6805 isl_schedule_constraints
*sc
;
6807 sc
= isl_schedule_constraints_on_domain(domain
);
6808 sc
= isl_schedule_constraints_set_validity(sc
, validity
);
6809 sc
= isl_schedule_constraints_set_proximity(sc
, proximity
);
6811 return isl_schedule_constraints_compute_schedule(sc
);