2 * Copyright 2011 INRIA Saclay
3 * Copyright 2012-2013 Ecole Normale Superieure
5 * Use of this software is governed by the MIT license
7 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
8 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
10 * and Ecole Normale Superieure, 45 rue d'Ulm, 75230 Paris, France
13 #include <isl_ctx_private.h>
14 #include <isl_map_private.h>
15 #include <isl_space_private.h>
16 #include <isl_aff_private.h>
18 #include <isl/constraint.h>
19 #include <isl/schedule.h>
20 #include <isl_mat_private.h>
21 #include <isl_vec_private.h>
25 #include <isl_dim_map.h>
26 #include <isl/map_to_basic_set.h>
28 #include <isl_schedule_private.h>
29 #include <isl_band_private.h>
30 #include <isl_options_private.h>
31 #include <isl_tarjan.h>
34 * The scheduling algorithm implemented in this file was inspired by
35 * Bondhugula et al., "Automatic Transformations for Communication-Minimized
36 * Parallelization and Locality Optimization in the Polyhedral Model".
39 /* Construct an isl_schedule_constraints object for computing a schedule
40 * on "domain". The initial object does not impose any constraints.
42 __isl_give isl_schedule_constraints
*isl_schedule_constraints_on_domain(
43 __isl_take isl_union_set
*domain
)
47 isl_schedule_constraints
*sc
;
54 ctx
= isl_union_set_get_ctx(domain
);
55 sc
= isl_calloc_type(ctx
, struct isl_schedule_constraints
);
57 return isl_union_set_free(domain
);
59 space
= isl_union_set_get_space(domain
);
61 empty
= isl_union_map_empty(space
);
62 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
63 sc
->constraint
[i
] = isl_union_map_copy(empty
);
64 if (!sc
->constraint
[i
])
65 sc
->domain
= isl_union_set_free(sc
->domain
);
67 isl_union_map_free(empty
);
70 return isl_schedule_constraints_free(sc
);
75 /* Replace the validity constraints of "sc" by "validity".
77 __isl_give isl_schedule_constraints
*isl_schedule_constraints_set_validity(
78 __isl_take isl_schedule_constraints
*sc
,
79 __isl_take isl_union_map
*validity
)
84 isl_union_map_free(sc
->constraint
[isl_edge_validity
]);
85 sc
->constraint
[isl_edge_validity
] = validity
;
89 isl_schedule_constraints_free(sc
);
90 isl_union_map_free(validity
);
94 /* Replace the proximity constraints of "sc" by "proximity".
96 __isl_give isl_schedule_constraints
*isl_schedule_constraints_set_proximity(
97 __isl_take isl_schedule_constraints
*sc
,
98 __isl_take isl_union_map
*proximity
)
100 if (!sc
|| !proximity
)
103 isl_union_map_free(sc
->constraint
[isl_edge_proximity
]);
104 sc
->constraint
[isl_edge_proximity
] = proximity
;
108 isl_schedule_constraints_free(sc
);
109 isl_union_map_free(proximity
);
113 void *isl_schedule_constraints_free(__isl_take isl_schedule_constraints
*sc
)
115 enum isl_edge_type i
;
120 isl_union_set_free(sc
->domain
);
121 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
)
122 isl_union_map_free(sc
->constraint
[i
]);
129 isl_ctx
*isl_schedule_constraints_get_ctx(
130 __isl_keep isl_schedule_constraints
*sc
)
132 return sc
? isl_union_set_get_ctx(sc
->domain
) : NULL
;
135 void isl_schedule_constraints_dump(__isl_keep isl_schedule_constraints
*sc
)
140 fprintf(stderr
, "domain: ");
141 isl_union_set_dump(sc
->domain
);
142 fprintf(stderr
, "validity: ");
143 isl_union_map_dump(sc
->constraint
[isl_edge_validity
]);
144 fprintf(stderr
, "proximity: ");
145 isl_union_map_dump(sc
->constraint
[isl_edge_proximity
]);
148 /* Align the parameters of the fields of "sc".
150 static __isl_give isl_schedule_constraints
*
151 isl_schedule_constraints_align_params(__isl_take isl_schedule_constraints
*sc
)
154 enum isl_edge_type i
;
159 space
= isl_union_set_get_space(sc
->domain
);
160 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
)
161 space
= isl_space_align_params(space
,
162 isl_union_map_get_space(sc
->constraint
[i
]));
164 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
165 sc
->constraint
[i
] = isl_union_map_align_params(
166 sc
->constraint
[i
], isl_space_copy(space
));
167 if (!sc
->constraint
[i
])
168 space
= isl_space_free(space
);
170 sc
->domain
= isl_union_set_align_params(sc
->domain
, space
);
172 return isl_schedule_constraints_free(sc
);
177 /* Return the total number of isl_maps in the constraints of "sc".
179 static __isl_give
int isl_schedule_constraints_n_map(
180 __isl_keep isl_schedule_constraints
*sc
)
182 enum isl_edge_type i
;
185 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
)
186 n
+= isl_union_map_n_map(sc
->constraint
[i
]);
191 /* Internal information about a node that is used during the construction
193 * dim represents the space in which the domain lives
194 * sched is a matrix representation of the schedule being constructed
196 * sched_map is an isl_map representation of the same (partial) schedule
197 * sched_map may be NULL
198 * rank is the number of linearly independent rows in the linear part
200 * the columns of cmap represent a change of basis for the schedule
201 * coefficients; the first rank columns span the linear part of
203 * cinv is the inverse of cmap.
204 * start is the first variable in the LP problem in the sequences that
205 * represents the schedule coefficients of this node
206 * nvar is the dimension of the domain
207 * nparam is the number of parameters or 0 if we are not constructing
208 * a parametric schedule
210 * scc is the index of SCC (or WCC) this node belongs to
212 * band contains the band index for each of the rows of the schedule.
213 * band_id is used to differentiate between separate bands at the same
214 * level within the same parent band, i.e., bands that are separated
215 * by the parent band or bands that are independent of each other.
216 * zero contains a boolean for each of the rows of the schedule,
217 * indicating whether the corresponding scheduling dimension results
218 * in zero dependence distances within its band and with respect
219 * to the proximity edges.
221 struct isl_sched_node
{
239 static int node_has_dim(const void *entry
, const void *val
)
241 struct isl_sched_node
*node
= (struct isl_sched_node
*)entry
;
242 isl_space
*dim
= (isl_space
*)val
;
244 return isl_space_is_equal(node
->dim
, dim
);
247 /* An edge in the dependence graph. An edge may be used to
248 * ensure validity of the generated schedule, to minimize the dependence
251 * map is the dependence relation
252 * src is the source node
253 * dst is the sink node
254 * validity is set if the edge is used to ensure correctness
255 * proximity is set if the edge is used to minimize dependence distances
257 * For validity edges, start and end mark the sequence of inequality
258 * constraints in the LP problem that encode the validity constraint
259 * corresponding to this edge.
261 struct isl_sched_edge
{
264 struct isl_sched_node
*src
;
265 struct isl_sched_node
*dst
;
274 /* Internal information about the dependence graph used during
275 * the construction of the schedule.
277 * intra_hmap is a cache, mapping dependence relations to their dual,
278 * for dependences from a node to itself
279 * inter_hmap is a cache, mapping dependence relations to their dual,
280 * for dependences between distinct nodes
282 * n is the number of nodes
283 * node is the list of nodes
284 * maxvar is the maximal number of variables over all nodes
285 * max_row is the allocated number of rows in the schedule
286 * n_row is the current (maximal) number of linearly independent
287 * rows in the node schedules
288 * n_total_row is the current number of rows in the node schedules
289 * n_band is the current number of completed bands
290 * band_start is the starting row in the node schedules of the current band
291 * root is set if this graph is the original dependence graph,
292 * without any splitting
294 * sorted contains a list of node indices sorted according to the
295 * SCC to which a node belongs
297 * n_edge is the number of edges
298 * edge is the list of edges
299 * max_edge contains the maximal number of edges of each type;
300 * in particular, it contains the number of edges in the inital graph.
301 * edge_table contains pointers into the edge array, hashed on the source
302 * and sink spaces; there is one such table for each type;
303 * a given edge may be referenced from more than one table
304 * if the corresponding relation appears in more than of the
305 * sets of dependences
307 * node_table contains pointers into the node array, hashed on the space
309 * region contains a list of variable sequences that should be non-trivial
311 * lp contains the (I)LP problem used to obtain new schedule rows
313 * src_scc and dst_scc are the source and sink SCCs of an edge with
314 * conflicting constraints
316 * scc represents the number of components
318 struct isl_sched_graph
{
319 isl_map_to_basic_set
*intra_hmap
;
320 isl_map_to_basic_set
*inter_hmap
;
322 struct isl_sched_node
*node
;
336 struct isl_sched_edge
*edge
;
338 int max_edge
[isl_edge_last
+ 1];
339 struct isl_hash_table
*edge_table
[isl_edge_last
+ 1];
341 struct isl_hash_table
*node_table
;
342 struct isl_region
*region
;
352 /* Initialize node_table based on the list of nodes.
354 static int graph_init_table(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
358 graph
->node_table
= isl_hash_table_alloc(ctx
, graph
->n
);
359 if (!graph
->node_table
)
362 for (i
= 0; i
< graph
->n
; ++i
) {
363 struct isl_hash_table_entry
*entry
;
366 hash
= isl_space_get_hash(graph
->node
[i
].dim
);
367 entry
= isl_hash_table_find(ctx
, graph
->node_table
, hash
,
369 graph
->node
[i
].dim
, 1);
372 entry
->data
= &graph
->node
[i
];
378 /* Return a pointer to the node that lives within the given space,
379 * or NULL if there is no such node.
381 static struct isl_sched_node
*graph_find_node(isl_ctx
*ctx
,
382 struct isl_sched_graph
*graph
, __isl_keep isl_space
*dim
)
384 struct isl_hash_table_entry
*entry
;
387 hash
= isl_space_get_hash(dim
);
388 entry
= isl_hash_table_find(ctx
, graph
->node_table
, hash
,
389 &node_has_dim
, dim
, 0);
391 return entry
? entry
->data
: NULL
;
394 static int edge_has_src_and_dst(const void *entry
, const void *val
)
396 const struct isl_sched_edge
*edge
= entry
;
397 const struct isl_sched_edge
*temp
= val
;
399 return edge
->src
== temp
->src
&& edge
->dst
== temp
->dst
;
402 /* Add the given edge to graph->edge_table[type].
404 static int graph_edge_table_add(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
405 enum isl_edge_type type
, struct isl_sched_edge
*edge
)
407 struct isl_hash_table_entry
*entry
;
410 hash
= isl_hash_init();
411 hash
= isl_hash_builtin(hash
, edge
->src
);
412 hash
= isl_hash_builtin(hash
, edge
->dst
);
413 entry
= isl_hash_table_find(ctx
, graph
->edge_table
[type
], hash
,
414 &edge_has_src_and_dst
, edge
, 1);
422 /* Allocate the edge_tables based on the maximal number of edges of
425 static int graph_init_edge_tables(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
429 for (i
= 0; i
<= isl_edge_last
; ++i
) {
430 graph
->edge_table
[i
] = isl_hash_table_alloc(ctx
,
432 if (!graph
->edge_table
[i
])
439 /* If graph->edge_table[type] contains an edge from the given source
440 * to the given destination, then return the hash table entry of this edge.
441 * Otherwise, return NULL.
443 static struct isl_hash_table_entry
*graph_find_edge_entry(
444 struct isl_sched_graph
*graph
,
445 enum isl_edge_type type
,
446 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
448 isl_ctx
*ctx
= isl_space_get_ctx(src
->dim
);
450 struct isl_sched_edge temp
= { .src
= src
, .dst
= dst
};
452 hash
= isl_hash_init();
453 hash
= isl_hash_builtin(hash
, temp
.src
);
454 hash
= isl_hash_builtin(hash
, temp
.dst
);
455 return isl_hash_table_find(ctx
, graph
->edge_table
[type
], hash
,
456 &edge_has_src_and_dst
, &temp
, 0);
460 /* If graph->edge_table[type] contains an edge from the given source
461 * to the given destination, then return this edge.
462 * Otherwise, return NULL.
464 static struct isl_sched_edge
*graph_find_edge(struct isl_sched_graph
*graph
,
465 enum isl_edge_type type
,
466 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
468 struct isl_hash_table_entry
*entry
;
470 entry
= graph_find_edge_entry(graph
, type
, src
, dst
);
477 /* Check whether the dependence graph has an edge of the given type
478 * between the given two nodes.
480 static int graph_has_edge(struct isl_sched_graph
*graph
,
481 enum isl_edge_type type
,
482 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
484 struct isl_sched_edge
*edge
;
487 edge
= graph_find_edge(graph
, type
, src
, dst
);
491 empty
= isl_map_plain_is_empty(edge
->map
);
498 /* If there is an edge from the given source to the given destination
499 * of any type then return this edge.
500 * Otherwise, return NULL.
502 static struct isl_sched_edge
*graph_find_any_edge(struct isl_sched_graph
*graph
,
503 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
505 enum isl_edge_type i
;
506 struct isl_sched_edge
*edge
;
508 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
509 edge
= graph_find_edge(graph
, i
, src
, dst
);
517 /* Remove the given edge from all the edge_tables that refer to it.
519 static void graph_remove_edge(struct isl_sched_graph
*graph
,
520 struct isl_sched_edge
*edge
)
522 isl_ctx
*ctx
= isl_map_get_ctx(edge
->map
);
523 enum isl_edge_type i
;
525 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
526 struct isl_hash_table_entry
*entry
;
528 entry
= graph_find_edge_entry(graph
, i
, edge
->src
, edge
->dst
);
531 if (entry
->data
!= edge
)
533 isl_hash_table_remove(ctx
, graph
->edge_table
[i
], entry
);
537 /* Check whether the dependence graph has any edge
538 * between the given two nodes.
540 static int graph_has_any_edge(struct isl_sched_graph
*graph
,
541 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
543 enum isl_edge_type i
;
546 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
547 r
= graph_has_edge(graph
, i
, src
, dst
);
555 /* Check whether the dependence graph has a validity edge
556 * between the given two nodes.
558 static int graph_has_validity_edge(struct isl_sched_graph
*graph
,
559 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
561 return graph_has_edge(graph
, isl_edge_validity
, src
, dst
);
564 static int graph_alloc(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
565 int n_node
, int n_edge
)
570 graph
->n_edge
= n_edge
;
571 graph
->node
= isl_calloc_array(ctx
, struct isl_sched_node
, graph
->n
);
572 graph
->sorted
= isl_calloc_array(ctx
, int, graph
->n
);
573 graph
->region
= isl_alloc_array(ctx
, struct isl_region
, graph
->n
);
574 graph
->edge
= isl_calloc_array(ctx
,
575 struct isl_sched_edge
, graph
->n_edge
);
577 graph
->intra_hmap
= isl_map_to_basic_set_alloc(ctx
, 2 * n_edge
);
578 graph
->inter_hmap
= isl_map_to_basic_set_alloc(ctx
, 2 * n_edge
);
580 if (!graph
->node
|| !graph
->region
|| (graph
->n_edge
&& !graph
->edge
) ||
584 for(i
= 0; i
< graph
->n
; ++i
)
585 graph
->sorted
[i
] = i
;
590 static void graph_free(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
594 isl_map_to_basic_set_free(graph
->intra_hmap
);
595 isl_map_to_basic_set_free(graph
->inter_hmap
);
597 for (i
= 0; i
< graph
->n
; ++i
) {
598 isl_space_free(graph
->node
[i
].dim
);
599 isl_mat_free(graph
->node
[i
].sched
);
600 isl_map_free(graph
->node
[i
].sched_map
);
601 isl_mat_free(graph
->node
[i
].cmap
);
602 isl_mat_free(graph
->node
[i
].cinv
);
604 free(graph
->node
[i
].band
);
605 free(graph
->node
[i
].band_id
);
606 free(graph
->node
[i
].zero
);
611 for (i
= 0; i
< graph
->n_edge
; ++i
)
612 isl_map_free(graph
->edge
[i
].map
);
615 for (i
= 0; i
<= isl_edge_last
; ++i
)
616 isl_hash_table_free(ctx
, graph
->edge_table
[i
]);
617 isl_hash_table_free(ctx
, graph
->node_table
);
618 isl_basic_set_free(graph
->lp
);
621 /* For each "set" on which this function is called, increment
622 * graph->n by one and update graph->maxvar.
624 static int init_n_maxvar(__isl_take isl_set
*set
, void *user
)
626 struct isl_sched_graph
*graph
= user
;
627 int nvar
= isl_set_dim(set
, isl_dim_set
);
630 if (nvar
> graph
->maxvar
)
631 graph
->maxvar
= nvar
;
638 /* Compute the number of rows that should be allocated for the schedule.
639 * The graph can be split at most "n - 1" times, there can be at most
640 * two rows for each dimension in the iteration domains (in particular,
641 * we usually have one row, but it may be split by split_scaled),
642 * and there can be one extra row for ordering the statements.
643 * Note that if we have actually split "n - 1" times, then no ordering
644 * is needed, so in principle we could use "graph->n + 2 * graph->maxvar - 1".
646 static int compute_max_row(struct isl_sched_graph
*graph
,
647 __isl_keep isl_union_set
*domain
)
651 if (isl_union_set_foreach_set(domain
, &init_n_maxvar
, graph
) < 0)
653 graph
->max_row
= graph
->n
+ 2 * graph
->maxvar
;
658 /* Add a new node to the graph representing the given set.
660 static int extract_node(__isl_take isl_set
*set
, void *user
)
666 struct isl_sched_graph
*graph
= user
;
667 int *band
, *band_id
, *zero
;
669 ctx
= isl_set_get_ctx(set
);
670 dim
= isl_set_get_space(set
);
672 nvar
= isl_space_dim(dim
, isl_dim_set
);
673 nparam
= isl_space_dim(dim
, isl_dim_param
);
674 if (!ctx
->opt
->schedule_parametric
)
676 sched
= isl_mat_alloc(ctx
, 0, 1 + nparam
+ nvar
);
677 graph
->node
[graph
->n
].dim
= dim
;
678 graph
->node
[graph
->n
].nvar
= nvar
;
679 graph
->node
[graph
->n
].nparam
= nparam
;
680 graph
->node
[graph
->n
].sched
= sched
;
681 graph
->node
[graph
->n
].sched_map
= NULL
;
682 band
= isl_alloc_array(ctx
, int, graph
->max_row
);
683 graph
->node
[graph
->n
].band
= band
;
684 band_id
= isl_calloc_array(ctx
, int, graph
->max_row
);
685 graph
->node
[graph
->n
].band_id
= band_id
;
686 zero
= isl_calloc_array(ctx
, int, graph
->max_row
);
687 graph
->node
[graph
->n
].zero
= zero
;
690 if (!sched
|| (graph
->max_row
&& (!band
|| !band_id
|| !zero
)))
696 struct isl_extract_edge_data
{
697 enum isl_edge_type type
;
698 struct isl_sched_graph
*graph
;
701 /* Add a new edge to the graph based on the given map
702 * and add it to data->graph->edge_table[data->type].
703 * If a dependence relation of a given type happens to be identical
704 * to one of the dependence relations of a type that was added before,
705 * then we don't create a new edge, but instead mark the original edge
706 * as also representing a dependence of the current type.
708 static int extract_edge(__isl_take isl_map
*map
, void *user
)
710 isl_ctx
*ctx
= isl_map_get_ctx(map
);
711 struct isl_extract_edge_data
*data
= user
;
712 struct isl_sched_graph
*graph
= data
->graph
;
713 struct isl_sched_node
*src
, *dst
;
715 struct isl_sched_edge
*edge
;
718 dim
= isl_space_domain(isl_map_get_space(map
));
719 src
= graph_find_node(ctx
, graph
, dim
);
721 dim
= isl_space_range(isl_map_get_space(map
));
722 dst
= graph_find_node(ctx
, graph
, dim
);
730 graph
->edge
[graph
->n_edge
].src
= src
;
731 graph
->edge
[graph
->n_edge
].dst
= dst
;
732 graph
->edge
[graph
->n_edge
].map
= map
;
733 if (data
->type
== isl_edge_validity
) {
734 graph
->edge
[graph
->n_edge
].validity
= 1;
735 graph
->edge
[graph
->n_edge
].proximity
= 0;
737 if (data
->type
== isl_edge_proximity
) {
738 graph
->edge
[graph
->n_edge
].validity
= 0;
739 graph
->edge
[graph
->n_edge
].proximity
= 1;
743 edge
= graph_find_any_edge(graph
, src
, dst
);
745 return graph_edge_table_add(ctx
, graph
, data
->type
,
746 &graph
->edge
[graph
->n_edge
- 1]);
747 is_equal
= isl_map_plain_is_equal(map
, edge
->map
);
751 return graph_edge_table_add(ctx
, graph
, data
->type
,
752 &graph
->edge
[graph
->n_edge
- 1]);
755 edge
->validity
|= graph
->edge
[graph
->n_edge
].validity
;
756 edge
->proximity
|= graph
->edge
[graph
->n_edge
].proximity
;
759 return graph_edge_table_add(ctx
, graph
, data
->type
, edge
);
762 /* Check whether there is any dependence from node[j] to node[i]
763 * or from node[i] to node[j].
765 static int node_follows_weak(int i
, int j
, void *user
)
768 struct isl_sched_graph
*graph
= user
;
770 f
= graph_has_any_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
773 return graph_has_any_edge(graph
, &graph
->node
[i
], &graph
->node
[j
]);
776 /* Check whether there is a validity dependence from node[j] to node[i],
777 * forcing node[i] to follow node[j].
779 static int node_follows_strong(int i
, int j
, void *user
)
781 struct isl_sched_graph
*graph
= user
;
783 return graph_has_validity_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
786 /* Use Tarjan's algorithm for computing the strongly connected components
787 * in the dependence graph (only validity edges).
788 * If weak is set, we consider the graph to be undirected and
789 * we effectively compute the (weakly) connected components.
790 * Additionally, we also consider other edges when weak is set.
792 static int detect_ccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
, int weak
)
795 struct isl_tarjan_graph
*g
= NULL
;
797 g
= isl_tarjan_graph_init(ctx
, graph
->n
,
798 weak
? &node_follows_weak
: &node_follows_strong
, graph
);
806 while (g
->order
[i
] != -1) {
807 graph
->node
[g
->order
[i
]].scc
= graph
->scc
;
815 isl_tarjan_graph_free(g
);
820 /* Apply Tarjan's algorithm to detect the strongly connected components
821 * in the dependence graph.
823 static int detect_sccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
825 return detect_ccs(ctx
, graph
, 0);
828 /* Apply Tarjan's algorithm to detect the (weakly) connected components
829 * in the dependence graph.
831 static int detect_wccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
833 return detect_ccs(ctx
, graph
, 1);
836 static int cmp_scc(const void *a
, const void *b
, void *data
)
838 struct isl_sched_graph
*graph
= data
;
842 return graph
->node
[*i1
].scc
- graph
->node
[*i2
].scc
;
845 /* Sort the elements of graph->sorted according to the corresponding SCCs.
847 static int sort_sccs(struct isl_sched_graph
*graph
)
849 return isl_sort(graph
->sorted
, graph
->n
, sizeof(int), &cmp_scc
, graph
);
852 /* Given a dependence relation R from a node to itself,
853 * construct the set of coefficients of valid constraints for elements
854 * in that dependence relation.
855 * In particular, the result contains tuples of coefficients
856 * c_0, c_n, c_x such that
858 * c_0 + c_n n + c_x y - c_x x >= 0 for each (x,y) in R
862 * c_0 + c_n n + c_x d >= 0 for each d in delta R = { y - x | (x,y) in R }
864 * We choose here to compute the dual of delta R.
865 * Alternatively, we could have computed the dual of R, resulting
866 * in a set of tuples c_0, c_n, c_x, c_y, and then
867 * plugged in (c_0, c_n, c_x, -c_x).
869 static __isl_give isl_basic_set
*intra_coefficients(
870 struct isl_sched_graph
*graph
, __isl_take isl_map
*map
)
875 if (isl_map_to_basic_set_has(graph
->intra_hmap
, map
))
876 return isl_map_to_basic_set_get(graph
->intra_hmap
, map
);
878 delta
= isl_set_remove_divs(isl_map_deltas(isl_map_copy(map
)));
879 coef
= isl_set_coefficients(delta
);
880 graph
->intra_hmap
= isl_map_to_basic_set_set(graph
->intra_hmap
, map
,
881 isl_basic_set_copy(coef
));
886 /* Given a dependence relation R, * construct the set of coefficients
887 * of valid constraints for elements in that dependence relation.
888 * In particular, the result contains tuples of coefficients
889 * c_0, c_n, c_x, c_y such that
891 * c_0 + c_n n + c_x x + c_y y >= 0 for each (x,y) in R
894 static __isl_give isl_basic_set
*inter_coefficients(
895 struct isl_sched_graph
*graph
, __isl_take isl_map
*map
)
900 if (isl_map_to_basic_set_has(graph
->inter_hmap
, map
))
901 return isl_map_to_basic_set_get(graph
->inter_hmap
, map
);
903 set
= isl_map_wrap(isl_map_remove_divs(isl_map_copy(map
)));
904 coef
= isl_set_coefficients(set
);
905 graph
->inter_hmap
= isl_map_to_basic_set_set(graph
->inter_hmap
, map
,
906 isl_basic_set_copy(coef
));
911 /* Add constraints to graph->lp that force validity for the given
912 * dependence from a node i to itself.
913 * That is, add constraints that enforce
915 * (c_i_0 + c_i_n n + c_i_x y) - (c_i_0 + c_i_n n + c_i_x x)
916 * = c_i_x (y - x) >= 0
918 * for each (x,y) in R.
919 * We obtain general constraints on coefficients (c_0, c_n, c_x)
920 * of valid constraints for (y - x) and then plug in (0, 0, c_i_x^+ - c_i_x^-),
921 * where c_i_x = c_i_x^+ - c_i_x^-, with c_i_x^+ and c_i_x^- non-negative.
922 * In graph->lp, the c_i_x^- appear before their c_i_x^+ counterpart.
924 * Actually, we do not construct constraints for the c_i_x themselves,
925 * but for the coefficients of c_i_x written as a linear combination
926 * of the columns in node->cmap.
928 static int add_intra_validity_constraints(struct isl_sched_graph
*graph
,
929 struct isl_sched_edge
*edge
)
932 isl_map
*map
= isl_map_copy(edge
->map
);
933 isl_ctx
*ctx
= isl_map_get_ctx(map
);
935 isl_dim_map
*dim_map
;
937 struct isl_sched_node
*node
= edge
->src
;
939 coef
= intra_coefficients(graph
, map
);
941 dim
= isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef
)));
943 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
944 isl_space_dim(dim
, isl_dim_set
), isl_mat_copy(node
->cmap
));
948 total
= isl_basic_set_total_dim(graph
->lp
);
949 dim_map
= isl_dim_map_alloc(ctx
, total
);
950 isl_dim_map_range(dim_map
, node
->start
+ 2 * node
->nparam
+ 1, 2,
951 isl_space_dim(dim
, isl_dim_set
), 1,
953 isl_dim_map_range(dim_map
, node
->start
+ 2 * node
->nparam
+ 2, 2,
954 isl_space_dim(dim
, isl_dim_set
), 1,
956 graph
->lp
= isl_basic_set_extend_constraints(graph
->lp
,
957 coef
->n_eq
, coef
->n_ineq
);
958 graph
->lp
= isl_basic_set_add_constraints_dim_map(graph
->lp
,
968 /* Add constraints to graph->lp that force validity for the given
969 * dependence from node i to node j.
970 * That is, add constraints that enforce
972 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) >= 0
974 * for each (x,y) in R.
975 * We obtain general constraints on coefficients (c_0, c_n, c_x, c_y)
976 * of valid constraints for R and then plug in
977 * (c_j_0 - c_i_0, c_j_n^+ - c_j_n^- - (c_i_n^+ - c_i_n^-),
978 * c_j_x^+ - c_j_x^- - (c_i_x^+ - c_i_x^-)),
979 * where c_* = c_*^+ - c_*^-, with c_*^+ and c_*^- non-negative.
980 * In graph->lp, the c_*^- appear before their c_*^+ counterpart.
982 * Actually, we do not construct constraints for the c_*_x themselves,
983 * but for the coefficients of c_*_x written as a linear combination
984 * of the columns in node->cmap.
986 static int add_inter_validity_constraints(struct isl_sched_graph
*graph
,
987 struct isl_sched_edge
*edge
)
990 isl_map
*map
= isl_map_copy(edge
->map
);
991 isl_ctx
*ctx
= isl_map_get_ctx(map
);
993 isl_dim_map
*dim_map
;
995 struct isl_sched_node
*src
= edge
->src
;
996 struct isl_sched_node
*dst
= edge
->dst
;
998 coef
= inter_coefficients(graph
, map
);
1000 dim
= isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef
)));
1002 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
1003 isl_space_dim(dim
, isl_dim_set
), isl_mat_copy(src
->cmap
));
1004 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
1005 isl_space_dim(dim
, isl_dim_set
) + src
->nvar
,
1006 isl_mat_copy(dst
->cmap
));
1010 total
= isl_basic_set_total_dim(graph
->lp
);
1011 dim_map
= isl_dim_map_alloc(ctx
, total
);
1013 isl_dim_map_range(dim_map
, dst
->start
, 0, 0, 0, 1, 1);
1014 isl_dim_map_range(dim_map
, dst
->start
+ 1, 2, 1, 1, dst
->nparam
, -1);
1015 isl_dim_map_range(dim_map
, dst
->start
+ 2, 2, 1, 1, dst
->nparam
, 1);
1016 isl_dim_map_range(dim_map
, dst
->start
+ 2 * dst
->nparam
+ 1, 2,
1017 isl_space_dim(dim
, isl_dim_set
) + src
->nvar
, 1,
1019 isl_dim_map_range(dim_map
, dst
->start
+ 2 * dst
->nparam
+ 2, 2,
1020 isl_space_dim(dim
, isl_dim_set
) + src
->nvar
, 1,
1023 isl_dim_map_range(dim_map
, src
->start
, 0, 0, 0, 1, -1);
1024 isl_dim_map_range(dim_map
, src
->start
+ 1, 2, 1, 1, src
->nparam
, 1);
1025 isl_dim_map_range(dim_map
, src
->start
+ 2, 2, 1, 1, src
->nparam
, -1);
1026 isl_dim_map_range(dim_map
, src
->start
+ 2 * src
->nparam
+ 1, 2,
1027 isl_space_dim(dim
, isl_dim_set
), 1,
1029 isl_dim_map_range(dim_map
, src
->start
+ 2 * src
->nparam
+ 2, 2,
1030 isl_space_dim(dim
, isl_dim_set
), 1,
1033 edge
->start
= graph
->lp
->n_ineq
;
1034 graph
->lp
= isl_basic_set_extend_constraints(graph
->lp
,
1035 coef
->n_eq
, coef
->n_ineq
);
1036 graph
->lp
= isl_basic_set_add_constraints_dim_map(graph
->lp
,
1040 isl_space_free(dim
);
1041 edge
->end
= graph
->lp
->n_ineq
;
1045 isl_space_free(dim
);
1049 /* Add constraints to graph->lp that bound the dependence distance for the given
1050 * dependence from a node i to itself.
1051 * If s = 1, we add the constraint
1053 * c_i_x (y - x) <= m_0 + m_n n
1057 * -c_i_x (y - x) + m_0 + m_n n >= 0
1059 * for each (x,y) in R.
1060 * If s = -1, we add the constraint
1062 * -c_i_x (y - x) <= m_0 + m_n n
1066 * c_i_x (y - x) + m_0 + m_n n >= 0
1068 * for each (x,y) in R.
1069 * We obtain general constraints on coefficients (c_0, c_n, c_x)
1070 * of valid constraints for (y - x) and then plug in (m_0, m_n, -s * c_i_x),
1071 * with each coefficient (except m_0) represented as a pair of non-negative
1074 * Actually, we do not construct constraints for the c_i_x themselves,
1075 * but for the coefficients of c_i_x written as a linear combination
1076 * of the columns in node->cmap.
1078 static int add_intra_proximity_constraints(struct isl_sched_graph
*graph
,
1079 struct isl_sched_edge
*edge
, int s
)
1083 isl_map
*map
= isl_map_copy(edge
->map
);
1084 isl_ctx
*ctx
= isl_map_get_ctx(map
);
1086 isl_dim_map
*dim_map
;
1087 isl_basic_set
*coef
;
1088 struct isl_sched_node
*node
= edge
->src
;
1090 coef
= intra_coefficients(graph
, map
);
1092 dim
= isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef
)));
1094 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
1095 isl_space_dim(dim
, isl_dim_set
), isl_mat_copy(node
->cmap
));
1099 nparam
= isl_space_dim(node
->dim
, isl_dim_param
);
1100 total
= isl_basic_set_total_dim(graph
->lp
);
1101 dim_map
= isl_dim_map_alloc(ctx
, total
);
1102 isl_dim_map_range(dim_map
, 1, 0, 0, 0, 1, 1);
1103 isl_dim_map_range(dim_map
, 4, 2, 1, 1, nparam
, -1);
1104 isl_dim_map_range(dim_map
, 5, 2, 1, 1, nparam
, 1);
1105 isl_dim_map_range(dim_map
, node
->start
+ 2 * node
->nparam
+ 1, 2,
1106 isl_space_dim(dim
, isl_dim_set
), 1,
1108 isl_dim_map_range(dim_map
, node
->start
+ 2 * node
->nparam
+ 2, 2,
1109 isl_space_dim(dim
, isl_dim_set
), 1,
1111 graph
->lp
= isl_basic_set_extend_constraints(graph
->lp
,
1112 coef
->n_eq
, coef
->n_ineq
);
1113 graph
->lp
= isl_basic_set_add_constraints_dim_map(graph
->lp
,
1115 isl_space_free(dim
);
1119 isl_space_free(dim
);
1123 /* Add constraints to graph->lp that bound the dependence distance for the given
1124 * dependence from node i to node j.
1125 * If s = 1, we add the constraint
1127 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x)
1132 * -(c_j_0 + c_j_n n + c_j_x y) + (c_i_0 + c_i_n n + c_i_x x) +
1135 * for each (x,y) in R.
1136 * If s = -1, we add the constraint
1138 * -((c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x))
1143 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) +
1146 * for each (x,y) in R.
1147 * We obtain general constraints on coefficients (c_0, c_n, c_x, c_y)
1148 * of valid constraints for R and then plug in
1149 * (m_0 - s*c_j_0 + s*c_i_0, m_n - s*c_j_n + s*c_i_n,
1151 * with each coefficient (except m_0, c_j_0 and c_i_0)
1152 * represented as a pair of non-negative coefficients.
1154 * Actually, we do not construct constraints for the c_*_x themselves,
1155 * but for the coefficients of c_*_x written as a linear combination
1156 * of the columns in node->cmap.
1158 static int add_inter_proximity_constraints(struct isl_sched_graph
*graph
,
1159 struct isl_sched_edge
*edge
, int s
)
1163 isl_map
*map
= isl_map_copy(edge
->map
);
1164 isl_ctx
*ctx
= isl_map_get_ctx(map
);
1166 isl_dim_map
*dim_map
;
1167 isl_basic_set
*coef
;
1168 struct isl_sched_node
*src
= edge
->src
;
1169 struct isl_sched_node
*dst
= edge
->dst
;
1171 coef
= inter_coefficients(graph
, map
);
1173 dim
= isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef
)));
1175 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
1176 isl_space_dim(dim
, isl_dim_set
), isl_mat_copy(src
->cmap
));
1177 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
1178 isl_space_dim(dim
, isl_dim_set
) + src
->nvar
,
1179 isl_mat_copy(dst
->cmap
));
1183 nparam
= isl_space_dim(src
->dim
, isl_dim_param
);
1184 total
= isl_basic_set_total_dim(graph
->lp
);
1185 dim_map
= isl_dim_map_alloc(ctx
, total
);
1187 isl_dim_map_range(dim_map
, 1, 0, 0, 0, 1, 1);
1188 isl_dim_map_range(dim_map
, 4, 2, 1, 1, nparam
, -1);
1189 isl_dim_map_range(dim_map
, 5, 2, 1, 1, nparam
, 1);
1191 isl_dim_map_range(dim_map
, dst
->start
, 0, 0, 0, 1, -s
);
1192 isl_dim_map_range(dim_map
, dst
->start
+ 1, 2, 1, 1, dst
->nparam
, s
);
1193 isl_dim_map_range(dim_map
, dst
->start
+ 2, 2, 1, 1, dst
->nparam
, -s
);
1194 isl_dim_map_range(dim_map
, dst
->start
+ 2 * dst
->nparam
+ 1, 2,
1195 isl_space_dim(dim
, isl_dim_set
) + src
->nvar
, 1,
1197 isl_dim_map_range(dim_map
, dst
->start
+ 2 * dst
->nparam
+ 2, 2,
1198 isl_space_dim(dim
, isl_dim_set
) + src
->nvar
, 1,
1201 isl_dim_map_range(dim_map
, src
->start
, 0, 0, 0, 1, s
);
1202 isl_dim_map_range(dim_map
, src
->start
+ 1, 2, 1, 1, src
->nparam
, -s
);
1203 isl_dim_map_range(dim_map
, src
->start
+ 2, 2, 1, 1, src
->nparam
, s
);
1204 isl_dim_map_range(dim_map
, src
->start
+ 2 * src
->nparam
+ 1, 2,
1205 isl_space_dim(dim
, isl_dim_set
), 1,
1207 isl_dim_map_range(dim_map
, src
->start
+ 2 * src
->nparam
+ 2, 2,
1208 isl_space_dim(dim
, isl_dim_set
), 1,
1211 graph
->lp
= isl_basic_set_extend_constraints(graph
->lp
,
1212 coef
->n_eq
, coef
->n_ineq
);
1213 graph
->lp
= isl_basic_set_add_constraints_dim_map(graph
->lp
,
1215 isl_space_free(dim
);
1219 isl_space_free(dim
);
1223 static int add_all_validity_constraints(struct isl_sched_graph
*graph
)
1227 for (i
= 0; i
< graph
->n_edge
; ++i
) {
1228 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
1229 if (!edge
->validity
)
1231 if (edge
->src
!= edge
->dst
)
1233 if (add_intra_validity_constraints(graph
, edge
) < 0)
1237 for (i
= 0; i
< graph
->n_edge
; ++i
) {
1238 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
1239 if (!edge
->validity
)
1241 if (edge
->src
== edge
->dst
)
1243 if (add_inter_validity_constraints(graph
, edge
) < 0)
1250 /* Add constraints to graph->lp that bound the dependence distance
1251 * for all dependence relations.
1252 * If a given proximity dependence is identical to a validity
1253 * dependence, then the dependence distance is already bounded
1254 * from below (by zero), so we only need to bound the distance
1256 * Otherwise, we need to bound the distance both from above and from below.
1258 static int add_all_proximity_constraints(struct isl_sched_graph
*graph
)
1262 for (i
= 0; i
< graph
->n_edge
; ++i
) {
1263 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
1264 if (!edge
->proximity
)
1266 if (edge
->src
== edge
->dst
&&
1267 add_intra_proximity_constraints(graph
, edge
, 1) < 0)
1269 if (edge
->src
!= edge
->dst
&&
1270 add_inter_proximity_constraints(graph
, edge
, 1) < 0)
1274 if (edge
->src
== edge
->dst
&&
1275 add_intra_proximity_constraints(graph
, edge
, -1) < 0)
1277 if (edge
->src
!= edge
->dst
&&
1278 add_inter_proximity_constraints(graph
, edge
, -1) < 0)
1285 /* Compute a basis for the rows in the linear part of the schedule
1286 * and extend this basis to a full basis. The remaining rows
1287 * can then be used to force linear independence from the rows
1290 * In particular, given the schedule rows S, we compute
1295 * with H the Hermite normal form of S. That is, all but the
1296 * first rank columns of H are zero and so each row in S is
1297 * a linear combination of the first rank rows of Q.
1298 * The matrix Q is then transposed because we will write the
1299 * coefficients of the next schedule row as a column vector s
1300 * and express this s as a linear combination s = Q c of the
1302 * Similarly, the matrix U is transposed such that we can
1303 * compute the coefficients c = U s from a schedule row s.
1305 static int node_update_cmap(struct isl_sched_node
*node
)
1308 int n_row
= isl_mat_rows(node
->sched
);
1310 H
= isl_mat_sub_alloc(node
->sched
, 0, n_row
,
1311 1 + node
->nparam
, node
->nvar
);
1313 H
= isl_mat_left_hermite(H
, 0, &U
, &Q
);
1314 isl_mat_free(node
->cmap
);
1315 isl_mat_free(node
->cinv
);
1316 node
->cmap
= isl_mat_transpose(Q
);
1317 node
->cinv
= isl_mat_transpose(U
);
1318 node
->rank
= isl_mat_initial_non_zero_cols(H
);
1321 if (!node
->cmap
|| !node
->cinv
|| node
->rank
< 0)
1326 /* Count the number of equality and inequality constraints
1327 * that will be added for the given map.
1328 * If carry is set, then we are counting the number of (validity)
1329 * constraints that will be added in setup_carry_lp and we count
1330 * each edge exactly once. Otherwise, we count as follows
1331 * validity -> 1 (>= 0)
1332 * validity+proximity -> 2 (>= 0 and upper bound)
1333 * proximity -> 2 (lower and upper bound)
1335 static int count_map_constraints(struct isl_sched_graph
*graph
,
1336 struct isl_sched_edge
*edge
, __isl_take isl_map
*map
,
1337 int *n_eq
, int *n_ineq
, int carry
)
1339 isl_basic_set
*coef
;
1340 int f
= carry
? 1 : edge
->proximity
? 2 : 1;
1342 if (carry
&& !edge
->validity
) {
1347 if (edge
->src
== edge
->dst
)
1348 coef
= intra_coefficients(graph
, map
);
1350 coef
= inter_coefficients(graph
, map
);
1353 *n_eq
+= f
* coef
->n_eq
;
1354 *n_ineq
+= f
* coef
->n_ineq
;
1355 isl_basic_set_free(coef
);
1360 /* Count the number of equality and inequality constraints
1361 * that will be added to the main lp problem.
1362 * We count as follows
1363 * validity -> 1 (>= 0)
1364 * validity+proximity -> 2 (>= 0 and upper bound)
1365 * proximity -> 2 (lower and upper bound)
1367 static int count_constraints(struct isl_sched_graph
*graph
,
1368 int *n_eq
, int *n_ineq
)
1372 *n_eq
= *n_ineq
= 0;
1373 for (i
= 0; i
< graph
->n_edge
; ++i
) {
1374 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
1375 isl_map
*map
= isl_map_copy(edge
->map
);
1377 if (count_map_constraints(graph
, edge
, map
,
1378 n_eq
, n_ineq
, 0) < 0)
1385 /* Count the number of constraints that will be added by
1386 * add_bound_coefficient_constraints and increment *n_eq and *n_ineq
1389 * In practice, add_bound_coefficient_constraints only adds inequalities.
1391 static int count_bound_coefficient_constraints(isl_ctx
*ctx
,
1392 struct isl_sched_graph
*graph
, int *n_eq
, int *n_ineq
)
1396 if (ctx
->opt
->schedule_max_coefficient
== -1)
1399 for (i
= 0; i
< graph
->n
; ++i
)
1400 *n_ineq
+= 2 * graph
->node
[i
].nparam
+ 2 * graph
->node
[i
].nvar
;
1405 /* Add constraints that bound the values of the variable and parameter
1406 * coefficients of the schedule.
1408 * The maximal value of the coefficients is defined by the option
1409 * 'schedule_max_coefficient'.
1411 static int add_bound_coefficient_constraints(isl_ctx
*ctx
,
1412 struct isl_sched_graph
*graph
)
1415 int max_coefficient
;
1418 max_coefficient
= ctx
->opt
->schedule_max_coefficient
;
1420 if (max_coefficient
== -1)
1423 total
= isl_basic_set_total_dim(graph
->lp
);
1425 for (i
= 0; i
< graph
->n
; ++i
) {
1426 struct isl_sched_node
*node
= &graph
->node
[i
];
1427 for (j
= 0; j
< 2 * node
->nparam
+ 2 * node
->nvar
; ++j
) {
1429 k
= isl_basic_set_alloc_inequality(graph
->lp
);
1432 dim
= 1 + node
->start
+ 1 + j
;
1433 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
1434 isl_int_set_si(graph
->lp
->ineq
[k
][dim
], -1);
1435 isl_int_set_si(graph
->lp
->ineq
[k
][0], max_coefficient
);
1442 /* Construct an ILP problem for finding schedule coefficients
1443 * that result in non-negative, but small dependence distances
1444 * over all dependences.
1445 * In particular, the dependence distances over proximity edges
1446 * are bounded by m_0 + m_n n and we compute schedule coefficients
1447 * with small values (preferably zero) of m_n and m_0.
1449 * All variables of the ILP are non-negative. The actual coefficients
1450 * may be negative, so each coefficient is represented as the difference
1451 * of two non-negative variables. The negative part always appears
1452 * immediately before the positive part.
1453 * Other than that, the variables have the following order
1455 * - sum of positive and negative parts of m_n coefficients
1457 * - sum of positive and negative parts of all c_n coefficients
1458 * (unconstrained when computing non-parametric schedules)
1459 * - sum of positive and negative parts of all c_x coefficients
1460 * - positive and negative parts of m_n coefficients
1463 * - positive and negative parts of c_i_n (if parametric)
1464 * - positive and negative parts of c_i_x
1466 * The c_i_x are not represented directly, but through the columns of
1467 * node->cmap. That is, the computed values are for variable t_i_x
1468 * such that c_i_x = Q t_i_x with Q equal to node->cmap.
1470 * The constraints are those from the edges plus two or three equalities
1471 * to express the sums.
1473 * If force_zero is set, then we add equalities to ensure that
1474 * the sum of the m_n coefficients and m_0 are both zero.
1476 static int setup_lp(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
1487 int max_constant_term
;
1489 max_constant_term
= ctx
->opt
->schedule_max_constant_term
;
1491 parametric
= ctx
->opt
->schedule_parametric
;
1492 nparam
= isl_space_dim(graph
->node
[0].dim
, isl_dim_param
);
1494 total
= param_pos
+ 2 * nparam
;
1495 for (i
= 0; i
< graph
->n
; ++i
) {
1496 struct isl_sched_node
*node
= &graph
->node
[graph
->sorted
[i
]];
1497 if (node_update_cmap(node
) < 0)
1499 node
->start
= total
;
1500 total
+= 1 + 2 * (node
->nparam
+ node
->nvar
);
1503 if (count_constraints(graph
, &n_eq
, &n_ineq
) < 0)
1505 if (count_bound_coefficient_constraints(ctx
, graph
, &n_eq
, &n_ineq
) < 0)
1508 dim
= isl_space_set_alloc(ctx
, 0, total
);
1509 isl_basic_set_free(graph
->lp
);
1510 n_eq
+= 2 + parametric
+ force_zero
;
1511 if (max_constant_term
!= -1)
1514 graph
->lp
= isl_basic_set_alloc_space(dim
, 0, n_eq
, n_ineq
);
1516 k
= isl_basic_set_alloc_equality(graph
->lp
);
1519 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
1521 isl_int_set_si(graph
->lp
->eq
[k
][1], -1);
1522 for (i
= 0; i
< 2 * nparam
; ++i
)
1523 isl_int_set_si(graph
->lp
->eq
[k
][1 + param_pos
+ i
], 1);
1526 k
= isl_basic_set_alloc_equality(graph
->lp
);
1529 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
1530 isl_int_set_si(graph
->lp
->eq
[k
][2], -1);
1534 k
= isl_basic_set_alloc_equality(graph
->lp
);
1537 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
1538 isl_int_set_si(graph
->lp
->eq
[k
][3], -1);
1539 for (i
= 0; i
< graph
->n
; ++i
) {
1540 int pos
= 1 + graph
->node
[i
].start
+ 1;
1542 for (j
= 0; j
< 2 * graph
->node
[i
].nparam
; ++j
)
1543 isl_int_set_si(graph
->lp
->eq
[k
][pos
+ j
], 1);
1547 k
= isl_basic_set_alloc_equality(graph
->lp
);
1550 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
1551 isl_int_set_si(graph
->lp
->eq
[k
][4], -1);
1552 for (i
= 0; i
< graph
->n
; ++i
) {
1553 struct isl_sched_node
*node
= &graph
->node
[i
];
1554 int pos
= 1 + node
->start
+ 1 + 2 * node
->nparam
;
1556 for (j
= 0; j
< 2 * node
->nvar
; ++j
)
1557 isl_int_set_si(graph
->lp
->eq
[k
][pos
+ j
], 1);
1560 if (max_constant_term
!= -1)
1561 for (i
= 0; i
< graph
->n
; ++i
) {
1562 struct isl_sched_node
*node
= &graph
->node
[i
];
1563 k
= isl_basic_set_alloc_inequality(graph
->lp
);
1566 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
1567 isl_int_set_si(graph
->lp
->ineq
[k
][1 + node
->start
], -1);
1568 isl_int_set_si(graph
->lp
->ineq
[k
][0], max_constant_term
);
1571 if (add_bound_coefficient_constraints(ctx
, graph
) < 0)
1573 if (add_all_validity_constraints(graph
) < 0)
1575 if (add_all_proximity_constraints(graph
) < 0)
1581 /* Analyze the conflicting constraint found by
1582 * isl_tab_basic_set_non_trivial_lexmin. If it corresponds to the validity
1583 * constraint of one of the edges between distinct nodes, living, moreover
1584 * in distinct SCCs, then record the source and sink SCC as this may
1585 * be a good place to cut between SCCs.
1587 static int check_conflict(int con
, void *user
)
1590 struct isl_sched_graph
*graph
= user
;
1592 if (graph
->src_scc
>= 0)
1595 con
-= graph
->lp
->n_eq
;
1597 if (con
>= graph
->lp
->n_ineq
)
1600 for (i
= 0; i
< graph
->n_edge
; ++i
) {
1601 if (!graph
->edge
[i
].validity
)
1603 if (graph
->edge
[i
].src
== graph
->edge
[i
].dst
)
1605 if (graph
->edge
[i
].src
->scc
== graph
->edge
[i
].dst
->scc
)
1607 if (graph
->edge
[i
].start
> con
)
1609 if (graph
->edge
[i
].end
<= con
)
1611 graph
->src_scc
= graph
->edge
[i
].src
->scc
;
1612 graph
->dst_scc
= graph
->edge
[i
].dst
->scc
;
1618 /* Check whether the next schedule row of the given node needs to be
1619 * non-trivial. Lower-dimensional domains may have some trivial rows,
1620 * but as soon as the number of remaining required non-trivial rows
1621 * is as large as the number or remaining rows to be computed,
1622 * all remaining rows need to be non-trivial.
1624 static int needs_row(struct isl_sched_graph
*graph
, struct isl_sched_node
*node
)
1626 return node
->nvar
- node
->rank
>= graph
->maxvar
- graph
->n_row
;
1629 /* Solve the ILP problem constructed in setup_lp.
1630 * For each node such that all the remaining rows of its schedule
1631 * need to be non-trivial, we construct a non-triviality region.
1632 * This region imposes that the next row is independent of previous rows.
1633 * In particular the coefficients c_i_x are represented by t_i_x
1634 * variables with c_i_x = Q t_i_x and Q a unimodular matrix such that
1635 * its first columns span the rows of the previously computed part
1636 * of the schedule. The non-triviality region enforces that at least
1637 * one of the remaining components of t_i_x is non-zero, i.e.,
1638 * that the new schedule row depends on at least one of the remaining
1641 static __isl_give isl_vec
*solve_lp(struct isl_sched_graph
*graph
)
1647 for (i
= 0; i
< graph
->n
; ++i
) {
1648 struct isl_sched_node
*node
= &graph
->node
[i
];
1649 int skip
= node
->rank
;
1650 graph
->region
[i
].pos
= node
->start
+ 1 + 2*(node
->nparam
+skip
);
1651 if (needs_row(graph
, node
))
1652 graph
->region
[i
].len
= 2 * (node
->nvar
- skip
);
1654 graph
->region
[i
].len
= 0;
1656 lp
= isl_basic_set_copy(graph
->lp
);
1657 sol
= isl_tab_basic_set_non_trivial_lexmin(lp
, 2, graph
->n
,
1658 graph
->region
, &check_conflict
, graph
);
1662 /* Update the schedules of all nodes based on the given solution
1663 * of the LP problem.
1664 * The new row is added to the current band.
1665 * All possibly negative coefficients are encoded as a difference
1666 * of two non-negative variables, so we need to perform the subtraction
1667 * here. Moreover, if use_cmap is set, then the solution does
1668 * not refer to the actual coefficients c_i_x, but instead to variables
1669 * t_i_x such that c_i_x = Q t_i_x and Q is equal to node->cmap.
1670 * In this case, we then also need to perform this multiplication
1671 * to obtain the values of c_i_x.
1673 * If check_zero is set, then the first two coordinates of sol are
1674 * assumed to correspond to the dependence distance. If these two
1675 * coordinates are zero, then the corresponding scheduling dimension
1676 * is marked as being zero distance.
1678 static int update_schedule(struct isl_sched_graph
*graph
,
1679 __isl_take isl_vec
*sol
, int use_cmap
, int check_zero
)
1683 isl_vec
*csol
= NULL
;
1688 isl_die(sol
->ctx
, isl_error_internal
,
1689 "no solution found", goto error
);
1690 if (graph
->n_total_row
>= graph
->max_row
)
1691 isl_die(sol
->ctx
, isl_error_internal
,
1692 "too many schedule rows", goto error
);
1695 zero
= isl_int_is_zero(sol
->el
[1]) &&
1696 isl_int_is_zero(sol
->el
[2]);
1698 for (i
= 0; i
< graph
->n
; ++i
) {
1699 struct isl_sched_node
*node
= &graph
->node
[i
];
1700 int pos
= node
->start
;
1701 int row
= isl_mat_rows(node
->sched
);
1704 csol
= isl_vec_alloc(sol
->ctx
, node
->nvar
);
1708 isl_map_free(node
->sched_map
);
1709 node
->sched_map
= NULL
;
1710 node
->sched
= isl_mat_add_rows(node
->sched
, 1);
1713 node
->sched
= isl_mat_set_element(node
->sched
, row
, 0,
1715 for (j
= 0; j
< node
->nparam
+ node
->nvar
; ++j
)
1716 isl_int_sub(sol
->el
[1 + pos
+ 1 + 2 * j
+ 1],
1717 sol
->el
[1 + pos
+ 1 + 2 * j
+ 1],
1718 sol
->el
[1 + pos
+ 1 + 2 * j
]);
1719 for (j
= 0; j
< node
->nparam
; ++j
)
1720 node
->sched
= isl_mat_set_element(node
->sched
,
1721 row
, 1 + j
, sol
->el
[1+pos
+1+2*j
+1]);
1722 for (j
= 0; j
< node
->nvar
; ++j
)
1723 isl_int_set(csol
->el
[j
],
1724 sol
->el
[1+pos
+1+2*(node
->nparam
+j
)+1]);
1726 csol
= isl_mat_vec_product(isl_mat_copy(node
->cmap
),
1730 for (j
= 0; j
< node
->nvar
; ++j
)
1731 node
->sched
= isl_mat_set_element(node
->sched
,
1732 row
, 1 + node
->nparam
+ j
, csol
->el
[j
]);
1733 node
->band
[graph
->n_total_row
] = graph
->n_band
;
1734 node
->zero
[graph
->n_total_row
] = zero
;
1740 graph
->n_total_row
++;
1749 /* Convert row "row" of node->sched into an isl_aff living in "ls"
1750 * and return this isl_aff.
1752 static __isl_give isl_aff
*extract_schedule_row(__isl_take isl_local_space
*ls
,
1753 struct isl_sched_node
*node
, int row
)
1761 aff
= isl_aff_zero_on_domain(ls
);
1762 isl_mat_get_element(node
->sched
, row
, 0, &v
);
1763 aff
= isl_aff_set_constant(aff
, v
);
1764 for (j
= 0; j
< node
->nparam
; ++j
) {
1765 isl_mat_get_element(node
->sched
, row
, 1 + j
, &v
);
1766 aff
= isl_aff_set_coefficient(aff
, isl_dim_param
, j
, v
);
1768 for (j
= 0; j
< node
->nvar
; ++j
) {
1769 isl_mat_get_element(node
->sched
, row
, 1 + node
->nparam
+ j
, &v
);
1770 aff
= isl_aff_set_coefficient(aff
, isl_dim_in
, j
, v
);
1778 /* Convert node->sched into a multi_aff and return this multi_aff.
1780 static __isl_give isl_multi_aff
*node_extract_schedule_multi_aff(
1781 struct isl_sched_node
*node
)
1785 isl_local_space
*ls
;
1790 nrow
= isl_mat_rows(node
->sched
);
1791 ncol
= isl_mat_cols(node
->sched
) - 1;
1792 space
= isl_space_from_domain(isl_space_copy(node
->dim
));
1793 space
= isl_space_add_dims(space
, isl_dim_out
, nrow
);
1794 ma
= isl_multi_aff_zero(space
);
1795 ls
= isl_local_space_from_space(isl_space_copy(node
->dim
));
1797 for (i
= 0; i
< nrow
; ++i
) {
1798 aff
= extract_schedule_row(isl_local_space_copy(ls
), node
, i
);
1799 ma
= isl_multi_aff_set_aff(ma
, i
, aff
);
1802 isl_local_space_free(ls
);
1807 /* Convert node->sched into a map and return this map.
1809 * The result is cached in node->sched_map, which needs to be released
1810 * whenever node->sched is updated.
1812 static __isl_give isl_map
*node_extract_schedule(struct isl_sched_node
*node
)
1814 if (!node
->sched_map
) {
1817 ma
= node_extract_schedule_multi_aff(node
);
1818 node
->sched_map
= isl_map_from_multi_aff(ma
);
1821 return isl_map_copy(node
->sched_map
);
1824 /* Update the given dependence relation based on the current schedule.
1825 * That is, intersect the dependence relation with a map expressing
1826 * that source and sink are executed within the same iteration of
1827 * the current schedule.
1828 * This is not the most efficient way, but this shouldn't be a critical
1831 static __isl_give isl_map
*specialize(__isl_take isl_map
*map
,
1832 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
1834 isl_map
*src_sched
, *dst_sched
, *id
;
1836 src_sched
= node_extract_schedule(src
);
1837 dst_sched
= node_extract_schedule(dst
);
1838 id
= isl_map_apply_range(src_sched
, isl_map_reverse(dst_sched
));
1839 return isl_map_intersect(map
, id
);
1842 /* Update the dependence relations of all edges based on the current schedule.
1843 * If a dependence is carried completely by the current schedule, then
1844 * it is removed from the edge_tables. It is kept in the list of edges
1845 * as otherwise all edge_tables would have to be recomputed.
1847 static int update_edges(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
1851 for (i
= graph
->n_edge
- 1; i
>= 0; --i
) {
1852 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
1853 edge
->map
= specialize(edge
->map
, edge
->src
, edge
->dst
);
1857 if (isl_map_plain_is_empty(edge
->map
))
1858 graph_remove_edge(graph
, edge
);
1864 static void next_band(struct isl_sched_graph
*graph
)
1866 graph
->band_start
= graph
->n_total_row
;
1870 /* Topologically sort statements mapped to the same schedule iteration
1871 * and add a row to the schedule corresponding to this order.
1873 static int sort_statements(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
1880 if (update_edges(ctx
, graph
) < 0)
1883 if (graph
->n_edge
== 0)
1886 if (detect_sccs(ctx
, graph
) < 0)
1889 if (graph
->n_total_row
>= graph
->max_row
)
1890 isl_die(ctx
, isl_error_internal
,
1891 "too many schedule rows", return -1);
1893 for (i
= 0; i
< graph
->n
; ++i
) {
1894 struct isl_sched_node
*node
= &graph
->node
[i
];
1895 int row
= isl_mat_rows(node
->sched
);
1896 int cols
= isl_mat_cols(node
->sched
);
1898 isl_map_free(node
->sched_map
);
1899 node
->sched_map
= NULL
;
1900 node
->sched
= isl_mat_add_rows(node
->sched
, 1);
1903 node
->sched
= isl_mat_set_element_si(node
->sched
, row
, 0,
1905 for (j
= 1; j
< cols
; ++j
)
1906 node
->sched
= isl_mat_set_element_si(node
->sched
,
1908 node
->band
[graph
->n_total_row
] = graph
->n_band
;
1911 graph
->n_total_row
++;
1917 /* Construct an isl_schedule based on the computed schedule stored
1918 * in graph and with parameters specified by dim.
1920 static __isl_give isl_schedule
*extract_schedule(struct isl_sched_graph
*graph
,
1921 __isl_take isl_space
*dim
)
1925 isl_schedule
*sched
= NULL
;
1930 ctx
= isl_space_get_ctx(dim
);
1931 sched
= isl_calloc(ctx
, struct isl_schedule
,
1932 sizeof(struct isl_schedule
) +
1933 (graph
->n
- 1) * sizeof(struct isl_schedule_node
));
1938 sched
->n
= graph
->n
;
1939 sched
->n_band
= graph
->n_band
;
1940 sched
->n_total_row
= graph
->n_total_row
;
1942 for (i
= 0; i
< sched
->n
; ++i
) {
1944 int *band_end
, *band_id
, *zero
;
1946 sched
->node
[i
].sched
=
1947 node_extract_schedule_multi_aff(&graph
->node
[i
]);
1948 if (!sched
->node
[i
].sched
)
1951 sched
->node
[i
].n_band
= graph
->n_band
;
1952 if (graph
->n_band
== 0)
1955 band_end
= isl_alloc_array(ctx
, int, graph
->n_band
);
1956 band_id
= isl_alloc_array(ctx
, int, graph
->n_band
);
1957 zero
= isl_alloc_array(ctx
, int, graph
->n_total_row
);
1958 sched
->node
[i
].band_end
= band_end
;
1959 sched
->node
[i
].band_id
= band_id
;
1960 sched
->node
[i
].zero
= zero
;
1961 if (!band_end
|| !band_id
|| !zero
)
1964 for (r
= 0; r
< graph
->n_total_row
; ++r
)
1965 zero
[r
] = graph
->node
[i
].zero
[r
];
1966 for (r
= b
= 0; r
< graph
->n_total_row
; ++r
) {
1967 if (graph
->node
[i
].band
[r
] == b
)
1970 if (graph
->node
[i
].band
[r
] == -1)
1973 if (r
== graph
->n_total_row
)
1975 sched
->node
[i
].n_band
= b
;
1976 for (--b
; b
>= 0; --b
)
1977 band_id
[b
] = graph
->node
[i
].band_id
[b
];
1984 isl_space_free(dim
);
1985 isl_schedule_free(sched
);
1989 /* Copy nodes that satisfy node_pred from the src dependence graph
1990 * to the dst dependence graph.
1992 static int copy_nodes(struct isl_sched_graph
*dst
, struct isl_sched_graph
*src
,
1993 int (*node_pred
)(struct isl_sched_node
*node
, int data
), int data
)
1998 for (i
= 0; i
< src
->n
; ++i
) {
1999 if (!node_pred(&src
->node
[i
], data
))
2001 dst
->node
[dst
->n
].dim
= isl_space_copy(src
->node
[i
].dim
);
2002 dst
->node
[dst
->n
].nvar
= src
->node
[i
].nvar
;
2003 dst
->node
[dst
->n
].nparam
= src
->node
[i
].nparam
;
2004 dst
->node
[dst
->n
].sched
= isl_mat_copy(src
->node
[i
].sched
);
2005 dst
->node
[dst
->n
].sched_map
=
2006 isl_map_copy(src
->node
[i
].sched_map
);
2007 dst
->node
[dst
->n
].band
= src
->node
[i
].band
;
2008 dst
->node
[dst
->n
].band_id
= src
->node
[i
].band_id
;
2009 dst
->node
[dst
->n
].zero
= src
->node
[i
].zero
;
2016 /* Copy non-empty edges that satisfy edge_pred from the src dependence graph
2017 * to the dst dependence graph.
2018 * If the source or destination node of the edge is not in the destination
2019 * graph, then it must be a backward proximity edge and it should simply
2022 static int copy_edges(isl_ctx
*ctx
, struct isl_sched_graph
*dst
,
2023 struct isl_sched_graph
*src
,
2024 int (*edge_pred
)(struct isl_sched_edge
*edge
, int data
), int data
)
2027 enum isl_edge_type t
;
2030 for (i
= 0; i
< src
->n_edge
; ++i
) {
2031 struct isl_sched_edge
*edge
= &src
->edge
[i
];
2033 struct isl_sched_node
*dst_src
, *dst_dst
;
2035 if (!edge_pred(edge
, data
))
2038 if (isl_map_plain_is_empty(edge
->map
))
2041 dst_src
= graph_find_node(ctx
, dst
, edge
->src
->dim
);
2042 dst_dst
= graph_find_node(ctx
, dst
, edge
->dst
->dim
);
2043 if (!dst_src
|| !dst_dst
) {
2045 isl_die(ctx
, isl_error_internal
,
2046 "backward validity edge", return -1);
2050 map
= isl_map_copy(edge
->map
);
2052 dst
->edge
[dst
->n_edge
].src
= dst_src
;
2053 dst
->edge
[dst
->n_edge
].dst
= dst_dst
;
2054 dst
->edge
[dst
->n_edge
].map
= map
;
2055 dst
->edge
[dst
->n_edge
].validity
= edge
->validity
;
2056 dst
->edge
[dst
->n_edge
].proximity
= edge
->proximity
;
2059 for (t
= isl_edge_first
; t
<= isl_edge_last
; ++t
) {
2061 graph_find_edge(src
, t
, edge
->src
, edge
->dst
))
2063 if (graph_edge_table_add(ctx
, dst
, t
,
2064 &dst
->edge
[dst
->n_edge
- 1]) < 0)
2072 /* Given a "src" dependence graph that contains the nodes from "dst"
2073 * that satisfy node_pred, copy the schedule computed in "src"
2074 * for those nodes back to "dst".
2076 static int copy_schedule(struct isl_sched_graph
*dst
,
2077 struct isl_sched_graph
*src
,
2078 int (*node_pred
)(struct isl_sched_node
*node
, int data
), int data
)
2083 for (i
= 0; i
< dst
->n
; ++i
) {
2084 if (!node_pred(&dst
->node
[i
], data
))
2086 isl_mat_free(dst
->node
[i
].sched
);
2087 isl_map_free(dst
->node
[i
].sched_map
);
2088 dst
->node
[i
].sched
= isl_mat_copy(src
->node
[src
->n
].sched
);
2089 dst
->node
[i
].sched_map
=
2090 isl_map_copy(src
->node
[src
->n
].sched_map
);
2094 dst
->max_row
= src
->max_row
;
2095 dst
->n_total_row
= src
->n_total_row
;
2096 dst
->n_band
= src
->n_band
;
2101 /* Compute the maximal number of variables over all nodes.
2102 * This is the maximal number of linearly independent schedule
2103 * rows that we need to compute.
2104 * Just in case we end up in a part of the dependence graph
2105 * with only lower-dimensional domains, we make sure we will
2106 * compute the required amount of extra linearly independent rows.
2108 static int compute_maxvar(struct isl_sched_graph
*graph
)
2113 for (i
= 0; i
< graph
->n
; ++i
) {
2114 struct isl_sched_node
*node
= &graph
->node
[i
];
2117 if (node_update_cmap(node
) < 0)
2119 nvar
= node
->nvar
+ graph
->n_row
- node
->rank
;
2120 if (nvar
> graph
->maxvar
)
2121 graph
->maxvar
= nvar
;
2127 static int compute_schedule(isl_ctx
*ctx
, struct isl_sched_graph
*graph
);
2128 static int compute_schedule_wcc(isl_ctx
*ctx
, struct isl_sched_graph
*graph
);
2130 /* Compute a schedule for a subgraph of "graph". In particular, for
2131 * the graph composed of nodes that satisfy node_pred and edges that
2132 * that satisfy edge_pred. The caller should precompute the number
2133 * of nodes and edges that satisfy these predicates and pass them along
2134 * as "n" and "n_edge".
2135 * If the subgraph is known to consist of a single component, then wcc should
2136 * be set and then we call compute_schedule_wcc on the constructed subgraph.
2137 * Otherwise, we call compute_schedule, which will check whether the subgraph
2140 static int compute_sub_schedule(isl_ctx
*ctx
,
2141 struct isl_sched_graph
*graph
, int n
, int n_edge
,
2142 int (*node_pred
)(struct isl_sched_node
*node
, int data
),
2143 int (*edge_pred
)(struct isl_sched_edge
*edge
, int data
),
2146 struct isl_sched_graph split
= { 0 };
2149 if (graph_alloc(ctx
, &split
, n
, n_edge
) < 0)
2151 if (copy_nodes(&split
, graph
, node_pred
, data
) < 0)
2153 if (graph_init_table(ctx
, &split
) < 0)
2155 for (t
= 0; t
<= isl_edge_last
; ++t
)
2156 split
.max_edge
[t
] = graph
->max_edge
[t
];
2157 if (graph_init_edge_tables(ctx
, &split
) < 0)
2159 if (copy_edges(ctx
, &split
, graph
, edge_pred
, data
) < 0)
2161 split
.n_row
= graph
->n_row
;
2162 split
.max_row
= graph
->max_row
;
2163 split
.n_total_row
= graph
->n_total_row
;
2164 split
.n_band
= graph
->n_band
;
2165 split
.band_start
= graph
->band_start
;
2167 if (wcc
&& compute_schedule_wcc(ctx
, &split
) < 0)
2169 if (!wcc
&& compute_schedule(ctx
, &split
) < 0)
2172 copy_schedule(graph
, &split
, node_pred
, data
);
2174 graph_free(ctx
, &split
);
2177 graph_free(ctx
, &split
);
2181 static int node_scc_exactly(struct isl_sched_node
*node
, int scc
)
2183 return node
->scc
== scc
;
2186 static int node_scc_at_most(struct isl_sched_node
*node
, int scc
)
2188 return node
->scc
<= scc
;
2191 static int node_scc_at_least(struct isl_sched_node
*node
, int scc
)
2193 return node
->scc
>= scc
;
2196 static int edge_scc_exactly(struct isl_sched_edge
*edge
, int scc
)
2198 return edge
->src
->scc
== scc
&& edge
->dst
->scc
== scc
;
2201 static int edge_dst_scc_at_most(struct isl_sched_edge
*edge
, int scc
)
2203 return edge
->dst
->scc
<= scc
;
2206 static int edge_src_scc_at_least(struct isl_sched_edge
*edge
, int scc
)
2208 return edge
->src
->scc
>= scc
;
2211 /* Pad the schedules of all nodes with zero rows such that in the end
2212 * they all have graph->n_total_row rows.
2213 * The extra rows don't belong to any band, so they get assigned band number -1.
2215 static int pad_schedule(struct isl_sched_graph
*graph
)
2219 for (i
= 0; i
< graph
->n
; ++i
) {
2220 struct isl_sched_node
*node
= &graph
->node
[i
];
2221 int row
= isl_mat_rows(node
->sched
);
2222 if (graph
->n_total_row
> row
) {
2223 isl_map_free(node
->sched_map
);
2224 node
->sched_map
= NULL
;
2226 node
->sched
= isl_mat_add_zero_rows(node
->sched
,
2227 graph
->n_total_row
- row
);
2230 for (j
= row
; j
< graph
->n_total_row
; ++j
)
2237 /* Split the current graph into two parts and compute a schedule for each
2238 * part individually. In particular, one part consists of all SCCs up
2239 * to and including graph->src_scc, while the other part contains the other
2242 * The split is enforced in the schedule by constant rows with two different
2243 * values (0 and 1). These constant rows replace the previously computed rows
2244 * in the current band.
2245 * It would be possible to reuse them as the first rows in the next
2246 * band, but recomputing them may result in better rows as we are looking
2247 * at a smaller part of the dependence graph.
2248 * compute_split_schedule is only called when no zero-distance schedule row
2249 * could be found on the entire graph, so we wark the splitting row as
2250 * non zero-distance.
2252 * The band_id of the second group is set to n, where n is the number
2253 * of nodes in the first group. This ensures that the band_ids over
2254 * the two groups remain disjoint, even if either or both of the two
2255 * groups contain independent components.
2257 static int compute_split_schedule(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2259 int i
, j
, n
, e1
, e2
;
2260 int n_total_row
, orig_total_row
;
2261 int n_band
, orig_band
;
2264 if (graph
->n_total_row
>= graph
->max_row
)
2265 isl_die(ctx
, isl_error_internal
,
2266 "too many schedule rows", return -1);
2268 drop
= graph
->n_total_row
- graph
->band_start
;
2269 graph
->n_total_row
-= drop
;
2270 graph
->n_row
-= drop
;
2273 for (i
= 0; i
< graph
->n
; ++i
) {
2274 struct isl_sched_node
*node
= &graph
->node
[i
];
2275 int row
= isl_mat_rows(node
->sched
) - drop
;
2276 int cols
= isl_mat_cols(node
->sched
);
2277 int before
= node
->scc
<= graph
->src_scc
;
2282 isl_map_free(node
->sched_map
);
2283 node
->sched_map
= NULL
;
2284 node
->sched
= isl_mat_drop_rows(node
->sched
,
2285 graph
->band_start
, drop
);
2286 node
->sched
= isl_mat_add_rows(node
->sched
, 1);
2289 node
->sched
= isl_mat_set_element_si(node
->sched
, row
, 0,
2291 for (j
= 1; j
< cols
; ++j
)
2292 node
->sched
= isl_mat_set_element_si(node
->sched
,
2294 node
->band
[graph
->n_total_row
] = graph
->n_band
;
2295 node
->zero
[graph
->n_total_row
] = 0;
2299 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2300 if (graph
->edge
[i
].dst
->scc
<= graph
->src_scc
)
2302 if (graph
->edge
[i
].src
->scc
> graph
->src_scc
)
2306 graph
->n_total_row
++;
2309 for (i
= 0; i
< graph
->n
; ++i
) {
2310 struct isl_sched_node
*node
= &graph
->node
[i
];
2311 if (node
->scc
> graph
->src_scc
)
2312 node
->band_id
[graph
->n_band
] = n
;
2315 orig_total_row
= graph
->n_total_row
;
2316 orig_band
= graph
->n_band
;
2317 if (compute_sub_schedule(ctx
, graph
, n
, e1
,
2318 &node_scc_at_most
, &edge_dst_scc_at_most
,
2319 graph
->src_scc
, 0) < 0)
2321 n_total_row
= graph
->n_total_row
;
2322 graph
->n_total_row
= orig_total_row
;
2323 n_band
= graph
->n_band
;
2324 graph
->n_band
= orig_band
;
2325 if (compute_sub_schedule(ctx
, graph
, graph
->n
- n
, e2
,
2326 &node_scc_at_least
, &edge_src_scc_at_least
,
2327 graph
->src_scc
+ 1, 0) < 0)
2329 if (n_total_row
> graph
->n_total_row
)
2330 graph
->n_total_row
= n_total_row
;
2331 if (n_band
> graph
->n_band
)
2332 graph
->n_band
= n_band
;
2334 return pad_schedule(graph
);
2337 /* Compute the next band of the schedule after updating the dependence
2338 * relations based on the the current schedule.
2340 static int compute_next_band(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2342 if (update_edges(ctx
, graph
) < 0)
2346 return compute_schedule(ctx
, graph
);
2349 /* Add constraints to graph->lp that force the dependence "map" (which
2350 * is part of the dependence relation of "edge")
2351 * to be respected and attempt to carry it, where the edge is one from
2352 * a node j to itself. "pos" is the sequence number of the given map.
2353 * That is, add constraints that enforce
2355 * (c_j_0 + c_j_n n + c_j_x y) - (c_j_0 + c_j_n n + c_j_x x)
2356 * = c_j_x (y - x) >= e_i
2358 * for each (x,y) in R.
2359 * We obtain general constraints on coefficients (c_0, c_n, c_x)
2360 * of valid constraints for (y - x) and then plug in (-e_i, 0, c_j_x),
2361 * with each coefficient in c_j_x represented as a pair of non-negative
2364 static int add_intra_constraints(struct isl_sched_graph
*graph
,
2365 struct isl_sched_edge
*edge
, __isl_take isl_map
*map
, int pos
)
2368 isl_ctx
*ctx
= isl_map_get_ctx(map
);
2370 isl_dim_map
*dim_map
;
2371 isl_basic_set
*coef
;
2372 struct isl_sched_node
*node
= edge
->src
;
2374 coef
= intra_coefficients(graph
, map
);
2378 dim
= isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef
)));
2380 total
= isl_basic_set_total_dim(graph
->lp
);
2381 dim_map
= isl_dim_map_alloc(ctx
, total
);
2382 isl_dim_map_range(dim_map
, 3 + pos
, 0, 0, 0, 1, -1);
2383 isl_dim_map_range(dim_map
, node
->start
+ 2 * node
->nparam
+ 1, 2,
2384 isl_space_dim(dim
, isl_dim_set
), 1,
2386 isl_dim_map_range(dim_map
, node
->start
+ 2 * node
->nparam
+ 2, 2,
2387 isl_space_dim(dim
, isl_dim_set
), 1,
2389 graph
->lp
= isl_basic_set_extend_constraints(graph
->lp
,
2390 coef
->n_eq
, coef
->n_ineq
);
2391 graph
->lp
= isl_basic_set_add_constraints_dim_map(graph
->lp
,
2393 isl_space_free(dim
);
2398 /* Add constraints to graph->lp that force the dependence "map" (which
2399 * is part of the dependence relation of "edge")
2400 * to be respected and attempt to carry it, where the edge is one from
2401 * node j to node k. "pos" is the sequence number of the given map.
2402 * That is, add constraints that enforce
2404 * (c_k_0 + c_k_n n + c_k_x y) - (c_j_0 + c_j_n n + c_j_x x) >= e_i
2406 * for each (x,y) in R.
2407 * We obtain general constraints on coefficients (c_0, c_n, c_x)
2408 * of valid constraints for R and then plug in
2409 * (-e_i + c_k_0 - c_j_0, c_k_n - c_j_n, c_k_x - c_j_x)
2410 * with each coefficient (except e_i, c_k_0 and c_j_0)
2411 * represented as a pair of non-negative coefficients.
2413 static int add_inter_constraints(struct isl_sched_graph
*graph
,
2414 struct isl_sched_edge
*edge
, __isl_take isl_map
*map
, int pos
)
2417 isl_ctx
*ctx
= isl_map_get_ctx(map
);
2419 isl_dim_map
*dim_map
;
2420 isl_basic_set
*coef
;
2421 struct isl_sched_node
*src
= edge
->src
;
2422 struct isl_sched_node
*dst
= edge
->dst
;
2424 coef
= inter_coefficients(graph
, map
);
2428 dim
= isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef
)));
2430 total
= isl_basic_set_total_dim(graph
->lp
);
2431 dim_map
= isl_dim_map_alloc(ctx
, total
);
2433 isl_dim_map_range(dim_map
, 3 + pos
, 0, 0, 0, 1, -1);
2435 isl_dim_map_range(dim_map
, dst
->start
, 0, 0, 0, 1, 1);
2436 isl_dim_map_range(dim_map
, dst
->start
+ 1, 2, 1, 1, dst
->nparam
, -1);
2437 isl_dim_map_range(dim_map
, dst
->start
+ 2, 2, 1, 1, dst
->nparam
, 1);
2438 isl_dim_map_range(dim_map
, dst
->start
+ 2 * dst
->nparam
+ 1, 2,
2439 isl_space_dim(dim
, isl_dim_set
) + src
->nvar
, 1,
2441 isl_dim_map_range(dim_map
, dst
->start
+ 2 * dst
->nparam
+ 2, 2,
2442 isl_space_dim(dim
, isl_dim_set
) + src
->nvar
, 1,
2445 isl_dim_map_range(dim_map
, src
->start
, 0, 0, 0, 1, -1);
2446 isl_dim_map_range(dim_map
, src
->start
+ 1, 2, 1, 1, src
->nparam
, 1);
2447 isl_dim_map_range(dim_map
, src
->start
+ 2, 2, 1, 1, src
->nparam
, -1);
2448 isl_dim_map_range(dim_map
, src
->start
+ 2 * src
->nparam
+ 1, 2,
2449 isl_space_dim(dim
, isl_dim_set
), 1,
2451 isl_dim_map_range(dim_map
, src
->start
+ 2 * src
->nparam
+ 2, 2,
2452 isl_space_dim(dim
, isl_dim_set
), 1,
2455 graph
->lp
= isl_basic_set_extend_constraints(graph
->lp
,
2456 coef
->n_eq
, coef
->n_ineq
);
2457 graph
->lp
= isl_basic_set_add_constraints_dim_map(graph
->lp
,
2459 isl_space_free(dim
);
2464 /* Add constraints to graph->lp that force all validity dependences
2465 * to be respected and attempt to carry them.
2467 static int add_all_constraints(struct isl_sched_graph
*graph
)
2473 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2474 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
2476 if (!edge
->validity
)
2479 for (j
= 0; j
< edge
->map
->n
; ++j
) {
2480 isl_basic_map
*bmap
;
2483 bmap
= isl_basic_map_copy(edge
->map
->p
[j
]);
2484 map
= isl_map_from_basic_map(bmap
);
2486 if (edge
->src
== edge
->dst
&&
2487 add_intra_constraints(graph
, edge
, map
, pos
) < 0)
2489 if (edge
->src
!= edge
->dst
&&
2490 add_inter_constraints(graph
, edge
, map
, pos
) < 0)
2499 /* Count the number of equality and inequality constraints
2500 * that will be added to the carry_lp problem.
2501 * We count each edge exactly once.
2503 static int count_all_constraints(struct isl_sched_graph
*graph
,
2504 int *n_eq
, int *n_ineq
)
2508 *n_eq
= *n_ineq
= 0;
2509 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2510 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
2511 for (j
= 0; j
< edge
->map
->n
; ++j
) {
2512 isl_basic_map
*bmap
;
2515 bmap
= isl_basic_map_copy(edge
->map
->p
[j
]);
2516 map
= isl_map_from_basic_map(bmap
);
2518 if (count_map_constraints(graph
, edge
, map
,
2519 n_eq
, n_ineq
, 1) < 0)
2527 /* Construct an LP problem for finding schedule coefficients
2528 * such that the schedule carries as many dependences as possible.
2529 * In particular, for each dependence i, we bound the dependence distance
2530 * from below by e_i, with 0 <= e_i <= 1 and then maximize the sum
2531 * of all e_i's. Dependence with e_i = 0 in the solution are simply
2532 * respected, while those with e_i > 0 (in practice e_i = 1) are carried.
2533 * Note that if the dependence relation is a union of basic maps,
2534 * then we have to consider each basic map individually as it may only
2535 * be possible to carry the dependences expressed by some of those
2536 * basic maps and not all off them.
2537 * Below, we consider each of those basic maps as a separate "edge".
2539 * All variables of the LP are non-negative. The actual coefficients
2540 * may be negative, so each coefficient is represented as the difference
2541 * of two non-negative variables. The negative part always appears
2542 * immediately before the positive part.
2543 * Other than that, the variables have the following order
2545 * - sum of (1 - e_i) over all edges
2546 * - sum of positive and negative parts of all c_n coefficients
2547 * (unconstrained when computing non-parametric schedules)
2548 * - sum of positive and negative parts of all c_x coefficients
2553 * - positive and negative parts of c_i_n (if parametric)
2554 * - positive and negative parts of c_i_x
2556 * The constraints are those from the (validity) edges plus three equalities
2557 * to express the sums and n_edge inequalities to express e_i <= 1.
2559 static int setup_carry_lp(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2569 for (i
= 0; i
< graph
->n_edge
; ++i
)
2570 n_edge
+= graph
->edge
[i
].map
->n
;
2573 for (i
= 0; i
< graph
->n
; ++i
) {
2574 struct isl_sched_node
*node
= &graph
->node
[graph
->sorted
[i
]];
2575 node
->start
= total
;
2576 total
+= 1 + 2 * (node
->nparam
+ node
->nvar
);
2579 if (count_all_constraints(graph
, &n_eq
, &n_ineq
) < 0)
2581 if (count_bound_coefficient_constraints(ctx
, graph
, &n_eq
, &n_ineq
) < 0)
2584 dim
= isl_space_set_alloc(ctx
, 0, total
);
2585 isl_basic_set_free(graph
->lp
);
2588 graph
->lp
= isl_basic_set_alloc_space(dim
, 0, n_eq
, n_ineq
);
2589 graph
->lp
= isl_basic_set_set_rational(graph
->lp
);
2591 k
= isl_basic_set_alloc_equality(graph
->lp
);
2594 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2595 isl_int_set_si(graph
->lp
->eq
[k
][0], -n_edge
);
2596 isl_int_set_si(graph
->lp
->eq
[k
][1], 1);
2597 for (i
= 0; i
< n_edge
; ++i
)
2598 isl_int_set_si(graph
->lp
->eq
[k
][4 + i
], 1);
2600 k
= isl_basic_set_alloc_equality(graph
->lp
);
2603 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2604 isl_int_set_si(graph
->lp
->eq
[k
][2], -1);
2605 for (i
= 0; i
< graph
->n
; ++i
) {
2606 int pos
= 1 + graph
->node
[i
].start
+ 1;
2608 for (j
= 0; j
< 2 * graph
->node
[i
].nparam
; ++j
)
2609 isl_int_set_si(graph
->lp
->eq
[k
][pos
+ j
], 1);
2612 k
= isl_basic_set_alloc_equality(graph
->lp
);
2615 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2616 isl_int_set_si(graph
->lp
->eq
[k
][3], -1);
2617 for (i
= 0; i
< graph
->n
; ++i
) {
2618 struct isl_sched_node
*node
= &graph
->node
[i
];
2619 int pos
= 1 + node
->start
+ 1 + 2 * node
->nparam
;
2621 for (j
= 0; j
< 2 * node
->nvar
; ++j
)
2622 isl_int_set_si(graph
->lp
->eq
[k
][pos
+ j
], 1);
2625 for (i
= 0; i
< n_edge
; ++i
) {
2626 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2629 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
2630 isl_int_set_si(graph
->lp
->ineq
[k
][4 + i
], -1);
2631 isl_int_set_si(graph
->lp
->ineq
[k
][0], 1);
2634 if (add_bound_coefficient_constraints(ctx
, graph
) < 0)
2636 if (add_all_constraints(graph
) < 0)
2642 /* If the schedule_split_scaled option is set and if the linear
2643 * parts of the scheduling rows for all nodes in the graphs have
2644 * non-trivial common divisor, then split off the constant term
2645 * from the linear part.
2646 * The constant term is then placed in a separate band and
2647 * the linear part is reduced.
2649 static int split_scaled(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2655 if (!ctx
->opt
->schedule_split_scaled
)
2660 if (graph
->n_total_row
>= graph
->max_row
)
2661 isl_die(ctx
, isl_error_internal
,
2662 "too many schedule rows", return -1);
2665 isl_int_init(gcd_i
);
2667 isl_int_set_si(gcd
, 0);
2669 row
= isl_mat_rows(graph
->node
[0].sched
) - 1;
2671 for (i
= 0; i
< graph
->n
; ++i
) {
2672 struct isl_sched_node
*node
= &graph
->node
[i
];
2673 int cols
= isl_mat_cols(node
->sched
);
2675 isl_seq_gcd(node
->sched
->row
[row
] + 1, cols
- 1, &gcd_i
);
2676 isl_int_gcd(gcd
, gcd
, gcd_i
);
2679 isl_int_clear(gcd_i
);
2681 if (isl_int_cmp_si(gcd
, 1) <= 0) {
2688 for (i
= 0; i
< graph
->n
; ++i
) {
2689 struct isl_sched_node
*node
= &graph
->node
[i
];
2691 isl_map_free(node
->sched_map
);
2692 node
->sched_map
= NULL
;
2693 node
->sched
= isl_mat_add_zero_rows(node
->sched
, 1);
2696 isl_int_fdiv_r(node
->sched
->row
[row
+ 1][0],
2697 node
->sched
->row
[row
][0], gcd
);
2698 isl_int_fdiv_q(node
->sched
->row
[row
][0],
2699 node
->sched
->row
[row
][0], gcd
);
2700 isl_int_mul(node
->sched
->row
[row
][0],
2701 node
->sched
->row
[row
][0], gcd
);
2702 node
->sched
= isl_mat_scale_down_row(node
->sched
, row
, gcd
);
2705 node
->band
[graph
->n_total_row
] = graph
->n_band
;
2708 graph
->n_total_row
++;
2717 static int compute_component_schedule(isl_ctx
*ctx
,
2718 struct isl_sched_graph
*graph
);
2720 /* Is the schedule row "sol" trivial on node "node"?
2721 * That is, is the solution zero on the dimensions orthogonal to
2722 * the previously found solutions?
2723 * Return 1 if the solution is trivial, 0 if it is not and -1 on error.
2725 * Each coefficient is represented as the difference between
2726 * two non-negative values in "sol". "sol" has been computed
2727 * in terms of the original iterators (i.e., without use of cmap).
2728 * We construct the schedule row s and write it as a linear
2729 * combination of (linear combinations of) previously computed schedule rows.
2730 * s = Q c or c = U s.
2731 * If the final entries of c are all zero, then the solution is trivial.
2733 static int is_trivial(struct isl_sched_node
*node
, __isl_keep isl_vec
*sol
)
2743 if (node
->nvar
== node
->rank
)
2746 ctx
= isl_vec_get_ctx(sol
);
2747 node_sol
= isl_vec_alloc(ctx
, node
->nvar
);
2751 pos
= 1 + node
->start
+ 1 + 2 * node
->nparam
;
2753 for (i
= 0; i
< node
->nvar
; ++i
)
2754 isl_int_sub(node_sol
->el
[i
],
2755 sol
->el
[pos
+ 2 * i
+ 1], sol
->el
[pos
+ 2 * i
]);
2757 node_sol
= isl_mat_vec_product(isl_mat_copy(node
->cinv
), node_sol
);
2762 trivial
= isl_seq_first_non_zero(node_sol
->el
+ node
->rank
,
2763 node
->nvar
- node
->rank
) == -1;
2765 isl_vec_free(node_sol
);
2770 /* Is the schedule row "sol" trivial on any node where it should
2772 * "sol" has been computed in terms of the original iterators
2773 * (i.e., without use of cmap).
2774 * Return 1 if any solution is trivial, 0 if they are not and -1 on error.
2776 static int is_any_trivial(struct isl_sched_graph
*graph
,
2777 __isl_keep isl_vec
*sol
)
2781 for (i
= 0; i
< graph
->n
; ++i
) {
2782 struct isl_sched_node
*node
= &graph
->node
[i
];
2785 if (!needs_row(graph
, node
))
2787 trivial
= is_trivial(node
, sol
);
2788 if (trivial
< 0 || trivial
)
2795 /* Construct a schedule row for each node such that as many dependences
2796 * as possible are carried and then continue with the next band.
2798 * If the computed schedule row turns out to be trivial on one or
2799 * more nodes where it should not be trivial, then we throw it away
2800 * and try again on each component separately.
2802 static int carry_dependences(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2811 for (i
= 0; i
< graph
->n_edge
; ++i
)
2812 n_edge
+= graph
->edge
[i
].map
->n
;
2814 if (setup_carry_lp(ctx
, graph
) < 0)
2817 lp
= isl_basic_set_copy(graph
->lp
);
2818 sol
= isl_tab_basic_set_non_neg_lexmin(lp
);
2822 if (sol
->size
== 0) {
2824 isl_die(ctx
, isl_error_internal
,
2825 "error in schedule construction", return -1);
2828 isl_int_divexact(sol
->el
[1], sol
->el
[1], sol
->el
[0]);
2829 if (isl_int_cmp_si(sol
->el
[1], n_edge
) >= 0) {
2831 isl_die(ctx
, isl_error_unknown
,
2832 "unable to carry dependences", return -1);
2835 trivial
= is_any_trivial(graph
, sol
);
2837 sol
= isl_vec_free(sol
);
2838 } else if (trivial
) {
2841 return compute_component_schedule(ctx
, graph
);
2842 isl_die(ctx
, isl_error_unknown
,
2843 "unable to construct non-trivial solution", return -1);
2846 if (update_schedule(graph
, sol
, 0, 0) < 0)
2849 if (split_scaled(ctx
, graph
) < 0)
2852 return compute_next_band(ctx
, graph
);
2855 /* Are there any (non-empty) validity edges in the graph?
2857 static int has_validity_edges(struct isl_sched_graph
*graph
)
2861 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2864 empty
= isl_map_plain_is_empty(graph
->edge
[i
].map
);
2869 if (graph
->edge
[i
].validity
)
2876 /* Should we apply a Feautrier step?
2877 * That is, did the user request the Feautrier algorithm and are
2878 * there any validity dependences (left)?
2880 static int need_feautrier_step(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2882 if (ctx
->opt
->schedule_algorithm
!= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
)
2885 return has_validity_edges(graph
);
2888 /* Compute a schedule for a connected dependence graph using Feautrier's
2889 * multi-dimensional scheduling algorithm.
2890 * The original algorithm is described in [1].
2891 * The main idea is to minimize the number of scheduling dimensions, by
2892 * trying to satisfy as many dependences as possible per scheduling dimension.
2894 * [1] P. Feautrier, Some Efficient Solutions to the Affine Scheduling
2895 * Problem, Part II: Multi-Dimensional Time.
2896 * In Intl. Journal of Parallel Programming, 1992.
2898 static int compute_schedule_wcc_feautrier(isl_ctx
*ctx
,
2899 struct isl_sched_graph
*graph
)
2901 return carry_dependences(ctx
, graph
);
2904 /* Compute a schedule for a connected dependence graph.
2905 * We try to find a sequence of as many schedule rows as possible that result
2906 * in non-negative dependence distances (independent of the previous rows
2907 * in the sequence, i.e., such that the sequence is tilable).
2908 * If we can't find any more rows we either
2909 * - split between SCCs and start over (assuming we found an interesting
2910 * pair of SCCs between which to split)
2911 * - continue with the next band (assuming the current band has at least
2913 * - try to carry as many dependences as possible and continue with the next
2916 * If Feautrier's algorithm is selected, we first recursively try to satisfy
2917 * as many validity dependences as possible. When all validity dependences
2918 * are satisfied we extend the schedule to a full-dimensional schedule.
2920 * If we manage to complete the schedule, we finish off by topologically
2921 * sorting the statements based on the remaining dependences.
2923 * If ctx->opt->schedule_outer_zero_distance is set, then we force the
2924 * outermost dimension in the current band to be zero distance. If this
2925 * turns out to be impossible, we fall back on the general scheme above
2926 * and try to carry as many dependences as possible.
2928 static int compute_schedule_wcc(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2932 if (detect_sccs(ctx
, graph
) < 0)
2934 if (sort_sccs(graph
) < 0)
2937 if (compute_maxvar(graph
) < 0)
2940 if (need_feautrier_step(ctx
, graph
))
2941 return compute_schedule_wcc_feautrier(ctx
, graph
);
2943 if (ctx
->opt
->schedule_outer_zero_distance
)
2946 while (graph
->n_row
< graph
->maxvar
) {
2949 graph
->src_scc
= -1;
2950 graph
->dst_scc
= -1;
2952 if (setup_lp(ctx
, graph
, force_zero
) < 0)
2954 sol
= solve_lp(graph
);
2957 if (sol
->size
== 0) {
2959 if (!ctx
->opt
->schedule_maximize_band_depth
&&
2960 graph
->n_total_row
> graph
->band_start
)
2961 return compute_next_band(ctx
, graph
);
2962 if (graph
->src_scc
>= 0)
2963 return compute_split_schedule(ctx
, graph
);
2964 if (graph
->n_total_row
> graph
->band_start
)
2965 return compute_next_band(ctx
, graph
);
2966 return carry_dependences(ctx
, graph
);
2968 if (update_schedule(graph
, sol
, 1, 1) < 0)
2973 if (graph
->n_total_row
> graph
->band_start
)
2975 return sort_statements(ctx
, graph
);
2978 /* Add a row to the schedules that separates the SCCs and move
2981 static int split_on_scc(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2985 if (graph
->n_total_row
>= graph
->max_row
)
2986 isl_die(ctx
, isl_error_internal
,
2987 "too many schedule rows", return -1);
2989 for (i
= 0; i
< graph
->n
; ++i
) {
2990 struct isl_sched_node
*node
= &graph
->node
[i
];
2991 int row
= isl_mat_rows(node
->sched
);
2993 isl_map_free(node
->sched_map
);
2994 node
->sched_map
= NULL
;
2995 node
->sched
= isl_mat_add_zero_rows(node
->sched
, 1);
2996 node
->sched
= isl_mat_set_element_si(node
->sched
, row
, 0,
3000 node
->band
[graph
->n_total_row
] = graph
->n_band
;
3003 graph
->n_total_row
++;
3009 /* Compute a schedule for each component (identified by node->scc)
3010 * of the dependence graph separately and then combine the results.
3011 * Depending on the setting of schedule_fuse, a component may be
3012 * either weakly or strongly connected.
3014 * The band_id is adjusted such that each component has a separate id.
3015 * Note that the band_id may have already been set to a value different
3016 * from zero by compute_split_schedule.
3018 static int compute_component_schedule(isl_ctx
*ctx
,
3019 struct isl_sched_graph
*graph
)
3023 int n_total_row
, orig_total_row
;
3024 int n_band
, orig_band
;
3026 if (ctx
->opt
->schedule_fuse
== ISL_SCHEDULE_FUSE_MIN
||
3027 ctx
->opt
->schedule_separate_components
)
3028 if (split_on_scc(ctx
, graph
) < 0)
3032 orig_total_row
= graph
->n_total_row
;
3034 orig_band
= graph
->n_band
;
3035 for (i
= 0; i
< graph
->n
; ++i
)
3036 graph
->node
[i
].band_id
[graph
->n_band
] += graph
->node
[i
].scc
;
3037 for (wcc
= 0; wcc
< graph
->scc
; ++wcc
) {
3039 for (i
= 0; i
< graph
->n
; ++i
)
3040 if (graph
->node
[i
].scc
== wcc
)
3043 for (i
= 0; i
< graph
->n_edge
; ++i
)
3044 if (graph
->edge
[i
].src
->scc
== wcc
&&
3045 graph
->edge
[i
].dst
->scc
== wcc
)
3048 if (compute_sub_schedule(ctx
, graph
, n
, n_edge
,
3050 &edge_scc_exactly
, wcc
, 1) < 0)
3052 if (graph
->n_total_row
> n_total_row
)
3053 n_total_row
= graph
->n_total_row
;
3054 graph
->n_total_row
= orig_total_row
;
3055 if (graph
->n_band
> n_band
)
3056 n_band
= graph
->n_band
;
3057 graph
->n_band
= orig_band
;
3060 graph
->n_total_row
= n_total_row
;
3061 graph
->n_band
= n_band
;
3063 return pad_schedule(graph
);
3066 /* Compute a schedule for the given dependence graph.
3067 * We first check if the graph is connected (through validity dependences)
3068 * and, if not, compute a schedule for each component separately.
3069 * If schedule_fuse is set to minimal fusion, then we check for strongly
3070 * connected components instead and compute a separate schedule for
3071 * each such strongly connected component.
3073 static int compute_schedule(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
3075 if (ctx
->opt
->schedule_fuse
== ISL_SCHEDULE_FUSE_MIN
) {
3076 if (detect_sccs(ctx
, graph
) < 0)
3079 if (detect_wccs(ctx
, graph
) < 0)
3084 return compute_component_schedule(ctx
, graph
);
3086 return compute_schedule_wcc(ctx
, graph
);
3089 /* Compute a schedule on sc->domain that respects the given schedule
3092 * In particular, the schedule respects all the validity dependences.
3093 * If the default isl scheduling algorithm is used, it tries to minimize
3094 * the dependence distances over the proximity dependences.
3095 * If Feautrier's scheduling algorithm is used, the proximity dependence
3096 * distances are only minimized during the extension to a full-dimensional
3099 __isl_give isl_schedule
*isl_schedule_constraints_compute_schedule(
3100 __isl_take isl_schedule_constraints
*sc
)
3102 isl_ctx
*ctx
= isl_schedule_constraints_get_ctx(sc
);
3103 struct isl_sched_graph graph
= { 0 };
3104 isl_schedule
*sched
;
3105 struct isl_extract_edge_data data
;
3106 enum isl_edge_type i
;
3108 sc
= isl_schedule_constraints_align_params(sc
);
3112 graph
.n
= isl_union_set_n_set(sc
->domain
);
3115 if (graph_alloc(ctx
, &graph
, graph
.n
,
3116 isl_schedule_constraints_n_map(sc
)) < 0)
3118 if (compute_max_row(&graph
, sc
->domain
) < 0)
3122 if (isl_union_set_foreach_set(sc
->domain
, &extract_node
, &graph
) < 0)
3124 if (graph_init_table(ctx
, &graph
) < 0)
3126 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
)
3127 graph
.max_edge
[i
] = isl_union_map_n_map(sc
->constraint
[i
]);
3128 if (graph_init_edge_tables(ctx
, &graph
) < 0)
3131 data
.graph
= &graph
;
3132 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
3134 if (isl_union_map_foreach_map(sc
->constraint
[i
],
3135 &extract_edge
, &data
) < 0)
3139 if (compute_schedule(ctx
, &graph
) < 0)
3143 sched
= extract_schedule(&graph
, isl_union_set_get_space(sc
->domain
));
3145 graph_free(ctx
, &graph
);
3146 isl_schedule_constraints_free(sc
);
3150 graph_free(ctx
, &graph
);
3151 isl_schedule_constraints_free(sc
);
3155 /* Compute a schedule for the given union of domains that respects
3156 * all the validity dependences and minimizes
3157 * the dependence distances over the proximity dependences.
3159 * This function is kept for backward compatibility.
3161 __isl_give isl_schedule
*isl_union_set_compute_schedule(
3162 __isl_take isl_union_set
*domain
,
3163 __isl_take isl_union_map
*validity
,
3164 __isl_take isl_union_map
*proximity
)
3166 isl_schedule_constraints
*sc
;
3168 sc
= isl_schedule_constraints_on_domain(domain
);
3169 sc
= isl_schedule_constraints_set_validity(sc
, validity
);
3170 sc
= isl_schedule_constraints_set_proximity(sc
, proximity
);
3172 return isl_schedule_constraints_compute_schedule(sc
);
3175 void *isl_schedule_free(__isl_take isl_schedule
*sched
)
3181 if (--sched
->ref
> 0)
3184 for (i
= 0; i
< sched
->n
; ++i
) {
3185 isl_multi_aff_free(sched
->node
[i
].sched
);
3186 free(sched
->node
[i
].band_end
);
3187 free(sched
->node
[i
].band_id
);
3188 free(sched
->node
[i
].zero
);
3190 isl_space_free(sched
->dim
);
3191 isl_band_list_free(sched
->band_forest
);
3196 isl_ctx
*isl_schedule_get_ctx(__isl_keep isl_schedule
*schedule
)
3198 return schedule
? isl_space_get_ctx(schedule
->dim
) : NULL
;
3201 /* Set max_out to the maximal number of output dimensions over
3204 static int update_max_out(__isl_take isl_map
*map
, void *user
)
3206 int *max_out
= user
;
3207 int n_out
= isl_map_dim(map
, isl_dim_out
);
3209 if (n_out
> *max_out
)
3216 /* Internal data structure for map_pad_range.
3218 * "max_out" is the maximal schedule dimension.
3219 * "res" collects the results.
3221 struct isl_pad_schedule_map_data
{
3226 /* Pad the range of the given map with zeros to data->max_out and
3227 * then add the result to data->res.
3229 static int map_pad_range(__isl_take isl_map
*map
, void *user
)
3231 struct isl_pad_schedule_map_data
*data
= user
;
3233 int n_out
= isl_map_dim(map
, isl_dim_out
);
3235 map
= isl_map_add_dims(map
, isl_dim_out
, data
->max_out
- n_out
);
3236 for (i
= n_out
; i
< data
->max_out
; ++i
)
3237 map
= isl_map_fix_si(map
, isl_dim_out
, i
, 0);
3239 data
->res
= isl_union_map_add_map(data
->res
, map
);
3246 /* Pad the ranges of the maps in the union map with zeros such they all have
3247 * the same dimension.
3249 static __isl_give isl_union_map
*pad_schedule_map(
3250 __isl_take isl_union_map
*umap
)
3252 struct isl_pad_schedule_map_data data
;
3256 if (isl_union_map_n_map(umap
) <= 1)
3260 if (isl_union_map_foreach_map(umap
, &update_max_out
, &data
.max_out
) < 0)
3261 return isl_union_map_free(umap
);
3263 data
.res
= isl_union_map_empty(isl_union_map_get_space(umap
));
3264 if (isl_union_map_foreach_map(umap
, &map_pad_range
, &data
) < 0)
3265 data
.res
= isl_union_map_free(data
.res
);
3267 isl_union_map_free(umap
);
3271 /* Return an isl_union_map of the schedule. If we have already constructed
3272 * a band forest, then this band forest may have been modified so we need
3273 * to extract the isl_union_map from the forest rather than from
3274 * the originally computed schedule. This reconstructed schedule map
3275 * then needs to be padded with zeros to unify the schedule space
3276 * since the result of isl_band_list_get_suffix_schedule may not have
3277 * a unified schedule space.
3279 __isl_give isl_union_map
*isl_schedule_get_map(__isl_keep isl_schedule
*sched
)
3282 isl_union_map
*umap
;
3287 if (sched
->band_forest
) {
3288 umap
= isl_band_list_get_suffix_schedule(sched
->band_forest
);
3289 return pad_schedule_map(umap
);
3292 umap
= isl_union_map_empty(isl_space_copy(sched
->dim
));
3293 for (i
= 0; i
< sched
->n
; ++i
) {
3296 ma
= isl_multi_aff_copy(sched
->node
[i
].sched
);
3297 umap
= isl_union_map_add_map(umap
, isl_map_from_multi_aff(ma
));
3303 static __isl_give isl_band_list
*construct_band_list(
3304 __isl_keep isl_schedule
*schedule
, __isl_keep isl_band
*parent
,
3305 int band_nr
, int *parent_active
, int n_active
);
3307 /* Construct an isl_band structure for the band in the given schedule
3308 * with sequence number band_nr for the n_active nodes marked by active.
3309 * If the nodes don't have a band with the given sequence number,
3310 * then a band without members is created.
3312 * Because of the way the schedule is constructed, we know that
3313 * the position of the band inside the schedule of a node is the same
3314 * for all active nodes.
3316 * The partial schedule for the band is created before the children
3317 * are created to that construct_band_list can refer to the partial
3318 * schedule of the parent.
3320 static __isl_give isl_band
*construct_band(__isl_keep isl_schedule
*schedule
,
3321 __isl_keep isl_band
*parent
,
3322 int band_nr
, int *active
, int n_active
)
3325 isl_ctx
*ctx
= isl_schedule_get_ctx(schedule
);
3327 unsigned start
, end
;
3329 band
= isl_band_alloc(ctx
);
3333 band
->schedule
= schedule
;
3334 band
->parent
= parent
;
3336 for (i
= 0; i
< schedule
->n
; ++i
)
3340 if (i
>= schedule
->n
)
3341 isl_die(ctx
, isl_error_internal
,
3342 "band without active statements", goto error
);
3344 start
= band_nr
? schedule
->node
[i
].band_end
[band_nr
- 1] : 0;
3345 end
= band_nr
< schedule
->node
[i
].n_band
?
3346 schedule
->node
[i
].band_end
[band_nr
] : start
;
3347 band
->n
= end
- start
;
3349 band
->zero
= isl_alloc_array(ctx
, int, band
->n
);
3350 if (band
->n
&& !band
->zero
)
3353 for (j
= 0; j
< band
->n
; ++j
)
3354 band
->zero
[j
] = schedule
->node
[i
].zero
[start
+ j
];
3356 band
->pma
= isl_union_pw_multi_aff_empty(isl_space_copy(schedule
->dim
));
3357 for (i
= 0; i
< schedule
->n
; ++i
) {
3359 isl_pw_multi_aff
*pma
;
3365 ma
= isl_multi_aff_copy(schedule
->node
[i
].sched
);
3366 n_out
= isl_multi_aff_dim(ma
, isl_dim_out
);
3367 ma
= isl_multi_aff_drop_dims(ma
, isl_dim_out
, end
, n_out
- end
);
3368 ma
= isl_multi_aff_drop_dims(ma
, isl_dim_out
, 0, start
);
3369 pma
= isl_pw_multi_aff_from_multi_aff(ma
);
3370 band
->pma
= isl_union_pw_multi_aff_add_pw_multi_aff(band
->pma
,
3376 for (i
= 0; i
< schedule
->n
; ++i
)
3377 if (active
[i
] && schedule
->node
[i
].n_band
> band_nr
+ 1)
3380 if (i
< schedule
->n
) {
3381 band
->children
= construct_band_list(schedule
, band
,
3382 band_nr
+ 1, active
, n_active
);
3383 if (!band
->children
)
3389 isl_band_free(band
);
3393 /* Internal data structure used inside cmp_band and pw_multi_aff_extract_int.
3395 * r is set to a negative value if anything goes wrong.
3397 * c1 stores the result of extract_int.
3398 * c2 is a temporary value used inside cmp_band_in_ancestor.
3399 * t is a temporary value used inside extract_int.
3401 * first and equal are used inside extract_int.
3402 * first is set if we are looking at the first isl_multi_aff inside
3403 * the isl_union_pw_multi_aff.
3404 * equal is set if all the isl_multi_affs have been equal so far.
3406 struct isl_cmp_band_data
{
3417 /* Check if "ma" assigns a constant value.
3418 * Note that this function is only called on isl_multi_affs
3419 * with a single output dimension.
3421 * If "ma" assigns a constant value then we compare it to data->c1
3422 * or assign it to data->c1 if this is the first isl_multi_aff we consider.
3423 * If "ma" does not assign a constant value or if it assigns a value
3424 * that is different from data->c1, then we set data->equal to zero
3425 * and terminate the check.
3427 static int multi_aff_extract_int(__isl_take isl_set
*set
,
3428 __isl_take isl_multi_aff
*ma
, void *user
)
3431 struct isl_cmp_band_data
*data
= user
;
3433 aff
= isl_multi_aff_get_aff(ma
, 0);
3434 data
->r
= isl_aff_is_cst(aff
);
3435 if (data
->r
>= 0 && data
->r
) {
3436 isl_aff_get_constant(aff
, &data
->t
);
3438 isl_int_set(data
->c1
, data
->t
);
3440 } else if (!isl_int_eq(data
->c1
, data
->t
))
3442 } else if (data
->r
>= 0 && !data
->r
)
3447 isl_multi_aff_free(ma
);
3456 /* This function is called for each isl_pw_multi_aff in
3457 * the isl_union_pw_multi_aff checked by extract_int.
3458 * Check all the isl_multi_affs inside "pma".
3460 static int pw_multi_aff_extract_int(__isl_take isl_pw_multi_aff
*pma
,
3465 r
= isl_pw_multi_aff_foreach_piece(pma
, &multi_aff_extract_int
, user
);
3466 isl_pw_multi_aff_free(pma
);
3471 /* Check if "upma" assigns a single constant value to its domain.
3472 * If so, return 1 and store the result in data->c1.
3475 * A negative return value from isl_union_pw_multi_aff_foreach_pw_multi_aff
3476 * means that either an error occurred or that we have broken off the check
3477 * because we already know the result is going to be negative.
3478 * In the latter case, data->equal is set to zero.
3480 static int extract_int(__isl_keep isl_union_pw_multi_aff
*upma
,
3481 struct isl_cmp_band_data
*data
)
3486 if (isl_union_pw_multi_aff_foreach_pw_multi_aff(upma
,
3487 &pw_multi_aff_extract_int
, data
) < 0) {
3493 return !data
->first
&& data
->equal
;
3496 /* Compare "b1" and "b2" based on the parent schedule of their ancestor
3499 * If the parent of "ancestor" also has a single member, then we
3500 * first try to compare the two band based on the partial schedule
3503 * Otherwise, or if the result is inconclusive, we look at the partial schedule
3504 * of "ancestor" itself.
3505 * In particular, we specialize the parent schedule based
3506 * on the domains of the child schedules, check if both assign
3507 * a single constant value and, if so, compare the two constant values.
3508 * If the specialized parent schedules do not assign a constant value,
3509 * then they cannot be used to order the two bands and so in this case
3512 static int cmp_band_in_ancestor(__isl_keep isl_band
*b1
,
3513 __isl_keep isl_band
*b2
, struct isl_cmp_band_data
*data
,
3514 __isl_keep isl_band
*ancestor
)
3516 isl_union_pw_multi_aff
*upma
;
3517 isl_union_set
*domain
;
3523 if (ancestor
->parent
&& ancestor
->parent
->n
== 1) {
3524 r
= cmp_band_in_ancestor(b1
, b2
, data
, ancestor
->parent
);
3531 upma
= isl_union_pw_multi_aff_copy(b1
->pma
);
3532 domain
= isl_union_pw_multi_aff_domain(upma
);
3533 upma
= isl_union_pw_multi_aff_copy(ancestor
->pma
);
3534 upma
= isl_union_pw_multi_aff_intersect_domain(upma
, domain
);
3535 r
= extract_int(upma
, data
);
3536 isl_union_pw_multi_aff_free(upma
);
3543 isl_int_set(data
->c2
, data
->c1
);
3545 upma
= isl_union_pw_multi_aff_copy(b2
->pma
);
3546 domain
= isl_union_pw_multi_aff_domain(upma
);
3547 upma
= isl_union_pw_multi_aff_copy(ancestor
->pma
);
3548 upma
= isl_union_pw_multi_aff_intersect_domain(upma
, domain
);
3549 r
= extract_int(upma
, data
);
3550 isl_union_pw_multi_aff_free(upma
);
3557 return isl_int_cmp(data
->c2
, data
->c1
);
3560 /* Compare "a" and "b" based on the parent schedule of their parent.
3562 static int cmp_band(const void *a
, const void *b
, void *user
)
3564 isl_band
*b1
= *(isl_band
* const *) a
;
3565 isl_band
*b2
= *(isl_band
* const *) b
;
3566 struct isl_cmp_band_data
*data
= user
;
3568 return cmp_band_in_ancestor(b1
, b2
, data
, b1
->parent
);
3571 /* Sort the elements in "list" based on the partial schedules of its parent
3572 * (and ancestors). In particular if the parent assigns constant values
3573 * to the domains of the bands in "list", then the elements are sorted
3574 * according to that order.
3575 * This order should be a more "natural" order for the user, but otherwise
3576 * shouldn't have any effect.
3577 * If we would be constructing an isl_band forest directly in
3578 * isl_schedule_constraints_compute_schedule then there wouldn't be any need
3579 * for a reordering, since the children would be added to the list
3580 * in their natural order automatically.
3582 * If there is only one element in the list, then there is no need to sort
3584 * If the partial schedule of the parent has more than one member
3585 * (or if there is no parent), then it's
3586 * defnitely not assigning constant values to the different children in
3587 * the list and so we wouldn't be able to use it to sort the list.
3589 static __isl_give isl_band_list
*sort_band_list(__isl_take isl_band_list
*list
,
3590 __isl_keep isl_band
*parent
)
3592 struct isl_cmp_band_data data
;
3598 if (!parent
|| parent
->n
!= 1)
3602 isl_int_init(data
.c1
);
3603 isl_int_init(data
.c2
);
3604 isl_int_init(data
.t
);
3605 isl_sort(list
->p
, list
->n
, sizeof(list
->p
[0]), &cmp_band
, &data
);
3607 list
= isl_band_list_free(list
);
3608 isl_int_clear(data
.c1
);
3609 isl_int_clear(data
.c2
);
3610 isl_int_clear(data
.t
);
3615 /* Construct a list of bands that start at the same position (with
3616 * sequence number band_nr) in the schedules of the nodes that
3617 * were active in the parent band.
3619 * A separate isl_band structure is created for each band_id
3620 * and for each node that does not have a band with sequence
3621 * number band_nr. In the latter case, a band without members
3623 * This ensures that if a band has any children, then each node
3624 * that was active in the band is active in exactly one of the children.
3626 static __isl_give isl_band_list
*construct_band_list(
3627 __isl_keep isl_schedule
*schedule
, __isl_keep isl_band
*parent
,
3628 int band_nr
, int *parent_active
, int n_active
)
3631 isl_ctx
*ctx
= isl_schedule_get_ctx(schedule
);
3634 isl_band_list
*list
;
3637 for (i
= 0; i
< n_active
; ++i
) {
3638 for (j
= 0; j
< schedule
->n
; ++j
) {
3639 if (!parent_active
[j
])
3641 if (schedule
->node
[j
].n_band
<= band_nr
)
3643 if (schedule
->node
[j
].band_id
[band_nr
] == i
) {
3649 for (j
= 0; j
< schedule
->n
; ++j
)
3650 if (schedule
->node
[j
].n_band
<= band_nr
)
3655 list
= isl_band_list_alloc(ctx
, n_band
);
3656 band
= construct_band(schedule
, parent
, band_nr
,
3657 parent_active
, n_active
);
3658 return isl_band_list_add(list
, band
);
3661 active
= isl_alloc_array(ctx
, int, schedule
->n
);
3662 if (schedule
->n
&& !active
)
3665 list
= isl_band_list_alloc(ctx
, n_band
);
3667 for (i
= 0; i
< n_active
; ++i
) {
3671 for (j
= 0; j
< schedule
->n
; ++j
) {
3672 active
[j
] = parent_active
[j
] &&
3673 schedule
->node
[j
].n_band
> band_nr
&&
3674 schedule
->node
[j
].band_id
[band_nr
] == i
;
3681 band
= construct_band(schedule
, parent
, band_nr
, active
, n
);
3683 list
= isl_band_list_add(list
, band
);
3685 for (i
= 0; i
< schedule
->n
; ++i
) {
3687 if (!parent_active
[i
])
3689 if (schedule
->node
[i
].n_band
> band_nr
)
3691 for (j
= 0; j
< schedule
->n
; ++j
)
3693 band
= construct_band(schedule
, parent
, band_nr
, active
, 1);
3694 list
= isl_band_list_add(list
, band
);
3699 list
= sort_band_list(list
, parent
);
3704 /* Construct a band forest representation of the schedule and
3705 * return the list of roots.
3707 static __isl_give isl_band_list
*construct_forest(
3708 __isl_keep isl_schedule
*schedule
)
3711 isl_ctx
*ctx
= isl_schedule_get_ctx(schedule
);
3712 isl_band_list
*forest
;
3715 active
= isl_alloc_array(ctx
, int, schedule
->n
);
3716 if (schedule
->n
&& !active
)
3719 for (i
= 0; i
< schedule
->n
; ++i
)
3722 forest
= construct_band_list(schedule
, NULL
, 0, active
, schedule
->n
);
3729 /* Return the roots of a band forest representation of the schedule.
3731 __isl_give isl_band_list
*isl_schedule_get_band_forest(
3732 __isl_keep isl_schedule
*schedule
)
3736 if (!schedule
->band_forest
)
3737 schedule
->band_forest
= construct_forest(schedule
);
3738 return isl_band_list_dup(schedule
->band_forest
);
3741 /* Call "fn" on each band in the schedule in depth-first post-order.
3743 int isl_schedule_foreach_band(__isl_keep isl_schedule
*sched
,
3744 int (*fn
)(__isl_keep isl_band
*band
, void *user
), void *user
)
3747 isl_band_list
*forest
;
3752 forest
= isl_schedule_get_band_forest(sched
);
3753 r
= isl_band_list_foreach_band(forest
, fn
, user
);
3754 isl_band_list_free(forest
);
3759 static __isl_give isl_printer
*print_band_list(__isl_take isl_printer
*p
,
3760 __isl_keep isl_band_list
*list
);
3762 static __isl_give isl_printer
*print_band(__isl_take isl_printer
*p
,
3763 __isl_keep isl_band
*band
)
3765 isl_band_list
*children
;
3767 p
= isl_printer_start_line(p
);
3768 p
= isl_printer_print_union_pw_multi_aff(p
, band
->pma
);
3769 p
= isl_printer_end_line(p
);
3771 if (!isl_band_has_children(band
))
3774 children
= isl_band_get_children(band
);
3776 p
= isl_printer_indent(p
, 4);
3777 p
= print_band_list(p
, children
);
3778 p
= isl_printer_indent(p
, -4);
3780 isl_band_list_free(children
);
3785 static __isl_give isl_printer
*print_band_list(__isl_take isl_printer
*p
,
3786 __isl_keep isl_band_list
*list
)
3790 n
= isl_band_list_n_band(list
);
3791 for (i
= 0; i
< n
; ++i
) {
3793 band
= isl_band_list_get_band(list
, i
);
3794 p
= print_band(p
, band
);
3795 isl_band_free(band
);
3801 __isl_give isl_printer
*isl_printer_print_schedule(__isl_take isl_printer
*p
,
3802 __isl_keep isl_schedule
*schedule
)
3804 isl_band_list
*forest
;
3806 forest
= isl_schedule_get_band_forest(schedule
);
3808 p
= print_band_list(p
, forest
);
3810 isl_band_list_free(forest
);
3815 void isl_schedule_dump(__isl_keep isl_schedule
*schedule
)
3817 isl_printer
*printer
;
3822 printer
= isl_printer_to_file(isl_schedule_get_ctx(schedule
), stderr
);
3823 printer
= isl_printer_print_schedule(printer
, schedule
);
3825 isl_printer_free(printer
);