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".
40 /* Internal information about a node that is used during the construction
42 * dim represents the space in which the domain lives
43 * sched is a matrix representation of the schedule being constructed
45 * sched_map is an isl_map representation of the same (partial) schedule
46 * sched_map may be NULL
47 * rank is the number of linearly independent rows in the linear part
49 * the columns of cmap represent a change of basis for the schedule
50 * coefficients; the first rank columns span the linear part of
52 * cinv is the inverse of cmap.
53 * start is the first variable in the LP problem in the sequences that
54 * represents the schedule coefficients of this node
55 * nvar is the dimension of the domain
56 * nparam is the number of parameters or 0 if we are not constructing
57 * a parametric schedule
59 * scc is the index of SCC (or WCC) this node belongs to
61 * band contains the band index for each of the rows of the schedule.
62 * band_id is used to differentiate between separate bands at the same
63 * level within the same parent band, i.e., bands that are separated
64 * by the parent band or bands that are independent of each other.
65 * zero contains a boolean for each of the rows of the schedule,
66 * indicating whether the corresponding scheduling dimension results
67 * in zero dependence distances within its band and with respect
68 * to the proximity edges.
70 struct isl_sched_node
{
88 static int node_has_dim(const void *entry
, const void *val
)
90 struct isl_sched_node
*node
= (struct isl_sched_node
*)entry
;
91 isl_space
*dim
= (isl_space
*)val
;
93 return isl_space_is_equal(node
->dim
, dim
);
96 /* An edge in the dependence graph. An edge may be used to
97 * ensure validity of the generated schedule, to minimize the dependence
100 * map is the dependence relation
101 * src is the source node
102 * dst is the sink node
103 * validity is set if the edge is used to ensure correctness
104 * proximity is set if the edge is used to minimize dependence distances
106 * For validity edges, start and end mark the sequence of inequality
107 * constraints in the LP problem that encode the validity constraint
108 * corresponding to this edge.
110 struct isl_sched_edge
{
113 struct isl_sched_node
*src
;
114 struct isl_sched_node
*dst
;
124 isl_edge_validity
= 0,
125 isl_edge_first
= isl_edge_validity
,
127 isl_edge_last
= isl_edge_proximity
130 /* Internal information about the dependence graph used during
131 * the construction of the schedule.
133 * intra_hmap is a cache, mapping dependence relations to their dual,
134 * for dependences from a node to itself
135 * inter_hmap is a cache, mapping dependence relations to their dual,
136 * for dependences between distinct nodes
138 * n is the number of nodes
139 * node is the list of nodes
140 * maxvar is the maximal number of variables over all nodes
141 * max_row is the allocated number of rows in the schedule
142 * n_row is the current (maximal) number of linearly independent
143 * rows in the node schedules
144 * n_total_row is the current number of rows in the node schedules
145 * n_band is the current number of completed bands
146 * band_start is the starting row in the node schedules of the current band
147 * root is set if this graph is the original dependence graph,
148 * without any splitting
150 * sorted contains a list of node indices sorted according to the
151 * SCC to which a node belongs
153 * n_edge is the number of edges
154 * edge is the list of edges
155 * max_edge contains the maximal number of edges of each type;
156 * in particular, it contains the number of edges in the inital graph.
157 * edge_table contains pointers into the edge array, hashed on the source
158 * and sink spaces; there is one such table for each type;
159 * a given edge may be referenced from more than one table
160 * if the corresponding relation appears in more than of the
161 * sets of dependences
163 * node_table contains pointers into the node array, hashed on the space
165 * region contains a list of variable sequences that should be non-trivial
167 * lp contains the (I)LP problem used to obtain new schedule rows
169 * src_scc and dst_scc are the source and sink SCCs of an edge with
170 * conflicting constraints
172 * scc represents the number of components
174 struct isl_sched_graph
{
175 isl_map_to_basic_set
*intra_hmap
;
176 isl_map_to_basic_set
*inter_hmap
;
178 struct isl_sched_node
*node
;
192 struct isl_sched_edge
*edge
;
194 int max_edge
[isl_edge_last
+ 1];
195 struct isl_hash_table
*edge_table
[isl_edge_last
+ 1];
197 struct isl_hash_table
*node_table
;
198 struct isl_region
*region
;
208 /* Initialize node_table based on the list of nodes.
210 static int graph_init_table(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
214 graph
->node_table
= isl_hash_table_alloc(ctx
, graph
->n
);
215 if (!graph
->node_table
)
218 for (i
= 0; i
< graph
->n
; ++i
) {
219 struct isl_hash_table_entry
*entry
;
222 hash
= isl_space_get_hash(graph
->node
[i
].dim
);
223 entry
= isl_hash_table_find(ctx
, graph
->node_table
, hash
,
225 graph
->node
[i
].dim
, 1);
228 entry
->data
= &graph
->node
[i
];
234 /* Return a pointer to the node that lives within the given space,
235 * or NULL if there is no such node.
237 static struct isl_sched_node
*graph_find_node(isl_ctx
*ctx
,
238 struct isl_sched_graph
*graph
, __isl_keep isl_space
*dim
)
240 struct isl_hash_table_entry
*entry
;
243 hash
= isl_space_get_hash(dim
);
244 entry
= isl_hash_table_find(ctx
, graph
->node_table
, hash
,
245 &node_has_dim
, dim
, 0);
247 return entry
? entry
->data
: NULL
;
250 static int edge_has_src_and_dst(const void *entry
, const void *val
)
252 const struct isl_sched_edge
*edge
= entry
;
253 const struct isl_sched_edge
*temp
= val
;
255 return edge
->src
== temp
->src
&& edge
->dst
== temp
->dst
;
258 /* Add the given edge to graph->edge_table[type].
260 static int graph_edge_table_add(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
261 enum isl_edge_type type
, struct isl_sched_edge
*edge
)
263 struct isl_hash_table_entry
*entry
;
266 hash
= isl_hash_init();
267 hash
= isl_hash_builtin(hash
, edge
->src
);
268 hash
= isl_hash_builtin(hash
, edge
->dst
);
269 entry
= isl_hash_table_find(ctx
, graph
->edge_table
[type
], hash
,
270 &edge_has_src_and_dst
, edge
, 1);
278 /* Allocate the edge_tables based on the maximal number of edges of
281 static int graph_init_edge_tables(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
285 for (i
= 0; i
<= isl_edge_last
; ++i
) {
286 graph
->edge_table
[i
] = isl_hash_table_alloc(ctx
,
288 if (!graph
->edge_table
[i
])
295 /* If graph->edge_table[type] contains an edge from the given source
296 * to the given destination, then return the hash table entry of this edge.
297 * Otherwise, return NULL.
299 static struct isl_hash_table_entry
*graph_find_edge_entry(
300 struct isl_sched_graph
*graph
,
301 enum isl_edge_type type
,
302 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
304 isl_ctx
*ctx
= isl_space_get_ctx(src
->dim
);
306 struct isl_sched_edge temp
= { .src
= src
, .dst
= dst
};
308 hash
= isl_hash_init();
309 hash
= isl_hash_builtin(hash
, temp
.src
);
310 hash
= isl_hash_builtin(hash
, temp
.dst
);
311 return isl_hash_table_find(ctx
, graph
->edge_table
[type
], hash
,
312 &edge_has_src_and_dst
, &temp
, 0);
316 /* If graph->edge_table[type] contains an edge from the given source
317 * to the given destination, then return this edge.
318 * Otherwise, return NULL.
320 static struct isl_sched_edge
*graph_find_edge(struct isl_sched_graph
*graph
,
321 enum isl_edge_type type
,
322 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
324 struct isl_hash_table_entry
*entry
;
326 entry
= graph_find_edge_entry(graph
, type
, src
, dst
);
333 /* Check whether the dependence graph has an edge of the given type
334 * between the given two nodes.
336 static int graph_has_edge(struct isl_sched_graph
*graph
,
337 enum isl_edge_type type
,
338 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
340 struct isl_sched_edge
*edge
;
343 edge
= graph_find_edge(graph
, type
, src
, dst
);
347 empty
= isl_map_plain_is_empty(edge
->map
);
354 /* If there is an edge from the given source to the given destination
355 * of any type then return this edge.
356 * Otherwise, return NULL.
358 static struct isl_sched_edge
*graph_find_any_edge(struct isl_sched_graph
*graph
,
359 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
361 enum isl_edge_type i
;
362 struct isl_sched_edge
*edge
;
364 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
365 edge
= graph_find_edge(graph
, i
, src
, dst
);
373 /* Remove the given edge from all the edge_tables that refer to it.
375 static void graph_remove_edge(struct isl_sched_graph
*graph
,
376 struct isl_sched_edge
*edge
)
378 isl_ctx
*ctx
= isl_map_get_ctx(edge
->map
);
379 enum isl_edge_type i
;
381 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
382 struct isl_hash_table_entry
*entry
;
384 entry
= graph_find_edge_entry(graph
, i
, edge
->src
, edge
->dst
);
387 if (entry
->data
!= edge
)
389 isl_hash_table_remove(ctx
, graph
->edge_table
[i
], entry
);
393 /* Check whether the dependence graph has any edge
394 * between the given two nodes.
396 static int graph_has_any_edge(struct isl_sched_graph
*graph
,
397 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
399 enum isl_edge_type i
;
402 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
403 r
= graph_has_edge(graph
, i
, src
, dst
);
411 /* Check whether the dependence graph has a validity edge
412 * between the given two nodes.
414 static int graph_has_validity_edge(struct isl_sched_graph
*graph
,
415 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
417 return graph_has_edge(graph
, isl_edge_validity
, src
, dst
);
420 static int graph_alloc(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
421 int n_node
, int n_edge
)
426 graph
->n_edge
= n_edge
;
427 graph
->node
= isl_calloc_array(ctx
, struct isl_sched_node
, graph
->n
);
428 graph
->sorted
= isl_calloc_array(ctx
, int, graph
->n
);
429 graph
->region
= isl_alloc_array(ctx
, struct isl_region
, graph
->n
);
430 graph
->edge
= isl_calloc_array(ctx
,
431 struct isl_sched_edge
, graph
->n_edge
);
433 graph
->intra_hmap
= isl_map_to_basic_set_alloc(ctx
, 2 * n_edge
);
434 graph
->inter_hmap
= isl_map_to_basic_set_alloc(ctx
, 2 * n_edge
);
436 if (!graph
->node
|| !graph
->region
|| (graph
->n_edge
&& !graph
->edge
) ||
440 for(i
= 0; i
< graph
->n
; ++i
)
441 graph
->sorted
[i
] = i
;
446 static void graph_free(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
450 isl_map_to_basic_set_free(graph
->intra_hmap
);
451 isl_map_to_basic_set_free(graph
->inter_hmap
);
453 for (i
= 0; i
< graph
->n
; ++i
) {
454 isl_space_free(graph
->node
[i
].dim
);
455 isl_mat_free(graph
->node
[i
].sched
);
456 isl_map_free(graph
->node
[i
].sched_map
);
457 isl_mat_free(graph
->node
[i
].cmap
);
458 isl_mat_free(graph
->node
[i
].cinv
);
460 free(graph
->node
[i
].band
);
461 free(graph
->node
[i
].band_id
);
462 free(graph
->node
[i
].zero
);
467 for (i
= 0; i
< graph
->n_edge
; ++i
)
468 isl_map_free(graph
->edge
[i
].map
);
471 for (i
= 0; i
<= isl_edge_last
; ++i
)
472 isl_hash_table_free(ctx
, graph
->edge_table
[i
]);
473 isl_hash_table_free(ctx
, graph
->node_table
);
474 isl_basic_set_free(graph
->lp
);
477 /* For each "set" on which this function is called, increment
478 * graph->n by one and update graph->maxvar.
480 static int init_n_maxvar(__isl_take isl_set
*set
, void *user
)
482 struct isl_sched_graph
*graph
= user
;
483 int nvar
= isl_set_dim(set
, isl_dim_set
);
486 if (nvar
> graph
->maxvar
)
487 graph
->maxvar
= nvar
;
494 /* Compute the number of rows that should be allocated for the schedule.
495 * The graph can be split at most "n - 1" times, there can be at most
496 * two rows for each dimension in the iteration domains (in particular,
497 * we usually have one row, but it may be split by split_scaled),
498 * and there can be one extra row for ordering the statements.
499 * Note that if we have actually split "n - 1" times, then no ordering
500 * is needed, so in principle we could use "graph->n + 2 * graph->maxvar - 1".
502 static int compute_max_row(struct isl_sched_graph
*graph
,
503 __isl_keep isl_union_set
*domain
)
507 if (isl_union_set_foreach_set(domain
, &init_n_maxvar
, graph
) < 0)
509 graph
->max_row
= graph
->n
+ 2 * graph
->maxvar
;
514 /* Add a new node to the graph representing the given set.
516 static int extract_node(__isl_take isl_set
*set
, void *user
)
522 struct isl_sched_graph
*graph
= user
;
523 int *band
, *band_id
, *zero
;
525 ctx
= isl_set_get_ctx(set
);
526 dim
= isl_set_get_space(set
);
528 nvar
= isl_space_dim(dim
, isl_dim_set
);
529 nparam
= isl_space_dim(dim
, isl_dim_param
);
530 if (!ctx
->opt
->schedule_parametric
)
532 sched
= isl_mat_alloc(ctx
, 0, 1 + nparam
+ nvar
);
533 graph
->node
[graph
->n
].dim
= dim
;
534 graph
->node
[graph
->n
].nvar
= nvar
;
535 graph
->node
[graph
->n
].nparam
= nparam
;
536 graph
->node
[graph
->n
].sched
= sched
;
537 graph
->node
[graph
->n
].sched_map
= NULL
;
538 band
= isl_alloc_array(ctx
, int, graph
->max_row
);
539 graph
->node
[graph
->n
].band
= band
;
540 band_id
= isl_calloc_array(ctx
, int, graph
->max_row
);
541 graph
->node
[graph
->n
].band_id
= band_id
;
542 zero
= isl_calloc_array(ctx
, int, graph
->max_row
);
543 graph
->node
[graph
->n
].zero
= zero
;
546 if (!sched
|| (graph
->max_row
&& (!band
|| !band_id
|| !zero
)))
552 struct isl_extract_edge_data
{
553 enum isl_edge_type type
;
554 struct isl_sched_graph
*graph
;
557 /* Add a new edge to the graph based on the given map
558 * and add it to data->graph->edge_table[data->type].
559 * If a dependence relation of a given type happens to be identical
560 * to one of the dependence relations of a type that was added before,
561 * then we don't create a new edge, but instead mark the original edge
562 * as also representing a dependence of the current type.
564 static int extract_edge(__isl_take isl_map
*map
, void *user
)
566 isl_ctx
*ctx
= isl_map_get_ctx(map
);
567 struct isl_extract_edge_data
*data
= user
;
568 struct isl_sched_graph
*graph
= data
->graph
;
569 struct isl_sched_node
*src
, *dst
;
571 struct isl_sched_edge
*edge
;
574 dim
= isl_space_domain(isl_map_get_space(map
));
575 src
= graph_find_node(ctx
, graph
, dim
);
577 dim
= isl_space_range(isl_map_get_space(map
));
578 dst
= graph_find_node(ctx
, graph
, dim
);
586 graph
->edge
[graph
->n_edge
].src
= src
;
587 graph
->edge
[graph
->n_edge
].dst
= dst
;
588 graph
->edge
[graph
->n_edge
].map
= map
;
589 if (data
->type
== isl_edge_validity
) {
590 graph
->edge
[graph
->n_edge
].validity
= 1;
591 graph
->edge
[graph
->n_edge
].proximity
= 0;
593 if (data
->type
== isl_edge_proximity
) {
594 graph
->edge
[graph
->n_edge
].validity
= 0;
595 graph
->edge
[graph
->n_edge
].proximity
= 1;
599 edge
= graph_find_any_edge(graph
, src
, dst
);
601 return graph_edge_table_add(ctx
, graph
, data
->type
,
602 &graph
->edge
[graph
->n_edge
- 1]);
603 is_equal
= isl_map_plain_is_equal(map
, edge
->map
);
607 return graph_edge_table_add(ctx
, graph
, data
->type
,
608 &graph
->edge
[graph
->n_edge
- 1]);
611 edge
->validity
|= graph
->edge
[graph
->n_edge
].validity
;
612 edge
->proximity
|= graph
->edge
[graph
->n_edge
].proximity
;
615 return graph_edge_table_add(ctx
, graph
, data
->type
, edge
);
618 /* Check whether there is any dependence from node[j] to node[i]
619 * or from node[i] to node[j].
621 static int node_follows_weak(int i
, int j
, void *user
)
624 struct isl_sched_graph
*graph
= user
;
626 f
= graph_has_any_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
629 return graph_has_any_edge(graph
, &graph
->node
[i
], &graph
->node
[j
]);
632 /* Check whether there is a validity dependence from node[j] to node[i],
633 * forcing node[i] to follow node[j].
635 static int node_follows_strong(int i
, int j
, void *user
)
637 struct isl_sched_graph
*graph
= user
;
639 return graph_has_validity_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
642 /* Use Tarjan's algorithm for computing the strongly connected components
643 * in the dependence graph (only validity edges).
644 * If weak is set, we consider the graph to be undirected and
645 * we effectively compute the (weakly) connected components.
646 * Additionally, we also consider other edges when weak is set.
648 static int detect_ccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
, int weak
)
651 struct isl_tarjan_graph
*g
= NULL
;
653 g
= isl_tarjan_graph_init(ctx
, graph
->n
,
654 weak
? &node_follows_weak
: &node_follows_strong
, graph
);
662 while (g
->order
[i
] != -1) {
663 graph
->node
[g
->order
[i
]].scc
= graph
->scc
;
671 isl_tarjan_graph_free(g
);
676 /* Apply Tarjan's algorithm to detect the strongly connected components
677 * in the dependence graph.
679 static int detect_sccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
681 return detect_ccs(ctx
, graph
, 0);
684 /* Apply Tarjan's algorithm to detect the (weakly) connected components
685 * in the dependence graph.
687 static int detect_wccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
689 return detect_ccs(ctx
, graph
, 1);
692 static int cmp_scc(const void *a
, const void *b
, void *data
)
694 struct isl_sched_graph
*graph
= data
;
698 return graph
->node
[*i1
].scc
- graph
->node
[*i2
].scc
;
701 /* Sort the elements of graph->sorted according to the corresponding SCCs.
703 static int sort_sccs(struct isl_sched_graph
*graph
)
705 return isl_sort(graph
->sorted
, graph
->n
, sizeof(int), &cmp_scc
, graph
);
708 /* Given a dependence relation R from a node to itself,
709 * construct the set of coefficients of valid constraints for elements
710 * in that dependence relation.
711 * In particular, the result contains tuples of coefficients
712 * c_0, c_n, c_x such that
714 * c_0 + c_n n + c_x y - c_x x >= 0 for each (x,y) in R
718 * c_0 + c_n n + c_x d >= 0 for each d in delta R = { y - x | (x,y) in R }
720 * We choose here to compute the dual of delta R.
721 * Alternatively, we could have computed the dual of R, resulting
722 * in a set of tuples c_0, c_n, c_x, c_y, and then
723 * plugged in (c_0, c_n, c_x, -c_x).
725 static __isl_give isl_basic_set
*intra_coefficients(
726 struct isl_sched_graph
*graph
, __isl_take isl_map
*map
)
731 if (isl_map_to_basic_set_has(graph
->intra_hmap
, map
))
732 return isl_map_to_basic_set_get(graph
->intra_hmap
, map
);
734 delta
= isl_set_remove_divs(isl_map_deltas(isl_map_copy(map
)));
735 coef
= isl_set_coefficients(delta
);
736 graph
->intra_hmap
= isl_map_to_basic_set_set(graph
->intra_hmap
, map
,
737 isl_basic_set_copy(coef
));
742 /* Given a dependence relation R, * construct the set of coefficients
743 * of valid constraints for elements in that dependence relation.
744 * In particular, the result contains tuples of coefficients
745 * c_0, c_n, c_x, c_y such that
747 * c_0 + c_n n + c_x x + c_y y >= 0 for each (x,y) in R
750 static __isl_give isl_basic_set
*inter_coefficients(
751 struct isl_sched_graph
*graph
, __isl_take isl_map
*map
)
756 if (isl_map_to_basic_set_has(graph
->inter_hmap
, map
))
757 return isl_map_to_basic_set_get(graph
->inter_hmap
, map
);
759 set
= isl_map_wrap(isl_map_remove_divs(isl_map_copy(map
)));
760 coef
= isl_set_coefficients(set
);
761 graph
->inter_hmap
= isl_map_to_basic_set_set(graph
->inter_hmap
, map
,
762 isl_basic_set_copy(coef
));
767 /* Add constraints to graph->lp that force validity for the given
768 * dependence from a node i to itself.
769 * That is, add constraints that enforce
771 * (c_i_0 + c_i_n n + c_i_x y) - (c_i_0 + c_i_n n + c_i_x x)
772 * = c_i_x (y - x) >= 0
774 * for each (x,y) in R.
775 * We obtain general constraints on coefficients (c_0, c_n, c_x)
776 * of valid constraints for (y - x) and then plug in (0, 0, c_i_x^+ - c_i_x^-),
777 * where c_i_x = c_i_x^+ - c_i_x^-, with c_i_x^+ and c_i_x^- non-negative.
778 * In graph->lp, the c_i_x^- appear before their c_i_x^+ counterpart.
780 * Actually, we do not construct constraints for the c_i_x themselves,
781 * but for the coefficients of c_i_x written as a linear combination
782 * of the columns in node->cmap.
784 static int add_intra_validity_constraints(struct isl_sched_graph
*graph
,
785 struct isl_sched_edge
*edge
)
788 isl_map
*map
= isl_map_copy(edge
->map
);
789 isl_ctx
*ctx
= isl_map_get_ctx(map
);
791 isl_dim_map
*dim_map
;
793 struct isl_sched_node
*node
= edge
->src
;
795 coef
= intra_coefficients(graph
, map
);
797 dim
= isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef
)));
799 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
800 isl_space_dim(dim
, isl_dim_set
), isl_mat_copy(node
->cmap
));
804 total
= isl_basic_set_total_dim(graph
->lp
);
805 dim_map
= isl_dim_map_alloc(ctx
, total
);
806 isl_dim_map_range(dim_map
, node
->start
+ 2 * node
->nparam
+ 1, 2,
807 isl_space_dim(dim
, isl_dim_set
), 1,
809 isl_dim_map_range(dim_map
, node
->start
+ 2 * node
->nparam
+ 2, 2,
810 isl_space_dim(dim
, isl_dim_set
), 1,
812 graph
->lp
= isl_basic_set_extend_constraints(graph
->lp
,
813 coef
->n_eq
, coef
->n_ineq
);
814 graph
->lp
= isl_basic_set_add_constraints_dim_map(graph
->lp
,
824 /* Add constraints to graph->lp that force validity for the given
825 * dependence from node i to node j.
826 * That is, add constraints that enforce
828 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) >= 0
830 * for each (x,y) in R.
831 * We obtain general constraints on coefficients (c_0, c_n, c_x, c_y)
832 * of valid constraints for R and then plug in
833 * (c_j_0 - c_i_0, c_j_n^+ - c_j_n^- - (c_i_n^+ - c_i_n^-),
834 * c_j_x^+ - c_j_x^- - (c_i_x^+ - c_i_x^-)),
835 * where c_* = c_*^+ - c_*^-, with c_*^+ and c_*^- non-negative.
836 * In graph->lp, the c_*^- appear before their c_*^+ counterpart.
838 * Actually, we do not construct constraints for the c_*_x themselves,
839 * but for the coefficients of c_*_x written as a linear combination
840 * of the columns in node->cmap.
842 static int add_inter_validity_constraints(struct isl_sched_graph
*graph
,
843 struct isl_sched_edge
*edge
)
846 isl_map
*map
= isl_map_copy(edge
->map
);
847 isl_ctx
*ctx
= isl_map_get_ctx(map
);
849 isl_dim_map
*dim_map
;
851 struct isl_sched_node
*src
= edge
->src
;
852 struct isl_sched_node
*dst
= edge
->dst
;
854 coef
= inter_coefficients(graph
, map
);
856 dim
= isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef
)));
858 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
859 isl_space_dim(dim
, isl_dim_set
), isl_mat_copy(src
->cmap
));
860 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
861 isl_space_dim(dim
, isl_dim_set
) + src
->nvar
,
862 isl_mat_copy(dst
->cmap
));
866 total
= isl_basic_set_total_dim(graph
->lp
);
867 dim_map
= isl_dim_map_alloc(ctx
, total
);
869 isl_dim_map_range(dim_map
, dst
->start
, 0, 0, 0, 1, 1);
870 isl_dim_map_range(dim_map
, dst
->start
+ 1, 2, 1, 1, dst
->nparam
, -1);
871 isl_dim_map_range(dim_map
, dst
->start
+ 2, 2, 1, 1, dst
->nparam
, 1);
872 isl_dim_map_range(dim_map
, dst
->start
+ 2 * dst
->nparam
+ 1, 2,
873 isl_space_dim(dim
, isl_dim_set
) + src
->nvar
, 1,
875 isl_dim_map_range(dim_map
, dst
->start
+ 2 * dst
->nparam
+ 2, 2,
876 isl_space_dim(dim
, isl_dim_set
) + src
->nvar
, 1,
879 isl_dim_map_range(dim_map
, src
->start
, 0, 0, 0, 1, -1);
880 isl_dim_map_range(dim_map
, src
->start
+ 1, 2, 1, 1, src
->nparam
, 1);
881 isl_dim_map_range(dim_map
, src
->start
+ 2, 2, 1, 1, src
->nparam
, -1);
882 isl_dim_map_range(dim_map
, src
->start
+ 2 * src
->nparam
+ 1, 2,
883 isl_space_dim(dim
, isl_dim_set
), 1,
885 isl_dim_map_range(dim_map
, src
->start
+ 2 * src
->nparam
+ 2, 2,
886 isl_space_dim(dim
, isl_dim_set
), 1,
889 edge
->start
= graph
->lp
->n_ineq
;
890 graph
->lp
= isl_basic_set_extend_constraints(graph
->lp
,
891 coef
->n_eq
, coef
->n_ineq
);
892 graph
->lp
= isl_basic_set_add_constraints_dim_map(graph
->lp
,
897 edge
->end
= graph
->lp
->n_ineq
;
905 /* Add constraints to graph->lp that bound the dependence distance for the given
906 * dependence from a node i to itself.
907 * If s = 1, we add the constraint
909 * c_i_x (y - x) <= m_0 + m_n n
913 * -c_i_x (y - x) + m_0 + m_n n >= 0
915 * for each (x,y) in R.
916 * If s = -1, we add the constraint
918 * -c_i_x (y - x) <= m_0 + m_n n
922 * c_i_x (y - x) + m_0 + m_n n >= 0
924 * for each (x,y) in R.
925 * We obtain general constraints on coefficients (c_0, c_n, c_x)
926 * of valid constraints for (y - x) and then plug in (m_0, m_n, -s * c_i_x),
927 * with each coefficient (except m_0) represented as a pair of non-negative
930 * Actually, we do not construct constraints for the c_i_x themselves,
931 * but for the coefficients of c_i_x written as a linear combination
932 * of the columns in node->cmap.
934 static int add_intra_proximity_constraints(struct isl_sched_graph
*graph
,
935 struct isl_sched_edge
*edge
, int s
)
939 isl_map
*map
= isl_map_copy(edge
->map
);
940 isl_ctx
*ctx
= isl_map_get_ctx(map
);
942 isl_dim_map
*dim_map
;
944 struct isl_sched_node
*node
= edge
->src
;
946 coef
= intra_coefficients(graph
, map
);
948 dim
= isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef
)));
950 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
951 isl_space_dim(dim
, isl_dim_set
), isl_mat_copy(node
->cmap
));
955 nparam
= isl_space_dim(node
->dim
, isl_dim_param
);
956 total
= isl_basic_set_total_dim(graph
->lp
);
957 dim_map
= isl_dim_map_alloc(ctx
, total
);
958 isl_dim_map_range(dim_map
, 1, 0, 0, 0, 1, 1);
959 isl_dim_map_range(dim_map
, 4, 2, 1, 1, nparam
, -1);
960 isl_dim_map_range(dim_map
, 5, 2, 1, 1, nparam
, 1);
961 isl_dim_map_range(dim_map
, node
->start
+ 2 * node
->nparam
+ 1, 2,
962 isl_space_dim(dim
, isl_dim_set
), 1,
964 isl_dim_map_range(dim_map
, node
->start
+ 2 * node
->nparam
+ 2, 2,
965 isl_space_dim(dim
, isl_dim_set
), 1,
967 graph
->lp
= isl_basic_set_extend_constraints(graph
->lp
,
968 coef
->n_eq
, coef
->n_ineq
);
969 graph
->lp
= isl_basic_set_add_constraints_dim_map(graph
->lp
,
979 /* Add constraints to graph->lp that bound the dependence distance for the given
980 * dependence from node i to node j.
981 * If s = 1, we add the constraint
983 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x)
988 * -(c_j_0 + c_j_n n + c_j_x y) + (c_i_0 + c_i_n n + c_i_x x) +
991 * for each (x,y) in R.
992 * If s = -1, we add the constraint
994 * -((c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x))
999 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) +
1002 * for each (x,y) in R.
1003 * We obtain general constraints on coefficients (c_0, c_n, c_x, c_y)
1004 * of valid constraints for R and then plug in
1005 * (m_0 - s*c_j_0 + s*c_i_0, m_n - s*c_j_n + s*c_i_n,
1007 * with each coefficient (except m_0, c_j_0 and c_i_0)
1008 * represented as a pair of non-negative coefficients.
1010 * Actually, we do not construct constraints for the c_*_x themselves,
1011 * but for the coefficients of c_*_x written as a linear combination
1012 * of the columns in node->cmap.
1014 static int add_inter_proximity_constraints(struct isl_sched_graph
*graph
,
1015 struct isl_sched_edge
*edge
, int s
)
1019 isl_map
*map
= isl_map_copy(edge
->map
);
1020 isl_ctx
*ctx
= isl_map_get_ctx(map
);
1022 isl_dim_map
*dim_map
;
1023 isl_basic_set
*coef
;
1024 struct isl_sched_node
*src
= edge
->src
;
1025 struct isl_sched_node
*dst
= edge
->dst
;
1027 coef
= inter_coefficients(graph
, map
);
1029 dim
= isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef
)));
1031 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
1032 isl_space_dim(dim
, isl_dim_set
), isl_mat_copy(src
->cmap
));
1033 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
1034 isl_space_dim(dim
, isl_dim_set
) + src
->nvar
,
1035 isl_mat_copy(dst
->cmap
));
1039 nparam
= isl_space_dim(src
->dim
, isl_dim_param
);
1040 total
= isl_basic_set_total_dim(graph
->lp
);
1041 dim_map
= isl_dim_map_alloc(ctx
, total
);
1043 isl_dim_map_range(dim_map
, 1, 0, 0, 0, 1, 1);
1044 isl_dim_map_range(dim_map
, 4, 2, 1, 1, nparam
, -1);
1045 isl_dim_map_range(dim_map
, 5, 2, 1, 1, nparam
, 1);
1047 isl_dim_map_range(dim_map
, dst
->start
, 0, 0, 0, 1, -s
);
1048 isl_dim_map_range(dim_map
, dst
->start
+ 1, 2, 1, 1, dst
->nparam
, s
);
1049 isl_dim_map_range(dim_map
, dst
->start
+ 2, 2, 1, 1, dst
->nparam
, -s
);
1050 isl_dim_map_range(dim_map
, dst
->start
+ 2 * dst
->nparam
+ 1, 2,
1051 isl_space_dim(dim
, isl_dim_set
) + src
->nvar
, 1,
1053 isl_dim_map_range(dim_map
, dst
->start
+ 2 * dst
->nparam
+ 2, 2,
1054 isl_space_dim(dim
, isl_dim_set
) + src
->nvar
, 1,
1057 isl_dim_map_range(dim_map
, src
->start
, 0, 0, 0, 1, s
);
1058 isl_dim_map_range(dim_map
, src
->start
+ 1, 2, 1, 1, src
->nparam
, -s
);
1059 isl_dim_map_range(dim_map
, src
->start
+ 2, 2, 1, 1, src
->nparam
, s
);
1060 isl_dim_map_range(dim_map
, src
->start
+ 2 * src
->nparam
+ 1, 2,
1061 isl_space_dim(dim
, isl_dim_set
), 1,
1063 isl_dim_map_range(dim_map
, src
->start
+ 2 * src
->nparam
+ 2, 2,
1064 isl_space_dim(dim
, isl_dim_set
), 1,
1067 graph
->lp
= isl_basic_set_extend_constraints(graph
->lp
,
1068 coef
->n_eq
, coef
->n_ineq
);
1069 graph
->lp
= isl_basic_set_add_constraints_dim_map(graph
->lp
,
1071 isl_space_free(dim
);
1075 isl_space_free(dim
);
1079 static int add_all_validity_constraints(struct isl_sched_graph
*graph
)
1083 for (i
= 0; i
< graph
->n_edge
; ++i
) {
1084 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
1085 if (!edge
->validity
)
1087 if (edge
->src
!= edge
->dst
)
1089 if (add_intra_validity_constraints(graph
, edge
) < 0)
1093 for (i
= 0; i
< graph
->n_edge
; ++i
) {
1094 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
1095 if (!edge
->validity
)
1097 if (edge
->src
== edge
->dst
)
1099 if (add_inter_validity_constraints(graph
, edge
) < 0)
1106 /* Add constraints to graph->lp that bound the dependence distance
1107 * for all dependence relations.
1108 * If a given proximity dependence is identical to a validity
1109 * dependence, then the dependence distance is already bounded
1110 * from below (by zero), so we only need to bound the distance
1112 * Otherwise, we need to bound the distance both from above and from below.
1114 static int add_all_proximity_constraints(struct isl_sched_graph
*graph
)
1118 for (i
= 0; i
< graph
->n_edge
; ++i
) {
1119 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
1120 if (!edge
->proximity
)
1122 if (edge
->src
== edge
->dst
&&
1123 add_intra_proximity_constraints(graph
, edge
, 1) < 0)
1125 if (edge
->src
!= edge
->dst
&&
1126 add_inter_proximity_constraints(graph
, edge
, 1) < 0)
1130 if (edge
->src
== edge
->dst
&&
1131 add_intra_proximity_constraints(graph
, edge
, -1) < 0)
1133 if (edge
->src
!= edge
->dst
&&
1134 add_inter_proximity_constraints(graph
, edge
, -1) < 0)
1141 /* Compute a basis for the rows in the linear part of the schedule
1142 * and extend this basis to a full basis. The remaining rows
1143 * can then be used to force linear independence from the rows
1146 * In particular, given the schedule rows S, we compute
1151 * with H the Hermite normal form of S. That is, all but the
1152 * first rank columns of H are zero and so each row in S is
1153 * a linear combination of the first rank rows of Q.
1154 * The matrix Q is then transposed because we will write the
1155 * coefficients of the next schedule row as a column vector s
1156 * and express this s as a linear combination s = Q c of the
1158 * Similarly, the matrix U is transposed such that we can
1159 * compute the coefficients c = U s from a schedule row s.
1161 static int node_update_cmap(struct isl_sched_node
*node
)
1164 int n_row
= isl_mat_rows(node
->sched
);
1166 H
= isl_mat_sub_alloc(node
->sched
, 0, n_row
,
1167 1 + node
->nparam
, node
->nvar
);
1169 H
= isl_mat_left_hermite(H
, 0, &U
, &Q
);
1170 isl_mat_free(node
->cmap
);
1171 isl_mat_free(node
->cinv
);
1172 node
->cmap
= isl_mat_transpose(Q
);
1173 node
->cinv
= isl_mat_transpose(U
);
1174 node
->rank
= isl_mat_initial_non_zero_cols(H
);
1177 if (!node
->cmap
|| !node
->cinv
|| node
->rank
< 0)
1182 /* Count the number of equality and inequality constraints
1183 * that will be added for the given map.
1184 * If carry is set, then we are counting the number of (validity)
1185 * constraints that will be added in setup_carry_lp and we count
1186 * each edge exactly once. Otherwise, we count as follows
1187 * validity -> 1 (>= 0)
1188 * validity+proximity -> 2 (>= 0 and upper bound)
1189 * proximity -> 2 (lower and upper bound)
1191 static int count_map_constraints(struct isl_sched_graph
*graph
,
1192 struct isl_sched_edge
*edge
, __isl_take isl_map
*map
,
1193 int *n_eq
, int *n_ineq
, int carry
)
1195 isl_basic_set
*coef
;
1196 int f
= carry
? 1 : edge
->proximity
? 2 : 1;
1198 if (carry
&& !edge
->validity
) {
1203 if (edge
->src
== edge
->dst
)
1204 coef
= intra_coefficients(graph
, map
);
1206 coef
= inter_coefficients(graph
, map
);
1209 *n_eq
+= f
* coef
->n_eq
;
1210 *n_ineq
+= f
* coef
->n_ineq
;
1211 isl_basic_set_free(coef
);
1216 /* Count the number of equality and inequality constraints
1217 * that will be added to the main lp problem.
1218 * We count as follows
1219 * validity -> 1 (>= 0)
1220 * validity+proximity -> 2 (>= 0 and upper bound)
1221 * proximity -> 2 (lower and upper bound)
1223 static int count_constraints(struct isl_sched_graph
*graph
,
1224 int *n_eq
, int *n_ineq
)
1228 *n_eq
= *n_ineq
= 0;
1229 for (i
= 0; i
< graph
->n_edge
; ++i
) {
1230 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
1231 isl_map
*map
= isl_map_copy(edge
->map
);
1233 if (count_map_constraints(graph
, edge
, map
,
1234 n_eq
, n_ineq
, 0) < 0)
1241 /* Count the number of constraints that will be added by
1242 * add_bound_coefficient_constraints and increment *n_eq and *n_ineq
1245 * In practice, add_bound_coefficient_constraints only adds inequalities.
1247 static int count_bound_coefficient_constraints(isl_ctx
*ctx
,
1248 struct isl_sched_graph
*graph
, int *n_eq
, int *n_ineq
)
1252 if (ctx
->opt
->schedule_max_coefficient
== -1)
1255 for (i
= 0; i
< graph
->n
; ++i
)
1256 *n_ineq
+= 2 * graph
->node
[i
].nparam
+ 2 * graph
->node
[i
].nvar
;
1261 /* Add constraints that bound the values of the variable and parameter
1262 * coefficients of the schedule.
1264 * The maximal value of the coefficients is defined by the option
1265 * 'schedule_max_coefficient'.
1267 static int add_bound_coefficient_constraints(isl_ctx
*ctx
,
1268 struct isl_sched_graph
*graph
)
1271 int max_coefficient
;
1274 max_coefficient
= ctx
->opt
->schedule_max_coefficient
;
1276 if (max_coefficient
== -1)
1279 total
= isl_basic_set_total_dim(graph
->lp
);
1281 for (i
= 0; i
< graph
->n
; ++i
) {
1282 struct isl_sched_node
*node
= &graph
->node
[i
];
1283 for (j
= 0; j
< 2 * node
->nparam
+ 2 * node
->nvar
; ++j
) {
1285 k
= isl_basic_set_alloc_inequality(graph
->lp
);
1288 dim
= 1 + node
->start
+ 1 + j
;
1289 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
1290 isl_int_set_si(graph
->lp
->ineq
[k
][dim
], -1);
1291 isl_int_set_si(graph
->lp
->ineq
[k
][0], max_coefficient
);
1298 /* Construct an ILP problem for finding schedule coefficients
1299 * that result in non-negative, but small dependence distances
1300 * over all dependences.
1301 * In particular, the dependence distances over proximity edges
1302 * are bounded by m_0 + m_n n and we compute schedule coefficients
1303 * with small values (preferably zero) of m_n and m_0.
1305 * All variables of the ILP are non-negative. The actual coefficients
1306 * may be negative, so each coefficient is represented as the difference
1307 * of two non-negative variables. The negative part always appears
1308 * immediately before the positive part.
1309 * Other than that, the variables have the following order
1311 * - sum of positive and negative parts of m_n coefficients
1313 * - sum of positive and negative parts of all c_n coefficients
1314 * (unconstrained when computing non-parametric schedules)
1315 * - sum of positive and negative parts of all c_x coefficients
1316 * - positive and negative parts of m_n coefficients
1319 * - positive and negative parts of c_i_n (if parametric)
1320 * - positive and negative parts of c_i_x
1322 * The c_i_x are not represented directly, but through the columns of
1323 * node->cmap. That is, the computed values are for variable t_i_x
1324 * such that c_i_x = Q t_i_x with Q equal to node->cmap.
1326 * The constraints are those from the edges plus two or three equalities
1327 * to express the sums.
1329 * If force_zero is set, then we add equalities to ensure that
1330 * the sum of the m_n coefficients and m_0 are both zero.
1332 static int setup_lp(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
1343 int max_constant_term
;
1345 max_constant_term
= ctx
->opt
->schedule_max_constant_term
;
1347 parametric
= ctx
->opt
->schedule_parametric
;
1348 nparam
= isl_space_dim(graph
->node
[0].dim
, isl_dim_param
);
1350 total
= param_pos
+ 2 * nparam
;
1351 for (i
= 0; i
< graph
->n
; ++i
) {
1352 struct isl_sched_node
*node
= &graph
->node
[graph
->sorted
[i
]];
1353 if (node_update_cmap(node
) < 0)
1355 node
->start
= total
;
1356 total
+= 1 + 2 * (node
->nparam
+ node
->nvar
);
1359 if (count_constraints(graph
, &n_eq
, &n_ineq
) < 0)
1361 if (count_bound_coefficient_constraints(ctx
, graph
, &n_eq
, &n_ineq
) < 0)
1364 dim
= isl_space_set_alloc(ctx
, 0, total
);
1365 isl_basic_set_free(graph
->lp
);
1366 n_eq
+= 2 + parametric
+ force_zero
;
1367 if (max_constant_term
!= -1)
1370 graph
->lp
= isl_basic_set_alloc_space(dim
, 0, n_eq
, n_ineq
);
1372 k
= isl_basic_set_alloc_equality(graph
->lp
);
1375 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
1377 isl_int_set_si(graph
->lp
->eq
[k
][1], -1);
1378 for (i
= 0; i
< 2 * nparam
; ++i
)
1379 isl_int_set_si(graph
->lp
->eq
[k
][1 + param_pos
+ i
], 1);
1382 k
= isl_basic_set_alloc_equality(graph
->lp
);
1385 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
1386 isl_int_set_si(graph
->lp
->eq
[k
][2], -1);
1390 k
= isl_basic_set_alloc_equality(graph
->lp
);
1393 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
1394 isl_int_set_si(graph
->lp
->eq
[k
][3], -1);
1395 for (i
= 0; i
< graph
->n
; ++i
) {
1396 int pos
= 1 + graph
->node
[i
].start
+ 1;
1398 for (j
= 0; j
< 2 * graph
->node
[i
].nparam
; ++j
)
1399 isl_int_set_si(graph
->lp
->eq
[k
][pos
+ j
], 1);
1403 k
= isl_basic_set_alloc_equality(graph
->lp
);
1406 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
1407 isl_int_set_si(graph
->lp
->eq
[k
][4], -1);
1408 for (i
= 0; i
< graph
->n
; ++i
) {
1409 struct isl_sched_node
*node
= &graph
->node
[i
];
1410 int pos
= 1 + node
->start
+ 1 + 2 * node
->nparam
;
1412 for (j
= 0; j
< 2 * node
->nvar
; ++j
)
1413 isl_int_set_si(graph
->lp
->eq
[k
][pos
+ j
], 1);
1416 if (max_constant_term
!= -1)
1417 for (i
= 0; i
< graph
->n
; ++i
) {
1418 struct isl_sched_node
*node
= &graph
->node
[i
];
1419 k
= isl_basic_set_alloc_inequality(graph
->lp
);
1422 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
1423 isl_int_set_si(graph
->lp
->ineq
[k
][1 + node
->start
], -1);
1424 isl_int_set_si(graph
->lp
->ineq
[k
][0], max_constant_term
);
1427 if (add_bound_coefficient_constraints(ctx
, graph
) < 0)
1429 if (add_all_validity_constraints(graph
) < 0)
1431 if (add_all_proximity_constraints(graph
) < 0)
1437 /* Analyze the conflicting constraint found by
1438 * isl_tab_basic_set_non_trivial_lexmin. If it corresponds to the validity
1439 * constraint of one of the edges between distinct nodes, living, moreover
1440 * in distinct SCCs, then record the source and sink SCC as this may
1441 * be a good place to cut between SCCs.
1443 static int check_conflict(int con
, void *user
)
1446 struct isl_sched_graph
*graph
= user
;
1448 if (graph
->src_scc
>= 0)
1451 con
-= graph
->lp
->n_eq
;
1453 if (con
>= graph
->lp
->n_ineq
)
1456 for (i
= 0; i
< graph
->n_edge
; ++i
) {
1457 if (!graph
->edge
[i
].validity
)
1459 if (graph
->edge
[i
].src
== graph
->edge
[i
].dst
)
1461 if (graph
->edge
[i
].src
->scc
== graph
->edge
[i
].dst
->scc
)
1463 if (graph
->edge
[i
].start
> con
)
1465 if (graph
->edge
[i
].end
<= con
)
1467 graph
->src_scc
= graph
->edge
[i
].src
->scc
;
1468 graph
->dst_scc
= graph
->edge
[i
].dst
->scc
;
1474 /* Check whether the next schedule row of the given node needs to be
1475 * non-trivial. Lower-dimensional domains may have some trivial rows,
1476 * but as soon as the number of remaining required non-trivial rows
1477 * is as large as the number or remaining rows to be computed,
1478 * all remaining rows need to be non-trivial.
1480 static int needs_row(struct isl_sched_graph
*graph
, struct isl_sched_node
*node
)
1482 return node
->nvar
- node
->rank
>= graph
->maxvar
- graph
->n_row
;
1485 /* Solve the ILP problem constructed in setup_lp.
1486 * For each node such that all the remaining rows of its schedule
1487 * need to be non-trivial, we construct a non-triviality region.
1488 * This region imposes that the next row is independent of previous rows.
1489 * In particular the coefficients c_i_x are represented by t_i_x
1490 * variables with c_i_x = Q t_i_x and Q a unimodular matrix such that
1491 * its first columns span the rows of the previously computed part
1492 * of the schedule. The non-triviality region enforces that at least
1493 * one of the remaining components of t_i_x is non-zero, i.e.,
1494 * that the new schedule row depends on at least one of the remaining
1497 static __isl_give isl_vec
*solve_lp(struct isl_sched_graph
*graph
)
1503 for (i
= 0; i
< graph
->n
; ++i
) {
1504 struct isl_sched_node
*node
= &graph
->node
[i
];
1505 int skip
= node
->rank
;
1506 graph
->region
[i
].pos
= node
->start
+ 1 + 2*(node
->nparam
+skip
);
1507 if (needs_row(graph
, node
))
1508 graph
->region
[i
].len
= 2 * (node
->nvar
- skip
);
1510 graph
->region
[i
].len
= 0;
1512 lp
= isl_basic_set_copy(graph
->lp
);
1513 sol
= isl_tab_basic_set_non_trivial_lexmin(lp
, 2, graph
->n
,
1514 graph
->region
, &check_conflict
, graph
);
1518 /* Update the schedules of all nodes based on the given solution
1519 * of the LP problem.
1520 * The new row is added to the current band.
1521 * All possibly negative coefficients are encoded as a difference
1522 * of two non-negative variables, so we need to perform the subtraction
1523 * here. Moreover, if use_cmap is set, then the solution does
1524 * not refer to the actual coefficients c_i_x, but instead to variables
1525 * t_i_x such that c_i_x = Q t_i_x and Q is equal to node->cmap.
1526 * In this case, we then also need to perform this multiplication
1527 * to obtain the values of c_i_x.
1529 * If check_zero is set, then the first two coordinates of sol are
1530 * assumed to correspond to the dependence distance. If these two
1531 * coordinates are zero, then the corresponding scheduling dimension
1532 * is marked as being zero distance.
1534 static int update_schedule(struct isl_sched_graph
*graph
,
1535 __isl_take isl_vec
*sol
, int use_cmap
, int check_zero
)
1539 isl_vec
*csol
= NULL
;
1544 isl_die(sol
->ctx
, isl_error_internal
,
1545 "no solution found", goto error
);
1546 if (graph
->n_total_row
>= graph
->max_row
)
1547 isl_die(sol
->ctx
, isl_error_internal
,
1548 "too many schedule rows", goto error
);
1551 zero
= isl_int_is_zero(sol
->el
[1]) &&
1552 isl_int_is_zero(sol
->el
[2]);
1554 for (i
= 0; i
< graph
->n
; ++i
) {
1555 struct isl_sched_node
*node
= &graph
->node
[i
];
1556 int pos
= node
->start
;
1557 int row
= isl_mat_rows(node
->sched
);
1560 csol
= isl_vec_alloc(sol
->ctx
, node
->nvar
);
1564 isl_map_free(node
->sched_map
);
1565 node
->sched_map
= NULL
;
1566 node
->sched
= isl_mat_add_rows(node
->sched
, 1);
1569 node
->sched
= isl_mat_set_element(node
->sched
, row
, 0,
1571 for (j
= 0; j
< node
->nparam
+ node
->nvar
; ++j
)
1572 isl_int_sub(sol
->el
[1 + pos
+ 1 + 2 * j
+ 1],
1573 sol
->el
[1 + pos
+ 1 + 2 * j
+ 1],
1574 sol
->el
[1 + pos
+ 1 + 2 * j
]);
1575 for (j
= 0; j
< node
->nparam
; ++j
)
1576 node
->sched
= isl_mat_set_element(node
->sched
,
1577 row
, 1 + j
, sol
->el
[1+pos
+1+2*j
+1]);
1578 for (j
= 0; j
< node
->nvar
; ++j
)
1579 isl_int_set(csol
->el
[j
],
1580 sol
->el
[1+pos
+1+2*(node
->nparam
+j
)+1]);
1582 csol
= isl_mat_vec_product(isl_mat_copy(node
->cmap
),
1586 for (j
= 0; j
< node
->nvar
; ++j
)
1587 node
->sched
= isl_mat_set_element(node
->sched
,
1588 row
, 1 + node
->nparam
+ j
, csol
->el
[j
]);
1589 node
->band
[graph
->n_total_row
] = graph
->n_band
;
1590 node
->zero
[graph
->n_total_row
] = zero
;
1596 graph
->n_total_row
++;
1605 /* Convert node->sched into a multi_aff and return this multi_aff.
1607 static __isl_give isl_multi_aff
*node_extract_schedule_multi_aff(
1608 struct isl_sched_node
*node
)
1612 isl_local_space
*ls
;
1618 nrow
= isl_mat_rows(node
->sched
);
1619 ncol
= isl_mat_cols(node
->sched
) - 1;
1620 space
= isl_space_from_domain(isl_space_copy(node
->dim
));
1621 space
= isl_space_add_dims(space
, isl_dim_out
, nrow
);
1622 ma
= isl_multi_aff_zero(space
);
1623 ls
= isl_local_space_from_space(isl_space_copy(node
->dim
));
1627 for (i
= 0; i
< nrow
; ++i
) {
1628 aff
= isl_aff_zero_on_domain(isl_local_space_copy(ls
));
1629 isl_mat_get_element(node
->sched
, i
, 0, &v
);
1630 aff
= isl_aff_set_constant(aff
, v
);
1631 for (j
= 0; j
< node
->nparam
; ++j
) {
1632 isl_mat_get_element(node
->sched
, i
, 1 + j
, &v
);
1633 aff
= isl_aff_set_coefficient(aff
, isl_dim_param
, j
, v
);
1635 for (j
= 0; j
< node
->nvar
; ++j
) {
1636 isl_mat_get_element(node
->sched
,
1637 i
, 1 + node
->nparam
+ j
, &v
);
1638 aff
= isl_aff_set_coefficient(aff
, isl_dim_in
, j
, v
);
1640 ma
= isl_multi_aff_set_aff(ma
, i
, aff
);
1645 isl_local_space_free(ls
);
1650 /* Convert node->sched into a map and return this map.
1652 * The result is cached in node->sched_map, which needs to be released
1653 * whenever node->sched is updated.
1655 static __isl_give isl_map
*node_extract_schedule(struct isl_sched_node
*node
)
1657 if (!node
->sched_map
) {
1660 ma
= node_extract_schedule_multi_aff(node
);
1661 node
->sched_map
= isl_map_from_multi_aff(ma
);
1664 return isl_map_copy(node
->sched_map
);
1667 /* Update the given dependence relation based on the current schedule.
1668 * That is, intersect the dependence relation with a map expressing
1669 * that source and sink are executed within the same iteration of
1670 * the current schedule.
1671 * This is not the most efficient way, but this shouldn't be a critical
1674 static __isl_give isl_map
*specialize(__isl_take isl_map
*map
,
1675 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
1677 isl_map
*src_sched
, *dst_sched
, *id
;
1679 src_sched
= node_extract_schedule(src
);
1680 dst_sched
= node_extract_schedule(dst
);
1681 id
= isl_map_apply_range(src_sched
, isl_map_reverse(dst_sched
));
1682 return isl_map_intersect(map
, id
);
1685 /* Update the dependence relations of all edges based on the current schedule.
1686 * If a dependence is carried completely by the current schedule, then
1687 * it is removed from the edge_tables. It is kept in the list of edges
1688 * as otherwise all edge_tables would have to be recomputed.
1690 static int update_edges(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
1694 for (i
= graph
->n_edge
- 1; i
>= 0; --i
) {
1695 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
1696 edge
->map
= specialize(edge
->map
, edge
->src
, edge
->dst
);
1700 if (isl_map_plain_is_empty(edge
->map
))
1701 graph_remove_edge(graph
, edge
);
1707 static void next_band(struct isl_sched_graph
*graph
)
1709 graph
->band_start
= graph
->n_total_row
;
1713 /* Topologically sort statements mapped to the same schedule iteration
1714 * and add a row to the schedule corresponding to this order.
1716 static int sort_statements(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
1723 if (update_edges(ctx
, graph
) < 0)
1726 if (graph
->n_edge
== 0)
1729 if (detect_sccs(ctx
, graph
) < 0)
1732 if (graph
->n_total_row
>= graph
->max_row
)
1733 isl_die(ctx
, isl_error_internal
,
1734 "too many schedule rows", return -1);
1736 for (i
= 0; i
< graph
->n
; ++i
) {
1737 struct isl_sched_node
*node
= &graph
->node
[i
];
1738 int row
= isl_mat_rows(node
->sched
);
1739 int cols
= isl_mat_cols(node
->sched
);
1741 isl_map_free(node
->sched_map
);
1742 node
->sched_map
= NULL
;
1743 node
->sched
= isl_mat_add_rows(node
->sched
, 1);
1746 node
->sched
= isl_mat_set_element_si(node
->sched
, row
, 0,
1748 for (j
= 1; j
< cols
; ++j
)
1749 node
->sched
= isl_mat_set_element_si(node
->sched
,
1751 node
->band
[graph
->n_total_row
] = graph
->n_band
;
1754 graph
->n_total_row
++;
1760 /* Construct an isl_schedule based on the computed schedule stored
1761 * in graph and with parameters specified by dim.
1763 static __isl_give isl_schedule
*extract_schedule(struct isl_sched_graph
*graph
,
1764 __isl_take isl_space
*dim
)
1768 isl_schedule
*sched
= NULL
;
1773 ctx
= isl_space_get_ctx(dim
);
1774 sched
= isl_calloc(ctx
, struct isl_schedule
,
1775 sizeof(struct isl_schedule
) +
1776 (graph
->n
- 1) * sizeof(struct isl_schedule_node
));
1781 sched
->n
= graph
->n
;
1782 sched
->n_band
= graph
->n_band
;
1783 sched
->n_total_row
= graph
->n_total_row
;
1785 for (i
= 0; i
< sched
->n
; ++i
) {
1787 int *band_end
, *band_id
, *zero
;
1789 sched
->node
[i
].sched
=
1790 node_extract_schedule_multi_aff(&graph
->node
[i
]);
1791 if (!sched
->node
[i
].sched
)
1794 sched
->node
[i
].n_band
= graph
->n_band
;
1795 if (graph
->n_band
== 0)
1798 band_end
= isl_alloc_array(ctx
, int, graph
->n_band
);
1799 band_id
= isl_alloc_array(ctx
, int, graph
->n_band
);
1800 zero
= isl_alloc_array(ctx
, int, graph
->n_total_row
);
1801 sched
->node
[i
].band_end
= band_end
;
1802 sched
->node
[i
].band_id
= band_id
;
1803 sched
->node
[i
].zero
= zero
;
1804 if (!band_end
|| !band_id
|| !zero
)
1807 for (r
= 0; r
< graph
->n_total_row
; ++r
)
1808 zero
[r
] = graph
->node
[i
].zero
[r
];
1809 for (r
= b
= 0; r
< graph
->n_total_row
; ++r
) {
1810 if (graph
->node
[i
].band
[r
] == b
)
1813 if (graph
->node
[i
].band
[r
] == -1)
1816 if (r
== graph
->n_total_row
)
1818 sched
->node
[i
].n_band
= b
;
1819 for (--b
; b
>= 0; --b
)
1820 band_id
[b
] = graph
->node
[i
].band_id
[b
];
1827 isl_space_free(dim
);
1828 isl_schedule_free(sched
);
1832 /* Copy nodes that satisfy node_pred from the src dependence graph
1833 * to the dst dependence graph.
1835 static int copy_nodes(struct isl_sched_graph
*dst
, struct isl_sched_graph
*src
,
1836 int (*node_pred
)(struct isl_sched_node
*node
, int data
), int data
)
1841 for (i
= 0; i
< src
->n
; ++i
) {
1842 if (!node_pred(&src
->node
[i
], data
))
1844 dst
->node
[dst
->n
].dim
= isl_space_copy(src
->node
[i
].dim
);
1845 dst
->node
[dst
->n
].nvar
= src
->node
[i
].nvar
;
1846 dst
->node
[dst
->n
].nparam
= src
->node
[i
].nparam
;
1847 dst
->node
[dst
->n
].sched
= isl_mat_copy(src
->node
[i
].sched
);
1848 dst
->node
[dst
->n
].sched_map
=
1849 isl_map_copy(src
->node
[i
].sched_map
);
1850 dst
->node
[dst
->n
].band
= src
->node
[i
].band
;
1851 dst
->node
[dst
->n
].band_id
= src
->node
[i
].band_id
;
1852 dst
->node
[dst
->n
].zero
= src
->node
[i
].zero
;
1859 /* Copy non-empty edges that satisfy edge_pred from the src dependence graph
1860 * to the dst dependence graph.
1861 * If the source or destination node of the edge is not in the destination
1862 * graph, then it must be a backward proximity edge and it should simply
1865 static int copy_edges(isl_ctx
*ctx
, struct isl_sched_graph
*dst
,
1866 struct isl_sched_graph
*src
,
1867 int (*edge_pred
)(struct isl_sched_edge
*edge
, int data
), int data
)
1870 enum isl_edge_type t
;
1873 for (i
= 0; i
< src
->n_edge
; ++i
) {
1874 struct isl_sched_edge
*edge
= &src
->edge
[i
];
1876 struct isl_sched_node
*dst_src
, *dst_dst
;
1878 if (!edge_pred(edge
, data
))
1881 if (isl_map_plain_is_empty(edge
->map
))
1884 dst_src
= graph_find_node(ctx
, dst
, edge
->src
->dim
);
1885 dst_dst
= graph_find_node(ctx
, dst
, edge
->dst
->dim
);
1886 if (!dst_src
|| !dst_dst
) {
1888 isl_die(ctx
, isl_error_internal
,
1889 "backward validity edge", return -1);
1893 map
= isl_map_copy(edge
->map
);
1895 dst
->edge
[dst
->n_edge
].src
= dst_src
;
1896 dst
->edge
[dst
->n_edge
].dst
= dst_dst
;
1897 dst
->edge
[dst
->n_edge
].map
= map
;
1898 dst
->edge
[dst
->n_edge
].validity
= edge
->validity
;
1899 dst
->edge
[dst
->n_edge
].proximity
= edge
->proximity
;
1902 for (t
= isl_edge_first
; t
<= isl_edge_last
; ++t
) {
1904 graph_find_edge(src
, t
, edge
->src
, edge
->dst
))
1906 if (graph_edge_table_add(ctx
, dst
, t
,
1907 &dst
->edge
[dst
->n_edge
- 1]) < 0)
1915 /* Given a "src" dependence graph that contains the nodes from "dst"
1916 * that satisfy node_pred, copy the schedule computed in "src"
1917 * for those nodes back to "dst".
1919 static int copy_schedule(struct isl_sched_graph
*dst
,
1920 struct isl_sched_graph
*src
,
1921 int (*node_pred
)(struct isl_sched_node
*node
, int data
), int data
)
1926 for (i
= 0; i
< dst
->n
; ++i
) {
1927 if (!node_pred(&dst
->node
[i
], data
))
1929 isl_mat_free(dst
->node
[i
].sched
);
1930 isl_map_free(dst
->node
[i
].sched_map
);
1931 dst
->node
[i
].sched
= isl_mat_copy(src
->node
[src
->n
].sched
);
1932 dst
->node
[i
].sched_map
=
1933 isl_map_copy(src
->node
[src
->n
].sched_map
);
1937 dst
->max_row
= src
->max_row
;
1938 dst
->n_total_row
= src
->n_total_row
;
1939 dst
->n_band
= src
->n_band
;
1944 /* Compute the maximal number of variables over all nodes.
1945 * This is the maximal number of linearly independent schedule
1946 * rows that we need to compute.
1947 * Just in case we end up in a part of the dependence graph
1948 * with only lower-dimensional domains, we make sure we will
1949 * compute the required amount of extra linearly independent rows.
1951 static int compute_maxvar(struct isl_sched_graph
*graph
)
1956 for (i
= 0; i
< graph
->n
; ++i
) {
1957 struct isl_sched_node
*node
= &graph
->node
[i
];
1960 if (node_update_cmap(node
) < 0)
1962 nvar
= node
->nvar
+ graph
->n_row
- node
->rank
;
1963 if (nvar
> graph
->maxvar
)
1964 graph
->maxvar
= nvar
;
1970 static int compute_schedule(isl_ctx
*ctx
, struct isl_sched_graph
*graph
);
1971 static int compute_schedule_wcc(isl_ctx
*ctx
, struct isl_sched_graph
*graph
);
1973 /* Compute a schedule for a subgraph of "graph". In particular, for
1974 * the graph composed of nodes that satisfy node_pred and edges that
1975 * that satisfy edge_pred. The caller should precompute the number
1976 * of nodes and edges that satisfy these predicates and pass them along
1977 * as "n" and "n_edge".
1978 * If the subgraph is known to consist of a single component, then wcc should
1979 * be set and then we call compute_schedule_wcc on the constructed subgraph.
1980 * Otherwise, we call compute_schedule, which will check whether the subgraph
1983 static int compute_sub_schedule(isl_ctx
*ctx
,
1984 struct isl_sched_graph
*graph
, int n
, int n_edge
,
1985 int (*node_pred
)(struct isl_sched_node
*node
, int data
),
1986 int (*edge_pred
)(struct isl_sched_edge
*edge
, int data
),
1989 struct isl_sched_graph split
= { 0 };
1992 if (graph_alloc(ctx
, &split
, n
, n_edge
) < 0)
1994 if (copy_nodes(&split
, graph
, node_pred
, data
) < 0)
1996 if (graph_init_table(ctx
, &split
) < 0)
1998 for (t
= 0; t
<= isl_edge_last
; ++t
)
1999 split
.max_edge
[t
] = graph
->max_edge
[t
];
2000 if (graph_init_edge_tables(ctx
, &split
) < 0)
2002 if (copy_edges(ctx
, &split
, graph
, edge_pred
, data
) < 0)
2004 split
.n_row
= graph
->n_row
;
2005 split
.max_row
= graph
->max_row
;
2006 split
.n_total_row
= graph
->n_total_row
;
2007 split
.n_band
= graph
->n_band
;
2008 split
.band_start
= graph
->band_start
;
2010 if (wcc
&& compute_schedule_wcc(ctx
, &split
) < 0)
2012 if (!wcc
&& compute_schedule(ctx
, &split
) < 0)
2015 copy_schedule(graph
, &split
, node_pred
, data
);
2017 graph_free(ctx
, &split
);
2020 graph_free(ctx
, &split
);
2024 static int node_scc_exactly(struct isl_sched_node
*node
, int scc
)
2026 return node
->scc
== scc
;
2029 static int node_scc_at_most(struct isl_sched_node
*node
, int scc
)
2031 return node
->scc
<= scc
;
2034 static int node_scc_at_least(struct isl_sched_node
*node
, int scc
)
2036 return node
->scc
>= scc
;
2039 static int edge_scc_exactly(struct isl_sched_edge
*edge
, int scc
)
2041 return edge
->src
->scc
== scc
&& edge
->dst
->scc
== scc
;
2044 static int edge_dst_scc_at_most(struct isl_sched_edge
*edge
, int scc
)
2046 return edge
->dst
->scc
<= scc
;
2049 static int edge_src_scc_at_least(struct isl_sched_edge
*edge
, int scc
)
2051 return edge
->src
->scc
>= scc
;
2054 /* Pad the schedules of all nodes with zero rows such that in the end
2055 * they all have graph->n_total_row rows.
2056 * The extra rows don't belong to any band, so they get assigned band number -1.
2058 static int pad_schedule(struct isl_sched_graph
*graph
)
2062 for (i
= 0; i
< graph
->n
; ++i
) {
2063 struct isl_sched_node
*node
= &graph
->node
[i
];
2064 int row
= isl_mat_rows(node
->sched
);
2065 if (graph
->n_total_row
> row
) {
2066 isl_map_free(node
->sched_map
);
2067 node
->sched_map
= NULL
;
2069 node
->sched
= isl_mat_add_zero_rows(node
->sched
,
2070 graph
->n_total_row
- row
);
2073 for (j
= row
; j
< graph
->n_total_row
; ++j
)
2080 /* Split the current graph into two parts and compute a schedule for each
2081 * part individually. In particular, one part consists of all SCCs up
2082 * to and including graph->src_scc, while the other part contains the other
2085 * The split is enforced in the schedule by constant rows with two different
2086 * values (0 and 1). These constant rows replace the previously computed rows
2087 * in the current band.
2088 * It would be possible to reuse them as the first rows in the next
2089 * band, but recomputing them may result in better rows as we are looking
2090 * at a smaller part of the dependence graph.
2091 * compute_split_schedule is only called when no zero-distance schedule row
2092 * could be found on the entire graph, so we wark the splitting row as
2093 * non zero-distance.
2095 * The band_id of the second group is set to n, where n is the number
2096 * of nodes in the first group. This ensures that the band_ids over
2097 * the two groups remain disjoint, even if either or both of the two
2098 * groups contain independent components.
2100 static int compute_split_schedule(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2102 int i
, j
, n
, e1
, e2
;
2103 int n_total_row
, orig_total_row
;
2104 int n_band
, orig_band
;
2107 if (graph
->n_total_row
>= graph
->max_row
)
2108 isl_die(ctx
, isl_error_internal
,
2109 "too many schedule rows", return -1);
2111 drop
= graph
->n_total_row
- graph
->band_start
;
2112 graph
->n_total_row
-= drop
;
2113 graph
->n_row
-= drop
;
2116 for (i
= 0; i
< graph
->n
; ++i
) {
2117 struct isl_sched_node
*node
= &graph
->node
[i
];
2118 int row
= isl_mat_rows(node
->sched
) - drop
;
2119 int cols
= isl_mat_cols(node
->sched
);
2120 int before
= node
->scc
<= graph
->src_scc
;
2125 isl_map_free(node
->sched_map
);
2126 node
->sched_map
= NULL
;
2127 node
->sched
= isl_mat_drop_rows(node
->sched
,
2128 graph
->band_start
, drop
);
2129 node
->sched
= isl_mat_add_rows(node
->sched
, 1);
2132 node
->sched
= isl_mat_set_element_si(node
->sched
, row
, 0,
2134 for (j
= 1; j
< cols
; ++j
)
2135 node
->sched
= isl_mat_set_element_si(node
->sched
,
2137 node
->band
[graph
->n_total_row
] = graph
->n_band
;
2138 node
->zero
[graph
->n_total_row
] = 0;
2142 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2143 if (graph
->edge
[i
].dst
->scc
<= graph
->src_scc
)
2145 if (graph
->edge
[i
].src
->scc
> graph
->src_scc
)
2149 graph
->n_total_row
++;
2152 for (i
= 0; i
< graph
->n
; ++i
) {
2153 struct isl_sched_node
*node
= &graph
->node
[i
];
2154 if (node
->scc
> graph
->src_scc
)
2155 node
->band_id
[graph
->n_band
] = n
;
2158 orig_total_row
= graph
->n_total_row
;
2159 orig_band
= graph
->n_band
;
2160 if (compute_sub_schedule(ctx
, graph
, n
, e1
,
2161 &node_scc_at_most
, &edge_dst_scc_at_most
,
2162 graph
->src_scc
, 0) < 0)
2164 n_total_row
= graph
->n_total_row
;
2165 graph
->n_total_row
= orig_total_row
;
2166 n_band
= graph
->n_band
;
2167 graph
->n_band
= orig_band
;
2168 if (compute_sub_schedule(ctx
, graph
, graph
->n
- n
, e2
,
2169 &node_scc_at_least
, &edge_src_scc_at_least
,
2170 graph
->src_scc
+ 1, 0) < 0)
2172 if (n_total_row
> graph
->n_total_row
)
2173 graph
->n_total_row
= n_total_row
;
2174 if (n_band
> graph
->n_band
)
2175 graph
->n_band
= n_band
;
2177 return pad_schedule(graph
);
2180 /* Compute the next band of the schedule after updating the dependence
2181 * relations based on the the current schedule.
2183 static int compute_next_band(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2185 if (update_edges(ctx
, graph
) < 0)
2189 return compute_schedule(ctx
, graph
);
2192 /* Add constraints to graph->lp that force the dependence "map" (which
2193 * is part of the dependence relation of "edge")
2194 * to be respected and attempt to carry it, where the edge is one from
2195 * a node j to itself. "pos" is the sequence number of the given map.
2196 * That is, add constraints that enforce
2198 * (c_j_0 + c_j_n n + c_j_x y) - (c_j_0 + c_j_n n + c_j_x x)
2199 * = c_j_x (y - x) >= e_i
2201 * for each (x,y) in R.
2202 * We obtain general constraints on coefficients (c_0, c_n, c_x)
2203 * of valid constraints for (y - x) and then plug in (-e_i, 0, c_j_x),
2204 * with each coefficient in c_j_x represented as a pair of non-negative
2207 static int add_intra_constraints(struct isl_sched_graph
*graph
,
2208 struct isl_sched_edge
*edge
, __isl_take isl_map
*map
, int pos
)
2211 isl_ctx
*ctx
= isl_map_get_ctx(map
);
2213 isl_dim_map
*dim_map
;
2214 isl_basic_set
*coef
;
2215 struct isl_sched_node
*node
= edge
->src
;
2217 coef
= intra_coefficients(graph
, map
);
2221 dim
= isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef
)));
2223 total
= isl_basic_set_total_dim(graph
->lp
);
2224 dim_map
= isl_dim_map_alloc(ctx
, total
);
2225 isl_dim_map_range(dim_map
, 3 + pos
, 0, 0, 0, 1, -1);
2226 isl_dim_map_range(dim_map
, node
->start
+ 2 * node
->nparam
+ 1, 2,
2227 isl_space_dim(dim
, isl_dim_set
), 1,
2229 isl_dim_map_range(dim_map
, node
->start
+ 2 * node
->nparam
+ 2, 2,
2230 isl_space_dim(dim
, isl_dim_set
), 1,
2232 graph
->lp
= isl_basic_set_extend_constraints(graph
->lp
,
2233 coef
->n_eq
, coef
->n_ineq
);
2234 graph
->lp
= isl_basic_set_add_constraints_dim_map(graph
->lp
,
2236 isl_space_free(dim
);
2241 /* Add constraints to graph->lp that force the dependence "map" (which
2242 * is part of the dependence relation of "edge")
2243 * to be respected and attempt to carry it, where the edge is one from
2244 * node j to node k. "pos" is the sequence number of the given map.
2245 * That is, add constraints that enforce
2247 * (c_k_0 + c_k_n n + c_k_x y) - (c_j_0 + c_j_n n + c_j_x x) >= e_i
2249 * for each (x,y) in R.
2250 * We obtain general constraints on coefficients (c_0, c_n, c_x)
2251 * of valid constraints for R and then plug in
2252 * (-e_i + c_k_0 - c_j_0, c_k_n - c_j_n, c_k_x - c_j_x)
2253 * with each coefficient (except e_i, c_k_0 and c_j_0)
2254 * represented as a pair of non-negative coefficients.
2256 static int add_inter_constraints(struct isl_sched_graph
*graph
,
2257 struct isl_sched_edge
*edge
, __isl_take isl_map
*map
, int pos
)
2260 isl_ctx
*ctx
= isl_map_get_ctx(map
);
2262 isl_dim_map
*dim_map
;
2263 isl_basic_set
*coef
;
2264 struct isl_sched_node
*src
= edge
->src
;
2265 struct isl_sched_node
*dst
= edge
->dst
;
2267 coef
= inter_coefficients(graph
, map
);
2271 dim
= isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef
)));
2273 total
= isl_basic_set_total_dim(graph
->lp
);
2274 dim_map
= isl_dim_map_alloc(ctx
, total
);
2276 isl_dim_map_range(dim_map
, 3 + pos
, 0, 0, 0, 1, -1);
2278 isl_dim_map_range(dim_map
, dst
->start
, 0, 0, 0, 1, 1);
2279 isl_dim_map_range(dim_map
, dst
->start
+ 1, 2, 1, 1, dst
->nparam
, -1);
2280 isl_dim_map_range(dim_map
, dst
->start
+ 2, 2, 1, 1, dst
->nparam
, 1);
2281 isl_dim_map_range(dim_map
, dst
->start
+ 2 * dst
->nparam
+ 1, 2,
2282 isl_space_dim(dim
, isl_dim_set
) + src
->nvar
, 1,
2284 isl_dim_map_range(dim_map
, dst
->start
+ 2 * dst
->nparam
+ 2, 2,
2285 isl_space_dim(dim
, isl_dim_set
) + src
->nvar
, 1,
2288 isl_dim_map_range(dim_map
, src
->start
, 0, 0, 0, 1, -1);
2289 isl_dim_map_range(dim_map
, src
->start
+ 1, 2, 1, 1, src
->nparam
, 1);
2290 isl_dim_map_range(dim_map
, src
->start
+ 2, 2, 1, 1, src
->nparam
, -1);
2291 isl_dim_map_range(dim_map
, src
->start
+ 2 * src
->nparam
+ 1, 2,
2292 isl_space_dim(dim
, isl_dim_set
), 1,
2294 isl_dim_map_range(dim_map
, src
->start
+ 2 * src
->nparam
+ 2, 2,
2295 isl_space_dim(dim
, isl_dim_set
), 1,
2298 graph
->lp
= isl_basic_set_extend_constraints(graph
->lp
,
2299 coef
->n_eq
, coef
->n_ineq
);
2300 graph
->lp
= isl_basic_set_add_constraints_dim_map(graph
->lp
,
2302 isl_space_free(dim
);
2307 /* Add constraints to graph->lp that force all validity dependences
2308 * to be respected and attempt to carry them.
2310 static int add_all_constraints(struct isl_sched_graph
*graph
)
2316 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2317 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
2319 if (!edge
->validity
)
2322 for (j
= 0; j
< edge
->map
->n
; ++j
) {
2323 isl_basic_map
*bmap
;
2326 bmap
= isl_basic_map_copy(edge
->map
->p
[j
]);
2327 map
= isl_map_from_basic_map(bmap
);
2329 if (edge
->src
== edge
->dst
&&
2330 add_intra_constraints(graph
, edge
, map
, pos
) < 0)
2332 if (edge
->src
!= edge
->dst
&&
2333 add_inter_constraints(graph
, edge
, map
, pos
) < 0)
2342 /* Count the number of equality and inequality constraints
2343 * that will be added to the carry_lp problem.
2344 * We count each edge exactly once.
2346 static int count_all_constraints(struct isl_sched_graph
*graph
,
2347 int *n_eq
, int *n_ineq
)
2351 *n_eq
= *n_ineq
= 0;
2352 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2353 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
2354 for (j
= 0; j
< edge
->map
->n
; ++j
) {
2355 isl_basic_map
*bmap
;
2358 bmap
= isl_basic_map_copy(edge
->map
->p
[j
]);
2359 map
= isl_map_from_basic_map(bmap
);
2361 if (count_map_constraints(graph
, edge
, map
,
2362 n_eq
, n_ineq
, 1) < 0)
2370 /* Construct an LP problem for finding schedule coefficients
2371 * such that the schedule carries as many dependences as possible.
2372 * In particular, for each dependence i, we bound the dependence distance
2373 * from below by e_i, with 0 <= e_i <= 1 and then maximize the sum
2374 * of all e_i's. Dependence with e_i = 0 in the solution are simply
2375 * respected, while those with e_i > 0 (in practice e_i = 1) are carried.
2376 * Note that if the dependence relation is a union of basic maps,
2377 * then we have to consider each basic map individually as it may only
2378 * be possible to carry the dependences expressed by some of those
2379 * basic maps and not all off them.
2380 * Below, we consider each of those basic maps as a separate "edge".
2382 * All variables of the LP are non-negative. The actual coefficients
2383 * may be negative, so each coefficient is represented as the difference
2384 * of two non-negative variables. The negative part always appears
2385 * immediately before the positive part.
2386 * Other than that, the variables have the following order
2388 * - sum of (1 - e_i) over all edges
2389 * - sum of positive and negative parts of all c_n coefficients
2390 * (unconstrained when computing non-parametric schedules)
2391 * - sum of positive and negative parts of all c_x coefficients
2396 * - positive and negative parts of c_i_n (if parametric)
2397 * - positive and negative parts of c_i_x
2399 * The constraints are those from the (validity) edges plus three equalities
2400 * to express the sums and n_edge inequalities to express e_i <= 1.
2402 static int setup_carry_lp(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2412 for (i
= 0; i
< graph
->n_edge
; ++i
)
2413 n_edge
+= graph
->edge
[i
].map
->n
;
2416 for (i
= 0; i
< graph
->n
; ++i
) {
2417 struct isl_sched_node
*node
= &graph
->node
[graph
->sorted
[i
]];
2418 node
->start
= total
;
2419 total
+= 1 + 2 * (node
->nparam
+ node
->nvar
);
2422 if (count_all_constraints(graph
, &n_eq
, &n_ineq
) < 0)
2424 if (count_bound_coefficient_constraints(ctx
, graph
, &n_eq
, &n_ineq
) < 0)
2427 dim
= isl_space_set_alloc(ctx
, 0, total
);
2428 isl_basic_set_free(graph
->lp
);
2431 graph
->lp
= isl_basic_set_alloc_space(dim
, 0, n_eq
, n_ineq
);
2432 graph
->lp
= isl_basic_set_set_rational(graph
->lp
);
2434 k
= isl_basic_set_alloc_equality(graph
->lp
);
2437 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2438 isl_int_set_si(graph
->lp
->eq
[k
][0], -n_edge
);
2439 isl_int_set_si(graph
->lp
->eq
[k
][1], 1);
2440 for (i
= 0; i
< n_edge
; ++i
)
2441 isl_int_set_si(graph
->lp
->eq
[k
][4 + i
], 1);
2443 k
= isl_basic_set_alloc_equality(graph
->lp
);
2446 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2447 isl_int_set_si(graph
->lp
->eq
[k
][2], -1);
2448 for (i
= 0; i
< graph
->n
; ++i
) {
2449 int pos
= 1 + graph
->node
[i
].start
+ 1;
2451 for (j
= 0; j
< 2 * graph
->node
[i
].nparam
; ++j
)
2452 isl_int_set_si(graph
->lp
->eq
[k
][pos
+ j
], 1);
2455 k
= isl_basic_set_alloc_equality(graph
->lp
);
2458 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2459 isl_int_set_si(graph
->lp
->eq
[k
][3], -1);
2460 for (i
= 0; i
< graph
->n
; ++i
) {
2461 struct isl_sched_node
*node
= &graph
->node
[i
];
2462 int pos
= 1 + node
->start
+ 1 + 2 * node
->nparam
;
2464 for (j
= 0; j
< 2 * node
->nvar
; ++j
)
2465 isl_int_set_si(graph
->lp
->eq
[k
][pos
+ j
], 1);
2468 for (i
= 0; i
< n_edge
; ++i
) {
2469 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2472 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
2473 isl_int_set_si(graph
->lp
->ineq
[k
][4 + i
], -1);
2474 isl_int_set_si(graph
->lp
->ineq
[k
][0], 1);
2477 if (add_bound_coefficient_constraints(ctx
, graph
) < 0)
2479 if (add_all_constraints(graph
) < 0)
2485 /* If the schedule_split_scaled option is set and if the linear
2486 * parts of the scheduling rows for all nodes in the graphs have
2487 * non-trivial common divisor, then split off the constant term
2488 * from the linear part.
2489 * The constant term is then placed in a separate band and
2490 * the linear part is reduced.
2492 static int split_scaled(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2498 if (!ctx
->opt
->schedule_split_scaled
)
2503 if (graph
->n_total_row
>= graph
->max_row
)
2504 isl_die(ctx
, isl_error_internal
,
2505 "too many schedule rows", return -1);
2508 isl_int_init(gcd_i
);
2510 isl_int_set_si(gcd
, 0);
2512 row
= isl_mat_rows(graph
->node
[0].sched
) - 1;
2514 for (i
= 0; i
< graph
->n
; ++i
) {
2515 struct isl_sched_node
*node
= &graph
->node
[i
];
2516 int cols
= isl_mat_cols(node
->sched
);
2518 isl_seq_gcd(node
->sched
->row
[row
] + 1, cols
- 1, &gcd_i
);
2519 isl_int_gcd(gcd
, gcd
, gcd_i
);
2522 isl_int_clear(gcd_i
);
2524 if (isl_int_cmp_si(gcd
, 1) <= 0) {
2531 for (i
= 0; i
< graph
->n
; ++i
) {
2532 struct isl_sched_node
*node
= &graph
->node
[i
];
2534 isl_map_free(node
->sched_map
);
2535 node
->sched_map
= NULL
;
2536 node
->sched
= isl_mat_add_zero_rows(node
->sched
, 1);
2539 isl_int_fdiv_r(node
->sched
->row
[row
+ 1][0],
2540 node
->sched
->row
[row
][0], gcd
);
2541 isl_int_fdiv_q(node
->sched
->row
[row
][0],
2542 node
->sched
->row
[row
][0], gcd
);
2543 isl_int_mul(node
->sched
->row
[row
][0],
2544 node
->sched
->row
[row
][0], gcd
);
2545 node
->sched
= isl_mat_scale_down_row(node
->sched
, row
, gcd
);
2548 node
->band
[graph
->n_total_row
] = graph
->n_band
;
2551 graph
->n_total_row
++;
2560 static int compute_component_schedule(isl_ctx
*ctx
,
2561 struct isl_sched_graph
*graph
);
2563 /* Is the schedule row "sol" trivial on node "node"?
2564 * That is, is the solution zero on the dimensions orthogonal to
2565 * the previously found solutions?
2566 * Return 1 if the solution is trivial, 0 if it is not and -1 on error.
2568 * Each coefficient is represented as the difference between
2569 * two non-negative values in "sol". "sol" has been computed
2570 * in terms of the original iterators (i.e., without use of cmap).
2571 * We construct the schedule row s and write it as a linear
2572 * combination of (linear combinations of) previously computed schedule rows.
2573 * s = Q c or c = U s.
2574 * If the final entries of c are all zero, then the solution is trivial.
2576 static int is_trivial(struct isl_sched_node
*node
, __isl_keep isl_vec
*sol
)
2586 if (node
->nvar
== node
->rank
)
2589 ctx
= isl_vec_get_ctx(sol
);
2590 node_sol
= isl_vec_alloc(ctx
, node
->nvar
);
2594 pos
= 1 + node
->start
+ 1 + 2 * node
->nparam
;
2596 for (i
= 0; i
< node
->nvar
; ++i
)
2597 isl_int_sub(node_sol
->el
[i
],
2598 sol
->el
[pos
+ 2 * i
+ 1], sol
->el
[pos
+ 2 * i
]);
2600 node_sol
= isl_mat_vec_product(isl_mat_copy(node
->cinv
), node_sol
);
2605 trivial
= isl_seq_first_non_zero(node_sol
->el
+ node
->rank
,
2606 node
->nvar
- node
->rank
) == -1;
2608 isl_vec_free(node_sol
);
2613 /* Is the schedule row "sol" trivial on any node where it should
2615 * "sol" has been computed in terms of the original iterators
2616 * (i.e., without use of cmap).
2617 * Return 1 if any solution is trivial, 0 if they are not and -1 on error.
2619 static int is_any_trivial(struct isl_sched_graph
*graph
,
2620 __isl_keep isl_vec
*sol
)
2624 for (i
= 0; i
< graph
->n
; ++i
) {
2625 struct isl_sched_node
*node
= &graph
->node
[i
];
2628 if (!needs_row(graph
, node
))
2630 trivial
= is_trivial(node
, sol
);
2631 if (trivial
< 0 || trivial
)
2638 /* Construct a schedule row for each node such that as many dependences
2639 * as possible are carried and then continue with the next band.
2641 * If the computed schedule row turns out to be trivial on one or
2642 * more nodes where it should not be trivial, then we throw it away
2643 * and try again on each component separately.
2645 static int carry_dependences(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2654 for (i
= 0; i
< graph
->n_edge
; ++i
)
2655 n_edge
+= graph
->edge
[i
].map
->n
;
2657 if (setup_carry_lp(ctx
, graph
) < 0)
2660 lp
= isl_basic_set_copy(graph
->lp
);
2661 sol
= isl_tab_basic_set_non_neg_lexmin(lp
);
2665 if (sol
->size
== 0) {
2667 isl_die(ctx
, isl_error_internal
,
2668 "error in schedule construction", return -1);
2671 isl_int_divexact(sol
->el
[1], sol
->el
[1], sol
->el
[0]);
2672 if (isl_int_cmp_si(sol
->el
[1], n_edge
) >= 0) {
2674 isl_die(ctx
, isl_error_unknown
,
2675 "unable to carry dependences", return -1);
2678 trivial
= is_any_trivial(graph
, sol
);
2680 sol
= isl_vec_free(sol
);
2681 } else if (trivial
) {
2684 return compute_component_schedule(ctx
, graph
);
2685 isl_die(ctx
, isl_error_unknown
,
2686 "unable to construct non-trivial solution", return -1);
2689 if (update_schedule(graph
, sol
, 0, 0) < 0)
2692 if (split_scaled(ctx
, graph
) < 0)
2695 return compute_next_band(ctx
, graph
);
2698 /* Are there any (non-empty) validity edges in the graph?
2700 static int has_validity_edges(struct isl_sched_graph
*graph
)
2704 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2707 empty
= isl_map_plain_is_empty(graph
->edge
[i
].map
);
2712 if (graph
->edge
[i
].validity
)
2719 /* Should we apply a Feautrier step?
2720 * That is, did the user request the Feautrier algorithm and are
2721 * there any validity dependences (left)?
2723 static int need_feautrier_step(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2725 if (ctx
->opt
->schedule_algorithm
!= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
)
2728 return has_validity_edges(graph
);
2731 /* Compute a schedule for a connected dependence graph using Feautrier's
2732 * multi-dimensional scheduling algorithm.
2733 * The original algorithm is described in [1].
2734 * The main idea is to minimize the number of scheduling dimensions, by
2735 * trying to satisfy as many dependences as possible per scheduling dimension.
2737 * [1] P. Feautrier, Some Efficient Solutions to the Affine Scheduling
2738 * Problem, Part II: Multi-Dimensional Time.
2739 * In Intl. Journal of Parallel Programming, 1992.
2741 static int compute_schedule_wcc_feautrier(isl_ctx
*ctx
,
2742 struct isl_sched_graph
*graph
)
2744 return carry_dependences(ctx
, graph
);
2747 /* Compute a schedule for a connected dependence graph.
2748 * We try to find a sequence of as many schedule rows as possible that result
2749 * in non-negative dependence distances (independent of the previous rows
2750 * in the sequence, i.e., such that the sequence is tilable).
2751 * If we can't find any more rows we either
2752 * - split between SCCs and start over (assuming we found an interesting
2753 * pair of SCCs between which to split)
2754 * - continue with the next band (assuming the current band has at least
2756 * - try to carry as many dependences as possible and continue with the next
2759 * If Feautrier's algorithm is selected, we first recursively try to satisfy
2760 * as many validity dependences as possible. When all validity dependences
2761 * are satisfied we extend the schedule to a full-dimensional schedule.
2763 * If we manage to complete the schedule, we finish off by topologically
2764 * sorting the statements based on the remaining dependences.
2766 * If ctx->opt->schedule_outer_zero_distance is set, then we force the
2767 * outermost dimension in the current band to be zero distance. If this
2768 * turns out to be impossible, we fall back on the general scheme above
2769 * and try to carry as many dependences as possible.
2771 static int compute_schedule_wcc(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2775 if (detect_sccs(ctx
, graph
) < 0)
2777 if (sort_sccs(graph
) < 0)
2780 if (compute_maxvar(graph
) < 0)
2783 if (need_feautrier_step(ctx
, graph
))
2784 return compute_schedule_wcc_feautrier(ctx
, graph
);
2786 if (ctx
->opt
->schedule_outer_zero_distance
)
2789 while (graph
->n_row
< graph
->maxvar
) {
2792 graph
->src_scc
= -1;
2793 graph
->dst_scc
= -1;
2795 if (setup_lp(ctx
, graph
, force_zero
) < 0)
2797 sol
= solve_lp(graph
);
2800 if (sol
->size
== 0) {
2802 if (!ctx
->opt
->schedule_maximize_band_depth
&&
2803 graph
->n_total_row
> graph
->band_start
)
2804 return compute_next_band(ctx
, graph
);
2805 if (graph
->src_scc
>= 0)
2806 return compute_split_schedule(ctx
, graph
);
2807 if (graph
->n_total_row
> graph
->band_start
)
2808 return compute_next_band(ctx
, graph
);
2809 return carry_dependences(ctx
, graph
);
2811 if (update_schedule(graph
, sol
, 1, 1) < 0)
2816 if (graph
->n_total_row
> graph
->band_start
)
2818 return sort_statements(ctx
, graph
);
2821 /* Add a row to the schedules that separates the SCCs and move
2824 static int split_on_scc(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2828 if (graph
->n_total_row
>= graph
->max_row
)
2829 isl_die(ctx
, isl_error_internal
,
2830 "too many schedule rows", return -1);
2832 for (i
= 0; i
< graph
->n
; ++i
) {
2833 struct isl_sched_node
*node
= &graph
->node
[i
];
2834 int row
= isl_mat_rows(node
->sched
);
2836 isl_map_free(node
->sched_map
);
2837 node
->sched_map
= NULL
;
2838 node
->sched
= isl_mat_add_zero_rows(node
->sched
, 1);
2839 node
->sched
= isl_mat_set_element_si(node
->sched
, row
, 0,
2843 node
->band
[graph
->n_total_row
] = graph
->n_band
;
2846 graph
->n_total_row
++;
2852 /* Compute a schedule for each component (identified by node->scc)
2853 * of the dependence graph separately and then combine the results.
2854 * Depending on the setting of schedule_fuse, a component may be
2855 * either weakly or strongly connected.
2857 * The band_id is adjusted such that each component has a separate id.
2858 * Note that the band_id may have already been set to a value different
2859 * from zero by compute_split_schedule.
2861 static int compute_component_schedule(isl_ctx
*ctx
,
2862 struct isl_sched_graph
*graph
)
2866 int n_total_row
, orig_total_row
;
2867 int n_band
, orig_band
;
2869 if (ctx
->opt
->schedule_fuse
== ISL_SCHEDULE_FUSE_MIN
||
2870 ctx
->opt
->schedule_separate_components
)
2871 if (split_on_scc(ctx
, graph
) < 0)
2875 orig_total_row
= graph
->n_total_row
;
2877 orig_band
= graph
->n_band
;
2878 for (i
= 0; i
< graph
->n
; ++i
)
2879 graph
->node
[i
].band_id
[graph
->n_band
] += graph
->node
[i
].scc
;
2880 for (wcc
= 0; wcc
< graph
->scc
; ++wcc
) {
2882 for (i
= 0; i
< graph
->n
; ++i
)
2883 if (graph
->node
[i
].scc
== wcc
)
2886 for (i
= 0; i
< graph
->n_edge
; ++i
)
2887 if (graph
->edge
[i
].src
->scc
== wcc
&&
2888 graph
->edge
[i
].dst
->scc
== wcc
)
2891 if (compute_sub_schedule(ctx
, graph
, n
, n_edge
,
2893 &edge_scc_exactly
, wcc
, 1) < 0)
2895 if (graph
->n_total_row
> n_total_row
)
2896 n_total_row
= graph
->n_total_row
;
2897 graph
->n_total_row
= orig_total_row
;
2898 if (graph
->n_band
> n_band
)
2899 n_band
= graph
->n_band
;
2900 graph
->n_band
= orig_band
;
2903 graph
->n_total_row
= n_total_row
;
2904 graph
->n_band
= n_band
;
2906 return pad_schedule(graph
);
2909 /* Compute a schedule for the given dependence graph.
2910 * We first check if the graph is connected (through validity dependences)
2911 * and, if not, compute a schedule for each component separately.
2912 * If schedule_fuse is set to minimal fusion, then we check for strongly
2913 * connected components instead and compute a separate schedule for
2914 * each such strongly connected component.
2916 static int compute_schedule(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2918 if (ctx
->opt
->schedule_fuse
== ISL_SCHEDULE_FUSE_MIN
) {
2919 if (detect_sccs(ctx
, graph
) < 0)
2922 if (detect_wccs(ctx
, graph
) < 0)
2927 return compute_component_schedule(ctx
, graph
);
2929 return compute_schedule_wcc(ctx
, graph
);
2932 /* Compute a schedule for the given union of domains that respects
2933 * all the validity dependences.
2934 * If the default isl scheduling algorithm is used, it tries to minimize
2935 * the dependence distances over the proximity dependences.
2936 * If Feautrier's scheduling algorithm is used, the proximity dependence
2937 * distances are only minimized during the extension to a full-dimensional
2940 __isl_give isl_schedule
*isl_union_set_compute_schedule(
2941 __isl_take isl_union_set
*domain
,
2942 __isl_take isl_union_map
*validity
,
2943 __isl_take isl_union_map
*proximity
)
2945 isl_ctx
*ctx
= isl_union_set_get_ctx(domain
);
2947 struct isl_sched_graph graph
= { 0 };
2948 isl_schedule
*sched
;
2949 struct isl_extract_edge_data data
;
2951 domain
= isl_union_set_align_params(domain
,
2952 isl_union_map_get_space(validity
));
2953 domain
= isl_union_set_align_params(domain
,
2954 isl_union_map_get_space(proximity
));
2955 dim
= isl_union_set_get_space(domain
);
2956 validity
= isl_union_map_align_params(validity
, isl_space_copy(dim
));
2957 proximity
= isl_union_map_align_params(proximity
, dim
);
2962 graph
.n
= isl_union_set_n_set(domain
);
2965 if (graph_alloc(ctx
, &graph
, graph
.n
,
2966 isl_union_map_n_map(validity
) + isl_union_map_n_map(proximity
)) < 0)
2968 if (compute_max_row(&graph
, domain
) < 0)
2972 if (isl_union_set_foreach_set(domain
, &extract_node
, &graph
) < 0)
2974 if (graph_init_table(ctx
, &graph
) < 0)
2976 graph
.max_edge
[isl_edge_validity
] = isl_union_map_n_map(validity
);
2977 graph
.max_edge
[isl_edge_proximity
] = isl_union_map_n_map(proximity
);
2978 if (graph_init_edge_tables(ctx
, &graph
) < 0)
2981 data
.graph
= &graph
;
2982 data
.type
= isl_edge_validity
;
2983 if (isl_union_map_foreach_map(validity
, &extract_edge
, &data
) < 0)
2985 data
.type
= isl_edge_proximity
;
2986 if (isl_union_map_foreach_map(proximity
, &extract_edge
, &data
) < 0)
2989 if (compute_schedule(ctx
, &graph
) < 0)
2993 sched
= extract_schedule(&graph
, isl_union_set_get_space(domain
));
2995 graph_free(ctx
, &graph
);
2996 isl_union_set_free(domain
);
2997 isl_union_map_free(validity
);
2998 isl_union_map_free(proximity
);
3002 graph_free(ctx
, &graph
);
3003 isl_union_set_free(domain
);
3004 isl_union_map_free(validity
);
3005 isl_union_map_free(proximity
);
3009 void *isl_schedule_free(__isl_take isl_schedule
*sched
)
3015 if (--sched
->ref
> 0)
3018 for (i
= 0; i
< sched
->n
; ++i
) {
3019 isl_multi_aff_free(sched
->node
[i
].sched
);
3020 free(sched
->node
[i
].band_end
);
3021 free(sched
->node
[i
].band_id
);
3022 free(sched
->node
[i
].zero
);
3024 isl_space_free(sched
->dim
);
3025 isl_band_list_free(sched
->band_forest
);
3030 isl_ctx
*isl_schedule_get_ctx(__isl_keep isl_schedule
*schedule
)
3032 return schedule
? isl_space_get_ctx(schedule
->dim
) : NULL
;
3035 /* Set max_out to the maximal number of output dimensions over
3038 static int update_max_out(__isl_take isl_map
*map
, void *user
)
3040 int *max_out
= user
;
3041 int n_out
= isl_map_dim(map
, isl_dim_out
);
3043 if (n_out
> *max_out
)
3050 /* Internal data structure for map_pad_range.
3052 * "max_out" is the maximal schedule dimension.
3053 * "res" collects the results.
3055 struct isl_pad_schedule_map_data
{
3060 /* Pad the range of the given map with zeros to data->max_out and
3061 * then add the result to data->res.
3063 static int map_pad_range(__isl_take isl_map
*map
, void *user
)
3065 struct isl_pad_schedule_map_data
*data
= user
;
3067 int n_out
= isl_map_dim(map
, isl_dim_out
);
3069 map
= isl_map_add_dims(map
, isl_dim_out
, data
->max_out
- n_out
);
3070 for (i
= n_out
; i
< data
->max_out
; ++i
)
3071 map
= isl_map_fix_si(map
, isl_dim_out
, i
, 0);
3073 data
->res
= isl_union_map_add_map(data
->res
, map
);
3080 /* Pad the ranges of the maps in the union map with zeros such they all have
3081 * the same dimension.
3083 static __isl_give isl_union_map
*pad_schedule_map(
3084 __isl_take isl_union_map
*umap
)
3086 struct isl_pad_schedule_map_data data
;
3090 if (isl_union_map_n_map(umap
) <= 1)
3094 if (isl_union_map_foreach_map(umap
, &update_max_out
, &data
.max_out
) < 0)
3095 return isl_union_map_free(umap
);
3097 data
.res
= isl_union_map_empty(isl_union_map_get_space(umap
));
3098 if (isl_union_map_foreach_map(umap
, &map_pad_range
, &data
) < 0)
3099 data
.res
= isl_union_map_free(data
.res
);
3101 isl_union_map_free(umap
);
3105 /* Return an isl_union_map of the schedule. If we have already constructed
3106 * a band forest, then this band forest may have been modified so we need
3107 * to extract the isl_union_map from the forest rather than from
3108 * the originally computed schedule. This reconstructed schedule map
3109 * then needs to be padded with zeros to unify the schedule space
3110 * since the result of isl_band_list_get_suffix_schedule may not have
3111 * a unified schedule space.
3113 __isl_give isl_union_map
*isl_schedule_get_map(__isl_keep isl_schedule
*sched
)
3116 isl_union_map
*umap
;
3121 if (sched
->band_forest
) {
3122 umap
= isl_band_list_get_suffix_schedule(sched
->band_forest
);
3123 return pad_schedule_map(umap
);
3126 umap
= isl_union_map_empty(isl_space_copy(sched
->dim
));
3127 for (i
= 0; i
< sched
->n
; ++i
) {
3130 ma
= isl_multi_aff_copy(sched
->node
[i
].sched
);
3131 umap
= isl_union_map_add_map(umap
, isl_map_from_multi_aff(ma
));
3137 static __isl_give isl_band_list
*construct_band_list(
3138 __isl_keep isl_schedule
*schedule
, __isl_keep isl_band
*parent
,
3139 int band_nr
, int *parent_active
, int n_active
);
3141 /* Construct an isl_band structure for the band in the given schedule
3142 * with sequence number band_nr for the n_active nodes marked by active.
3143 * If the nodes don't have a band with the given sequence number,
3144 * then a band without members is created.
3146 * Because of the way the schedule is constructed, we know that
3147 * the position of the band inside the schedule of a node is the same
3148 * for all active nodes.
3150 * The partial schedule for the band is created before the children
3151 * are created to that construct_band_list can refer to the partial
3152 * schedule of the parent.
3154 static __isl_give isl_band
*construct_band(__isl_keep isl_schedule
*schedule
,
3155 __isl_keep isl_band
*parent
,
3156 int band_nr
, int *active
, int n_active
)
3159 isl_ctx
*ctx
= isl_schedule_get_ctx(schedule
);
3161 unsigned start
, end
;
3163 band
= isl_band_alloc(ctx
);
3167 band
->schedule
= schedule
;
3168 band
->parent
= parent
;
3170 for (i
= 0; i
< schedule
->n
; ++i
)
3174 if (i
>= schedule
->n
)
3175 isl_die(ctx
, isl_error_internal
,
3176 "band without active statements", goto error
);
3178 start
= band_nr
? schedule
->node
[i
].band_end
[band_nr
- 1] : 0;
3179 end
= band_nr
< schedule
->node
[i
].n_band
?
3180 schedule
->node
[i
].band_end
[band_nr
] : start
;
3181 band
->n
= end
- start
;
3183 band
->zero
= isl_alloc_array(ctx
, int, band
->n
);
3184 if (band
->n
&& !band
->zero
)
3187 for (j
= 0; j
< band
->n
; ++j
)
3188 band
->zero
[j
] = schedule
->node
[i
].zero
[start
+ j
];
3190 band
->pma
= isl_union_pw_multi_aff_empty(isl_space_copy(schedule
->dim
));
3191 for (i
= 0; i
< schedule
->n
; ++i
) {
3193 isl_pw_multi_aff
*pma
;
3199 ma
= isl_multi_aff_copy(schedule
->node
[i
].sched
);
3200 n_out
= isl_multi_aff_dim(ma
, isl_dim_out
);
3201 ma
= isl_multi_aff_drop_dims(ma
, isl_dim_out
, end
, n_out
- end
);
3202 ma
= isl_multi_aff_drop_dims(ma
, isl_dim_out
, 0, start
);
3203 pma
= isl_pw_multi_aff_from_multi_aff(ma
);
3204 band
->pma
= isl_union_pw_multi_aff_add_pw_multi_aff(band
->pma
,
3210 for (i
= 0; i
< schedule
->n
; ++i
)
3211 if (active
[i
] && schedule
->node
[i
].n_band
> band_nr
+ 1)
3214 if (i
< schedule
->n
) {
3215 band
->children
= construct_band_list(schedule
, band
,
3216 band_nr
+ 1, active
, n_active
);
3217 if (!band
->children
)
3223 isl_band_free(band
);
3227 /* Internal data structure used inside cmp_band and pw_multi_aff_extract_int.
3229 * r is set to a negative value if anything goes wrong.
3231 * c1 stores the result of extract_int.
3232 * c2 is a temporary value used inside cmp_band_in_ancestor.
3233 * t is a temporary value used inside extract_int.
3235 * first and equal are used inside extract_int.
3236 * first is set if we are looking at the first isl_multi_aff inside
3237 * the isl_union_pw_multi_aff.
3238 * equal is set if all the isl_multi_affs have been equal so far.
3240 struct isl_cmp_band_data
{
3251 /* Check if "ma" assigns a constant value.
3252 * Note that this function is only called on isl_multi_affs
3253 * with a single output dimension.
3255 * If "ma" assigns a constant value then we compare it to data->c1
3256 * or assign it to data->c1 if this is the first isl_multi_aff we consider.
3257 * If "ma" does not assign a constant value or if it assigns a value
3258 * that is different from data->c1, then we set data->equal to zero
3259 * and terminate the check.
3261 static int multi_aff_extract_int(__isl_take isl_set
*set
,
3262 __isl_take isl_multi_aff
*ma
, void *user
)
3265 struct isl_cmp_band_data
*data
= user
;
3267 aff
= isl_multi_aff_get_aff(ma
, 0);
3268 data
->r
= isl_aff_is_cst(aff
);
3269 if (data
->r
>= 0 && data
->r
) {
3270 isl_aff_get_constant(aff
, &data
->t
);
3272 isl_int_set(data
->c1
, data
->t
);
3274 } else if (!isl_int_eq(data
->c1
, data
->t
))
3276 } else if (data
->r
>= 0 && !data
->r
)
3281 isl_multi_aff_free(ma
);
3290 /* This function is called for each isl_pw_multi_aff in
3291 * the isl_union_pw_multi_aff checked by extract_int.
3292 * Check all the isl_multi_affs inside "pma".
3294 static int pw_multi_aff_extract_int(__isl_take isl_pw_multi_aff
*pma
,
3299 r
= isl_pw_multi_aff_foreach_piece(pma
, &multi_aff_extract_int
, user
);
3300 isl_pw_multi_aff_free(pma
);
3305 /* Check if "upma" assigns a single constant value to its domain.
3306 * If so, return 1 and store the result in data->c1.
3309 * A negative return value from isl_union_pw_multi_aff_foreach_pw_multi_aff
3310 * means that either an error occurred or that we have broken off the check
3311 * because we already know the result is going to be negative.
3312 * In the latter case, data->equal is set to zero.
3314 static int extract_int(__isl_keep isl_union_pw_multi_aff
*upma
,
3315 struct isl_cmp_band_data
*data
)
3320 if (isl_union_pw_multi_aff_foreach_pw_multi_aff(upma
,
3321 &pw_multi_aff_extract_int
, data
) < 0) {
3327 return !data
->first
&& data
->equal
;
3330 /* Compare "b1" and "b2" based on the parent schedule of their ancestor
3333 * If the parent of "ancestor" also has a single member, then we
3334 * first try to compare the two band based on the partial schedule
3337 * Otherwise, or if the result is inconclusive, we look at the partial schedule
3338 * of "ancestor" itself.
3339 * In particular, we specialize the parent schedule based
3340 * on the domains of the child schedules, check if both assign
3341 * a single constant value and, if so, compare the two constant values.
3342 * If the specialized parent schedules do not assign a constant value,
3343 * then they cannot be used to order the two bands and so in this case
3346 static int cmp_band_in_ancestor(__isl_keep isl_band
*b1
,
3347 __isl_keep isl_band
*b2
, struct isl_cmp_band_data
*data
,
3348 __isl_keep isl_band
*ancestor
)
3350 isl_union_pw_multi_aff
*upma
;
3351 isl_union_set
*domain
;
3357 if (ancestor
->parent
&& ancestor
->parent
->n
== 1) {
3358 r
= cmp_band_in_ancestor(b1
, b2
, data
, ancestor
->parent
);
3365 upma
= isl_union_pw_multi_aff_copy(b1
->pma
);
3366 domain
= isl_union_pw_multi_aff_domain(upma
);
3367 upma
= isl_union_pw_multi_aff_copy(ancestor
->pma
);
3368 upma
= isl_union_pw_multi_aff_intersect_domain(upma
, domain
);
3369 r
= extract_int(upma
, data
);
3370 isl_union_pw_multi_aff_free(upma
);
3377 isl_int_set(data
->c2
, data
->c1
);
3379 upma
= isl_union_pw_multi_aff_copy(b2
->pma
);
3380 domain
= isl_union_pw_multi_aff_domain(upma
);
3381 upma
= isl_union_pw_multi_aff_copy(ancestor
->pma
);
3382 upma
= isl_union_pw_multi_aff_intersect_domain(upma
, domain
);
3383 r
= extract_int(upma
, data
);
3384 isl_union_pw_multi_aff_free(upma
);
3391 return isl_int_cmp(data
->c2
, data
->c1
);
3394 /* Compare "a" and "b" based on the parent schedule of their parent.
3396 static int cmp_band(const void *a
, const void *b
, void *user
)
3398 isl_band
*b1
= *(isl_band
* const *) a
;
3399 isl_band
*b2
= *(isl_band
* const *) b
;
3400 struct isl_cmp_band_data
*data
= user
;
3402 return cmp_band_in_ancestor(b1
, b2
, data
, b1
->parent
);
3405 /* Sort the elements in "list" based on the partial schedules of its parent
3406 * (and ancestors). In particular if the parent assigns constant values
3407 * to the domains of the bands in "list", then the elements are sorted
3408 * according to that order.
3409 * This order should be a more "natural" order for the user, but otherwise
3410 * shouldn't have any effect.
3411 * If we would be constructing an isl_band forest directly in
3412 * isl_union_set_compute_schedule then there wouldn't be any need
3413 * for a reordering, since the children would be added to the list
3414 * in their natural order automatically.
3416 * If there is only one element in the list, then there is no need to sort
3418 * If the partial schedule of the parent has more than one member
3419 * (or if there is no parent), then it's
3420 * defnitely not assigning constant values to the different children in
3421 * the list and so we wouldn't be able to use it to sort the list.
3423 static __isl_give isl_band_list
*sort_band_list(__isl_take isl_band_list
*list
,
3424 __isl_keep isl_band
*parent
)
3426 struct isl_cmp_band_data data
;
3432 if (!parent
|| parent
->n
!= 1)
3436 isl_int_init(data
.c1
);
3437 isl_int_init(data
.c2
);
3438 isl_int_init(data
.t
);
3439 isl_sort(list
->p
, list
->n
, sizeof(list
->p
[0]), &cmp_band
, &data
);
3441 list
= isl_band_list_free(list
);
3442 isl_int_clear(data
.c1
);
3443 isl_int_clear(data
.c2
);
3444 isl_int_clear(data
.t
);
3449 /* Construct a list of bands that start at the same position (with
3450 * sequence number band_nr) in the schedules of the nodes that
3451 * were active in the parent band.
3453 * A separate isl_band structure is created for each band_id
3454 * and for each node that does not have a band with sequence
3455 * number band_nr. In the latter case, a band without members
3457 * This ensures that if a band has any children, then each node
3458 * that was active in the band is active in exactly one of the children.
3460 static __isl_give isl_band_list
*construct_band_list(
3461 __isl_keep isl_schedule
*schedule
, __isl_keep isl_band
*parent
,
3462 int band_nr
, int *parent_active
, int n_active
)
3465 isl_ctx
*ctx
= isl_schedule_get_ctx(schedule
);
3468 isl_band_list
*list
;
3471 for (i
= 0; i
< n_active
; ++i
) {
3472 for (j
= 0; j
< schedule
->n
; ++j
) {
3473 if (!parent_active
[j
])
3475 if (schedule
->node
[j
].n_band
<= band_nr
)
3477 if (schedule
->node
[j
].band_id
[band_nr
] == i
) {
3483 for (j
= 0; j
< schedule
->n
; ++j
)
3484 if (schedule
->node
[j
].n_band
<= band_nr
)
3489 list
= isl_band_list_alloc(ctx
, n_band
);
3490 band
= construct_band(schedule
, parent
, band_nr
,
3491 parent_active
, n_active
);
3492 return isl_band_list_add(list
, band
);
3495 active
= isl_alloc_array(ctx
, int, schedule
->n
);
3496 if (schedule
->n
&& !active
)
3499 list
= isl_band_list_alloc(ctx
, n_band
);
3501 for (i
= 0; i
< n_active
; ++i
) {
3505 for (j
= 0; j
< schedule
->n
; ++j
) {
3506 active
[j
] = parent_active
[j
] &&
3507 schedule
->node
[j
].n_band
> band_nr
&&
3508 schedule
->node
[j
].band_id
[band_nr
] == i
;
3515 band
= construct_band(schedule
, parent
, band_nr
, active
, n
);
3517 list
= isl_band_list_add(list
, band
);
3519 for (i
= 0; i
< schedule
->n
; ++i
) {
3521 if (!parent_active
[i
])
3523 if (schedule
->node
[i
].n_band
> band_nr
)
3525 for (j
= 0; j
< schedule
->n
; ++j
)
3527 band
= construct_band(schedule
, parent
, band_nr
, active
, 1);
3528 list
= isl_band_list_add(list
, band
);
3533 list
= sort_band_list(list
, parent
);
3538 /* Construct a band forest representation of the schedule and
3539 * return the list of roots.
3541 static __isl_give isl_band_list
*construct_forest(
3542 __isl_keep isl_schedule
*schedule
)
3545 isl_ctx
*ctx
= isl_schedule_get_ctx(schedule
);
3546 isl_band_list
*forest
;
3549 active
= isl_alloc_array(ctx
, int, schedule
->n
);
3550 if (schedule
->n
&& !active
)
3553 for (i
= 0; i
< schedule
->n
; ++i
)
3556 forest
= construct_band_list(schedule
, NULL
, 0, active
, schedule
->n
);
3563 /* Return the roots of a band forest representation of the schedule.
3565 __isl_give isl_band_list
*isl_schedule_get_band_forest(
3566 __isl_keep isl_schedule
*schedule
)
3570 if (!schedule
->band_forest
)
3571 schedule
->band_forest
= construct_forest(schedule
);
3572 return isl_band_list_dup(schedule
->band_forest
);
3575 /* Call "fn" on each band in the schedule in depth-first post-order.
3577 int isl_schedule_foreach_band(__isl_keep isl_schedule
*sched
,
3578 int (*fn
)(__isl_keep isl_band
*band
, void *user
), void *user
)
3581 isl_band_list
*forest
;
3586 forest
= isl_schedule_get_band_forest(sched
);
3587 r
= isl_band_list_foreach_band(forest
, fn
, user
);
3588 isl_band_list_free(forest
);
3593 static __isl_give isl_printer
*print_band_list(__isl_take isl_printer
*p
,
3594 __isl_keep isl_band_list
*list
);
3596 static __isl_give isl_printer
*print_band(__isl_take isl_printer
*p
,
3597 __isl_keep isl_band
*band
)
3599 isl_band_list
*children
;
3601 p
= isl_printer_start_line(p
);
3602 p
= isl_printer_print_union_pw_multi_aff(p
, band
->pma
);
3603 p
= isl_printer_end_line(p
);
3605 if (!isl_band_has_children(band
))
3608 children
= isl_band_get_children(band
);
3610 p
= isl_printer_indent(p
, 4);
3611 p
= print_band_list(p
, children
);
3612 p
= isl_printer_indent(p
, -4);
3614 isl_band_list_free(children
);
3619 static __isl_give isl_printer
*print_band_list(__isl_take isl_printer
*p
,
3620 __isl_keep isl_band_list
*list
)
3624 n
= isl_band_list_n_band(list
);
3625 for (i
= 0; i
< n
; ++i
) {
3627 band
= isl_band_list_get_band(list
, i
);
3628 p
= print_band(p
, band
);
3629 isl_band_free(band
);
3635 __isl_give isl_printer
*isl_printer_print_schedule(__isl_take isl_printer
*p
,
3636 __isl_keep isl_schedule
*schedule
)
3638 isl_band_list
*forest
;
3640 forest
= isl_schedule_get_band_forest(schedule
);
3642 p
= print_band_list(p
, forest
);
3644 isl_band_list_free(forest
);
3649 void isl_schedule_dump(__isl_keep isl_schedule
*schedule
)
3651 isl_printer
*printer
;
3656 printer
= isl_printer_to_file(isl_schedule_get_ctx(schedule
), stderr
);
3657 printer
= isl_printer_print_schedule(printer
, schedule
);
3659 isl_printer_free(printer
);