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>
18 #include <isl/constraint.h>
19 #include <isl/schedule.h>
20 #include <isl_mat_private.h>
24 #include <isl_dim_map.h>
25 #include <isl_hmap_map_basic_set.h>
27 #include <isl_schedule_private.h>
28 #include <isl_band_private.h>
29 #include <isl_options_private.h>
30 #include <isl_tarjan.h>
33 * The scheduling algorithm implemented in this file was inspired by
34 * Bondhugula et al., "Automatic Transformations for Communication-Minimized
35 * Parallelization and Locality Optimization in the Polyhedral Model".
39 /* Internal information about a node that is used during the construction
41 * dim represents the space in which the domain lives
42 * sched is a matrix representation of the schedule being constructed
44 * sched_map is an isl_map representation of the same (partial) schedule
45 * sched_map may be NULL
46 * rank is the number of linearly independent rows in the linear part
48 * the columns of cmap represent a change of basis for the schedule
49 * coefficients; the first rank columns span the linear part of
51 * cinv is the inverse of cmap.
52 * start is the first variable in the LP problem in the sequences that
53 * represents the schedule coefficients of this node
54 * nvar is the dimension of the domain
55 * nparam is the number of parameters or 0 if we are not constructing
56 * a parametric schedule
58 * scc is the index of SCC (or WCC) this node belongs to
60 * band contains the band index for each of the rows of the schedule.
61 * band_id is used to differentiate between separate bands at the same
62 * level within the same parent band, i.e., bands that are separated
63 * by the parent band or bands that are independent of each other.
64 * zero contains a boolean for each of the rows of the schedule,
65 * indicating whether the corresponding scheduling dimension results
66 * in zero dependence distances within its band and with respect
67 * to the proximity edges.
69 struct isl_sched_node
{
87 static int node_has_dim(const void *entry
, const void *val
)
89 struct isl_sched_node
*node
= (struct isl_sched_node
*)entry
;
90 isl_space
*dim
= (isl_space
*)val
;
92 return isl_space_is_equal(node
->dim
, dim
);
95 /* An edge in the dependence graph. An edge may be used to
96 * ensure validity of the generated schedule, to minimize the dependence
99 * map is the dependence relation
100 * src is the source node
101 * dst is the sink node
102 * validity is set if the edge is used to ensure correctness
103 * proximity is set if the edge is used to minimize dependence distances
105 * For validity edges, start and end mark the sequence of inequality
106 * constraints in the LP problem that encode the validity constraint
107 * corresponding to this edge.
109 struct isl_sched_edge
{
112 struct isl_sched_node
*src
;
113 struct isl_sched_node
*dst
;
123 isl_edge_validity
= 0,
124 isl_edge_first
= isl_edge_validity
,
126 isl_edge_last
= isl_edge_proximity
129 /* Internal information about the dependence graph used during
130 * the construction of the schedule.
132 * intra_hmap is a cache, mapping dependence relations to their dual,
133 * for dependences from a node to itself
134 * inter_hmap is a cache, mapping dependence relations to their dual,
135 * for dependences between distinct nodes
137 * n is the number of nodes
138 * node is the list of nodes
139 * maxvar is the maximal number of variables over all nodes
140 * max_row is the allocated number of rows in the schedule
141 * n_row is the current (maximal) number of linearly independent
142 * rows in the node schedules
143 * n_total_row is the current number of rows in the node schedules
144 * n_band is the current number of completed bands
145 * band_start is the starting row in the node schedules of the current band
146 * root is set if this graph is the original dependence graph,
147 * without any splitting
149 * sorted contains a list of node indices sorted according to the
150 * SCC to which a node belongs
152 * n_edge is the number of edges
153 * edge is the list of edges
154 * max_edge contains the maximal number of edges of each type;
155 * in particular, it contains the number of edges in the inital graph.
156 * edge_table contains pointers into the edge array, hashed on the source
157 * and sink spaces; there is one such table for each type;
158 * a given edge may be referenced from more than one table
159 * if the corresponding relation appears in more than of the
160 * sets of dependences
162 * node_table contains pointers into the node array, hashed on the space
164 * region contains a list of variable sequences that should be non-trivial
166 * lp contains the (I)LP problem used to obtain new schedule rows
168 * src_scc and dst_scc are the source and sink SCCs of an edge with
169 * conflicting constraints
171 * scc represents the number of components
173 struct isl_sched_graph
{
174 isl_hmap_map_basic_set
*intra_hmap
;
175 isl_hmap_map_basic_set
*inter_hmap
;
177 struct isl_sched_node
*node
;
191 struct isl_sched_edge
*edge
;
193 int max_edge
[isl_edge_last
+ 1];
194 struct isl_hash_table
*edge_table
[isl_edge_last
+ 1];
196 struct isl_hash_table
*node_table
;
197 struct isl_region
*region
;
207 /* Initialize node_table based on the list of nodes.
209 static int graph_init_table(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
213 graph
->node_table
= isl_hash_table_alloc(ctx
, graph
->n
);
214 if (!graph
->node_table
)
217 for (i
= 0; i
< graph
->n
; ++i
) {
218 struct isl_hash_table_entry
*entry
;
221 hash
= isl_space_get_hash(graph
->node
[i
].dim
);
222 entry
= isl_hash_table_find(ctx
, graph
->node_table
, hash
,
224 graph
->node
[i
].dim
, 1);
227 entry
->data
= &graph
->node
[i
];
233 /* Return a pointer to the node that lives within the given space,
234 * or NULL if there is no such node.
236 static struct isl_sched_node
*graph_find_node(isl_ctx
*ctx
,
237 struct isl_sched_graph
*graph
, __isl_keep isl_space
*dim
)
239 struct isl_hash_table_entry
*entry
;
242 hash
= isl_space_get_hash(dim
);
243 entry
= isl_hash_table_find(ctx
, graph
->node_table
, hash
,
244 &node_has_dim
, dim
, 0);
246 return entry
? entry
->data
: NULL
;
249 static int edge_has_src_and_dst(const void *entry
, const void *val
)
251 const struct isl_sched_edge
*edge
= entry
;
252 const struct isl_sched_edge
*temp
= val
;
254 return edge
->src
== temp
->src
&& edge
->dst
== temp
->dst
;
257 /* Add the given edge to graph->edge_table[type].
259 static int graph_edge_table_add(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
260 enum isl_edge_type type
, struct isl_sched_edge
*edge
)
262 struct isl_hash_table_entry
*entry
;
265 hash
= isl_hash_init();
266 hash
= isl_hash_builtin(hash
, edge
->src
);
267 hash
= isl_hash_builtin(hash
, edge
->dst
);
268 entry
= isl_hash_table_find(ctx
, graph
->edge_table
[type
], hash
,
269 &edge_has_src_and_dst
, edge
, 1);
277 /* Allocate the edge_tables based on the maximal number of edges of
280 static int graph_init_edge_tables(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
284 for (i
= 0; i
<= isl_edge_last
; ++i
) {
285 graph
->edge_table
[i
] = isl_hash_table_alloc(ctx
,
287 if (!graph
->edge_table
[i
])
294 /* If graph->edge_table[type] contains an edge from the given source
295 * to the given destination, then return the hash table entry of this edge.
296 * Otherwise, return NULL.
298 static struct isl_hash_table_entry
*graph_find_edge_entry(
299 struct isl_sched_graph
*graph
,
300 enum isl_edge_type type
,
301 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
303 isl_ctx
*ctx
= isl_space_get_ctx(src
->dim
);
305 struct isl_sched_edge temp
= { .src
= src
, .dst
= dst
};
307 hash
= isl_hash_init();
308 hash
= isl_hash_builtin(hash
, temp
.src
);
309 hash
= isl_hash_builtin(hash
, temp
.dst
);
310 return isl_hash_table_find(ctx
, graph
->edge_table
[type
], hash
,
311 &edge_has_src_and_dst
, &temp
, 0);
315 /* If graph->edge_table[type] contains an edge from the given source
316 * to the given destination, then return this edge.
317 * Otherwise, return NULL.
319 static struct isl_sched_edge
*graph_find_edge(struct isl_sched_graph
*graph
,
320 enum isl_edge_type type
,
321 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
323 struct isl_hash_table_entry
*entry
;
325 entry
= graph_find_edge_entry(graph
, type
, src
, dst
);
332 /* Check whether the dependence graph has an edge of the given type
333 * between the given two nodes.
335 static int graph_has_edge(struct isl_sched_graph
*graph
,
336 enum isl_edge_type type
,
337 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
339 struct isl_sched_edge
*edge
;
342 edge
= graph_find_edge(graph
, type
, src
, dst
);
346 empty
= isl_map_plain_is_empty(edge
->map
);
353 /* If there is an edge from the given source to the given destination
354 * of any type then return this edge.
355 * Otherwise, return NULL.
357 static struct isl_sched_edge
*graph_find_any_edge(struct isl_sched_graph
*graph
,
358 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
360 enum isl_edge_type i
;
361 struct isl_sched_edge
*edge
;
363 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
364 edge
= graph_find_edge(graph
, i
, src
, dst
);
372 /* Remove the given edge from all the edge_tables that refer to it.
374 static void graph_remove_edge(struct isl_sched_graph
*graph
,
375 struct isl_sched_edge
*edge
)
377 isl_ctx
*ctx
= isl_map_get_ctx(edge
->map
);
378 enum isl_edge_type i
;
380 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
381 struct isl_hash_table_entry
*entry
;
383 entry
= graph_find_edge_entry(graph
, i
, edge
->src
, edge
->dst
);
386 if (entry
->data
!= edge
)
388 isl_hash_table_remove(ctx
, graph
->edge_table
[i
], entry
);
392 /* Check whether the dependence graph has any edge
393 * between the given two nodes.
395 static int graph_has_any_edge(struct isl_sched_graph
*graph
,
396 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
398 enum isl_edge_type i
;
401 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
402 r
= graph_has_edge(graph
, i
, src
, dst
);
410 /* Check whether the dependence graph has a validity edge
411 * between the given two nodes.
413 static int graph_has_validity_edge(struct isl_sched_graph
*graph
,
414 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
416 return graph_has_edge(graph
, isl_edge_validity
, src
, dst
);
419 static int graph_alloc(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
420 int n_node
, int n_edge
)
425 graph
->n_edge
= n_edge
;
426 graph
->node
= isl_calloc_array(ctx
, struct isl_sched_node
, graph
->n
);
427 graph
->sorted
= isl_calloc_array(ctx
, int, graph
->n
);
428 graph
->region
= isl_alloc_array(ctx
, struct isl_region
, graph
->n
);
429 graph
->edge
= isl_calloc_array(ctx
,
430 struct isl_sched_edge
, graph
->n_edge
);
432 graph
->intra_hmap
= isl_hmap_map_basic_set_alloc(ctx
, 2 * n_edge
);
433 graph
->inter_hmap
= isl_hmap_map_basic_set_alloc(ctx
, 2 * n_edge
);
435 if (!graph
->node
|| !graph
->region
|| (graph
->n_edge
&& !graph
->edge
) ||
439 for(i
= 0; i
< graph
->n
; ++i
)
440 graph
->sorted
[i
] = i
;
445 static void graph_free(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
449 isl_hmap_map_basic_set_free(ctx
, graph
->intra_hmap
);
450 isl_hmap_map_basic_set_free(ctx
, 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
);
468 for (i
= 0; i
< graph
->n_edge
; ++i
)
469 isl_map_free(graph
->edge
[i
].map
);
472 for (i
= 0; i
<= isl_edge_last
; ++i
)
473 isl_hash_table_free(ctx
, graph
->edge_table
[i
]);
474 isl_hash_table_free(ctx
, graph
->node_table
);
475 isl_basic_set_free(graph
->lp
);
478 /* For each "set" on which this function is called, increment
479 * graph->n by one and update graph->maxvar.
481 static int init_n_maxvar(__isl_take isl_set
*set
, void *user
)
483 struct isl_sched_graph
*graph
= user
;
484 int nvar
= isl_set_dim(set
, isl_dim_set
);
487 if (nvar
> graph
->maxvar
)
488 graph
->maxvar
= nvar
;
495 /* Compute the number of rows that should be allocated for the schedule.
496 * The graph can be split at most "n - 1" times, there can be at most
497 * two rows for each dimension in the iteration domains (in particular,
498 * we usually have one row, but it may be split by split_scaled),
499 * and there can be one extra row for ordering the statements.
500 * Note that if we have actually split "n - 1" times, then no ordering
501 * is needed, so in principle we could use "graph->n + 2 * graph->maxvar - 1".
503 static int compute_max_row(struct isl_sched_graph
*graph
,
504 __isl_keep isl_union_set
*domain
)
508 if (isl_union_set_foreach_set(domain
, &init_n_maxvar
, graph
) < 0)
510 graph
->max_row
= graph
->n
+ 2 * graph
->maxvar
;
515 /* Add a new node to the graph representing the given set.
517 static int extract_node(__isl_take isl_set
*set
, void *user
)
523 struct isl_sched_graph
*graph
= user
;
524 int *band
, *band_id
, *zero
;
526 ctx
= isl_set_get_ctx(set
);
527 dim
= isl_set_get_space(set
);
529 nvar
= isl_space_dim(dim
, isl_dim_set
);
530 nparam
= isl_space_dim(dim
, isl_dim_param
);
531 if (!ctx
->opt
->schedule_parametric
)
533 sched
= isl_mat_alloc(ctx
, 0, 1 + nparam
+ nvar
);
534 graph
->node
[graph
->n
].dim
= dim
;
535 graph
->node
[graph
->n
].nvar
= nvar
;
536 graph
->node
[graph
->n
].nparam
= nparam
;
537 graph
->node
[graph
->n
].sched
= sched
;
538 graph
->node
[graph
->n
].sched_map
= NULL
;
539 band
= isl_alloc_array(ctx
, int, graph
->max_row
);
540 graph
->node
[graph
->n
].band
= band
;
541 band_id
= isl_calloc_array(ctx
, int, graph
->max_row
);
542 graph
->node
[graph
->n
].band_id
= band_id
;
543 zero
= isl_calloc_array(ctx
, int, graph
->max_row
);
544 graph
->node
[graph
->n
].zero
= zero
;
547 if (!sched
|| (graph
->max_row
&& (!band
|| !band_id
|| !zero
)))
553 struct isl_extract_edge_data
{
554 enum isl_edge_type type
;
555 struct isl_sched_graph
*graph
;
558 /* Add a new edge to the graph based on the given map
559 * and add it to data->graph->edge_table[data->type].
560 * If a dependence relation of a given type happens to be identical
561 * to one of the dependence relations of a type that was added before,
562 * then we don't create a new edge, but instead mark the original edge
563 * as also representing a dependence of the current type.
565 static int extract_edge(__isl_take isl_map
*map
, void *user
)
567 isl_ctx
*ctx
= isl_map_get_ctx(map
);
568 struct isl_extract_edge_data
*data
= user
;
569 struct isl_sched_graph
*graph
= data
->graph
;
570 struct isl_sched_node
*src
, *dst
;
572 struct isl_sched_edge
*edge
;
575 dim
= isl_space_domain(isl_map_get_space(map
));
576 src
= graph_find_node(ctx
, graph
, dim
);
578 dim
= isl_space_range(isl_map_get_space(map
));
579 dst
= graph_find_node(ctx
, graph
, dim
);
587 graph
->edge
[graph
->n_edge
].src
= src
;
588 graph
->edge
[graph
->n_edge
].dst
= dst
;
589 graph
->edge
[graph
->n_edge
].map
= map
;
590 if (data
->type
== isl_edge_validity
) {
591 graph
->edge
[graph
->n_edge
].validity
= 1;
592 graph
->edge
[graph
->n_edge
].proximity
= 0;
594 if (data
->type
== isl_edge_proximity
) {
595 graph
->edge
[graph
->n_edge
].validity
= 0;
596 graph
->edge
[graph
->n_edge
].proximity
= 1;
600 edge
= graph_find_any_edge(graph
, src
, dst
);
602 return graph_edge_table_add(ctx
, graph
, data
->type
,
603 &graph
->edge
[graph
->n_edge
- 1]);
604 is_equal
= isl_map_plain_is_equal(map
, edge
->map
);
608 return graph_edge_table_add(ctx
, graph
, data
->type
,
609 &graph
->edge
[graph
->n_edge
- 1]);
612 edge
->validity
|= graph
->edge
[graph
->n_edge
].validity
;
613 edge
->proximity
|= graph
->edge
[graph
->n_edge
].proximity
;
616 return graph_edge_table_add(ctx
, graph
, data
->type
, edge
);
619 /* Check whether there is any dependence from node[j] to node[i]
620 * or from node[i] to node[j].
622 static int node_follows_weak(int i
, int j
, void *user
)
625 struct isl_sched_graph
*graph
= user
;
627 f
= graph_has_any_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
630 return graph_has_any_edge(graph
, &graph
->node
[i
], &graph
->node
[j
]);
633 /* Check whether there is a validity dependence from node[j] to node[i],
634 * forcing node[i] to follow node[j].
636 static int node_follows_strong(int i
, int j
, void *user
)
638 struct isl_sched_graph
*graph
= user
;
640 return graph_has_validity_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
643 /* Use Tarjan's algorithm for computing the strongly connected components
644 * in the dependence graph (only validity edges).
645 * If weak is set, we consider the graph to be undirected and
646 * we effectively compute the (weakly) connected components.
647 * Additionally, we also consider other edges when weak is set.
649 static int detect_ccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
, int weak
)
652 struct isl_tarjan_graph
*g
= NULL
;
654 g
= isl_tarjan_graph_init(ctx
, graph
->n
,
655 weak
? &node_follows_weak
: &node_follows_strong
, graph
);
663 while (g
->order
[i
] != -1) {
664 graph
->node
[g
->order
[i
]].scc
= graph
->scc
;
672 isl_tarjan_graph_free(g
);
677 /* Apply Tarjan's algorithm to detect the strongly connected components
678 * in the dependence graph.
680 static int detect_sccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
682 return detect_ccs(ctx
, graph
, 0);
685 /* Apply Tarjan's algorithm to detect the (weakly) connected components
686 * in the dependence graph.
688 static int detect_wccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
690 return detect_ccs(ctx
, graph
, 1);
693 static int cmp_scc(const void *a
, const void *b
, void *data
)
695 struct isl_sched_graph
*graph
= data
;
699 return graph
->node
[*i1
].scc
- graph
->node
[*i2
].scc
;
702 /* Sort the elements of graph->sorted according to the corresponding SCCs.
704 static int sort_sccs(struct isl_sched_graph
*graph
)
706 return isl_sort(graph
->sorted
, graph
->n
, sizeof(int), &cmp_scc
, graph
);
709 /* Given a dependence relation R from a node to itself,
710 * construct the set of coefficients of valid constraints for elements
711 * in that dependence relation.
712 * In particular, the result contains tuples of coefficients
713 * c_0, c_n, c_x such that
715 * c_0 + c_n n + c_x y - c_x x >= 0 for each (x,y) in R
719 * c_0 + c_n n + c_x d >= 0 for each d in delta R = { y - x | (x,y) in R }
721 * We choose here to compute the dual of delta R.
722 * Alternatively, we could have computed the dual of R, resulting
723 * in a set of tuples c_0, c_n, c_x, c_y, and then
724 * plugged in (c_0, c_n, c_x, -c_x).
726 static __isl_give isl_basic_set
*intra_coefficients(
727 struct isl_sched_graph
*graph
, __isl_take isl_map
*map
)
729 isl_ctx
*ctx
= isl_map_get_ctx(map
);
733 if (isl_hmap_map_basic_set_has(ctx
, graph
->intra_hmap
, map
))
734 return isl_hmap_map_basic_set_get(ctx
, graph
->intra_hmap
, map
);
736 delta
= isl_set_remove_divs(isl_map_deltas(isl_map_copy(map
)));
737 coef
= isl_set_coefficients(delta
);
738 isl_hmap_map_basic_set_set(ctx
, graph
->intra_hmap
, map
,
739 isl_basic_set_copy(coef
));
744 /* Given a dependence relation R, * construct the set of coefficients
745 * of valid constraints for elements in that dependence relation.
746 * In particular, the result contains tuples of coefficients
747 * c_0, c_n, c_x, c_y such that
749 * c_0 + c_n n + c_x x + c_y y >= 0 for each (x,y) in R
752 static __isl_give isl_basic_set
*inter_coefficients(
753 struct isl_sched_graph
*graph
, __isl_take isl_map
*map
)
755 isl_ctx
*ctx
= isl_map_get_ctx(map
);
759 if (isl_hmap_map_basic_set_has(ctx
, graph
->inter_hmap
, map
))
760 return isl_hmap_map_basic_set_get(ctx
, graph
->inter_hmap
, map
);
762 set
= isl_map_wrap(isl_map_remove_divs(isl_map_copy(map
)));
763 coef
= isl_set_coefficients(set
);
764 isl_hmap_map_basic_set_set(ctx
, graph
->inter_hmap
, map
,
765 isl_basic_set_copy(coef
));
770 /* Add constraints to graph->lp that force validity for the given
771 * dependence from a node i to itself.
772 * That is, add constraints that enforce
774 * (c_i_0 + c_i_n n + c_i_x y) - (c_i_0 + c_i_n n + c_i_x x)
775 * = c_i_x (y - x) >= 0
777 * for each (x,y) in R.
778 * We obtain general constraints on coefficients (c_0, c_n, c_x)
779 * of valid constraints for (y - x) and then plug in (0, 0, c_i_x^+ - c_i_x^-),
780 * where c_i_x = c_i_x^+ - c_i_x^-, with c_i_x^+ and c_i_x^- non-negative.
781 * In graph->lp, the c_i_x^- appear before their c_i_x^+ counterpart.
783 * Actually, we do not construct constraints for the c_i_x themselves,
784 * but for the coefficients of c_i_x written as a linear combination
785 * of the columns in node->cmap.
787 static int add_intra_validity_constraints(struct isl_sched_graph
*graph
,
788 struct isl_sched_edge
*edge
)
791 isl_map
*map
= isl_map_copy(edge
->map
);
792 isl_ctx
*ctx
= isl_map_get_ctx(map
);
794 isl_dim_map
*dim_map
;
796 struct isl_sched_node
*node
= edge
->src
;
798 coef
= intra_coefficients(graph
, map
);
800 dim
= isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef
)));
802 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
803 isl_space_dim(dim
, isl_dim_set
), isl_mat_copy(node
->cmap
));
807 total
= isl_basic_set_total_dim(graph
->lp
);
808 dim_map
= isl_dim_map_alloc(ctx
, total
);
809 isl_dim_map_range(dim_map
, node
->start
+ 2 * node
->nparam
+ 1, 2,
810 isl_space_dim(dim
, isl_dim_set
), 1,
812 isl_dim_map_range(dim_map
, node
->start
+ 2 * node
->nparam
+ 2, 2,
813 isl_space_dim(dim
, isl_dim_set
), 1,
815 graph
->lp
= isl_basic_set_extend_constraints(graph
->lp
,
816 coef
->n_eq
, coef
->n_ineq
);
817 graph
->lp
= isl_basic_set_add_constraints_dim_map(graph
->lp
,
827 /* Add constraints to graph->lp that force validity for the given
828 * dependence from node i to node j.
829 * That is, add constraints that enforce
831 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) >= 0
833 * for each (x,y) in R.
834 * We obtain general constraints on coefficients (c_0, c_n, c_x, c_y)
835 * of valid constraints for R and then plug in
836 * (c_j_0 - c_i_0, c_j_n^+ - c_j_n^- - (c_i_n^+ - c_i_n^-),
837 * c_j_x^+ - c_j_x^- - (c_i_x^+ - c_i_x^-)),
838 * where c_* = c_*^+ - c_*^-, with c_*^+ and c_*^- non-negative.
839 * In graph->lp, the c_*^- appear before their c_*^+ counterpart.
841 * Actually, we do not construct constraints for the c_*_x themselves,
842 * but for the coefficients of c_*_x written as a linear combination
843 * of the columns in node->cmap.
845 static int add_inter_validity_constraints(struct isl_sched_graph
*graph
,
846 struct isl_sched_edge
*edge
)
849 isl_map
*map
= isl_map_copy(edge
->map
);
850 isl_ctx
*ctx
= isl_map_get_ctx(map
);
852 isl_dim_map
*dim_map
;
854 struct isl_sched_node
*src
= edge
->src
;
855 struct isl_sched_node
*dst
= edge
->dst
;
857 coef
= inter_coefficients(graph
, map
);
859 dim
= isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef
)));
861 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
862 isl_space_dim(dim
, isl_dim_set
), isl_mat_copy(src
->cmap
));
863 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
864 isl_space_dim(dim
, isl_dim_set
) + src
->nvar
,
865 isl_mat_copy(dst
->cmap
));
869 total
= isl_basic_set_total_dim(graph
->lp
);
870 dim_map
= isl_dim_map_alloc(ctx
, total
);
872 isl_dim_map_range(dim_map
, dst
->start
, 0, 0, 0, 1, 1);
873 isl_dim_map_range(dim_map
, dst
->start
+ 1, 2, 1, 1, dst
->nparam
, -1);
874 isl_dim_map_range(dim_map
, dst
->start
+ 2, 2, 1, 1, dst
->nparam
, 1);
875 isl_dim_map_range(dim_map
, dst
->start
+ 2 * dst
->nparam
+ 1, 2,
876 isl_space_dim(dim
, isl_dim_set
) + src
->nvar
, 1,
878 isl_dim_map_range(dim_map
, dst
->start
+ 2 * dst
->nparam
+ 2, 2,
879 isl_space_dim(dim
, isl_dim_set
) + src
->nvar
, 1,
882 isl_dim_map_range(dim_map
, src
->start
, 0, 0, 0, 1, -1);
883 isl_dim_map_range(dim_map
, src
->start
+ 1, 2, 1, 1, src
->nparam
, 1);
884 isl_dim_map_range(dim_map
, src
->start
+ 2, 2, 1, 1, src
->nparam
, -1);
885 isl_dim_map_range(dim_map
, src
->start
+ 2 * src
->nparam
+ 1, 2,
886 isl_space_dim(dim
, isl_dim_set
), 1,
888 isl_dim_map_range(dim_map
, src
->start
+ 2 * src
->nparam
+ 2, 2,
889 isl_space_dim(dim
, isl_dim_set
), 1,
892 edge
->start
= graph
->lp
->n_ineq
;
893 graph
->lp
= isl_basic_set_extend_constraints(graph
->lp
,
894 coef
->n_eq
, coef
->n_ineq
);
895 graph
->lp
= isl_basic_set_add_constraints_dim_map(graph
->lp
,
900 edge
->end
= graph
->lp
->n_ineq
;
908 /* Add constraints to graph->lp that bound the dependence distance for the given
909 * dependence from a node i to itself.
910 * If s = 1, we add the constraint
912 * c_i_x (y - x) <= m_0 + m_n n
916 * -c_i_x (y - x) + m_0 + m_n n >= 0
918 * for each (x,y) in R.
919 * If s = -1, we add the constraint
921 * -c_i_x (y - x) <= m_0 + m_n n
925 * c_i_x (y - x) + m_0 + m_n n >= 0
927 * for each (x,y) in R.
928 * We obtain general constraints on coefficients (c_0, c_n, c_x)
929 * of valid constraints for (y - x) and then plug in (m_0, m_n, -s * c_i_x),
930 * with each coefficient (except m_0) represented as a pair of non-negative
933 * Actually, we do not construct constraints for the c_i_x themselves,
934 * but for the coefficients of c_i_x written as a linear combination
935 * of the columns in node->cmap.
937 static int add_intra_proximity_constraints(struct isl_sched_graph
*graph
,
938 struct isl_sched_edge
*edge
, int s
)
942 isl_map
*map
= isl_map_copy(edge
->map
);
943 isl_ctx
*ctx
= isl_map_get_ctx(map
);
945 isl_dim_map
*dim_map
;
947 struct isl_sched_node
*node
= edge
->src
;
949 coef
= intra_coefficients(graph
, map
);
951 dim
= isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef
)));
953 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
954 isl_space_dim(dim
, isl_dim_set
), isl_mat_copy(node
->cmap
));
958 nparam
= isl_space_dim(node
->dim
, isl_dim_param
);
959 total
= isl_basic_set_total_dim(graph
->lp
);
960 dim_map
= isl_dim_map_alloc(ctx
, total
);
961 isl_dim_map_range(dim_map
, 1, 0, 0, 0, 1, 1);
962 isl_dim_map_range(dim_map
, 4, 2, 1, 1, nparam
, -1);
963 isl_dim_map_range(dim_map
, 5, 2, 1, 1, nparam
, 1);
964 isl_dim_map_range(dim_map
, node
->start
+ 2 * node
->nparam
+ 1, 2,
965 isl_space_dim(dim
, isl_dim_set
), 1,
967 isl_dim_map_range(dim_map
, node
->start
+ 2 * node
->nparam
+ 2, 2,
968 isl_space_dim(dim
, isl_dim_set
), 1,
970 graph
->lp
= isl_basic_set_extend_constraints(graph
->lp
,
971 coef
->n_eq
, coef
->n_ineq
);
972 graph
->lp
= isl_basic_set_add_constraints_dim_map(graph
->lp
,
982 /* Add constraints to graph->lp that bound the dependence distance for the given
983 * dependence from node i to node j.
984 * If s = 1, we add the constraint
986 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x)
991 * -(c_j_0 + c_j_n n + c_j_x y) + (c_i_0 + c_i_n n + c_i_x x) +
994 * for each (x,y) in R.
995 * If s = -1, we add the constraint
997 * -((c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x))
1002 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) +
1005 * for each (x,y) in R.
1006 * We obtain general constraints on coefficients (c_0, c_n, c_x, c_y)
1007 * of valid constraints for R and then plug in
1008 * (m_0 - s*c_j_0 + s*c_i_0, m_n - s*c_j_n + s*c_i_n,
1010 * with each coefficient (except m_0, c_j_0 and c_i_0)
1011 * represented as a pair of non-negative coefficients.
1013 * Actually, we do not construct constraints for the c_*_x themselves,
1014 * but for the coefficients of c_*_x written as a linear combination
1015 * of the columns in node->cmap.
1017 static int add_inter_proximity_constraints(struct isl_sched_graph
*graph
,
1018 struct isl_sched_edge
*edge
, int s
)
1022 isl_map
*map
= isl_map_copy(edge
->map
);
1023 isl_ctx
*ctx
= isl_map_get_ctx(map
);
1025 isl_dim_map
*dim_map
;
1026 isl_basic_set
*coef
;
1027 struct isl_sched_node
*src
= edge
->src
;
1028 struct isl_sched_node
*dst
= edge
->dst
;
1030 coef
= inter_coefficients(graph
, map
);
1032 dim
= isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef
)));
1034 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
1035 isl_space_dim(dim
, isl_dim_set
), isl_mat_copy(src
->cmap
));
1036 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
1037 isl_space_dim(dim
, isl_dim_set
) + src
->nvar
,
1038 isl_mat_copy(dst
->cmap
));
1042 nparam
= isl_space_dim(src
->dim
, isl_dim_param
);
1043 total
= isl_basic_set_total_dim(graph
->lp
);
1044 dim_map
= isl_dim_map_alloc(ctx
, total
);
1046 isl_dim_map_range(dim_map
, 1, 0, 0, 0, 1, 1);
1047 isl_dim_map_range(dim_map
, 4, 2, 1, 1, nparam
, -1);
1048 isl_dim_map_range(dim_map
, 5, 2, 1, 1, nparam
, 1);
1050 isl_dim_map_range(dim_map
, dst
->start
, 0, 0, 0, 1, -s
);
1051 isl_dim_map_range(dim_map
, dst
->start
+ 1, 2, 1, 1, dst
->nparam
, s
);
1052 isl_dim_map_range(dim_map
, dst
->start
+ 2, 2, 1, 1, dst
->nparam
, -s
);
1053 isl_dim_map_range(dim_map
, dst
->start
+ 2 * dst
->nparam
+ 1, 2,
1054 isl_space_dim(dim
, isl_dim_set
) + src
->nvar
, 1,
1056 isl_dim_map_range(dim_map
, dst
->start
+ 2 * dst
->nparam
+ 2, 2,
1057 isl_space_dim(dim
, isl_dim_set
) + src
->nvar
, 1,
1060 isl_dim_map_range(dim_map
, src
->start
, 0, 0, 0, 1, s
);
1061 isl_dim_map_range(dim_map
, src
->start
+ 1, 2, 1, 1, src
->nparam
, -s
);
1062 isl_dim_map_range(dim_map
, src
->start
+ 2, 2, 1, 1, src
->nparam
, s
);
1063 isl_dim_map_range(dim_map
, src
->start
+ 2 * src
->nparam
+ 1, 2,
1064 isl_space_dim(dim
, isl_dim_set
), 1,
1066 isl_dim_map_range(dim_map
, src
->start
+ 2 * src
->nparam
+ 2, 2,
1067 isl_space_dim(dim
, isl_dim_set
), 1,
1070 graph
->lp
= isl_basic_set_extend_constraints(graph
->lp
,
1071 coef
->n_eq
, coef
->n_ineq
);
1072 graph
->lp
= isl_basic_set_add_constraints_dim_map(graph
->lp
,
1074 isl_space_free(dim
);
1078 isl_space_free(dim
);
1082 static int add_all_validity_constraints(struct isl_sched_graph
*graph
)
1086 for (i
= 0; i
< graph
->n_edge
; ++i
) {
1087 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
1088 if (!edge
->validity
)
1090 if (edge
->src
!= edge
->dst
)
1092 if (add_intra_validity_constraints(graph
, edge
) < 0)
1096 for (i
= 0; i
< graph
->n_edge
; ++i
) {
1097 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
1098 if (!edge
->validity
)
1100 if (edge
->src
== edge
->dst
)
1102 if (add_inter_validity_constraints(graph
, edge
) < 0)
1109 /* Add constraints to graph->lp that bound the dependence distance
1110 * for all dependence relations.
1111 * If a given proximity dependence is identical to a validity
1112 * dependence, then the dependence distance is already bounded
1113 * from below (by zero), so we only need to bound the distance
1115 * Otherwise, we need to bound the distance both from above and from below.
1117 static int add_all_proximity_constraints(struct isl_sched_graph
*graph
)
1121 for (i
= 0; i
< graph
->n_edge
; ++i
) {
1122 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
1123 if (!edge
->proximity
)
1125 if (edge
->src
== edge
->dst
&&
1126 add_intra_proximity_constraints(graph
, edge
, 1) < 0)
1128 if (edge
->src
!= edge
->dst
&&
1129 add_inter_proximity_constraints(graph
, edge
, 1) < 0)
1133 if (edge
->src
== edge
->dst
&&
1134 add_intra_proximity_constraints(graph
, edge
, -1) < 0)
1136 if (edge
->src
!= edge
->dst
&&
1137 add_inter_proximity_constraints(graph
, edge
, -1) < 0)
1144 /* Compute a basis for the rows in the linear part of the schedule
1145 * and extend this basis to a full basis. The remaining rows
1146 * can then be used to force linear independence from the rows
1149 * In particular, given the schedule rows S, we compute
1154 * with H the Hermite normal form of S. That is, all but the
1155 * first rank columns of Q are zero and so each row in S is
1156 * a linear combination of the first rank rows of Q.
1157 * The matrix Q is then transposed because we will write the
1158 * coefficients of the next schedule row as a column vector s
1159 * and express this s as a linear combination s = Q c of the
1161 * Similarly, the matrix U is transposed such that we can
1162 * compute the coefficients c = U s from a schedule row s.
1164 static int node_update_cmap(struct isl_sched_node
*node
)
1167 int n_row
= isl_mat_rows(node
->sched
);
1169 H
= isl_mat_sub_alloc(node
->sched
, 0, n_row
,
1170 1 + node
->nparam
, node
->nvar
);
1172 H
= isl_mat_left_hermite(H
, 0, &U
, &Q
);
1173 isl_mat_free(node
->cmap
);
1174 isl_mat_free(node
->cinv
);
1175 node
->cmap
= isl_mat_transpose(Q
);
1176 node
->cinv
= isl_mat_transpose(U
);
1177 node
->rank
= isl_mat_initial_non_zero_cols(H
);
1180 if (!node
->cmap
|| !node
->cinv
|| node
->rank
< 0)
1185 /* Count the number of equality and inequality constraints
1186 * that will be added for the given map.
1187 * If carry is set, then we are counting the number of (validity)
1188 * constraints that will be added in setup_carry_lp and we count
1189 * each edge exactly once. Otherwise, we count as follows
1190 * validity -> 1 (>= 0)
1191 * validity+proximity -> 2 (>= 0 and upper bound)
1192 * proximity -> 2 (lower and upper bound)
1194 static int count_map_constraints(struct isl_sched_graph
*graph
,
1195 struct isl_sched_edge
*edge
, __isl_take isl_map
*map
,
1196 int *n_eq
, int *n_ineq
, int carry
)
1198 isl_basic_set
*coef
;
1199 int f
= carry
? 1 : edge
->proximity
? 2 : 1;
1201 if (carry
&& !edge
->validity
) {
1206 if (edge
->src
== edge
->dst
)
1207 coef
= intra_coefficients(graph
, map
);
1209 coef
= inter_coefficients(graph
, map
);
1212 *n_eq
+= f
* coef
->n_eq
;
1213 *n_ineq
+= f
* coef
->n_ineq
;
1214 isl_basic_set_free(coef
);
1219 /* Count the number of equality and inequality constraints
1220 * that will be added to the main lp problem.
1221 * We count as follows
1222 * validity -> 1 (>= 0)
1223 * validity+proximity -> 2 (>= 0 and upper bound)
1224 * proximity -> 2 (lower and upper bound)
1226 static int count_constraints(struct isl_sched_graph
*graph
,
1227 int *n_eq
, int *n_ineq
)
1231 *n_eq
= *n_ineq
= 0;
1232 for (i
= 0; i
< graph
->n_edge
; ++i
) {
1233 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
1234 isl_map
*map
= isl_map_copy(edge
->map
);
1236 if (count_map_constraints(graph
, edge
, map
,
1237 n_eq
, n_ineq
, 0) < 0)
1244 /* Add constraints that bound the values of the variable and parameter
1245 * coefficients of the schedule.
1247 * The maximal value of the coefficients is defined by the option
1248 * 'schedule_max_coefficient'.
1250 static int add_bound_coefficient_constraints(isl_ctx
*ctx
,
1251 struct isl_sched_graph
*graph
)
1254 int max_coefficient
;
1257 max_coefficient
= ctx
->opt
->schedule_max_coefficient
;
1259 if (max_coefficient
== -1)
1262 total
= isl_basic_set_total_dim(graph
->lp
);
1264 for (i
= 0; i
< graph
->n
; ++i
) {
1265 struct isl_sched_node
*node
= &graph
->node
[i
];
1266 for (j
= 0; j
< 2 * node
->nparam
+ 2 * node
->nvar
; ++j
) {
1268 k
= isl_basic_set_alloc_inequality(graph
->lp
);
1271 dim
= 1 + node
->start
+ 1 + j
;
1272 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
1273 isl_int_set_si(graph
->lp
->ineq
[k
][dim
], -1);
1274 isl_int_set_si(graph
->lp
->ineq
[k
][0], max_coefficient
);
1281 /* Construct an ILP problem for finding schedule coefficients
1282 * that result in non-negative, but small dependence distances
1283 * over all dependences.
1284 * In particular, the dependence distances over proximity edges
1285 * are bounded by m_0 + m_n n and we compute schedule coefficients
1286 * with small values (preferably zero) of m_n and m_0.
1288 * All variables of the ILP are non-negative. The actual coefficients
1289 * may be negative, so each coefficient is represented as the difference
1290 * of two non-negative variables. The negative part always appears
1291 * immediately before the positive part.
1292 * Other than that, the variables have the following order
1294 * - sum of positive and negative parts of m_n coefficients
1296 * - sum of positive and negative parts of all c_n coefficients
1297 * (unconstrained when computing non-parametric schedules)
1298 * - sum of positive and negative parts of all c_x coefficients
1299 * - positive and negative parts of m_n coefficients
1302 * - positive and negative parts of c_i_n (if parametric)
1303 * - positive and negative parts of c_i_x
1305 * The c_i_x are not represented directly, but through the columns of
1306 * node->cmap. That is, the computed values are for variable t_i_x
1307 * such that c_i_x = Q t_i_x with Q equal to node->cmap.
1309 * The constraints are those from the edges plus two or three equalities
1310 * to express the sums.
1312 * If force_zero is set, then we add equalities to ensure that
1313 * the sum of the m_n coefficients and m_0 are both zero.
1315 static int setup_lp(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
1326 int max_constant_term
;
1327 int max_coefficient
;
1329 max_constant_term
= ctx
->opt
->schedule_max_constant_term
;
1330 max_coefficient
= ctx
->opt
->schedule_max_coefficient
;
1332 parametric
= ctx
->opt
->schedule_parametric
;
1333 nparam
= isl_space_dim(graph
->node
[0].dim
, isl_dim_param
);
1335 total
= param_pos
+ 2 * nparam
;
1336 for (i
= 0; i
< graph
->n
; ++i
) {
1337 struct isl_sched_node
*node
= &graph
->node
[graph
->sorted
[i
]];
1338 if (node_update_cmap(node
) < 0)
1340 node
->start
= total
;
1341 total
+= 1 + 2 * (node
->nparam
+ node
->nvar
);
1344 if (count_constraints(graph
, &n_eq
, &n_ineq
) < 0)
1347 dim
= isl_space_set_alloc(ctx
, 0, total
);
1348 isl_basic_set_free(graph
->lp
);
1349 n_eq
+= 2 + parametric
+ force_zero
;
1350 if (max_constant_term
!= -1)
1352 if (max_coefficient
!= -1)
1353 for (i
= 0; i
< graph
->n
; ++i
)
1354 n_ineq
+= 2 * graph
->node
[i
].nparam
+
1355 2 * graph
->node
[i
].nvar
;
1357 graph
->lp
= isl_basic_set_alloc_space(dim
, 0, n_eq
, n_ineq
);
1359 k
= isl_basic_set_alloc_equality(graph
->lp
);
1362 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
1364 isl_int_set_si(graph
->lp
->eq
[k
][1], -1);
1365 for (i
= 0; i
< 2 * nparam
; ++i
)
1366 isl_int_set_si(graph
->lp
->eq
[k
][1 + param_pos
+ i
], 1);
1369 k
= isl_basic_set_alloc_equality(graph
->lp
);
1372 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
1373 isl_int_set_si(graph
->lp
->eq
[k
][2], -1);
1377 k
= isl_basic_set_alloc_equality(graph
->lp
);
1380 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
1381 isl_int_set_si(graph
->lp
->eq
[k
][3], -1);
1382 for (i
= 0; i
< graph
->n
; ++i
) {
1383 int pos
= 1 + graph
->node
[i
].start
+ 1;
1385 for (j
= 0; j
< 2 * graph
->node
[i
].nparam
; ++j
)
1386 isl_int_set_si(graph
->lp
->eq
[k
][pos
+ j
], 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
][4], -1);
1395 for (i
= 0; i
< graph
->n
; ++i
) {
1396 struct isl_sched_node
*node
= &graph
->node
[i
];
1397 int pos
= 1 + node
->start
+ 1 + 2 * node
->nparam
;
1399 for (j
= 0; j
< 2 * node
->nvar
; ++j
)
1400 isl_int_set_si(graph
->lp
->eq
[k
][pos
+ j
], 1);
1403 if (max_constant_term
!= -1)
1404 for (i
= 0; i
< graph
->n
; ++i
) {
1405 struct isl_sched_node
*node
= &graph
->node
[i
];
1406 k
= isl_basic_set_alloc_inequality(graph
->lp
);
1409 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
1410 isl_int_set_si(graph
->lp
->ineq
[k
][1 + node
->start
], -1);
1411 isl_int_set_si(graph
->lp
->ineq
[k
][0], max_constant_term
);
1414 if (add_bound_coefficient_constraints(ctx
, graph
) < 0)
1416 if (add_all_validity_constraints(graph
) < 0)
1418 if (add_all_proximity_constraints(graph
) < 0)
1424 /* Analyze the conflicting constraint found by
1425 * isl_tab_basic_set_non_trivial_lexmin. If it corresponds to the validity
1426 * constraint of one of the edges between distinct nodes, living, moreover
1427 * in distinct SCCs, then record the source and sink SCC as this may
1428 * be a good place to cut between SCCs.
1430 static int check_conflict(int con
, void *user
)
1433 struct isl_sched_graph
*graph
= user
;
1435 if (graph
->src_scc
>= 0)
1438 con
-= graph
->lp
->n_eq
;
1440 if (con
>= graph
->lp
->n_ineq
)
1443 for (i
= 0; i
< graph
->n_edge
; ++i
) {
1444 if (!graph
->edge
[i
].validity
)
1446 if (graph
->edge
[i
].src
== graph
->edge
[i
].dst
)
1448 if (graph
->edge
[i
].src
->scc
== graph
->edge
[i
].dst
->scc
)
1450 if (graph
->edge
[i
].start
> con
)
1452 if (graph
->edge
[i
].end
<= con
)
1454 graph
->src_scc
= graph
->edge
[i
].src
->scc
;
1455 graph
->dst_scc
= graph
->edge
[i
].dst
->scc
;
1461 /* Check whether the next schedule row of the given node needs to be
1462 * non-trivial. Lower-dimensional domains may have some trivial rows,
1463 * but as soon as the number of remaining required non-trivial rows
1464 * is as large as the number or remaining rows to be computed,
1465 * all remaining rows need to be non-trivial.
1467 static int needs_row(struct isl_sched_graph
*graph
, struct isl_sched_node
*node
)
1469 return node
->nvar
- node
->rank
>= graph
->maxvar
- graph
->n_row
;
1472 /* Solve the ILP problem constructed in setup_lp.
1473 * For each node such that all the remaining rows of its schedule
1474 * need to be non-trivial, we construct a non-triviality region.
1475 * This region imposes that the next row is independent of previous rows.
1476 * In particular the coefficients c_i_x are represented by t_i_x
1477 * variables with c_i_x = Q t_i_x and Q a unimodular matrix such that
1478 * its first columns span the rows of the previously computed part
1479 * of the schedule. The non-triviality region enforces that at least
1480 * one of the remaining components of t_i_x is non-zero, i.e.,
1481 * that the new schedule row depends on at least one of the remaining
1484 static __isl_give isl_vec
*solve_lp(struct isl_sched_graph
*graph
)
1490 for (i
= 0; i
< graph
->n
; ++i
) {
1491 struct isl_sched_node
*node
= &graph
->node
[i
];
1492 int skip
= node
->rank
;
1493 graph
->region
[i
].pos
= node
->start
+ 1 + 2*(node
->nparam
+skip
);
1494 if (needs_row(graph
, node
))
1495 graph
->region
[i
].len
= 2 * (node
->nvar
- skip
);
1497 graph
->region
[i
].len
= 0;
1499 lp
= isl_basic_set_copy(graph
->lp
);
1500 sol
= isl_tab_basic_set_non_trivial_lexmin(lp
, 2, graph
->n
,
1501 graph
->region
, &check_conflict
, graph
);
1505 /* Update the schedules of all nodes based on the given solution
1506 * of the LP problem.
1507 * The new row is added to the current band.
1508 * All possibly negative coefficients are encoded as a difference
1509 * of two non-negative variables, so we need to perform the subtraction
1510 * here. Moreover, if use_cmap is set, then the solution does
1511 * not refer to the actual coefficients c_i_x, but instead to variables
1512 * t_i_x such that c_i_x = Q t_i_x and Q is equal to node->cmap.
1513 * In this case, we then also need to perform this multiplication
1514 * to obtain the values of c_i_x.
1516 * If check_zero is set, then the first two coordinates of sol are
1517 * assumed to correspond to the dependence distance. If these two
1518 * coordinates are zero, then the corresponding scheduling dimension
1519 * is marked as being zero distance.
1521 static int update_schedule(struct isl_sched_graph
*graph
,
1522 __isl_take isl_vec
*sol
, int use_cmap
, int check_zero
)
1526 isl_vec
*csol
= NULL
;
1531 isl_die(sol
->ctx
, isl_error_internal
,
1532 "no solution found", goto error
);
1533 if (graph
->n_total_row
>= graph
->max_row
)
1534 isl_die(sol
->ctx
, isl_error_internal
,
1535 "too many schedule rows", goto error
);
1538 zero
= isl_int_is_zero(sol
->el
[1]) &&
1539 isl_int_is_zero(sol
->el
[2]);
1541 for (i
= 0; i
< graph
->n
; ++i
) {
1542 struct isl_sched_node
*node
= &graph
->node
[i
];
1543 int pos
= node
->start
;
1544 int row
= isl_mat_rows(node
->sched
);
1547 csol
= isl_vec_alloc(sol
->ctx
, node
->nvar
);
1551 isl_map_free(node
->sched_map
);
1552 node
->sched_map
= NULL
;
1553 node
->sched
= isl_mat_add_rows(node
->sched
, 1);
1556 node
->sched
= isl_mat_set_element(node
->sched
, row
, 0,
1558 for (j
= 0; j
< node
->nparam
+ node
->nvar
; ++j
)
1559 isl_int_sub(sol
->el
[1 + pos
+ 1 + 2 * j
+ 1],
1560 sol
->el
[1 + pos
+ 1 + 2 * j
+ 1],
1561 sol
->el
[1 + pos
+ 1 + 2 * j
]);
1562 for (j
= 0; j
< node
->nparam
; ++j
)
1563 node
->sched
= isl_mat_set_element(node
->sched
,
1564 row
, 1 + j
, sol
->el
[1+pos
+1+2*j
+1]);
1565 for (j
= 0; j
< node
->nvar
; ++j
)
1566 isl_int_set(csol
->el
[j
],
1567 sol
->el
[1+pos
+1+2*(node
->nparam
+j
)+1]);
1569 csol
= isl_mat_vec_product(isl_mat_copy(node
->cmap
),
1573 for (j
= 0; j
< node
->nvar
; ++j
)
1574 node
->sched
= isl_mat_set_element(node
->sched
,
1575 row
, 1 + node
->nparam
+ j
, csol
->el
[j
]);
1576 node
->band
[graph
->n_total_row
] = graph
->n_band
;
1577 node
->zero
[graph
->n_total_row
] = zero
;
1583 graph
->n_total_row
++;
1592 /* Convert node->sched into a multi_aff and return this multi_aff.
1594 static __isl_give isl_multi_aff
*node_extract_schedule_multi_aff(
1595 struct isl_sched_node
*node
)
1599 isl_local_space
*ls
;
1605 nrow
= isl_mat_rows(node
->sched
);
1606 ncol
= isl_mat_cols(node
->sched
) - 1;
1607 space
= isl_space_from_domain(isl_space_copy(node
->dim
));
1608 space
= isl_space_add_dims(space
, isl_dim_out
, nrow
);
1609 ma
= isl_multi_aff_zero(space
);
1610 ls
= isl_local_space_from_space(isl_space_copy(node
->dim
));
1614 for (i
= 0; i
< nrow
; ++i
) {
1615 aff
= isl_aff_zero_on_domain(isl_local_space_copy(ls
));
1616 isl_mat_get_element(node
->sched
, i
, 0, &v
);
1617 aff
= isl_aff_set_constant(aff
, v
);
1618 for (j
= 0; j
< node
->nparam
; ++j
) {
1619 isl_mat_get_element(node
->sched
, i
, 1 + j
, &v
);
1620 aff
= isl_aff_set_coefficient(aff
, isl_dim_param
, j
, v
);
1622 for (j
= 0; j
< node
->nvar
; ++j
) {
1623 isl_mat_get_element(node
->sched
,
1624 i
, 1 + node
->nparam
+ j
, &v
);
1625 aff
= isl_aff_set_coefficient(aff
, isl_dim_in
, j
, v
);
1627 ma
= isl_multi_aff_set_aff(ma
, i
, aff
);
1632 isl_local_space_free(ls
);
1637 /* Convert node->sched into a map and return this map.
1639 * The result is cached in node->sched_map, which needs to be released
1640 * whenever node->sched is updated.
1642 static __isl_give isl_map
*node_extract_schedule(struct isl_sched_node
*node
)
1644 if (!node
->sched_map
) {
1647 ma
= node_extract_schedule_multi_aff(node
);
1648 node
->sched_map
= isl_map_from_multi_aff(ma
);
1651 return isl_map_copy(node
->sched_map
);
1654 /* Update the given dependence relation based on the current schedule.
1655 * That is, intersect the dependence relation with a map expressing
1656 * that source and sink are executed within the same iteration of
1657 * the current schedule.
1658 * This is not the most efficient way, but this shouldn't be a critical
1661 static __isl_give isl_map
*specialize(__isl_take isl_map
*map
,
1662 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
1664 isl_map
*src_sched
, *dst_sched
, *id
;
1666 src_sched
= node_extract_schedule(src
);
1667 dst_sched
= node_extract_schedule(dst
);
1668 id
= isl_map_apply_range(src_sched
, isl_map_reverse(dst_sched
));
1669 return isl_map_intersect(map
, id
);
1672 /* Update the dependence relations of all edges based on the current schedule.
1673 * If a dependence is carried completely by the current schedule, then
1674 * it is removed from the edge_tables. It is kept in the list of edges
1675 * as otherwise all edge_tables would have to be recomputed.
1677 static int update_edges(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
1681 for (i
= graph
->n_edge
- 1; i
>= 0; --i
) {
1682 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
1683 edge
->map
= specialize(edge
->map
, edge
->src
, edge
->dst
);
1687 if (isl_map_plain_is_empty(edge
->map
))
1688 graph_remove_edge(graph
, edge
);
1694 static void next_band(struct isl_sched_graph
*graph
)
1696 graph
->band_start
= graph
->n_total_row
;
1700 /* Topologically sort statements mapped to the same schedule iteration
1701 * and add a row to the schedule corresponding to this order.
1703 static int sort_statements(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
1710 if (update_edges(ctx
, graph
) < 0)
1713 if (graph
->n_edge
== 0)
1716 if (detect_sccs(ctx
, graph
) < 0)
1719 if (graph
->n_total_row
>= graph
->max_row
)
1720 isl_die(ctx
, isl_error_internal
,
1721 "too many schedule rows", return -1);
1723 for (i
= 0; i
< graph
->n
; ++i
) {
1724 struct isl_sched_node
*node
= &graph
->node
[i
];
1725 int row
= isl_mat_rows(node
->sched
);
1726 int cols
= isl_mat_cols(node
->sched
);
1728 isl_map_free(node
->sched_map
);
1729 node
->sched_map
= NULL
;
1730 node
->sched
= isl_mat_add_rows(node
->sched
, 1);
1733 node
->sched
= isl_mat_set_element_si(node
->sched
, row
, 0,
1735 for (j
= 1; j
< cols
; ++j
)
1736 node
->sched
= isl_mat_set_element_si(node
->sched
,
1738 node
->band
[graph
->n_total_row
] = graph
->n_band
;
1741 graph
->n_total_row
++;
1747 /* Construct an isl_schedule based on the computed schedule stored
1748 * in graph and with parameters specified by dim.
1750 static __isl_give isl_schedule
*extract_schedule(struct isl_sched_graph
*graph
,
1751 __isl_take isl_space
*dim
)
1755 isl_schedule
*sched
= NULL
;
1760 ctx
= isl_space_get_ctx(dim
);
1761 sched
= isl_calloc(ctx
, struct isl_schedule
,
1762 sizeof(struct isl_schedule
) +
1763 (graph
->n
- 1) * sizeof(struct isl_schedule_node
));
1768 sched
->n
= graph
->n
;
1769 sched
->n_band
= graph
->n_band
;
1770 sched
->n_total_row
= graph
->n_total_row
;
1772 for (i
= 0; i
< sched
->n
; ++i
) {
1774 int *band_end
, *band_id
, *zero
;
1776 sched
->node
[i
].sched
=
1777 node_extract_schedule_multi_aff(&graph
->node
[i
]);
1778 if (!sched
->node
[i
].sched
)
1781 sched
->node
[i
].n_band
= graph
->n_band
;
1782 if (graph
->n_band
== 0)
1785 band_end
= isl_alloc_array(ctx
, int, graph
->n_band
);
1786 band_id
= isl_alloc_array(ctx
, int, graph
->n_band
);
1787 zero
= isl_alloc_array(ctx
, int, graph
->n_total_row
);
1788 sched
->node
[i
].band_end
= band_end
;
1789 sched
->node
[i
].band_id
= band_id
;
1790 sched
->node
[i
].zero
= zero
;
1791 if (!band_end
|| !band_id
|| !zero
)
1794 for (r
= 0; r
< graph
->n_total_row
; ++r
)
1795 zero
[r
] = graph
->node
[i
].zero
[r
];
1796 for (r
= b
= 0; r
< graph
->n_total_row
; ++r
) {
1797 if (graph
->node
[i
].band
[r
] == b
)
1800 if (graph
->node
[i
].band
[r
] == -1)
1803 if (r
== graph
->n_total_row
)
1805 sched
->node
[i
].n_band
= b
;
1806 for (--b
; b
>= 0; --b
)
1807 band_id
[b
] = graph
->node
[i
].band_id
[b
];
1814 isl_space_free(dim
);
1815 isl_schedule_free(sched
);
1819 /* Copy nodes that satisfy node_pred from the src dependence graph
1820 * to the dst dependence graph.
1822 static int copy_nodes(struct isl_sched_graph
*dst
, struct isl_sched_graph
*src
,
1823 int (*node_pred
)(struct isl_sched_node
*node
, int data
), int data
)
1828 for (i
= 0; i
< src
->n
; ++i
) {
1829 if (!node_pred(&src
->node
[i
], data
))
1831 dst
->node
[dst
->n
].dim
= isl_space_copy(src
->node
[i
].dim
);
1832 dst
->node
[dst
->n
].nvar
= src
->node
[i
].nvar
;
1833 dst
->node
[dst
->n
].nparam
= src
->node
[i
].nparam
;
1834 dst
->node
[dst
->n
].sched
= isl_mat_copy(src
->node
[i
].sched
);
1835 dst
->node
[dst
->n
].sched_map
=
1836 isl_map_copy(src
->node
[i
].sched_map
);
1837 dst
->node
[dst
->n
].band
= src
->node
[i
].band
;
1838 dst
->node
[dst
->n
].band_id
= src
->node
[i
].band_id
;
1839 dst
->node
[dst
->n
].zero
= src
->node
[i
].zero
;
1846 /* Copy non-empty edges that satisfy edge_pred from the src dependence graph
1847 * to the dst dependence graph.
1848 * If the source or destination node of the edge is not in the destination
1849 * graph, then it must be a backward proximity edge and it should simply
1852 static int copy_edges(isl_ctx
*ctx
, struct isl_sched_graph
*dst
,
1853 struct isl_sched_graph
*src
,
1854 int (*edge_pred
)(struct isl_sched_edge
*edge
, int data
), int data
)
1857 enum isl_edge_type t
;
1860 for (i
= 0; i
< src
->n_edge
; ++i
) {
1861 struct isl_sched_edge
*edge
= &src
->edge
[i
];
1863 struct isl_sched_node
*dst_src
, *dst_dst
;
1865 if (!edge_pred(edge
, data
))
1868 if (isl_map_plain_is_empty(edge
->map
))
1871 dst_src
= graph_find_node(ctx
, dst
, edge
->src
->dim
);
1872 dst_dst
= graph_find_node(ctx
, dst
, edge
->dst
->dim
);
1873 if (!dst_src
|| !dst_dst
) {
1875 isl_die(ctx
, isl_error_internal
,
1876 "backward validity edge", return -1);
1880 map
= isl_map_copy(edge
->map
);
1882 dst
->edge
[dst
->n_edge
].src
= dst_src
;
1883 dst
->edge
[dst
->n_edge
].dst
= dst_dst
;
1884 dst
->edge
[dst
->n_edge
].map
= map
;
1885 dst
->edge
[dst
->n_edge
].validity
= edge
->validity
;
1886 dst
->edge
[dst
->n_edge
].proximity
= edge
->proximity
;
1889 for (t
= isl_edge_first
; t
<= isl_edge_last
; ++t
) {
1891 graph_find_edge(src
, t
, edge
->src
, edge
->dst
))
1893 if (graph_edge_table_add(ctx
, dst
, t
,
1894 &dst
->edge
[dst
->n_edge
- 1]) < 0)
1902 /* Given a "src" dependence graph that contains the nodes from "dst"
1903 * that satisfy node_pred, copy the schedule computed in "src"
1904 * for those nodes back to "dst".
1906 static int copy_schedule(struct isl_sched_graph
*dst
,
1907 struct isl_sched_graph
*src
,
1908 int (*node_pred
)(struct isl_sched_node
*node
, int data
), int data
)
1913 for (i
= 0; i
< dst
->n
; ++i
) {
1914 if (!node_pred(&dst
->node
[i
], data
))
1916 isl_mat_free(dst
->node
[i
].sched
);
1917 isl_map_free(dst
->node
[i
].sched_map
);
1918 dst
->node
[i
].sched
= isl_mat_copy(src
->node
[src
->n
].sched
);
1919 dst
->node
[i
].sched_map
=
1920 isl_map_copy(src
->node
[src
->n
].sched_map
);
1924 dst
->max_row
= src
->max_row
;
1925 dst
->n_total_row
= src
->n_total_row
;
1926 dst
->n_band
= src
->n_band
;
1931 /* Compute the maximal number of variables over all nodes.
1932 * This is the maximal number of linearly independent schedule
1933 * rows that we need to compute.
1934 * Just in case we end up in a part of the dependence graph
1935 * with only lower-dimensional domains, we make sure we will
1936 * compute the required amount of extra linearly independent rows.
1938 static int compute_maxvar(struct isl_sched_graph
*graph
)
1943 for (i
= 0; i
< graph
->n
; ++i
) {
1944 struct isl_sched_node
*node
= &graph
->node
[i
];
1947 if (node_update_cmap(node
) < 0)
1949 nvar
= node
->nvar
+ graph
->n_row
- node
->rank
;
1950 if (nvar
> graph
->maxvar
)
1951 graph
->maxvar
= nvar
;
1957 static int compute_schedule(isl_ctx
*ctx
, struct isl_sched_graph
*graph
);
1958 static int compute_schedule_wcc(isl_ctx
*ctx
, struct isl_sched_graph
*graph
);
1960 /* Compute a schedule for a subgraph of "graph". In particular, for
1961 * the graph composed of nodes that satisfy node_pred and edges that
1962 * that satisfy edge_pred. The caller should precompute the number
1963 * of nodes and edges that satisfy these predicates and pass them along
1964 * as "n" and "n_edge".
1965 * If the subgraph is known to consist of a single component, then wcc should
1966 * be set and then we call compute_schedule_wcc on the constructed subgraph.
1967 * Otherwise, we call compute_schedule, which will check whether the subgraph
1970 static int compute_sub_schedule(isl_ctx
*ctx
,
1971 struct isl_sched_graph
*graph
, int n
, int n_edge
,
1972 int (*node_pred
)(struct isl_sched_node
*node
, int data
),
1973 int (*edge_pred
)(struct isl_sched_edge
*edge
, int data
),
1976 struct isl_sched_graph split
= { 0 };
1979 if (graph_alloc(ctx
, &split
, n
, n_edge
) < 0)
1981 if (copy_nodes(&split
, graph
, node_pred
, data
) < 0)
1983 if (graph_init_table(ctx
, &split
) < 0)
1985 for (t
= 0; t
<= isl_edge_last
; ++t
)
1986 split
.max_edge
[t
] = graph
->max_edge
[t
];
1987 if (graph_init_edge_tables(ctx
, &split
) < 0)
1989 if (copy_edges(ctx
, &split
, graph
, edge_pred
, data
) < 0)
1991 split
.n_row
= graph
->n_row
;
1992 split
.max_row
= graph
->max_row
;
1993 split
.n_total_row
= graph
->n_total_row
;
1994 split
.n_band
= graph
->n_band
;
1995 split
.band_start
= graph
->band_start
;
1997 if (wcc
&& compute_schedule_wcc(ctx
, &split
) < 0)
1999 if (!wcc
&& compute_schedule(ctx
, &split
) < 0)
2002 copy_schedule(graph
, &split
, node_pred
, data
);
2004 graph_free(ctx
, &split
);
2007 graph_free(ctx
, &split
);
2011 static int node_scc_exactly(struct isl_sched_node
*node
, int scc
)
2013 return node
->scc
== scc
;
2016 static int node_scc_at_most(struct isl_sched_node
*node
, int scc
)
2018 return node
->scc
<= scc
;
2021 static int node_scc_at_least(struct isl_sched_node
*node
, int scc
)
2023 return node
->scc
>= scc
;
2026 static int edge_scc_exactly(struct isl_sched_edge
*edge
, int scc
)
2028 return edge
->src
->scc
== scc
&& edge
->dst
->scc
== scc
;
2031 static int edge_dst_scc_at_most(struct isl_sched_edge
*edge
, int scc
)
2033 return edge
->dst
->scc
<= scc
;
2036 static int edge_src_scc_at_least(struct isl_sched_edge
*edge
, int scc
)
2038 return edge
->src
->scc
>= scc
;
2041 /* Pad the schedules of all nodes with zero rows such that in the end
2042 * they all have graph->n_total_row rows.
2043 * The extra rows don't belong to any band, so they get assigned band number -1.
2045 static int pad_schedule(struct isl_sched_graph
*graph
)
2049 for (i
= 0; i
< graph
->n
; ++i
) {
2050 struct isl_sched_node
*node
= &graph
->node
[i
];
2051 int row
= isl_mat_rows(node
->sched
);
2052 if (graph
->n_total_row
> row
) {
2053 isl_map_free(node
->sched_map
);
2054 node
->sched_map
= NULL
;
2056 node
->sched
= isl_mat_add_zero_rows(node
->sched
,
2057 graph
->n_total_row
- row
);
2060 for (j
= row
; j
< graph
->n_total_row
; ++j
)
2067 /* Split the current graph into two parts and compute a schedule for each
2068 * part individually. In particular, one part consists of all SCCs up
2069 * to and including graph->src_scc, while the other part contains the other
2072 * The split is enforced in the schedule by constant rows with two different
2073 * values (0 and 1). These constant rows replace the previously computed rows
2074 * in the current band.
2075 * It would be possible to reuse them as the first rows in the next
2076 * band, but recomputing them may result in better rows as we are looking
2077 * at a smaller part of the dependence graph.
2078 * compute_split_schedule is only called when no zero-distance schedule row
2079 * could be found on the entire graph, so we wark the splitting row as
2080 * non zero-distance.
2082 * The band_id of the second group is set to n, where n is the number
2083 * of nodes in the first group. This ensures that the band_ids over
2084 * the two groups remain disjoint, even if either or both of the two
2085 * groups contain independent components.
2087 static int compute_split_schedule(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2089 int i
, j
, n
, e1
, e2
;
2090 int n_total_row
, orig_total_row
;
2091 int n_band
, orig_band
;
2094 if (graph
->n_total_row
>= graph
->max_row
)
2095 isl_die(ctx
, isl_error_internal
,
2096 "too many schedule rows", return -1);
2098 drop
= graph
->n_total_row
- graph
->band_start
;
2099 graph
->n_total_row
-= drop
;
2100 graph
->n_row
-= drop
;
2103 for (i
= 0; i
< graph
->n
; ++i
) {
2104 struct isl_sched_node
*node
= &graph
->node
[i
];
2105 int row
= isl_mat_rows(node
->sched
) - drop
;
2106 int cols
= isl_mat_cols(node
->sched
);
2107 int before
= node
->scc
<= graph
->src_scc
;
2112 isl_map_free(node
->sched_map
);
2113 node
->sched_map
= NULL
;
2114 node
->sched
= isl_mat_drop_rows(node
->sched
,
2115 graph
->band_start
, drop
);
2116 node
->sched
= isl_mat_add_rows(node
->sched
, 1);
2119 node
->sched
= isl_mat_set_element_si(node
->sched
, row
, 0,
2121 for (j
= 1; j
< cols
; ++j
)
2122 node
->sched
= isl_mat_set_element_si(node
->sched
,
2124 node
->band
[graph
->n_total_row
] = graph
->n_band
;
2125 node
->zero
[graph
->n_total_row
] = 0;
2129 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2130 if (graph
->edge
[i
].dst
->scc
<= graph
->src_scc
)
2132 if (graph
->edge
[i
].src
->scc
> graph
->src_scc
)
2136 graph
->n_total_row
++;
2139 for (i
= 0; i
< graph
->n
; ++i
) {
2140 struct isl_sched_node
*node
= &graph
->node
[i
];
2141 if (node
->scc
> graph
->src_scc
)
2142 node
->band_id
[graph
->n_band
] = n
;
2145 orig_total_row
= graph
->n_total_row
;
2146 orig_band
= graph
->n_band
;
2147 if (compute_sub_schedule(ctx
, graph
, n
, e1
,
2148 &node_scc_at_most
, &edge_dst_scc_at_most
,
2149 graph
->src_scc
, 0) < 0)
2151 n_total_row
= graph
->n_total_row
;
2152 graph
->n_total_row
= orig_total_row
;
2153 n_band
= graph
->n_band
;
2154 graph
->n_band
= orig_band
;
2155 if (compute_sub_schedule(ctx
, graph
, graph
->n
- n
, e2
,
2156 &node_scc_at_least
, &edge_src_scc_at_least
,
2157 graph
->src_scc
+ 1, 0) < 0)
2159 if (n_total_row
> graph
->n_total_row
)
2160 graph
->n_total_row
= n_total_row
;
2161 if (n_band
> graph
->n_band
)
2162 graph
->n_band
= n_band
;
2164 return pad_schedule(graph
);
2167 /* Compute the next band of the schedule after updating the dependence
2168 * relations based on the the current schedule.
2170 static int compute_next_band(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2172 if (update_edges(ctx
, graph
) < 0)
2176 return compute_schedule(ctx
, graph
);
2179 /* Add constraints to graph->lp that force the dependence "map" (which
2180 * is part of the dependence relation of "edge")
2181 * to be respected and attempt to carry it, where the edge is one from
2182 * a node j to itself. "pos" is the sequence number of the given map.
2183 * That is, add constraints that enforce
2185 * (c_j_0 + c_j_n n + c_j_x y) - (c_j_0 + c_j_n n + c_j_x x)
2186 * = c_j_x (y - x) >= e_i
2188 * for each (x,y) in R.
2189 * We obtain general constraints on coefficients (c_0, c_n, c_x)
2190 * of valid constraints for (y - x) and then plug in (-e_i, 0, c_j_x),
2191 * with each coefficient in c_j_x represented as a pair of non-negative
2194 static int add_intra_constraints(struct isl_sched_graph
*graph
,
2195 struct isl_sched_edge
*edge
, __isl_take isl_map
*map
, int pos
)
2198 isl_ctx
*ctx
= isl_map_get_ctx(map
);
2200 isl_dim_map
*dim_map
;
2201 isl_basic_set
*coef
;
2202 struct isl_sched_node
*node
= edge
->src
;
2204 coef
= intra_coefficients(graph
, map
);
2208 dim
= isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef
)));
2210 total
= isl_basic_set_total_dim(graph
->lp
);
2211 dim_map
= isl_dim_map_alloc(ctx
, total
);
2212 isl_dim_map_range(dim_map
, 3 + pos
, 0, 0, 0, 1, -1);
2213 isl_dim_map_range(dim_map
, node
->start
+ 2 * node
->nparam
+ 1, 2,
2214 isl_space_dim(dim
, isl_dim_set
), 1,
2216 isl_dim_map_range(dim_map
, node
->start
+ 2 * node
->nparam
+ 2, 2,
2217 isl_space_dim(dim
, isl_dim_set
), 1,
2219 graph
->lp
= isl_basic_set_extend_constraints(graph
->lp
,
2220 coef
->n_eq
, coef
->n_ineq
);
2221 graph
->lp
= isl_basic_set_add_constraints_dim_map(graph
->lp
,
2223 isl_space_free(dim
);
2228 /* Add constraints to graph->lp that force the dependence "map" (which
2229 * is part of the dependence relation of "edge")
2230 * to be respected and attempt to carry it, where the edge is one from
2231 * node j to node k. "pos" is the sequence number of the given map.
2232 * That is, add constraints that enforce
2234 * (c_k_0 + c_k_n n + c_k_x y) - (c_j_0 + c_j_n n + c_j_x x) >= e_i
2236 * for each (x,y) in R.
2237 * We obtain general constraints on coefficients (c_0, c_n, c_x)
2238 * of valid constraints for R and then plug in
2239 * (-e_i + c_k_0 - c_j_0, c_k_n - c_j_n, c_k_x - c_j_x)
2240 * with each coefficient (except e_i, c_k_0 and c_j_0)
2241 * represented as a pair of non-negative coefficients.
2243 static int add_inter_constraints(struct isl_sched_graph
*graph
,
2244 struct isl_sched_edge
*edge
, __isl_take isl_map
*map
, int pos
)
2247 isl_ctx
*ctx
= isl_map_get_ctx(map
);
2249 isl_dim_map
*dim_map
;
2250 isl_basic_set
*coef
;
2251 struct isl_sched_node
*src
= edge
->src
;
2252 struct isl_sched_node
*dst
= edge
->dst
;
2254 coef
= inter_coefficients(graph
, map
);
2258 dim
= isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef
)));
2260 total
= isl_basic_set_total_dim(graph
->lp
);
2261 dim_map
= isl_dim_map_alloc(ctx
, total
);
2263 isl_dim_map_range(dim_map
, 3 + pos
, 0, 0, 0, 1, -1);
2265 isl_dim_map_range(dim_map
, dst
->start
, 0, 0, 0, 1, 1);
2266 isl_dim_map_range(dim_map
, dst
->start
+ 1, 2, 1, 1, dst
->nparam
, -1);
2267 isl_dim_map_range(dim_map
, dst
->start
+ 2, 2, 1, 1, dst
->nparam
, 1);
2268 isl_dim_map_range(dim_map
, dst
->start
+ 2 * dst
->nparam
+ 1, 2,
2269 isl_space_dim(dim
, isl_dim_set
) + src
->nvar
, 1,
2271 isl_dim_map_range(dim_map
, dst
->start
+ 2 * dst
->nparam
+ 2, 2,
2272 isl_space_dim(dim
, isl_dim_set
) + src
->nvar
, 1,
2275 isl_dim_map_range(dim_map
, src
->start
, 0, 0, 0, 1, -1);
2276 isl_dim_map_range(dim_map
, src
->start
+ 1, 2, 1, 1, src
->nparam
, 1);
2277 isl_dim_map_range(dim_map
, src
->start
+ 2, 2, 1, 1, src
->nparam
, -1);
2278 isl_dim_map_range(dim_map
, src
->start
+ 2 * src
->nparam
+ 1, 2,
2279 isl_space_dim(dim
, isl_dim_set
), 1,
2281 isl_dim_map_range(dim_map
, src
->start
+ 2 * src
->nparam
+ 2, 2,
2282 isl_space_dim(dim
, isl_dim_set
), 1,
2285 graph
->lp
= isl_basic_set_extend_constraints(graph
->lp
,
2286 coef
->n_eq
, coef
->n_ineq
);
2287 graph
->lp
= isl_basic_set_add_constraints_dim_map(graph
->lp
,
2289 isl_space_free(dim
);
2294 /* Add constraints to graph->lp that force all validity dependences
2295 * to be respected and attempt to carry them.
2297 static int add_all_constraints(struct isl_sched_graph
*graph
)
2303 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2304 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
2306 if (!edge
->validity
)
2309 for (j
= 0; j
< edge
->map
->n
; ++j
) {
2310 isl_basic_map
*bmap
;
2313 bmap
= isl_basic_map_copy(edge
->map
->p
[j
]);
2314 map
= isl_map_from_basic_map(bmap
);
2316 if (edge
->src
== edge
->dst
&&
2317 add_intra_constraints(graph
, edge
, map
, pos
) < 0)
2319 if (edge
->src
!= edge
->dst
&&
2320 add_inter_constraints(graph
, edge
, map
, pos
) < 0)
2329 /* Count the number of equality and inequality constraints
2330 * that will be added to the carry_lp problem.
2331 * We count each edge exactly once.
2333 static int count_all_constraints(struct isl_sched_graph
*graph
,
2334 int *n_eq
, int *n_ineq
)
2338 *n_eq
= *n_ineq
= 0;
2339 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2340 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
2341 for (j
= 0; j
< edge
->map
->n
; ++j
) {
2342 isl_basic_map
*bmap
;
2345 bmap
= isl_basic_map_copy(edge
->map
->p
[j
]);
2346 map
= isl_map_from_basic_map(bmap
);
2348 if (count_map_constraints(graph
, edge
, map
,
2349 n_eq
, n_ineq
, 1) < 0)
2357 /* Construct an LP problem for finding schedule coefficients
2358 * such that the schedule carries as many dependences as possible.
2359 * In particular, for each dependence i, we bound the dependence distance
2360 * from below by e_i, with 0 <= e_i <= 1 and then maximize the sum
2361 * of all e_i's. Dependence with e_i = 0 in the solution are simply
2362 * respected, while those with e_i > 0 (in practice e_i = 1) are carried.
2363 * Note that if the dependence relation is a union of basic maps,
2364 * then we have to consider each basic map individually as it may only
2365 * be possible to carry the dependences expressed by some of those
2366 * basic maps and not all off them.
2367 * Below, we consider each of those basic maps as a separate "edge".
2369 * All variables of the LP are non-negative. The actual coefficients
2370 * may be negative, so each coefficient is represented as the difference
2371 * of two non-negative variables. The negative part always appears
2372 * immediately before the positive part.
2373 * Other than that, the variables have the following order
2375 * - sum of (1 - e_i) over all edges
2376 * - sum of positive and negative parts of all c_n coefficients
2377 * (unconstrained when computing non-parametric schedules)
2378 * - sum of positive and negative parts of all c_x coefficients
2383 * - positive and negative parts of c_i_n (if parametric)
2384 * - positive and negative parts of c_i_x
2386 * The constraints are those from the (validity) edges plus three equalities
2387 * to express the sums and n_edge inequalities to express e_i <= 1.
2389 static int setup_carry_lp(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2399 for (i
= 0; i
< graph
->n_edge
; ++i
)
2400 n_edge
+= graph
->edge
[i
].map
->n
;
2403 for (i
= 0; i
< graph
->n
; ++i
) {
2404 struct isl_sched_node
*node
= &graph
->node
[graph
->sorted
[i
]];
2405 node
->start
= total
;
2406 total
+= 1 + 2 * (node
->nparam
+ node
->nvar
);
2409 if (count_all_constraints(graph
, &n_eq
, &n_ineq
) < 0)
2412 dim
= isl_space_set_alloc(ctx
, 0, total
);
2413 isl_basic_set_free(graph
->lp
);
2416 graph
->lp
= isl_basic_set_alloc_space(dim
, 0, n_eq
, n_ineq
);
2417 graph
->lp
= isl_basic_set_set_rational(graph
->lp
);
2419 k
= isl_basic_set_alloc_equality(graph
->lp
);
2422 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2423 isl_int_set_si(graph
->lp
->eq
[k
][0], -n_edge
);
2424 isl_int_set_si(graph
->lp
->eq
[k
][1], 1);
2425 for (i
= 0; i
< n_edge
; ++i
)
2426 isl_int_set_si(graph
->lp
->eq
[k
][4 + i
], 1);
2428 k
= isl_basic_set_alloc_equality(graph
->lp
);
2431 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2432 isl_int_set_si(graph
->lp
->eq
[k
][2], -1);
2433 for (i
= 0; i
< graph
->n
; ++i
) {
2434 int pos
= 1 + graph
->node
[i
].start
+ 1;
2436 for (j
= 0; j
< 2 * graph
->node
[i
].nparam
; ++j
)
2437 isl_int_set_si(graph
->lp
->eq
[k
][pos
+ j
], 1);
2440 k
= isl_basic_set_alloc_equality(graph
->lp
);
2443 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2444 isl_int_set_si(graph
->lp
->eq
[k
][3], -1);
2445 for (i
= 0; i
< graph
->n
; ++i
) {
2446 struct isl_sched_node
*node
= &graph
->node
[i
];
2447 int pos
= 1 + node
->start
+ 1 + 2 * node
->nparam
;
2449 for (j
= 0; j
< 2 * node
->nvar
; ++j
)
2450 isl_int_set_si(graph
->lp
->eq
[k
][pos
+ j
], 1);
2453 for (i
= 0; i
< n_edge
; ++i
) {
2454 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2457 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
2458 isl_int_set_si(graph
->lp
->ineq
[k
][4 + i
], -1);
2459 isl_int_set_si(graph
->lp
->ineq
[k
][0], 1);
2462 if (add_all_constraints(graph
) < 0)
2468 /* If the schedule_split_scaled option is set and if the linear
2469 * parts of the scheduling rows for all nodes in the graphs have
2470 * non-trivial common divisor, then split off the constant term
2471 * from the linear part.
2472 * The constant term is then placed in a separate band and
2473 * the linear part is reduced.
2475 static int split_scaled(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2481 if (!ctx
->opt
->schedule_split_scaled
)
2486 if (graph
->n_total_row
>= graph
->max_row
)
2487 isl_die(ctx
, isl_error_internal
,
2488 "too many schedule rows", return -1);
2491 isl_int_init(gcd_i
);
2493 isl_int_set_si(gcd
, 0);
2495 row
= isl_mat_rows(graph
->node
[0].sched
) - 1;
2497 for (i
= 0; i
< graph
->n
; ++i
) {
2498 struct isl_sched_node
*node
= &graph
->node
[i
];
2499 int cols
= isl_mat_cols(node
->sched
);
2501 isl_seq_gcd(node
->sched
->row
[row
] + 1, cols
- 1, &gcd_i
);
2502 isl_int_gcd(gcd
, gcd
, gcd_i
);
2505 isl_int_clear(gcd_i
);
2507 if (isl_int_cmp_si(gcd
, 1) <= 0) {
2514 for (i
= 0; i
< graph
->n
; ++i
) {
2515 struct isl_sched_node
*node
= &graph
->node
[i
];
2517 isl_map_free(node
->sched_map
);
2518 node
->sched_map
= NULL
;
2519 node
->sched
= isl_mat_add_zero_rows(node
->sched
, 1);
2522 isl_int_fdiv_r(node
->sched
->row
[row
+ 1][0],
2523 node
->sched
->row
[row
][0], gcd
);
2524 isl_int_fdiv_q(node
->sched
->row
[row
][0],
2525 node
->sched
->row
[row
][0], gcd
);
2526 isl_int_mul(node
->sched
->row
[row
][0],
2527 node
->sched
->row
[row
][0], gcd
);
2528 node
->sched
= isl_mat_scale_down_row(node
->sched
, row
, gcd
);
2531 node
->band
[graph
->n_total_row
] = graph
->n_band
;
2534 graph
->n_total_row
++;
2543 static int compute_component_schedule(isl_ctx
*ctx
,
2544 struct isl_sched_graph
*graph
);
2546 /* Is the schedule row "sol" trivial on node "node"?
2547 * That is, is the solution zero on the dimensions orthogonal to
2548 * the previously found solutions?
2549 * Return 1 if the solution is trivial, 0 if it is not and -1 on error.
2551 * Each coefficient is represented as the difference between
2552 * two non-negative values in "sol". "sol" has been computed
2553 * in terms of the original iterators (i.e., without use of cmap).
2554 * We construct the schedule row s and write it as a linear
2555 * combination of (linear combinations of) previously computed schedule rows.
2556 * s = Q c or c = U s.
2557 * If the final entries of c are all zero, then the solution is trivial.
2559 static int is_trivial(struct isl_sched_node
*node
, __isl_keep isl_vec
*sol
)
2569 if (node
->nvar
== node
->rank
)
2572 ctx
= isl_vec_get_ctx(sol
);
2573 node_sol
= isl_vec_alloc(ctx
, node
->nvar
);
2577 pos
= 1 + node
->start
+ 1 + 2 * node
->nparam
;
2579 for (i
= 0; i
< node
->nvar
; ++i
)
2580 isl_int_sub(node_sol
->el
[i
],
2581 sol
->el
[pos
+ 2 * i
+ 1], sol
->el
[pos
+ 2 * i
]);
2583 node_sol
= isl_mat_vec_product(isl_mat_copy(node
->cinv
), node_sol
);
2588 trivial
= isl_seq_first_non_zero(node_sol
->el
+ node
->rank
,
2589 node
->nvar
- node
->rank
) == -1;
2591 isl_vec_free(node_sol
);
2596 /* Is the schedule row "sol" trivial on any node where it should
2598 * "sol" has been computed in terms of the original iterators
2599 * (i.e., without use of cmap).
2600 * Return 1 if any solution is trivial, 0 if they are not and -1 on error.
2602 static int is_any_trivial(struct isl_sched_graph
*graph
,
2603 __isl_keep isl_vec
*sol
)
2607 for (i
= 0; i
< graph
->n
; ++i
) {
2608 struct isl_sched_node
*node
= &graph
->node
[i
];
2611 if (!needs_row(graph
, node
))
2613 trivial
= is_trivial(node
, sol
);
2614 if (trivial
< 0 || trivial
)
2621 /* Construct a schedule row for each node such that as many dependences
2622 * as possible are carried and then continue with the next band.
2624 * If the computed schedule row turns out to be trivial on one or
2625 * more nodes where it should not be trivial, then we throw it away
2626 * and try again on each component separately.
2628 static int carry_dependences(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2637 for (i
= 0; i
< graph
->n_edge
; ++i
)
2638 n_edge
+= graph
->edge
[i
].map
->n
;
2640 if (setup_carry_lp(ctx
, graph
) < 0)
2643 lp
= isl_basic_set_copy(graph
->lp
);
2644 sol
= isl_tab_basic_set_non_neg_lexmin(lp
);
2648 if (sol
->size
== 0) {
2650 isl_die(ctx
, isl_error_internal
,
2651 "error in schedule construction", return -1);
2654 isl_int_divexact(sol
->el
[1], sol
->el
[1], sol
->el
[0]);
2655 if (isl_int_cmp_si(sol
->el
[1], n_edge
) >= 0) {
2657 isl_die(ctx
, isl_error_unknown
,
2658 "unable to carry dependences", return -1);
2661 trivial
= is_any_trivial(graph
, sol
);
2663 sol
= isl_vec_free(sol
);
2664 } else if (trivial
) {
2667 return compute_component_schedule(ctx
, graph
);
2668 isl_die(ctx
, isl_error_unknown
,
2669 "unable to construct non-trivial solution", return -1);
2672 if (update_schedule(graph
, sol
, 0, 0) < 0)
2675 if (split_scaled(ctx
, graph
) < 0)
2678 return compute_next_band(ctx
, graph
);
2681 /* Are there any (non-empty) validity edges in the graph?
2683 static int has_validity_edges(struct isl_sched_graph
*graph
)
2687 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2690 empty
= isl_map_plain_is_empty(graph
->edge
[i
].map
);
2695 if (graph
->edge
[i
].validity
)
2702 /* Should we apply a Feautrier step?
2703 * That is, did the user request the Feautrier algorithm and are
2704 * there any validity dependences (left)?
2706 static int need_feautrier_step(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2708 if (ctx
->opt
->schedule_algorithm
!= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
)
2711 return has_validity_edges(graph
);
2714 /* Compute a schedule for a connected dependence graph using Feautrier's
2715 * multi-dimensional scheduling algorithm.
2716 * The original algorithm is described in [1].
2717 * The main idea is to minimize the number of scheduling dimensions, by
2718 * trying to satisfy as many dependences as possible per scheduling dimension.
2720 * [1] P. Feautrier, Some Efficient Solutions to the Affine Scheduling
2721 * Problem, Part II: Multi-Dimensional Time.
2722 * In Intl. Journal of Parallel Programming, 1992.
2724 static int compute_schedule_wcc_feautrier(isl_ctx
*ctx
,
2725 struct isl_sched_graph
*graph
)
2727 return carry_dependences(ctx
, graph
);
2730 /* Compute a schedule for a connected dependence graph.
2731 * We try to find a sequence of as many schedule rows as possible that result
2732 * in non-negative dependence distances (independent of the previous rows
2733 * in the sequence, i.e., such that the sequence is tilable).
2734 * If we can't find any more rows we either
2735 * - split between SCCs and start over (assuming we found an interesting
2736 * pair of SCCs between which to split)
2737 * - continue with the next band (assuming the current band has at least
2739 * - try to carry as many dependences as possible and continue with the next
2742 * If Feautrier's algorithm is selected, we first recursively try to satisfy
2743 * as many validity dependences as possible. When all validity dependences
2744 * are satisfied we extend the schedule to a full-dimensional schedule.
2746 * If we manage to complete the schedule, we finish off by topologically
2747 * sorting the statements based on the remaining dependences.
2749 * If ctx->opt->schedule_outer_zero_distance is set, then we force the
2750 * outermost dimension in the current band to be zero distance. If this
2751 * turns out to be impossible, we fall back on the general scheme above
2752 * and try to carry as many dependences as possible.
2754 static int compute_schedule_wcc(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2758 if (detect_sccs(ctx
, graph
) < 0)
2760 if (sort_sccs(graph
) < 0)
2763 if (compute_maxvar(graph
) < 0)
2766 if (need_feautrier_step(ctx
, graph
))
2767 return compute_schedule_wcc_feautrier(ctx
, graph
);
2769 if (ctx
->opt
->schedule_outer_zero_distance
)
2772 while (graph
->n_row
< graph
->maxvar
) {
2775 graph
->src_scc
= -1;
2776 graph
->dst_scc
= -1;
2778 if (setup_lp(ctx
, graph
, force_zero
) < 0)
2780 sol
= solve_lp(graph
);
2783 if (sol
->size
== 0) {
2785 if (!ctx
->opt
->schedule_maximize_band_depth
&&
2786 graph
->n_total_row
> graph
->band_start
)
2787 return compute_next_band(ctx
, graph
);
2788 if (graph
->src_scc
>= 0)
2789 return compute_split_schedule(ctx
, graph
);
2790 if (graph
->n_total_row
> graph
->band_start
)
2791 return compute_next_band(ctx
, graph
);
2792 return carry_dependences(ctx
, graph
);
2794 if (update_schedule(graph
, sol
, 1, 1) < 0)
2799 if (graph
->n_total_row
> graph
->band_start
)
2801 return sort_statements(ctx
, graph
);
2804 /* Add a row to the schedules that separates the SCCs and move
2807 static int split_on_scc(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2811 if (graph
->n_total_row
>= graph
->max_row
)
2812 isl_die(ctx
, isl_error_internal
,
2813 "too many schedule rows", return -1);
2815 for (i
= 0; i
< graph
->n
; ++i
) {
2816 struct isl_sched_node
*node
= &graph
->node
[i
];
2817 int row
= isl_mat_rows(node
->sched
);
2819 isl_map_free(node
->sched_map
);
2820 node
->sched_map
= NULL
;
2821 node
->sched
= isl_mat_add_zero_rows(node
->sched
, 1);
2822 node
->sched
= isl_mat_set_element_si(node
->sched
, row
, 0,
2826 node
->band
[graph
->n_total_row
] = graph
->n_band
;
2829 graph
->n_total_row
++;
2835 /* Compute a schedule for each component (identified by node->scc)
2836 * of the dependence graph separately and then combine the results.
2837 * Depending on the setting of schedule_fuse, a component may be
2838 * either weakly or strongly connected.
2840 * The band_id is adjusted such that each component has a separate id.
2841 * Note that the band_id may have already been set to a value different
2842 * from zero by compute_split_schedule.
2844 static int compute_component_schedule(isl_ctx
*ctx
,
2845 struct isl_sched_graph
*graph
)
2849 int n_total_row
, orig_total_row
;
2850 int n_band
, orig_band
;
2852 if (ctx
->opt
->schedule_fuse
== ISL_SCHEDULE_FUSE_MIN
||
2853 ctx
->opt
->schedule_separate_components
)
2854 if (split_on_scc(ctx
, graph
) < 0)
2858 orig_total_row
= graph
->n_total_row
;
2860 orig_band
= graph
->n_band
;
2861 for (i
= 0; i
< graph
->n
; ++i
)
2862 graph
->node
[i
].band_id
[graph
->n_band
] += graph
->node
[i
].scc
;
2863 for (wcc
= 0; wcc
< graph
->scc
; ++wcc
) {
2865 for (i
= 0; i
< graph
->n
; ++i
)
2866 if (graph
->node
[i
].scc
== wcc
)
2869 for (i
= 0; i
< graph
->n_edge
; ++i
)
2870 if (graph
->edge
[i
].src
->scc
== wcc
&&
2871 graph
->edge
[i
].dst
->scc
== wcc
)
2874 if (compute_sub_schedule(ctx
, graph
, n
, n_edge
,
2876 &edge_scc_exactly
, wcc
, 1) < 0)
2878 if (graph
->n_total_row
> n_total_row
)
2879 n_total_row
= graph
->n_total_row
;
2880 graph
->n_total_row
= orig_total_row
;
2881 if (graph
->n_band
> n_band
)
2882 n_band
= graph
->n_band
;
2883 graph
->n_band
= orig_band
;
2886 graph
->n_total_row
= n_total_row
;
2887 graph
->n_band
= n_band
;
2889 return pad_schedule(graph
);
2892 /* Compute a schedule for the given dependence graph.
2893 * We first check if the graph is connected (through validity dependences)
2894 * and, if not, compute a schedule for each component separately.
2895 * If schedule_fuse is set to minimal fusion, then we check for strongly
2896 * connected components instead and compute a separate schedule for
2897 * each such strongly connected component.
2899 static int compute_schedule(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2901 if (ctx
->opt
->schedule_fuse
== ISL_SCHEDULE_FUSE_MIN
) {
2902 if (detect_sccs(ctx
, graph
) < 0)
2905 if (detect_wccs(ctx
, graph
) < 0)
2910 return compute_component_schedule(ctx
, graph
);
2912 return compute_schedule_wcc(ctx
, graph
);
2915 /* Compute a schedule for the given union of domains that respects
2916 * all the validity dependences.
2917 * If the default isl scheduling algorithm is used, it tries to minimize
2918 * the dependence distances over the proximity dependences.
2919 * If Feautrier's scheduling algorithm is used, the proximity dependence
2920 * distances are only minimized during the extension to a full-dimensional
2923 __isl_give isl_schedule
*isl_union_set_compute_schedule(
2924 __isl_take isl_union_set
*domain
,
2925 __isl_take isl_union_map
*validity
,
2926 __isl_take isl_union_map
*proximity
)
2928 isl_ctx
*ctx
= isl_union_set_get_ctx(domain
);
2930 struct isl_sched_graph graph
= { 0 };
2931 isl_schedule
*sched
;
2932 struct isl_extract_edge_data data
;
2934 domain
= isl_union_set_align_params(domain
,
2935 isl_union_map_get_space(validity
));
2936 domain
= isl_union_set_align_params(domain
,
2937 isl_union_map_get_space(proximity
));
2938 dim
= isl_union_set_get_space(domain
);
2939 validity
= isl_union_map_align_params(validity
, isl_space_copy(dim
));
2940 proximity
= isl_union_map_align_params(proximity
, dim
);
2945 graph
.n
= isl_union_set_n_set(domain
);
2948 if (graph_alloc(ctx
, &graph
, graph
.n
,
2949 isl_union_map_n_map(validity
) + isl_union_map_n_map(proximity
)) < 0)
2951 if (compute_max_row(&graph
, domain
) < 0)
2955 if (isl_union_set_foreach_set(domain
, &extract_node
, &graph
) < 0)
2957 if (graph_init_table(ctx
, &graph
) < 0)
2959 graph
.max_edge
[isl_edge_validity
] = isl_union_map_n_map(validity
);
2960 graph
.max_edge
[isl_edge_proximity
] = isl_union_map_n_map(proximity
);
2961 if (graph_init_edge_tables(ctx
, &graph
) < 0)
2964 data
.graph
= &graph
;
2965 data
.type
= isl_edge_validity
;
2966 if (isl_union_map_foreach_map(validity
, &extract_edge
, &data
) < 0)
2968 data
.type
= isl_edge_proximity
;
2969 if (isl_union_map_foreach_map(proximity
, &extract_edge
, &data
) < 0)
2972 if (compute_schedule(ctx
, &graph
) < 0)
2976 sched
= extract_schedule(&graph
, isl_union_set_get_space(domain
));
2978 graph_free(ctx
, &graph
);
2979 isl_union_set_free(domain
);
2980 isl_union_map_free(validity
);
2981 isl_union_map_free(proximity
);
2985 graph_free(ctx
, &graph
);
2986 isl_union_set_free(domain
);
2987 isl_union_map_free(validity
);
2988 isl_union_map_free(proximity
);
2992 void *isl_schedule_free(__isl_take isl_schedule
*sched
)
2998 if (--sched
->ref
> 0)
3001 for (i
= 0; i
< sched
->n
; ++i
) {
3002 isl_multi_aff_free(sched
->node
[i
].sched
);
3003 free(sched
->node
[i
].band_end
);
3004 free(sched
->node
[i
].band_id
);
3005 free(sched
->node
[i
].zero
);
3007 isl_space_free(sched
->dim
);
3008 isl_band_list_free(sched
->band_forest
);
3013 isl_ctx
*isl_schedule_get_ctx(__isl_keep isl_schedule
*schedule
)
3015 return schedule
? isl_space_get_ctx(schedule
->dim
) : NULL
;
3018 /* Set max_out to the maximal number of output dimensions over
3021 static int update_max_out(__isl_take isl_map
*map
, void *user
)
3023 int *max_out
= user
;
3024 int n_out
= isl_map_dim(map
, isl_dim_out
);
3026 if (n_out
> *max_out
)
3033 /* Internal data structure for map_pad_range.
3035 * "max_out" is the maximal schedule dimension.
3036 * "res" collects the results.
3038 struct isl_pad_schedule_map_data
{
3043 /* Pad the range of the given map with zeros to data->max_out and
3044 * then add the result to data->res.
3046 static int map_pad_range(__isl_take isl_map
*map
, void *user
)
3048 struct isl_pad_schedule_map_data
*data
= user
;
3050 int n_out
= isl_map_dim(map
, isl_dim_out
);
3052 map
= isl_map_add_dims(map
, isl_dim_out
, data
->max_out
- n_out
);
3053 for (i
= n_out
; i
< data
->max_out
; ++i
)
3054 map
= isl_map_fix_si(map
, isl_dim_out
, i
, 0);
3056 data
->res
= isl_union_map_add_map(data
->res
, map
);
3063 /* Pad the ranges of the maps in the union map with zeros such they all have
3064 * the same dimension.
3066 static __isl_give isl_union_map
*pad_schedule_map(
3067 __isl_take isl_union_map
*umap
)
3069 struct isl_pad_schedule_map_data data
;
3073 if (isl_union_map_n_map(umap
) <= 1)
3077 if (isl_union_map_foreach_map(umap
, &update_max_out
, &data
.max_out
) < 0)
3078 return isl_union_map_free(umap
);
3080 data
.res
= isl_union_map_empty(isl_union_map_get_space(umap
));
3081 if (isl_union_map_foreach_map(umap
, &map_pad_range
, &data
) < 0)
3082 data
.res
= isl_union_map_free(data
.res
);
3084 isl_union_map_free(umap
);
3088 /* Return an isl_union_map of the schedule. If we have already constructed
3089 * a band forest, then this band forest may have been modified so we need
3090 * to extract the isl_union_map from the forest rather than from
3091 * the originally computed schedule. This reconstructed schedule map
3092 * then needs to be padded with zeros to unify the schedule space
3093 * since the result of isl_band_list_get_suffix_schedule may not have
3094 * a unified schedule space.
3096 __isl_give isl_union_map
*isl_schedule_get_map(__isl_keep isl_schedule
*sched
)
3099 isl_union_map
*umap
;
3104 if (sched
->band_forest
) {
3105 umap
= isl_band_list_get_suffix_schedule(sched
->band_forest
);
3106 return pad_schedule_map(umap
);
3109 umap
= isl_union_map_empty(isl_space_copy(sched
->dim
));
3110 for (i
= 0; i
< sched
->n
; ++i
) {
3113 ma
= isl_multi_aff_copy(sched
->node
[i
].sched
);
3114 umap
= isl_union_map_add_map(umap
, isl_map_from_multi_aff(ma
));
3120 static __isl_give isl_band_list
*construct_band_list(
3121 __isl_keep isl_schedule
*schedule
, __isl_keep isl_band
*parent
,
3122 int band_nr
, int *parent_active
, int n_active
);
3124 /* Construct an isl_band structure for the band in the given schedule
3125 * with sequence number band_nr for the n_active nodes marked by active.
3126 * If the nodes don't have a band with the given sequence number,
3127 * then a band without members is created.
3129 * Because of the way the schedule is constructed, we know that
3130 * the position of the band inside the schedule of a node is the same
3131 * for all active nodes.
3133 * The partial schedule for the band is created before the children
3134 * are created to that construct_band_list can refer to the partial
3135 * schedule of the parent.
3137 static __isl_give isl_band
*construct_band(__isl_keep isl_schedule
*schedule
,
3138 __isl_keep isl_band
*parent
,
3139 int band_nr
, int *active
, int n_active
)
3142 isl_ctx
*ctx
= isl_schedule_get_ctx(schedule
);
3144 unsigned start
, end
;
3146 band
= isl_band_alloc(ctx
);
3150 band
->schedule
= schedule
;
3151 band
->parent
= parent
;
3153 for (i
= 0; i
< schedule
->n
; ++i
)
3157 if (i
>= schedule
->n
)
3158 isl_die(ctx
, isl_error_internal
,
3159 "band without active statements", goto error
);
3161 start
= band_nr
? schedule
->node
[i
].band_end
[band_nr
- 1] : 0;
3162 end
= band_nr
< schedule
->node
[i
].n_band
?
3163 schedule
->node
[i
].band_end
[band_nr
] : start
;
3164 band
->n
= end
- start
;
3166 band
->zero
= isl_alloc_array(ctx
, int, band
->n
);
3167 if (band
->n
&& !band
->zero
)
3170 for (j
= 0; j
< band
->n
; ++j
)
3171 band
->zero
[j
] = schedule
->node
[i
].zero
[start
+ j
];
3173 band
->pma
= isl_union_pw_multi_aff_empty(isl_space_copy(schedule
->dim
));
3174 for (i
= 0; i
< schedule
->n
; ++i
) {
3176 isl_pw_multi_aff
*pma
;
3182 ma
= isl_multi_aff_copy(schedule
->node
[i
].sched
);
3183 n_out
= isl_multi_aff_dim(ma
, isl_dim_out
);
3184 ma
= isl_multi_aff_drop_dims(ma
, isl_dim_out
, end
, n_out
- end
);
3185 ma
= isl_multi_aff_drop_dims(ma
, isl_dim_out
, 0, start
);
3186 pma
= isl_pw_multi_aff_from_multi_aff(ma
);
3187 band
->pma
= isl_union_pw_multi_aff_add_pw_multi_aff(band
->pma
,
3193 for (i
= 0; i
< schedule
->n
; ++i
)
3194 if (active
[i
] && schedule
->node
[i
].n_band
> band_nr
+ 1)
3197 if (i
< schedule
->n
) {
3198 band
->children
= construct_band_list(schedule
, band
,
3199 band_nr
+ 1, active
, n_active
);
3200 if (!band
->children
)
3206 isl_band_free(band
);
3210 /* Internal data structure used inside cmp_band and pw_multi_aff_extract_int.
3212 * r is set to a negative value if anything goes wrong.
3214 * c1 stores the result of extract_int.
3215 * c2 is a temporary value used inside cmp_band_in_ancestor.
3216 * t is a temporary value used inside extract_int.
3218 * first and equal are used inside extract_int.
3219 * first is set if we are looking at the first isl_multi_aff inside
3220 * the isl_union_pw_multi_aff.
3221 * equal is set if all the isl_multi_affs have been equal so far.
3223 struct isl_cmp_band_data
{
3234 /* Check if "ma" assigns a constant value.
3235 * Note that this function is only called on isl_multi_affs
3236 * with a single output dimension.
3238 * If "ma" assigns a constant value then we compare it to data->c1
3239 * or assign it to data->c1 if this is the first isl_multi_aff we consider.
3240 * If "ma" does not assign a constant value or if it assigns a value
3241 * that is different from data->c1, then we set data->equal to zero
3242 * and terminate the check.
3244 static int multi_aff_extract_int(__isl_take isl_set
*set
,
3245 __isl_take isl_multi_aff
*ma
, void *user
)
3248 struct isl_cmp_band_data
*data
= user
;
3250 aff
= isl_multi_aff_get_aff(ma
, 0);
3251 data
->r
= isl_aff_is_cst(aff
);
3252 if (data
->r
>= 0 && data
->r
) {
3253 isl_aff_get_constant(aff
, &data
->t
);
3255 isl_int_set(data
->c1
, data
->t
);
3257 } else if (!isl_int_eq(data
->c1
, data
->t
))
3259 } else if (data
->r
>= 0 && !data
->r
)
3264 isl_multi_aff_free(ma
);
3273 /* This function is called for each isl_pw_multi_aff in
3274 * the isl_union_pw_multi_aff checked by extract_int.
3275 * Check all the isl_multi_affs inside "pma".
3277 static int pw_multi_aff_extract_int(__isl_take isl_pw_multi_aff
*pma
,
3282 r
= isl_pw_multi_aff_foreach_piece(pma
, &multi_aff_extract_int
, user
);
3283 isl_pw_multi_aff_free(pma
);
3288 /* Check if "upma" assigns a single constant value to its domain.
3289 * If so, return 1 and store the result in data->c1.
3292 * A negative return value from isl_union_pw_multi_aff_foreach_pw_multi_aff
3293 * means that either an error occurred or that we have broken off the check
3294 * because we already know the result is going to be negative.
3295 * In the latter case, data->equal is set to zero.
3297 static int extract_int(__isl_keep isl_union_pw_multi_aff
*upma
,
3298 struct isl_cmp_band_data
*data
)
3303 if (isl_union_pw_multi_aff_foreach_pw_multi_aff(upma
,
3304 &pw_multi_aff_extract_int
, data
) < 0) {
3310 return !data
->first
&& data
->equal
;
3313 /* Compare "b1" and "b2" based on the parent schedule of their ancestor
3316 * If the parent of "ancestor" also has a single member, then we
3317 * first try to compare the two band based on the partial schedule
3320 * Otherwise, or if the result is inconclusive, we look at the partial schedule
3321 * of "ancestor" itself.
3322 * In particular, we specialize the parent schedule based
3323 * on the domains of the child schedules, check if both assign
3324 * a single constant value and, if so, compare the two constant values.
3325 * If the specialized parent schedules do not assign a constant value,
3326 * then they cannot be used to order the two bands and so in this case
3329 static int cmp_band_in_ancestor(__isl_keep isl_band
*b1
,
3330 __isl_keep isl_band
*b2
, struct isl_cmp_band_data
*data
,
3331 __isl_keep isl_band
*ancestor
)
3333 isl_union_pw_multi_aff
*upma
;
3334 isl_union_set
*domain
;
3340 if (ancestor
->parent
&& ancestor
->parent
->n
== 1) {
3341 r
= cmp_band_in_ancestor(b1
, b2
, data
, ancestor
->parent
);
3348 upma
= isl_union_pw_multi_aff_copy(b1
->pma
);
3349 domain
= isl_union_pw_multi_aff_domain(upma
);
3350 upma
= isl_union_pw_multi_aff_copy(ancestor
->pma
);
3351 upma
= isl_union_pw_multi_aff_intersect_domain(upma
, domain
);
3352 r
= extract_int(upma
, data
);
3353 isl_union_pw_multi_aff_free(upma
);
3360 isl_int_set(data
->c2
, data
->c1
);
3362 upma
= isl_union_pw_multi_aff_copy(b2
->pma
);
3363 domain
= isl_union_pw_multi_aff_domain(upma
);
3364 upma
= isl_union_pw_multi_aff_copy(ancestor
->pma
);
3365 upma
= isl_union_pw_multi_aff_intersect_domain(upma
, domain
);
3366 r
= extract_int(upma
, data
);
3367 isl_union_pw_multi_aff_free(upma
);
3374 return isl_int_cmp(data
->c2
, data
->c1
);
3377 /* Compare "a" and "b" based on the parent schedule of their parent.
3379 static int cmp_band(const void *a
, const void *b
, void *user
)
3381 isl_band
*b1
= *(isl_band
* const *) a
;
3382 isl_band
*b2
= *(isl_band
* const *) b
;
3383 struct isl_cmp_band_data
*data
= user
;
3385 return cmp_band_in_ancestor(b1
, b2
, data
, b1
->parent
);
3388 /* Sort the elements in "list" based on the partial schedules of its parent
3389 * (and ancestors). In particular if the parent assigns constant values
3390 * to the domains of the bands in "list", then the elements are sorted
3391 * according to that order.
3392 * This order should be a more "natural" order for the user, but otherwise
3393 * shouldn't have any effect.
3394 * If we would be constructing an isl_band forest directly in
3395 * isl_union_set_compute_schedule then there wouldn't be any need
3396 * for a reordering, since the children would be added to the list
3397 * in their natural order automatically.
3399 * If there is only one element in the list, then there is no need to sort
3401 * If the partial schedule of the parent has more than one member
3402 * (or if there is no parent), then it's
3403 * defnitely not assigning constant values to the different children in
3404 * the list and so we wouldn't be able to use it to sort the list.
3406 static __isl_give isl_band_list
*sort_band_list(__isl_take isl_band_list
*list
,
3407 __isl_keep isl_band
*parent
)
3409 struct isl_cmp_band_data data
;
3415 if (!parent
|| parent
->n
!= 1)
3419 isl_int_init(data
.c1
);
3420 isl_int_init(data
.c2
);
3421 isl_int_init(data
.t
);
3422 isl_sort(list
->p
, list
->n
, sizeof(list
->p
[0]), &cmp_band
, &data
);
3424 list
= isl_band_list_free(list
);
3425 isl_int_clear(data
.c1
);
3426 isl_int_clear(data
.c2
);
3427 isl_int_clear(data
.t
);
3432 /* Construct a list of bands that start at the same position (with
3433 * sequence number band_nr) in the schedules of the nodes that
3434 * were active in the parent band.
3436 * A separate isl_band structure is created for each band_id
3437 * and for each node that does not have a band with sequence
3438 * number band_nr. In the latter case, a band without members
3440 * This ensures that if a band has any children, then each node
3441 * that was active in the band is active in exactly one of the children.
3443 static __isl_give isl_band_list
*construct_band_list(
3444 __isl_keep isl_schedule
*schedule
, __isl_keep isl_band
*parent
,
3445 int band_nr
, int *parent_active
, int n_active
)
3448 isl_ctx
*ctx
= isl_schedule_get_ctx(schedule
);
3451 isl_band_list
*list
;
3454 for (i
= 0; i
< n_active
; ++i
) {
3455 for (j
= 0; j
< schedule
->n
; ++j
) {
3456 if (!parent_active
[j
])
3458 if (schedule
->node
[j
].n_band
<= band_nr
)
3460 if (schedule
->node
[j
].band_id
[band_nr
] == i
) {
3466 for (j
= 0; j
< schedule
->n
; ++j
)
3467 if (schedule
->node
[j
].n_band
<= band_nr
)
3472 list
= isl_band_list_alloc(ctx
, n_band
);
3473 band
= construct_band(schedule
, parent
, band_nr
,
3474 parent_active
, n_active
);
3475 return isl_band_list_add(list
, band
);
3478 active
= isl_alloc_array(ctx
, int, schedule
->n
);
3479 if (schedule
->n
&& !active
)
3482 list
= isl_band_list_alloc(ctx
, n_band
);
3484 for (i
= 0; i
< n_active
; ++i
) {
3488 for (j
= 0; j
< schedule
->n
; ++j
) {
3489 active
[j
] = parent_active
[j
] &&
3490 schedule
->node
[j
].n_band
> band_nr
&&
3491 schedule
->node
[j
].band_id
[band_nr
] == i
;
3498 band
= construct_band(schedule
, parent
, band_nr
, active
, n
);
3500 list
= isl_band_list_add(list
, band
);
3502 for (i
= 0; i
< schedule
->n
; ++i
) {
3504 if (!parent_active
[i
])
3506 if (schedule
->node
[i
].n_band
> band_nr
)
3508 for (j
= 0; j
< schedule
->n
; ++j
)
3510 band
= construct_band(schedule
, parent
, band_nr
, active
, 1);
3511 list
= isl_band_list_add(list
, band
);
3516 list
= sort_band_list(list
, parent
);
3521 /* Construct a band forest representation of the schedule and
3522 * return the list of roots.
3524 static __isl_give isl_band_list
*construct_forest(
3525 __isl_keep isl_schedule
*schedule
)
3528 isl_ctx
*ctx
= isl_schedule_get_ctx(schedule
);
3529 isl_band_list
*forest
;
3532 active
= isl_alloc_array(ctx
, int, schedule
->n
);
3533 if (schedule
->n
&& !active
)
3536 for (i
= 0; i
< schedule
->n
; ++i
)
3539 forest
= construct_band_list(schedule
, NULL
, 0, active
, schedule
->n
);
3546 /* Return the roots of a band forest representation of the schedule.
3548 __isl_give isl_band_list
*isl_schedule_get_band_forest(
3549 __isl_keep isl_schedule
*schedule
)
3553 if (!schedule
->band_forest
)
3554 schedule
->band_forest
= construct_forest(schedule
);
3555 return isl_band_list_dup(schedule
->band_forest
);
3558 /* Call "fn" on each band in the schedule in depth-first post-order.
3560 int isl_schedule_foreach_band(__isl_keep isl_schedule
*sched
,
3561 int (*fn
)(__isl_keep isl_band
*band
, void *user
), void *user
)
3564 isl_band_list
*forest
;
3569 forest
= isl_schedule_get_band_forest(sched
);
3570 r
= isl_band_list_foreach_band(forest
, fn
, user
);
3571 isl_band_list_free(forest
);
3576 static __isl_give isl_printer
*print_band_list(__isl_take isl_printer
*p
,
3577 __isl_keep isl_band_list
*list
);
3579 static __isl_give isl_printer
*print_band(__isl_take isl_printer
*p
,
3580 __isl_keep isl_band
*band
)
3582 isl_band_list
*children
;
3584 p
= isl_printer_start_line(p
);
3585 p
= isl_printer_print_union_pw_multi_aff(p
, band
->pma
);
3586 p
= isl_printer_end_line(p
);
3588 if (!isl_band_has_children(band
))
3591 children
= isl_band_get_children(band
);
3593 p
= isl_printer_indent(p
, 4);
3594 p
= print_band_list(p
, children
);
3595 p
= isl_printer_indent(p
, -4);
3597 isl_band_list_free(children
);
3602 static __isl_give isl_printer
*print_band_list(__isl_take isl_printer
*p
,
3603 __isl_keep isl_band_list
*list
)
3607 n
= isl_band_list_n_band(list
);
3608 for (i
= 0; i
< n
; ++i
) {
3610 band
= isl_band_list_get_band(list
, i
);
3611 p
= print_band(p
, band
);
3612 isl_band_free(band
);
3618 __isl_give isl_printer
*isl_printer_print_schedule(__isl_take isl_printer
*p
,
3619 __isl_keep isl_schedule
*schedule
)
3621 isl_band_list
*forest
;
3623 forest
= isl_schedule_get_band_forest(schedule
);
3625 p
= print_band_list(p
, forest
);
3627 isl_band_list_free(forest
);
3632 void isl_schedule_dump(__isl_keep isl_schedule
*schedule
)
3634 isl_printer
*printer
;
3639 printer
= isl_printer_to_file(isl_schedule_get_ctx(schedule
), stderr
);
3640 printer
= isl_printer_print_schedule(printer
, schedule
);
3642 isl_printer_free(printer
);