2 * Copyright 2011 INRIA Saclay
3 * Copyright 2012-2013 Ecole Normale Superieure
5 * Use of this software is governed by the MIT license
7 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
8 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
10 * and Ecole Normale Superieure, 45 rue d'Ulm, 75230 Paris, France
13 #include <isl_ctx_private.h>
14 #include <isl_map_private.h>
15 #include <isl_space_private.h>
16 #include <isl_aff_private.h>
18 #include <isl/constraint.h>
19 #include <isl/schedule.h>
20 #include <isl_mat_private.h>
21 #include <isl_vec_private.h>
25 #include <isl_dim_map.h>
26 #include <isl_hmap_map_basic_set.h>
28 #include <isl_schedule_private.h>
29 #include <isl_band_private.h>
30 #include <isl_options_private.h>
31 #include <isl_tarjan.h>
34 * The scheduling algorithm implemented in this file was inspired by
35 * Bondhugula et al., "Automatic Transformations for Communication-Minimized
36 * Parallelization and Locality Optimization in the Polyhedral Model".
40 /* Internal information about a node that is used during the construction
42 * dim represents the space in which the domain lives
43 * sched is a matrix representation of the schedule being constructed
45 * sched_map is an isl_map representation of the same (partial) schedule
46 * sched_map may be NULL
47 * rank is the number of linearly independent rows in the linear part
49 * the columns of cmap represent a change of basis for the schedule
50 * coefficients; the first rank columns span the linear part of
52 * 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
{
86 static int node_has_dim(const void *entry
, const void *val
)
88 struct isl_sched_node
*node
= (struct isl_sched_node
*)entry
;
89 isl_space
*dim
= (isl_space
*)val
;
91 return isl_space_is_equal(node
->dim
, dim
);
94 /* An edge in the dependence graph. An edge may be used to
95 * ensure validity of the generated schedule, to minimize the dependence
98 * map is the dependence relation
99 * src is the source node
100 * dst is the sink node
101 * validity is set if the edge is used to ensure correctness
102 * proximity is set if the edge is used to minimize dependence distances
104 * For validity edges, start and end mark the sequence of inequality
105 * constraints in the LP problem that encode the validity constraint
106 * corresponding to this edge.
108 struct isl_sched_edge
{
111 struct isl_sched_node
*src
;
112 struct isl_sched_node
*dst
;
122 isl_edge_validity
= 0,
123 isl_edge_first
= isl_edge_validity
,
125 isl_edge_last
= isl_edge_proximity
128 /* Internal information about the dependence graph used during
129 * the construction of the schedule.
131 * intra_hmap is a cache, mapping dependence relations to their dual,
132 * for dependences from a node to itself
133 * inter_hmap is a cache, mapping dependence relations to their dual,
134 * for dependences between distinct nodes
136 * n is the number of nodes
137 * node is the list of nodes
138 * maxvar is the maximal number of variables over all nodes
139 * max_row is the allocated number of rows in the schedule
140 * n_row is the current (maximal) number of linearly independent
141 * rows in the node schedules
142 * n_total_row is the current number of rows in the node schedules
143 * n_band is the current number of completed bands
144 * band_start is the starting row in the node schedules of the current band
145 * root is set if this graph is the original dependence graph,
146 * without any splitting
148 * sorted contains a list of node indices sorted according to the
149 * SCC to which a node belongs
151 * n_edge is the number of edges
152 * edge is the list of edges
153 * max_edge contains the maximal number of edges of each type;
154 * in particular, it contains the number of edges in the inital graph.
155 * edge_table contains pointers into the edge array, hashed on the source
156 * and sink spaces; there is one such table for each type;
157 * a given edge may be referenced from more than one table
158 * if the corresponding relation appears in more than of the
159 * sets of dependences
161 * node_table contains pointers into the node array, hashed on the space
163 * region contains a list of variable sequences that should be non-trivial
165 * lp contains the (I)LP problem used to obtain new schedule rows
167 * src_scc and dst_scc are the source and sink SCCs of an edge with
168 * conflicting constraints
170 * scc represents the number of components
172 struct isl_sched_graph
{
173 isl_hmap_map_basic_set
*intra_hmap
;
174 isl_hmap_map_basic_set
*inter_hmap
;
176 struct isl_sched_node
*node
;
190 struct isl_sched_edge
*edge
;
192 int max_edge
[isl_edge_last
+ 1];
193 struct isl_hash_table
*edge_table
[isl_edge_last
+ 1];
195 struct isl_hash_table
*node_table
;
196 struct isl_region
*region
;
206 /* Initialize node_table based on the list of nodes.
208 static int graph_init_table(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
212 graph
->node_table
= isl_hash_table_alloc(ctx
, graph
->n
);
213 if (!graph
->node_table
)
216 for (i
= 0; i
< graph
->n
; ++i
) {
217 struct isl_hash_table_entry
*entry
;
220 hash
= isl_space_get_hash(graph
->node
[i
].dim
);
221 entry
= isl_hash_table_find(ctx
, graph
->node_table
, hash
,
223 graph
->node
[i
].dim
, 1);
226 entry
->data
= &graph
->node
[i
];
232 /* Return a pointer to the node that lives within the given space,
233 * or NULL if there is no such node.
235 static struct isl_sched_node
*graph_find_node(isl_ctx
*ctx
,
236 struct isl_sched_graph
*graph
, __isl_keep isl_space
*dim
)
238 struct isl_hash_table_entry
*entry
;
241 hash
= isl_space_get_hash(dim
);
242 entry
= isl_hash_table_find(ctx
, graph
->node_table
, hash
,
243 &node_has_dim
, dim
, 0);
245 return entry
? entry
->data
: NULL
;
248 static int edge_has_src_and_dst(const void *entry
, const void *val
)
250 const struct isl_sched_edge
*edge
= entry
;
251 const struct isl_sched_edge
*temp
= val
;
253 return edge
->src
== temp
->src
&& edge
->dst
== temp
->dst
;
256 /* Add the given edge to graph->edge_table[type].
258 static int graph_edge_table_add(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
259 enum isl_edge_type type
, struct isl_sched_edge
*edge
)
261 struct isl_hash_table_entry
*entry
;
264 hash
= isl_hash_init();
265 hash
= isl_hash_builtin(hash
, edge
->src
);
266 hash
= isl_hash_builtin(hash
, edge
->dst
);
267 entry
= isl_hash_table_find(ctx
, graph
->edge_table
[type
], hash
,
268 &edge_has_src_and_dst
, edge
, 1);
276 /* Allocate the edge_tables based on the maximal number of edges of
279 static int graph_init_edge_tables(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
283 for (i
= 0; i
<= isl_edge_last
; ++i
) {
284 graph
->edge_table
[i
] = isl_hash_table_alloc(ctx
,
286 if (!graph
->edge_table
[i
])
293 /* If graph->edge_table[type] contains an edge from the given source
294 * to the given destination, then return the hash table entry of this edge.
295 * Otherwise, return NULL.
297 static struct isl_hash_table_entry
*graph_find_edge_entry(
298 struct isl_sched_graph
*graph
,
299 enum isl_edge_type type
,
300 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
302 isl_ctx
*ctx
= isl_space_get_ctx(src
->dim
);
304 struct isl_sched_edge temp
= { .src
= src
, .dst
= dst
};
306 hash
= isl_hash_init();
307 hash
= isl_hash_builtin(hash
, temp
.src
);
308 hash
= isl_hash_builtin(hash
, temp
.dst
);
309 return isl_hash_table_find(ctx
, graph
->edge_table
[type
], hash
,
310 &edge_has_src_and_dst
, &temp
, 0);
314 /* If graph->edge_table[type] contains an edge from the given source
315 * to the given destination, then return this edge.
316 * Otherwise, return NULL.
318 static struct isl_sched_edge
*graph_find_edge(struct isl_sched_graph
*graph
,
319 enum isl_edge_type type
,
320 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
322 struct isl_hash_table_entry
*entry
;
324 entry
= graph_find_edge_entry(graph
, type
, src
, dst
);
331 /* Check whether the dependence graph has an edge of the given type
332 * between the given two nodes.
334 static int graph_has_edge(struct isl_sched_graph
*graph
,
335 enum isl_edge_type type
,
336 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
338 struct isl_sched_edge
*edge
;
341 edge
= graph_find_edge(graph
, type
, src
, dst
);
345 empty
= isl_map_plain_is_empty(edge
->map
);
352 /* If there is an edge from the given source to the given destination
353 * of any type then return this edge.
354 * Otherwise, return NULL.
356 static struct isl_sched_edge
*graph_find_any_edge(struct isl_sched_graph
*graph
,
357 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
359 enum isl_edge_type i
;
360 struct isl_sched_edge
*edge
;
362 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
363 edge
= graph_find_edge(graph
, i
, src
, dst
);
371 /* Remove the given edge from all the edge_tables that refer to it.
373 static void graph_remove_edge(struct isl_sched_graph
*graph
,
374 struct isl_sched_edge
*edge
)
376 isl_ctx
*ctx
= isl_map_get_ctx(edge
->map
);
377 enum isl_edge_type i
;
379 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
380 struct isl_hash_table_entry
*entry
;
382 entry
= graph_find_edge_entry(graph
, i
, edge
->src
, edge
->dst
);
385 if (entry
->data
!= edge
)
387 isl_hash_table_remove(ctx
, graph
->edge_table
[i
], entry
);
391 /* Check whether the dependence graph has any edge
392 * between the given two nodes.
394 static int graph_has_any_edge(struct isl_sched_graph
*graph
,
395 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
397 enum isl_edge_type i
;
400 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
401 r
= graph_has_edge(graph
, i
, src
, dst
);
409 /* Check whether the dependence graph has a validity edge
410 * between the given two nodes.
412 static int graph_has_validity_edge(struct isl_sched_graph
*graph
,
413 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
415 return graph_has_edge(graph
, isl_edge_validity
, src
, dst
);
418 static int graph_alloc(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
419 int n_node
, int n_edge
)
424 graph
->n_edge
= n_edge
;
425 graph
->node
= isl_calloc_array(ctx
, struct isl_sched_node
, graph
->n
);
426 graph
->sorted
= isl_calloc_array(ctx
, int, graph
->n
);
427 graph
->region
= isl_alloc_array(ctx
, struct isl_region
, graph
->n
);
428 graph
->edge
= isl_calloc_array(ctx
,
429 struct isl_sched_edge
, graph
->n_edge
);
431 graph
->intra_hmap
= isl_hmap_map_basic_set_alloc(ctx
, 2 * n_edge
);
432 graph
->inter_hmap
= isl_hmap_map_basic_set_alloc(ctx
, 2 * n_edge
);
434 if (!graph
->node
|| !graph
->region
|| !graph
->edge
|| !graph
->sorted
)
437 for(i
= 0; i
< graph
->n
; ++i
)
438 graph
->sorted
[i
] = i
;
443 static void graph_free(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
447 isl_hmap_map_basic_set_free(ctx
, graph
->intra_hmap
);
448 isl_hmap_map_basic_set_free(ctx
, graph
->inter_hmap
);
450 for (i
= 0; i
< graph
->n
; ++i
) {
451 isl_space_free(graph
->node
[i
].dim
);
452 isl_mat_free(graph
->node
[i
].sched
);
453 isl_map_free(graph
->node
[i
].sched_map
);
454 isl_mat_free(graph
->node
[i
].cmap
);
456 free(graph
->node
[i
].band
);
457 free(graph
->node
[i
].band_id
);
458 free(graph
->node
[i
].zero
);
463 for (i
= 0; i
< graph
->n_edge
; ++i
)
464 isl_map_free(graph
->edge
[i
].map
);
467 for (i
= 0; i
<= isl_edge_last
; ++i
)
468 isl_hash_table_free(ctx
, graph
->edge_table
[i
]);
469 isl_hash_table_free(ctx
, graph
->node_table
);
470 isl_basic_set_free(graph
->lp
);
473 /* For each "set" on which this function is called, increment
474 * graph->n by one and update graph->maxvar.
476 static int init_n_maxvar(__isl_take isl_set
*set
, void *user
)
478 struct isl_sched_graph
*graph
= user
;
479 int nvar
= isl_set_dim(set
, isl_dim_set
);
482 if (nvar
> graph
->maxvar
)
483 graph
->maxvar
= nvar
;
490 /* Compute the number of rows that should be allocated for the schedule.
491 * The graph can be split at most "n - 1" times, there can be at most
492 * two rows for each dimension in the iteration domains (in particular,
493 * we usually have one row, but it may be split by split_scaled),
494 * and there can be one extra row for ordering the statements.
495 * Note that if we have actually split "n - 1" times, then no ordering
496 * is needed, so in principle we could use "graph->n + 2 * graph->maxvar - 1".
498 static int compute_max_row(struct isl_sched_graph
*graph
,
499 __isl_keep isl_union_set
*domain
)
503 if (isl_union_set_foreach_set(domain
, &init_n_maxvar
, graph
) < 0)
505 graph
->max_row
= graph
->n
+ 2 * graph
->maxvar
;
510 /* Add a new node to the graph representing the given set.
512 static int extract_node(__isl_take isl_set
*set
, void *user
)
518 struct isl_sched_graph
*graph
= user
;
519 int *band
, *band_id
, *zero
;
521 ctx
= isl_set_get_ctx(set
);
522 dim
= isl_set_get_space(set
);
524 nvar
= isl_space_dim(dim
, isl_dim_set
);
525 nparam
= isl_space_dim(dim
, isl_dim_param
);
526 if (!ctx
->opt
->schedule_parametric
)
528 sched
= isl_mat_alloc(ctx
, 0, 1 + nparam
+ nvar
);
529 graph
->node
[graph
->n
].dim
= dim
;
530 graph
->node
[graph
->n
].nvar
= nvar
;
531 graph
->node
[graph
->n
].nparam
= nparam
;
532 graph
->node
[graph
->n
].sched
= sched
;
533 graph
->node
[graph
->n
].sched_map
= NULL
;
534 band
= isl_alloc_array(ctx
, int, graph
->max_row
);
535 graph
->node
[graph
->n
].band
= band
;
536 band_id
= isl_calloc_array(ctx
, int, graph
->max_row
);
537 graph
->node
[graph
->n
].band_id
= band_id
;
538 zero
= isl_calloc_array(ctx
, int, graph
->max_row
);
539 graph
->node
[graph
->n
].zero
= zero
;
542 if (!sched
|| !band
|| !band_id
|| !zero
)
548 struct isl_extract_edge_data
{
549 enum isl_edge_type type
;
550 struct isl_sched_graph
*graph
;
553 /* Add a new edge to the graph based on the given map
554 * and add it to data->graph->edge_table[data->type].
555 * If a dependence relation of a given type happens to be identical
556 * to one of the dependence relations of a type that was added before,
557 * then we don't create a new edge, but instead mark the original edge
558 * as also representing a dependence of the current type.
560 static int extract_edge(__isl_take isl_map
*map
, void *user
)
562 isl_ctx
*ctx
= isl_map_get_ctx(map
);
563 struct isl_extract_edge_data
*data
= user
;
564 struct isl_sched_graph
*graph
= data
->graph
;
565 struct isl_sched_node
*src
, *dst
;
567 struct isl_sched_edge
*edge
;
570 dim
= isl_space_domain(isl_map_get_space(map
));
571 src
= graph_find_node(ctx
, graph
, dim
);
573 dim
= isl_space_range(isl_map_get_space(map
));
574 dst
= graph_find_node(ctx
, graph
, dim
);
582 graph
->edge
[graph
->n_edge
].src
= src
;
583 graph
->edge
[graph
->n_edge
].dst
= dst
;
584 graph
->edge
[graph
->n_edge
].map
= map
;
585 if (data
->type
== isl_edge_validity
) {
586 graph
->edge
[graph
->n_edge
].validity
= 1;
587 graph
->edge
[graph
->n_edge
].proximity
= 0;
589 if (data
->type
== isl_edge_proximity
) {
590 graph
->edge
[graph
->n_edge
].validity
= 0;
591 graph
->edge
[graph
->n_edge
].proximity
= 1;
595 edge
= graph_find_any_edge(graph
, src
, dst
);
597 return graph_edge_table_add(ctx
, graph
, data
->type
,
598 &graph
->edge
[graph
->n_edge
- 1]);
599 is_equal
= isl_map_plain_is_equal(map
, edge
->map
);
603 return graph_edge_table_add(ctx
, graph
, data
->type
,
604 &graph
->edge
[graph
->n_edge
- 1]);
607 edge
->validity
|= graph
->edge
[graph
->n_edge
].validity
;
608 edge
->proximity
|= graph
->edge
[graph
->n_edge
].proximity
;
611 return graph_edge_table_add(ctx
, graph
, data
->type
, edge
);
614 /* Check whether there is any dependence from node[j] to node[i]
615 * or from node[i] to node[j].
617 static int node_follows_weak(int i
, int j
, void *user
)
620 struct isl_sched_graph
*graph
= user
;
622 f
= graph_has_any_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
625 return graph_has_any_edge(graph
, &graph
->node
[i
], &graph
->node
[j
]);
628 /* Check whether there is a validity dependence from node[j] to node[i],
629 * forcing node[i] to follow node[j].
631 static int node_follows_strong(int i
, int j
, void *user
)
633 struct isl_sched_graph
*graph
= user
;
635 return graph_has_validity_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
638 /* Use Tarjan's algorithm for computing the strongly connected components
639 * in the dependence graph (only validity edges).
640 * If weak is set, we consider the graph to be undirected and
641 * we effectively compute the (weakly) connected components.
642 * Additionally, we also consider other edges when weak is set.
644 static int detect_ccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
, int weak
)
647 struct isl_tarjan_graph
*g
= NULL
;
649 g
= isl_tarjan_graph_init(ctx
, graph
->n
,
650 weak
? &node_follows_weak
: &node_follows_strong
, graph
);
658 while (g
->order
[i
] != -1) {
659 graph
->node
[g
->order
[i
]].scc
= graph
->scc
;
667 isl_tarjan_graph_free(g
);
672 /* Apply Tarjan's algorithm to detect the strongly connected components
673 * in the dependence graph.
675 static int detect_sccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
677 return detect_ccs(ctx
, graph
, 0);
680 /* Apply Tarjan's algorithm to detect the (weakly) connected components
681 * in the dependence graph.
683 static int detect_wccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
685 return detect_ccs(ctx
, graph
, 1);
688 static int cmp_scc(const void *a
, const void *b
, void *data
)
690 struct isl_sched_graph
*graph
= data
;
694 return graph
->node
[*i1
].scc
- graph
->node
[*i2
].scc
;
697 /* Sort the elements of graph->sorted according to the corresponding SCCs.
699 static int sort_sccs(struct isl_sched_graph
*graph
)
701 return isl_sort(graph
->sorted
, graph
->n
, sizeof(int), &cmp_scc
, graph
);
704 /* Given a dependence relation R from a node to itself,
705 * construct the set of coefficients of valid constraints for elements
706 * in that dependence relation.
707 * In particular, the result contains tuples of coefficients
708 * c_0, c_n, c_x such that
710 * c_0 + c_n n + c_x y - c_x x >= 0 for each (x,y) in R
714 * c_0 + c_n n + c_x d >= 0 for each d in delta R = { y - x | (x,y) in R }
716 * We choose here to compute the dual of delta R.
717 * Alternatively, we could have computed the dual of R, resulting
718 * in a set of tuples c_0, c_n, c_x, c_y, and then
719 * plugged in (c_0, c_n, c_x, -c_x).
721 static __isl_give isl_basic_set
*intra_coefficients(
722 struct isl_sched_graph
*graph
, __isl_take isl_map
*map
)
724 isl_ctx
*ctx
= isl_map_get_ctx(map
);
728 if (isl_hmap_map_basic_set_has(ctx
, graph
->intra_hmap
, map
))
729 return isl_hmap_map_basic_set_get(ctx
, graph
->intra_hmap
, map
);
731 delta
= isl_set_remove_divs(isl_map_deltas(isl_map_copy(map
)));
732 coef
= isl_set_coefficients(delta
);
733 isl_hmap_map_basic_set_set(ctx
, graph
->intra_hmap
, map
,
734 isl_basic_set_copy(coef
));
739 /* Given a dependence relation R, * construct the set of coefficients
740 * of valid constraints for elements in that dependence relation.
741 * In particular, the result contains tuples of coefficients
742 * c_0, c_n, c_x, c_y such that
744 * c_0 + c_n n + c_x x + c_y y >= 0 for each (x,y) in R
747 static __isl_give isl_basic_set
*inter_coefficients(
748 struct isl_sched_graph
*graph
, __isl_take isl_map
*map
)
750 isl_ctx
*ctx
= isl_map_get_ctx(map
);
754 if (isl_hmap_map_basic_set_has(ctx
, graph
->inter_hmap
, map
))
755 return isl_hmap_map_basic_set_get(ctx
, graph
->inter_hmap
, map
);
757 set
= isl_map_wrap(isl_map_remove_divs(isl_map_copy(map
)));
758 coef
= isl_set_coefficients(set
);
759 isl_hmap_map_basic_set_set(ctx
, graph
->inter_hmap
, map
,
760 isl_basic_set_copy(coef
));
765 /* Add constraints to graph->lp that force validity for the given
766 * dependence from a node i to itself.
767 * That is, add constraints that enforce
769 * (c_i_0 + c_i_n n + c_i_x y) - (c_i_0 + c_i_n n + c_i_x x)
770 * = c_i_x (y - x) >= 0
772 * for each (x,y) in R.
773 * We obtain general constraints on coefficients (c_0, c_n, c_x)
774 * of valid constraints for (y - x) and then plug in (0, 0, c_i_x^+ - c_i_x^-),
775 * where c_i_x = c_i_x^+ - c_i_x^-, with c_i_x^+ and c_i_x^- non-negative.
776 * In graph->lp, the c_i_x^- appear before their c_i_x^+ counterpart.
778 * Actually, we do not construct constraints for the c_i_x themselves,
779 * but for the coefficients of c_i_x written as a linear combination
780 * of the columns in node->cmap.
782 static int add_intra_validity_constraints(struct isl_sched_graph
*graph
,
783 struct isl_sched_edge
*edge
)
786 isl_map
*map
= isl_map_copy(edge
->map
);
787 isl_ctx
*ctx
= isl_map_get_ctx(map
);
789 isl_dim_map
*dim_map
;
791 struct isl_sched_node
*node
= edge
->src
;
793 coef
= intra_coefficients(graph
, map
);
795 dim
= isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef
)));
797 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
798 isl_space_dim(dim
, isl_dim_set
), isl_mat_copy(node
->cmap
));
802 total
= isl_basic_set_total_dim(graph
->lp
);
803 dim_map
= isl_dim_map_alloc(ctx
, total
);
804 isl_dim_map_range(dim_map
, node
->start
+ 2 * node
->nparam
+ 1, 2,
805 isl_space_dim(dim
, isl_dim_set
), 1,
807 isl_dim_map_range(dim_map
, node
->start
+ 2 * node
->nparam
+ 2, 2,
808 isl_space_dim(dim
, isl_dim_set
), 1,
810 graph
->lp
= isl_basic_set_extend_constraints(graph
->lp
,
811 coef
->n_eq
, coef
->n_ineq
);
812 graph
->lp
= isl_basic_set_add_constraints_dim_map(graph
->lp
,
822 /* Add constraints to graph->lp that force validity for the given
823 * dependence from node i to node j.
824 * That is, add constraints that enforce
826 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) >= 0
828 * for each (x,y) in R.
829 * We obtain general constraints on coefficients (c_0, c_n, c_x, c_y)
830 * of valid constraints for R and then plug in
831 * (c_j_0 - c_i_0, c_j_n^+ - c_j_n^- - (c_i_n^+ - c_i_n^-),
832 * c_j_x^+ - c_j_x^- - (c_i_x^+ - c_i_x^-)),
833 * where c_* = c_*^+ - c_*^-, with c_*^+ and c_*^- non-negative.
834 * In graph->lp, the c_*^- appear before their c_*^+ counterpart.
836 * Actually, we do not construct constraints for the c_*_x themselves,
837 * but for the coefficients of c_*_x written as a linear combination
838 * of the columns in node->cmap.
840 static int add_inter_validity_constraints(struct isl_sched_graph
*graph
,
841 struct isl_sched_edge
*edge
)
844 isl_map
*map
= isl_map_copy(edge
->map
);
845 isl_ctx
*ctx
= isl_map_get_ctx(map
);
847 isl_dim_map
*dim_map
;
849 struct isl_sched_node
*src
= edge
->src
;
850 struct isl_sched_node
*dst
= edge
->dst
;
852 coef
= inter_coefficients(graph
, map
);
854 dim
= isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef
)));
856 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
857 isl_space_dim(dim
, isl_dim_set
), isl_mat_copy(src
->cmap
));
858 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
859 isl_space_dim(dim
, isl_dim_set
) + src
->nvar
,
860 isl_mat_copy(dst
->cmap
));
864 total
= isl_basic_set_total_dim(graph
->lp
);
865 dim_map
= isl_dim_map_alloc(ctx
, total
);
867 isl_dim_map_range(dim_map
, dst
->start
, 0, 0, 0, 1, 1);
868 isl_dim_map_range(dim_map
, dst
->start
+ 1, 2, 1, 1, dst
->nparam
, -1);
869 isl_dim_map_range(dim_map
, dst
->start
+ 2, 2, 1, 1, dst
->nparam
, 1);
870 isl_dim_map_range(dim_map
, dst
->start
+ 2 * dst
->nparam
+ 1, 2,
871 isl_space_dim(dim
, isl_dim_set
) + src
->nvar
, 1,
873 isl_dim_map_range(dim_map
, dst
->start
+ 2 * dst
->nparam
+ 2, 2,
874 isl_space_dim(dim
, isl_dim_set
) + src
->nvar
, 1,
877 isl_dim_map_range(dim_map
, src
->start
, 0, 0, 0, 1, -1);
878 isl_dim_map_range(dim_map
, src
->start
+ 1, 2, 1, 1, src
->nparam
, 1);
879 isl_dim_map_range(dim_map
, src
->start
+ 2, 2, 1, 1, src
->nparam
, -1);
880 isl_dim_map_range(dim_map
, src
->start
+ 2 * src
->nparam
+ 1, 2,
881 isl_space_dim(dim
, isl_dim_set
), 1,
883 isl_dim_map_range(dim_map
, src
->start
+ 2 * src
->nparam
+ 2, 2,
884 isl_space_dim(dim
, isl_dim_set
), 1,
887 edge
->start
= graph
->lp
->n_ineq
;
888 graph
->lp
= isl_basic_set_extend_constraints(graph
->lp
,
889 coef
->n_eq
, coef
->n_ineq
);
890 graph
->lp
= isl_basic_set_add_constraints_dim_map(graph
->lp
,
895 edge
->end
= graph
->lp
->n_ineq
;
903 /* Add constraints to graph->lp that bound the dependence distance for the given
904 * dependence from a node i to itself.
905 * If s = 1, we add the constraint
907 * c_i_x (y - x) <= m_0 + m_n n
911 * -c_i_x (y - x) + m_0 + m_n n >= 0
913 * for each (x,y) in R.
914 * If s = -1, we add the constraint
916 * -c_i_x (y - x) <= m_0 + m_n n
920 * c_i_x (y - x) + m_0 + m_n n >= 0
922 * for each (x,y) in R.
923 * We obtain general constraints on coefficients (c_0, c_n, c_x)
924 * of valid constraints for (y - x) and then plug in (m_0, m_n, -s * c_i_x),
925 * with each coefficient (except m_0) represented as a pair of non-negative
928 * Actually, we do not construct constraints for the c_i_x themselves,
929 * but for the coefficients of c_i_x written as a linear combination
930 * of the columns in node->cmap.
932 static int add_intra_proximity_constraints(struct isl_sched_graph
*graph
,
933 struct isl_sched_edge
*edge
, int s
)
937 isl_map
*map
= isl_map_copy(edge
->map
);
938 isl_ctx
*ctx
= isl_map_get_ctx(map
);
940 isl_dim_map
*dim_map
;
942 struct isl_sched_node
*node
= edge
->src
;
944 coef
= intra_coefficients(graph
, map
);
946 dim
= isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef
)));
948 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
949 isl_space_dim(dim
, isl_dim_set
), isl_mat_copy(node
->cmap
));
953 nparam
= isl_space_dim(node
->dim
, isl_dim_param
);
954 total
= isl_basic_set_total_dim(graph
->lp
);
955 dim_map
= isl_dim_map_alloc(ctx
, total
);
956 isl_dim_map_range(dim_map
, 1, 0, 0, 0, 1, 1);
957 isl_dim_map_range(dim_map
, 4, 2, 1, 1, nparam
, -1);
958 isl_dim_map_range(dim_map
, 5, 2, 1, 1, nparam
, 1);
959 isl_dim_map_range(dim_map
, node
->start
+ 2 * node
->nparam
+ 1, 2,
960 isl_space_dim(dim
, isl_dim_set
), 1,
962 isl_dim_map_range(dim_map
, node
->start
+ 2 * node
->nparam
+ 2, 2,
963 isl_space_dim(dim
, isl_dim_set
), 1,
965 graph
->lp
= isl_basic_set_extend_constraints(graph
->lp
,
966 coef
->n_eq
, coef
->n_ineq
);
967 graph
->lp
= isl_basic_set_add_constraints_dim_map(graph
->lp
,
977 /* Add constraints to graph->lp that bound the dependence distance for the given
978 * dependence from node i to node j.
979 * If s = 1, we add the constraint
981 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x)
986 * -(c_j_0 + c_j_n n + c_j_x y) + (c_i_0 + c_i_n n + c_i_x x) +
989 * for each (x,y) in R.
990 * If s = -1, we add the constraint
992 * -((c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x))
997 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) +
1000 * for each (x,y) in R.
1001 * We obtain general constraints on coefficients (c_0, c_n, c_x, c_y)
1002 * of valid constraints for R and then plug in
1003 * (m_0 - s*c_j_0 + s*c_i_0, m_n - s*c_j_n + s*c_i_n,
1005 * with each coefficient (except m_0, c_j_0 and c_i_0)
1006 * represented as a pair of non-negative coefficients.
1008 * Actually, we do not construct constraints for the c_*_x themselves,
1009 * but for the coefficients of c_*_x written as a linear combination
1010 * of the columns in node->cmap.
1012 static int add_inter_proximity_constraints(struct isl_sched_graph
*graph
,
1013 struct isl_sched_edge
*edge
, int s
)
1017 isl_map
*map
= isl_map_copy(edge
->map
);
1018 isl_ctx
*ctx
= isl_map_get_ctx(map
);
1020 isl_dim_map
*dim_map
;
1021 isl_basic_set
*coef
;
1022 struct isl_sched_node
*src
= edge
->src
;
1023 struct isl_sched_node
*dst
= edge
->dst
;
1025 coef
= inter_coefficients(graph
, map
);
1027 dim
= isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef
)));
1029 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
1030 isl_space_dim(dim
, isl_dim_set
), isl_mat_copy(src
->cmap
));
1031 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
1032 isl_space_dim(dim
, isl_dim_set
) + src
->nvar
,
1033 isl_mat_copy(dst
->cmap
));
1037 nparam
= isl_space_dim(src
->dim
, isl_dim_param
);
1038 total
= isl_basic_set_total_dim(graph
->lp
);
1039 dim_map
= isl_dim_map_alloc(ctx
, total
);
1041 isl_dim_map_range(dim_map
, 1, 0, 0, 0, 1, 1);
1042 isl_dim_map_range(dim_map
, 4, 2, 1, 1, nparam
, -1);
1043 isl_dim_map_range(dim_map
, 5, 2, 1, 1, nparam
, 1);
1045 isl_dim_map_range(dim_map
, dst
->start
, 0, 0, 0, 1, -s
);
1046 isl_dim_map_range(dim_map
, dst
->start
+ 1, 2, 1, 1, dst
->nparam
, s
);
1047 isl_dim_map_range(dim_map
, dst
->start
+ 2, 2, 1, 1, dst
->nparam
, -s
);
1048 isl_dim_map_range(dim_map
, dst
->start
+ 2 * dst
->nparam
+ 1, 2,
1049 isl_space_dim(dim
, isl_dim_set
) + src
->nvar
, 1,
1051 isl_dim_map_range(dim_map
, dst
->start
+ 2 * dst
->nparam
+ 2, 2,
1052 isl_space_dim(dim
, isl_dim_set
) + src
->nvar
, 1,
1055 isl_dim_map_range(dim_map
, src
->start
, 0, 0, 0, 1, s
);
1056 isl_dim_map_range(dim_map
, src
->start
+ 1, 2, 1, 1, src
->nparam
, -s
);
1057 isl_dim_map_range(dim_map
, src
->start
+ 2, 2, 1, 1, src
->nparam
, s
);
1058 isl_dim_map_range(dim_map
, src
->start
+ 2 * src
->nparam
+ 1, 2,
1059 isl_space_dim(dim
, isl_dim_set
), 1,
1061 isl_dim_map_range(dim_map
, src
->start
+ 2 * src
->nparam
+ 2, 2,
1062 isl_space_dim(dim
, isl_dim_set
), 1,
1065 graph
->lp
= isl_basic_set_extend_constraints(graph
->lp
,
1066 coef
->n_eq
, coef
->n_ineq
);
1067 graph
->lp
= isl_basic_set_add_constraints_dim_map(graph
->lp
,
1069 isl_space_free(dim
);
1073 isl_space_free(dim
);
1077 static int add_all_validity_constraints(struct isl_sched_graph
*graph
)
1081 for (i
= 0; i
< graph
->n_edge
; ++i
) {
1082 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
1083 if (!edge
->validity
)
1085 if (edge
->src
!= edge
->dst
)
1087 if (add_intra_validity_constraints(graph
, edge
) < 0)
1091 for (i
= 0; i
< graph
->n_edge
; ++i
) {
1092 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
1093 if (!edge
->validity
)
1095 if (edge
->src
== edge
->dst
)
1097 if (add_inter_validity_constraints(graph
, edge
) < 0)
1104 /* Add constraints to graph->lp that bound the dependence distance
1105 * for all dependence relations.
1106 * If a given proximity dependence is identical to a validity
1107 * dependence, then the dependence distance is already bounded
1108 * from below (by zero), so we only need to bound the distance
1110 * Otherwise, we need to bound the distance both from above and from below.
1112 static int add_all_proximity_constraints(struct isl_sched_graph
*graph
)
1116 for (i
= 0; i
< graph
->n_edge
; ++i
) {
1117 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
1118 if (!edge
->proximity
)
1120 if (edge
->src
== edge
->dst
&&
1121 add_intra_proximity_constraints(graph
, edge
, 1) < 0)
1123 if (edge
->src
!= edge
->dst
&&
1124 add_inter_proximity_constraints(graph
, edge
, 1) < 0)
1128 if (edge
->src
== edge
->dst
&&
1129 add_intra_proximity_constraints(graph
, edge
, -1) < 0)
1131 if (edge
->src
!= edge
->dst
&&
1132 add_inter_proximity_constraints(graph
, edge
, -1) < 0)
1139 /* Compute a basis for the rows in the linear part of the schedule
1140 * and extend this basis to a full basis. The remaining rows
1141 * can then be used to force linear independence from the rows
1144 * In particular, given the schedule rows S, we compute
1148 * with H the Hermite normal form of S. That is, all but the
1149 * first rank columns of Q are zero and so each row in S is
1150 * a linear combination of the first rank rows of Q.
1151 * The matrix Q is then transposed because we will write the
1152 * coefficients of the next schedule row as a column vector s
1153 * and express this s as a linear combination s = Q c of the
1156 static int node_update_cmap(struct isl_sched_node
*node
)
1159 int n_row
= isl_mat_rows(node
->sched
);
1161 H
= isl_mat_sub_alloc(node
->sched
, 0, n_row
,
1162 1 + node
->nparam
, node
->nvar
);
1164 H
= isl_mat_left_hermite(H
, 0, NULL
, &Q
);
1165 isl_mat_free(node
->cmap
);
1166 node
->cmap
= isl_mat_transpose(Q
);
1167 node
->rank
= isl_mat_initial_non_zero_cols(H
);
1170 if (!node
->cmap
|| node
->rank
< 0)
1175 /* Count the number of equality and inequality constraints
1176 * that will be added for the given map.
1177 * If carry is set, then we are counting the number of (validity)
1178 * constraints that will be added in setup_carry_lp and we count
1179 * each edge exactly once. Otherwise, we count as follows
1180 * validity -> 1 (>= 0)
1181 * validity+proximity -> 2 (>= 0 and upper bound)
1182 * proximity -> 2 (lower and upper bound)
1184 static int count_map_constraints(struct isl_sched_graph
*graph
,
1185 struct isl_sched_edge
*edge
, __isl_take isl_map
*map
,
1186 int *n_eq
, int *n_ineq
, int carry
)
1188 isl_basic_set
*coef
;
1189 int f
= carry
? 1 : edge
->proximity
? 2 : 1;
1191 if (carry
&& !edge
->validity
) {
1196 if (edge
->src
== edge
->dst
)
1197 coef
= intra_coefficients(graph
, map
);
1199 coef
= inter_coefficients(graph
, map
);
1202 *n_eq
+= f
* coef
->n_eq
;
1203 *n_ineq
+= f
* coef
->n_ineq
;
1204 isl_basic_set_free(coef
);
1209 /* Count the number of equality and inequality constraints
1210 * that will be added to the main lp problem.
1211 * We count as follows
1212 * validity -> 1 (>= 0)
1213 * validity+proximity -> 2 (>= 0 and upper bound)
1214 * proximity -> 2 (lower and upper bound)
1216 static int count_constraints(struct isl_sched_graph
*graph
,
1217 int *n_eq
, int *n_ineq
)
1221 *n_eq
= *n_ineq
= 0;
1222 for (i
= 0; i
< graph
->n_edge
; ++i
) {
1223 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
1224 isl_map
*map
= isl_map_copy(edge
->map
);
1226 if (count_map_constraints(graph
, edge
, map
,
1227 n_eq
, n_ineq
, 0) < 0)
1234 /* Count the number of constraints that will be added by
1235 * add_bound_coefficient_constraints and increment *n_eq and *n_ineq
1238 * In practice, add_bound_coefficient_constraints only adds inequalities.
1240 static int count_bound_coefficient_constraints(isl_ctx
*ctx
,
1241 struct isl_sched_graph
*graph
, int *n_eq
, int *n_ineq
)
1245 if (ctx
->opt
->schedule_max_coefficient
== -1)
1248 for (i
= 0; i
< graph
->n
; ++i
)
1249 *n_ineq
+= 2 * graph
->node
[i
].nparam
+ 2 * graph
->node
[i
].nvar
;
1254 /* Add constraints that bound the values of the variable and parameter
1255 * coefficients of the schedule.
1257 * The maximal value of the coefficients is defined by the option
1258 * 'schedule_max_coefficient'.
1260 static int add_bound_coefficient_constraints(isl_ctx
*ctx
,
1261 struct isl_sched_graph
*graph
)
1264 int max_coefficient
;
1267 max_coefficient
= ctx
->opt
->schedule_max_coefficient
;
1269 if (max_coefficient
== -1)
1272 total
= isl_basic_set_total_dim(graph
->lp
);
1274 for (i
= 0; i
< graph
->n
; ++i
) {
1275 struct isl_sched_node
*node
= &graph
->node
[i
];
1276 for (j
= 0; j
< 2 * node
->nparam
+ 2 * node
->nvar
; ++j
) {
1278 k
= isl_basic_set_alloc_inequality(graph
->lp
);
1281 dim
= 1 + node
->start
+ 1 + j
;
1282 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
1283 isl_int_set_si(graph
->lp
->ineq
[k
][dim
], -1);
1284 isl_int_set_si(graph
->lp
->ineq
[k
][0], max_coefficient
);
1291 /* Construct an ILP problem for finding schedule coefficients
1292 * that result in non-negative, but small dependence distances
1293 * over all dependences.
1294 * In particular, the dependence distances over proximity edges
1295 * are bounded by m_0 + m_n n and we compute schedule coefficients
1296 * with small values (preferably zero) of m_n and m_0.
1298 * All variables of the ILP are non-negative. The actual coefficients
1299 * may be negative, so each coefficient is represented as the difference
1300 * of two non-negative variables. The negative part always appears
1301 * immediately before the positive part.
1302 * Other than that, the variables have the following order
1304 * - sum of positive and negative parts of m_n coefficients
1306 * - sum of positive and negative parts of all c_n coefficients
1307 * (unconstrained when computing non-parametric schedules)
1308 * - sum of positive and negative parts of all c_x coefficients
1309 * - positive and negative parts of m_n coefficients
1312 * - positive and negative parts of c_i_n (if parametric)
1313 * - positive and negative parts of c_i_x
1315 * The c_i_x are not represented directly, but through the columns of
1316 * node->cmap. That is, the computed values are for variable t_i_x
1317 * such that c_i_x = Q t_i_x with Q equal to node->cmap.
1319 * The constraints are those from the edges plus two or three equalities
1320 * to express the sums.
1322 * If force_zero is set, then we add equalities to ensure that
1323 * the sum of the m_n coefficients and m_0 are both zero.
1325 static int setup_lp(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
1336 int max_constant_term
;
1338 max_constant_term
= ctx
->opt
->schedule_max_constant_term
;
1340 parametric
= ctx
->opt
->schedule_parametric
;
1341 nparam
= isl_space_dim(graph
->node
[0].dim
, isl_dim_param
);
1343 total
= param_pos
+ 2 * nparam
;
1344 for (i
= 0; i
< graph
->n
; ++i
) {
1345 struct isl_sched_node
*node
= &graph
->node
[graph
->sorted
[i
]];
1346 if (node_update_cmap(node
) < 0)
1348 node
->start
= total
;
1349 total
+= 1 + 2 * (node
->nparam
+ node
->nvar
);
1352 if (count_constraints(graph
, &n_eq
, &n_ineq
) < 0)
1354 if (count_bound_coefficient_constraints(ctx
, graph
, &n_eq
, &n_ineq
) < 0)
1357 dim
= isl_space_set_alloc(ctx
, 0, total
);
1358 isl_basic_set_free(graph
->lp
);
1359 n_eq
+= 2 + parametric
+ force_zero
;
1360 if (max_constant_term
!= -1)
1363 graph
->lp
= isl_basic_set_alloc_space(dim
, 0, n_eq
, n_ineq
);
1365 k
= isl_basic_set_alloc_equality(graph
->lp
);
1368 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
1370 isl_int_set_si(graph
->lp
->eq
[k
][1], -1);
1371 for (i
= 0; i
< 2 * nparam
; ++i
)
1372 isl_int_set_si(graph
->lp
->eq
[k
][1 + param_pos
+ i
], 1);
1375 k
= isl_basic_set_alloc_equality(graph
->lp
);
1378 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
1379 isl_int_set_si(graph
->lp
->eq
[k
][2], -1);
1383 k
= isl_basic_set_alloc_equality(graph
->lp
);
1386 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
1387 isl_int_set_si(graph
->lp
->eq
[k
][3], -1);
1388 for (i
= 0; i
< graph
->n
; ++i
) {
1389 int pos
= 1 + graph
->node
[i
].start
+ 1;
1391 for (j
= 0; j
< 2 * graph
->node
[i
].nparam
; ++j
)
1392 isl_int_set_si(graph
->lp
->eq
[k
][pos
+ j
], 1);
1396 k
= isl_basic_set_alloc_equality(graph
->lp
);
1399 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
1400 isl_int_set_si(graph
->lp
->eq
[k
][4], -1);
1401 for (i
= 0; i
< graph
->n
; ++i
) {
1402 struct isl_sched_node
*node
= &graph
->node
[i
];
1403 int pos
= 1 + node
->start
+ 1 + 2 * node
->nparam
;
1405 for (j
= 0; j
< 2 * node
->nvar
; ++j
)
1406 isl_int_set_si(graph
->lp
->eq
[k
][pos
+ j
], 1);
1409 if (max_constant_term
!= -1)
1410 for (i
= 0; i
< graph
->n
; ++i
) {
1411 struct isl_sched_node
*node
= &graph
->node
[i
];
1412 k
= isl_basic_set_alloc_inequality(graph
->lp
);
1415 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
1416 isl_int_set_si(graph
->lp
->ineq
[k
][1 + node
->start
], -1);
1417 isl_int_set_si(graph
->lp
->ineq
[k
][0], max_constant_term
);
1420 if (add_bound_coefficient_constraints(ctx
, graph
) < 0)
1422 if (add_all_validity_constraints(graph
) < 0)
1424 if (add_all_proximity_constraints(graph
) < 0)
1430 /* Analyze the conflicting constraint found by
1431 * isl_tab_basic_set_non_trivial_lexmin. If it corresponds to the validity
1432 * constraint of one of the edges between distinct nodes, living, moreover
1433 * in distinct SCCs, then record the source and sink SCC as this may
1434 * be a good place to cut between SCCs.
1436 static int check_conflict(int con
, void *user
)
1439 struct isl_sched_graph
*graph
= user
;
1441 if (graph
->src_scc
>= 0)
1444 con
-= graph
->lp
->n_eq
;
1446 if (con
>= graph
->lp
->n_ineq
)
1449 for (i
= 0; i
< graph
->n_edge
; ++i
) {
1450 if (!graph
->edge
[i
].validity
)
1452 if (graph
->edge
[i
].src
== graph
->edge
[i
].dst
)
1454 if (graph
->edge
[i
].src
->scc
== graph
->edge
[i
].dst
->scc
)
1456 if (graph
->edge
[i
].start
> con
)
1458 if (graph
->edge
[i
].end
<= con
)
1460 graph
->src_scc
= graph
->edge
[i
].src
->scc
;
1461 graph
->dst_scc
= graph
->edge
[i
].dst
->scc
;
1467 /* Check whether the next schedule row of the given node needs to be
1468 * non-trivial. Lower-dimensional domains may have some trivial rows,
1469 * but as soon as the number of remaining required non-trivial rows
1470 * is as large as the number or remaining rows to be computed,
1471 * all remaining rows need to be non-trivial.
1473 static int needs_row(struct isl_sched_graph
*graph
, struct isl_sched_node
*node
)
1475 return node
->nvar
- node
->rank
>= graph
->maxvar
- graph
->n_row
;
1478 /* Solve the ILP problem constructed in setup_lp.
1479 * For each node such that all the remaining rows of its schedule
1480 * need to be non-trivial, we construct a non-triviality region.
1481 * This region imposes that the next row is independent of previous rows.
1482 * In particular the coefficients c_i_x are represented by t_i_x
1483 * variables with c_i_x = Q t_i_x and Q a unimodular matrix such that
1484 * its first columns span the rows of the previously computed part
1485 * of the schedule. The non-triviality region enforces that at least
1486 * one of the remaining components of t_i_x is non-zero, i.e.,
1487 * that the new schedule row depends on at least one of the remaining
1490 static __isl_give isl_vec
*solve_lp(struct isl_sched_graph
*graph
)
1496 for (i
= 0; i
< graph
->n
; ++i
) {
1497 struct isl_sched_node
*node
= &graph
->node
[i
];
1498 int skip
= node
->rank
;
1499 graph
->region
[i
].pos
= node
->start
+ 1 + 2*(node
->nparam
+skip
);
1500 if (needs_row(graph
, node
))
1501 graph
->region
[i
].len
= 2 * (node
->nvar
- skip
);
1503 graph
->region
[i
].len
= 0;
1505 lp
= isl_basic_set_copy(graph
->lp
);
1506 sol
= isl_tab_basic_set_non_trivial_lexmin(lp
, 2, graph
->n
,
1507 graph
->region
, &check_conflict
, graph
);
1511 /* Update the schedules of all nodes based on the given solution
1512 * of the LP problem.
1513 * The new row is added to the current band.
1514 * All possibly negative coefficients are encoded as a difference
1515 * of two non-negative variables, so we need to perform the subtraction
1516 * here. Moreover, if use_cmap is set, then the solution does
1517 * not refer to the actual coefficients c_i_x, but instead to variables
1518 * t_i_x such that c_i_x = Q t_i_x and Q is equal to node->cmap.
1519 * In this case, we then also need to perform this multiplication
1520 * to obtain the values of c_i_x.
1522 * If check_zero is set, then the first two coordinates of sol are
1523 * assumed to correspond to the dependence distance. If these two
1524 * coordinates are zero, then the corresponding scheduling dimension
1525 * is marked as being zero distance.
1527 static int update_schedule(struct isl_sched_graph
*graph
,
1528 __isl_take isl_vec
*sol
, int use_cmap
, int check_zero
)
1532 isl_vec
*csol
= NULL
;
1537 isl_die(sol
->ctx
, isl_error_internal
,
1538 "no solution found", goto error
);
1539 if (graph
->n_total_row
>= graph
->max_row
)
1540 isl_die(sol
->ctx
, isl_error_internal
,
1541 "too many schedule rows", goto error
);
1544 zero
= isl_int_is_zero(sol
->el
[1]) &&
1545 isl_int_is_zero(sol
->el
[2]);
1547 for (i
= 0; i
< graph
->n
; ++i
) {
1548 struct isl_sched_node
*node
= &graph
->node
[i
];
1549 int pos
= node
->start
;
1550 int row
= isl_mat_rows(node
->sched
);
1553 csol
= isl_vec_alloc(sol
->ctx
, node
->nvar
);
1557 isl_map_free(node
->sched_map
);
1558 node
->sched_map
= NULL
;
1559 node
->sched
= isl_mat_add_rows(node
->sched
, 1);
1562 node
->sched
= isl_mat_set_element(node
->sched
, row
, 0,
1564 for (j
= 0; j
< node
->nparam
+ node
->nvar
; ++j
)
1565 isl_int_sub(sol
->el
[1 + pos
+ 1 + 2 * j
+ 1],
1566 sol
->el
[1 + pos
+ 1 + 2 * j
+ 1],
1567 sol
->el
[1 + pos
+ 1 + 2 * j
]);
1568 for (j
= 0; j
< node
->nparam
; ++j
)
1569 node
->sched
= isl_mat_set_element(node
->sched
,
1570 row
, 1 + j
, sol
->el
[1+pos
+1+2*j
+1]);
1571 for (j
= 0; j
< node
->nvar
; ++j
)
1572 isl_int_set(csol
->el
[j
],
1573 sol
->el
[1+pos
+1+2*(node
->nparam
+j
)+1]);
1575 csol
= isl_mat_vec_product(isl_mat_copy(node
->cmap
),
1579 for (j
= 0; j
< node
->nvar
; ++j
)
1580 node
->sched
= isl_mat_set_element(node
->sched
,
1581 row
, 1 + node
->nparam
+ j
, csol
->el
[j
]);
1582 node
->band
[graph
->n_total_row
] = graph
->n_band
;
1583 node
->zero
[graph
->n_total_row
] = zero
;
1589 graph
->n_total_row
++;
1598 /* Convert node->sched into a multi_aff and return this multi_aff.
1600 static __isl_give isl_multi_aff
*node_extract_schedule_multi_aff(
1601 struct isl_sched_node
*node
)
1605 isl_local_space
*ls
;
1611 nrow
= isl_mat_rows(node
->sched
);
1612 ncol
= isl_mat_cols(node
->sched
) - 1;
1613 space
= isl_space_from_domain(isl_space_copy(node
->dim
));
1614 space
= isl_space_add_dims(space
, isl_dim_out
, nrow
);
1615 ma
= isl_multi_aff_zero(space
);
1616 ls
= isl_local_space_from_space(isl_space_copy(node
->dim
));
1620 for (i
= 0; i
< nrow
; ++i
) {
1621 aff
= isl_aff_zero_on_domain(isl_local_space_copy(ls
));
1622 isl_mat_get_element(node
->sched
, i
, 0, &v
);
1623 aff
= isl_aff_set_constant(aff
, v
);
1624 for (j
= 0; j
< node
->nparam
; ++j
) {
1625 isl_mat_get_element(node
->sched
, i
, 1 + j
, &v
);
1626 aff
= isl_aff_set_coefficient(aff
, isl_dim_param
, j
, v
);
1628 for (j
= 0; j
< node
->nvar
; ++j
) {
1629 isl_mat_get_element(node
->sched
,
1630 i
, 1 + node
->nparam
+ j
, &v
);
1631 aff
= isl_aff_set_coefficient(aff
, isl_dim_in
, j
, v
);
1633 ma
= isl_multi_aff_set_aff(ma
, i
, aff
);
1638 isl_local_space_free(ls
);
1643 /* Convert node->sched into a map and return this map.
1645 * The result is cached in node->sched_map, which needs to be released
1646 * whenever node->sched is updated.
1648 static __isl_give isl_map
*node_extract_schedule(struct isl_sched_node
*node
)
1650 if (!node
->sched_map
) {
1653 ma
= node_extract_schedule_multi_aff(node
);
1654 node
->sched_map
= isl_map_from_multi_aff(ma
);
1657 return isl_map_copy(node
->sched_map
);
1660 /* Update the given dependence relation based on the current schedule.
1661 * That is, intersect the dependence relation with a map expressing
1662 * that source and sink are executed within the same iteration of
1663 * the current schedule.
1664 * This is not the most efficient way, but this shouldn't be a critical
1667 static __isl_give isl_map
*specialize(__isl_take isl_map
*map
,
1668 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
1670 isl_map
*src_sched
, *dst_sched
, *id
;
1672 src_sched
= node_extract_schedule(src
);
1673 dst_sched
= node_extract_schedule(dst
);
1674 id
= isl_map_apply_range(src_sched
, isl_map_reverse(dst_sched
));
1675 return isl_map_intersect(map
, id
);
1678 /* Update the dependence relations of all edges based on the current schedule.
1679 * If a dependence is carried completely by the current schedule, then
1680 * it is removed from the edge_tables. It is kept in the list of edges
1681 * as otherwise all edge_tables would have to be recomputed.
1683 static int update_edges(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
1687 for (i
= graph
->n_edge
- 1; i
>= 0; --i
) {
1688 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
1689 edge
->map
= specialize(edge
->map
, edge
->src
, edge
->dst
);
1693 if (isl_map_plain_is_empty(edge
->map
))
1694 graph_remove_edge(graph
, edge
);
1700 static void next_band(struct isl_sched_graph
*graph
)
1702 graph
->band_start
= graph
->n_total_row
;
1706 /* Topologically sort statements mapped to the same schedule iteration
1707 * and add a row to the schedule corresponding to this order.
1709 static int sort_statements(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
1716 if (update_edges(ctx
, graph
) < 0)
1719 if (graph
->n_edge
== 0)
1722 if (detect_sccs(ctx
, graph
) < 0)
1725 if (graph
->n_total_row
>= graph
->max_row
)
1726 isl_die(ctx
, isl_error_internal
,
1727 "too many schedule rows", return -1);
1729 for (i
= 0; i
< graph
->n
; ++i
) {
1730 struct isl_sched_node
*node
= &graph
->node
[i
];
1731 int row
= isl_mat_rows(node
->sched
);
1732 int cols
= isl_mat_cols(node
->sched
);
1734 isl_map_free(node
->sched_map
);
1735 node
->sched_map
= NULL
;
1736 node
->sched
= isl_mat_add_rows(node
->sched
, 1);
1739 node
->sched
= isl_mat_set_element_si(node
->sched
, row
, 0,
1741 for (j
= 1; j
< cols
; ++j
)
1742 node
->sched
= isl_mat_set_element_si(node
->sched
,
1744 node
->band
[graph
->n_total_row
] = graph
->n_band
;
1747 graph
->n_total_row
++;
1753 /* Construct an isl_schedule based on the computed schedule stored
1754 * in graph and with parameters specified by dim.
1756 static __isl_give isl_schedule
*extract_schedule(struct isl_sched_graph
*graph
,
1757 __isl_take isl_space
*dim
)
1761 isl_schedule
*sched
= NULL
;
1766 ctx
= isl_space_get_ctx(dim
);
1767 sched
= isl_calloc(ctx
, struct isl_schedule
,
1768 sizeof(struct isl_schedule
) +
1769 (graph
->n
- 1) * sizeof(struct isl_schedule_node
));
1774 sched
->n
= graph
->n
;
1775 sched
->n_band
= graph
->n_band
;
1776 sched
->n_total_row
= graph
->n_total_row
;
1778 for (i
= 0; i
< sched
->n
; ++i
) {
1780 int *band_end
, *band_id
, *zero
;
1782 sched
->node
[i
].sched
=
1783 node_extract_schedule_multi_aff(&graph
->node
[i
]);
1784 if (!sched
->node
[i
].sched
)
1787 sched
->node
[i
].n_band
= graph
->n_band
;
1788 if (graph
->n_band
== 0)
1791 band_end
= isl_alloc_array(ctx
, int, graph
->n_band
);
1792 band_id
= isl_alloc_array(ctx
, int, graph
->n_band
);
1793 zero
= isl_alloc_array(ctx
, int, graph
->n_total_row
);
1794 sched
->node
[i
].band_end
= band_end
;
1795 sched
->node
[i
].band_id
= band_id
;
1796 sched
->node
[i
].zero
= zero
;
1797 if (!band_end
|| !band_id
|| !zero
)
1800 for (r
= 0; r
< graph
->n_total_row
; ++r
)
1801 zero
[r
] = graph
->node
[i
].zero
[r
];
1802 for (r
= b
= 0; r
< graph
->n_total_row
; ++r
) {
1803 if (graph
->node
[i
].band
[r
] == b
)
1806 if (graph
->node
[i
].band
[r
] == -1)
1809 if (r
== graph
->n_total_row
)
1811 sched
->node
[i
].n_band
= b
;
1812 for (--b
; b
>= 0; --b
)
1813 band_id
[b
] = graph
->node
[i
].band_id
[b
];
1820 isl_space_free(dim
);
1821 isl_schedule_free(sched
);
1825 /* Copy nodes that satisfy node_pred from the src dependence graph
1826 * to the dst dependence graph.
1828 static int copy_nodes(struct isl_sched_graph
*dst
, struct isl_sched_graph
*src
,
1829 int (*node_pred
)(struct isl_sched_node
*node
, int data
), int data
)
1834 for (i
= 0; i
< src
->n
; ++i
) {
1835 if (!node_pred(&src
->node
[i
], data
))
1837 dst
->node
[dst
->n
].dim
= isl_space_copy(src
->node
[i
].dim
);
1838 dst
->node
[dst
->n
].nvar
= src
->node
[i
].nvar
;
1839 dst
->node
[dst
->n
].nparam
= src
->node
[i
].nparam
;
1840 dst
->node
[dst
->n
].sched
= isl_mat_copy(src
->node
[i
].sched
);
1841 dst
->node
[dst
->n
].sched_map
=
1842 isl_map_copy(src
->node
[i
].sched_map
);
1843 dst
->node
[dst
->n
].band
= src
->node
[i
].band
;
1844 dst
->node
[dst
->n
].band_id
= src
->node
[i
].band_id
;
1845 dst
->node
[dst
->n
].zero
= src
->node
[i
].zero
;
1852 /* Copy non-empty edges that satisfy edge_pred from the src dependence graph
1853 * to the dst dependence graph.
1854 * If the source or destination node of the edge is not in the destination
1855 * graph, then it must be a backward proximity edge and it should simply
1858 static int copy_edges(isl_ctx
*ctx
, struct isl_sched_graph
*dst
,
1859 struct isl_sched_graph
*src
,
1860 int (*edge_pred
)(struct isl_sched_edge
*edge
, int data
), int data
)
1863 enum isl_edge_type t
;
1866 for (i
= 0; i
< src
->n_edge
; ++i
) {
1867 struct isl_sched_edge
*edge
= &src
->edge
[i
];
1869 struct isl_sched_node
*dst_src
, *dst_dst
;
1871 if (!edge_pred(edge
, data
))
1874 if (isl_map_plain_is_empty(edge
->map
))
1877 dst_src
= graph_find_node(ctx
, dst
, edge
->src
->dim
);
1878 dst_dst
= graph_find_node(ctx
, dst
, edge
->dst
->dim
);
1879 if (!dst_src
|| !dst_dst
) {
1881 isl_die(ctx
, isl_error_internal
,
1882 "backward validity edge", return -1);
1886 map
= isl_map_copy(edge
->map
);
1888 dst
->edge
[dst
->n_edge
].src
= dst_src
;
1889 dst
->edge
[dst
->n_edge
].dst
= dst_dst
;
1890 dst
->edge
[dst
->n_edge
].map
= map
;
1891 dst
->edge
[dst
->n_edge
].validity
= edge
->validity
;
1892 dst
->edge
[dst
->n_edge
].proximity
= edge
->proximity
;
1895 for (t
= isl_edge_first
; t
<= isl_edge_last
; ++t
) {
1897 graph_find_edge(src
, t
, edge
->src
, edge
->dst
))
1899 if (graph_edge_table_add(ctx
, dst
, t
,
1900 &dst
->edge
[dst
->n_edge
- 1]) < 0)
1908 /* Given a "src" dependence graph that contains the nodes from "dst"
1909 * that satisfy node_pred, copy the schedule computed in "src"
1910 * for those nodes back to "dst".
1912 static int copy_schedule(struct isl_sched_graph
*dst
,
1913 struct isl_sched_graph
*src
,
1914 int (*node_pred
)(struct isl_sched_node
*node
, int data
), int data
)
1919 for (i
= 0; i
< dst
->n
; ++i
) {
1920 if (!node_pred(&dst
->node
[i
], data
))
1922 isl_mat_free(dst
->node
[i
].sched
);
1923 isl_map_free(dst
->node
[i
].sched_map
);
1924 dst
->node
[i
].sched
= isl_mat_copy(src
->node
[src
->n
].sched
);
1925 dst
->node
[i
].sched_map
=
1926 isl_map_copy(src
->node
[src
->n
].sched_map
);
1930 dst
->max_row
= src
->max_row
;
1931 dst
->n_total_row
= src
->n_total_row
;
1932 dst
->n_band
= src
->n_band
;
1937 /* Compute the maximal number of variables over all nodes.
1938 * This is the maximal number of linearly independent schedule
1939 * rows that we need to compute.
1940 * Just in case we end up in a part of the dependence graph
1941 * with only lower-dimensional domains, we make sure we will
1942 * compute the required amount of extra linearly independent rows.
1944 static int compute_maxvar(struct isl_sched_graph
*graph
)
1949 for (i
= 0; i
< graph
->n
; ++i
) {
1950 struct isl_sched_node
*node
= &graph
->node
[i
];
1953 if (node_update_cmap(node
) < 0)
1955 nvar
= node
->nvar
+ graph
->n_row
- node
->rank
;
1956 if (nvar
> graph
->maxvar
)
1957 graph
->maxvar
= nvar
;
1963 static int compute_schedule(isl_ctx
*ctx
, struct isl_sched_graph
*graph
);
1964 static int compute_schedule_wcc(isl_ctx
*ctx
, struct isl_sched_graph
*graph
);
1966 /* Compute a schedule for a subgraph of "graph". In particular, for
1967 * the graph composed of nodes that satisfy node_pred and edges that
1968 * that satisfy edge_pred. The caller should precompute the number
1969 * of nodes and edges that satisfy these predicates and pass them along
1970 * as "n" and "n_edge".
1971 * If the subgraph is known to consist of a single component, then wcc should
1972 * be set and then we call compute_schedule_wcc on the constructed subgraph.
1973 * Otherwise, we call compute_schedule, which will check whether the subgraph
1976 static int compute_sub_schedule(isl_ctx
*ctx
,
1977 struct isl_sched_graph
*graph
, int n
, int n_edge
,
1978 int (*node_pred
)(struct isl_sched_node
*node
, int data
),
1979 int (*edge_pred
)(struct isl_sched_edge
*edge
, int data
),
1982 struct isl_sched_graph split
= { 0 };
1985 if (graph_alloc(ctx
, &split
, n
, n_edge
) < 0)
1987 if (copy_nodes(&split
, graph
, node_pred
, data
) < 0)
1989 if (graph_init_table(ctx
, &split
) < 0)
1991 for (t
= 0; t
<= isl_edge_last
; ++t
)
1992 split
.max_edge
[t
] = graph
->max_edge
[t
];
1993 if (graph_init_edge_tables(ctx
, &split
) < 0)
1995 if (copy_edges(ctx
, &split
, graph
, edge_pred
, data
) < 0)
1997 split
.n_row
= graph
->n_row
;
1998 split
.max_row
= graph
->max_row
;
1999 split
.n_total_row
= graph
->n_total_row
;
2000 split
.n_band
= graph
->n_band
;
2001 split
.band_start
= graph
->band_start
;
2003 if (wcc
&& compute_schedule_wcc(ctx
, &split
) < 0)
2005 if (!wcc
&& compute_schedule(ctx
, &split
) < 0)
2008 copy_schedule(graph
, &split
, node_pred
, data
);
2010 graph_free(ctx
, &split
);
2013 graph_free(ctx
, &split
);
2017 static int node_scc_exactly(struct isl_sched_node
*node
, int scc
)
2019 return node
->scc
== scc
;
2022 static int node_scc_at_most(struct isl_sched_node
*node
, int scc
)
2024 return node
->scc
<= scc
;
2027 static int node_scc_at_least(struct isl_sched_node
*node
, int scc
)
2029 return node
->scc
>= scc
;
2032 static int edge_scc_exactly(struct isl_sched_edge
*edge
, int scc
)
2034 return edge
->src
->scc
== scc
&& edge
->dst
->scc
== scc
;
2037 static int edge_dst_scc_at_most(struct isl_sched_edge
*edge
, int scc
)
2039 return edge
->dst
->scc
<= scc
;
2042 static int edge_src_scc_at_least(struct isl_sched_edge
*edge
, int scc
)
2044 return edge
->src
->scc
>= scc
;
2047 /* Pad the schedules of all nodes with zero rows such that in the end
2048 * they all have graph->n_total_row rows.
2049 * The extra rows don't belong to any band, so they get assigned band number -1.
2051 static int pad_schedule(struct isl_sched_graph
*graph
)
2055 for (i
= 0; i
< graph
->n
; ++i
) {
2056 struct isl_sched_node
*node
= &graph
->node
[i
];
2057 int row
= isl_mat_rows(node
->sched
);
2058 if (graph
->n_total_row
> row
) {
2059 isl_map_free(node
->sched_map
);
2060 node
->sched_map
= NULL
;
2062 node
->sched
= isl_mat_add_zero_rows(node
->sched
,
2063 graph
->n_total_row
- row
);
2066 for (j
= row
; j
< graph
->n_total_row
; ++j
)
2073 /* Split the current graph into two parts and compute a schedule for each
2074 * part individually. In particular, one part consists of all SCCs up
2075 * to and including graph->src_scc, while the other part contains the other
2078 * The split is enforced in the schedule by constant rows with two different
2079 * values (0 and 1). These constant rows replace the previously computed rows
2080 * in the current band.
2081 * It would be possible to reuse them as the first rows in the next
2082 * band, but recomputing them may result in better rows as we are looking
2083 * at a smaller part of the dependence graph.
2084 * compute_split_schedule is only called when no zero-distance schedule row
2085 * could be found on the entire graph, so we wark the splitting row as
2086 * non zero-distance.
2088 * The band_id of the second group is set to n, where n is the number
2089 * of nodes in the first group. This ensures that the band_ids over
2090 * the two groups remain disjoint, even if either or both of the two
2091 * groups contain independent components.
2093 static int compute_split_schedule(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2095 int i
, j
, n
, e1
, e2
;
2096 int n_total_row
, orig_total_row
;
2097 int n_band
, orig_band
;
2100 if (graph
->n_total_row
>= graph
->max_row
)
2101 isl_die(ctx
, isl_error_internal
,
2102 "too many schedule rows", return -1);
2104 drop
= graph
->n_total_row
- graph
->band_start
;
2105 graph
->n_total_row
-= drop
;
2106 graph
->n_row
-= drop
;
2109 for (i
= 0; i
< graph
->n
; ++i
) {
2110 struct isl_sched_node
*node
= &graph
->node
[i
];
2111 int row
= isl_mat_rows(node
->sched
) - drop
;
2112 int cols
= isl_mat_cols(node
->sched
);
2113 int before
= node
->scc
<= graph
->src_scc
;
2118 isl_map_free(node
->sched_map
);
2119 node
->sched_map
= NULL
;
2120 node
->sched
= isl_mat_drop_rows(node
->sched
,
2121 graph
->band_start
, drop
);
2122 node
->sched
= isl_mat_add_rows(node
->sched
, 1);
2125 node
->sched
= isl_mat_set_element_si(node
->sched
, row
, 0,
2127 for (j
= 1; j
< cols
; ++j
)
2128 node
->sched
= isl_mat_set_element_si(node
->sched
,
2130 node
->band
[graph
->n_total_row
] = graph
->n_band
;
2131 node
->zero
[graph
->n_total_row
] = 0;
2135 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2136 if (graph
->edge
[i
].dst
->scc
<= graph
->src_scc
)
2138 if (graph
->edge
[i
].src
->scc
> graph
->src_scc
)
2142 graph
->n_total_row
++;
2145 for (i
= 0; i
< graph
->n
; ++i
) {
2146 struct isl_sched_node
*node
= &graph
->node
[i
];
2147 if (node
->scc
> graph
->src_scc
)
2148 node
->band_id
[graph
->n_band
] = n
;
2151 orig_total_row
= graph
->n_total_row
;
2152 orig_band
= graph
->n_band
;
2153 if (compute_sub_schedule(ctx
, graph
, n
, e1
,
2154 &node_scc_at_most
, &edge_dst_scc_at_most
,
2155 graph
->src_scc
, 0) < 0)
2157 n_total_row
= graph
->n_total_row
;
2158 graph
->n_total_row
= orig_total_row
;
2159 n_band
= graph
->n_band
;
2160 graph
->n_band
= orig_band
;
2161 if (compute_sub_schedule(ctx
, graph
, graph
->n
- n
, e2
,
2162 &node_scc_at_least
, &edge_src_scc_at_least
,
2163 graph
->src_scc
+ 1, 0) < 0)
2165 if (n_total_row
> graph
->n_total_row
)
2166 graph
->n_total_row
= n_total_row
;
2167 if (n_band
> graph
->n_band
)
2168 graph
->n_band
= n_band
;
2170 return pad_schedule(graph
);
2173 /* Compute the next band of the schedule after updating the dependence
2174 * relations based on the the current schedule.
2176 static int compute_next_band(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2178 if (update_edges(ctx
, graph
) < 0)
2182 return compute_schedule(ctx
, graph
);
2185 /* Add constraints to graph->lp that force the dependence "map" (which
2186 * is part of the dependence relation of "edge")
2187 * to be respected and attempt to carry it, where the edge is one from
2188 * a node j to itself. "pos" is the sequence number of the given map.
2189 * That is, add constraints that enforce
2191 * (c_j_0 + c_j_n n + c_j_x y) - (c_j_0 + c_j_n n + c_j_x x)
2192 * = c_j_x (y - x) >= e_i
2194 * for each (x,y) in R.
2195 * We obtain general constraints on coefficients (c_0, c_n, c_x)
2196 * of valid constraints for (y - x) and then plug in (-e_i, 0, c_j_x),
2197 * with each coefficient in c_j_x represented as a pair of non-negative
2200 static int add_intra_constraints(struct isl_sched_graph
*graph
,
2201 struct isl_sched_edge
*edge
, __isl_take isl_map
*map
, int pos
)
2204 isl_ctx
*ctx
= isl_map_get_ctx(map
);
2206 isl_dim_map
*dim_map
;
2207 isl_basic_set
*coef
;
2208 struct isl_sched_node
*node
= edge
->src
;
2210 coef
= intra_coefficients(graph
, map
);
2214 dim
= isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef
)));
2216 total
= isl_basic_set_total_dim(graph
->lp
);
2217 dim_map
= isl_dim_map_alloc(ctx
, total
);
2218 isl_dim_map_range(dim_map
, 3 + pos
, 0, 0, 0, 1, -1);
2219 isl_dim_map_range(dim_map
, node
->start
+ 2 * node
->nparam
+ 1, 2,
2220 isl_space_dim(dim
, isl_dim_set
), 1,
2222 isl_dim_map_range(dim_map
, node
->start
+ 2 * node
->nparam
+ 2, 2,
2223 isl_space_dim(dim
, isl_dim_set
), 1,
2225 graph
->lp
= isl_basic_set_extend_constraints(graph
->lp
,
2226 coef
->n_eq
, coef
->n_ineq
);
2227 graph
->lp
= isl_basic_set_add_constraints_dim_map(graph
->lp
,
2229 isl_space_free(dim
);
2234 /* Add constraints to graph->lp that force the dependence "map" (which
2235 * is part of the dependence relation of "edge")
2236 * to be respected and attempt to carry it, where the edge is one from
2237 * node j to node k. "pos" is the sequence number of the given map.
2238 * That is, add constraints that enforce
2240 * (c_k_0 + c_k_n n + c_k_x y) - (c_j_0 + c_j_n n + c_j_x x) >= e_i
2242 * for each (x,y) in R.
2243 * We obtain general constraints on coefficients (c_0, c_n, c_x)
2244 * of valid constraints for R and then plug in
2245 * (-e_i + c_k_0 - c_j_0, c_k_n - c_j_n, c_k_x - c_j_x)
2246 * with each coefficient (except e_i, c_k_0 and c_j_0)
2247 * represented as a pair of non-negative coefficients.
2249 static int add_inter_constraints(struct isl_sched_graph
*graph
,
2250 struct isl_sched_edge
*edge
, __isl_take isl_map
*map
, int pos
)
2253 isl_ctx
*ctx
= isl_map_get_ctx(map
);
2255 isl_dim_map
*dim_map
;
2256 isl_basic_set
*coef
;
2257 struct isl_sched_node
*src
= edge
->src
;
2258 struct isl_sched_node
*dst
= edge
->dst
;
2260 coef
= inter_coefficients(graph
, map
);
2264 dim
= isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef
)));
2266 total
= isl_basic_set_total_dim(graph
->lp
);
2267 dim_map
= isl_dim_map_alloc(ctx
, total
);
2269 isl_dim_map_range(dim_map
, 3 + pos
, 0, 0, 0, 1, -1);
2271 isl_dim_map_range(dim_map
, dst
->start
, 0, 0, 0, 1, 1);
2272 isl_dim_map_range(dim_map
, dst
->start
+ 1, 2, 1, 1, dst
->nparam
, -1);
2273 isl_dim_map_range(dim_map
, dst
->start
+ 2, 2, 1, 1, dst
->nparam
, 1);
2274 isl_dim_map_range(dim_map
, dst
->start
+ 2 * dst
->nparam
+ 1, 2,
2275 isl_space_dim(dim
, isl_dim_set
) + src
->nvar
, 1,
2277 isl_dim_map_range(dim_map
, dst
->start
+ 2 * dst
->nparam
+ 2, 2,
2278 isl_space_dim(dim
, isl_dim_set
) + src
->nvar
, 1,
2281 isl_dim_map_range(dim_map
, src
->start
, 0, 0, 0, 1, -1);
2282 isl_dim_map_range(dim_map
, src
->start
+ 1, 2, 1, 1, src
->nparam
, 1);
2283 isl_dim_map_range(dim_map
, src
->start
+ 2, 2, 1, 1, src
->nparam
, -1);
2284 isl_dim_map_range(dim_map
, src
->start
+ 2 * src
->nparam
+ 1, 2,
2285 isl_space_dim(dim
, isl_dim_set
), 1,
2287 isl_dim_map_range(dim_map
, src
->start
+ 2 * src
->nparam
+ 2, 2,
2288 isl_space_dim(dim
, isl_dim_set
), 1,
2291 graph
->lp
= isl_basic_set_extend_constraints(graph
->lp
,
2292 coef
->n_eq
, coef
->n_ineq
);
2293 graph
->lp
= isl_basic_set_add_constraints_dim_map(graph
->lp
,
2295 isl_space_free(dim
);
2300 /* Add constraints to graph->lp that force all validity dependences
2301 * to be respected and attempt to carry them.
2303 static int add_all_constraints(struct isl_sched_graph
*graph
)
2309 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2310 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
2312 if (!edge
->validity
)
2315 for (j
= 0; j
< edge
->map
->n
; ++j
) {
2316 isl_basic_map
*bmap
;
2319 bmap
= isl_basic_map_copy(edge
->map
->p
[j
]);
2320 map
= isl_map_from_basic_map(bmap
);
2322 if (edge
->src
== edge
->dst
&&
2323 add_intra_constraints(graph
, edge
, map
, pos
) < 0)
2325 if (edge
->src
!= edge
->dst
&&
2326 add_inter_constraints(graph
, edge
, map
, pos
) < 0)
2335 /* Count the number of equality and inequality constraints
2336 * that will be added to the carry_lp problem.
2337 * We count each edge exactly once.
2339 static int count_all_constraints(struct isl_sched_graph
*graph
,
2340 int *n_eq
, int *n_ineq
)
2344 *n_eq
= *n_ineq
= 0;
2345 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2346 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
2347 for (j
= 0; j
< edge
->map
->n
; ++j
) {
2348 isl_basic_map
*bmap
;
2351 bmap
= isl_basic_map_copy(edge
->map
->p
[j
]);
2352 map
= isl_map_from_basic_map(bmap
);
2354 if (count_map_constraints(graph
, edge
, map
,
2355 n_eq
, n_ineq
, 1) < 0)
2363 /* Construct an LP problem for finding schedule coefficients
2364 * such that the schedule carries as many dependences as possible.
2365 * In particular, for each dependence i, we bound the dependence distance
2366 * from below by e_i, with 0 <= e_i <= 1 and then maximize the sum
2367 * of all e_i's. Dependence with e_i = 0 in the solution are simply
2368 * respected, while those with e_i > 0 (in practice e_i = 1) are carried.
2369 * Note that if the dependence relation is a union of basic maps,
2370 * then we have to consider each basic map individually as it may only
2371 * be possible to carry the dependences expressed by some of those
2372 * basic maps and not all off them.
2373 * Below, we consider each of those basic maps as a separate "edge".
2375 * All variables of the LP are non-negative. The actual coefficients
2376 * may be negative, so each coefficient is represented as the difference
2377 * of two non-negative variables. The negative part always appears
2378 * immediately before the positive part.
2379 * Other than that, the variables have the following order
2381 * - sum of (1 - e_i) over all edges
2382 * - sum of positive and negative parts of all c_n coefficients
2383 * (unconstrained when computing non-parametric schedules)
2384 * - sum of positive and negative parts of all c_x coefficients
2389 * - positive and negative parts of c_i_n (if parametric)
2390 * - positive and negative parts of c_i_x
2392 * The constraints are those from the (validity) edges plus three equalities
2393 * to express the sums and n_edge inequalities to express e_i <= 1.
2395 static int setup_carry_lp(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2405 for (i
= 0; i
< graph
->n_edge
; ++i
)
2406 n_edge
+= graph
->edge
[i
].map
->n
;
2409 for (i
= 0; i
< graph
->n
; ++i
) {
2410 struct isl_sched_node
*node
= &graph
->node
[graph
->sorted
[i
]];
2411 node
->start
= total
;
2412 total
+= 1 + 2 * (node
->nparam
+ node
->nvar
);
2415 if (count_all_constraints(graph
, &n_eq
, &n_ineq
) < 0)
2417 if (count_bound_coefficient_constraints(ctx
, graph
, &n_eq
, &n_ineq
) < 0)
2420 dim
= isl_space_set_alloc(ctx
, 0, total
);
2421 isl_basic_set_free(graph
->lp
);
2424 graph
->lp
= isl_basic_set_alloc_space(dim
, 0, n_eq
, n_ineq
);
2425 graph
->lp
= isl_basic_set_set_rational(graph
->lp
);
2427 k
= isl_basic_set_alloc_equality(graph
->lp
);
2430 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2431 isl_int_set_si(graph
->lp
->eq
[k
][0], -n_edge
);
2432 isl_int_set_si(graph
->lp
->eq
[k
][1], 1);
2433 for (i
= 0; i
< n_edge
; ++i
)
2434 isl_int_set_si(graph
->lp
->eq
[k
][4 + i
], 1);
2436 k
= isl_basic_set_alloc_equality(graph
->lp
);
2439 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2440 isl_int_set_si(graph
->lp
->eq
[k
][2], -1);
2441 for (i
= 0; i
< graph
->n
; ++i
) {
2442 int pos
= 1 + graph
->node
[i
].start
+ 1;
2444 for (j
= 0; j
< 2 * graph
->node
[i
].nparam
; ++j
)
2445 isl_int_set_si(graph
->lp
->eq
[k
][pos
+ j
], 1);
2448 k
= isl_basic_set_alloc_equality(graph
->lp
);
2451 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2452 isl_int_set_si(graph
->lp
->eq
[k
][3], -1);
2453 for (i
= 0; i
< graph
->n
; ++i
) {
2454 struct isl_sched_node
*node
= &graph
->node
[i
];
2455 int pos
= 1 + node
->start
+ 1 + 2 * node
->nparam
;
2457 for (j
= 0; j
< 2 * node
->nvar
; ++j
)
2458 isl_int_set_si(graph
->lp
->eq
[k
][pos
+ j
], 1);
2461 for (i
= 0; i
< n_edge
; ++i
) {
2462 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2465 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
2466 isl_int_set_si(graph
->lp
->ineq
[k
][4 + i
], -1);
2467 isl_int_set_si(graph
->lp
->ineq
[k
][0], 1);
2470 if (add_bound_coefficient_constraints(ctx
, graph
) < 0)
2472 if (add_all_constraints(graph
) < 0)
2478 /* If the schedule_split_scaled option is set and if the linear
2479 * parts of the scheduling rows for all nodes in the graphs have
2480 * non-trivial common divisor, then split off the constant term
2481 * from the linear part.
2482 * The constant term is then placed in a separate band and
2483 * the linear part is reduced.
2485 static int split_scaled(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2491 if (!ctx
->opt
->schedule_split_scaled
)
2496 if (graph
->n_total_row
>= graph
->max_row
)
2497 isl_die(ctx
, isl_error_internal
,
2498 "too many schedule rows", return -1);
2501 isl_int_init(gcd_i
);
2503 isl_int_set_si(gcd
, 0);
2505 row
= isl_mat_rows(graph
->node
[0].sched
) - 1;
2507 for (i
= 0; i
< graph
->n
; ++i
) {
2508 struct isl_sched_node
*node
= &graph
->node
[i
];
2509 int cols
= isl_mat_cols(node
->sched
);
2511 isl_seq_gcd(node
->sched
->row
[row
] + 1, cols
- 1, &gcd_i
);
2512 isl_int_gcd(gcd
, gcd
, gcd_i
);
2515 isl_int_clear(gcd_i
);
2517 if (isl_int_cmp_si(gcd
, 1) <= 0) {
2524 for (i
= 0; i
< graph
->n
; ++i
) {
2525 struct isl_sched_node
*node
= &graph
->node
[i
];
2527 isl_map_free(node
->sched_map
);
2528 node
->sched_map
= NULL
;
2529 node
->sched
= isl_mat_add_zero_rows(node
->sched
, 1);
2532 isl_int_fdiv_r(node
->sched
->row
[row
+ 1][0],
2533 node
->sched
->row
[row
][0], gcd
);
2534 isl_int_fdiv_q(node
->sched
->row
[row
][0],
2535 node
->sched
->row
[row
][0], gcd
);
2536 isl_int_mul(node
->sched
->row
[row
][0],
2537 node
->sched
->row
[row
][0], gcd
);
2538 node
->sched
= isl_mat_scale_down_row(node
->sched
, row
, gcd
);
2541 node
->band
[graph
->n_total_row
] = graph
->n_band
;
2544 graph
->n_total_row
++;
2553 static int compute_component_schedule(isl_ctx
*ctx
,
2554 struct isl_sched_graph
*graph
);
2556 /* Is the schedule row "sol" trivial on node "node"?
2557 * That is, is the solution zero on the dimensions orthogonal to
2558 * the previously found solutions?
2559 * Each coefficient is represented as the difference between
2560 * two non-negative values in "sol". The coefficient is then
2561 * zero if those two values are equal to each other.
2563 static int is_trivial(struct isl_sched_node
*node
, __isl_keep isl_vec
*sol
)
2569 pos
= 1 + node
->start
+ 1 + 2 * (node
->nparam
+ node
->rank
);
2570 len
= 2 * (node
->nvar
- node
->rank
);
2575 for (i
= 0; i
< len
; i
+= 2)
2576 if (isl_int_ne(sol
->el
[pos
+ i
], sol
->el
[pos
+ i
+ 1]))
2582 /* Is the schedule row "sol" trivial on any node where it should
2585 static int is_any_trivial(struct isl_sched_graph
*graph
,
2586 __isl_keep isl_vec
*sol
)
2590 for (i
= 0; i
< graph
->n
; ++i
) {
2591 struct isl_sched_node
*node
= &graph
->node
[i
];
2593 if (!needs_row(graph
, node
))
2595 if (is_trivial(node
, sol
))
2602 /* Construct a schedule row for each node such that as many dependences
2603 * as possible are carried and then continue with the next band.
2605 * If the computed schedule row turns out to be trivial on one or
2606 * more nodes where it should not be trivial, then we throw it away
2607 * and try again on each component separately.
2609 static int carry_dependences(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2617 for (i
= 0; i
< graph
->n_edge
; ++i
)
2618 n_edge
+= graph
->edge
[i
].map
->n
;
2620 if (setup_carry_lp(ctx
, graph
) < 0)
2623 lp
= isl_basic_set_copy(graph
->lp
);
2624 sol
= isl_tab_basic_set_non_neg_lexmin(lp
);
2628 if (sol
->size
== 0) {
2630 isl_die(ctx
, isl_error_internal
,
2631 "error in schedule construction", return -1);
2634 isl_int_divexact(sol
->el
[1], sol
->el
[1], sol
->el
[0]);
2635 if (isl_int_cmp_si(sol
->el
[1], n_edge
) >= 0) {
2637 isl_die(ctx
, isl_error_unknown
,
2638 "unable to carry dependences", return -1);
2641 if (is_any_trivial(graph
, sol
)) {
2644 return compute_component_schedule(ctx
, graph
);
2645 isl_die(ctx
, isl_error_unknown
,
2646 "unable to construct non-trivial solution", return -1);
2649 if (update_schedule(graph
, sol
, 0, 0) < 0)
2652 if (split_scaled(ctx
, graph
) < 0)
2655 return compute_next_band(ctx
, graph
);
2658 /* Are there any (non-empty) validity edges in the graph?
2660 static int has_validity_edges(struct isl_sched_graph
*graph
)
2664 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2667 empty
= isl_map_plain_is_empty(graph
->edge
[i
].map
);
2672 if (graph
->edge
[i
].validity
)
2679 /* Should we apply a Feautrier step?
2680 * That is, did the user request the Feautrier algorithm and are
2681 * there any validity dependences (left)?
2683 static int need_feautrier_step(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2685 if (ctx
->opt
->schedule_algorithm
!= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
)
2688 return has_validity_edges(graph
);
2691 /* Compute a schedule for a connected dependence graph using Feautrier's
2692 * multi-dimensional scheduling algorithm.
2693 * The original algorithm is described in [1].
2694 * The main idea is to minimize the number of scheduling dimensions, by
2695 * trying to satisfy as many dependences as possible per scheduling dimension.
2697 * [1] P. Feautrier, Some Efficient Solutions to the Affine Scheduling
2698 * Problem, Part II: Multi-Dimensional Time.
2699 * In Intl. Journal of Parallel Programming, 1992.
2701 static int compute_schedule_wcc_feautrier(isl_ctx
*ctx
,
2702 struct isl_sched_graph
*graph
)
2704 return carry_dependences(ctx
, graph
);
2707 /* Compute a schedule for a connected dependence graph.
2708 * We try to find a sequence of as many schedule rows as possible that result
2709 * in non-negative dependence distances (independent of the previous rows
2710 * in the sequence, i.e., such that the sequence is tilable).
2711 * If we can't find any more rows we either
2712 * - split between SCCs and start over (assuming we found an interesting
2713 * pair of SCCs between which to split)
2714 * - continue with the next band (assuming the current band has at least
2716 * - try to carry as many dependences as possible and continue with the next
2719 * If Feautrier's algorithm is selected, we first recursively try to satisfy
2720 * as many validity dependences as possible. When all validity dependences
2721 * are satisfied we extend the schedule to a full-dimensional schedule.
2723 * If we manage to complete the schedule, we finish off by topologically
2724 * sorting the statements based on the remaining dependences.
2726 * If ctx->opt->schedule_outer_zero_distance is set, then we force the
2727 * outermost dimension in the current band to be zero distance. If this
2728 * turns out to be impossible, we fall back on the general scheme above
2729 * and try to carry as many dependences as possible.
2731 static int compute_schedule_wcc(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2735 if (detect_sccs(ctx
, graph
) < 0)
2737 if (sort_sccs(graph
) < 0)
2740 if (compute_maxvar(graph
) < 0)
2743 if (need_feautrier_step(ctx
, graph
))
2744 return compute_schedule_wcc_feautrier(ctx
, graph
);
2746 if (ctx
->opt
->schedule_outer_zero_distance
)
2749 while (graph
->n_row
< graph
->maxvar
) {
2752 graph
->src_scc
= -1;
2753 graph
->dst_scc
= -1;
2755 if (setup_lp(ctx
, graph
, force_zero
) < 0)
2757 sol
= solve_lp(graph
);
2760 if (sol
->size
== 0) {
2762 if (!ctx
->opt
->schedule_maximize_band_depth
&&
2763 graph
->n_total_row
> graph
->band_start
)
2764 return compute_next_band(ctx
, graph
);
2765 if (graph
->src_scc
>= 0)
2766 return compute_split_schedule(ctx
, graph
);
2767 if (graph
->n_total_row
> graph
->band_start
)
2768 return compute_next_band(ctx
, graph
);
2769 return carry_dependences(ctx
, graph
);
2771 if (update_schedule(graph
, sol
, 1, 1) < 0)
2776 if (graph
->n_total_row
> graph
->band_start
)
2778 return sort_statements(ctx
, graph
);
2781 /* Add a row to the schedules that separates the SCCs and move
2784 static int split_on_scc(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2788 if (graph
->n_total_row
>= graph
->max_row
)
2789 isl_die(ctx
, isl_error_internal
,
2790 "too many schedule rows", return -1);
2792 for (i
= 0; i
< graph
->n
; ++i
) {
2793 struct isl_sched_node
*node
= &graph
->node
[i
];
2794 int row
= isl_mat_rows(node
->sched
);
2796 isl_map_free(node
->sched_map
);
2797 node
->sched_map
= NULL
;
2798 node
->sched
= isl_mat_add_zero_rows(node
->sched
, 1);
2799 node
->sched
= isl_mat_set_element_si(node
->sched
, row
, 0,
2803 node
->band
[graph
->n_total_row
] = graph
->n_band
;
2806 graph
->n_total_row
++;
2812 /* Compute a schedule for each component (identified by node->scc)
2813 * of the dependence graph separately and then combine the results.
2814 * Depending on the setting of schedule_fuse, a component may be
2815 * either weakly or strongly connected.
2817 * The band_id is adjusted such that each component has a separate id.
2818 * Note that the band_id may have already been set to a value different
2819 * from zero by compute_split_schedule.
2821 static int compute_component_schedule(isl_ctx
*ctx
,
2822 struct isl_sched_graph
*graph
)
2826 int n_total_row
, orig_total_row
;
2827 int n_band
, orig_band
;
2829 if (ctx
->opt
->schedule_fuse
== ISL_SCHEDULE_FUSE_MIN
||
2830 ctx
->opt
->schedule_separate_components
)
2831 if (split_on_scc(ctx
, graph
) < 0)
2835 orig_total_row
= graph
->n_total_row
;
2837 orig_band
= graph
->n_band
;
2838 for (i
= 0; i
< graph
->n
; ++i
)
2839 graph
->node
[i
].band_id
[graph
->n_band
] += graph
->node
[i
].scc
;
2840 for (wcc
= 0; wcc
< graph
->scc
; ++wcc
) {
2842 for (i
= 0; i
< graph
->n
; ++i
)
2843 if (graph
->node
[i
].scc
== wcc
)
2846 for (i
= 0; i
< graph
->n_edge
; ++i
)
2847 if (graph
->edge
[i
].src
->scc
== wcc
&&
2848 graph
->edge
[i
].dst
->scc
== wcc
)
2851 if (compute_sub_schedule(ctx
, graph
, n
, n_edge
,
2853 &edge_scc_exactly
, wcc
, 1) < 0)
2855 if (graph
->n_total_row
> n_total_row
)
2856 n_total_row
= graph
->n_total_row
;
2857 graph
->n_total_row
= orig_total_row
;
2858 if (graph
->n_band
> n_band
)
2859 n_band
= graph
->n_band
;
2860 graph
->n_band
= orig_band
;
2863 graph
->n_total_row
= n_total_row
;
2864 graph
->n_band
= n_band
;
2866 return pad_schedule(graph
);
2869 /* Compute a schedule for the given dependence graph.
2870 * We first check if the graph is connected (through validity dependences)
2871 * and, if not, compute a schedule for each component separately.
2872 * If schedule_fuse is set to minimal fusion, then we check for strongly
2873 * connected components instead and compute a separate schedule for
2874 * each such strongly connected component.
2876 static int compute_schedule(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2878 if (ctx
->opt
->schedule_fuse
== ISL_SCHEDULE_FUSE_MIN
) {
2879 if (detect_sccs(ctx
, graph
) < 0)
2882 if (detect_wccs(ctx
, graph
) < 0)
2887 return compute_component_schedule(ctx
, graph
);
2889 return compute_schedule_wcc(ctx
, graph
);
2892 /* Compute a schedule for the given union of domains that respects
2893 * all the validity dependences.
2894 * If the default isl scheduling algorithm is used, it tries to minimize
2895 * the dependence distances over the proximity dependences.
2896 * If Feautrier's scheduling algorithm is used, the proximity dependence
2897 * distances are only minimized during the extension to a full-dimensional
2900 __isl_give isl_schedule
*isl_union_set_compute_schedule(
2901 __isl_take isl_union_set
*domain
,
2902 __isl_take isl_union_map
*validity
,
2903 __isl_take isl_union_map
*proximity
)
2905 isl_ctx
*ctx
= isl_union_set_get_ctx(domain
);
2907 struct isl_sched_graph graph
= { 0 };
2908 isl_schedule
*sched
;
2909 struct isl_extract_edge_data data
;
2911 domain
= isl_union_set_align_params(domain
,
2912 isl_union_map_get_space(validity
));
2913 domain
= isl_union_set_align_params(domain
,
2914 isl_union_map_get_space(proximity
));
2915 dim
= isl_union_set_get_space(domain
);
2916 validity
= isl_union_map_align_params(validity
, isl_space_copy(dim
));
2917 proximity
= isl_union_map_align_params(proximity
, dim
);
2922 graph
.n
= isl_union_set_n_set(domain
);
2925 if (graph_alloc(ctx
, &graph
, graph
.n
,
2926 isl_union_map_n_map(validity
) + isl_union_map_n_map(proximity
)) < 0)
2928 if (compute_max_row(&graph
, domain
) < 0)
2932 if (isl_union_set_foreach_set(domain
, &extract_node
, &graph
) < 0)
2934 if (graph_init_table(ctx
, &graph
) < 0)
2936 graph
.max_edge
[isl_edge_validity
] = isl_union_map_n_map(validity
);
2937 graph
.max_edge
[isl_edge_proximity
] = isl_union_map_n_map(proximity
);
2938 if (graph_init_edge_tables(ctx
, &graph
) < 0)
2941 data
.graph
= &graph
;
2942 data
.type
= isl_edge_validity
;
2943 if (isl_union_map_foreach_map(validity
, &extract_edge
, &data
) < 0)
2945 data
.type
= isl_edge_proximity
;
2946 if (isl_union_map_foreach_map(proximity
, &extract_edge
, &data
) < 0)
2949 if (compute_schedule(ctx
, &graph
) < 0)
2953 sched
= extract_schedule(&graph
, isl_union_set_get_space(domain
));
2955 graph_free(ctx
, &graph
);
2956 isl_union_set_free(domain
);
2957 isl_union_map_free(validity
);
2958 isl_union_map_free(proximity
);
2962 graph_free(ctx
, &graph
);
2963 isl_union_set_free(domain
);
2964 isl_union_map_free(validity
);
2965 isl_union_map_free(proximity
);
2969 void *isl_schedule_free(__isl_take isl_schedule
*sched
)
2975 if (--sched
->ref
> 0)
2978 for (i
= 0; i
< sched
->n
; ++i
) {
2979 isl_multi_aff_free(sched
->node
[i
].sched
);
2980 free(sched
->node
[i
].band_end
);
2981 free(sched
->node
[i
].band_id
);
2982 free(sched
->node
[i
].zero
);
2984 isl_space_free(sched
->dim
);
2985 isl_band_list_free(sched
->band_forest
);
2990 isl_ctx
*isl_schedule_get_ctx(__isl_keep isl_schedule
*schedule
)
2992 return schedule
? isl_space_get_ctx(schedule
->dim
) : NULL
;
2995 /* Set max_out to the maximal number of output dimensions over
2998 static int update_max_out(__isl_take isl_map
*map
, void *user
)
3000 int *max_out
= user
;
3001 int n_out
= isl_map_dim(map
, isl_dim_out
);
3003 if (n_out
> *max_out
)
3010 /* Internal data structure for map_pad_range.
3012 * "max_out" is the maximal schedule dimension.
3013 * "res" collects the results.
3015 struct isl_pad_schedule_map_data
{
3020 /* Pad the range of the given map with zeros to data->max_out and
3021 * then add the result to data->res.
3023 static int map_pad_range(__isl_take isl_map
*map
, void *user
)
3025 struct isl_pad_schedule_map_data
*data
= user
;
3027 int n_out
= isl_map_dim(map
, isl_dim_out
);
3029 map
= isl_map_add_dims(map
, isl_dim_out
, data
->max_out
- n_out
);
3030 for (i
= n_out
; i
< data
->max_out
; ++i
)
3031 map
= isl_map_fix_si(map
, isl_dim_out
, i
, 0);
3033 data
->res
= isl_union_map_add_map(data
->res
, map
);
3040 /* Pad the ranges of the maps in the union map with zeros such they all have
3041 * the same dimension.
3043 static __isl_give isl_union_map
*pad_schedule_map(
3044 __isl_take isl_union_map
*umap
)
3046 struct isl_pad_schedule_map_data data
;
3050 if (isl_union_map_n_map(umap
) <= 1)
3054 if (isl_union_map_foreach_map(umap
, &update_max_out
, &data
.max_out
) < 0)
3055 return isl_union_map_free(umap
);
3057 data
.res
= isl_union_map_empty(isl_union_map_get_space(umap
));
3058 if (isl_union_map_foreach_map(umap
, &map_pad_range
, &data
) < 0)
3059 data
.res
= isl_union_map_free(data
.res
);
3061 isl_union_map_free(umap
);
3065 /* Return an isl_union_map of the schedule. If we have already constructed
3066 * a band forest, then this band forest may have been modified so we need
3067 * to extract the isl_union_map from the forest rather than from
3068 * the originally computed schedule. This reconstructed schedule map
3069 * then needs to be padded with zeros to unify the schedule space
3070 * since the result of isl_band_list_get_suffix_schedule may not have
3071 * a unified schedule space.
3073 __isl_give isl_union_map
*isl_schedule_get_map(__isl_keep isl_schedule
*sched
)
3076 isl_union_map
*umap
;
3081 if (sched
->band_forest
) {
3082 umap
= isl_band_list_get_suffix_schedule(sched
->band_forest
);
3083 return pad_schedule_map(umap
);
3086 umap
= isl_union_map_empty(isl_space_copy(sched
->dim
));
3087 for (i
= 0; i
< sched
->n
; ++i
) {
3090 ma
= isl_multi_aff_copy(sched
->node
[i
].sched
);
3091 umap
= isl_union_map_add_map(umap
, isl_map_from_multi_aff(ma
));
3097 static __isl_give isl_band_list
*construct_band_list(
3098 __isl_keep isl_schedule
*schedule
, __isl_keep isl_band
*parent
,
3099 int band_nr
, int *parent_active
, int n_active
);
3101 /* Construct an isl_band structure for the band in the given schedule
3102 * with sequence number band_nr for the n_active nodes marked by active.
3103 * If the nodes don't have a band with the given sequence number,
3104 * then a band without members is created.
3106 * Because of the way the schedule is constructed, we know that
3107 * the position of the band inside the schedule of a node is the same
3108 * for all active nodes.
3110 * The partial schedule for the band is created before the children
3111 * are created to that construct_band_list can refer to the partial
3112 * schedule of the parent.
3114 static __isl_give isl_band
*construct_band(__isl_keep isl_schedule
*schedule
,
3115 __isl_keep isl_band
*parent
,
3116 int band_nr
, int *active
, int n_active
)
3119 isl_ctx
*ctx
= isl_schedule_get_ctx(schedule
);
3121 unsigned start
, end
;
3123 band
= isl_band_alloc(ctx
);
3127 band
->schedule
= schedule
;
3128 band
->parent
= parent
;
3130 for (i
= 0; i
< schedule
->n
; ++i
)
3134 if (i
>= schedule
->n
)
3135 isl_die(ctx
, isl_error_internal
,
3136 "band without active statements", goto error
);
3138 start
= band_nr
? schedule
->node
[i
].band_end
[band_nr
- 1] : 0;
3139 end
= band_nr
< schedule
->node
[i
].n_band
?
3140 schedule
->node
[i
].band_end
[band_nr
] : start
;
3141 band
->n
= end
- start
;
3143 band
->zero
= isl_alloc_array(ctx
, int, band
->n
);
3147 for (j
= 0; j
< band
->n
; ++j
)
3148 band
->zero
[j
] = schedule
->node
[i
].zero
[start
+ j
];
3150 band
->pma
= isl_union_pw_multi_aff_empty(isl_space_copy(schedule
->dim
));
3151 for (i
= 0; i
< schedule
->n
; ++i
) {
3153 isl_pw_multi_aff
*pma
;
3159 ma
= isl_multi_aff_copy(schedule
->node
[i
].sched
);
3160 n_out
= isl_multi_aff_dim(ma
, isl_dim_out
);
3161 ma
= isl_multi_aff_drop_dims(ma
, isl_dim_out
, end
, n_out
- end
);
3162 ma
= isl_multi_aff_drop_dims(ma
, isl_dim_out
, 0, start
);
3163 pma
= isl_pw_multi_aff_from_multi_aff(ma
);
3164 band
->pma
= isl_union_pw_multi_aff_add_pw_multi_aff(band
->pma
,
3170 for (i
= 0; i
< schedule
->n
; ++i
)
3171 if (active
[i
] && schedule
->node
[i
].n_band
> band_nr
+ 1)
3174 if (i
< schedule
->n
) {
3175 band
->children
= construct_band_list(schedule
, band
,
3176 band_nr
+ 1, active
, n_active
);
3177 if (!band
->children
)
3183 isl_band_free(band
);
3187 /* Internal data structure used inside cmp_band and pw_multi_aff_extract_int.
3189 * r is set to a negative value if anything goes wrong.
3191 * c1 stores the result of extract_int.
3192 * c2 is a temporary value used inside cmp_band_in_ancestor.
3193 * t is a temporary value used inside extract_int.
3195 * first and equal are used inside extract_int.
3196 * first is set if we are looking at the first isl_multi_aff inside
3197 * the isl_union_pw_multi_aff.
3198 * equal is set if all the isl_multi_affs have been equal so far.
3200 struct isl_cmp_band_data
{
3211 /* Check if "ma" assigns a constant value.
3212 * Note that this function is only called on isl_multi_affs
3213 * with a single output dimension.
3215 * If "ma" assigns a constant value then we compare it to data->c1
3216 * or assign it to data->c1 if this is the first isl_multi_aff we consider.
3217 * If "ma" does not assign a constant value or if it assigns a value
3218 * that is different from data->c1, then we set data->equal to zero
3219 * and terminate the check.
3221 static int multi_aff_extract_int(__isl_take isl_set
*set
,
3222 __isl_take isl_multi_aff
*ma
, void *user
)
3225 struct isl_cmp_band_data
*data
= user
;
3227 aff
= isl_multi_aff_get_aff(ma
, 0);
3228 data
->r
= isl_aff_is_cst(aff
);
3229 if (data
->r
>= 0 && data
->r
) {
3230 isl_aff_get_constant(aff
, &data
->t
);
3232 isl_int_set(data
->c1
, data
->t
);
3234 } else if (!isl_int_eq(data
->c1
, data
->t
))
3236 } else if (data
->r
>= 0 && !data
->r
)
3241 isl_multi_aff_free(ma
);
3250 /* This function is called for each isl_pw_multi_aff in
3251 * the isl_union_pw_multi_aff checked by extract_int.
3252 * Check all the isl_multi_affs inside "pma".
3254 static int pw_multi_aff_extract_int(__isl_take isl_pw_multi_aff
*pma
,
3259 r
= isl_pw_multi_aff_foreach_piece(pma
, &multi_aff_extract_int
, user
);
3260 isl_pw_multi_aff_free(pma
);
3265 /* Check if "upma" assigns a single constant value to its domain.
3266 * If so, return 1 and store the result in data->c1.
3269 * A negative return value from isl_union_pw_multi_aff_foreach_pw_multi_aff
3270 * means that either an error occurred or that we have broken off the check
3271 * because we already know the result is going to be negative.
3272 * In the latter case, data->equal is set to zero.
3274 static int extract_int(__isl_keep isl_union_pw_multi_aff
*upma
,
3275 struct isl_cmp_band_data
*data
)
3280 if (isl_union_pw_multi_aff_foreach_pw_multi_aff(upma
,
3281 &pw_multi_aff_extract_int
, data
) < 0) {
3287 return !data
->first
&& data
->equal
;
3290 /* Compare "b1" and "b2" based on the parent schedule of their ancestor
3293 * If the parent of "ancestor" also has a single member, then we
3294 * first try to compare the two band based on the partial schedule
3297 * Otherwise, or if the result is inconclusive, we look at the partial schedule
3298 * of "ancestor" itself.
3299 * In particular, we specialize the parent schedule based
3300 * on the domains of the child schedules, check if both assign
3301 * a single constant value and, if so, compare the two constant values.
3302 * If the specialized parent schedules do not assign a constant value,
3303 * then they cannot be used to order the two bands and so in this case
3306 static int cmp_band_in_ancestor(__isl_keep isl_band
*b1
,
3307 __isl_keep isl_band
*b2
, struct isl_cmp_band_data
*data
,
3308 __isl_keep isl_band
*ancestor
)
3310 isl_union_pw_multi_aff
*upma
;
3311 isl_union_set
*domain
;
3317 if (ancestor
->parent
&& ancestor
->parent
->n
== 1) {
3318 r
= cmp_band_in_ancestor(b1
, b2
, data
, ancestor
->parent
);
3325 upma
= isl_union_pw_multi_aff_copy(b1
->pma
);
3326 domain
= isl_union_pw_multi_aff_domain(upma
);
3327 upma
= isl_union_pw_multi_aff_copy(ancestor
->pma
);
3328 upma
= isl_union_pw_multi_aff_intersect_domain(upma
, domain
);
3329 r
= extract_int(upma
, data
);
3330 isl_union_pw_multi_aff_free(upma
);
3337 isl_int_set(data
->c2
, data
->c1
);
3339 upma
= isl_union_pw_multi_aff_copy(b2
->pma
);
3340 domain
= isl_union_pw_multi_aff_domain(upma
);
3341 upma
= isl_union_pw_multi_aff_copy(ancestor
->pma
);
3342 upma
= isl_union_pw_multi_aff_intersect_domain(upma
, domain
);
3343 r
= extract_int(upma
, data
);
3344 isl_union_pw_multi_aff_free(upma
);
3351 return isl_int_cmp(data
->c2
, data
->c1
);
3354 /* Compare "a" and "b" based on the parent schedule of their parent.
3356 static int cmp_band(const void *a
, const void *b
, void *user
)
3358 isl_band
*b1
= *(isl_band
* const *) a
;
3359 isl_band
*b2
= *(isl_band
* const *) b
;
3360 struct isl_cmp_band_data
*data
= user
;
3362 return cmp_band_in_ancestor(b1
, b2
, data
, b1
->parent
);
3365 /* Sort the elements in "list" based on the partial schedules of its parent
3366 * (and ancestors). In particular if the parent assigns constant values
3367 * to the domains of the bands in "list", then the elements are sorted
3368 * according to that order.
3369 * This order should be a more "natural" order for the user, but otherwise
3370 * shouldn't have any effect.
3371 * If we would be constructing an isl_band forest directly in
3372 * isl_union_set_compute_schedule then there wouldn't be any need
3373 * for a reordering, since the children would be added to the list
3374 * in their natural order automatically.
3376 * If there is only one element in the list, then there is no need to sort
3378 * If the partial schedule of the parent has more than one member
3379 * (or if there is no parent), then it's
3380 * defnitely not assigning constant values to the different children in
3381 * the list and so we wouldn't be able to use it to sort the list.
3383 static __isl_give isl_band_list
*sort_band_list(__isl_take isl_band_list
*list
,
3384 __isl_keep isl_band
*parent
)
3386 struct isl_cmp_band_data data
;
3392 if (!parent
|| parent
->n
!= 1)
3396 isl_int_init(data
.c1
);
3397 isl_int_init(data
.c2
);
3398 isl_int_init(data
.t
);
3399 isl_sort(list
->p
, list
->n
, sizeof(list
->p
[0]), &cmp_band
, &data
);
3401 list
= isl_band_list_free(list
);
3402 isl_int_clear(data
.c1
);
3403 isl_int_clear(data
.c2
);
3404 isl_int_clear(data
.t
);
3409 /* Construct a list of bands that start at the same position (with
3410 * sequence number band_nr) in the schedules of the nodes that
3411 * were active in the parent band.
3413 * A separate isl_band structure is created for each band_id
3414 * and for each node that does not have a band with sequence
3415 * number band_nr. In the latter case, a band without members
3417 * This ensures that if a band has any children, then each node
3418 * that was active in the band is active in exactly one of the children.
3420 static __isl_give isl_band_list
*construct_band_list(
3421 __isl_keep isl_schedule
*schedule
, __isl_keep isl_band
*parent
,
3422 int band_nr
, int *parent_active
, int n_active
)
3425 isl_ctx
*ctx
= isl_schedule_get_ctx(schedule
);
3428 isl_band_list
*list
;
3431 for (i
= 0; i
< n_active
; ++i
) {
3432 for (j
= 0; j
< schedule
->n
; ++j
) {
3433 if (!parent_active
[j
])
3435 if (schedule
->node
[j
].n_band
<= band_nr
)
3437 if (schedule
->node
[j
].band_id
[band_nr
] == i
) {
3443 for (j
= 0; j
< schedule
->n
; ++j
)
3444 if (schedule
->node
[j
].n_band
<= band_nr
)
3449 list
= isl_band_list_alloc(ctx
, n_band
);
3450 band
= construct_band(schedule
, parent
, band_nr
,
3451 parent_active
, n_active
);
3452 return isl_band_list_add(list
, band
);
3455 active
= isl_alloc_array(ctx
, int, schedule
->n
);
3459 list
= isl_band_list_alloc(ctx
, n_band
);
3461 for (i
= 0; i
< n_active
; ++i
) {
3465 for (j
= 0; j
< schedule
->n
; ++j
) {
3466 active
[j
] = parent_active
[j
] &&
3467 schedule
->node
[j
].n_band
> band_nr
&&
3468 schedule
->node
[j
].band_id
[band_nr
] == i
;
3475 band
= construct_band(schedule
, parent
, band_nr
, active
, n
);
3477 list
= isl_band_list_add(list
, band
);
3479 for (i
= 0; i
< schedule
->n
; ++i
) {
3481 if (!parent_active
[i
])
3483 if (schedule
->node
[i
].n_band
> band_nr
)
3485 for (j
= 0; j
< schedule
->n
; ++j
)
3487 band
= construct_band(schedule
, parent
, band_nr
, active
, 1);
3488 list
= isl_band_list_add(list
, band
);
3493 list
= sort_band_list(list
, parent
);
3498 /* Construct a band forest representation of the schedule and
3499 * return the list of roots.
3501 static __isl_give isl_band_list
*construct_forest(
3502 __isl_keep isl_schedule
*schedule
)
3505 isl_ctx
*ctx
= isl_schedule_get_ctx(schedule
);
3506 isl_band_list
*forest
;
3509 active
= isl_alloc_array(ctx
, int, schedule
->n
);
3513 for (i
= 0; i
< schedule
->n
; ++i
)
3516 forest
= construct_band_list(schedule
, NULL
, 0, active
, schedule
->n
);
3523 /* Return the roots of a band forest representation of the schedule.
3525 __isl_give isl_band_list
*isl_schedule_get_band_forest(
3526 __isl_keep isl_schedule
*schedule
)
3530 if (!schedule
->band_forest
)
3531 schedule
->band_forest
= construct_forest(schedule
);
3532 return isl_band_list_dup(schedule
->band_forest
);
3535 /* Call "fn" on each band in the schedule in depth-first post-order.
3537 int isl_schedule_foreach_band(__isl_keep isl_schedule
*sched
,
3538 int (*fn
)(__isl_keep isl_band
*band
, void *user
), void *user
)
3541 isl_band_list
*forest
;
3546 forest
= isl_schedule_get_band_forest(sched
);
3547 r
= isl_band_list_foreach_band(forest
, fn
, user
);
3548 isl_band_list_free(forest
);
3553 static __isl_give isl_printer
*print_band_list(__isl_take isl_printer
*p
,
3554 __isl_keep isl_band_list
*list
);
3556 static __isl_give isl_printer
*print_band(__isl_take isl_printer
*p
,
3557 __isl_keep isl_band
*band
)
3559 isl_band_list
*children
;
3561 p
= isl_printer_start_line(p
);
3562 p
= isl_printer_print_union_pw_multi_aff(p
, band
->pma
);
3563 p
= isl_printer_end_line(p
);
3565 if (!isl_band_has_children(band
))
3568 children
= isl_band_get_children(band
);
3570 p
= isl_printer_indent(p
, 4);
3571 p
= print_band_list(p
, children
);
3572 p
= isl_printer_indent(p
, -4);
3574 isl_band_list_free(children
);
3579 static __isl_give isl_printer
*print_band_list(__isl_take isl_printer
*p
,
3580 __isl_keep isl_band_list
*list
)
3584 n
= isl_band_list_n_band(list
);
3585 for (i
= 0; i
< n
; ++i
) {
3587 band
= isl_band_list_get_band(list
, i
);
3588 p
= print_band(p
, band
);
3589 isl_band_free(band
);
3595 __isl_give isl_printer
*isl_printer_print_schedule(__isl_take isl_printer
*p
,
3596 __isl_keep isl_schedule
*schedule
)
3598 isl_band_list
*forest
;
3600 forest
= isl_schedule_get_band_forest(schedule
);
3602 p
= print_band_list(p
, forest
);
3604 isl_band_list_free(forest
);
3609 void isl_schedule_dump(__isl_keep isl_schedule
*schedule
)
3611 isl_printer
*printer
;
3616 printer
= isl_printer_to_file(isl_schedule_get_ctx(schedule
), stderr
);
3617 printer
= isl_printer_print_schedule(printer
, schedule
);
3619 isl_printer_free(printer
);