2 * Copyright 2011 INRIA Saclay
3 * Copyright 2012-2014 Ecole Normale Superieure
4 * Copyright 2015-2016 Sven Verdoolaege
5 * Copyright 2016 INRIA Paris
6 * Copyright 2017 Sven Verdoolaege
8 * Use of this software is governed by the MIT license
10 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
11 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
13 * and Ecole Normale Superieure, 45 rue d'Ulm, 75230 Paris, France
14 * and Centre de Recherche Inria de Paris, 2 rue Simone Iff - Voie DQ12,
15 * CS 42112, 75589 Paris Cedex 12, France
18 #include <isl_ctx_private.h>
19 #include <isl_map_private.h>
20 #include <isl_space_private.h>
21 #include <isl_aff_private.h>
23 #include <isl/constraint.h>
24 #include <isl/schedule.h>
25 #include <isl_schedule_constraints.h>
26 #include <isl/schedule_node.h>
27 #include <isl_mat_private.h>
28 #include <isl_vec_private.h>
30 #include <isl/union_set.h>
33 #include <isl_dim_map.h>
34 #include <isl/map_to_basic_set.h>
36 #include <isl_options_private.h>
37 #include <isl_tarjan.h>
38 #include <isl_morph.h>
40 #include <isl_val_private.h>
43 * The scheduling algorithm implemented in this file was inspired by
44 * Bondhugula et al., "Automatic Transformations for Communication-Minimized
45 * Parallelization and Locality Optimization in the Polyhedral Model".
49 /* Internal information about a node that is used during the construction
51 * space represents the original space in which the domain lives;
52 * that is, the space is not affected by compression
53 * sched is a matrix representation of the schedule being constructed
54 * for this node; if compressed is set, then this schedule is
55 * defined over the compressed domain space
56 * sched_map is an isl_map representation of the same (partial) schedule
57 * sched_map may be NULL; if compressed is set, then this map
58 * is defined over the uncompressed domain space
59 * rank is the number of linearly independent rows in the linear part
61 * the rows of "vmap" represent a change of basis for the node
62 * variables; the first rank rows span the linear part of
63 * the schedule rows; the remaining rows are linearly independent
64 * the rows of "indep" represent linear combinations of the schedule
65 * coefficients that are non-zero when the schedule coefficients are
66 * linearly independent of previously computed schedule rows.
67 * start is the first variable in the LP problem in the sequences that
68 * represents the schedule coefficients of this node
69 * nvar is the dimension of the domain
70 * nparam is the number of parameters or 0 if we are not constructing
71 * a parametric schedule
73 * If compressed is set, then hull represents the constraints
74 * that were used to derive the compression, while compress and
75 * decompress map the original space to the compressed space and
78 * scc is the index of SCC (or WCC) this node belongs to
80 * "cluster" is only used inside extract_clusters and identifies
81 * the cluster of SCCs that the node belongs to.
83 * coincident contains a boolean for each of the rows of the schedule,
84 * indicating whether the corresponding scheduling dimension satisfies
85 * the coincidence constraints in the sense that the corresponding
86 * dependence distances are zero.
88 * If the schedule_treat_coalescing option is set, then
89 * "sizes" contains the sizes of the (compressed) instance set
90 * in each direction. If there is no fixed size in a given direction,
91 * then the corresponding size value is set to infinity.
92 * If the schedule_treat_coalescing option or the schedule_max_coefficient
93 * option is set, then "max" contains the maximal values for
94 * schedule coefficients of the (compressed) variables. If no bound
95 * needs to be imposed on a particular variable, then the corresponding
98 struct isl_sched_node
{
102 isl_multi_aff
*compress
;
103 isl_multi_aff
*decompress
;
118 isl_multi_val
*sizes
;
122 static int node_has_tuples(const void *entry
, const void *val
)
124 struct isl_sched_node
*node
= (struct isl_sched_node
*)entry
;
125 isl_space
*space
= (isl_space
*) val
;
127 return isl_space_has_equal_tuples(node
->space
, space
);
130 static int node_scc_exactly(struct isl_sched_node
*node
, int scc
)
132 return node
->scc
== scc
;
135 static int node_scc_at_most(struct isl_sched_node
*node
, int scc
)
137 return node
->scc
<= scc
;
140 static int node_scc_at_least(struct isl_sched_node
*node
, int scc
)
142 return node
->scc
>= scc
;
145 /* An edge in the dependence graph. An edge may be used to
146 * ensure validity of the generated schedule, to minimize the dependence
149 * map is the dependence relation, with i -> j in the map if j depends on i
150 * tagged_condition and tagged_validity contain the union of all tagged
151 * condition or conditional validity dependence relations that
152 * specialize the dependence relation "map"; that is,
153 * if (i -> a) -> (j -> b) is an element of "tagged_condition"
154 * or "tagged_validity", then i -> j is an element of "map".
155 * If these fields are NULL, then they represent the empty relation.
156 * src is the source node
157 * dst is the sink node
159 * types is a bit vector containing the types of this edge.
160 * validity is set if the edge is used to ensure correctness
161 * coincidence is used to enforce zero dependence distances
162 * proximity is set if the edge is used to minimize dependence distances
163 * condition is set if the edge represents a condition
164 * for a conditional validity schedule constraint
165 * local can only be set for condition edges and indicates that
166 * the dependence distance over the edge should be zero
167 * conditional_validity is set if the edge is used to conditionally
170 * For validity edges, start and end mark the sequence of inequality
171 * constraints in the LP problem that encode the validity constraint
172 * corresponding to this edge.
174 * During clustering, an edge may be marked "no_merge" if it should
175 * not be used to merge clusters.
176 * The weight is also only used during clustering and it is
177 * an indication of how many schedule dimensions on either side
178 * of the schedule constraints can be aligned.
179 * If the weight is negative, then this means that this edge was postponed
180 * by has_bounded_distances or any_no_merge. The original weight can
181 * be retrieved by adding 1 + graph->max_weight, with "graph"
182 * the graph containing this edge.
184 struct isl_sched_edge
{
186 isl_union_map
*tagged_condition
;
187 isl_union_map
*tagged_validity
;
189 struct isl_sched_node
*src
;
190 struct isl_sched_node
*dst
;
201 /* Is "edge" marked as being of type "type"?
203 static int is_type(struct isl_sched_edge
*edge
, enum isl_edge_type type
)
205 return ISL_FL_ISSET(edge
->types
, 1 << type
);
208 /* Mark "edge" as being of type "type".
210 static void set_type(struct isl_sched_edge
*edge
, enum isl_edge_type type
)
212 ISL_FL_SET(edge
->types
, 1 << type
);
215 /* No longer mark "edge" as being of type "type"?
217 static void clear_type(struct isl_sched_edge
*edge
, enum isl_edge_type type
)
219 ISL_FL_CLR(edge
->types
, 1 << type
);
222 /* Is "edge" marked as a validity edge?
224 static int is_validity(struct isl_sched_edge
*edge
)
226 return is_type(edge
, isl_edge_validity
);
229 /* Mark "edge" as a validity edge.
231 static void set_validity(struct isl_sched_edge
*edge
)
233 set_type(edge
, isl_edge_validity
);
236 /* Is "edge" marked as a proximity edge?
238 static int is_proximity(struct isl_sched_edge
*edge
)
240 return is_type(edge
, isl_edge_proximity
);
243 /* Is "edge" marked as a local edge?
245 static int is_local(struct isl_sched_edge
*edge
)
247 return is_type(edge
, isl_edge_local
);
250 /* Mark "edge" as a local edge.
252 static void set_local(struct isl_sched_edge
*edge
)
254 set_type(edge
, isl_edge_local
);
257 /* No longer mark "edge" as a local edge.
259 static void clear_local(struct isl_sched_edge
*edge
)
261 clear_type(edge
, isl_edge_local
);
264 /* Is "edge" marked as a coincidence edge?
266 static int is_coincidence(struct isl_sched_edge
*edge
)
268 return is_type(edge
, isl_edge_coincidence
);
271 /* Is "edge" marked as a condition edge?
273 static int is_condition(struct isl_sched_edge
*edge
)
275 return is_type(edge
, isl_edge_condition
);
278 /* Is "edge" marked as a conditional validity edge?
280 static int is_conditional_validity(struct isl_sched_edge
*edge
)
282 return is_type(edge
, isl_edge_conditional_validity
);
285 /* Internal information about the dependence graph used during
286 * the construction of the schedule.
288 * intra_hmap is a cache, mapping dependence relations to their dual,
289 * for dependences from a node to itself
290 * inter_hmap is a cache, mapping dependence relations to their dual,
291 * for dependences between distinct nodes
292 * if compression is involved then the key for these maps
293 * is the original, uncompressed dependence relation, while
294 * the value is the dual of the compressed dependence relation.
296 * n is the number of nodes
297 * node is the list of nodes
298 * maxvar is the maximal number of variables over all nodes
299 * max_row is the allocated number of rows in the schedule
300 * n_row is the current (maximal) number of linearly independent
301 * rows in the node schedules
302 * n_total_row is the current number of rows in the node schedules
303 * band_start is the starting row in the node schedules of the current band
304 * root is set if this graph is the original dependence graph,
305 * without any splitting
307 * sorted contains a list of node indices sorted according to the
308 * SCC to which a node belongs
310 * n_edge is the number of edges
311 * edge is the list of edges
312 * max_edge contains the maximal number of edges of each type;
313 * in particular, it contains the number of edges in the inital graph.
314 * edge_table contains pointers into the edge array, hashed on the source
315 * and sink spaces; there is one such table for each type;
316 * a given edge may be referenced from more than one table
317 * if the corresponding relation appears in more than one of the
318 * sets of dependences; however, for each type there is only
319 * a single edge between a given pair of source and sink space
320 * in the entire graph
322 * node_table contains pointers into the node array, hashed on the space tuples
324 * region contains a list of variable sequences that should be non-trivial
326 * lp contains the (I)LP problem used to obtain new schedule rows
328 * src_scc and dst_scc are the source and sink SCCs of an edge with
329 * conflicting constraints
331 * scc represents the number of components
332 * weak is set if the components are weakly connected
334 * max_weight is used during clustering and represents the maximal
335 * weight of the relevant proximity edges.
337 struct isl_sched_graph
{
338 isl_map_to_basic_set
*intra_hmap
;
339 isl_map_to_basic_set
*inter_hmap
;
341 struct isl_sched_node
*node
;
354 struct isl_sched_edge
*edge
;
356 int max_edge
[isl_edge_last
+ 1];
357 struct isl_hash_table
*edge_table
[isl_edge_last
+ 1];
359 struct isl_hash_table
*node_table
;
360 struct isl_trivial_region
*region
;
373 /* Initialize node_table based on the list of nodes.
375 static int graph_init_table(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
379 graph
->node_table
= isl_hash_table_alloc(ctx
, graph
->n
);
380 if (!graph
->node_table
)
383 for (i
= 0; i
< graph
->n
; ++i
) {
384 struct isl_hash_table_entry
*entry
;
387 hash
= isl_space_get_tuple_hash(graph
->node
[i
].space
);
388 entry
= isl_hash_table_find(ctx
, graph
->node_table
, hash
,
390 graph
->node
[i
].space
, 1);
393 entry
->data
= &graph
->node
[i
];
399 /* Return a pointer to the node that lives within the given space,
400 * or NULL if there is no such node.
402 static struct isl_sched_node
*graph_find_node(isl_ctx
*ctx
,
403 struct isl_sched_graph
*graph
, __isl_keep isl_space
*space
)
405 struct isl_hash_table_entry
*entry
;
408 hash
= isl_space_get_tuple_hash(space
);
409 entry
= isl_hash_table_find(ctx
, graph
->node_table
, hash
,
410 &node_has_tuples
, space
, 0);
412 return entry
? entry
->data
: NULL
;
415 static int edge_has_src_and_dst(const void *entry
, const void *val
)
417 const struct isl_sched_edge
*edge
= entry
;
418 const struct isl_sched_edge
*temp
= val
;
420 return edge
->src
== temp
->src
&& edge
->dst
== temp
->dst
;
423 /* Add the given edge to graph->edge_table[type].
425 static isl_stat
graph_edge_table_add(isl_ctx
*ctx
,
426 struct isl_sched_graph
*graph
, enum isl_edge_type type
,
427 struct isl_sched_edge
*edge
)
429 struct isl_hash_table_entry
*entry
;
432 hash
= isl_hash_init();
433 hash
= isl_hash_builtin(hash
, edge
->src
);
434 hash
= isl_hash_builtin(hash
, edge
->dst
);
435 entry
= isl_hash_table_find(ctx
, graph
->edge_table
[type
], hash
,
436 &edge_has_src_and_dst
, edge
, 1);
438 return isl_stat_error
;
444 /* Allocate the edge_tables based on the maximal number of edges of
447 static int graph_init_edge_tables(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
451 for (i
= 0; i
<= isl_edge_last
; ++i
) {
452 graph
->edge_table
[i
] = isl_hash_table_alloc(ctx
,
454 if (!graph
->edge_table
[i
])
461 /* If graph->edge_table[type] contains an edge from the given source
462 * to the given destination, then return the hash table entry of this edge.
463 * Otherwise, return NULL.
465 static struct isl_hash_table_entry
*graph_find_edge_entry(
466 struct isl_sched_graph
*graph
,
467 enum isl_edge_type type
,
468 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
470 isl_ctx
*ctx
= isl_space_get_ctx(src
->space
);
472 struct isl_sched_edge temp
= { .src
= src
, .dst
= dst
};
474 hash
= isl_hash_init();
475 hash
= isl_hash_builtin(hash
, temp
.src
);
476 hash
= isl_hash_builtin(hash
, temp
.dst
);
477 return isl_hash_table_find(ctx
, graph
->edge_table
[type
], hash
,
478 &edge_has_src_and_dst
, &temp
, 0);
482 /* If graph->edge_table[type] contains an edge from the given source
483 * to the given destination, then return this edge.
484 * Otherwise, return NULL.
486 static struct isl_sched_edge
*graph_find_edge(struct isl_sched_graph
*graph
,
487 enum isl_edge_type type
,
488 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
490 struct isl_hash_table_entry
*entry
;
492 entry
= graph_find_edge_entry(graph
, type
, src
, dst
);
499 /* Check whether the dependence graph has an edge of the given type
500 * between the given two nodes.
502 static isl_bool
graph_has_edge(struct isl_sched_graph
*graph
,
503 enum isl_edge_type type
,
504 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
506 struct isl_sched_edge
*edge
;
509 edge
= graph_find_edge(graph
, type
, src
, dst
);
513 empty
= isl_map_plain_is_empty(edge
->map
);
515 return isl_bool_error
;
520 /* Look for any edge with the same src, dst and map fields as "model".
522 * Return the matching edge if one can be found.
523 * Return "model" if no matching edge is found.
524 * Return NULL on error.
526 static struct isl_sched_edge
*graph_find_matching_edge(
527 struct isl_sched_graph
*graph
, struct isl_sched_edge
*model
)
529 enum isl_edge_type i
;
530 struct isl_sched_edge
*edge
;
532 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
535 edge
= graph_find_edge(graph
, i
, model
->src
, model
->dst
);
538 is_equal
= isl_map_plain_is_equal(model
->map
, edge
->map
);
548 /* Remove the given edge from all the edge_tables that refer to it.
550 static void graph_remove_edge(struct isl_sched_graph
*graph
,
551 struct isl_sched_edge
*edge
)
553 isl_ctx
*ctx
= isl_map_get_ctx(edge
->map
);
554 enum isl_edge_type i
;
556 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
557 struct isl_hash_table_entry
*entry
;
559 entry
= graph_find_edge_entry(graph
, i
, edge
->src
, edge
->dst
);
562 if (entry
->data
!= edge
)
564 isl_hash_table_remove(ctx
, graph
->edge_table
[i
], entry
);
568 /* Check whether the dependence graph has any edge
569 * between the given two nodes.
571 static isl_bool
graph_has_any_edge(struct isl_sched_graph
*graph
,
572 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
574 enum isl_edge_type i
;
577 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
578 r
= graph_has_edge(graph
, i
, src
, dst
);
586 /* Check whether the dependence graph has a validity edge
587 * between the given two nodes.
589 * Conditional validity edges are essentially validity edges that
590 * can be ignored if the corresponding condition edges are iteration private.
591 * Here, we are only checking for the presence of validity
592 * edges, so we need to consider the conditional validity edges too.
593 * In particular, this function is used during the detection
594 * of strongly connected components and we cannot ignore
595 * conditional validity edges during this detection.
597 static isl_bool
graph_has_validity_edge(struct isl_sched_graph
*graph
,
598 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
602 r
= graph_has_edge(graph
, isl_edge_validity
, src
, dst
);
606 return graph_has_edge(graph
, isl_edge_conditional_validity
, src
, dst
);
609 static int graph_alloc(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
610 int n_node
, int n_edge
)
615 graph
->n_edge
= n_edge
;
616 graph
->node
= isl_calloc_array(ctx
, struct isl_sched_node
, graph
->n
);
617 graph
->sorted
= isl_calloc_array(ctx
, int, graph
->n
);
618 graph
->region
= isl_alloc_array(ctx
,
619 struct isl_trivial_region
, graph
->n
);
620 graph
->edge
= isl_calloc_array(ctx
,
621 struct isl_sched_edge
, graph
->n_edge
);
623 graph
->intra_hmap
= isl_map_to_basic_set_alloc(ctx
, 2 * n_edge
);
624 graph
->inter_hmap
= isl_map_to_basic_set_alloc(ctx
, 2 * n_edge
);
626 if (!graph
->node
|| !graph
->region
|| (graph
->n_edge
&& !graph
->edge
) ||
630 for(i
= 0; i
< graph
->n
; ++i
)
631 graph
->sorted
[i
] = i
;
636 static void graph_free(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
640 isl_map_to_basic_set_free(graph
->intra_hmap
);
641 isl_map_to_basic_set_free(graph
->inter_hmap
);
644 for (i
= 0; i
< graph
->n
; ++i
) {
645 isl_space_free(graph
->node
[i
].space
);
646 isl_set_free(graph
->node
[i
].hull
);
647 isl_multi_aff_free(graph
->node
[i
].compress
);
648 isl_multi_aff_free(graph
->node
[i
].decompress
);
649 isl_mat_free(graph
->node
[i
].sched
);
650 isl_map_free(graph
->node
[i
].sched_map
);
651 isl_mat_free(graph
->node
[i
].indep
);
652 isl_mat_free(graph
->node
[i
].vmap
);
654 free(graph
->node
[i
].coincident
);
655 isl_multi_val_free(graph
->node
[i
].sizes
);
656 isl_vec_free(graph
->node
[i
].max
);
661 for (i
= 0; i
< graph
->n_edge
; ++i
) {
662 isl_map_free(graph
->edge
[i
].map
);
663 isl_union_map_free(graph
->edge
[i
].tagged_condition
);
664 isl_union_map_free(graph
->edge
[i
].tagged_validity
);
668 for (i
= 0; i
<= isl_edge_last
; ++i
)
669 isl_hash_table_free(ctx
, graph
->edge_table
[i
]);
670 isl_hash_table_free(ctx
, graph
->node_table
);
671 isl_basic_set_free(graph
->lp
);
674 /* For each "set" on which this function is called, increment
675 * graph->n by one and update graph->maxvar.
677 static isl_stat
init_n_maxvar(__isl_take isl_set
*set
, void *user
)
679 struct isl_sched_graph
*graph
= user
;
680 int nvar
= isl_set_dim(set
, isl_dim_set
);
683 if (nvar
> graph
->maxvar
)
684 graph
->maxvar
= nvar
;
691 /* Compute the number of rows that should be allocated for the schedule.
692 * In particular, we need one row for each variable or one row
693 * for each basic map in the dependences.
694 * Note that it is practically impossible to exhaust both
695 * the number of dependences and the number of variables.
697 static isl_stat
compute_max_row(struct isl_sched_graph
*graph
,
698 __isl_keep isl_schedule_constraints
*sc
)
702 isl_union_set
*domain
;
706 domain
= isl_schedule_constraints_get_domain(sc
);
707 r
= isl_union_set_foreach_set(domain
, &init_n_maxvar
, graph
);
708 isl_union_set_free(domain
);
710 return isl_stat_error
;
711 n_edge
= isl_schedule_constraints_n_basic_map(sc
);
713 return isl_stat_error
;
714 graph
->max_row
= n_edge
+ graph
->maxvar
;
719 /* Does "bset" have any defining equalities for its set variables?
721 static isl_bool
has_any_defining_equality(__isl_keep isl_basic_set
*bset
)
726 return isl_bool_error
;
728 n
= isl_basic_set_dim(bset
, isl_dim_set
);
729 for (i
= 0; i
< n
; ++i
) {
732 has
= isl_basic_set_has_defining_equality(bset
, isl_dim_set
, i
,
738 return isl_bool_false
;
741 /* Set the entries of node->max to the value of the schedule_max_coefficient
744 static isl_stat
set_max_coefficient(isl_ctx
*ctx
, struct isl_sched_node
*node
)
748 max
= isl_options_get_schedule_max_coefficient(ctx
);
752 node
->max
= isl_vec_alloc(ctx
, node
->nvar
);
753 node
->max
= isl_vec_set_si(node
->max
, max
);
755 return isl_stat_error
;
760 /* Set the entries of node->max to the minimum of the schedule_max_coefficient
761 * option (if set) and half of the minimum of the sizes in the other
762 * dimensions. If the minimum of the sizes is one, half of the size
763 * is zero and this value is reset to one.
764 * If the global minimum is unbounded (i.e., if both
765 * the schedule_max_coefficient is not set and the sizes in the other
766 * dimensions are unbounded), then store a negative value.
767 * If the schedule coefficient is close to the size of the instance set
768 * in another dimension, then the schedule may represent a loop
769 * coalescing transformation (especially if the coefficient
770 * in that other dimension is one). Forcing the coefficient to be
771 * smaller than or equal to half the minimal size should avoid this
774 static isl_stat
compute_max_coefficient(isl_ctx
*ctx
,
775 struct isl_sched_node
*node
)
781 max
= isl_options_get_schedule_max_coefficient(ctx
);
782 v
= isl_vec_alloc(ctx
, node
->nvar
);
784 return isl_stat_error
;
786 for (i
= 0; i
< node
->nvar
; ++i
) {
787 isl_int_set_si(v
->el
[i
], max
);
788 isl_int_mul_si(v
->el
[i
], v
->el
[i
], 2);
791 for (i
= 0; i
< node
->nvar
; ++i
) {
794 size
= isl_multi_val_get_val(node
->sizes
, i
);
797 if (!isl_val_is_int(size
)) {
801 for (j
= 0; j
< node
->nvar
; ++j
) {
804 if (isl_int_is_neg(v
->el
[j
]) ||
805 isl_int_gt(v
->el
[j
], size
->n
))
806 isl_int_set(v
->el
[j
], size
->n
);
811 for (i
= 0; i
< node
->nvar
; ++i
) {
812 isl_int_fdiv_q_ui(v
->el
[i
], v
->el
[i
], 2);
813 if (isl_int_is_zero(v
->el
[i
]))
814 isl_int_set_si(v
->el
[i
], 1);
821 return isl_stat_error
;
824 /* Compute and return the size of "set" in dimension "dim".
825 * The size is taken to be the difference in values for that variable
826 * for fixed values of the other variables.
827 * In particular, the variable is first isolated from the other variables
828 * in the range of a map
830 * [i_0, ..., i_dim-1, i_dim+1, ...] -> [i_dim]
832 * and then duplicated
834 * [i_0, ..., i_dim-1, i_dim+1, ...] -> [[i_dim] -> [i_dim']]
836 * The shared variables are then projected out and the maximal value
837 * of i_dim' - i_dim is computed.
839 static __isl_give isl_val
*compute_size(__isl_take isl_set
*set
, int dim
)
846 map
= isl_set_project_onto_map(set
, isl_dim_set
, dim
, 1);
847 map
= isl_map_project_out(map
, isl_dim_in
, dim
, 1);
848 map
= isl_map_range_product(map
, isl_map_copy(map
));
849 map
= isl_set_unwrap(isl_map_range(map
));
850 set
= isl_map_deltas(map
);
851 ls
= isl_local_space_from_space(isl_set_get_space(set
));
852 obj
= isl_aff_var_on_domain(ls
, isl_dim_set
, 0);
853 v
= isl_set_max_val(set
, obj
);
860 /* Compute the size of the instance set "set" of "node", after compression,
861 * as well as bounds on the corresponding coefficients, if needed.
863 * The sizes are needed when the schedule_treat_coalescing option is set.
864 * The bounds are needed when the schedule_treat_coalescing option or
865 * the schedule_max_coefficient option is set.
867 * If the schedule_treat_coalescing option is not set, then at most
868 * the bounds need to be set and this is done in set_max_coefficient.
869 * Otherwise, compress the domain if needed, compute the size
870 * in each direction and store the results in node->size.
871 * Finally, set the bounds on the coefficients based on the sizes
872 * and the schedule_max_coefficient option in compute_max_coefficient.
874 static isl_stat
compute_sizes_and_max(isl_ctx
*ctx
, struct isl_sched_node
*node
,
875 __isl_take isl_set
*set
)
880 if (!isl_options_get_schedule_treat_coalescing(ctx
)) {
882 return set_max_coefficient(ctx
, node
);
885 if (node
->compressed
)
886 set
= isl_set_preimage_multi_aff(set
,
887 isl_multi_aff_copy(node
->decompress
));
888 mv
= isl_multi_val_zero(isl_set_get_space(set
));
889 n
= isl_set_dim(set
, isl_dim_set
);
890 for (j
= 0; j
< n
; ++j
) {
893 v
= compute_size(isl_set_copy(set
), j
);
894 mv
= isl_multi_val_set_val(mv
, j
, v
);
899 return isl_stat_error
;
900 return compute_max_coefficient(ctx
, node
);
903 /* Add a new node to the graph representing the given instance set.
904 * "nvar" is the (possibly compressed) number of variables and
905 * may be smaller than then number of set variables in "set"
906 * if "compressed" is set.
907 * If "compressed" is set, then "hull" represents the constraints
908 * that were used to derive the compression, while "compress" and
909 * "decompress" map the original space to the compressed space and
911 * If "compressed" is not set, then "hull", "compress" and "decompress"
914 * Compute the size of the instance set and bounds on the coefficients,
917 static isl_stat
add_node(struct isl_sched_graph
*graph
,
918 __isl_take isl_set
*set
, int nvar
, int compressed
,
919 __isl_take isl_set
*hull
, __isl_take isl_multi_aff
*compress
,
920 __isl_take isl_multi_aff
*decompress
)
927 struct isl_sched_node
*node
;
930 return isl_stat_error
;
932 ctx
= isl_set_get_ctx(set
);
933 nparam
= isl_set_dim(set
, isl_dim_param
);
934 if (!ctx
->opt
->schedule_parametric
)
936 sched
= isl_mat_alloc(ctx
, 0, 1 + nparam
+ nvar
);
937 node
= &graph
->node
[graph
->n
];
939 space
= isl_set_get_space(set
);
942 node
->nparam
= nparam
;
944 node
->sched_map
= NULL
;
945 coincident
= isl_calloc_array(ctx
, int, graph
->max_row
);
946 node
->coincident
= coincident
;
947 node
->compressed
= compressed
;
949 node
->compress
= compress
;
950 node
->decompress
= decompress
;
951 if (compute_sizes_and_max(ctx
, node
, set
) < 0)
952 return isl_stat_error
;
954 if (!space
|| !sched
|| (graph
->max_row
&& !coincident
))
955 return isl_stat_error
;
956 if (compressed
&& (!hull
|| !compress
|| !decompress
))
957 return isl_stat_error
;
962 /* Construct an identifier for node "node", which will represent "set".
963 * The name of the identifier is either "compressed" or
964 * "compressed_<name>", with <name> the name of the space of "set".
965 * The user pointer of the identifier points to "node".
967 static __isl_give isl_id
*construct_compressed_id(__isl_keep isl_set
*set
,
968 struct isl_sched_node
*node
)
977 has_name
= isl_set_has_tuple_name(set
);
981 ctx
= isl_set_get_ctx(set
);
983 return isl_id_alloc(ctx
, "compressed", node
);
985 p
= isl_printer_to_str(ctx
);
986 name
= isl_set_get_tuple_name(set
);
987 p
= isl_printer_print_str(p
, "compressed_");
988 p
= isl_printer_print_str(p
, name
);
989 id_name
= isl_printer_get_str(p
);
992 id
= isl_id_alloc(ctx
, id_name
, node
);
998 /* Add a new node to the graph representing the given set.
1000 * If any of the set variables is defined by an equality, then
1001 * we perform variable compression such that we can perform
1002 * the scheduling on the compressed domain.
1003 * In this case, an identifier is used that references the new node
1004 * such that each compressed space is unique and
1005 * such that the node can be recovered from the compressed space.
1007 static isl_stat
extract_node(__isl_take isl_set
*set
, void *user
)
1010 isl_bool has_equality
;
1012 isl_basic_set
*hull
;
1015 isl_multi_aff
*compress
, *decompress
;
1016 struct isl_sched_graph
*graph
= user
;
1018 hull
= isl_set_affine_hull(isl_set_copy(set
));
1019 hull
= isl_basic_set_remove_divs(hull
);
1020 nvar
= isl_set_dim(set
, isl_dim_set
);
1021 has_equality
= has_any_defining_equality(hull
);
1023 if (has_equality
< 0)
1025 if (!has_equality
) {
1026 isl_basic_set_free(hull
);
1027 return add_node(graph
, set
, nvar
, 0, NULL
, NULL
, NULL
);
1030 id
= construct_compressed_id(set
, &graph
->node
[graph
->n
]);
1031 morph
= isl_basic_set_variable_compression_with_id(hull
,
1034 nvar
= isl_morph_ran_dim(morph
, isl_dim_set
);
1035 compress
= isl_morph_get_var_multi_aff(morph
);
1036 morph
= isl_morph_inverse(morph
);
1037 decompress
= isl_morph_get_var_multi_aff(morph
);
1038 isl_morph_free(morph
);
1040 hull_set
= isl_set_from_basic_set(hull
);
1041 return add_node(graph
, set
, nvar
, 1, hull_set
, compress
, decompress
);
1043 isl_basic_set_free(hull
);
1045 return isl_stat_error
;
1048 struct isl_extract_edge_data
{
1049 enum isl_edge_type type
;
1050 struct isl_sched_graph
*graph
;
1053 /* Merge edge2 into edge1, freeing the contents of edge2.
1054 * Return 0 on success and -1 on failure.
1056 * edge1 and edge2 are assumed to have the same value for the map field.
1058 static int merge_edge(struct isl_sched_edge
*edge1
,
1059 struct isl_sched_edge
*edge2
)
1061 edge1
->types
|= edge2
->types
;
1062 isl_map_free(edge2
->map
);
1064 if (is_condition(edge2
)) {
1065 if (!edge1
->tagged_condition
)
1066 edge1
->tagged_condition
= edge2
->tagged_condition
;
1068 edge1
->tagged_condition
=
1069 isl_union_map_union(edge1
->tagged_condition
,
1070 edge2
->tagged_condition
);
1073 if (is_conditional_validity(edge2
)) {
1074 if (!edge1
->tagged_validity
)
1075 edge1
->tagged_validity
= edge2
->tagged_validity
;
1077 edge1
->tagged_validity
=
1078 isl_union_map_union(edge1
->tagged_validity
,
1079 edge2
->tagged_validity
);
1082 if (is_condition(edge2
) && !edge1
->tagged_condition
)
1084 if (is_conditional_validity(edge2
) && !edge1
->tagged_validity
)
1090 /* Insert dummy tags in domain and range of "map".
1092 * In particular, if "map" is of the form
1098 * [A -> dummy_tag] -> [B -> dummy_tag]
1100 * where the dummy_tags are identical and equal to any dummy tags
1101 * introduced by any other call to this function.
1103 static __isl_give isl_map
*insert_dummy_tags(__isl_take isl_map
*map
)
1109 isl_set
*domain
, *range
;
1111 ctx
= isl_map_get_ctx(map
);
1113 id
= isl_id_alloc(ctx
, NULL
, &dummy
);
1114 space
= isl_space_params(isl_map_get_space(map
));
1115 space
= isl_space_set_from_params(space
);
1116 space
= isl_space_set_tuple_id(space
, isl_dim_set
, id
);
1117 space
= isl_space_map_from_set(space
);
1119 domain
= isl_map_wrap(map
);
1120 range
= isl_map_wrap(isl_map_universe(space
));
1121 map
= isl_map_from_domain_and_range(domain
, range
);
1122 map
= isl_map_zip(map
);
1127 /* Given that at least one of "src" or "dst" is compressed, return
1128 * a map between the spaces of these nodes restricted to the affine
1129 * hull that was used in the compression.
1131 static __isl_give isl_map
*extract_hull(struct isl_sched_node
*src
,
1132 struct isl_sched_node
*dst
)
1136 if (src
->compressed
)
1137 dom
= isl_set_copy(src
->hull
);
1139 dom
= isl_set_universe(isl_space_copy(src
->space
));
1140 if (dst
->compressed
)
1141 ran
= isl_set_copy(dst
->hull
);
1143 ran
= isl_set_universe(isl_space_copy(dst
->space
));
1145 return isl_map_from_domain_and_range(dom
, ran
);
1148 /* Intersect the domains of the nested relations in domain and range
1149 * of "tagged" with "map".
1151 static __isl_give isl_map
*map_intersect_domains(__isl_take isl_map
*tagged
,
1152 __isl_keep isl_map
*map
)
1156 tagged
= isl_map_zip(tagged
);
1157 set
= isl_map_wrap(isl_map_copy(map
));
1158 tagged
= isl_map_intersect_domain(tagged
, set
);
1159 tagged
= isl_map_zip(tagged
);
1163 /* Return a pointer to the node that lives in the domain space of "map"
1164 * or NULL if there is no such node.
1166 static struct isl_sched_node
*find_domain_node(isl_ctx
*ctx
,
1167 struct isl_sched_graph
*graph
, __isl_keep isl_map
*map
)
1169 struct isl_sched_node
*node
;
1172 space
= isl_space_domain(isl_map_get_space(map
));
1173 node
= graph_find_node(ctx
, graph
, space
);
1174 isl_space_free(space
);
1179 /* Return a pointer to the node that lives in the range space of "map"
1180 * or NULL if there is no such node.
1182 static struct isl_sched_node
*find_range_node(isl_ctx
*ctx
,
1183 struct isl_sched_graph
*graph
, __isl_keep isl_map
*map
)
1185 struct isl_sched_node
*node
;
1188 space
= isl_space_range(isl_map_get_space(map
));
1189 node
= graph_find_node(ctx
, graph
, space
);
1190 isl_space_free(space
);
1195 /* Add a new edge to the graph based on the given map
1196 * and add it to data->graph->edge_table[data->type].
1197 * If a dependence relation of a given type happens to be identical
1198 * to one of the dependence relations of a type that was added before,
1199 * then we don't create a new edge, but instead mark the original edge
1200 * as also representing a dependence of the current type.
1202 * Edges of type isl_edge_condition or isl_edge_conditional_validity
1203 * may be specified as "tagged" dependence relations. That is, "map"
1204 * may contain elements (i -> a) -> (j -> b), where i -> j denotes
1205 * the dependence on iterations and a and b are tags.
1206 * edge->map is set to the relation containing the elements i -> j,
1207 * while edge->tagged_condition and edge->tagged_validity contain
1208 * the union of all the "map" relations
1209 * for which extract_edge is called that result in the same edge->map.
1211 * If the source or the destination node is compressed, then
1212 * intersect both "map" and "tagged" with the constraints that
1213 * were used to construct the compression.
1214 * This ensures that there are no schedule constraints defined
1215 * outside of these domains, while the scheduler no longer has
1216 * any control over those outside parts.
1218 static isl_stat
extract_edge(__isl_take isl_map
*map
, void *user
)
1220 isl_ctx
*ctx
= isl_map_get_ctx(map
);
1221 struct isl_extract_edge_data
*data
= user
;
1222 struct isl_sched_graph
*graph
= data
->graph
;
1223 struct isl_sched_node
*src
, *dst
;
1224 struct isl_sched_edge
*edge
;
1225 isl_map
*tagged
= NULL
;
1227 if (data
->type
== isl_edge_condition
||
1228 data
->type
== isl_edge_conditional_validity
) {
1229 if (isl_map_can_zip(map
)) {
1230 tagged
= isl_map_copy(map
);
1231 map
= isl_set_unwrap(isl_map_domain(isl_map_zip(map
)));
1233 tagged
= insert_dummy_tags(isl_map_copy(map
));
1237 src
= find_domain_node(ctx
, graph
, map
);
1238 dst
= find_range_node(ctx
, graph
, map
);
1242 isl_map_free(tagged
);
1246 if (src
->compressed
|| dst
->compressed
) {
1248 hull
= extract_hull(src
, dst
);
1250 tagged
= map_intersect_domains(tagged
, hull
);
1251 map
= isl_map_intersect(map
, hull
);
1254 graph
->edge
[graph
->n_edge
].src
= src
;
1255 graph
->edge
[graph
->n_edge
].dst
= dst
;
1256 graph
->edge
[graph
->n_edge
].map
= map
;
1257 graph
->edge
[graph
->n_edge
].types
= 0;
1258 graph
->edge
[graph
->n_edge
].tagged_condition
= NULL
;
1259 graph
->edge
[graph
->n_edge
].tagged_validity
= NULL
;
1260 set_type(&graph
->edge
[graph
->n_edge
], data
->type
);
1261 if (data
->type
== isl_edge_condition
)
1262 graph
->edge
[graph
->n_edge
].tagged_condition
=
1263 isl_union_map_from_map(tagged
);
1264 if (data
->type
== isl_edge_conditional_validity
)
1265 graph
->edge
[graph
->n_edge
].tagged_validity
=
1266 isl_union_map_from_map(tagged
);
1268 edge
= graph_find_matching_edge(graph
, &graph
->edge
[graph
->n_edge
]);
1271 return isl_stat_error
;
1273 if (edge
== &graph
->edge
[graph
->n_edge
])
1274 return graph_edge_table_add(ctx
, graph
, data
->type
,
1275 &graph
->edge
[graph
->n_edge
++]);
1277 if (merge_edge(edge
, &graph
->edge
[graph
->n_edge
]) < 0)
1280 return graph_edge_table_add(ctx
, graph
, data
->type
, edge
);
1283 /* Initialize the schedule graph "graph" from the schedule constraints "sc".
1285 * The context is included in the domain before the nodes of
1286 * the graphs are extracted in order to be able to exploit
1287 * any possible additional equalities.
1288 * Note that this intersection is only performed locally here.
1290 static isl_stat
graph_init(struct isl_sched_graph
*graph
,
1291 __isl_keep isl_schedule_constraints
*sc
)
1294 isl_union_set
*domain
;
1296 struct isl_extract_edge_data data
;
1297 enum isl_edge_type i
;
1301 return isl_stat_error
;
1303 ctx
= isl_schedule_constraints_get_ctx(sc
);
1305 domain
= isl_schedule_constraints_get_domain(sc
);
1306 graph
->n
= isl_union_set_n_set(domain
);
1307 isl_union_set_free(domain
);
1309 if (graph_alloc(ctx
, graph
, graph
->n
,
1310 isl_schedule_constraints_n_map(sc
)) < 0)
1311 return isl_stat_error
;
1313 if (compute_max_row(graph
, sc
) < 0)
1314 return isl_stat_error
;
1317 domain
= isl_schedule_constraints_get_domain(sc
);
1318 domain
= isl_union_set_intersect_params(domain
,
1319 isl_schedule_constraints_get_context(sc
));
1320 r
= isl_union_set_foreach_set(domain
, &extract_node
, graph
);
1321 isl_union_set_free(domain
);
1323 return isl_stat_error
;
1324 if (graph_init_table(ctx
, graph
) < 0)
1325 return isl_stat_error
;
1326 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
1327 c
= isl_schedule_constraints_get(sc
, i
);
1328 graph
->max_edge
[i
] = isl_union_map_n_map(c
);
1329 isl_union_map_free(c
);
1331 return isl_stat_error
;
1333 if (graph_init_edge_tables(ctx
, graph
) < 0)
1334 return isl_stat_error
;
1337 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
1341 c
= isl_schedule_constraints_get(sc
, i
);
1342 r
= isl_union_map_foreach_map(c
, &extract_edge
, &data
);
1343 isl_union_map_free(c
);
1345 return isl_stat_error
;
1351 /* Check whether there is any dependence from node[j] to node[i]
1352 * or from node[i] to node[j].
1354 static isl_bool
node_follows_weak(int i
, int j
, void *user
)
1357 struct isl_sched_graph
*graph
= user
;
1359 f
= graph_has_any_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
1362 return graph_has_any_edge(graph
, &graph
->node
[i
], &graph
->node
[j
]);
1365 /* Check whether there is a (conditional) validity dependence from node[j]
1366 * to node[i], forcing node[i] to follow node[j].
1368 static isl_bool
node_follows_strong(int i
, int j
, void *user
)
1370 struct isl_sched_graph
*graph
= user
;
1372 return graph_has_validity_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
1375 /* Use Tarjan's algorithm for computing the strongly connected components
1376 * in the dependence graph only considering those edges defined by "follows".
1378 static int detect_ccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
1379 isl_bool (*follows
)(int i
, int j
, void *user
))
1382 struct isl_tarjan_graph
*g
= NULL
;
1384 g
= isl_tarjan_graph_init(ctx
, graph
->n
, follows
, graph
);
1392 while (g
->order
[i
] != -1) {
1393 graph
->node
[g
->order
[i
]].scc
= graph
->scc
;
1401 isl_tarjan_graph_free(g
);
1406 /* Apply Tarjan's algorithm to detect the strongly connected components
1407 * in the dependence graph.
1408 * Only consider the (conditional) validity dependences and clear "weak".
1410 static int detect_sccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
1413 return detect_ccs(ctx
, graph
, &node_follows_strong
);
1416 /* Apply Tarjan's algorithm to detect the (weakly) connected components
1417 * in the dependence graph.
1418 * Consider all dependences and set "weak".
1420 static int detect_wccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
1423 return detect_ccs(ctx
, graph
, &node_follows_weak
);
1426 static int cmp_scc(const void *a
, const void *b
, void *data
)
1428 struct isl_sched_graph
*graph
= data
;
1432 return graph
->node
[*i1
].scc
- graph
->node
[*i2
].scc
;
1435 /* Sort the elements of graph->sorted according to the corresponding SCCs.
1437 static int sort_sccs(struct isl_sched_graph
*graph
)
1439 return isl_sort(graph
->sorted
, graph
->n
, sizeof(int), &cmp_scc
, graph
);
1442 /* Given a dependence relation R from "node" to itself,
1443 * construct the set of coefficients of valid constraints for elements
1444 * in that dependence relation.
1445 * In particular, the result contains tuples of coefficients
1446 * c_0, c_n, c_x such that
1448 * c_0 + c_n n + c_x y - c_x x >= 0 for each (x,y) in R
1452 * c_0 + c_n n + c_x d >= 0 for each d in delta R = { y - x | (x,y) in R }
1454 * We choose here to compute the dual of delta R.
1455 * Alternatively, we could have computed the dual of R, resulting
1456 * in a set of tuples c_0, c_n, c_x, c_y, and then
1457 * plugged in (c_0, c_n, c_x, -c_x).
1459 * If "node" has been compressed, then the dependence relation
1460 * is also compressed before the set of coefficients is computed.
1462 static __isl_give isl_basic_set
*intra_coefficients(
1463 struct isl_sched_graph
*graph
, struct isl_sched_node
*node
,
1464 __isl_take isl_map
*map
)
1468 isl_basic_set
*coef
;
1469 isl_maybe_isl_basic_set m
;
1471 m
= isl_map_to_basic_set_try_get(graph
->intra_hmap
, map
);
1472 if (m
.valid
< 0 || m
.valid
) {
1477 key
= isl_map_copy(map
);
1478 if (node
->compressed
) {
1479 map
= isl_map_preimage_domain_multi_aff(map
,
1480 isl_multi_aff_copy(node
->decompress
));
1481 map
= isl_map_preimage_range_multi_aff(map
,
1482 isl_multi_aff_copy(node
->decompress
));
1484 delta
= isl_set_remove_divs(isl_map_deltas(map
));
1485 coef
= isl_set_coefficients(delta
);
1486 graph
->intra_hmap
= isl_map_to_basic_set_set(graph
->intra_hmap
, key
,
1487 isl_basic_set_copy(coef
));
1492 /* Given a dependence relation R, construct the set of coefficients
1493 * of valid constraints for elements in that dependence relation.
1494 * In particular, the result contains tuples of coefficients
1495 * c_0, c_n, c_x, c_y such that
1497 * c_0 + c_n n + c_x x + c_y y >= 0 for each (x,y) in R
1499 * If the source or destination nodes of "edge" have been compressed,
1500 * then the dependence relation is also compressed before
1501 * the set of coefficients is computed.
1503 static __isl_give isl_basic_set
*inter_coefficients(
1504 struct isl_sched_graph
*graph
, struct isl_sched_edge
*edge
,
1505 __isl_take isl_map
*map
)
1509 isl_basic_set
*coef
;
1510 isl_maybe_isl_basic_set m
;
1512 m
= isl_map_to_basic_set_try_get(graph
->inter_hmap
, map
);
1513 if (m
.valid
< 0 || m
.valid
) {
1518 key
= isl_map_copy(map
);
1519 if (edge
->src
->compressed
)
1520 map
= isl_map_preimage_domain_multi_aff(map
,
1521 isl_multi_aff_copy(edge
->src
->decompress
));
1522 if (edge
->dst
->compressed
)
1523 map
= isl_map_preimage_range_multi_aff(map
,
1524 isl_multi_aff_copy(edge
->dst
->decompress
));
1525 set
= isl_map_wrap(isl_map_remove_divs(map
));
1526 coef
= isl_set_coefficients(set
);
1527 graph
->inter_hmap
= isl_map_to_basic_set_set(graph
->inter_hmap
, key
,
1528 isl_basic_set_copy(coef
));
1533 /* Return the position of the coefficients of the variables in
1534 * the coefficients constraints "coef".
1536 * The space of "coef" is of the form
1538 * { coefficients[[cst, params] -> S] }
1540 * Return the position of S.
1542 static int coef_var_offset(__isl_keep isl_basic_set
*coef
)
1547 space
= isl_space_unwrap(isl_basic_set_get_space(coef
));
1548 offset
= isl_space_dim(space
, isl_dim_in
);
1549 isl_space_free(space
);
1554 /* Return the offset of the coefficient of the constant term of "node"
1557 * Within each node, the coefficients have the following order:
1558 * - positive and negative parts of c_i_x
1559 * - c_i_n (if parametric)
1562 static int node_cst_coef_offset(struct isl_sched_node
*node
)
1564 return node
->start
+ 2 * node
->nvar
+ node
->nparam
;
1567 /* Return the offset of the coefficients of the parameters of "node"
1570 * Within each node, the coefficients have the following order:
1571 * - positive and negative parts of c_i_x
1572 * - c_i_n (if parametric)
1575 static int node_par_coef_offset(struct isl_sched_node
*node
)
1577 return node
->start
+ 2 * node
->nvar
;
1580 /* Return the offset of the coefficients of the variables of "node"
1583 * Within each node, the coefficients have the following order:
1584 * - positive and negative parts of c_i_x
1585 * - c_i_n (if parametric)
1588 static int node_var_coef_offset(struct isl_sched_node
*node
)
1593 /* Return the position of the pair of variables encoding
1594 * coefficient "i" of "node".
1596 * The order of these variable pairs is the opposite of
1597 * that of the coefficients, with 2 variables per coefficient.
1599 static int node_var_coef_pos(struct isl_sched_node
*node
, int i
)
1601 return node_var_coef_offset(node
) + 2 * (node
->nvar
- 1 - i
);
1604 /* Construct an isl_dim_map for mapping constraints on coefficients
1605 * for "node" to the corresponding positions in graph->lp.
1606 * "offset" is the offset of the coefficients for the variables
1607 * in the input constraints.
1608 * "s" is the sign of the mapping.
1610 * The input constraints are given in terms of the coefficients (c_0, c_n, c_x).
1611 * The mapping produced by this function essentially plugs in
1612 * (0, 0, c_i_x^+ - c_i_x^-) if s = 1 and
1613 * (0, 0, -c_i_x^+ + c_i_x^-) if s = -1.
1614 * In graph->lp, the c_i_x^- appear before their c_i_x^+ counterpart.
1615 * Furthermore, the order of these pairs is the opposite of that
1616 * of the corresponding coefficients.
1618 * The caller can extend the mapping to also map the other coefficients
1619 * (and therefore not plug in 0).
1621 static __isl_give isl_dim_map
*intra_dim_map(isl_ctx
*ctx
,
1622 struct isl_sched_graph
*graph
, struct isl_sched_node
*node
,
1627 isl_dim_map
*dim_map
;
1632 total
= isl_basic_set_total_dim(graph
->lp
);
1633 pos
= node_var_coef_pos(node
, 0);
1634 dim_map
= isl_dim_map_alloc(ctx
, total
);
1635 isl_dim_map_range(dim_map
, pos
, -2, offset
, 1, node
->nvar
, -s
);
1636 isl_dim_map_range(dim_map
, pos
+ 1, -2, offset
, 1, node
->nvar
, s
);
1641 /* Construct an isl_dim_map for mapping constraints on coefficients
1642 * for "src" (node i) and "dst" (node j) to the corresponding positions
1644 * "offset" is the offset of the coefficients for the variables of "src"
1645 * in the input constraints.
1646 * "s" is the sign of the mapping.
1648 * The input constraints are given in terms of the coefficients
1649 * (c_0, c_n, c_x, c_y).
1650 * The mapping produced by this function essentially plugs in
1651 * (c_j_0 - c_i_0, c_j_n - c_i_n,
1652 * -(c_i_x^+ - c_i_x^-), c_j_x^+ - c_j_x^-) if s = 1 and
1653 * (-c_j_0 + c_i_0, -c_j_n + c_i_n,
1654 * c_i_x^+ - c_i_x^-, -(c_j_x^+ - c_j_x^-)) if s = -1.
1655 * In graph->lp, the c_*^- appear before their c_*^+ counterpart.
1656 * Furthermore, the order of these pairs is the opposite of that
1657 * of the corresponding coefficients.
1659 * The caller can further extend the mapping.
1661 static __isl_give isl_dim_map
*inter_dim_map(isl_ctx
*ctx
,
1662 struct isl_sched_graph
*graph
, struct isl_sched_node
*src
,
1663 struct isl_sched_node
*dst
, int offset
, int s
)
1667 isl_dim_map
*dim_map
;
1672 total
= isl_basic_set_total_dim(graph
->lp
);
1673 dim_map
= isl_dim_map_alloc(ctx
, total
);
1675 pos
= node_cst_coef_offset(dst
);
1676 isl_dim_map_range(dim_map
, pos
, 0, 0, 0, 1, s
);
1677 pos
= node_par_coef_offset(dst
);
1678 isl_dim_map_range(dim_map
, pos
, 1, 1, 1, dst
->nparam
, s
);
1679 pos
= node_var_coef_pos(dst
, 0);
1680 isl_dim_map_range(dim_map
, pos
, -2, offset
+ src
->nvar
, 1,
1682 isl_dim_map_range(dim_map
, pos
+ 1, -2, offset
+ src
->nvar
, 1,
1685 pos
= node_cst_coef_offset(src
);
1686 isl_dim_map_range(dim_map
, pos
, 0, 0, 0, 1, -s
);
1687 pos
= node_par_coef_offset(src
);
1688 isl_dim_map_range(dim_map
, pos
, 1, 1, 1, src
->nparam
, -s
);
1689 pos
= node_var_coef_pos(src
, 0);
1690 isl_dim_map_range(dim_map
, pos
, -2, offset
, 1, src
->nvar
, s
);
1691 isl_dim_map_range(dim_map
, pos
+ 1, -2, offset
, 1, src
->nvar
, -s
);
1696 /* Add the constraints from "src" to "dst" using "dim_map",
1697 * after making sure there is enough room in "dst" for the extra constraints.
1699 static __isl_give isl_basic_set
*add_constraints_dim_map(
1700 __isl_take isl_basic_set
*dst
, __isl_take isl_basic_set
*src
,
1701 __isl_take isl_dim_map
*dim_map
)
1705 n_eq
= isl_basic_set_n_equality(src
);
1706 n_ineq
= isl_basic_set_n_inequality(src
);
1707 dst
= isl_basic_set_extend_constraints(dst
, n_eq
, n_ineq
);
1708 dst
= isl_basic_set_add_constraints_dim_map(dst
, src
, dim_map
);
1712 /* Add constraints to graph->lp that force validity for the given
1713 * dependence from a node i to itself.
1714 * That is, add constraints that enforce
1716 * (c_i_0 + c_i_n n + c_i_x y) - (c_i_0 + c_i_n n + c_i_x x)
1717 * = c_i_x (y - x) >= 0
1719 * for each (x,y) in R.
1720 * We obtain general constraints on coefficients (c_0, c_n, c_x)
1721 * of valid constraints for (y - x) and then plug in (0, 0, c_i_x^+ - c_i_x^-),
1722 * where c_i_x = c_i_x^+ - c_i_x^-, with c_i_x^+ and c_i_x^- non-negative.
1723 * In graph->lp, the c_i_x^- appear before their c_i_x^+ counterpart.
1725 static isl_stat
add_intra_validity_constraints(struct isl_sched_graph
*graph
,
1726 struct isl_sched_edge
*edge
)
1729 isl_map
*map
= isl_map_copy(edge
->map
);
1730 isl_ctx
*ctx
= isl_map_get_ctx(map
);
1731 isl_dim_map
*dim_map
;
1732 isl_basic_set
*coef
;
1733 struct isl_sched_node
*node
= edge
->src
;
1735 coef
= intra_coefficients(graph
, node
, map
);
1737 offset
= coef_var_offset(coef
);
1740 return isl_stat_error
;
1742 dim_map
= intra_dim_map(ctx
, graph
, node
, offset
, 1);
1743 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
1748 /* Add constraints to graph->lp that force validity for the given
1749 * dependence from node i to node j.
1750 * That is, add constraints that enforce
1752 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) >= 0
1754 * for each (x,y) in R.
1755 * We obtain general constraints on coefficients (c_0, c_n, c_x, c_y)
1756 * of valid constraints for R and then plug in
1757 * (c_j_0 - c_i_0, c_j_n - c_i_n, -(c_i_x^+ - c_i_x^-), c_j_x^+ - c_j_x^-),
1758 * where c_* = c_*^+ - c_*^-, with c_*^+ and c_*^- non-negative.
1759 * In graph->lp, the c_*^- appear before their c_*^+ counterpart.
1761 static isl_stat
add_inter_validity_constraints(struct isl_sched_graph
*graph
,
1762 struct isl_sched_edge
*edge
)
1767 isl_dim_map
*dim_map
;
1768 isl_basic_set
*coef
;
1769 struct isl_sched_node
*src
= edge
->src
;
1770 struct isl_sched_node
*dst
= edge
->dst
;
1773 return isl_stat_error
;
1775 map
= isl_map_copy(edge
->map
);
1776 ctx
= isl_map_get_ctx(map
);
1777 coef
= inter_coefficients(graph
, edge
, map
);
1779 offset
= coef_var_offset(coef
);
1782 return isl_stat_error
;
1784 dim_map
= inter_dim_map(ctx
, graph
, src
, dst
, offset
, 1);
1786 edge
->start
= graph
->lp
->n_ineq
;
1787 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
1789 return isl_stat_error
;
1790 edge
->end
= graph
->lp
->n_ineq
;
1795 /* Add constraints to graph->lp that bound the dependence distance for the given
1796 * dependence from a node i to itself.
1797 * If s = 1, we add the constraint
1799 * c_i_x (y - x) <= m_0 + m_n n
1803 * -c_i_x (y - x) + m_0 + m_n n >= 0
1805 * for each (x,y) in R.
1806 * If s = -1, we add the constraint
1808 * -c_i_x (y - x) <= m_0 + m_n n
1812 * c_i_x (y - x) + m_0 + m_n n >= 0
1814 * for each (x,y) in R.
1815 * We obtain general constraints on coefficients (c_0, c_n, c_x)
1816 * of valid constraints for (y - x) and then plug in (m_0, m_n, -s * c_i_x),
1817 * with each coefficient (except m_0) represented as a pair of non-negative
1821 * If "local" is set, then we add constraints
1823 * c_i_x (y - x) <= 0
1827 * -c_i_x (y - x) <= 0
1829 * instead, forcing the dependence distance to be (less than or) equal to 0.
1830 * That is, we plug in (0, 0, -s * c_i_x),
1831 * Note that dependences marked local are treated as validity constraints
1832 * by add_all_validity_constraints and therefore also have
1833 * their distances bounded by 0 from below.
1835 static isl_stat
add_intra_proximity_constraints(struct isl_sched_graph
*graph
,
1836 struct isl_sched_edge
*edge
, int s
, int local
)
1840 isl_map
*map
= isl_map_copy(edge
->map
);
1841 isl_ctx
*ctx
= isl_map_get_ctx(map
);
1842 isl_dim_map
*dim_map
;
1843 isl_basic_set
*coef
;
1844 struct isl_sched_node
*node
= edge
->src
;
1846 coef
= intra_coefficients(graph
, node
, map
);
1848 offset
= coef_var_offset(coef
);
1851 return isl_stat_error
;
1853 nparam
= isl_space_dim(node
->space
, isl_dim_param
);
1854 dim_map
= intra_dim_map(ctx
, graph
, node
, offset
, -s
);
1857 isl_dim_map_range(dim_map
, 1, 0, 0, 0, 1, 1);
1858 isl_dim_map_range(dim_map
, 4, 2, 1, 1, nparam
, -1);
1859 isl_dim_map_range(dim_map
, 5, 2, 1, 1, nparam
, 1);
1861 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
1866 /* Add constraints to graph->lp that bound the dependence distance for the given
1867 * dependence from node i to node j.
1868 * If s = 1, we add the constraint
1870 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x)
1875 * -(c_j_0 + c_j_n n + c_j_x y) + (c_i_0 + c_i_n n + c_i_x x) +
1878 * for each (x,y) in R.
1879 * If s = -1, we add the constraint
1881 * -((c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x))
1886 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) +
1889 * for each (x,y) in R.
1890 * We obtain general constraints on coefficients (c_0, c_n, c_x, c_y)
1891 * of valid constraints for R and then plug in
1892 * (m_0 - s*c_j_0 + s*c_i_0, m_n - s*c_j_n + s*c_i_n,
1893 * s*c_i_x, -s*c_j_x)
1894 * with each coefficient (except m_0, c_*_0 and c_*_n)
1895 * represented as a pair of non-negative coefficients.
1898 * If "local" is set (and s = 1), then we add constraints
1900 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) <= 0
1904 * -((c_j_0 + c_j_n n + c_j_x y) + (c_i_0 + c_i_n n + c_i_x x)) >= 0
1906 * instead, forcing the dependence distance to be (less than or) equal to 0.
1907 * That is, we plug in
1908 * (-s*c_j_0 + s*c_i_0, -s*c_j_n + s*c_i_n, s*c_i_x, -s*c_j_x).
1909 * Note that dependences marked local are treated as validity constraints
1910 * by add_all_validity_constraints and therefore also have
1911 * their distances bounded by 0 from below.
1913 static isl_stat
add_inter_proximity_constraints(struct isl_sched_graph
*graph
,
1914 struct isl_sched_edge
*edge
, int s
, int local
)
1918 isl_map
*map
= isl_map_copy(edge
->map
);
1919 isl_ctx
*ctx
= isl_map_get_ctx(map
);
1920 isl_dim_map
*dim_map
;
1921 isl_basic_set
*coef
;
1922 struct isl_sched_node
*src
= edge
->src
;
1923 struct isl_sched_node
*dst
= edge
->dst
;
1925 coef
= inter_coefficients(graph
, edge
, map
);
1927 offset
= coef_var_offset(coef
);
1930 return isl_stat_error
;
1932 nparam
= isl_space_dim(src
->space
, isl_dim_param
);
1933 dim_map
= inter_dim_map(ctx
, graph
, src
, dst
, offset
, -s
);
1936 isl_dim_map_range(dim_map
, 1, 0, 0, 0, 1, 1);
1937 isl_dim_map_range(dim_map
, 4, 2, 1, 1, nparam
, -1);
1938 isl_dim_map_range(dim_map
, 5, 2, 1, 1, nparam
, 1);
1941 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
1946 /* Add all validity constraints to graph->lp.
1948 * An edge that is forced to be local needs to have its dependence
1949 * distances equal to zero. We take care of bounding them by 0 from below
1950 * here. add_all_proximity_constraints takes care of bounding them by 0
1953 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
1954 * Otherwise, we ignore them.
1956 static int add_all_validity_constraints(struct isl_sched_graph
*graph
,
1957 int use_coincidence
)
1961 for (i
= 0; i
< graph
->n_edge
; ++i
) {
1962 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
1965 local
= is_local(edge
) ||
1966 (is_coincidence(edge
) && use_coincidence
);
1967 if (!is_validity(edge
) && !local
)
1969 if (edge
->src
!= edge
->dst
)
1971 if (add_intra_validity_constraints(graph
, edge
) < 0)
1975 for (i
= 0; i
< graph
->n_edge
; ++i
) {
1976 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
1979 local
= is_local(edge
) ||
1980 (is_coincidence(edge
) && use_coincidence
);
1981 if (!is_validity(edge
) && !local
)
1983 if (edge
->src
== edge
->dst
)
1985 if (add_inter_validity_constraints(graph
, edge
) < 0)
1992 /* Add constraints to graph->lp that bound the dependence distance
1993 * for all dependence relations.
1994 * If a given proximity dependence is identical to a validity
1995 * dependence, then the dependence distance is already bounded
1996 * from below (by zero), so we only need to bound the distance
1997 * from above. (This includes the case of "local" dependences
1998 * which are treated as validity dependence by add_all_validity_constraints.)
1999 * Otherwise, we need to bound the distance both from above and from below.
2001 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2002 * Otherwise, we ignore them.
2004 static int add_all_proximity_constraints(struct isl_sched_graph
*graph
,
2005 int use_coincidence
)
2009 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2010 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
2013 local
= is_local(edge
) ||
2014 (is_coincidence(edge
) && use_coincidence
);
2015 if (!is_proximity(edge
) && !local
)
2017 if (edge
->src
== edge
->dst
&&
2018 add_intra_proximity_constraints(graph
, edge
, 1, local
) < 0)
2020 if (edge
->src
!= edge
->dst
&&
2021 add_inter_proximity_constraints(graph
, edge
, 1, local
) < 0)
2023 if (is_validity(edge
) || local
)
2025 if (edge
->src
== edge
->dst
&&
2026 add_intra_proximity_constraints(graph
, edge
, -1, 0) < 0)
2028 if (edge
->src
!= edge
->dst
&&
2029 add_inter_proximity_constraints(graph
, edge
, -1, 0) < 0)
2036 /* Normalize the rows of "indep" such that all rows are lexicographically
2037 * positive and such that each row contains as many final zeros as possible,
2038 * given the choice for the previous rows.
2039 * Do this by performing elementary row operations.
2041 static __isl_give isl_mat
*normalize_independent(__isl_take isl_mat
*indep
)
2043 indep
= isl_mat_reverse_gauss(indep
);
2044 indep
= isl_mat_lexnonneg_rows(indep
);
2048 /* Compute a basis for the rows in the linear part of the schedule
2049 * and extend this basis to a full basis. The remaining rows
2050 * can then be used to force linear independence from the rows
2053 * In particular, given the schedule rows S, we compute
2058 * with H the Hermite normal form of S. That is, all but the
2059 * first rank columns of H are zero and so each row in S is
2060 * a linear combination of the first rank rows of Q.
2061 * The matrix Q can be used as a variable transformation
2062 * that isolates the directions of S in the first rank rows.
2063 * Transposing S U = H yields
2067 * with all but the first rank rows of H^T zero.
2068 * The last rows of U^T are therefore linear combinations
2069 * of schedule coefficients that are all zero on schedule
2070 * coefficients that are linearly dependent on the rows of S.
2071 * At least one of these combinations is non-zero on
2072 * linearly independent schedule coefficients.
2073 * The rows are normalized to involve as few of the last
2074 * coefficients as possible and to have a positive initial value.
2076 static int node_update_vmap(struct isl_sched_node
*node
)
2079 int n_row
= isl_mat_rows(node
->sched
);
2081 H
= isl_mat_sub_alloc(node
->sched
, 0, n_row
,
2082 1 + node
->nparam
, node
->nvar
);
2084 H
= isl_mat_left_hermite(H
, 0, &U
, &Q
);
2085 isl_mat_free(node
->indep
);
2086 isl_mat_free(node
->vmap
);
2088 node
->indep
= isl_mat_transpose(U
);
2089 node
->rank
= isl_mat_initial_non_zero_cols(H
);
2090 node
->indep
= isl_mat_drop_rows(node
->indep
, 0, node
->rank
);
2091 node
->indep
= normalize_independent(node
->indep
);
2094 if (!node
->indep
|| !node
->vmap
|| node
->rank
< 0)
2099 /* Is "edge" marked as a validity or a conditional validity edge?
2101 static int is_any_validity(struct isl_sched_edge
*edge
)
2103 return is_validity(edge
) || is_conditional_validity(edge
);
2106 /* How many times should we count the constraints in "edge"?
2108 * We count as follows
2109 * validity -> 1 (>= 0)
2110 * validity+proximity -> 2 (>= 0 and upper bound)
2111 * proximity -> 2 (lower and upper bound)
2112 * local(+any) -> 2 (>= 0 and <= 0)
2114 * If an edge is only marked conditional_validity then it counts
2115 * as zero since it is only checked afterwards.
2117 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2118 * Otherwise, we ignore them.
2120 static int edge_multiplicity(struct isl_sched_edge
*edge
, int use_coincidence
)
2122 if (is_proximity(edge
) || is_local(edge
))
2124 if (use_coincidence
&& is_coincidence(edge
))
2126 if (is_validity(edge
))
2131 /* Count the number of equality and inequality constraints
2132 * that will be added for the given map.
2134 * "use_coincidence" is set if we should take into account coincidence edges.
2136 static isl_stat
count_map_constraints(struct isl_sched_graph
*graph
,
2137 struct isl_sched_edge
*edge
, __isl_take isl_map
*map
,
2138 int *n_eq
, int *n_ineq
, int use_coincidence
)
2140 isl_basic_set
*coef
;
2141 int f
= edge_multiplicity(edge
, use_coincidence
);
2148 if (edge
->src
== edge
->dst
)
2149 coef
= intra_coefficients(graph
, edge
->src
, map
);
2151 coef
= inter_coefficients(graph
, edge
, map
);
2153 return isl_stat_error
;
2154 *n_eq
+= f
* isl_basic_set_n_equality(coef
);
2155 *n_ineq
+= f
* isl_basic_set_n_inequality(coef
);
2156 isl_basic_set_free(coef
);
2161 /* Count the number of equality and inequality constraints
2162 * that will be added to the main lp problem.
2163 * We count as follows
2164 * validity -> 1 (>= 0)
2165 * validity+proximity -> 2 (>= 0 and upper bound)
2166 * proximity -> 2 (lower and upper bound)
2167 * local(+any) -> 2 (>= 0 and <= 0)
2169 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2170 * Otherwise, we ignore them.
2172 static int count_constraints(struct isl_sched_graph
*graph
,
2173 int *n_eq
, int *n_ineq
, int use_coincidence
)
2177 *n_eq
= *n_ineq
= 0;
2178 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2179 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
2180 isl_map
*map
= isl_map_copy(edge
->map
);
2182 if (count_map_constraints(graph
, edge
, map
, n_eq
, n_ineq
,
2183 use_coincidence
) < 0)
2190 /* Count the number of constraints that will be added by
2191 * add_bound_constant_constraints to bound the values of the constant terms
2192 * and increment *n_eq and *n_ineq accordingly.
2194 * In practice, add_bound_constant_constraints only adds inequalities.
2196 static isl_stat
count_bound_constant_constraints(isl_ctx
*ctx
,
2197 struct isl_sched_graph
*graph
, int *n_eq
, int *n_ineq
)
2199 if (isl_options_get_schedule_max_constant_term(ctx
) == -1)
2202 *n_ineq
+= graph
->n
;
2207 /* Add constraints to bound the values of the constant terms in the schedule,
2208 * if requested by the user.
2210 * The maximal value of the constant terms is defined by the option
2211 * "schedule_max_constant_term".
2213 static isl_stat
add_bound_constant_constraints(isl_ctx
*ctx
,
2214 struct isl_sched_graph
*graph
)
2220 max
= isl_options_get_schedule_max_constant_term(ctx
);
2224 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2226 for (i
= 0; i
< graph
->n
; ++i
) {
2227 struct isl_sched_node
*node
= &graph
->node
[i
];
2230 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2232 return isl_stat_error
;
2233 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
2234 pos
= node_cst_coef_offset(node
);
2235 isl_int_set_si(graph
->lp
->ineq
[k
][1 + pos
], -1);
2236 isl_int_set_si(graph
->lp
->ineq
[k
][0], max
);
2242 /* Count the number of constraints that will be added by
2243 * add_bound_coefficient_constraints and increment *n_eq and *n_ineq
2246 * In practice, add_bound_coefficient_constraints only adds inequalities.
2248 static int count_bound_coefficient_constraints(isl_ctx
*ctx
,
2249 struct isl_sched_graph
*graph
, int *n_eq
, int *n_ineq
)
2253 if (isl_options_get_schedule_max_coefficient(ctx
) == -1 &&
2254 !isl_options_get_schedule_treat_coalescing(ctx
))
2257 for (i
= 0; i
< graph
->n
; ++i
)
2258 *n_ineq
+= graph
->node
[i
].nparam
+ 2 * graph
->node
[i
].nvar
;
2263 /* Add constraints to graph->lp that bound the values of
2264 * the parameter schedule coefficients of "node" to "max" and
2265 * the variable schedule coefficients to the corresponding entry
2267 * In either case, a negative value means that no bound needs to be imposed.
2269 * For parameter coefficients, this amounts to adding a constraint
2277 * The variables coefficients are, however, not represented directly.
2278 * Instead, the variable coefficients c_x are written as differences
2279 * c_x = c_x^+ - c_x^-.
2282 * -max_i <= c_x_i <= max_i
2286 * -max_i <= c_x_i^+ - c_x_i^- <= max_i
2290 * -(c_x_i^+ - c_x_i^-) + max_i >= 0
2291 * c_x_i^+ - c_x_i^- + max_i >= 0
2293 static isl_stat
node_add_coefficient_constraints(isl_ctx
*ctx
,
2294 struct isl_sched_graph
*graph
, struct isl_sched_node
*node
, int max
)
2300 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2302 for (j
= 0; j
< node
->nparam
; ++j
) {
2308 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2310 return isl_stat_error
;
2311 dim
= 1 + node_par_coef_offset(node
) + j
;
2312 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
2313 isl_int_set_si(graph
->lp
->ineq
[k
][dim
], -1);
2314 isl_int_set_si(graph
->lp
->ineq
[k
][0], max
);
2317 ineq
= isl_vec_alloc(ctx
, 1 + total
);
2318 ineq
= isl_vec_clr(ineq
);
2320 return isl_stat_error
;
2321 for (i
= 0; i
< node
->nvar
; ++i
) {
2322 int pos
= 1 + node_var_coef_pos(node
, i
);
2324 if (isl_int_is_neg(node
->max
->el
[i
]))
2327 isl_int_set_si(ineq
->el
[pos
], 1);
2328 isl_int_set_si(ineq
->el
[pos
+ 1], -1);
2329 isl_int_set(ineq
->el
[0], node
->max
->el
[i
]);
2331 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2334 isl_seq_cpy(graph
->lp
->ineq
[k
], ineq
->el
, 1 + total
);
2336 isl_seq_neg(ineq
->el
+ pos
, ineq
->el
+ pos
+ 2 * i
, 2);
2337 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2340 isl_seq_cpy(graph
->lp
->ineq
[k
], ineq
->el
, 1 + total
);
2347 return isl_stat_error
;
2350 /* Add constraints that bound the values of the variable and parameter
2351 * coefficients of the schedule.
2353 * The maximal value of the coefficients is defined by the option
2354 * 'schedule_max_coefficient' and the entries in node->max.
2355 * These latter entries are only set if either the schedule_max_coefficient
2356 * option or the schedule_treat_coalescing option is set.
2358 static isl_stat
add_bound_coefficient_constraints(isl_ctx
*ctx
,
2359 struct isl_sched_graph
*graph
)
2364 max
= isl_options_get_schedule_max_coefficient(ctx
);
2366 if (max
== -1 && !isl_options_get_schedule_treat_coalescing(ctx
))
2369 for (i
= 0; i
< graph
->n
; ++i
) {
2370 struct isl_sched_node
*node
= &graph
->node
[i
];
2372 if (node_add_coefficient_constraints(ctx
, graph
, node
, max
) < 0)
2373 return isl_stat_error
;
2379 /* Add a constraint to graph->lp that equates the value at position
2380 * "sum_pos" to the sum of the "n" values starting at "first".
2382 static isl_stat
add_sum_constraint(struct isl_sched_graph
*graph
,
2383 int sum_pos
, int first
, int n
)
2388 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2390 k
= isl_basic_set_alloc_equality(graph
->lp
);
2392 return isl_stat_error
;
2393 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2394 isl_int_set_si(graph
->lp
->eq
[k
][1 + sum_pos
], -1);
2395 for (i
= 0; i
< n
; ++i
)
2396 isl_int_set_si(graph
->lp
->eq
[k
][1 + first
+ i
], 1);
2401 /* Add a constraint to graph->lp that equates the value at position
2402 * "sum_pos" to the sum of the parameter coefficients of all nodes.
2404 static isl_stat
add_param_sum_constraint(struct isl_sched_graph
*graph
,
2410 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2412 k
= isl_basic_set_alloc_equality(graph
->lp
);
2414 return isl_stat_error
;
2415 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2416 isl_int_set_si(graph
->lp
->eq
[k
][1 + sum_pos
], -1);
2417 for (i
= 0; i
< graph
->n
; ++i
) {
2418 int pos
= 1 + node_par_coef_offset(&graph
->node
[i
]);
2420 for (j
= 0; j
< graph
->node
[i
].nparam
; ++j
)
2421 isl_int_set_si(graph
->lp
->eq
[k
][pos
+ j
], 1);
2427 /* Add a constraint to graph->lp that equates the value at position
2428 * "sum_pos" to the sum of the variable coefficients of all nodes.
2430 static isl_stat
add_var_sum_constraint(struct isl_sched_graph
*graph
,
2436 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2438 k
= isl_basic_set_alloc_equality(graph
->lp
);
2440 return isl_stat_error
;
2441 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2442 isl_int_set_si(graph
->lp
->eq
[k
][1 + sum_pos
], -1);
2443 for (i
= 0; i
< graph
->n
; ++i
) {
2444 struct isl_sched_node
*node
= &graph
->node
[i
];
2445 int pos
= 1 + node_var_coef_offset(node
);
2447 for (j
= 0; j
< 2 * node
->nvar
; ++j
)
2448 isl_int_set_si(graph
->lp
->eq
[k
][pos
+ j
], 1);
2454 /* Construct an ILP problem for finding schedule coefficients
2455 * that result in non-negative, but small dependence distances
2456 * over all dependences.
2457 * In particular, the dependence distances over proximity edges
2458 * are bounded by m_0 + m_n n and we compute schedule coefficients
2459 * with small values (preferably zero) of m_n and m_0.
2461 * All variables of the ILP are non-negative. The actual coefficients
2462 * may be negative, so each coefficient is represented as the difference
2463 * of two non-negative variables. The negative part always appears
2464 * immediately before the positive part.
2465 * Other than that, the variables have the following order
2467 * - sum of positive and negative parts of m_n coefficients
2469 * - sum of all c_n coefficients
2470 * (unconstrained when computing non-parametric schedules)
2471 * - sum of positive and negative parts of all c_x coefficients
2472 * - positive and negative parts of m_n coefficients
2474 * - positive and negative parts of c_i_x, in opposite order
2475 * - c_i_n (if parametric)
2478 * The constraints are those from the edges plus two or three equalities
2479 * to express the sums.
2481 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2482 * Otherwise, we ignore them.
2484 static isl_stat
setup_lp(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
2485 int use_coincidence
)
2495 parametric
= ctx
->opt
->schedule_parametric
;
2496 nparam
= isl_space_dim(graph
->node
[0].space
, isl_dim_param
);
2498 total
= param_pos
+ 2 * nparam
;
2499 for (i
= 0; i
< graph
->n
; ++i
) {
2500 struct isl_sched_node
*node
= &graph
->node
[graph
->sorted
[i
]];
2501 if (node_update_vmap(node
) < 0)
2502 return isl_stat_error
;
2503 node
->start
= total
;
2504 total
+= 1 + node
->nparam
+ 2 * node
->nvar
;
2507 if (count_constraints(graph
, &n_eq
, &n_ineq
, use_coincidence
) < 0)
2508 return isl_stat_error
;
2509 if (count_bound_constant_constraints(ctx
, graph
, &n_eq
, &n_ineq
) < 0)
2510 return isl_stat_error
;
2511 if (count_bound_coefficient_constraints(ctx
, graph
, &n_eq
, &n_ineq
) < 0)
2512 return isl_stat_error
;
2514 space
= isl_space_set_alloc(ctx
, 0, total
);
2515 isl_basic_set_free(graph
->lp
);
2516 n_eq
+= 2 + parametric
;
2518 graph
->lp
= isl_basic_set_alloc_space(space
, 0, n_eq
, n_ineq
);
2520 if (add_sum_constraint(graph
, 0, param_pos
, 2 * nparam
) < 0)
2521 return isl_stat_error
;
2522 if (parametric
&& add_param_sum_constraint(graph
, 2) < 0)
2523 return isl_stat_error
;
2524 if (add_var_sum_constraint(graph
, 3) < 0)
2525 return isl_stat_error
;
2526 if (add_bound_constant_constraints(ctx
, graph
) < 0)
2527 return isl_stat_error
;
2528 if (add_bound_coefficient_constraints(ctx
, graph
) < 0)
2529 return isl_stat_error
;
2530 if (add_all_validity_constraints(graph
, use_coincidence
) < 0)
2531 return isl_stat_error
;
2532 if (add_all_proximity_constraints(graph
, use_coincidence
) < 0)
2533 return isl_stat_error
;
2538 /* Analyze the conflicting constraint found by
2539 * isl_tab_basic_set_non_trivial_lexmin. If it corresponds to the validity
2540 * constraint of one of the edges between distinct nodes, living, moreover
2541 * in distinct SCCs, then record the source and sink SCC as this may
2542 * be a good place to cut between SCCs.
2544 static int check_conflict(int con
, void *user
)
2547 struct isl_sched_graph
*graph
= user
;
2549 if (graph
->src_scc
>= 0)
2552 con
-= graph
->lp
->n_eq
;
2554 if (con
>= graph
->lp
->n_ineq
)
2557 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2558 if (!is_validity(&graph
->edge
[i
]))
2560 if (graph
->edge
[i
].src
== graph
->edge
[i
].dst
)
2562 if (graph
->edge
[i
].src
->scc
== graph
->edge
[i
].dst
->scc
)
2564 if (graph
->edge
[i
].start
> con
)
2566 if (graph
->edge
[i
].end
<= con
)
2568 graph
->src_scc
= graph
->edge
[i
].src
->scc
;
2569 graph
->dst_scc
= graph
->edge
[i
].dst
->scc
;
2575 /* Check whether the next schedule row of the given node needs to be
2576 * non-trivial. Lower-dimensional domains may have some trivial rows,
2577 * but as soon as the number of remaining required non-trivial rows
2578 * is as large as the number or remaining rows to be computed,
2579 * all remaining rows need to be non-trivial.
2581 static int needs_row(struct isl_sched_graph
*graph
, struct isl_sched_node
*node
)
2583 return node
->nvar
- node
->rank
>= graph
->maxvar
- graph
->n_row
;
2586 /* Construct a non-triviality region with triviality directions
2587 * corresponding to the rows of "indep".
2588 * The rows of "indep" are expressed in terms of the schedule coefficients c_i,
2589 * while the triviality directions are expressed in terms of
2590 * pairs of non-negative variables c^+_i - c^-_i, with c^-_i appearing
2591 * before c^+_i. Furthermore,
2592 * the pairs of non-negative variables representing the coefficients
2593 * are stored in the opposite order.
2595 static __isl_give isl_mat
*construct_trivial(__isl_keep isl_mat
*indep
)
2604 ctx
= isl_mat_get_ctx(indep
);
2605 n
= isl_mat_rows(indep
);
2606 n_var
= isl_mat_cols(indep
);
2607 mat
= isl_mat_alloc(ctx
, n
, 2 * n_var
);
2610 for (i
= 0; i
< n
; ++i
) {
2611 for (j
= 0; j
< n_var
; ++j
) {
2612 int nj
= n_var
- 1 - j
;
2613 isl_int_neg(mat
->row
[i
][2 * nj
], indep
->row
[i
][j
]);
2614 isl_int_set(mat
->row
[i
][2 * nj
+ 1], indep
->row
[i
][j
]);
2621 /* Solve the ILP problem constructed in setup_lp.
2622 * For each node such that all the remaining rows of its schedule
2623 * need to be non-trivial, we construct a non-triviality region.
2624 * This region imposes that the next row is independent of previous rows.
2625 * In particular, the non-triviality region enforces that at least
2626 * one of the linear combinations in the rows of node->indep is non-zero.
2628 static __isl_give isl_vec
*solve_lp(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2634 for (i
= 0; i
< graph
->n
; ++i
) {
2635 struct isl_sched_node
*node
= &graph
->node
[i
];
2638 graph
->region
[i
].pos
= node_var_coef_offset(node
);
2639 if (needs_row(graph
, node
))
2640 trivial
= construct_trivial(node
->indep
);
2642 trivial
= isl_mat_zero(ctx
, 0, 0);
2643 graph
->region
[i
].trivial
= trivial
;
2645 lp
= isl_basic_set_copy(graph
->lp
);
2646 sol
= isl_tab_basic_set_non_trivial_lexmin(lp
, 2, graph
->n
,
2647 graph
->region
, &check_conflict
, graph
);
2648 for (i
= 0; i
< graph
->n
; ++i
)
2649 isl_mat_free(graph
->region
[i
].trivial
);
2653 /* Extract the coefficients for the variables of "node" from "sol".
2655 * Each schedule coefficient c_i_x is represented as the difference
2656 * between two non-negative variables c_i_x^+ - c_i_x^-.
2657 * The c_i_x^- appear before their c_i_x^+ counterpart.
2658 * Furthermore, the order of these pairs is the opposite of that
2659 * of the corresponding coefficients.
2661 * Return c_i_x = c_i_x^+ - c_i_x^-
2663 static __isl_give isl_vec
*extract_var_coef(struct isl_sched_node
*node
,
2664 __isl_keep isl_vec
*sol
)
2672 csol
= isl_vec_alloc(isl_vec_get_ctx(sol
), node
->nvar
);
2676 pos
= 1 + node_var_coef_offset(node
);
2677 for (i
= 0; i
< node
->nvar
; ++i
)
2678 isl_int_sub(csol
->el
[node
->nvar
- 1 - i
],
2679 sol
->el
[pos
+ 2 * i
+ 1], sol
->el
[pos
+ 2 * i
]);
2684 /* Update the schedules of all nodes based on the given solution
2685 * of the LP problem.
2686 * The new row is added to the current band.
2687 * All possibly negative coefficients are encoded as a difference
2688 * of two non-negative variables, so we need to perform the subtraction
2691 * If coincident is set, then the caller guarantees that the new
2692 * row satisfies the coincidence constraints.
2694 static int update_schedule(struct isl_sched_graph
*graph
,
2695 __isl_take isl_vec
*sol
, int coincident
)
2698 isl_vec
*csol
= NULL
;
2703 isl_die(sol
->ctx
, isl_error_internal
,
2704 "no solution found", goto error
);
2705 if (graph
->n_total_row
>= graph
->max_row
)
2706 isl_die(sol
->ctx
, isl_error_internal
,
2707 "too many schedule rows", goto error
);
2709 for (i
= 0; i
< graph
->n
; ++i
) {
2710 struct isl_sched_node
*node
= &graph
->node
[i
];
2712 int row
= isl_mat_rows(node
->sched
);
2715 csol
= extract_var_coef(node
, sol
);
2719 isl_map_free(node
->sched_map
);
2720 node
->sched_map
= NULL
;
2721 node
->sched
= isl_mat_add_rows(node
->sched
, 1);
2724 pos
= node_cst_coef_offset(node
);
2725 node
->sched
= isl_mat_set_element(node
->sched
,
2726 row
, 0, sol
->el
[1 + pos
]);
2727 pos
= node_par_coef_offset(node
);
2728 for (j
= 0; j
< node
->nparam
; ++j
)
2729 node
->sched
= isl_mat_set_element(node
->sched
,
2730 row
, 1 + j
, sol
->el
[1 + pos
+ j
]);
2731 for (j
= 0; j
< node
->nvar
; ++j
)
2732 node
->sched
= isl_mat_set_element(node
->sched
,
2733 row
, 1 + node
->nparam
+ j
, csol
->el
[j
]);
2734 node
->coincident
[graph
->n_total_row
] = coincident
;
2740 graph
->n_total_row
++;
2749 /* Convert row "row" of node->sched into an isl_aff living in "ls"
2750 * and return this isl_aff.
2752 static __isl_give isl_aff
*extract_schedule_row(__isl_take isl_local_space
*ls
,
2753 struct isl_sched_node
*node
, int row
)
2761 aff
= isl_aff_zero_on_domain(ls
);
2762 isl_mat_get_element(node
->sched
, row
, 0, &v
);
2763 aff
= isl_aff_set_constant(aff
, v
);
2764 for (j
= 0; j
< node
->nparam
; ++j
) {
2765 isl_mat_get_element(node
->sched
, row
, 1 + j
, &v
);
2766 aff
= isl_aff_set_coefficient(aff
, isl_dim_param
, j
, v
);
2768 for (j
= 0; j
< node
->nvar
; ++j
) {
2769 isl_mat_get_element(node
->sched
, row
, 1 + node
->nparam
+ j
, &v
);
2770 aff
= isl_aff_set_coefficient(aff
, isl_dim_in
, j
, v
);
2778 /* Convert the "n" rows starting at "first" of node->sched into a multi_aff
2779 * and return this multi_aff.
2781 * The result is defined over the uncompressed node domain.
2783 static __isl_give isl_multi_aff
*node_extract_partial_schedule_multi_aff(
2784 struct isl_sched_node
*node
, int first
, int n
)
2788 isl_local_space
*ls
;
2795 nrow
= isl_mat_rows(node
->sched
);
2796 if (node
->compressed
)
2797 space
= isl_multi_aff_get_domain_space(node
->decompress
);
2799 space
= isl_space_copy(node
->space
);
2800 ls
= isl_local_space_from_space(isl_space_copy(space
));
2801 space
= isl_space_from_domain(space
);
2802 space
= isl_space_add_dims(space
, isl_dim_out
, n
);
2803 ma
= isl_multi_aff_zero(space
);
2805 for (i
= first
; i
< first
+ n
; ++i
) {
2806 aff
= extract_schedule_row(isl_local_space_copy(ls
), node
, i
);
2807 ma
= isl_multi_aff_set_aff(ma
, i
- first
, aff
);
2810 isl_local_space_free(ls
);
2812 if (node
->compressed
)
2813 ma
= isl_multi_aff_pullback_multi_aff(ma
,
2814 isl_multi_aff_copy(node
->compress
));
2819 /* Convert node->sched into a multi_aff and return this multi_aff.
2821 * The result is defined over the uncompressed node domain.
2823 static __isl_give isl_multi_aff
*node_extract_schedule_multi_aff(
2824 struct isl_sched_node
*node
)
2828 nrow
= isl_mat_rows(node
->sched
);
2829 return node_extract_partial_schedule_multi_aff(node
, 0, nrow
);
2832 /* Convert node->sched into a map and return this map.
2834 * The result is cached in node->sched_map, which needs to be released
2835 * whenever node->sched is updated.
2836 * It is defined over the uncompressed node domain.
2838 static __isl_give isl_map
*node_extract_schedule(struct isl_sched_node
*node
)
2840 if (!node
->sched_map
) {
2843 ma
= node_extract_schedule_multi_aff(node
);
2844 node
->sched_map
= isl_map_from_multi_aff(ma
);
2847 return isl_map_copy(node
->sched_map
);
2850 /* Construct a map that can be used to update a dependence relation
2851 * based on the current schedule.
2852 * That is, construct a map expressing that source and sink
2853 * are executed within the same iteration of the current schedule.
2854 * This map can then be intersected with the dependence relation.
2855 * This is not the most efficient way, but this shouldn't be a critical
2858 static __isl_give isl_map
*specializer(struct isl_sched_node
*src
,
2859 struct isl_sched_node
*dst
)
2861 isl_map
*src_sched
, *dst_sched
;
2863 src_sched
= node_extract_schedule(src
);
2864 dst_sched
= node_extract_schedule(dst
);
2865 return isl_map_apply_range(src_sched
, isl_map_reverse(dst_sched
));
2868 /* Intersect the domains of the nested relations in domain and range
2869 * of "umap" with "map".
2871 static __isl_give isl_union_map
*intersect_domains(
2872 __isl_take isl_union_map
*umap
, __isl_keep isl_map
*map
)
2874 isl_union_set
*uset
;
2876 umap
= isl_union_map_zip(umap
);
2877 uset
= isl_union_set_from_set(isl_map_wrap(isl_map_copy(map
)));
2878 umap
= isl_union_map_intersect_domain(umap
, uset
);
2879 umap
= isl_union_map_zip(umap
);
2883 /* Update the dependence relation of the given edge based
2884 * on the current schedule.
2885 * If the dependence is carried completely by the current schedule, then
2886 * it is removed from the edge_tables. It is kept in the list of edges
2887 * as otherwise all edge_tables would have to be recomputed.
2889 static int update_edge(struct isl_sched_graph
*graph
,
2890 struct isl_sched_edge
*edge
)
2895 id
= specializer(edge
->src
, edge
->dst
);
2896 edge
->map
= isl_map_intersect(edge
->map
, isl_map_copy(id
));
2900 if (edge
->tagged_condition
) {
2901 edge
->tagged_condition
=
2902 intersect_domains(edge
->tagged_condition
, id
);
2903 if (!edge
->tagged_condition
)
2906 if (edge
->tagged_validity
) {
2907 edge
->tagged_validity
=
2908 intersect_domains(edge
->tagged_validity
, id
);
2909 if (!edge
->tagged_validity
)
2913 empty
= isl_map_plain_is_empty(edge
->map
);
2917 graph_remove_edge(graph
, edge
);
2926 /* Does the domain of "umap" intersect "uset"?
2928 static int domain_intersects(__isl_keep isl_union_map
*umap
,
2929 __isl_keep isl_union_set
*uset
)
2933 umap
= isl_union_map_copy(umap
);
2934 umap
= isl_union_map_intersect_domain(umap
, isl_union_set_copy(uset
));
2935 empty
= isl_union_map_is_empty(umap
);
2936 isl_union_map_free(umap
);
2938 return empty
< 0 ? -1 : !empty
;
2941 /* Does the range of "umap" intersect "uset"?
2943 static int range_intersects(__isl_keep isl_union_map
*umap
,
2944 __isl_keep isl_union_set
*uset
)
2948 umap
= isl_union_map_copy(umap
);
2949 umap
= isl_union_map_intersect_range(umap
, isl_union_set_copy(uset
));
2950 empty
= isl_union_map_is_empty(umap
);
2951 isl_union_map_free(umap
);
2953 return empty
< 0 ? -1 : !empty
;
2956 /* Are the condition dependences of "edge" local with respect to
2957 * the current schedule?
2959 * That is, are domain and range of the condition dependences mapped
2960 * to the same point?
2962 * In other words, is the condition false?
2964 static int is_condition_false(struct isl_sched_edge
*edge
)
2966 isl_union_map
*umap
;
2967 isl_map
*map
, *sched
, *test
;
2970 empty
= isl_union_map_is_empty(edge
->tagged_condition
);
2971 if (empty
< 0 || empty
)
2974 umap
= isl_union_map_copy(edge
->tagged_condition
);
2975 umap
= isl_union_map_zip(umap
);
2976 umap
= isl_union_set_unwrap(isl_union_map_domain(umap
));
2977 map
= isl_map_from_union_map(umap
);
2979 sched
= node_extract_schedule(edge
->src
);
2980 map
= isl_map_apply_domain(map
, sched
);
2981 sched
= node_extract_schedule(edge
->dst
);
2982 map
= isl_map_apply_range(map
, sched
);
2984 test
= isl_map_identity(isl_map_get_space(map
));
2985 local
= isl_map_is_subset(map
, test
);
2992 /* For each conditional validity constraint that is adjacent
2993 * to a condition with domain in condition_source or range in condition_sink,
2994 * turn it into an unconditional validity constraint.
2996 static int unconditionalize_adjacent_validity(struct isl_sched_graph
*graph
,
2997 __isl_take isl_union_set
*condition_source
,
2998 __isl_take isl_union_set
*condition_sink
)
3002 condition_source
= isl_union_set_coalesce(condition_source
);
3003 condition_sink
= isl_union_set_coalesce(condition_sink
);
3005 for (i
= 0; i
< graph
->n_edge
; ++i
) {
3007 isl_union_map
*validity
;
3009 if (!is_conditional_validity(&graph
->edge
[i
]))
3011 if (is_validity(&graph
->edge
[i
]))
3014 validity
= graph
->edge
[i
].tagged_validity
;
3015 adjacent
= domain_intersects(validity
, condition_sink
);
3016 if (adjacent
>= 0 && !adjacent
)
3017 adjacent
= range_intersects(validity
, condition_source
);
3023 set_validity(&graph
->edge
[i
]);
3026 isl_union_set_free(condition_source
);
3027 isl_union_set_free(condition_sink
);
3030 isl_union_set_free(condition_source
);
3031 isl_union_set_free(condition_sink
);
3035 /* Update the dependence relations of all edges based on the current schedule
3036 * and enforce conditional validity constraints that are adjacent
3037 * to satisfied condition constraints.
3039 * First check if any of the condition constraints are satisfied
3040 * (i.e., not local to the outer schedule) and keep track of
3041 * their domain and range.
3042 * Then update all dependence relations (which removes the non-local
3044 * Finally, if any condition constraints turned out to be satisfied,
3045 * then turn all adjacent conditional validity constraints into
3046 * unconditional validity constraints.
3048 static int update_edges(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
3052 isl_union_set
*source
, *sink
;
3054 source
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
3055 sink
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
3056 for (i
= 0; i
< graph
->n_edge
; ++i
) {
3058 isl_union_set
*uset
;
3059 isl_union_map
*umap
;
3061 if (!is_condition(&graph
->edge
[i
]))
3063 if (is_local(&graph
->edge
[i
]))
3065 local
= is_condition_false(&graph
->edge
[i
]);
3073 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_condition
);
3074 uset
= isl_union_map_domain(umap
);
3075 source
= isl_union_set_union(source
, uset
);
3077 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_condition
);
3078 uset
= isl_union_map_range(umap
);
3079 sink
= isl_union_set_union(sink
, uset
);
3082 for (i
= graph
->n_edge
- 1; i
>= 0; --i
) {
3083 if (update_edge(graph
, &graph
->edge
[i
]) < 0)
3088 return unconditionalize_adjacent_validity(graph
, source
, sink
);
3090 isl_union_set_free(source
);
3091 isl_union_set_free(sink
);
3094 isl_union_set_free(source
);
3095 isl_union_set_free(sink
);
3099 static void next_band(struct isl_sched_graph
*graph
)
3101 graph
->band_start
= graph
->n_total_row
;
3104 /* Return the union of the universe domains of the nodes in "graph"
3105 * that satisfy "pred".
3107 static __isl_give isl_union_set
*isl_sched_graph_domain(isl_ctx
*ctx
,
3108 struct isl_sched_graph
*graph
,
3109 int (*pred
)(struct isl_sched_node
*node
, int data
), int data
)
3115 for (i
= 0; i
< graph
->n
; ++i
)
3116 if (pred(&graph
->node
[i
], data
))
3120 isl_die(ctx
, isl_error_internal
,
3121 "empty component", return NULL
);
3123 set
= isl_set_universe(isl_space_copy(graph
->node
[i
].space
));
3124 dom
= isl_union_set_from_set(set
);
3126 for (i
= i
+ 1; i
< graph
->n
; ++i
) {
3127 if (!pred(&graph
->node
[i
], data
))
3129 set
= isl_set_universe(isl_space_copy(graph
->node
[i
].space
));
3130 dom
= isl_union_set_union(dom
, isl_union_set_from_set(set
));
3136 /* Return a list of unions of universe domains, where each element
3137 * in the list corresponds to an SCC (or WCC) indexed by node->scc.
3139 static __isl_give isl_union_set_list
*extract_sccs(isl_ctx
*ctx
,
3140 struct isl_sched_graph
*graph
)
3143 isl_union_set_list
*filters
;
3145 filters
= isl_union_set_list_alloc(ctx
, graph
->scc
);
3146 for (i
= 0; i
< graph
->scc
; ++i
) {
3149 dom
= isl_sched_graph_domain(ctx
, graph
, &node_scc_exactly
, i
);
3150 filters
= isl_union_set_list_add(filters
, dom
);
3156 /* Return a list of two unions of universe domains, one for the SCCs up
3157 * to and including graph->src_scc and another for the other SCCs.
3159 static __isl_give isl_union_set_list
*extract_split(isl_ctx
*ctx
,
3160 struct isl_sched_graph
*graph
)
3163 isl_union_set_list
*filters
;
3165 filters
= isl_union_set_list_alloc(ctx
, 2);
3166 dom
= isl_sched_graph_domain(ctx
, graph
,
3167 &node_scc_at_most
, graph
->src_scc
);
3168 filters
= isl_union_set_list_add(filters
, dom
);
3169 dom
= isl_sched_graph_domain(ctx
, graph
,
3170 &node_scc_at_least
, graph
->src_scc
+ 1);
3171 filters
= isl_union_set_list_add(filters
, dom
);
3176 /* Copy nodes that satisfy node_pred from the src dependence graph
3177 * to the dst dependence graph.
3179 static int copy_nodes(struct isl_sched_graph
*dst
, struct isl_sched_graph
*src
,
3180 int (*node_pred
)(struct isl_sched_node
*node
, int data
), int data
)
3185 for (i
= 0; i
< src
->n
; ++i
) {
3188 if (!node_pred(&src
->node
[i
], data
))
3192 dst
->node
[j
].space
= isl_space_copy(src
->node
[i
].space
);
3193 dst
->node
[j
].compressed
= src
->node
[i
].compressed
;
3194 dst
->node
[j
].hull
= isl_set_copy(src
->node
[i
].hull
);
3195 dst
->node
[j
].compress
=
3196 isl_multi_aff_copy(src
->node
[i
].compress
);
3197 dst
->node
[j
].decompress
=
3198 isl_multi_aff_copy(src
->node
[i
].decompress
);
3199 dst
->node
[j
].nvar
= src
->node
[i
].nvar
;
3200 dst
->node
[j
].nparam
= src
->node
[i
].nparam
;
3201 dst
->node
[j
].sched
= isl_mat_copy(src
->node
[i
].sched
);
3202 dst
->node
[j
].sched_map
= isl_map_copy(src
->node
[i
].sched_map
);
3203 dst
->node
[j
].coincident
= src
->node
[i
].coincident
;
3204 dst
->node
[j
].sizes
= isl_multi_val_copy(src
->node
[i
].sizes
);
3205 dst
->node
[j
].max
= isl_vec_copy(src
->node
[i
].max
);
3208 if (!dst
->node
[j
].space
|| !dst
->node
[j
].sched
)
3210 if (dst
->node
[j
].compressed
&&
3211 (!dst
->node
[j
].hull
|| !dst
->node
[j
].compress
||
3212 !dst
->node
[j
].decompress
))
3219 /* Copy non-empty edges that satisfy edge_pred from the src dependence graph
3220 * to the dst dependence graph.
3221 * If the source or destination node of the edge is not in the destination
3222 * graph, then it must be a backward proximity edge and it should simply
3225 static int copy_edges(isl_ctx
*ctx
, struct isl_sched_graph
*dst
,
3226 struct isl_sched_graph
*src
,
3227 int (*edge_pred
)(struct isl_sched_edge
*edge
, int data
), int data
)
3230 enum isl_edge_type t
;
3233 for (i
= 0; i
< src
->n_edge
; ++i
) {
3234 struct isl_sched_edge
*edge
= &src
->edge
[i
];
3236 isl_union_map
*tagged_condition
;
3237 isl_union_map
*tagged_validity
;
3238 struct isl_sched_node
*dst_src
, *dst_dst
;
3240 if (!edge_pred(edge
, data
))
3243 if (isl_map_plain_is_empty(edge
->map
))
3246 dst_src
= graph_find_node(ctx
, dst
, edge
->src
->space
);
3247 dst_dst
= graph_find_node(ctx
, dst
, edge
->dst
->space
);
3248 if (!dst_src
|| !dst_dst
) {
3249 if (is_validity(edge
) || is_conditional_validity(edge
))
3250 isl_die(ctx
, isl_error_internal
,
3251 "backward (conditional) validity edge",
3256 map
= isl_map_copy(edge
->map
);
3257 tagged_condition
= isl_union_map_copy(edge
->tagged_condition
);
3258 tagged_validity
= isl_union_map_copy(edge
->tagged_validity
);
3260 dst
->edge
[dst
->n_edge
].src
= dst_src
;
3261 dst
->edge
[dst
->n_edge
].dst
= dst_dst
;
3262 dst
->edge
[dst
->n_edge
].map
= map
;
3263 dst
->edge
[dst
->n_edge
].tagged_condition
= tagged_condition
;
3264 dst
->edge
[dst
->n_edge
].tagged_validity
= tagged_validity
;
3265 dst
->edge
[dst
->n_edge
].types
= edge
->types
;
3268 if (edge
->tagged_condition
&& !tagged_condition
)
3270 if (edge
->tagged_validity
&& !tagged_validity
)
3273 for (t
= isl_edge_first
; t
<= isl_edge_last
; ++t
) {
3275 graph_find_edge(src
, t
, edge
->src
, edge
->dst
))
3277 if (graph_edge_table_add(ctx
, dst
, t
,
3278 &dst
->edge
[dst
->n_edge
- 1]) < 0)
3286 /* Compute the maximal number of variables over all nodes.
3287 * This is the maximal number of linearly independent schedule
3288 * rows that we need to compute.
3289 * Just in case we end up in a part of the dependence graph
3290 * with only lower-dimensional domains, we make sure we will
3291 * compute the required amount of extra linearly independent rows.
3293 static int compute_maxvar(struct isl_sched_graph
*graph
)
3298 for (i
= 0; i
< graph
->n
; ++i
) {
3299 struct isl_sched_node
*node
= &graph
->node
[i
];
3302 if (node_update_vmap(node
) < 0)
3304 nvar
= node
->nvar
+ graph
->n_row
- node
->rank
;
3305 if (nvar
> graph
->maxvar
)
3306 graph
->maxvar
= nvar
;
3312 /* Extract the subgraph of "graph" that consists of the node satisfying
3313 * "node_pred" and the edges satisfying "edge_pred" and store
3314 * the result in "sub".
3316 static int extract_sub_graph(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
3317 int (*node_pred
)(struct isl_sched_node
*node
, int data
),
3318 int (*edge_pred
)(struct isl_sched_edge
*edge
, int data
),
3319 int data
, struct isl_sched_graph
*sub
)
3321 int i
, n
= 0, n_edge
= 0;
3324 for (i
= 0; i
< graph
->n
; ++i
)
3325 if (node_pred(&graph
->node
[i
], data
))
3327 for (i
= 0; i
< graph
->n_edge
; ++i
)
3328 if (edge_pred(&graph
->edge
[i
], data
))
3330 if (graph_alloc(ctx
, sub
, n
, n_edge
) < 0)
3332 if (copy_nodes(sub
, graph
, node_pred
, data
) < 0)
3334 if (graph_init_table(ctx
, sub
) < 0)
3336 for (t
= 0; t
<= isl_edge_last
; ++t
)
3337 sub
->max_edge
[t
] = graph
->max_edge
[t
];
3338 if (graph_init_edge_tables(ctx
, sub
) < 0)
3340 if (copy_edges(ctx
, sub
, graph
, edge_pred
, data
) < 0)
3342 sub
->n_row
= graph
->n_row
;
3343 sub
->max_row
= graph
->max_row
;
3344 sub
->n_total_row
= graph
->n_total_row
;
3345 sub
->band_start
= graph
->band_start
;
3350 static __isl_give isl_schedule_node
*compute_schedule(isl_schedule_node
*node
,
3351 struct isl_sched_graph
*graph
);
3352 static __isl_give isl_schedule_node
*compute_schedule_wcc(
3353 isl_schedule_node
*node
, struct isl_sched_graph
*graph
);
3355 /* Compute a schedule for a subgraph of "graph". In particular, for
3356 * the graph composed of nodes that satisfy node_pred and edges that
3357 * that satisfy edge_pred.
3358 * If the subgraph is known to consist of a single component, then wcc should
3359 * be set and then we call compute_schedule_wcc on the constructed subgraph.
3360 * Otherwise, we call compute_schedule, which will check whether the subgraph
3363 * The schedule is inserted at "node" and the updated schedule node
3366 static __isl_give isl_schedule_node
*compute_sub_schedule(
3367 __isl_take isl_schedule_node
*node
, isl_ctx
*ctx
,
3368 struct isl_sched_graph
*graph
,
3369 int (*node_pred
)(struct isl_sched_node
*node
, int data
),
3370 int (*edge_pred
)(struct isl_sched_edge
*edge
, int data
),
3373 struct isl_sched_graph split
= { 0 };
3375 if (extract_sub_graph(ctx
, graph
, node_pred
, edge_pred
, data
,
3380 node
= compute_schedule_wcc(node
, &split
);
3382 node
= compute_schedule(node
, &split
);
3384 graph_free(ctx
, &split
);
3387 graph_free(ctx
, &split
);
3388 return isl_schedule_node_free(node
);
3391 static int edge_scc_exactly(struct isl_sched_edge
*edge
, int scc
)
3393 return edge
->src
->scc
== scc
&& edge
->dst
->scc
== scc
;
3396 static int edge_dst_scc_at_most(struct isl_sched_edge
*edge
, int scc
)
3398 return edge
->dst
->scc
<= scc
;
3401 static int edge_src_scc_at_least(struct isl_sched_edge
*edge
, int scc
)
3403 return edge
->src
->scc
>= scc
;
3406 /* Reset the current band by dropping all its schedule rows.
3408 static int reset_band(struct isl_sched_graph
*graph
)
3413 drop
= graph
->n_total_row
- graph
->band_start
;
3414 graph
->n_total_row
-= drop
;
3415 graph
->n_row
-= drop
;
3417 for (i
= 0; i
< graph
->n
; ++i
) {
3418 struct isl_sched_node
*node
= &graph
->node
[i
];
3420 isl_map_free(node
->sched_map
);
3421 node
->sched_map
= NULL
;
3423 node
->sched
= isl_mat_drop_rows(node
->sched
,
3424 graph
->band_start
, drop
);
3433 /* Split the current graph into two parts and compute a schedule for each
3434 * part individually. In particular, one part consists of all SCCs up
3435 * to and including graph->src_scc, while the other part contains the other
3436 * SCCs. The split is enforced by a sequence node inserted at position "node"
3437 * in the schedule tree. Return the updated schedule node.
3438 * If either of these two parts consists of a sequence, then it is spliced
3439 * into the sequence containing the two parts.
3441 * The current band is reset. It would be possible to reuse
3442 * the previously computed rows as the first rows in the next
3443 * band, but recomputing them may result in better rows as we are looking
3444 * at a smaller part of the dependence graph.
3446 static __isl_give isl_schedule_node
*compute_split_schedule(
3447 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
3451 isl_union_set_list
*filters
;
3456 if (reset_band(graph
) < 0)
3457 return isl_schedule_node_free(node
);
3461 ctx
= isl_schedule_node_get_ctx(node
);
3462 filters
= extract_split(ctx
, graph
);
3463 node
= isl_schedule_node_insert_sequence(node
, filters
);
3464 node
= isl_schedule_node_child(node
, 1);
3465 node
= isl_schedule_node_child(node
, 0);
3467 node
= compute_sub_schedule(node
, ctx
, graph
,
3468 &node_scc_at_least
, &edge_src_scc_at_least
,
3469 graph
->src_scc
+ 1, 0);
3470 is_seq
= isl_schedule_node_get_type(node
) == isl_schedule_node_sequence
;
3471 node
= isl_schedule_node_parent(node
);
3472 node
= isl_schedule_node_parent(node
);
3474 node
= isl_schedule_node_sequence_splice_child(node
, 1);
3475 node
= isl_schedule_node_child(node
, 0);
3476 node
= isl_schedule_node_child(node
, 0);
3477 node
= compute_sub_schedule(node
, ctx
, graph
,
3478 &node_scc_at_most
, &edge_dst_scc_at_most
,
3480 is_seq
= isl_schedule_node_get_type(node
) == isl_schedule_node_sequence
;
3481 node
= isl_schedule_node_parent(node
);
3482 node
= isl_schedule_node_parent(node
);
3484 node
= isl_schedule_node_sequence_splice_child(node
, 0);
3489 /* Insert a band node at position "node" in the schedule tree corresponding
3490 * to the current band in "graph". Mark the band node permutable
3491 * if "permutable" is set.
3492 * The partial schedules and the coincidence property are extracted
3493 * from the graph nodes.
3494 * Return the updated schedule node.
3496 static __isl_give isl_schedule_node
*insert_current_band(
3497 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
3503 isl_multi_pw_aff
*mpa
;
3504 isl_multi_union_pw_aff
*mupa
;
3510 isl_die(isl_schedule_node_get_ctx(node
), isl_error_internal
,
3511 "graph should have at least one node",
3512 return isl_schedule_node_free(node
));
3514 start
= graph
->band_start
;
3515 end
= graph
->n_total_row
;
3518 ma
= node_extract_partial_schedule_multi_aff(&graph
->node
[0], start
, n
);
3519 mpa
= isl_multi_pw_aff_from_multi_aff(ma
);
3520 mupa
= isl_multi_union_pw_aff_from_multi_pw_aff(mpa
);
3522 for (i
= 1; i
< graph
->n
; ++i
) {
3523 isl_multi_union_pw_aff
*mupa_i
;
3525 ma
= node_extract_partial_schedule_multi_aff(&graph
->node
[i
],
3527 mpa
= isl_multi_pw_aff_from_multi_aff(ma
);
3528 mupa_i
= isl_multi_union_pw_aff_from_multi_pw_aff(mpa
);
3529 mupa
= isl_multi_union_pw_aff_union_add(mupa
, mupa_i
);
3531 node
= isl_schedule_node_insert_partial_schedule(node
, mupa
);
3533 for (i
= 0; i
< n
; ++i
)
3534 node
= isl_schedule_node_band_member_set_coincident(node
, i
,
3535 graph
->node
[0].coincident
[start
+ i
]);
3536 node
= isl_schedule_node_band_set_permutable(node
, permutable
);
3541 /* Update the dependence relations based on the current schedule,
3542 * add the current band to "node" and then continue with the computation
3544 * Return the updated schedule node.
3546 static __isl_give isl_schedule_node
*compute_next_band(
3547 __isl_take isl_schedule_node
*node
,
3548 struct isl_sched_graph
*graph
, int permutable
)
3555 ctx
= isl_schedule_node_get_ctx(node
);
3556 if (update_edges(ctx
, graph
) < 0)
3557 return isl_schedule_node_free(node
);
3558 node
= insert_current_band(node
, graph
, permutable
);
3561 node
= isl_schedule_node_child(node
, 0);
3562 node
= compute_schedule(node
, graph
);
3563 node
= isl_schedule_node_parent(node
);
3568 /* Add the constraints "coef" derived from an edge from "node" to itself
3569 * to graph->lp in order to respect the dependences and to try and carry them.
3570 * "pos" is the sequence number of the edge that needs to be carried.
3571 * "coef" represents general constraints on coefficients (c_0, c_n, c_x)
3572 * of valid constraints for (y - x) with x and y instances of the node.
3574 * The constraints added to graph->lp need to enforce
3576 * (c_j_0 + c_j_n n + c_j_x y) - (c_j_0 + c_j_n n + c_j_x x)
3577 * = c_j_x (y - x) >= e_i
3579 * for each (x,y) in the dependence relation of the edge.
3580 * That is, (-e_i, 0, c_j_x) needs to be plugged in for (c_0, c_n, c_x),
3581 * taking into account that each coefficient in c_j_x is represented
3582 * as a pair of non-negative coefficients.
3584 static isl_stat
add_intra_constraints(struct isl_sched_graph
*graph
,
3585 struct isl_sched_node
*node
, __isl_take isl_basic_set
*coef
, int pos
)
3589 isl_dim_map
*dim_map
;
3592 return isl_stat_error
;
3594 ctx
= isl_basic_set_get_ctx(coef
);
3595 offset
= coef_var_offset(coef
);
3596 dim_map
= intra_dim_map(ctx
, graph
, node
, offset
, 1);
3597 isl_dim_map_range(dim_map
, 3 + pos
, 0, 0, 0, 1, -1);
3598 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
3603 /* Add the constraints "coef" derived from an edge from "src" to "dst"
3604 * to graph->lp in order to respect the dependences and to try and carry them.
3605 * "pos" is the sequence number of the edge that needs to be carried.
3606 * "coef" represents general constraints on coefficients (c_0, c_n, c_x, c_y)
3607 * of valid constraints for (x, y) with x and y instances of "src" and "dst".
3609 * The constraints added to graph->lp need to enforce
3611 * (c_k_0 + c_k_n n + c_k_x y) - (c_j_0 + c_j_n n + c_j_x x) >= e_i
3613 * for each (x,y) in the dependence relation of the edge.
3615 * (-e_i + c_k_0 - c_j_0, c_k_n - c_j_n, -c_j_x, c_k_x)
3616 * needs to be plugged in for (c_0, c_n, c_x, c_y),
3617 * taking into account that each coefficient in c_j_x and c_k_x is represented
3618 * as a pair of non-negative coefficients.
3620 static isl_stat
add_inter_constraints(struct isl_sched_graph
*graph
,
3621 struct isl_sched_node
*src
, struct isl_sched_node
*dst
,
3622 __isl_take isl_basic_set
*coef
, int pos
)
3626 isl_dim_map
*dim_map
;
3629 return isl_stat_error
;
3631 ctx
= isl_basic_set_get_ctx(coef
);
3632 offset
= coef_var_offset(coef
);
3633 dim_map
= inter_dim_map(ctx
, graph
, src
, dst
, offset
, 1);
3634 isl_dim_map_range(dim_map
, 3 + pos
, 0, 0, 0, 1, -1);
3635 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
3640 /* Data structure collecting information used during the construction
3641 * of an LP for carrying dependences.
3643 * "intra" is a sequence of coefficient constraints for intra-node edges.
3644 * "inter" is a sequence of coefficient constraints for inter-node edges.
3647 isl_basic_set_list
*intra
;
3648 isl_basic_set_list
*inter
;
3651 /* Free all the data stored in "carry".
3653 static void isl_carry_clear(struct isl_carry
*carry
)
3655 isl_basic_set_list_free(carry
->intra
);
3656 isl_basic_set_list_free(carry
->inter
);
3659 /* Return a pointer to the node in "graph" that lives in "space".
3660 * If the requested node has been compressed, then "space"
3661 * corresponds to the compressed space.
3663 * First try and see if "space" is the space of an uncompressed node.
3664 * If so, return that node.
3665 * Otherwise, "space" was constructed by construct_compressed_id and
3666 * contains a user pointer pointing to the node in the tuple id.
3668 static struct isl_sched_node
*graph_find_compressed_node(isl_ctx
*ctx
,
3669 struct isl_sched_graph
*graph
, __isl_keep isl_space
*space
)
3672 struct isl_sched_node
*node
;
3677 node
= graph_find_node(ctx
, graph
, space
);
3681 id
= isl_space_get_tuple_id(space
, isl_dim_set
);
3682 node
= isl_id_get_user(id
);
3688 if (!(node
>= &graph
->node
[0] && node
< &graph
->node
[graph
->n
]))
3689 isl_die(ctx
, isl_error_internal
,
3690 "space points to invalid node", return NULL
);
3695 /* Internal data structure for add_all_constraints.
3697 * "graph" is the schedule constraint graph for which an LP problem
3698 * is being constructed.
3699 * "pos" is the position of the next edge that needs to be carried.
3701 struct isl_add_all_constraints_data
{
3703 struct isl_sched_graph
*graph
;
3707 /* Add the constraints "coef" derived from an edge from a node to itself
3708 * to data->graph->lp in order to respect the dependences and
3709 * to try and carry them.
3711 * The space of "coef" is of the form
3713 * coefficients[[c_cst, c_n] -> S[c_x]]
3715 * with S[c_x] the (compressed) space of the node.
3716 * Extract the node from the space and call add_intra_constraints.
3718 static isl_stat
lp_add_intra(__isl_take isl_basic_set
*coef
, void *user
)
3720 struct isl_add_all_constraints_data
*data
= user
;
3722 struct isl_sched_node
*node
;
3724 space
= isl_basic_set_get_space(coef
);
3725 space
= isl_space_range(isl_space_unwrap(space
));
3726 node
= graph_find_compressed_node(data
->ctx
, data
->graph
, space
);
3727 isl_space_free(space
);
3728 return add_intra_constraints(data
->graph
, node
, coef
, data
->pos
++);
3731 /* Add the constraints "coef" derived from an edge from a node j
3732 * to a node k to data->graph->lp in order to respect the dependences and
3733 * to try and carry them.
3735 * The space of "coef" is of the form
3737 * coefficients[[c_cst, c_n] -> [S_j[c_x] -> S_k[c_y]]]
3739 * with S_j[c_x] and S_k[c_y] the (compressed) spaces of the nodes.
3740 * Extract the nodes from the space and call add_inter_constraints.
3742 static isl_stat
lp_add_inter(__isl_take isl_basic_set
*coef
, void *user
)
3744 struct isl_add_all_constraints_data
*data
= user
;
3745 isl_space
*space
, *dom
;
3746 struct isl_sched_node
*src
, *dst
;
3748 space
= isl_basic_set_get_space(coef
);
3749 space
= isl_space_unwrap(isl_space_range(isl_space_unwrap(space
)));
3750 dom
= isl_space_domain(isl_space_copy(space
));
3751 src
= graph_find_compressed_node(data
->ctx
, data
->graph
, dom
);
3752 isl_space_free(dom
);
3753 space
= isl_space_range(space
);
3754 dst
= graph_find_compressed_node(data
->ctx
, data
->graph
, space
);
3755 isl_space_free(space
);
3757 return add_inter_constraints(data
->graph
, src
, dst
, coef
, data
->pos
++);
3760 /* Add constraints to graph->lp that force all (conditional) validity
3761 * dependences to be respected and attempt to carry them.
3762 * "intra" is the sequence of coefficient constraints for intra-node edges.
3763 * "inter" is the sequence of coefficient constraints for inter-node edges.
3765 static isl_stat
add_all_constraints(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
3766 __isl_keep isl_basic_set_list
*intra
,
3767 __isl_keep isl_basic_set_list
*inter
)
3769 struct isl_add_all_constraints_data data
= { ctx
, graph
};
3772 if (isl_basic_set_list_foreach(intra
, &lp_add_intra
, &data
) < 0)
3773 return isl_stat_error
;
3774 if (isl_basic_set_list_foreach(inter
, &lp_add_inter
, &data
) < 0)
3775 return isl_stat_error
;
3779 /* Internal data structure for count_all_constraints
3780 * for keeping track of the number of equality and inequality constraints.
3782 struct isl_sched_count
{
3787 /* Add the number of equality and inequality constraints of "bset"
3788 * to data->n_eq and data->n_ineq.
3790 static isl_stat
bset_update_count(__isl_take isl_basic_set
*bset
, void *user
)
3792 struct isl_sched_count
*data
= user
;
3794 data
->n_eq
+= isl_basic_set_n_equality(bset
);
3795 data
->n_ineq
+= isl_basic_set_n_inequality(bset
);
3796 isl_basic_set_free(bset
);
3801 /* Count the number of equality and inequality constraints
3802 * that will be added to the carry_lp problem.
3803 * We count each edge exactly once.
3804 * "intra" is the sequence of coefficient constraints for intra-node edges.
3805 * "inter" is the sequence of coefficient constraints for inter-node edges.
3807 static isl_stat
count_all_constraints(__isl_keep isl_basic_set_list
*intra
,
3808 __isl_keep isl_basic_set_list
*inter
, int *n_eq
, int *n_ineq
)
3810 struct isl_sched_count data
;
3812 data
.n_eq
= data
.n_ineq
= 0;
3813 if (isl_basic_set_list_foreach(inter
, &bset_update_count
, &data
) < 0)
3814 return isl_stat_error
;
3815 if (isl_basic_set_list_foreach(intra
, &bset_update_count
, &data
) < 0)
3816 return isl_stat_error
;
3819 *n_ineq
= data
.n_ineq
;
3824 /* Construct an LP problem for finding schedule coefficients
3825 * such that the schedule carries as many validity dependences as possible.
3826 * In particular, for each dependence i, we bound the dependence distance
3827 * from below by e_i, with 0 <= e_i <= 1 and then maximize the sum
3828 * of all e_i's. Dependences with e_i = 0 in the solution are simply
3829 * respected, while those with e_i > 0 (in practice e_i = 1) are carried.
3830 * "intra" is the sequence of coefficient constraints for intra-node edges.
3831 * "inter" is the sequence of coefficient constraints for inter-node edges.
3832 * "n_edge" is the total number of edges.
3834 * All variables of the LP are non-negative. The actual coefficients
3835 * may be negative, so each coefficient is represented as the difference
3836 * of two non-negative variables. The negative part always appears
3837 * immediately before the positive part.
3838 * Other than that, the variables have the following order
3840 * - sum of (1 - e_i) over all edges
3841 * - sum of all c_n coefficients
3842 * (unconstrained when computing non-parametric schedules)
3843 * - sum of positive and negative parts of all c_x coefficients
3847 * - positive and negative parts of c_i_x, in opposite order
3848 * - c_i_n (if parametric)
3851 * The constraints are those from the (validity) edges plus three equalities
3852 * to express the sums and n_edge inequalities to express e_i <= 1.
3854 static isl_stat
setup_carry_lp(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
3855 int n_edge
, __isl_keep isl_basic_set_list
*intra
,
3856 __isl_keep isl_basic_set_list
*inter
)
3865 for (i
= 0; i
< graph
->n
; ++i
) {
3866 struct isl_sched_node
*node
= &graph
->node
[graph
->sorted
[i
]];
3867 node
->start
= total
;
3868 total
+= 1 + node
->nparam
+ 2 * node
->nvar
;
3871 if (count_all_constraints(intra
, inter
, &n_eq
, &n_ineq
) < 0)
3872 return isl_stat_error
;
3874 dim
= isl_space_set_alloc(ctx
, 0, total
);
3875 isl_basic_set_free(graph
->lp
);
3878 graph
->lp
= isl_basic_set_alloc_space(dim
, 0, n_eq
, n_ineq
);
3879 graph
->lp
= isl_basic_set_set_rational(graph
->lp
);
3881 k
= isl_basic_set_alloc_equality(graph
->lp
);
3883 return isl_stat_error
;
3884 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
3885 isl_int_set_si(graph
->lp
->eq
[k
][0], -n_edge
);
3886 isl_int_set_si(graph
->lp
->eq
[k
][1], 1);
3887 for (i
= 0; i
< n_edge
; ++i
)
3888 isl_int_set_si(graph
->lp
->eq
[k
][4 + i
], 1);
3890 if (add_param_sum_constraint(graph
, 1) < 0)
3891 return isl_stat_error
;
3892 if (add_var_sum_constraint(graph
, 2) < 0)
3893 return isl_stat_error
;
3895 for (i
= 0; i
< n_edge
; ++i
) {
3896 k
= isl_basic_set_alloc_inequality(graph
->lp
);
3898 return isl_stat_error
;
3899 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
3900 isl_int_set_si(graph
->lp
->ineq
[k
][4 + i
], -1);
3901 isl_int_set_si(graph
->lp
->ineq
[k
][0], 1);
3904 if (add_all_constraints(ctx
, graph
, intra
, inter
) < 0)
3905 return isl_stat_error
;
3910 static __isl_give isl_schedule_node
*compute_component_schedule(
3911 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
3914 /* If the schedule_split_scaled option is set and if the linear
3915 * parts of the scheduling rows for all nodes in the graphs have
3916 * a non-trivial common divisor, then remove this
3917 * common divisor from the linear part.
3918 * Otherwise, insert a band node directly and continue with
3919 * the construction of the schedule.
3921 * If a non-trivial common divisor is found, then
3922 * the linear part is reduced and the remainder is ignored.
3923 * The pieces of the graph that are assigned different remainders
3924 * form (groups of) strongly connected components within
3925 * the scaled down band. If needed, they can therefore
3926 * be ordered along this remainder in a sequence node.
3927 * However, this ordering is not enforced here in order to allow
3928 * the scheduler to combine some of the strongly connected components.
3930 static __isl_give isl_schedule_node
*split_scaled(
3931 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
3941 ctx
= isl_schedule_node_get_ctx(node
);
3942 if (!ctx
->opt
->schedule_split_scaled
)
3943 return compute_next_band(node
, graph
, 0);
3945 return compute_next_band(node
, graph
, 0);
3948 isl_int_init(gcd_i
);
3950 isl_int_set_si(gcd
, 0);
3952 row
= isl_mat_rows(graph
->node
[0].sched
) - 1;
3954 for (i
= 0; i
< graph
->n
; ++i
) {
3955 struct isl_sched_node
*node
= &graph
->node
[i
];
3956 int cols
= isl_mat_cols(node
->sched
);
3958 isl_seq_gcd(node
->sched
->row
[row
] + 1, cols
- 1, &gcd_i
);
3959 isl_int_gcd(gcd
, gcd
, gcd_i
);
3962 isl_int_clear(gcd_i
);
3964 if (isl_int_cmp_si(gcd
, 1) <= 0) {
3966 return compute_next_band(node
, graph
, 0);
3969 for (i
= 0; i
< graph
->n
; ++i
) {
3970 struct isl_sched_node
*node
= &graph
->node
[i
];
3972 isl_int_fdiv_q(node
->sched
->row
[row
][0],
3973 node
->sched
->row
[row
][0], gcd
);
3974 isl_int_mul(node
->sched
->row
[row
][0],
3975 node
->sched
->row
[row
][0], gcd
);
3976 node
->sched
= isl_mat_scale_down_row(node
->sched
, row
, gcd
);
3983 return compute_next_band(node
, graph
, 0);
3986 return isl_schedule_node_free(node
);
3989 /* Is the schedule row "sol" trivial on node "node"?
3990 * That is, is the solution zero on the dimensions linearly independent of
3991 * the previously found solutions?
3992 * Return 1 if the solution is trivial, 0 if it is not and -1 on error.
3994 * Each coefficient is represented as the difference between
3995 * two non-negative values in "sol".
3996 * We construct the schedule row s and check if it is linearly
3997 * independent of previously computed schedule rows
3998 * by computing T s, with T the linear combinations that are zero
3999 * on linearly dependent schedule rows.
4000 * If the result consists of all zeros, then the solution is trivial.
4002 static int is_trivial(struct isl_sched_node
*node
, __isl_keep isl_vec
*sol
)
4009 if (node
->nvar
== node
->rank
)
4012 node_sol
= extract_var_coef(node
, sol
);
4013 node_sol
= isl_mat_vec_product(isl_mat_copy(node
->indep
), node_sol
);
4017 trivial
= isl_seq_first_non_zero(node_sol
->el
,
4018 node
->nvar
- node
->rank
) == -1;
4020 isl_vec_free(node_sol
);
4025 /* Is the schedule row "sol" trivial on any node where it should
4027 * Return 1 if any solution is trivial, 0 if they are not and -1 on error.
4029 static int is_any_trivial(struct isl_sched_graph
*graph
,
4030 __isl_keep isl_vec
*sol
)
4034 for (i
= 0; i
< graph
->n
; ++i
) {
4035 struct isl_sched_node
*node
= &graph
->node
[i
];
4038 if (!needs_row(graph
, node
))
4040 trivial
= is_trivial(node
, sol
);
4041 if (trivial
< 0 || trivial
)
4048 /* Does the schedule represented by "sol" perform loop coalescing on "node"?
4049 * If so, return the position of the coalesced dimension.
4050 * Otherwise, return node->nvar or -1 on error.
4052 * In particular, look for pairs of coefficients c_i and c_j such that
4053 * |c_j/c_i| >= size_i, i.e., |c_j| >= |c_i * size_i|.
4054 * If any such pair is found, then return i.
4055 * If size_i is infinity, then no check on c_i needs to be performed.
4057 static int find_node_coalescing(struct isl_sched_node
*node
,
4058 __isl_keep isl_vec
*sol
)
4064 if (node
->nvar
<= 1)
4067 csol
= extract_var_coef(node
, sol
);
4071 for (i
= 0; i
< node
->nvar
; ++i
) {
4074 if (isl_int_is_zero(csol
->el
[i
]))
4076 v
= isl_multi_val_get_val(node
->sizes
, i
);
4079 if (!isl_val_is_int(v
)) {
4083 isl_int_mul(max
, v
->n
, csol
->el
[i
]);
4086 for (j
= 0; j
< node
->nvar
; ++j
) {
4089 if (isl_int_abs_ge(csol
->el
[j
], max
))
4105 /* Force the schedule coefficient at position "pos" of "node" to be zero
4107 * The coefficient is encoded as the difference between two non-negative
4108 * variables. Force these two variables to have the same value.
4110 static __isl_give isl_tab_lexmin
*zero_out_node_coef(
4111 __isl_take isl_tab_lexmin
*tl
, struct isl_sched_node
*node
, int pos
)
4117 ctx
= isl_space_get_ctx(node
->space
);
4118 dim
= isl_tab_lexmin_dim(tl
);
4120 return isl_tab_lexmin_free(tl
);
4121 eq
= isl_vec_alloc(ctx
, 1 + dim
);
4122 eq
= isl_vec_clr(eq
);
4124 return isl_tab_lexmin_free(tl
);
4126 pos
= 1 + node_var_coef_pos(node
, pos
);
4127 isl_int_set_si(eq
->el
[pos
], 1);
4128 isl_int_set_si(eq
->el
[pos
+ 1], -1);
4129 tl
= isl_tab_lexmin_add_eq(tl
, eq
->el
);
4135 /* Return the lexicographically smallest rational point in the basic set
4136 * from which "tl" was constructed, double checking that this input set
4139 static __isl_give isl_vec
*non_empty_solution(__isl_keep isl_tab_lexmin
*tl
)
4143 sol
= isl_tab_lexmin_get_solution(tl
);
4147 isl_die(isl_vec_get_ctx(sol
), isl_error_internal
,
4148 "error in schedule construction",
4149 return isl_vec_free(sol
));
4153 /* Does the solution "sol" of the LP problem constructed by setup_carry_lp
4154 * carry any of the "n_edge" groups of dependences?
4155 * The value in the first position is the sum of (1 - e_i) over all "n_edge"
4156 * edges, with 0 <= e_i <= 1 equal to 1 when the dependences represented
4157 * by the edge are carried by the solution.
4158 * If the sum of the (1 - e_i) is smaller than "n_edge" then at least
4159 * one of those is carried.
4161 * Note that despite the fact that the problem is solved using a rational
4162 * solver, the solution is guaranteed to be integral.
4163 * Specifically, the dependence distance lower bounds e_i (and therefore
4164 * also their sum) are integers. See Lemma 5 of [1].
4166 * Any potential denominator of the sum is cleared by this function.
4167 * The denominator is not relevant for any of the other elements
4170 * [1] P. Feautrier, Some Efficient Solutions to the Affine Scheduling
4171 * Problem, Part II: Multi-Dimensional Time.
4172 * In Intl. Journal of Parallel Programming, 1992.
4174 static int carries_dependences(__isl_keep isl_vec
*sol
, int n_edge
)
4176 isl_int_divexact(sol
->el
[1], sol
->el
[1], sol
->el
[0]);
4177 isl_int_set_si(sol
->el
[0], 1);
4178 return isl_int_cmp_si(sol
->el
[1], n_edge
) < 0;
4181 /* Return the lexicographically smallest rational point in "lp",
4182 * assuming that all variables are non-negative and performing some
4183 * additional sanity checks.
4184 * If "want_integral" is set, then compute the lexicographically smallest
4185 * integer point instead.
4186 * In particular, "lp" should not be empty by construction.
4187 * Double check that this is the case.
4188 * If dependences are not carried for any of the "n_edge" edges,
4189 * then return an empty vector.
4191 * If the schedule_treat_coalescing option is set and
4192 * if the computed schedule performs loop coalescing on a given node,
4193 * i.e., if it is of the form
4195 * c_i i + c_j j + ...
4197 * with |c_j/c_i| >= size_i, then force the coefficient c_i to be zero
4198 * to cut out this solution. Repeat this process until no more loop
4199 * coalescing occurs or until no more dependences can be carried.
4200 * In the latter case, revert to the previously computed solution.
4202 * If the caller requests an integral solution and if coalescing should
4203 * be treated, then perform the coalescing treatment first as
4204 * an integral solution computed before coalescing treatment
4205 * would carry the same number of edges and would therefore probably
4206 * also be coalescing.
4208 * To allow the coalescing treatment to be performed first,
4209 * the initial solution is allowed to be rational and it is only
4210 * cut out (if needed) in the next iteration, if no coalescing measures
4213 static __isl_give isl_vec
*non_neg_lexmin(struct isl_sched_graph
*graph
,
4214 __isl_take isl_basic_set
*lp
, int n_edge
, int want_integral
)
4219 isl_vec
*sol
, *prev
= NULL
;
4220 int treat_coalescing
;
4224 ctx
= isl_basic_set_get_ctx(lp
);
4225 treat_coalescing
= isl_options_get_schedule_treat_coalescing(ctx
);
4226 tl
= isl_tab_lexmin_from_basic_set(lp
);
4233 tl
= isl_tab_lexmin_cut_to_integer(tl
);
4234 sol
= non_empty_solution(tl
);
4238 integral
= isl_int_is_one(sol
->el
[0]);
4239 if (!carries_dependences(sol
, n_edge
)) {
4241 prev
= isl_vec_alloc(ctx
, 0);
4246 prev
= isl_vec_free(prev
);
4247 cut
= want_integral
&& !integral
;
4250 if (!treat_coalescing
)
4252 for (i
= 0; i
< graph
->n
; ++i
) {
4253 struct isl_sched_node
*node
= &graph
->node
[i
];
4255 pos
= find_node_coalescing(node
, sol
);
4258 if (pos
< node
->nvar
)
4263 tl
= zero_out_node_coef(tl
, &graph
->node
[i
], pos
);
4268 isl_tab_lexmin_free(tl
);
4272 isl_tab_lexmin_free(tl
);
4278 /* If "edge" is an edge from a node to itself, then add the corresponding
4279 * dependence relation to "umap".
4280 * If "node" has been compressed, then the dependence relation
4281 * is also compressed first.
4283 static __isl_give isl_union_map
*add_intra(__isl_take isl_union_map
*umap
,
4284 struct isl_sched_edge
*edge
)
4287 struct isl_sched_node
*node
= edge
->src
;
4289 if (edge
->src
!= edge
->dst
)
4292 map
= isl_map_copy(edge
->map
);
4293 if (node
->compressed
) {
4294 map
= isl_map_preimage_domain_multi_aff(map
,
4295 isl_multi_aff_copy(node
->decompress
));
4296 map
= isl_map_preimage_range_multi_aff(map
,
4297 isl_multi_aff_copy(node
->decompress
));
4299 umap
= isl_union_map_add_map(umap
, map
);
4303 /* If "edge" is an edge from a node to another node, then add the corresponding
4304 * dependence relation to "umap".
4305 * If the source or destination nodes of "edge" have been compressed,
4306 * then the dependence relation is also compressed first.
4308 static __isl_give isl_union_map
*add_inter(__isl_take isl_union_map
*umap
,
4309 struct isl_sched_edge
*edge
)
4313 if (edge
->src
== edge
->dst
)
4316 map
= isl_map_copy(edge
->map
);
4317 if (edge
->src
->compressed
)
4318 map
= isl_map_preimage_domain_multi_aff(map
,
4319 isl_multi_aff_copy(edge
->src
->decompress
));
4320 if (edge
->dst
->compressed
)
4321 map
= isl_map_preimage_range_multi_aff(map
,
4322 isl_multi_aff_copy(edge
->dst
->decompress
));
4323 umap
= isl_union_map_add_map(umap
, map
);
4327 /* For each (conditional) validity edge in "graph",
4328 * add the corresponding dependence relation using "add"
4329 * to a collection of dependence relations and return the result.
4330 * If "coincidence" is set, then coincidence edges are considered as well.
4332 static __isl_give isl_union_map
*collect_validity(struct isl_sched_graph
*graph
,
4333 __isl_give isl_union_map
*(*add
)(__isl_take isl_union_map
*umap
,
4334 struct isl_sched_edge
*edge
), int coincidence
)
4338 isl_union_map
*umap
;
4340 space
= isl_space_copy(graph
->node
[0].space
);
4341 umap
= isl_union_map_empty(space
);
4343 for (i
= 0; i
< graph
->n_edge
; ++i
) {
4344 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
4346 if (!is_any_validity(edge
) &&
4347 (!coincidence
|| !is_coincidence(edge
)))
4350 umap
= add(umap
, edge
);
4356 /* For each dependence relation on a (conditional) validity edge
4357 * from a node to itself,
4358 * construct the set of coefficients of valid constraints for elements
4359 * in that dependence relation and collect the results.
4360 * If "coincidence" is set, then coincidence edges are considered as well.
4362 * In particular, for each dependence relation R, constraints
4363 * on coefficients (c_0, c_n, c_x) are constructed such that
4365 * c_0 + c_n n + c_x d >= 0 for each d in delta R = { y - x | (x,y) in R }
4367 * This computation is essentially the same as that performed
4368 * by intra_coefficients, except that it operates on multiple
4371 * Note that if a dependence relation is a union of basic maps,
4372 * then each basic map needs to be treated individually as it may only
4373 * be possible to carry the dependences expressed by some of those
4374 * basic maps and not all of them.
4375 * The collected validity constraints are therefore not coalesced and
4376 * it is assumed that they are not coalesced automatically.
4377 * Duplicate basic maps can be removed, however.
4378 * In particular, if the same basic map appears as a disjunct
4379 * in multiple edges, then it only needs to be carried once.
4381 static __isl_give isl_basic_set_list
*collect_intra_validity(
4382 struct isl_sched_graph
*graph
, int coincidence
)
4384 isl_union_map
*intra
;
4385 isl_union_set
*delta
;
4386 isl_basic_set_list
*list
;
4388 intra
= collect_validity(graph
, &add_intra
, coincidence
);
4389 delta
= isl_union_map_deltas(intra
);
4390 delta
= isl_union_set_remove_divs(delta
);
4391 list
= isl_union_set_get_basic_set_list(delta
);
4392 isl_union_set_free(delta
);
4394 return isl_basic_set_list_coefficients(list
);
4397 /* For each dependence relation on a (conditional) validity edge
4398 * from a node to some other node,
4399 * construct the set of coefficients of valid constraints for elements
4400 * in that dependence relation and collect the results.
4401 * If "coincidence" is set, then coincidence edges are considered as well.
4403 * In particular, for each dependence relation R, constraints
4404 * on coefficients (c_0, c_n, c_x, c_y) are constructed such that
4406 * c_0 + c_n n + c_x x + c_y y >= 0 for each (x,y) in R
4408 * This computation is essentially the same as that performed
4409 * by inter_coefficients, except that it operates on multiple
4412 * Note that if a dependence relation is a union of basic maps,
4413 * then each basic map needs to be treated individually as it may only
4414 * be possible to carry the dependences expressed by some of those
4415 * basic maps and not all of them.
4416 * The collected validity constraints are therefore not coalesced and
4417 * it is assumed that they are not coalesced automatically.
4418 * Duplicate basic maps can be removed, however.
4419 * In particular, if the same basic map appears as a disjunct
4420 * in multiple edges, then it only needs to be carried once.
4422 static __isl_give isl_basic_set_list
*collect_inter_validity(
4423 struct isl_sched_graph
*graph
, int coincidence
)
4425 isl_union_map
*inter
;
4426 isl_union_set
*wrap
;
4427 isl_basic_set_list
*list
;
4429 inter
= collect_validity(graph
, &add_inter
, coincidence
);
4430 inter
= isl_union_map_remove_divs(inter
);
4431 wrap
= isl_union_map_wrap(inter
);
4432 list
= isl_union_set_get_basic_set_list(wrap
);
4433 isl_union_set_free(wrap
);
4434 return isl_basic_set_list_coefficients(list
);
4437 /* Construct an LP problem for finding schedule coefficients
4438 * such that the schedule carries as many of the validity dependences
4440 * return the lexicographically smallest non-trivial solution.
4441 * If "fallback" is set, then the carrying is performed as a fallback
4442 * for the Pluto-like scheduler.
4443 * If "coincidence" is set, then try and carry coincidence edges as well.
4445 * The variable "n_edge" stores the number of groups that should be carried.
4446 * If none of the "n_edge" groups can be carried
4447 * then return an empty vector.
4448 * If, moreover, "n_edge" is zero, then the LP problem does not even
4449 * need to be constructed.
4451 * If a fallback solution is being computed, then compute an integral solution
4452 * for the coefficients rather than using the numerators
4453 * of a rational solution.
4455 static __isl_give isl_vec
*compute_carrying_sol(isl_ctx
*ctx
,
4456 struct isl_sched_graph
*graph
, int fallback
, int coincidence
)
4458 int n_intra
, n_inter
;
4461 struct isl_carry carry
= { 0 };
4463 carry
.intra
= collect_intra_validity(graph
, coincidence
);
4464 carry
.inter
= collect_inter_validity(graph
, coincidence
);
4465 if (!carry
.intra
|| !carry
.inter
)
4467 n_intra
= isl_basic_set_list_n_basic_set(carry
.intra
);
4468 n_inter
= isl_basic_set_list_n_basic_set(carry
.inter
);
4469 n_edge
= n_intra
+ n_inter
;
4471 isl_carry_clear(&carry
);
4472 return isl_vec_alloc(ctx
, 0);
4475 if (setup_carry_lp(ctx
, graph
, n_edge
, carry
.intra
, carry
.inter
) < 0)
4478 isl_carry_clear(&carry
);
4479 lp
= isl_basic_set_copy(graph
->lp
);
4480 return non_neg_lexmin(graph
, lp
, n_edge
, fallback
);
4482 isl_carry_clear(&carry
);
4486 /* Construct a schedule row for each node such that as many validity dependences
4487 * as possible are carried and then continue with the next band.
4488 * If "fallback" is set, then the carrying is performed as a fallback
4489 * for the Pluto-like scheduler.
4490 * If "coincidence" is set, then try and carry coincidence edges as well.
4492 * If there are no validity dependences, then no dependence can be carried and
4493 * the procedure is guaranteed to fail. If there is more than one component,
4494 * then try computing a schedule on each component separately
4495 * to prevent or at least postpone this failure.
4497 * If a schedule row is computed, then check that dependences are carried
4498 * for at least one of the edges.
4500 * If the computed schedule row turns out to be trivial on one or
4501 * more nodes where it should not be trivial, then we throw it away
4502 * and try again on each component separately.
4504 * If there is only one component, then we accept the schedule row anyway,
4505 * but we do not consider it as a complete row and therefore do not
4506 * increment graph->n_row. Note that the ranks of the nodes that
4507 * do get a non-trivial schedule part will get updated regardless and
4508 * graph->maxvar is computed based on these ranks. The test for
4509 * whether more schedule rows are required in compute_schedule_wcc
4510 * is therefore not affected.
4512 * Insert a band corresponding to the schedule row at position "node"
4513 * of the schedule tree and continue with the construction of the schedule.
4514 * This insertion and the continued construction is performed by split_scaled
4515 * after optionally checking for non-trivial common divisors.
4517 static __isl_give isl_schedule_node
*carry(__isl_take isl_schedule_node
*node
,
4518 struct isl_sched_graph
*graph
, int fallback
, int coincidence
)
4527 ctx
= isl_schedule_node_get_ctx(node
);
4528 sol
= compute_carrying_sol(ctx
, graph
, fallback
, coincidence
);
4530 return isl_schedule_node_free(node
);
4531 if (sol
->size
== 0) {
4534 return compute_component_schedule(node
, graph
, 1);
4535 isl_die(ctx
, isl_error_unknown
, "unable to carry dependences",
4536 return isl_schedule_node_free(node
));
4539 trivial
= is_any_trivial(graph
, sol
);
4541 sol
= isl_vec_free(sol
);
4542 } else if (trivial
&& graph
->scc
> 1) {
4544 return compute_component_schedule(node
, graph
, 1);
4547 if (update_schedule(graph
, sol
, 0) < 0)
4548 return isl_schedule_node_free(node
);
4552 return split_scaled(node
, graph
);
4555 /* Construct a schedule row for each node such that as many validity dependences
4556 * as possible are carried and then continue with the next band.
4557 * Do so as a fallback for the Pluto-like scheduler.
4558 * If "coincidence" is set, then try and carry coincidence edges as well.
4560 static __isl_give isl_schedule_node
*carry_fallback(
4561 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
4564 return carry(node
, graph
, 1, coincidence
);
4567 /* Construct a schedule row for each node such that as many validity dependences
4568 * as possible are carried and then continue with the next band.
4569 * Do so for the case where the Feautrier scheduler was selected
4572 static __isl_give isl_schedule_node
*carry_feautrier(
4573 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
4575 return carry(node
, graph
, 0, 0);
4578 /* Construct a schedule row for each node such that as many validity dependences
4579 * as possible are carried and then continue with the next band.
4580 * Do so as a fallback for the Pluto-like scheduler.
4582 static __isl_give isl_schedule_node
*carry_dependences(
4583 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
4585 return carry_fallback(node
, graph
, 0);
4588 /* Construct a schedule row for each node such that as many validity or
4589 * coincidence dependences as possible are carried and
4590 * then continue with the next band.
4591 * Do so as a fallback for the Pluto-like scheduler.
4593 static __isl_give isl_schedule_node
*carry_coincidence(
4594 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
4596 return carry_fallback(node
, graph
, 1);
4599 /* Topologically sort statements mapped to the same schedule iteration
4600 * and add insert a sequence node in front of "node"
4601 * corresponding to this order.
4602 * If "initialized" is set, then it may be assumed that compute_maxvar
4603 * has been called on the current band. Otherwise, call
4604 * compute_maxvar if and before carry_dependences gets called.
4606 * If it turns out to be impossible to sort the statements apart,
4607 * because different dependences impose different orderings
4608 * on the statements, then we extend the schedule such that
4609 * it carries at least one more dependence.
4611 static __isl_give isl_schedule_node
*sort_statements(
4612 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
4616 isl_union_set_list
*filters
;
4621 ctx
= isl_schedule_node_get_ctx(node
);
4623 isl_die(ctx
, isl_error_internal
,
4624 "graph should have at least one node",
4625 return isl_schedule_node_free(node
));
4630 if (update_edges(ctx
, graph
) < 0)
4631 return isl_schedule_node_free(node
);
4633 if (graph
->n_edge
== 0)
4636 if (detect_sccs(ctx
, graph
) < 0)
4637 return isl_schedule_node_free(node
);
4640 if (graph
->scc
< graph
->n
) {
4641 if (!initialized
&& compute_maxvar(graph
) < 0)
4642 return isl_schedule_node_free(node
);
4643 return carry_dependences(node
, graph
);
4646 filters
= extract_sccs(ctx
, graph
);
4647 node
= isl_schedule_node_insert_sequence(node
, filters
);
4652 /* Are there any (non-empty) (conditional) validity edges in the graph?
4654 static int has_validity_edges(struct isl_sched_graph
*graph
)
4658 for (i
= 0; i
< graph
->n_edge
; ++i
) {
4661 empty
= isl_map_plain_is_empty(graph
->edge
[i
].map
);
4666 if (is_any_validity(&graph
->edge
[i
]))
4673 /* Should we apply a Feautrier step?
4674 * That is, did the user request the Feautrier algorithm and are
4675 * there any validity dependences (left)?
4677 static int need_feautrier_step(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
4679 if (ctx
->opt
->schedule_algorithm
!= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
)
4682 return has_validity_edges(graph
);
4685 /* Compute a schedule for a connected dependence graph using Feautrier's
4686 * multi-dimensional scheduling algorithm and return the updated schedule node.
4688 * The original algorithm is described in [1].
4689 * The main idea is to minimize the number of scheduling dimensions, by
4690 * trying to satisfy as many dependences as possible per scheduling dimension.
4692 * [1] P. Feautrier, Some Efficient Solutions to the Affine Scheduling
4693 * Problem, Part II: Multi-Dimensional Time.
4694 * In Intl. Journal of Parallel Programming, 1992.
4696 static __isl_give isl_schedule_node
*compute_schedule_wcc_feautrier(
4697 isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
4699 return carry_feautrier(node
, graph
);
4702 /* Turn off the "local" bit on all (condition) edges.
4704 static void clear_local_edges(struct isl_sched_graph
*graph
)
4708 for (i
= 0; i
< graph
->n_edge
; ++i
)
4709 if (is_condition(&graph
->edge
[i
]))
4710 clear_local(&graph
->edge
[i
]);
4713 /* Does "graph" have both condition and conditional validity edges?
4715 static int need_condition_check(struct isl_sched_graph
*graph
)
4718 int any_condition
= 0;
4719 int any_conditional_validity
= 0;
4721 for (i
= 0; i
< graph
->n_edge
; ++i
) {
4722 if (is_condition(&graph
->edge
[i
]))
4724 if (is_conditional_validity(&graph
->edge
[i
]))
4725 any_conditional_validity
= 1;
4728 return any_condition
&& any_conditional_validity
;
4731 /* Does "graph" contain any coincidence edge?
4733 static int has_any_coincidence(struct isl_sched_graph
*graph
)
4737 for (i
= 0; i
< graph
->n_edge
; ++i
)
4738 if (is_coincidence(&graph
->edge
[i
]))
4744 /* Extract the final schedule row as a map with the iteration domain
4745 * of "node" as domain.
4747 static __isl_give isl_map
*final_row(struct isl_sched_node
*node
)
4752 row
= isl_mat_rows(node
->sched
) - 1;
4753 ma
= node_extract_partial_schedule_multi_aff(node
, row
, 1);
4754 return isl_map_from_multi_aff(ma
);
4757 /* Is the conditional validity dependence in the edge with index "edge_index"
4758 * violated by the latest (i.e., final) row of the schedule?
4759 * That is, is i scheduled after j
4760 * for any conditional validity dependence i -> j?
4762 static int is_violated(struct isl_sched_graph
*graph
, int edge_index
)
4764 isl_map
*src_sched
, *dst_sched
, *map
;
4765 struct isl_sched_edge
*edge
= &graph
->edge
[edge_index
];
4768 src_sched
= final_row(edge
->src
);
4769 dst_sched
= final_row(edge
->dst
);
4770 map
= isl_map_copy(edge
->map
);
4771 map
= isl_map_apply_domain(map
, src_sched
);
4772 map
= isl_map_apply_range(map
, dst_sched
);
4773 map
= isl_map_order_gt(map
, isl_dim_in
, 0, isl_dim_out
, 0);
4774 empty
= isl_map_is_empty(map
);
4783 /* Does "graph" have any satisfied condition edges that
4784 * are adjacent to the conditional validity constraint with
4785 * domain "conditional_source" and range "conditional_sink"?
4787 * A satisfied condition is one that is not local.
4788 * If a condition was forced to be local already (i.e., marked as local)
4789 * then there is no need to check if it is in fact local.
4791 * Additionally, mark all adjacent condition edges found as local.
4793 static int has_adjacent_true_conditions(struct isl_sched_graph
*graph
,
4794 __isl_keep isl_union_set
*conditional_source
,
4795 __isl_keep isl_union_set
*conditional_sink
)
4800 for (i
= 0; i
< graph
->n_edge
; ++i
) {
4801 int adjacent
, local
;
4802 isl_union_map
*condition
;
4804 if (!is_condition(&graph
->edge
[i
]))
4806 if (is_local(&graph
->edge
[i
]))
4809 condition
= graph
->edge
[i
].tagged_condition
;
4810 adjacent
= domain_intersects(condition
, conditional_sink
);
4811 if (adjacent
>= 0 && !adjacent
)
4812 adjacent
= range_intersects(condition
,
4813 conditional_source
);
4819 set_local(&graph
->edge
[i
]);
4821 local
= is_condition_false(&graph
->edge
[i
]);
4831 /* Are there any violated conditional validity dependences with
4832 * adjacent condition dependences that are not local with respect
4833 * to the current schedule?
4834 * That is, is the conditional validity constraint violated?
4836 * Additionally, mark all those adjacent condition dependences as local.
4837 * We also mark those adjacent condition dependences that were not marked
4838 * as local before, but just happened to be local already. This ensures
4839 * that they remain local if the schedule is recomputed.
4841 * We first collect domain and range of all violated conditional validity
4842 * dependences and then check if there are any adjacent non-local
4843 * condition dependences.
4845 static int has_violated_conditional_constraint(isl_ctx
*ctx
,
4846 struct isl_sched_graph
*graph
)
4850 isl_union_set
*source
, *sink
;
4852 source
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
4853 sink
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
4854 for (i
= 0; i
< graph
->n_edge
; ++i
) {
4855 isl_union_set
*uset
;
4856 isl_union_map
*umap
;
4859 if (!is_conditional_validity(&graph
->edge
[i
]))
4862 violated
= is_violated(graph
, i
);
4870 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_validity
);
4871 uset
= isl_union_map_domain(umap
);
4872 source
= isl_union_set_union(source
, uset
);
4873 source
= isl_union_set_coalesce(source
);
4875 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_validity
);
4876 uset
= isl_union_map_range(umap
);
4877 sink
= isl_union_set_union(sink
, uset
);
4878 sink
= isl_union_set_coalesce(sink
);
4882 any
= has_adjacent_true_conditions(graph
, source
, sink
);
4884 isl_union_set_free(source
);
4885 isl_union_set_free(sink
);
4888 isl_union_set_free(source
);
4889 isl_union_set_free(sink
);
4893 /* Examine the current band (the rows between graph->band_start and
4894 * graph->n_total_row), deciding whether to drop it or add it to "node"
4895 * and then continue with the computation of the next band, if any.
4896 * If "initialized" is set, then it may be assumed that compute_maxvar
4897 * has been called on the current band. Otherwise, call
4898 * compute_maxvar if and before carry_dependences gets called.
4900 * The caller keeps looking for a new row as long as
4901 * graph->n_row < graph->maxvar. If the latest attempt to find
4902 * such a row failed (i.e., we still have graph->n_row < graph->maxvar),
4904 * - split between SCCs and start over (assuming we found an interesting
4905 * pair of SCCs between which to split)
4906 * - continue with the next band (assuming the current band has at least
4908 * - if there is more than one SCC left, then split along all SCCs
4909 * - if outer coincidence needs to be enforced, then try to carry as many
4910 * validity or coincidence dependences as possible and
4911 * continue with the next band
4912 * - try to carry as many validity dependences as possible and
4913 * continue with the next band
4914 * In each case, we first insert a band node in the schedule tree
4915 * if any rows have been computed.
4917 * If the caller managed to complete the schedule, we insert a band node
4918 * (if any schedule rows were computed) and we finish off by topologically
4919 * sorting the statements based on the remaining dependences.
4921 static __isl_give isl_schedule_node
*compute_schedule_finish_band(
4922 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
4930 if (graph
->n_row
< graph
->maxvar
) {
4932 int empty
= graph
->n_total_row
== graph
->band_start
;
4934 ctx
= isl_schedule_node_get_ctx(node
);
4935 if (!ctx
->opt
->schedule_maximize_band_depth
&& !empty
)
4936 return compute_next_band(node
, graph
, 1);
4937 if (graph
->src_scc
>= 0)
4938 return compute_split_schedule(node
, graph
);
4940 return compute_next_band(node
, graph
, 1);
4942 return compute_component_schedule(node
, graph
, 1);
4943 if (!initialized
&& compute_maxvar(graph
) < 0)
4944 return isl_schedule_node_free(node
);
4945 if (isl_options_get_schedule_outer_coincidence(ctx
))
4946 return carry_coincidence(node
, graph
);
4947 return carry_dependences(node
, graph
);
4950 insert
= graph
->n_total_row
> graph
->band_start
;
4952 node
= insert_current_band(node
, graph
, 1);
4953 node
= isl_schedule_node_child(node
, 0);
4955 node
= sort_statements(node
, graph
, initialized
);
4957 node
= isl_schedule_node_parent(node
);
4962 /* Construct a band of schedule rows for a connected dependence graph.
4963 * The caller is responsible for determining the strongly connected
4964 * components and calling compute_maxvar first.
4966 * We try to find a sequence of as many schedule rows as possible that result
4967 * in non-negative dependence distances (independent of the previous rows
4968 * in the sequence, i.e., such that the sequence is tilable), with as
4969 * many of the initial rows as possible satisfying the coincidence constraints.
4970 * The computation stops if we can't find any more rows or if we have found
4971 * all the rows we wanted to find.
4973 * If ctx->opt->schedule_outer_coincidence is set, then we force the
4974 * outermost dimension to satisfy the coincidence constraints. If this
4975 * turns out to be impossible, we fall back on the general scheme above
4976 * and try to carry as many dependences as possible.
4978 * If "graph" contains both condition and conditional validity dependences,
4979 * then we need to check that that the conditional schedule constraint
4980 * is satisfied, i.e., there are no violated conditional validity dependences
4981 * that are adjacent to any non-local condition dependences.
4982 * If there are, then we mark all those adjacent condition dependences
4983 * as local and recompute the current band. Those dependences that
4984 * are marked local will then be forced to be local.
4985 * The initial computation is performed with no dependences marked as local.
4986 * If we are lucky, then there will be no violated conditional validity
4987 * dependences adjacent to any non-local condition dependences.
4988 * Otherwise, we mark some additional condition dependences as local and
4989 * recompute. We continue this process until there are no violations left or
4990 * until we are no longer able to compute a schedule.
4991 * Since there are only a finite number of dependences,
4992 * there will only be a finite number of iterations.
4994 static isl_stat
compute_schedule_wcc_band(isl_ctx
*ctx
,
4995 struct isl_sched_graph
*graph
)
4997 int has_coincidence
;
4998 int use_coincidence
;
4999 int force_coincidence
= 0;
5000 int check_conditional
;
5002 if (sort_sccs(graph
) < 0)
5003 return isl_stat_error
;
5005 clear_local_edges(graph
);
5006 check_conditional
= need_condition_check(graph
);
5007 has_coincidence
= has_any_coincidence(graph
);
5009 if (ctx
->opt
->schedule_outer_coincidence
)
5010 force_coincidence
= 1;
5012 use_coincidence
= has_coincidence
;
5013 while (graph
->n_row
< graph
->maxvar
) {
5018 graph
->src_scc
= -1;
5019 graph
->dst_scc
= -1;
5021 if (setup_lp(ctx
, graph
, use_coincidence
) < 0)
5022 return isl_stat_error
;
5023 sol
= solve_lp(ctx
, graph
);
5025 return isl_stat_error
;
5026 if (sol
->size
== 0) {
5027 int empty
= graph
->n_total_row
== graph
->band_start
;
5030 if (use_coincidence
&& (!force_coincidence
|| !empty
)) {
5031 use_coincidence
= 0;
5036 coincident
= !has_coincidence
|| use_coincidence
;
5037 if (update_schedule(graph
, sol
, coincident
) < 0)
5038 return isl_stat_error
;
5040 if (!check_conditional
)
5042 violated
= has_violated_conditional_constraint(ctx
, graph
);
5044 return isl_stat_error
;
5047 if (reset_band(graph
) < 0)
5048 return isl_stat_error
;
5049 use_coincidence
= has_coincidence
;
5055 /* Compute a schedule for a connected dependence graph by considering
5056 * the graph as a whole and return the updated schedule node.
5058 * The actual schedule rows of the current band are computed by
5059 * compute_schedule_wcc_band. compute_schedule_finish_band takes
5060 * care of integrating the band into "node" and continuing
5063 static __isl_give isl_schedule_node
*compute_schedule_wcc_whole(
5064 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
5071 ctx
= isl_schedule_node_get_ctx(node
);
5072 if (compute_schedule_wcc_band(ctx
, graph
) < 0)
5073 return isl_schedule_node_free(node
);
5075 return compute_schedule_finish_band(node
, graph
, 1);
5078 /* Clustering information used by compute_schedule_wcc_clustering.
5080 * "n" is the number of SCCs in the original dependence graph
5081 * "scc" is an array of "n" elements, each representing an SCC
5082 * of the original dependence graph. All entries in the same cluster
5083 * have the same number of schedule rows.
5084 * "scc_cluster" maps each SCC index to the cluster to which it belongs,
5085 * where each cluster is represented by the index of the first SCC
5086 * in the cluster. Initially, each SCC belongs to a cluster containing
5089 * "scc_in_merge" is used by merge_clusters_along_edge to keep
5090 * track of which SCCs need to be merged.
5092 * "cluster" contains the merged clusters of SCCs after the clustering
5095 * "scc_node" is a temporary data structure used inside copy_partial.
5096 * For each SCC, it keeps track of the number of nodes in the SCC
5097 * that have already been copied.
5099 struct isl_clustering
{
5101 struct isl_sched_graph
*scc
;
5102 struct isl_sched_graph
*cluster
;
5108 /* Initialize the clustering data structure "c" from "graph".
5110 * In particular, allocate memory, extract the SCCs from "graph"
5111 * into c->scc, initialize scc_cluster and construct
5112 * a band of schedule rows for each SCC.
5113 * Within each SCC, there is only one SCC by definition.
5114 * Each SCC initially belongs to a cluster containing only that SCC.
5116 static isl_stat
clustering_init(isl_ctx
*ctx
, struct isl_clustering
*c
,
5117 struct isl_sched_graph
*graph
)
5122 c
->scc
= isl_calloc_array(ctx
, struct isl_sched_graph
, c
->n
);
5123 c
->cluster
= isl_calloc_array(ctx
, struct isl_sched_graph
, c
->n
);
5124 c
->scc_cluster
= isl_calloc_array(ctx
, int, c
->n
);
5125 c
->scc_node
= isl_calloc_array(ctx
, int, c
->n
);
5126 c
->scc_in_merge
= isl_calloc_array(ctx
, int, c
->n
);
5127 if (!c
->scc
|| !c
->cluster
||
5128 !c
->scc_cluster
|| !c
->scc_node
|| !c
->scc_in_merge
)
5129 return isl_stat_error
;
5131 for (i
= 0; i
< c
->n
; ++i
) {
5132 if (extract_sub_graph(ctx
, graph
, &node_scc_exactly
,
5133 &edge_scc_exactly
, i
, &c
->scc
[i
]) < 0)
5134 return isl_stat_error
;
5136 if (compute_maxvar(&c
->scc
[i
]) < 0)
5137 return isl_stat_error
;
5138 if (compute_schedule_wcc_band(ctx
, &c
->scc
[i
]) < 0)
5139 return isl_stat_error
;
5140 c
->scc_cluster
[i
] = i
;
5146 /* Free all memory allocated for "c".
5148 static void clustering_free(isl_ctx
*ctx
, struct isl_clustering
*c
)
5153 for (i
= 0; i
< c
->n
; ++i
)
5154 graph_free(ctx
, &c
->scc
[i
]);
5157 for (i
= 0; i
< c
->n
; ++i
)
5158 graph_free(ctx
, &c
->cluster
[i
]);
5160 free(c
->scc_cluster
);
5162 free(c
->scc_in_merge
);
5165 /* Should we refrain from merging the cluster in "graph" with
5166 * any other cluster?
5167 * In particular, is its current schedule band empty and incomplete.
5169 static int bad_cluster(struct isl_sched_graph
*graph
)
5171 return graph
->n_row
< graph
->maxvar
&&
5172 graph
->n_total_row
== graph
->band_start
;
5175 /* Is "edge" a proximity edge with a non-empty dependence relation?
5177 static isl_bool
is_non_empty_proximity(struct isl_sched_edge
*edge
)
5179 if (!is_proximity(edge
))
5180 return isl_bool_false
;
5181 return isl_bool_not(isl_map_plain_is_empty(edge
->map
));
5184 /* Return the index of an edge in "graph" that can be used to merge
5185 * two clusters in "c".
5186 * Return graph->n_edge if no such edge can be found.
5187 * Return -1 on error.
5189 * In particular, return a proximity edge between two clusters
5190 * that is not marked "no_merge" and such that neither of the
5191 * two clusters has an incomplete, empty band.
5193 * If there are multiple such edges, then try and find the most
5194 * appropriate edge to use for merging. In particular, pick the edge
5195 * with the greatest weight. If there are multiple of those,
5196 * then pick one with the shortest distance between
5197 * the two cluster representatives.
5199 static int find_proximity(struct isl_sched_graph
*graph
,
5200 struct isl_clustering
*c
)
5202 int i
, best
= graph
->n_edge
, best_dist
, best_weight
;
5204 for (i
= 0; i
< graph
->n_edge
; ++i
) {
5205 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
5209 prox
= is_non_empty_proximity(edge
);
5216 if (bad_cluster(&c
->scc
[edge
->src
->scc
]) ||
5217 bad_cluster(&c
->scc
[edge
->dst
->scc
]))
5219 dist
= c
->scc_cluster
[edge
->dst
->scc
] -
5220 c
->scc_cluster
[edge
->src
->scc
];
5223 weight
= edge
->weight
;
5224 if (best
< graph
->n_edge
) {
5225 if (best_weight
> weight
)
5227 if (best_weight
== weight
&& best_dist
<= dist
)
5232 best_weight
= weight
;
5238 /* Internal data structure used in mark_merge_sccs.
5240 * "graph" is the dependence graph in which a strongly connected
5241 * component is constructed.
5242 * "scc_cluster" maps each SCC index to the cluster to which it belongs.
5243 * "src" and "dst" are the indices of the nodes that are being merged.
5245 struct isl_mark_merge_sccs_data
{
5246 struct isl_sched_graph
*graph
;
5252 /* Check whether the cluster containing node "i" depends on the cluster
5253 * containing node "j". If "i" and "j" belong to the same cluster,
5254 * then they are taken to depend on each other to ensure that
5255 * the resulting strongly connected component consists of complete
5256 * clusters. Furthermore, if "i" and "j" are the two nodes that
5257 * are being merged, then they are taken to depend on each other as well.
5258 * Otherwise, check if there is a (conditional) validity dependence
5259 * from node[j] to node[i], forcing node[i] to follow node[j].
5261 static isl_bool
cluster_follows(int i
, int j
, void *user
)
5263 struct isl_mark_merge_sccs_data
*data
= user
;
5264 struct isl_sched_graph
*graph
= data
->graph
;
5265 int *scc_cluster
= data
->scc_cluster
;
5267 if (data
->src
== i
&& data
->dst
== j
)
5268 return isl_bool_true
;
5269 if (data
->src
== j
&& data
->dst
== i
)
5270 return isl_bool_true
;
5271 if (scc_cluster
[graph
->node
[i
].scc
] == scc_cluster
[graph
->node
[j
].scc
])
5272 return isl_bool_true
;
5274 return graph_has_validity_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
5277 /* Mark all SCCs that belong to either of the two clusters in "c"
5278 * connected by the edge in "graph" with index "edge", or to any
5279 * of the intermediate clusters.
5280 * The marking is recorded in c->scc_in_merge.
5282 * The given edge has been selected for merging two clusters,
5283 * meaning that there is at least a proximity edge between the two nodes.
5284 * However, there may also be (indirect) validity dependences
5285 * between the two nodes. When merging the two clusters, all clusters
5286 * containing one or more of the intermediate nodes along the
5287 * indirect validity dependences need to be merged in as well.
5289 * First collect all such nodes by computing the strongly connected
5290 * component (SCC) containing the two nodes connected by the edge, where
5291 * the two nodes are considered to depend on each other to make
5292 * sure they end up in the same SCC. Similarly, each node is considered
5293 * to depend on every other node in the same cluster to ensure
5294 * that the SCC consists of complete clusters.
5296 * Then the original SCCs that contain any of these nodes are marked
5297 * in c->scc_in_merge.
5299 static isl_stat
mark_merge_sccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
5300 int edge
, struct isl_clustering
*c
)
5302 struct isl_mark_merge_sccs_data data
;
5303 struct isl_tarjan_graph
*g
;
5306 for (i
= 0; i
< c
->n
; ++i
)
5307 c
->scc_in_merge
[i
] = 0;
5310 data
.scc_cluster
= c
->scc_cluster
;
5311 data
.src
= graph
->edge
[edge
].src
- graph
->node
;
5312 data
.dst
= graph
->edge
[edge
].dst
- graph
->node
;
5314 g
= isl_tarjan_graph_component(ctx
, graph
->n
, data
.dst
,
5315 &cluster_follows
, &data
);
5321 isl_die(ctx
, isl_error_internal
,
5322 "expecting at least two nodes in component",
5324 if (g
->order
[--i
] != -1)
5325 isl_die(ctx
, isl_error_internal
,
5326 "expecting end of component marker", goto error
);
5328 for (--i
; i
>= 0 && g
->order
[i
] != -1; --i
) {
5329 int scc
= graph
->node
[g
->order
[i
]].scc
;
5330 c
->scc_in_merge
[scc
] = 1;
5333 isl_tarjan_graph_free(g
);
5336 isl_tarjan_graph_free(g
);
5337 return isl_stat_error
;
5340 /* Construct the identifier "cluster_i".
5342 static __isl_give isl_id
*cluster_id(isl_ctx
*ctx
, int i
)
5346 snprintf(name
, sizeof(name
), "cluster_%d", i
);
5347 return isl_id_alloc(ctx
, name
, NULL
);
5350 /* Construct the space of the cluster with index "i" containing
5351 * the strongly connected component "scc".
5353 * In particular, construct a space called cluster_i with dimension equal
5354 * to the number of schedule rows in the current band of "scc".
5356 static __isl_give isl_space
*cluster_space(struct isl_sched_graph
*scc
, int i
)
5362 nvar
= scc
->n_total_row
- scc
->band_start
;
5363 space
= isl_space_copy(scc
->node
[0].space
);
5364 space
= isl_space_params(space
);
5365 space
= isl_space_set_from_params(space
);
5366 space
= isl_space_add_dims(space
, isl_dim_set
, nvar
);
5367 id
= cluster_id(isl_space_get_ctx(space
), i
);
5368 space
= isl_space_set_tuple_id(space
, isl_dim_set
, id
);
5373 /* Collect the domain of the graph for merging clusters.
5375 * In particular, for each cluster with first SCC "i", construct
5376 * a set in the space called cluster_i with dimension equal
5377 * to the number of schedule rows in the current band of the cluster.
5379 static __isl_give isl_union_set
*collect_domain(isl_ctx
*ctx
,
5380 struct isl_sched_graph
*graph
, struct isl_clustering
*c
)
5384 isl_union_set
*domain
;
5386 space
= isl_space_params_alloc(ctx
, 0);
5387 domain
= isl_union_set_empty(space
);
5389 for (i
= 0; i
< graph
->scc
; ++i
) {
5392 if (!c
->scc_in_merge
[i
])
5394 if (c
->scc_cluster
[i
] != i
)
5396 space
= cluster_space(&c
->scc
[i
], i
);
5397 domain
= isl_union_set_add_set(domain
, isl_set_universe(space
));
5403 /* Construct a map from the original instances to the corresponding
5404 * cluster instance in the current bands of the clusters in "c".
5406 static __isl_give isl_union_map
*collect_cluster_map(isl_ctx
*ctx
,
5407 struct isl_sched_graph
*graph
, struct isl_clustering
*c
)
5411 isl_union_map
*cluster_map
;
5413 space
= isl_space_params_alloc(ctx
, 0);
5414 cluster_map
= isl_union_map_empty(space
);
5415 for (i
= 0; i
< graph
->scc
; ++i
) {
5419 if (!c
->scc_in_merge
[i
])
5422 id
= cluster_id(ctx
, c
->scc_cluster
[i
]);
5423 start
= c
->scc
[i
].band_start
;
5424 n
= c
->scc
[i
].n_total_row
- start
;
5425 for (j
= 0; j
< c
->scc
[i
].n
; ++j
) {
5428 struct isl_sched_node
*node
= &c
->scc
[i
].node
[j
];
5430 ma
= node_extract_partial_schedule_multi_aff(node
,
5432 ma
= isl_multi_aff_set_tuple_id(ma
, isl_dim_out
,
5434 map
= isl_map_from_multi_aff(ma
);
5435 cluster_map
= isl_union_map_add_map(cluster_map
, map
);
5443 /* Add "umap" to the schedule constraints "sc" of all types of "edge"
5444 * that are not isl_edge_condition or isl_edge_conditional_validity.
5446 static __isl_give isl_schedule_constraints
*add_non_conditional_constraints(
5447 struct isl_sched_edge
*edge
, __isl_keep isl_union_map
*umap
,
5448 __isl_take isl_schedule_constraints
*sc
)
5450 enum isl_edge_type t
;
5455 for (t
= isl_edge_first
; t
<= isl_edge_last
; ++t
) {
5456 if (t
== isl_edge_condition
||
5457 t
== isl_edge_conditional_validity
)
5459 if (!is_type(edge
, t
))
5461 sc
= isl_schedule_constraints_add(sc
, t
,
5462 isl_union_map_copy(umap
));
5468 /* Add schedule constraints of types isl_edge_condition and
5469 * isl_edge_conditional_validity to "sc" by applying "umap" to
5470 * the domains of the wrapped relations in domain and range
5471 * of the corresponding tagged constraints of "edge".
5473 static __isl_give isl_schedule_constraints
*add_conditional_constraints(
5474 struct isl_sched_edge
*edge
, __isl_keep isl_union_map
*umap
,
5475 __isl_take isl_schedule_constraints
*sc
)
5477 enum isl_edge_type t
;
5478 isl_union_map
*tagged
;
5480 for (t
= isl_edge_condition
; t
<= isl_edge_conditional_validity
; ++t
) {
5481 if (!is_type(edge
, t
))
5483 if (t
== isl_edge_condition
)
5484 tagged
= isl_union_map_copy(edge
->tagged_condition
);
5486 tagged
= isl_union_map_copy(edge
->tagged_validity
);
5487 tagged
= isl_union_map_zip(tagged
);
5488 tagged
= isl_union_map_apply_domain(tagged
,
5489 isl_union_map_copy(umap
));
5490 tagged
= isl_union_map_zip(tagged
);
5491 sc
= isl_schedule_constraints_add(sc
, t
, tagged
);
5499 /* Given a mapping "cluster_map" from the original instances to
5500 * the cluster instances, add schedule constraints on the clusters
5501 * to "sc" corresponding to the original constraints represented by "edge".
5503 * For non-tagged dependence constraints, the cluster constraints
5504 * are obtained by applying "cluster_map" to the edge->map.
5506 * For tagged dependence constraints, "cluster_map" needs to be applied
5507 * to the domains of the wrapped relations in domain and range
5508 * of the tagged dependence constraints. Pick out the mappings
5509 * from these domains from "cluster_map" and construct their product.
5510 * This mapping can then be applied to the pair of domains.
5512 static __isl_give isl_schedule_constraints
*collect_edge_constraints(
5513 struct isl_sched_edge
*edge
, __isl_keep isl_union_map
*cluster_map
,
5514 __isl_take isl_schedule_constraints
*sc
)
5516 isl_union_map
*umap
;
5518 isl_union_set
*uset
;
5519 isl_union_map
*umap1
, *umap2
;
5524 umap
= isl_union_map_from_map(isl_map_copy(edge
->map
));
5525 umap
= isl_union_map_apply_domain(umap
,
5526 isl_union_map_copy(cluster_map
));
5527 umap
= isl_union_map_apply_range(umap
,
5528 isl_union_map_copy(cluster_map
));
5529 sc
= add_non_conditional_constraints(edge
, umap
, sc
);
5530 isl_union_map_free(umap
);
5532 if (!sc
|| (!is_condition(edge
) && !is_conditional_validity(edge
)))
5535 space
= isl_space_domain(isl_map_get_space(edge
->map
));
5536 uset
= isl_union_set_from_set(isl_set_universe(space
));
5537 umap1
= isl_union_map_copy(cluster_map
);
5538 umap1
= isl_union_map_intersect_domain(umap1
, uset
);
5539 space
= isl_space_range(isl_map_get_space(edge
->map
));
5540 uset
= isl_union_set_from_set(isl_set_universe(space
));
5541 umap2
= isl_union_map_copy(cluster_map
);
5542 umap2
= isl_union_map_intersect_domain(umap2
, uset
);
5543 umap
= isl_union_map_product(umap1
, umap2
);
5545 sc
= add_conditional_constraints(edge
, umap
, sc
);
5547 isl_union_map_free(umap
);
5551 /* Given a mapping "cluster_map" from the original instances to
5552 * the cluster instances, add schedule constraints on the clusters
5553 * to "sc" corresponding to all edges in "graph" between nodes that
5554 * belong to SCCs that are marked for merging in "scc_in_merge".
5556 static __isl_give isl_schedule_constraints
*collect_constraints(
5557 struct isl_sched_graph
*graph
, int *scc_in_merge
,
5558 __isl_keep isl_union_map
*cluster_map
,
5559 __isl_take isl_schedule_constraints
*sc
)
5563 for (i
= 0; i
< graph
->n_edge
; ++i
) {
5564 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
5566 if (!scc_in_merge
[edge
->src
->scc
])
5568 if (!scc_in_merge
[edge
->dst
->scc
])
5570 sc
= collect_edge_constraints(edge
, cluster_map
, sc
);
5576 /* Construct a dependence graph for scheduling clusters with respect
5577 * to each other and store the result in "merge_graph".
5578 * In particular, the nodes of the graph correspond to the schedule
5579 * dimensions of the current bands of those clusters that have been
5580 * marked for merging in "c".
5582 * First construct an isl_schedule_constraints object for this domain
5583 * by transforming the edges in "graph" to the domain.
5584 * Then initialize a dependence graph for scheduling from these
5587 static isl_stat
init_merge_graph(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
5588 struct isl_clustering
*c
, struct isl_sched_graph
*merge_graph
)
5590 isl_union_set
*domain
;
5591 isl_union_map
*cluster_map
;
5592 isl_schedule_constraints
*sc
;
5595 domain
= collect_domain(ctx
, graph
, c
);
5596 sc
= isl_schedule_constraints_on_domain(domain
);
5598 return isl_stat_error
;
5599 cluster_map
= collect_cluster_map(ctx
, graph
, c
);
5600 sc
= collect_constraints(graph
, c
->scc_in_merge
, cluster_map
, sc
);
5601 isl_union_map_free(cluster_map
);
5603 r
= graph_init(merge_graph
, sc
);
5605 isl_schedule_constraints_free(sc
);
5610 /* Compute the maximal number of remaining schedule rows that still need
5611 * to be computed for the nodes that belong to clusters with the maximal
5612 * dimension for the current band (i.e., the band that is to be merged).
5613 * Only clusters that are about to be merged are considered.
5614 * "maxvar" is the maximal dimension for the current band.
5615 * "c" contains information about the clusters.
5617 * Return the maximal number of remaining schedule rows or -1 on error.
5619 static int compute_maxvar_max_slack(int maxvar
, struct isl_clustering
*c
)
5625 for (i
= 0; i
< c
->n
; ++i
) {
5627 struct isl_sched_graph
*scc
;
5629 if (!c
->scc_in_merge
[i
])
5632 nvar
= scc
->n_total_row
- scc
->band_start
;
5635 for (j
= 0; j
< scc
->n
; ++j
) {
5636 struct isl_sched_node
*node
= &scc
->node
[j
];
5639 if (node_update_vmap(node
) < 0)
5641 slack
= node
->nvar
- node
->rank
;
5642 if (slack
> max_slack
)
5650 /* If there are any clusters where the dimension of the current band
5651 * (i.e., the band that is to be merged) is smaller than "maxvar" and
5652 * if there are any nodes in such a cluster where the number
5653 * of remaining schedule rows that still need to be computed
5654 * is greater than "max_slack", then return the smallest current band
5655 * dimension of all these clusters. Otherwise return the original value
5656 * of "maxvar". Return -1 in case of any error.
5657 * Only clusters that are about to be merged are considered.
5658 * "c" contains information about the clusters.
5660 static int limit_maxvar_to_slack(int maxvar
, int max_slack
,
5661 struct isl_clustering
*c
)
5665 for (i
= 0; i
< c
->n
; ++i
) {
5667 struct isl_sched_graph
*scc
;
5669 if (!c
->scc_in_merge
[i
])
5672 nvar
= scc
->n_total_row
- scc
->band_start
;
5675 for (j
= 0; j
< scc
->n
; ++j
) {
5676 struct isl_sched_node
*node
= &scc
->node
[j
];
5679 if (node_update_vmap(node
) < 0)
5681 slack
= node
->nvar
- node
->rank
;
5682 if (slack
> max_slack
) {
5692 /* Adjust merge_graph->maxvar based on the number of remaining schedule rows
5693 * that still need to be computed. In particular, if there is a node
5694 * in a cluster where the dimension of the current band is smaller
5695 * than merge_graph->maxvar, but the number of remaining schedule rows
5696 * is greater than that of any node in a cluster with the maximal
5697 * dimension for the current band (i.e., merge_graph->maxvar),
5698 * then adjust merge_graph->maxvar to the (smallest) current band dimension
5699 * of those clusters. Without this adjustment, the total number of
5700 * schedule dimensions would be increased, resulting in a skewed view
5701 * of the number of coincident dimensions.
5702 * "c" contains information about the clusters.
5704 * If the maximize_band_depth option is set and merge_graph->maxvar is reduced,
5705 * then there is no point in attempting any merge since it will be rejected
5706 * anyway. Set merge_graph->maxvar to zero in such cases.
5708 static isl_stat
adjust_maxvar_to_slack(isl_ctx
*ctx
,
5709 struct isl_sched_graph
*merge_graph
, struct isl_clustering
*c
)
5711 int max_slack
, maxvar
;
5713 max_slack
= compute_maxvar_max_slack(merge_graph
->maxvar
, c
);
5715 return isl_stat_error
;
5716 maxvar
= limit_maxvar_to_slack(merge_graph
->maxvar
, max_slack
, c
);
5718 return isl_stat_error
;
5720 if (maxvar
< merge_graph
->maxvar
) {
5721 if (isl_options_get_schedule_maximize_band_depth(ctx
))
5722 merge_graph
->maxvar
= 0;
5724 merge_graph
->maxvar
= maxvar
;
5730 /* Return the number of coincident dimensions in the current band of "graph",
5731 * where the nodes of "graph" are assumed to be scheduled by a single band.
5733 static int get_n_coincident(struct isl_sched_graph
*graph
)
5737 for (i
= graph
->band_start
; i
< graph
->n_total_row
; ++i
)
5738 if (!graph
->node
[0].coincident
[i
])
5741 return i
- graph
->band_start
;
5744 /* Should the clusters be merged based on the cluster schedule
5745 * in the current (and only) band of "merge_graph", given that
5746 * coincidence should be maximized?
5748 * If the number of coincident schedule dimensions in the merged band
5749 * would be less than the maximal number of coincident schedule dimensions
5750 * in any of the merged clusters, then the clusters should not be merged.
5752 static isl_bool
ok_to_merge_coincident(struct isl_clustering
*c
,
5753 struct isl_sched_graph
*merge_graph
)
5760 for (i
= 0; i
< c
->n
; ++i
) {
5761 if (!c
->scc_in_merge
[i
])
5763 n_coincident
= get_n_coincident(&c
->scc
[i
]);
5764 if (n_coincident
> max_coincident
)
5765 max_coincident
= n_coincident
;
5768 n_coincident
= get_n_coincident(merge_graph
);
5770 return n_coincident
>= max_coincident
;
5773 /* Return the transformation on "node" expressed by the current (and only)
5774 * band of "merge_graph" applied to the clusters in "c".
5776 * First find the representation of "node" in its SCC in "c" and
5777 * extract the transformation expressed by the current band.
5778 * Then extract the transformation applied by "merge_graph"
5779 * to the cluster to which this SCC belongs.
5780 * Combine the two to obtain the complete transformation on the node.
5782 * Note that the range of the first transformation is an anonymous space,
5783 * while the domain of the second is named "cluster_X". The range
5784 * of the former therefore needs to be adjusted before the two
5787 static __isl_give isl_map
*extract_node_transformation(isl_ctx
*ctx
,
5788 struct isl_sched_node
*node
, struct isl_clustering
*c
,
5789 struct isl_sched_graph
*merge_graph
)
5791 struct isl_sched_node
*scc_node
, *cluster_node
;
5795 isl_multi_aff
*ma
, *ma2
;
5797 scc_node
= graph_find_node(ctx
, &c
->scc
[node
->scc
], node
->space
);
5798 start
= c
->scc
[node
->scc
].band_start
;
5799 n
= c
->scc
[node
->scc
].n_total_row
- start
;
5800 ma
= node_extract_partial_schedule_multi_aff(scc_node
, start
, n
);
5801 space
= cluster_space(&c
->scc
[node
->scc
], c
->scc_cluster
[node
->scc
]);
5802 cluster_node
= graph_find_node(ctx
, merge_graph
, space
);
5803 if (space
&& !cluster_node
)
5804 isl_die(ctx
, isl_error_internal
, "unable to find cluster",
5805 space
= isl_space_free(space
));
5806 id
= isl_space_get_tuple_id(space
, isl_dim_set
);
5807 ma
= isl_multi_aff_set_tuple_id(ma
, isl_dim_out
, id
);
5808 isl_space_free(space
);
5809 n
= merge_graph
->n_total_row
;
5810 ma2
= node_extract_partial_schedule_multi_aff(cluster_node
, 0, n
);
5811 ma
= isl_multi_aff_pullback_multi_aff(ma2
, ma
);
5813 return isl_map_from_multi_aff(ma
);
5816 /* Give a set of distances "set", are they bounded by a small constant
5817 * in direction "pos"?
5818 * In practice, check if they are bounded by 2 by checking that there
5819 * are no elements with a value greater than or equal to 3 or
5820 * smaller than or equal to -3.
5822 static isl_bool
distance_is_bounded(__isl_keep isl_set
*set
, int pos
)
5828 return isl_bool_error
;
5830 test
= isl_set_copy(set
);
5831 test
= isl_set_lower_bound_si(test
, isl_dim_set
, pos
, 3);
5832 bounded
= isl_set_is_empty(test
);
5835 if (bounded
< 0 || !bounded
)
5838 test
= isl_set_copy(set
);
5839 test
= isl_set_upper_bound_si(test
, isl_dim_set
, pos
, -3);
5840 bounded
= isl_set_is_empty(test
);
5846 /* Does the set "set" have a fixed (but possible parametric) value
5847 * at dimension "pos"?
5849 static isl_bool
has_single_value(__isl_keep isl_set
*set
, int pos
)
5855 return isl_bool_error
;
5856 set
= isl_set_copy(set
);
5857 n
= isl_set_dim(set
, isl_dim_set
);
5858 set
= isl_set_project_out(set
, isl_dim_set
, pos
+ 1, n
- (pos
+ 1));
5859 set
= isl_set_project_out(set
, isl_dim_set
, 0, pos
);
5860 single
= isl_set_is_singleton(set
);
5866 /* Does "map" have a fixed (but possible parametric) value
5867 * at dimension "pos" of either its domain or its range?
5869 static isl_bool
has_singular_src_or_dst(__isl_keep isl_map
*map
, int pos
)
5874 set
= isl_map_domain(isl_map_copy(map
));
5875 single
= has_single_value(set
, pos
);
5878 if (single
< 0 || single
)
5881 set
= isl_map_range(isl_map_copy(map
));
5882 single
= has_single_value(set
, pos
);
5888 /* Does the edge "edge" from "graph" have bounded dependence distances
5889 * in the merged graph "merge_graph" of a selection of clusters in "c"?
5891 * Extract the complete transformations of the source and destination
5892 * nodes of the edge, apply them to the edge constraints and
5893 * compute the differences. Finally, check if these differences are bounded
5894 * in each direction.
5896 * If the dimension of the band is greater than the number of
5897 * dimensions that can be expected to be optimized by the edge
5898 * (based on its weight), then also allow the differences to be unbounded
5899 * in the remaining dimensions, but only if either the source or
5900 * the destination has a fixed value in that direction.
5901 * This allows a statement that produces values that are used by
5902 * several instances of another statement to be merged with that
5904 * However, merging such clusters will introduce an inherently
5905 * large proximity distance inside the merged cluster, meaning
5906 * that proximity distances will no longer be optimized in
5907 * subsequent merges. These merges are therefore only allowed
5908 * after all other possible merges have been tried.
5909 * The first time such a merge is encountered, the weight of the edge
5910 * is replaced by a negative weight. The second time (i.e., after
5911 * all merges over edges with a non-negative weight have been tried),
5912 * the merge is allowed.
5914 static isl_bool
has_bounded_distances(isl_ctx
*ctx
, struct isl_sched_edge
*edge
,
5915 struct isl_sched_graph
*graph
, struct isl_clustering
*c
,
5916 struct isl_sched_graph
*merge_graph
)
5923 map
= isl_map_copy(edge
->map
);
5924 t
= extract_node_transformation(ctx
, edge
->src
, c
, merge_graph
);
5925 map
= isl_map_apply_domain(map
, t
);
5926 t
= extract_node_transformation(ctx
, edge
->dst
, c
, merge_graph
);
5927 map
= isl_map_apply_range(map
, t
);
5928 dist
= isl_map_deltas(isl_map_copy(map
));
5930 bounded
= isl_bool_true
;
5931 n
= isl_set_dim(dist
, isl_dim_set
);
5932 n_slack
= n
- edge
->weight
;
5933 if (edge
->weight
< 0)
5934 n_slack
-= graph
->max_weight
+ 1;
5935 for (i
= 0; i
< n
; ++i
) {
5936 isl_bool bounded_i
, singular_i
;
5938 bounded_i
= distance_is_bounded(dist
, i
);
5943 if (edge
->weight
>= 0)
5944 bounded
= isl_bool_false
;
5948 singular_i
= has_singular_src_or_dst(map
, i
);
5953 bounded
= isl_bool_false
;
5956 if (!bounded
&& i
>= n
&& edge
->weight
>= 0)
5957 edge
->weight
-= graph
->max_weight
+ 1;
5965 return isl_bool_error
;
5968 /* Should the clusters be merged based on the cluster schedule
5969 * in the current (and only) band of "merge_graph"?
5970 * "graph" is the original dependence graph, while "c" records
5971 * which SCCs are involved in the latest merge.
5973 * In particular, is there at least one proximity constraint
5974 * that is optimized by the merge?
5976 * A proximity constraint is considered to be optimized
5977 * if the dependence distances are small.
5979 static isl_bool
ok_to_merge_proximity(isl_ctx
*ctx
,
5980 struct isl_sched_graph
*graph
, struct isl_clustering
*c
,
5981 struct isl_sched_graph
*merge_graph
)
5985 for (i
= 0; i
< graph
->n_edge
; ++i
) {
5986 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
5989 if (!is_proximity(edge
))
5991 if (!c
->scc_in_merge
[edge
->src
->scc
])
5993 if (!c
->scc_in_merge
[edge
->dst
->scc
])
5995 if (c
->scc_cluster
[edge
->dst
->scc
] ==
5996 c
->scc_cluster
[edge
->src
->scc
])
5998 bounded
= has_bounded_distances(ctx
, edge
, graph
, c
,
6000 if (bounded
< 0 || bounded
)
6004 return isl_bool_false
;
6007 /* Should the clusters be merged based on the cluster schedule
6008 * in the current (and only) band of "merge_graph"?
6009 * "graph" is the original dependence graph, while "c" records
6010 * which SCCs are involved in the latest merge.
6012 * If the current band is empty, then the clusters should not be merged.
6014 * If the band depth should be maximized and the merge schedule
6015 * is incomplete (meaning that the dimension of some of the schedule
6016 * bands in the original schedule will be reduced), then the clusters
6017 * should not be merged.
6019 * If the schedule_maximize_coincidence option is set, then check that
6020 * the number of coincident schedule dimensions is not reduced.
6022 * Finally, only allow the merge if at least one proximity
6023 * constraint is optimized.
6025 static isl_bool
ok_to_merge(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
6026 struct isl_clustering
*c
, struct isl_sched_graph
*merge_graph
)
6028 if (merge_graph
->n_total_row
== merge_graph
->band_start
)
6029 return isl_bool_false
;
6031 if (isl_options_get_schedule_maximize_band_depth(ctx
) &&
6032 merge_graph
->n_total_row
< merge_graph
->maxvar
)
6033 return isl_bool_false
;
6035 if (isl_options_get_schedule_maximize_coincidence(ctx
)) {
6038 ok
= ok_to_merge_coincident(c
, merge_graph
);
6043 return ok_to_merge_proximity(ctx
, graph
, c
, merge_graph
);
6046 /* Apply the schedule in "t_node" to the "n" rows starting at "first"
6047 * of the schedule in "node" and return the result.
6049 * That is, essentially compute
6051 * T * N(first:first+n-1)
6053 * taking into account the constant term and the parameter coefficients
6056 static __isl_give isl_mat
*node_transformation(isl_ctx
*ctx
,
6057 struct isl_sched_node
*t_node
, struct isl_sched_node
*node
,
6062 int n_row
, n_col
, n_param
, n_var
;
6064 n_param
= node
->nparam
;
6066 n_row
= isl_mat_rows(t_node
->sched
);
6067 n_col
= isl_mat_cols(node
->sched
);
6068 t
= isl_mat_alloc(ctx
, n_row
, n_col
);
6071 for (i
= 0; i
< n_row
; ++i
) {
6072 isl_seq_cpy(t
->row
[i
], t_node
->sched
->row
[i
], 1 + n_param
);
6073 isl_seq_clr(t
->row
[i
] + 1 + n_param
, n_var
);
6074 for (j
= 0; j
< n
; ++j
)
6075 isl_seq_addmul(t
->row
[i
],
6076 t_node
->sched
->row
[i
][1 + n_param
+ j
],
6077 node
->sched
->row
[first
+ j
],
6078 1 + n_param
+ n_var
);
6083 /* Apply the cluster schedule in "t_node" to the current band
6084 * schedule of the nodes in "graph".
6086 * In particular, replace the rows starting at band_start
6087 * by the result of applying the cluster schedule in "t_node"
6088 * to the original rows.
6090 * The coincidence of the schedule is determined by the coincidence
6091 * of the cluster schedule.
6093 static isl_stat
transform(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
6094 struct isl_sched_node
*t_node
)
6100 start
= graph
->band_start
;
6101 n
= graph
->n_total_row
- start
;
6103 n_new
= isl_mat_rows(t_node
->sched
);
6104 for (i
= 0; i
< graph
->n
; ++i
) {
6105 struct isl_sched_node
*node
= &graph
->node
[i
];
6108 t
= node_transformation(ctx
, t_node
, node
, start
, n
);
6109 node
->sched
= isl_mat_drop_rows(node
->sched
, start
, n
);
6110 node
->sched
= isl_mat_concat(node
->sched
, t
);
6111 node
->sched_map
= isl_map_free(node
->sched_map
);
6113 return isl_stat_error
;
6114 for (j
= 0; j
< n_new
; ++j
)
6115 node
->coincident
[start
+ j
] = t_node
->coincident
[j
];
6117 graph
->n_total_row
-= n
;
6119 graph
->n_total_row
+= n_new
;
6120 graph
->n_row
+= n_new
;
6125 /* Merge the clusters marked for merging in "c" into a single
6126 * cluster using the cluster schedule in the current band of "merge_graph".
6127 * The representative SCC for the new cluster is the SCC with
6128 * the smallest index.
6130 * The current band schedule of each SCC in the new cluster is obtained
6131 * by applying the schedule of the corresponding original cluster
6132 * to the original band schedule.
6133 * All SCCs in the new cluster have the same number of schedule rows.
6135 static isl_stat
merge(isl_ctx
*ctx
, struct isl_clustering
*c
,
6136 struct isl_sched_graph
*merge_graph
)
6142 for (i
= 0; i
< c
->n
; ++i
) {
6143 struct isl_sched_node
*node
;
6145 if (!c
->scc_in_merge
[i
])
6149 space
= cluster_space(&c
->scc
[i
], c
->scc_cluster
[i
]);
6151 return isl_stat_error
;
6152 node
= graph_find_node(ctx
, merge_graph
, space
);
6153 isl_space_free(space
);
6155 isl_die(ctx
, isl_error_internal
,
6156 "unable to find cluster",
6157 return isl_stat_error
);
6158 if (transform(ctx
, &c
->scc
[i
], node
) < 0)
6159 return isl_stat_error
;
6160 c
->scc_cluster
[i
] = cluster
;
6166 /* Try and merge the clusters of SCCs marked in c->scc_in_merge
6167 * by scheduling the current cluster bands with respect to each other.
6169 * Construct a dependence graph with a space for each cluster and
6170 * with the coordinates of each space corresponding to the schedule
6171 * dimensions of the current band of that cluster.
6172 * Construct a cluster schedule in this cluster dependence graph and
6173 * apply it to the current cluster bands if it is applicable
6174 * according to ok_to_merge.
6176 * If the number of remaining schedule dimensions in a cluster
6177 * with a non-maximal current schedule dimension is greater than
6178 * the number of remaining schedule dimensions in clusters
6179 * with a maximal current schedule dimension, then restrict
6180 * the number of rows to be computed in the cluster schedule
6181 * to the minimal such non-maximal current schedule dimension.
6182 * Do this by adjusting merge_graph.maxvar.
6184 * Return isl_bool_true if the clusters have effectively been merged
6185 * into a single cluster.
6187 * Note that since the standard scheduling algorithm minimizes the maximal
6188 * distance over proximity constraints, the proximity constraints between
6189 * the merged clusters may not be optimized any further than what is
6190 * sufficient to bring the distances within the limits of the internal
6191 * proximity constraints inside the individual clusters.
6192 * It may therefore make sense to perform an additional translation step
6193 * to bring the clusters closer to each other, while maintaining
6194 * the linear part of the merging schedule found using the standard
6195 * scheduling algorithm.
6197 static isl_bool
try_merge(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
6198 struct isl_clustering
*c
)
6200 struct isl_sched_graph merge_graph
= { 0 };
6203 if (init_merge_graph(ctx
, graph
, c
, &merge_graph
) < 0)
6206 if (compute_maxvar(&merge_graph
) < 0)
6208 if (adjust_maxvar_to_slack(ctx
, &merge_graph
,c
) < 0)
6210 if (compute_schedule_wcc_band(ctx
, &merge_graph
) < 0)
6212 merged
= ok_to_merge(ctx
, graph
, c
, &merge_graph
);
6213 if (merged
&& merge(ctx
, c
, &merge_graph
) < 0)
6216 graph_free(ctx
, &merge_graph
);
6219 graph_free(ctx
, &merge_graph
);
6220 return isl_bool_error
;
6223 /* Is there any edge marked "no_merge" between two SCCs that are
6224 * about to be merged (i.e., that are set in "scc_in_merge")?
6225 * "merge_edge" is the proximity edge along which the clusters of SCCs
6226 * are going to be merged.
6228 * If there is any edge between two SCCs with a negative weight,
6229 * while the weight of "merge_edge" is non-negative, then this
6230 * means that the edge was postponed. "merge_edge" should then
6231 * also be postponed since merging along the edge with negative weight should
6232 * be postponed until all edges with non-negative weight have been tried.
6233 * Replace the weight of "merge_edge" by a negative weight as well and
6234 * tell the caller not to attempt a merge.
6236 static int any_no_merge(struct isl_sched_graph
*graph
, int *scc_in_merge
,
6237 struct isl_sched_edge
*merge_edge
)
6241 for (i
= 0; i
< graph
->n_edge
; ++i
) {
6242 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
6244 if (!scc_in_merge
[edge
->src
->scc
])
6246 if (!scc_in_merge
[edge
->dst
->scc
])
6250 if (merge_edge
->weight
>= 0 && edge
->weight
< 0) {
6251 merge_edge
->weight
-= graph
->max_weight
+ 1;
6259 /* Merge the two clusters in "c" connected by the edge in "graph"
6260 * with index "edge" into a single cluster.
6261 * If it turns out to be impossible to merge these two clusters,
6262 * then mark the edge as "no_merge" such that it will not be
6265 * First mark all SCCs that need to be merged. This includes the SCCs
6266 * in the two clusters, but it may also include the SCCs
6267 * of intermediate clusters.
6268 * If there is already a no_merge edge between any pair of such SCCs,
6269 * then simply mark the current edge as no_merge as well.
6270 * Likewise, if any of those edges was postponed by has_bounded_distances,
6271 * then postpone the current edge as well.
6272 * Otherwise, try and merge the clusters and mark "edge" as "no_merge"
6273 * if the clusters did not end up getting merged, unless the non-merge
6274 * is due to the fact that the edge was postponed. This postponement
6275 * can be recognized by a change in weight (from non-negative to negative).
6277 static isl_stat
merge_clusters_along_edge(isl_ctx
*ctx
,
6278 struct isl_sched_graph
*graph
, int edge
, struct isl_clustering
*c
)
6281 int edge_weight
= graph
->edge
[edge
].weight
;
6283 if (mark_merge_sccs(ctx
, graph
, edge
, c
) < 0)
6284 return isl_stat_error
;
6286 if (any_no_merge(graph
, c
->scc_in_merge
, &graph
->edge
[edge
]))
6287 merged
= isl_bool_false
;
6289 merged
= try_merge(ctx
, graph
, c
);
6291 return isl_stat_error
;
6292 if (!merged
&& edge_weight
== graph
->edge
[edge
].weight
)
6293 graph
->edge
[edge
].no_merge
= 1;
6298 /* Does "node" belong to the cluster identified by "cluster"?
6300 static int node_cluster_exactly(struct isl_sched_node
*node
, int cluster
)
6302 return node
->cluster
== cluster
;
6305 /* Does "edge" connect two nodes belonging to the cluster
6306 * identified by "cluster"?
6308 static int edge_cluster_exactly(struct isl_sched_edge
*edge
, int cluster
)
6310 return edge
->src
->cluster
== cluster
&& edge
->dst
->cluster
== cluster
;
6313 /* Swap the schedule of "node1" and "node2".
6314 * Both nodes have been derived from the same node in a common parent graph.
6315 * Since the "coincident" field is shared with that node
6316 * in the parent graph, there is no need to also swap this field.
6318 static void swap_sched(struct isl_sched_node
*node1
,
6319 struct isl_sched_node
*node2
)
6324 sched
= node1
->sched
;
6325 node1
->sched
= node2
->sched
;
6326 node2
->sched
= sched
;
6328 sched_map
= node1
->sched_map
;
6329 node1
->sched_map
= node2
->sched_map
;
6330 node2
->sched_map
= sched_map
;
6333 /* Copy the current band schedule from the SCCs that form the cluster
6334 * with index "pos" to the actual cluster at position "pos".
6335 * By construction, the index of the first SCC that belongs to the cluster
6338 * The order of the nodes inside both the SCCs and the cluster
6339 * is assumed to be same as the order in the original "graph".
6341 * Since the SCC graphs will no longer be used after this function,
6342 * the schedules are actually swapped rather than copied.
6344 static isl_stat
copy_partial(struct isl_sched_graph
*graph
,
6345 struct isl_clustering
*c
, int pos
)
6349 c
->cluster
[pos
].n_total_row
= c
->scc
[pos
].n_total_row
;
6350 c
->cluster
[pos
].n_row
= c
->scc
[pos
].n_row
;
6351 c
->cluster
[pos
].maxvar
= c
->scc
[pos
].maxvar
;
6353 for (i
= 0; i
< graph
->n
; ++i
) {
6357 if (graph
->node
[i
].cluster
!= pos
)
6359 s
= graph
->node
[i
].scc
;
6360 k
= c
->scc_node
[s
]++;
6361 swap_sched(&c
->cluster
[pos
].node
[j
], &c
->scc
[s
].node
[k
]);
6362 if (c
->scc
[s
].maxvar
> c
->cluster
[pos
].maxvar
)
6363 c
->cluster
[pos
].maxvar
= c
->scc
[s
].maxvar
;
6370 /* Is there a (conditional) validity dependence from node[j] to node[i],
6371 * forcing node[i] to follow node[j] or do the nodes belong to the same
6374 static isl_bool
node_follows_strong_or_same_cluster(int i
, int j
, void *user
)
6376 struct isl_sched_graph
*graph
= user
;
6378 if (graph
->node
[i
].cluster
== graph
->node
[j
].cluster
)
6379 return isl_bool_true
;
6380 return graph_has_validity_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
6383 /* Extract the merged clusters of SCCs in "graph", sort them, and
6384 * store them in c->clusters. Update c->scc_cluster accordingly.
6386 * First keep track of the cluster containing the SCC to which a node
6387 * belongs in the node itself.
6388 * Then extract the clusters into c->clusters, copying the current
6389 * band schedule from the SCCs that belong to the cluster.
6390 * Do this only once per cluster.
6392 * Finally, topologically sort the clusters and update c->scc_cluster
6393 * to match the new scc numbering. While the SCCs were originally
6394 * sorted already, some SCCs that depend on some other SCCs may
6395 * have been merged with SCCs that appear before these other SCCs.
6396 * A reordering may therefore be required.
6398 static isl_stat
extract_clusters(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
6399 struct isl_clustering
*c
)
6403 for (i
= 0; i
< graph
->n
; ++i
)
6404 graph
->node
[i
].cluster
= c
->scc_cluster
[graph
->node
[i
].scc
];
6406 for (i
= 0; i
< graph
->scc
; ++i
) {
6407 if (c
->scc_cluster
[i
] != i
)
6409 if (extract_sub_graph(ctx
, graph
, &node_cluster_exactly
,
6410 &edge_cluster_exactly
, i
, &c
->cluster
[i
]) < 0)
6411 return isl_stat_error
;
6412 c
->cluster
[i
].src_scc
= -1;
6413 c
->cluster
[i
].dst_scc
= -1;
6414 if (copy_partial(graph
, c
, i
) < 0)
6415 return isl_stat_error
;
6418 if (detect_ccs(ctx
, graph
, &node_follows_strong_or_same_cluster
) < 0)
6419 return isl_stat_error
;
6420 for (i
= 0; i
< graph
->n
; ++i
)
6421 c
->scc_cluster
[graph
->node
[i
].scc
] = graph
->node
[i
].cluster
;
6426 /* Compute weights on the proximity edges of "graph" that can
6427 * be used by find_proximity to find the most appropriate
6428 * proximity edge to use to merge two clusters in "c".
6429 * The weights are also used by has_bounded_distances to determine
6430 * whether the merge should be allowed.
6431 * Store the maximum of the computed weights in graph->max_weight.
6433 * The computed weight is a measure for the number of remaining schedule
6434 * dimensions that can still be completely aligned.
6435 * In particular, compute the number of equalities between
6436 * input dimensions and output dimensions in the proximity constraints.
6437 * The directions that are already handled by outer schedule bands
6438 * are projected out prior to determining this number.
6440 * Edges that will never be considered by find_proximity are ignored.
6442 static isl_stat
compute_weights(struct isl_sched_graph
*graph
,
6443 struct isl_clustering
*c
)
6447 graph
->max_weight
= 0;
6449 for (i
= 0; i
< graph
->n_edge
; ++i
) {
6450 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
6451 struct isl_sched_node
*src
= edge
->src
;
6452 struct isl_sched_node
*dst
= edge
->dst
;
6453 isl_basic_map
*hull
;
6457 prox
= is_non_empty_proximity(edge
);
6459 return isl_stat_error
;
6462 if (bad_cluster(&c
->scc
[edge
->src
->scc
]) ||
6463 bad_cluster(&c
->scc
[edge
->dst
->scc
]))
6465 if (c
->scc_cluster
[edge
->dst
->scc
] ==
6466 c
->scc_cluster
[edge
->src
->scc
])
6469 hull
= isl_map_affine_hull(isl_map_copy(edge
->map
));
6470 hull
= isl_basic_map_transform_dims(hull
, isl_dim_in
, 0,
6471 isl_mat_copy(src
->vmap
));
6472 hull
= isl_basic_map_transform_dims(hull
, isl_dim_out
, 0,
6473 isl_mat_copy(dst
->vmap
));
6474 hull
= isl_basic_map_project_out(hull
,
6475 isl_dim_in
, 0, src
->rank
);
6476 hull
= isl_basic_map_project_out(hull
,
6477 isl_dim_out
, 0, dst
->rank
);
6478 hull
= isl_basic_map_remove_divs(hull
);
6479 n_in
= isl_basic_map_dim(hull
, isl_dim_in
);
6480 n_out
= isl_basic_map_dim(hull
, isl_dim_out
);
6481 hull
= isl_basic_map_drop_constraints_not_involving_dims(hull
,
6482 isl_dim_in
, 0, n_in
);
6483 hull
= isl_basic_map_drop_constraints_not_involving_dims(hull
,
6484 isl_dim_out
, 0, n_out
);
6486 return isl_stat_error
;
6487 edge
->weight
= isl_basic_map_n_equality(hull
);
6488 isl_basic_map_free(hull
);
6490 if (edge
->weight
> graph
->max_weight
)
6491 graph
->max_weight
= edge
->weight
;
6497 /* Call compute_schedule_finish_band on each of the clusters in "c"
6498 * in their topological order. This order is determined by the scc
6499 * fields of the nodes in "graph".
6500 * Combine the results in a sequence expressing the topological order.
6502 * If there is only one cluster left, then there is no need to introduce
6503 * a sequence node. Also, in this case, the cluster necessarily contains
6504 * the SCC at position 0 in the original graph and is therefore also
6505 * stored in the first cluster of "c".
6507 static __isl_give isl_schedule_node
*finish_bands_clustering(
6508 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
6509 struct isl_clustering
*c
)
6513 isl_union_set_list
*filters
;
6515 if (graph
->scc
== 1)
6516 return compute_schedule_finish_band(node
, &c
->cluster
[0], 0);
6518 ctx
= isl_schedule_node_get_ctx(node
);
6520 filters
= extract_sccs(ctx
, graph
);
6521 node
= isl_schedule_node_insert_sequence(node
, filters
);
6523 for (i
= 0; i
< graph
->scc
; ++i
) {
6524 int j
= c
->scc_cluster
[i
];
6525 node
= isl_schedule_node_child(node
, i
);
6526 node
= isl_schedule_node_child(node
, 0);
6527 node
= compute_schedule_finish_band(node
, &c
->cluster
[j
], 0);
6528 node
= isl_schedule_node_parent(node
);
6529 node
= isl_schedule_node_parent(node
);
6535 /* Compute a schedule for a connected dependence graph by first considering
6536 * each strongly connected component (SCC) in the graph separately and then
6537 * incrementally combining them into clusters.
6538 * Return the updated schedule node.
6540 * Initially, each cluster consists of a single SCC, each with its
6541 * own band schedule. The algorithm then tries to merge pairs
6542 * of clusters along a proximity edge until no more suitable
6543 * proximity edges can be found. During this merging, the schedule
6544 * is maintained in the individual SCCs.
6545 * After the merging is completed, the full resulting clusters
6546 * are extracted and in finish_bands_clustering,
6547 * compute_schedule_finish_band is called on each of them to integrate
6548 * the band into "node" and to continue the computation.
6550 * compute_weights initializes the weights that are used by find_proximity.
6552 static __isl_give isl_schedule_node
*compute_schedule_wcc_clustering(
6553 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
6556 struct isl_clustering c
;
6559 ctx
= isl_schedule_node_get_ctx(node
);
6561 if (clustering_init(ctx
, &c
, graph
) < 0)
6564 if (compute_weights(graph
, &c
) < 0)
6568 i
= find_proximity(graph
, &c
);
6571 if (i
>= graph
->n_edge
)
6573 if (merge_clusters_along_edge(ctx
, graph
, i
, &c
) < 0)
6577 if (extract_clusters(ctx
, graph
, &c
) < 0)
6580 node
= finish_bands_clustering(node
, graph
, &c
);
6582 clustering_free(ctx
, &c
);
6585 clustering_free(ctx
, &c
);
6586 return isl_schedule_node_free(node
);
6589 /* Compute a schedule for a connected dependence graph and return
6590 * the updated schedule node.
6592 * If Feautrier's algorithm is selected, we first recursively try to satisfy
6593 * as many validity dependences as possible. When all validity dependences
6594 * are satisfied we extend the schedule to a full-dimensional schedule.
6596 * Call compute_schedule_wcc_whole or compute_schedule_wcc_clustering
6597 * depending on whether the user has selected the option to try and
6598 * compute a schedule for the entire (weakly connected) component first.
6599 * If there is only a single strongly connected component (SCC), then
6600 * there is no point in trying to combine SCCs
6601 * in compute_schedule_wcc_clustering, so compute_schedule_wcc_whole
6602 * is called instead.
6604 static __isl_give isl_schedule_node
*compute_schedule_wcc(
6605 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
6612 ctx
= isl_schedule_node_get_ctx(node
);
6613 if (detect_sccs(ctx
, graph
) < 0)
6614 return isl_schedule_node_free(node
);
6616 if (compute_maxvar(graph
) < 0)
6617 return isl_schedule_node_free(node
);
6619 if (need_feautrier_step(ctx
, graph
))
6620 return compute_schedule_wcc_feautrier(node
, graph
);
6622 if (graph
->scc
<= 1 || isl_options_get_schedule_whole_component(ctx
))
6623 return compute_schedule_wcc_whole(node
, graph
);
6625 return compute_schedule_wcc_clustering(node
, graph
);
6628 /* Compute a schedule for each group of nodes identified by node->scc
6629 * separately and then combine them in a sequence node (or as set node
6630 * if graph->weak is set) inserted at position "node" of the schedule tree.
6631 * Return the updated schedule node.
6633 * If "wcc" is set then each of the groups belongs to a single
6634 * weakly connected component in the dependence graph so that
6635 * there is no need for compute_sub_schedule to look for weakly
6636 * connected components.
6638 static __isl_give isl_schedule_node
*compute_component_schedule(
6639 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
6644 isl_union_set_list
*filters
;
6648 ctx
= isl_schedule_node_get_ctx(node
);
6650 filters
= extract_sccs(ctx
, graph
);
6652 node
= isl_schedule_node_insert_set(node
, filters
);
6654 node
= isl_schedule_node_insert_sequence(node
, filters
);
6656 for (component
= 0; component
< graph
->scc
; ++component
) {
6657 node
= isl_schedule_node_child(node
, component
);
6658 node
= isl_schedule_node_child(node
, 0);
6659 node
= compute_sub_schedule(node
, ctx
, graph
,
6661 &edge_scc_exactly
, component
, wcc
);
6662 node
= isl_schedule_node_parent(node
);
6663 node
= isl_schedule_node_parent(node
);
6669 /* Compute a schedule for the given dependence graph and insert it at "node".
6670 * Return the updated schedule node.
6672 * We first check if the graph is connected (through validity and conditional
6673 * validity dependences) and, if not, compute a schedule
6674 * for each component separately.
6675 * If the schedule_serialize_sccs option is set, then we check for strongly
6676 * connected components instead and compute a separate schedule for
6677 * each such strongly connected component.
6679 static __isl_give isl_schedule_node
*compute_schedule(isl_schedule_node
*node
,
6680 struct isl_sched_graph
*graph
)
6687 ctx
= isl_schedule_node_get_ctx(node
);
6688 if (isl_options_get_schedule_serialize_sccs(ctx
)) {
6689 if (detect_sccs(ctx
, graph
) < 0)
6690 return isl_schedule_node_free(node
);
6692 if (detect_wccs(ctx
, graph
) < 0)
6693 return isl_schedule_node_free(node
);
6697 return compute_component_schedule(node
, graph
, 1);
6699 return compute_schedule_wcc(node
, graph
);
6702 /* Compute a schedule on sc->domain that respects the given schedule
6705 * In particular, the schedule respects all the validity dependences.
6706 * If the default isl scheduling algorithm is used, it tries to minimize
6707 * the dependence distances over the proximity dependences.
6708 * If Feautrier's scheduling algorithm is used, the proximity dependence
6709 * distances are only minimized during the extension to a full-dimensional
6712 * If there are any condition and conditional validity dependences,
6713 * then the conditional validity dependences may be violated inside
6714 * a tilable band, provided they have no adjacent non-local
6715 * condition dependences.
6717 __isl_give isl_schedule
*isl_schedule_constraints_compute_schedule(
6718 __isl_take isl_schedule_constraints
*sc
)
6720 isl_ctx
*ctx
= isl_schedule_constraints_get_ctx(sc
);
6721 struct isl_sched_graph graph
= { 0 };
6722 isl_schedule
*sched
;
6723 isl_schedule_node
*node
;
6724 isl_union_set
*domain
;
6726 sc
= isl_schedule_constraints_align_params(sc
);
6728 domain
= isl_schedule_constraints_get_domain(sc
);
6729 if (isl_union_set_n_set(domain
) == 0) {
6730 isl_schedule_constraints_free(sc
);
6731 return isl_schedule_from_domain(domain
);
6734 if (graph_init(&graph
, sc
) < 0)
6735 domain
= isl_union_set_free(domain
);
6737 node
= isl_schedule_node_from_domain(domain
);
6738 node
= isl_schedule_node_child(node
, 0);
6740 node
= compute_schedule(node
, &graph
);
6741 sched
= isl_schedule_node_get_schedule(node
);
6742 isl_schedule_node_free(node
);
6744 graph_free(ctx
, &graph
);
6745 isl_schedule_constraints_free(sc
);
6750 /* Compute a schedule for the given union of domains that respects
6751 * all the validity dependences and minimizes
6752 * the dependence distances over the proximity dependences.
6754 * This function is kept for backward compatibility.
6756 __isl_give isl_schedule
*isl_union_set_compute_schedule(
6757 __isl_take isl_union_set
*domain
,
6758 __isl_take isl_union_map
*validity
,
6759 __isl_take isl_union_map
*proximity
)
6761 isl_schedule_constraints
*sc
;
6763 sc
= isl_schedule_constraints_on_domain(domain
);
6764 sc
= isl_schedule_constraints_set_validity(sc
, validity
);
6765 sc
= isl_schedule_constraints_set_proximity(sc
, proximity
);
6767 return isl_schedule_constraints_compute_schedule(sc
);