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 coefficients of the variables of "node"
1557 * Within each node, the coefficients have the following order:
1559 * - c_i_n (if parametric)
1560 * - positive and negative parts of c_i_x
1562 static int node_var_coef_offset(struct isl_sched_node
*node
)
1564 return node
->start
+ 1 + node
->nparam
;
1567 /* Return the position of the pair of variables encoding
1568 * coefficient "i" of "node".
1570 * The order of these variable pairs is the opposite of
1571 * that of the coefficients, with 2 variables per coefficient.
1573 static int node_var_coef_pos(struct isl_sched_node
*node
, int i
)
1575 return node_var_coef_offset(node
) + 2 * (node
->nvar
- 1 - i
);
1578 /* Construct an isl_dim_map for mapping constraints on coefficients
1579 * for "node" to the corresponding positions in graph->lp.
1580 * "offset" is the offset of the coefficients for the variables
1581 * in the input constraints.
1582 * "s" is the sign of the mapping.
1584 * The input constraints are given in terms of the coefficients (c_0, c_n, c_x).
1585 * The mapping produced by this function essentially plugs in
1586 * (0, 0, c_i_x^+ - c_i_x^-) if s = 1 and
1587 * (0, 0, -c_i_x^+ + c_i_x^-) if s = -1.
1588 * In graph->lp, the c_i_x^- appear before their c_i_x^+ counterpart.
1589 * Furthermore, the order of these pairs is the opposite of that
1590 * of the corresponding coefficients.
1592 * The caller can extend the mapping to also map the other coefficients
1593 * (and therefore not plug in 0).
1595 static __isl_give isl_dim_map
*intra_dim_map(isl_ctx
*ctx
,
1596 struct isl_sched_graph
*graph
, struct isl_sched_node
*node
,
1601 isl_dim_map
*dim_map
;
1606 total
= isl_basic_set_total_dim(graph
->lp
);
1607 pos
= node_var_coef_pos(node
, 0);
1608 dim_map
= isl_dim_map_alloc(ctx
, total
);
1609 isl_dim_map_range(dim_map
, pos
, -2, offset
, 1, node
->nvar
, -s
);
1610 isl_dim_map_range(dim_map
, pos
+ 1, -2, offset
, 1, node
->nvar
, s
);
1615 /* Construct an isl_dim_map for mapping constraints on coefficients
1616 * for "src" (node i) and "dst" (node j) to the corresponding positions
1618 * "offset" is the offset of the coefficients for the variables of "src"
1619 * in the input constraints.
1620 * "s" is the sign of the mapping.
1622 * The input constraints are given in terms of the coefficients
1623 * (c_0, c_n, c_x, c_y).
1624 * The mapping produced by this function essentially plugs in
1625 * (c_j_0 - c_i_0, c_j_n - c_i_n,
1626 * -(c_i_x^+ - c_i_x^-), c_j_x^+ - c_j_x^-) if s = 1 and
1627 * (-c_j_0 + c_i_0, -c_j_n + c_i_n,
1628 * c_i_x^+ - c_i_x^-, -(c_j_x^+ - c_j_x^-)) if s = -1.
1629 * In graph->lp, the c_*^- appear before their c_*^+ counterpart.
1630 * Furthermore, the order of these pairs is the opposite of that
1631 * of the corresponding coefficients.
1633 * The caller can further extend the mapping.
1635 static __isl_give isl_dim_map
*inter_dim_map(isl_ctx
*ctx
,
1636 struct isl_sched_graph
*graph
, struct isl_sched_node
*src
,
1637 struct isl_sched_node
*dst
, int offset
, int s
)
1641 isl_dim_map
*dim_map
;
1646 total
= isl_basic_set_total_dim(graph
->lp
);
1647 dim_map
= isl_dim_map_alloc(ctx
, total
);
1649 isl_dim_map_range(dim_map
, dst
->start
, 0, 0, 0, 1, s
);
1650 isl_dim_map_range(dim_map
, dst
->start
+ 1, 1, 1, 1, dst
->nparam
, s
);
1651 pos
= node_var_coef_pos(dst
, 0);
1652 isl_dim_map_range(dim_map
, pos
, -2, offset
+ src
->nvar
, 1,
1654 isl_dim_map_range(dim_map
, pos
+ 1, -2, offset
+ src
->nvar
, 1,
1657 isl_dim_map_range(dim_map
, src
->start
, 0, 0, 0, 1, -s
);
1658 isl_dim_map_range(dim_map
, src
->start
+ 1, 1, 1, 1, src
->nparam
, -s
);
1659 pos
= node_var_coef_pos(src
, 0);
1660 isl_dim_map_range(dim_map
, pos
, -2, offset
, 1, src
->nvar
, s
);
1661 isl_dim_map_range(dim_map
, pos
+ 1, -2, offset
, 1, src
->nvar
, -s
);
1666 /* Add the constraints from "src" to "dst" using "dim_map",
1667 * after making sure there is enough room in "dst" for the extra constraints.
1669 static __isl_give isl_basic_set
*add_constraints_dim_map(
1670 __isl_take isl_basic_set
*dst
, __isl_take isl_basic_set
*src
,
1671 __isl_take isl_dim_map
*dim_map
)
1675 n_eq
= isl_basic_set_n_equality(src
);
1676 n_ineq
= isl_basic_set_n_inequality(src
);
1677 dst
= isl_basic_set_extend_constraints(dst
, n_eq
, n_ineq
);
1678 dst
= isl_basic_set_add_constraints_dim_map(dst
, src
, dim_map
);
1682 /* Add constraints to graph->lp that force validity for the given
1683 * dependence from a node i to itself.
1684 * That is, add constraints that enforce
1686 * (c_i_0 + c_i_n n + c_i_x y) - (c_i_0 + c_i_n n + c_i_x x)
1687 * = c_i_x (y - x) >= 0
1689 * for each (x,y) in R.
1690 * We obtain general constraints on coefficients (c_0, c_n, c_x)
1691 * of valid constraints for (y - x) and then plug in (0, 0, c_i_x^+ - c_i_x^-),
1692 * where c_i_x = c_i_x^+ - c_i_x^-, with c_i_x^+ and c_i_x^- non-negative.
1693 * In graph->lp, the c_i_x^- appear before their c_i_x^+ counterpart.
1695 static isl_stat
add_intra_validity_constraints(struct isl_sched_graph
*graph
,
1696 struct isl_sched_edge
*edge
)
1699 isl_map
*map
= isl_map_copy(edge
->map
);
1700 isl_ctx
*ctx
= isl_map_get_ctx(map
);
1701 isl_dim_map
*dim_map
;
1702 isl_basic_set
*coef
;
1703 struct isl_sched_node
*node
= edge
->src
;
1705 coef
= intra_coefficients(graph
, node
, map
);
1707 offset
= coef_var_offset(coef
);
1710 return isl_stat_error
;
1712 dim_map
= intra_dim_map(ctx
, graph
, node
, offset
, 1);
1713 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
1718 /* Add constraints to graph->lp that force validity for the given
1719 * dependence from node i to node j.
1720 * That is, add constraints that enforce
1722 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) >= 0
1724 * for each (x,y) in R.
1725 * We obtain general constraints on coefficients (c_0, c_n, c_x, c_y)
1726 * of valid constraints for R and then plug in
1727 * (c_j_0 - c_i_0, c_j_n - c_i_n, -(c_i_x^+ - c_i_x^-), c_j_x^+ - c_j_x^-),
1728 * where c_* = c_*^+ - c_*^-, with c_*^+ and c_*^- non-negative.
1729 * In graph->lp, the c_*^- appear before their c_*^+ counterpart.
1731 static isl_stat
add_inter_validity_constraints(struct isl_sched_graph
*graph
,
1732 struct isl_sched_edge
*edge
)
1737 isl_dim_map
*dim_map
;
1738 isl_basic_set
*coef
;
1739 struct isl_sched_node
*src
= edge
->src
;
1740 struct isl_sched_node
*dst
= edge
->dst
;
1743 return isl_stat_error
;
1745 map
= isl_map_copy(edge
->map
);
1746 ctx
= isl_map_get_ctx(map
);
1747 coef
= inter_coefficients(graph
, edge
, map
);
1749 offset
= coef_var_offset(coef
);
1752 return isl_stat_error
;
1754 dim_map
= inter_dim_map(ctx
, graph
, src
, dst
, offset
, 1);
1756 edge
->start
= graph
->lp
->n_ineq
;
1757 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
1759 return isl_stat_error
;
1760 edge
->end
= graph
->lp
->n_ineq
;
1765 /* Add constraints to graph->lp that bound the dependence distance for the given
1766 * dependence from a node i to itself.
1767 * If s = 1, we add the constraint
1769 * c_i_x (y - x) <= m_0 + m_n n
1773 * -c_i_x (y - x) + m_0 + m_n n >= 0
1775 * for each (x,y) in R.
1776 * If s = -1, we add the constraint
1778 * -c_i_x (y - x) <= m_0 + m_n n
1782 * c_i_x (y - x) + m_0 + m_n n >= 0
1784 * for each (x,y) in R.
1785 * We obtain general constraints on coefficients (c_0, c_n, c_x)
1786 * of valid constraints for (y - x) and then plug in (m_0, m_n, -s * c_i_x),
1787 * with each coefficient (except m_0) represented as a pair of non-negative
1791 * If "local" is set, then we add constraints
1793 * c_i_x (y - x) <= 0
1797 * -c_i_x (y - x) <= 0
1799 * instead, forcing the dependence distance to be (less than or) equal to 0.
1800 * That is, we plug in (0, 0, -s * c_i_x),
1801 * Note that dependences marked local are treated as validity constraints
1802 * by add_all_validity_constraints and therefore also have
1803 * their distances bounded by 0 from below.
1805 static isl_stat
add_intra_proximity_constraints(struct isl_sched_graph
*graph
,
1806 struct isl_sched_edge
*edge
, int s
, int local
)
1810 isl_map
*map
= isl_map_copy(edge
->map
);
1811 isl_ctx
*ctx
= isl_map_get_ctx(map
);
1812 isl_dim_map
*dim_map
;
1813 isl_basic_set
*coef
;
1814 struct isl_sched_node
*node
= edge
->src
;
1816 coef
= intra_coefficients(graph
, node
, map
);
1818 offset
= coef_var_offset(coef
);
1821 return isl_stat_error
;
1823 nparam
= isl_space_dim(node
->space
, isl_dim_param
);
1824 dim_map
= intra_dim_map(ctx
, graph
, node
, offset
, -s
);
1827 isl_dim_map_range(dim_map
, 1, 0, 0, 0, 1, 1);
1828 isl_dim_map_range(dim_map
, 4, 2, 1, 1, nparam
, -1);
1829 isl_dim_map_range(dim_map
, 5, 2, 1, 1, nparam
, 1);
1831 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
1836 /* Add constraints to graph->lp that bound the dependence distance for the given
1837 * dependence from node i to node j.
1838 * If s = 1, we add the constraint
1840 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x)
1845 * -(c_j_0 + c_j_n n + c_j_x y) + (c_i_0 + c_i_n n + c_i_x x) +
1848 * for each (x,y) in R.
1849 * If s = -1, we add the constraint
1851 * -((c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x))
1856 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) +
1859 * for each (x,y) in R.
1860 * We obtain general constraints on coefficients (c_0, c_n, c_x, c_y)
1861 * of valid constraints for R and then plug in
1862 * (m_0 - s*c_j_0 + s*c_i_0, m_n - s*c_j_n + s*c_i_n,
1863 * s*c_i_x, -s*c_j_x)
1864 * with each coefficient (except m_0, c_*_0 and c_*_n)
1865 * represented as a pair of non-negative coefficients.
1868 * If "local" is set (and s = 1), then we add constraints
1870 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) <= 0
1874 * -((c_j_0 + c_j_n n + c_j_x y) + (c_i_0 + c_i_n n + c_i_x x)) >= 0
1876 * instead, forcing the dependence distance to be (less than or) equal to 0.
1877 * That is, we plug in
1878 * (-s*c_j_0 + s*c_i_0, -s*c_j_n + s*c_i_n, s*c_i_x, -s*c_j_x).
1879 * Note that dependences marked local are treated as validity constraints
1880 * by add_all_validity_constraints and therefore also have
1881 * their distances bounded by 0 from below.
1883 static isl_stat
add_inter_proximity_constraints(struct isl_sched_graph
*graph
,
1884 struct isl_sched_edge
*edge
, int s
, int local
)
1888 isl_map
*map
= isl_map_copy(edge
->map
);
1889 isl_ctx
*ctx
= isl_map_get_ctx(map
);
1890 isl_dim_map
*dim_map
;
1891 isl_basic_set
*coef
;
1892 struct isl_sched_node
*src
= edge
->src
;
1893 struct isl_sched_node
*dst
= edge
->dst
;
1895 coef
= inter_coefficients(graph
, edge
, map
);
1897 offset
= coef_var_offset(coef
);
1900 return isl_stat_error
;
1902 nparam
= isl_space_dim(src
->space
, isl_dim_param
);
1903 dim_map
= inter_dim_map(ctx
, graph
, src
, dst
, offset
, -s
);
1906 isl_dim_map_range(dim_map
, 1, 0, 0, 0, 1, 1);
1907 isl_dim_map_range(dim_map
, 4, 2, 1, 1, nparam
, -1);
1908 isl_dim_map_range(dim_map
, 5, 2, 1, 1, nparam
, 1);
1911 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
1916 /* Add all validity constraints to graph->lp.
1918 * An edge that is forced to be local needs to have its dependence
1919 * distances equal to zero. We take care of bounding them by 0 from below
1920 * here. add_all_proximity_constraints takes care of bounding them by 0
1923 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
1924 * Otherwise, we ignore them.
1926 static int add_all_validity_constraints(struct isl_sched_graph
*graph
,
1927 int use_coincidence
)
1931 for (i
= 0; i
< graph
->n_edge
; ++i
) {
1932 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
1935 local
= is_local(edge
) ||
1936 (is_coincidence(edge
) && use_coincidence
);
1937 if (!is_validity(edge
) && !local
)
1939 if (edge
->src
!= edge
->dst
)
1941 if (add_intra_validity_constraints(graph
, edge
) < 0)
1945 for (i
= 0; i
< graph
->n_edge
; ++i
) {
1946 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
1949 local
= is_local(edge
) ||
1950 (is_coincidence(edge
) && use_coincidence
);
1951 if (!is_validity(edge
) && !local
)
1953 if (edge
->src
== edge
->dst
)
1955 if (add_inter_validity_constraints(graph
, edge
) < 0)
1962 /* Add constraints to graph->lp that bound the dependence distance
1963 * for all dependence relations.
1964 * If a given proximity dependence is identical to a validity
1965 * dependence, then the dependence distance is already bounded
1966 * from below (by zero), so we only need to bound the distance
1967 * from above. (This includes the case of "local" dependences
1968 * which are treated as validity dependence by add_all_validity_constraints.)
1969 * Otherwise, we need to bound the distance both from above and from below.
1971 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
1972 * Otherwise, we ignore them.
1974 static int add_all_proximity_constraints(struct isl_sched_graph
*graph
,
1975 int use_coincidence
)
1979 for (i
= 0; i
< graph
->n_edge
; ++i
) {
1980 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
1983 local
= is_local(edge
) ||
1984 (is_coincidence(edge
) && use_coincidence
);
1985 if (!is_proximity(edge
) && !local
)
1987 if (edge
->src
== edge
->dst
&&
1988 add_intra_proximity_constraints(graph
, edge
, 1, local
) < 0)
1990 if (edge
->src
!= edge
->dst
&&
1991 add_inter_proximity_constraints(graph
, edge
, 1, local
) < 0)
1993 if (is_validity(edge
) || local
)
1995 if (edge
->src
== edge
->dst
&&
1996 add_intra_proximity_constraints(graph
, edge
, -1, 0) < 0)
1998 if (edge
->src
!= edge
->dst
&&
1999 add_inter_proximity_constraints(graph
, edge
, -1, 0) < 0)
2006 /* Normalize the rows of "indep" such that all rows are lexicographically
2007 * positive and such that each row contains as many final zeros as possible,
2008 * given the choice for the previous rows.
2009 * Do this by performing elementary row operations.
2011 static __isl_give isl_mat
*normalize_independent(__isl_take isl_mat
*indep
)
2013 indep
= isl_mat_reverse_gauss(indep
);
2014 indep
= isl_mat_lexnonneg_rows(indep
);
2018 /* Compute a basis for the rows in the linear part of the schedule
2019 * and extend this basis to a full basis. The remaining rows
2020 * can then be used to force linear independence from the rows
2023 * In particular, given the schedule rows S, we compute
2028 * with H the Hermite normal form of S. That is, all but the
2029 * first rank columns of H are zero and so each row in S is
2030 * a linear combination of the first rank rows of Q.
2031 * The matrix Q can be used as a variable transformation
2032 * that isolates the directions of S in the first rank rows.
2033 * Transposing S U = H yields
2037 * with all but the first rank rows of H^T zero.
2038 * The last rows of U^T are therefore linear combinations
2039 * of schedule coefficients that are all zero on schedule
2040 * coefficients that are linearly dependent on the rows of S.
2041 * At least one of these combinations is non-zero on
2042 * linearly independent schedule coefficients.
2043 * The rows are normalized to involve as few of the last
2044 * coefficients as possible and to have a positive initial value.
2046 static int node_update_vmap(struct isl_sched_node
*node
)
2049 int n_row
= isl_mat_rows(node
->sched
);
2051 H
= isl_mat_sub_alloc(node
->sched
, 0, n_row
,
2052 1 + node
->nparam
, node
->nvar
);
2054 H
= isl_mat_left_hermite(H
, 0, &U
, &Q
);
2055 isl_mat_free(node
->indep
);
2056 isl_mat_free(node
->vmap
);
2058 node
->indep
= isl_mat_transpose(U
);
2059 node
->rank
= isl_mat_initial_non_zero_cols(H
);
2060 node
->indep
= isl_mat_drop_rows(node
->indep
, 0, node
->rank
);
2061 node
->indep
= normalize_independent(node
->indep
);
2064 if (!node
->indep
|| !node
->vmap
|| node
->rank
< 0)
2069 /* Is "edge" marked as a validity or a conditional validity edge?
2071 static int is_any_validity(struct isl_sched_edge
*edge
)
2073 return is_validity(edge
) || is_conditional_validity(edge
);
2076 /* How many times should we count the constraints in "edge"?
2078 * We count as follows
2079 * validity -> 1 (>= 0)
2080 * validity+proximity -> 2 (>= 0 and upper bound)
2081 * proximity -> 2 (lower and upper bound)
2082 * local(+any) -> 2 (>= 0 and <= 0)
2084 * If an edge is only marked conditional_validity then it counts
2085 * as zero since it is only checked afterwards.
2087 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2088 * Otherwise, we ignore them.
2090 static int edge_multiplicity(struct isl_sched_edge
*edge
, int use_coincidence
)
2092 if (is_proximity(edge
) || is_local(edge
))
2094 if (use_coincidence
&& is_coincidence(edge
))
2096 if (is_validity(edge
))
2101 /* Count the number of equality and inequality constraints
2102 * that will be added for the given map.
2104 * "use_coincidence" is set if we should take into account coincidence edges.
2106 static isl_stat
count_map_constraints(struct isl_sched_graph
*graph
,
2107 struct isl_sched_edge
*edge
, __isl_take isl_map
*map
,
2108 int *n_eq
, int *n_ineq
, int use_coincidence
)
2110 isl_basic_set
*coef
;
2111 int f
= edge_multiplicity(edge
, use_coincidence
);
2118 if (edge
->src
== edge
->dst
)
2119 coef
= intra_coefficients(graph
, edge
->src
, map
);
2121 coef
= inter_coefficients(graph
, edge
, map
);
2123 return isl_stat_error
;
2124 *n_eq
+= f
* isl_basic_set_n_equality(coef
);
2125 *n_ineq
+= f
* isl_basic_set_n_inequality(coef
);
2126 isl_basic_set_free(coef
);
2131 /* Count the number of equality and inequality constraints
2132 * that will be added to the main lp problem.
2133 * We count as follows
2134 * validity -> 1 (>= 0)
2135 * validity+proximity -> 2 (>= 0 and upper bound)
2136 * proximity -> 2 (lower and upper bound)
2137 * local(+any) -> 2 (>= 0 and <= 0)
2139 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2140 * Otherwise, we ignore them.
2142 static int count_constraints(struct isl_sched_graph
*graph
,
2143 int *n_eq
, int *n_ineq
, int use_coincidence
)
2147 *n_eq
= *n_ineq
= 0;
2148 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2149 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
2150 isl_map
*map
= isl_map_copy(edge
->map
);
2152 if (count_map_constraints(graph
, edge
, map
, n_eq
, n_ineq
,
2153 use_coincidence
) < 0)
2160 /* Count the number of constraints that will be added by
2161 * add_bound_constant_constraints to bound the values of the constant terms
2162 * and increment *n_eq and *n_ineq accordingly.
2164 * In practice, add_bound_constant_constraints only adds inequalities.
2166 static isl_stat
count_bound_constant_constraints(isl_ctx
*ctx
,
2167 struct isl_sched_graph
*graph
, int *n_eq
, int *n_ineq
)
2169 if (isl_options_get_schedule_max_constant_term(ctx
) == -1)
2172 *n_ineq
+= graph
->n
;
2177 /* Add constraints to bound the values of the constant terms in the schedule,
2178 * if requested by the user.
2180 * The maximal value of the constant terms is defined by the option
2181 * "schedule_max_constant_term".
2183 * Within each node, the coefficients have the following order:
2185 * - c_i_n (if parametric)
2186 * - positive and negative parts of c_i_x
2188 static isl_stat
add_bound_constant_constraints(isl_ctx
*ctx
,
2189 struct isl_sched_graph
*graph
)
2195 max
= isl_options_get_schedule_max_constant_term(ctx
);
2199 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2201 for (i
= 0; i
< graph
->n
; ++i
) {
2202 struct isl_sched_node
*node
= &graph
->node
[i
];
2203 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2205 return isl_stat_error
;
2206 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
2207 isl_int_set_si(graph
->lp
->ineq
[k
][1 + node
->start
], -1);
2208 isl_int_set_si(graph
->lp
->ineq
[k
][0], max
);
2214 /* Count the number of constraints that will be added by
2215 * add_bound_coefficient_constraints and increment *n_eq and *n_ineq
2218 * In practice, add_bound_coefficient_constraints only adds inequalities.
2220 static int count_bound_coefficient_constraints(isl_ctx
*ctx
,
2221 struct isl_sched_graph
*graph
, int *n_eq
, int *n_ineq
)
2225 if (isl_options_get_schedule_max_coefficient(ctx
) == -1 &&
2226 !isl_options_get_schedule_treat_coalescing(ctx
))
2229 for (i
= 0; i
< graph
->n
; ++i
)
2230 *n_ineq
+= graph
->node
[i
].nparam
+ 2 * graph
->node
[i
].nvar
;
2235 /* Add constraints to graph->lp that bound the values of
2236 * the parameter schedule coefficients of "node" to "max" and
2237 * the variable schedule coefficients to the corresponding entry
2239 * In either case, a negative value means that no bound needs to be imposed.
2241 * For parameter coefficients, this amounts to adding a constraint
2249 * The variables coefficients are, however, not represented directly.
2250 * Instead, the variable coefficients c_x are written as differences
2251 * c_x = c_x^+ - c_x^-.
2254 * -max_i <= c_x_i <= max_i
2258 * -max_i <= c_x_i^+ - c_x_i^- <= max_i
2262 * -(c_x_i^+ - c_x_i^-) + max_i >= 0
2263 * c_x_i^+ - c_x_i^- + max_i >= 0
2265 static isl_stat
node_add_coefficient_constraints(isl_ctx
*ctx
,
2266 struct isl_sched_graph
*graph
, struct isl_sched_node
*node
, int max
)
2272 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2274 for (j
= 0; j
< node
->nparam
; ++j
) {
2280 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2282 return isl_stat_error
;
2283 dim
= 1 + node
->start
+ 1 + j
;
2284 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
2285 isl_int_set_si(graph
->lp
->ineq
[k
][dim
], -1);
2286 isl_int_set_si(graph
->lp
->ineq
[k
][0], max
);
2289 ineq
= isl_vec_alloc(ctx
, 1 + total
);
2290 ineq
= isl_vec_clr(ineq
);
2292 return isl_stat_error
;
2293 for (i
= 0; i
< node
->nvar
; ++i
) {
2294 int pos
= 1 + node_var_coef_pos(node
, i
);
2296 if (isl_int_is_neg(node
->max
->el
[i
]))
2299 isl_int_set_si(ineq
->el
[pos
], 1);
2300 isl_int_set_si(ineq
->el
[pos
+ 1], -1);
2301 isl_int_set(ineq
->el
[0], node
->max
->el
[i
]);
2303 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2306 isl_seq_cpy(graph
->lp
->ineq
[k
], ineq
->el
, 1 + total
);
2308 isl_seq_neg(ineq
->el
+ pos
, ineq
->el
+ pos
+ 2 * i
, 2);
2309 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2312 isl_seq_cpy(graph
->lp
->ineq
[k
], ineq
->el
, 1 + total
);
2319 return isl_stat_error
;
2322 /* Add constraints that bound the values of the variable and parameter
2323 * coefficients of the schedule.
2325 * The maximal value of the coefficients is defined by the option
2326 * 'schedule_max_coefficient' and the entries in node->max.
2327 * These latter entries are only set if either the schedule_max_coefficient
2328 * option or the schedule_treat_coalescing option is set.
2330 static isl_stat
add_bound_coefficient_constraints(isl_ctx
*ctx
,
2331 struct isl_sched_graph
*graph
)
2336 max
= isl_options_get_schedule_max_coefficient(ctx
);
2338 if (max
== -1 && !isl_options_get_schedule_treat_coalescing(ctx
))
2341 for (i
= 0; i
< graph
->n
; ++i
) {
2342 struct isl_sched_node
*node
= &graph
->node
[i
];
2344 if (node_add_coefficient_constraints(ctx
, graph
, node
, max
) < 0)
2345 return isl_stat_error
;
2351 /* Add a constraint to graph->lp that equates the value at position
2352 * "sum_pos" to the sum of the "n" values starting at "first".
2354 static isl_stat
add_sum_constraint(struct isl_sched_graph
*graph
,
2355 int sum_pos
, int first
, int n
)
2360 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2362 k
= isl_basic_set_alloc_equality(graph
->lp
);
2364 return isl_stat_error
;
2365 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2366 isl_int_set_si(graph
->lp
->eq
[k
][1 + sum_pos
], -1);
2367 for (i
= 0; i
< n
; ++i
)
2368 isl_int_set_si(graph
->lp
->eq
[k
][1 + first
+ i
], 1);
2373 /* Add a constraint to graph->lp that equates the value at position
2374 * "sum_pos" to the sum of the parameter coefficients of all nodes.
2376 * Within each node, the coefficients have the following order:
2378 * - c_i_n (if parametric)
2379 * - positive and negative parts of c_i_x
2381 static isl_stat
add_param_sum_constraint(struct isl_sched_graph
*graph
,
2387 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2389 k
= isl_basic_set_alloc_equality(graph
->lp
);
2391 return isl_stat_error
;
2392 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2393 isl_int_set_si(graph
->lp
->eq
[k
][1 + sum_pos
], -1);
2394 for (i
= 0; i
< graph
->n
; ++i
) {
2395 int pos
= 1 + graph
->node
[i
].start
+ 1;
2397 for (j
= 0; j
< graph
->node
[i
].nparam
; ++j
)
2398 isl_int_set_si(graph
->lp
->eq
[k
][pos
+ j
], 1);
2404 /* Add a constraint to graph->lp that equates the value at position
2405 * "sum_pos" to the sum of the variable coefficients of all nodes.
2407 static isl_stat
add_var_sum_constraint(struct isl_sched_graph
*graph
,
2413 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2415 k
= isl_basic_set_alloc_equality(graph
->lp
);
2417 return isl_stat_error
;
2418 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2419 isl_int_set_si(graph
->lp
->eq
[k
][1 + sum_pos
], -1);
2420 for (i
= 0; i
< graph
->n
; ++i
) {
2421 struct isl_sched_node
*node
= &graph
->node
[i
];
2422 int pos
= 1 + node_var_coef_offset(node
);
2424 for (j
= 0; j
< 2 * node
->nvar
; ++j
)
2425 isl_int_set_si(graph
->lp
->eq
[k
][pos
+ j
], 1);
2431 /* Construct an ILP problem for finding schedule coefficients
2432 * that result in non-negative, but small dependence distances
2433 * over all dependences.
2434 * In particular, the dependence distances over proximity edges
2435 * are bounded by m_0 + m_n n and we compute schedule coefficients
2436 * with small values (preferably zero) of m_n and m_0.
2438 * All variables of the ILP are non-negative. The actual coefficients
2439 * may be negative, so each coefficient is represented as the difference
2440 * of two non-negative variables. The negative part always appears
2441 * immediately before the positive part.
2442 * Other than that, the variables have the following order
2444 * - sum of positive and negative parts of m_n coefficients
2446 * - sum of all c_n coefficients
2447 * (unconstrained when computing non-parametric schedules)
2448 * - sum of positive and negative parts of all c_x coefficients
2449 * - positive and negative parts of m_n coefficients
2452 * - c_i_n (if parametric)
2453 * - positive and negative parts of c_i_x, in opposite order
2455 * The constraints are those from the edges plus two or three equalities
2456 * to express the sums.
2458 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2459 * Otherwise, we ignore them.
2461 static isl_stat
setup_lp(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
2462 int use_coincidence
)
2472 parametric
= ctx
->opt
->schedule_parametric
;
2473 nparam
= isl_space_dim(graph
->node
[0].space
, isl_dim_param
);
2475 total
= param_pos
+ 2 * nparam
;
2476 for (i
= 0; i
< graph
->n
; ++i
) {
2477 struct isl_sched_node
*node
= &graph
->node
[graph
->sorted
[i
]];
2478 if (node_update_vmap(node
) < 0)
2479 return isl_stat_error
;
2480 node
->start
= total
;
2481 total
+= 1 + node
->nparam
+ 2 * node
->nvar
;
2484 if (count_constraints(graph
, &n_eq
, &n_ineq
, use_coincidence
) < 0)
2485 return isl_stat_error
;
2486 if (count_bound_constant_constraints(ctx
, graph
, &n_eq
, &n_ineq
) < 0)
2487 return isl_stat_error
;
2488 if (count_bound_coefficient_constraints(ctx
, graph
, &n_eq
, &n_ineq
) < 0)
2489 return isl_stat_error
;
2491 space
= isl_space_set_alloc(ctx
, 0, total
);
2492 isl_basic_set_free(graph
->lp
);
2493 n_eq
+= 2 + parametric
;
2495 graph
->lp
= isl_basic_set_alloc_space(space
, 0, n_eq
, n_ineq
);
2497 if (add_sum_constraint(graph
, 0, param_pos
, 2 * nparam
) < 0)
2498 return isl_stat_error
;
2499 if (parametric
&& add_param_sum_constraint(graph
, 2) < 0)
2500 return isl_stat_error
;
2501 if (add_var_sum_constraint(graph
, 3) < 0)
2502 return isl_stat_error
;
2503 if (add_bound_constant_constraints(ctx
, graph
) < 0)
2504 return isl_stat_error
;
2505 if (add_bound_coefficient_constraints(ctx
, graph
) < 0)
2506 return isl_stat_error
;
2507 if (add_all_validity_constraints(graph
, use_coincidence
) < 0)
2508 return isl_stat_error
;
2509 if (add_all_proximity_constraints(graph
, use_coincidence
) < 0)
2510 return isl_stat_error
;
2515 /* Analyze the conflicting constraint found by
2516 * isl_tab_basic_set_non_trivial_lexmin. If it corresponds to the validity
2517 * constraint of one of the edges between distinct nodes, living, moreover
2518 * in distinct SCCs, then record the source and sink SCC as this may
2519 * be a good place to cut between SCCs.
2521 static int check_conflict(int con
, void *user
)
2524 struct isl_sched_graph
*graph
= user
;
2526 if (graph
->src_scc
>= 0)
2529 con
-= graph
->lp
->n_eq
;
2531 if (con
>= graph
->lp
->n_ineq
)
2534 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2535 if (!is_validity(&graph
->edge
[i
]))
2537 if (graph
->edge
[i
].src
== graph
->edge
[i
].dst
)
2539 if (graph
->edge
[i
].src
->scc
== graph
->edge
[i
].dst
->scc
)
2541 if (graph
->edge
[i
].start
> con
)
2543 if (graph
->edge
[i
].end
<= con
)
2545 graph
->src_scc
= graph
->edge
[i
].src
->scc
;
2546 graph
->dst_scc
= graph
->edge
[i
].dst
->scc
;
2552 /* Check whether the next schedule row of the given node needs to be
2553 * non-trivial. Lower-dimensional domains may have some trivial rows,
2554 * but as soon as the number of remaining required non-trivial rows
2555 * is as large as the number or remaining rows to be computed,
2556 * all remaining rows need to be non-trivial.
2558 static int needs_row(struct isl_sched_graph
*graph
, struct isl_sched_node
*node
)
2560 return node
->nvar
- node
->rank
>= graph
->maxvar
- graph
->n_row
;
2563 /* Construct a non-triviality region with triviality directions
2564 * corresponding to the rows of "indep".
2565 * The rows of "indep" are expressed in terms of the schedule coefficients c_i,
2566 * while the triviality directions are expressed in terms of
2567 * pairs of non-negative variables c^+_i - c^-_i, with c^-_i appearing
2568 * before c^+_i. Furthermore,
2569 * the pairs of non-negative variables representing the coefficients
2570 * are stored in the opposite order.
2572 static __isl_give isl_mat
*construct_trivial(__isl_keep isl_mat
*indep
)
2581 ctx
= isl_mat_get_ctx(indep
);
2582 n
= isl_mat_rows(indep
);
2583 n_var
= isl_mat_cols(indep
);
2584 mat
= isl_mat_alloc(ctx
, n
, 2 * n_var
);
2587 for (i
= 0; i
< n
; ++i
) {
2588 for (j
= 0; j
< n_var
; ++j
) {
2589 int nj
= n_var
- 1 - j
;
2590 isl_int_neg(mat
->row
[i
][2 * nj
], indep
->row
[i
][j
]);
2591 isl_int_set(mat
->row
[i
][2 * nj
+ 1], indep
->row
[i
][j
]);
2598 /* Solve the ILP problem constructed in setup_lp.
2599 * For each node such that all the remaining rows of its schedule
2600 * need to be non-trivial, we construct a non-triviality region.
2601 * This region imposes that the next row is independent of previous rows.
2602 * In particular, the non-triviality region enforces that at least
2603 * one of the linear combinations in the rows of node->indep is non-zero.
2605 static __isl_give isl_vec
*solve_lp(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2611 for (i
= 0; i
< graph
->n
; ++i
) {
2612 struct isl_sched_node
*node
= &graph
->node
[i
];
2615 graph
->region
[i
].pos
= node_var_coef_offset(node
);
2616 if (needs_row(graph
, node
))
2617 trivial
= construct_trivial(node
->indep
);
2619 trivial
= isl_mat_zero(ctx
, 0, 0);
2620 graph
->region
[i
].trivial
= trivial
;
2622 lp
= isl_basic_set_copy(graph
->lp
);
2623 sol
= isl_tab_basic_set_non_trivial_lexmin(lp
, 2, graph
->n
,
2624 graph
->region
, &check_conflict
, graph
);
2625 for (i
= 0; i
< graph
->n
; ++i
)
2626 isl_mat_free(graph
->region
[i
].trivial
);
2630 /* Extract the coefficients for the variables of "node" from "sol".
2632 * Each schedule coefficient c_i_x is represented as the difference
2633 * between two non-negative variables c_i_x^+ - c_i_x^-.
2634 * The c_i_x^- appear before their c_i_x^+ counterpart.
2635 * Furthermore, the order of these pairs is the opposite of that
2636 * of the corresponding coefficients.
2638 * Return c_i_x = c_i_x^+ - c_i_x^-
2640 static __isl_give isl_vec
*extract_var_coef(struct isl_sched_node
*node
,
2641 __isl_keep isl_vec
*sol
)
2649 csol
= isl_vec_alloc(isl_vec_get_ctx(sol
), node
->nvar
);
2653 pos
= 1 + node_var_coef_offset(node
);
2654 for (i
= 0; i
< node
->nvar
; ++i
)
2655 isl_int_sub(csol
->el
[node
->nvar
- 1 - i
],
2656 sol
->el
[pos
+ 2 * i
+ 1], sol
->el
[pos
+ 2 * i
]);
2661 /* Update the schedules of all nodes based on the given solution
2662 * of the LP problem.
2663 * The new row is added to the current band.
2664 * All possibly negative coefficients are encoded as a difference
2665 * of two non-negative variables, so we need to perform the subtraction
2668 * If coincident is set, then the caller guarantees that the new
2669 * row satisfies the coincidence constraints.
2671 static int update_schedule(struct isl_sched_graph
*graph
,
2672 __isl_take isl_vec
*sol
, int coincident
)
2675 isl_vec
*csol
= NULL
;
2680 isl_die(sol
->ctx
, isl_error_internal
,
2681 "no solution found", goto error
);
2682 if (graph
->n_total_row
>= graph
->max_row
)
2683 isl_die(sol
->ctx
, isl_error_internal
,
2684 "too many schedule rows", goto error
);
2686 for (i
= 0; i
< graph
->n
; ++i
) {
2687 struct isl_sched_node
*node
= &graph
->node
[i
];
2688 int pos
= node
->start
;
2689 int row
= isl_mat_rows(node
->sched
);
2692 csol
= extract_var_coef(node
, sol
);
2696 isl_map_free(node
->sched_map
);
2697 node
->sched_map
= NULL
;
2698 node
->sched
= isl_mat_add_rows(node
->sched
, 1);
2701 for (j
= 0; j
< 1 + node
->nparam
; ++j
)
2702 node
->sched
= isl_mat_set_element(node
->sched
,
2703 row
, j
, sol
->el
[1 + pos
+ j
]);
2704 for (j
= 0; j
< node
->nvar
; ++j
)
2705 node
->sched
= isl_mat_set_element(node
->sched
,
2706 row
, 1 + node
->nparam
+ j
, csol
->el
[j
]);
2707 node
->coincident
[graph
->n_total_row
] = coincident
;
2713 graph
->n_total_row
++;
2722 /* Convert row "row" of node->sched into an isl_aff living in "ls"
2723 * and return this isl_aff.
2725 static __isl_give isl_aff
*extract_schedule_row(__isl_take isl_local_space
*ls
,
2726 struct isl_sched_node
*node
, int row
)
2734 aff
= isl_aff_zero_on_domain(ls
);
2735 isl_mat_get_element(node
->sched
, row
, 0, &v
);
2736 aff
= isl_aff_set_constant(aff
, v
);
2737 for (j
= 0; j
< node
->nparam
; ++j
) {
2738 isl_mat_get_element(node
->sched
, row
, 1 + j
, &v
);
2739 aff
= isl_aff_set_coefficient(aff
, isl_dim_param
, j
, v
);
2741 for (j
= 0; j
< node
->nvar
; ++j
) {
2742 isl_mat_get_element(node
->sched
, row
, 1 + node
->nparam
+ j
, &v
);
2743 aff
= isl_aff_set_coefficient(aff
, isl_dim_in
, j
, v
);
2751 /* Convert the "n" rows starting at "first" of node->sched into a multi_aff
2752 * and return this multi_aff.
2754 * The result is defined over the uncompressed node domain.
2756 static __isl_give isl_multi_aff
*node_extract_partial_schedule_multi_aff(
2757 struct isl_sched_node
*node
, int first
, int n
)
2761 isl_local_space
*ls
;
2768 nrow
= isl_mat_rows(node
->sched
);
2769 if (node
->compressed
)
2770 space
= isl_multi_aff_get_domain_space(node
->decompress
);
2772 space
= isl_space_copy(node
->space
);
2773 ls
= isl_local_space_from_space(isl_space_copy(space
));
2774 space
= isl_space_from_domain(space
);
2775 space
= isl_space_add_dims(space
, isl_dim_out
, n
);
2776 ma
= isl_multi_aff_zero(space
);
2778 for (i
= first
; i
< first
+ n
; ++i
) {
2779 aff
= extract_schedule_row(isl_local_space_copy(ls
), node
, i
);
2780 ma
= isl_multi_aff_set_aff(ma
, i
- first
, aff
);
2783 isl_local_space_free(ls
);
2785 if (node
->compressed
)
2786 ma
= isl_multi_aff_pullback_multi_aff(ma
,
2787 isl_multi_aff_copy(node
->compress
));
2792 /* Convert node->sched into a multi_aff and return this multi_aff.
2794 * The result is defined over the uncompressed node domain.
2796 static __isl_give isl_multi_aff
*node_extract_schedule_multi_aff(
2797 struct isl_sched_node
*node
)
2801 nrow
= isl_mat_rows(node
->sched
);
2802 return node_extract_partial_schedule_multi_aff(node
, 0, nrow
);
2805 /* Convert node->sched into a map and return this map.
2807 * The result is cached in node->sched_map, which needs to be released
2808 * whenever node->sched is updated.
2809 * It is defined over the uncompressed node domain.
2811 static __isl_give isl_map
*node_extract_schedule(struct isl_sched_node
*node
)
2813 if (!node
->sched_map
) {
2816 ma
= node_extract_schedule_multi_aff(node
);
2817 node
->sched_map
= isl_map_from_multi_aff(ma
);
2820 return isl_map_copy(node
->sched_map
);
2823 /* Construct a map that can be used to update a dependence relation
2824 * based on the current schedule.
2825 * That is, construct a map expressing that source and sink
2826 * are executed within the same iteration of the current schedule.
2827 * This map can then be intersected with the dependence relation.
2828 * This is not the most efficient way, but this shouldn't be a critical
2831 static __isl_give isl_map
*specializer(struct isl_sched_node
*src
,
2832 struct isl_sched_node
*dst
)
2834 isl_map
*src_sched
, *dst_sched
;
2836 src_sched
= node_extract_schedule(src
);
2837 dst_sched
= node_extract_schedule(dst
);
2838 return isl_map_apply_range(src_sched
, isl_map_reverse(dst_sched
));
2841 /* Intersect the domains of the nested relations in domain and range
2842 * of "umap" with "map".
2844 static __isl_give isl_union_map
*intersect_domains(
2845 __isl_take isl_union_map
*umap
, __isl_keep isl_map
*map
)
2847 isl_union_set
*uset
;
2849 umap
= isl_union_map_zip(umap
);
2850 uset
= isl_union_set_from_set(isl_map_wrap(isl_map_copy(map
)));
2851 umap
= isl_union_map_intersect_domain(umap
, uset
);
2852 umap
= isl_union_map_zip(umap
);
2856 /* Update the dependence relation of the given edge based
2857 * on the current schedule.
2858 * If the dependence is carried completely by the current schedule, then
2859 * it is removed from the edge_tables. It is kept in the list of edges
2860 * as otherwise all edge_tables would have to be recomputed.
2862 static int update_edge(struct isl_sched_graph
*graph
,
2863 struct isl_sched_edge
*edge
)
2868 id
= specializer(edge
->src
, edge
->dst
);
2869 edge
->map
= isl_map_intersect(edge
->map
, isl_map_copy(id
));
2873 if (edge
->tagged_condition
) {
2874 edge
->tagged_condition
=
2875 intersect_domains(edge
->tagged_condition
, id
);
2876 if (!edge
->tagged_condition
)
2879 if (edge
->tagged_validity
) {
2880 edge
->tagged_validity
=
2881 intersect_domains(edge
->tagged_validity
, id
);
2882 if (!edge
->tagged_validity
)
2886 empty
= isl_map_plain_is_empty(edge
->map
);
2890 graph_remove_edge(graph
, edge
);
2899 /* Does the domain of "umap" intersect "uset"?
2901 static int domain_intersects(__isl_keep isl_union_map
*umap
,
2902 __isl_keep isl_union_set
*uset
)
2906 umap
= isl_union_map_copy(umap
);
2907 umap
= isl_union_map_intersect_domain(umap
, isl_union_set_copy(uset
));
2908 empty
= isl_union_map_is_empty(umap
);
2909 isl_union_map_free(umap
);
2911 return empty
< 0 ? -1 : !empty
;
2914 /* Does the range of "umap" intersect "uset"?
2916 static int range_intersects(__isl_keep isl_union_map
*umap
,
2917 __isl_keep isl_union_set
*uset
)
2921 umap
= isl_union_map_copy(umap
);
2922 umap
= isl_union_map_intersect_range(umap
, isl_union_set_copy(uset
));
2923 empty
= isl_union_map_is_empty(umap
);
2924 isl_union_map_free(umap
);
2926 return empty
< 0 ? -1 : !empty
;
2929 /* Are the condition dependences of "edge" local with respect to
2930 * the current schedule?
2932 * That is, are domain and range of the condition dependences mapped
2933 * to the same point?
2935 * In other words, is the condition false?
2937 static int is_condition_false(struct isl_sched_edge
*edge
)
2939 isl_union_map
*umap
;
2940 isl_map
*map
, *sched
, *test
;
2943 empty
= isl_union_map_is_empty(edge
->tagged_condition
);
2944 if (empty
< 0 || empty
)
2947 umap
= isl_union_map_copy(edge
->tagged_condition
);
2948 umap
= isl_union_map_zip(umap
);
2949 umap
= isl_union_set_unwrap(isl_union_map_domain(umap
));
2950 map
= isl_map_from_union_map(umap
);
2952 sched
= node_extract_schedule(edge
->src
);
2953 map
= isl_map_apply_domain(map
, sched
);
2954 sched
= node_extract_schedule(edge
->dst
);
2955 map
= isl_map_apply_range(map
, sched
);
2957 test
= isl_map_identity(isl_map_get_space(map
));
2958 local
= isl_map_is_subset(map
, test
);
2965 /* For each conditional validity constraint that is adjacent
2966 * to a condition with domain in condition_source or range in condition_sink,
2967 * turn it into an unconditional validity constraint.
2969 static int unconditionalize_adjacent_validity(struct isl_sched_graph
*graph
,
2970 __isl_take isl_union_set
*condition_source
,
2971 __isl_take isl_union_set
*condition_sink
)
2975 condition_source
= isl_union_set_coalesce(condition_source
);
2976 condition_sink
= isl_union_set_coalesce(condition_sink
);
2978 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2980 isl_union_map
*validity
;
2982 if (!is_conditional_validity(&graph
->edge
[i
]))
2984 if (is_validity(&graph
->edge
[i
]))
2987 validity
= graph
->edge
[i
].tagged_validity
;
2988 adjacent
= domain_intersects(validity
, condition_sink
);
2989 if (adjacent
>= 0 && !adjacent
)
2990 adjacent
= range_intersects(validity
, condition_source
);
2996 set_validity(&graph
->edge
[i
]);
2999 isl_union_set_free(condition_source
);
3000 isl_union_set_free(condition_sink
);
3003 isl_union_set_free(condition_source
);
3004 isl_union_set_free(condition_sink
);
3008 /* Update the dependence relations of all edges based on the current schedule
3009 * and enforce conditional validity constraints that are adjacent
3010 * to satisfied condition constraints.
3012 * First check if any of the condition constraints are satisfied
3013 * (i.e., not local to the outer schedule) and keep track of
3014 * their domain and range.
3015 * Then update all dependence relations (which removes the non-local
3017 * Finally, if any condition constraints turned out to be satisfied,
3018 * then turn all adjacent conditional validity constraints into
3019 * unconditional validity constraints.
3021 static int update_edges(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
3025 isl_union_set
*source
, *sink
;
3027 source
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
3028 sink
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
3029 for (i
= 0; i
< graph
->n_edge
; ++i
) {
3031 isl_union_set
*uset
;
3032 isl_union_map
*umap
;
3034 if (!is_condition(&graph
->edge
[i
]))
3036 if (is_local(&graph
->edge
[i
]))
3038 local
= is_condition_false(&graph
->edge
[i
]);
3046 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_condition
);
3047 uset
= isl_union_map_domain(umap
);
3048 source
= isl_union_set_union(source
, uset
);
3050 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_condition
);
3051 uset
= isl_union_map_range(umap
);
3052 sink
= isl_union_set_union(sink
, uset
);
3055 for (i
= graph
->n_edge
- 1; i
>= 0; --i
) {
3056 if (update_edge(graph
, &graph
->edge
[i
]) < 0)
3061 return unconditionalize_adjacent_validity(graph
, source
, sink
);
3063 isl_union_set_free(source
);
3064 isl_union_set_free(sink
);
3067 isl_union_set_free(source
);
3068 isl_union_set_free(sink
);
3072 static void next_band(struct isl_sched_graph
*graph
)
3074 graph
->band_start
= graph
->n_total_row
;
3077 /* Return the union of the universe domains of the nodes in "graph"
3078 * that satisfy "pred".
3080 static __isl_give isl_union_set
*isl_sched_graph_domain(isl_ctx
*ctx
,
3081 struct isl_sched_graph
*graph
,
3082 int (*pred
)(struct isl_sched_node
*node
, int data
), int data
)
3088 for (i
= 0; i
< graph
->n
; ++i
)
3089 if (pred(&graph
->node
[i
], data
))
3093 isl_die(ctx
, isl_error_internal
,
3094 "empty component", return NULL
);
3096 set
= isl_set_universe(isl_space_copy(graph
->node
[i
].space
));
3097 dom
= isl_union_set_from_set(set
);
3099 for (i
= i
+ 1; i
< graph
->n
; ++i
) {
3100 if (!pred(&graph
->node
[i
], data
))
3102 set
= isl_set_universe(isl_space_copy(graph
->node
[i
].space
));
3103 dom
= isl_union_set_union(dom
, isl_union_set_from_set(set
));
3109 /* Return a list of unions of universe domains, where each element
3110 * in the list corresponds to an SCC (or WCC) indexed by node->scc.
3112 static __isl_give isl_union_set_list
*extract_sccs(isl_ctx
*ctx
,
3113 struct isl_sched_graph
*graph
)
3116 isl_union_set_list
*filters
;
3118 filters
= isl_union_set_list_alloc(ctx
, graph
->scc
);
3119 for (i
= 0; i
< graph
->scc
; ++i
) {
3122 dom
= isl_sched_graph_domain(ctx
, graph
, &node_scc_exactly
, i
);
3123 filters
= isl_union_set_list_add(filters
, dom
);
3129 /* Return a list of two unions of universe domains, one for the SCCs up
3130 * to and including graph->src_scc and another for the other SCCs.
3132 static __isl_give isl_union_set_list
*extract_split(isl_ctx
*ctx
,
3133 struct isl_sched_graph
*graph
)
3136 isl_union_set_list
*filters
;
3138 filters
= isl_union_set_list_alloc(ctx
, 2);
3139 dom
= isl_sched_graph_domain(ctx
, graph
,
3140 &node_scc_at_most
, graph
->src_scc
);
3141 filters
= isl_union_set_list_add(filters
, dom
);
3142 dom
= isl_sched_graph_domain(ctx
, graph
,
3143 &node_scc_at_least
, graph
->src_scc
+ 1);
3144 filters
= isl_union_set_list_add(filters
, dom
);
3149 /* Copy nodes that satisfy node_pred from the src dependence graph
3150 * to the dst dependence graph.
3152 static int copy_nodes(struct isl_sched_graph
*dst
, struct isl_sched_graph
*src
,
3153 int (*node_pred
)(struct isl_sched_node
*node
, int data
), int data
)
3158 for (i
= 0; i
< src
->n
; ++i
) {
3161 if (!node_pred(&src
->node
[i
], data
))
3165 dst
->node
[j
].space
= isl_space_copy(src
->node
[i
].space
);
3166 dst
->node
[j
].compressed
= src
->node
[i
].compressed
;
3167 dst
->node
[j
].hull
= isl_set_copy(src
->node
[i
].hull
);
3168 dst
->node
[j
].compress
=
3169 isl_multi_aff_copy(src
->node
[i
].compress
);
3170 dst
->node
[j
].decompress
=
3171 isl_multi_aff_copy(src
->node
[i
].decompress
);
3172 dst
->node
[j
].nvar
= src
->node
[i
].nvar
;
3173 dst
->node
[j
].nparam
= src
->node
[i
].nparam
;
3174 dst
->node
[j
].sched
= isl_mat_copy(src
->node
[i
].sched
);
3175 dst
->node
[j
].sched_map
= isl_map_copy(src
->node
[i
].sched_map
);
3176 dst
->node
[j
].coincident
= src
->node
[i
].coincident
;
3177 dst
->node
[j
].sizes
= isl_multi_val_copy(src
->node
[i
].sizes
);
3178 dst
->node
[j
].max
= isl_vec_copy(src
->node
[i
].max
);
3181 if (!dst
->node
[j
].space
|| !dst
->node
[j
].sched
)
3183 if (dst
->node
[j
].compressed
&&
3184 (!dst
->node
[j
].hull
|| !dst
->node
[j
].compress
||
3185 !dst
->node
[j
].decompress
))
3192 /* Copy non-empty edges that satisfy edge_pred from the src dependence graph
3193 * to the dst dependence graph.
3194 * If the source or destination node of the edge is not in the destination
3195 * graph, then it must be a backward proximity edge and it should simply
3198 static int copy_edges(isl_ctx
*ctx
, struct isl_sched_graph
*dst
,
3199 struct isl_sched_graph
*src
,
3200 int (*edge_pred
)(struct isl_sched_edge
*edge
, int data
), int data
)
3203 enum isl_edge_type t
;
3206 for (i
= 0; i
< src
->n_edge
; ++i
) {
3207 struct isl_sched_edge
*edge
= &src
->edge
[i
];
3209 isl_union_map
*tagged_condition
;
3210 isl_union_map
*tagged_validity
;
3211 struct isl_sched_node
*dst_src
, *dst_dst
;
3213 if (!edge_pred(edge
, data
))
3216 if (isl_map_plain_is_empty(edge
->map
))
3219 dst_src
= graph_find_node(ctx
, dst
, edge
->src
->space
);
3220 dst_dst
= graph_find_node(ctx
, dst
, edge
->dst
->space
);
3221 if (!dst_src
|| !dst_dst
) {
3222 if (is_validity(edge
) || is_conditional_validity(edge
))
3223 isl_die(ctx
, isl_error_internal
,
3224 "backward (conditional) validity edge",
3229 map
= isl_map_copy(edge
->map
);
3230 tagged_condition
= isl_union_map_copy(edge
->tagged_condition
);
3231 tagged_validity
= isl_union_map_copy(edge
->tagged_validity
);
3233 dst
->edge
[dst
->n_edge
].src
= dst_src
;
3234 dst
->edge
[dst
->n_edge
].dst
= dst_dst
;
3235 dst
->edge
[dst
->n_edge
].map
= map
;
3236 dst
->edge
[dst
->n_edge
].tagged_condition
= tagged_condition
;
3237 dst
->edge
[dst
->n_edge
].tagged_validity
= tagged_validity
;
3238 dst
->edge
[dst
->n_edge
].types
= edge
->types
;
3241 if (edge
->tagged_condition
&& !tagged_condition
)
3243 if (edge
->tagged_validity
&& !tagged_validity
)
3246 for (t
= isl_edge_first
; t
<= isl_edge_last
; ++t
) {
3248 graph_find_edge(src
, t
, edge
->src
, edge
->dst
))
3250 if (graph_edge_table_add(ctx
, dst
, t
,
3251 &dst
->edge
[dst
->n_edge
- 1]) < 0)
3259 /* Compute the maximal number of variables over all nodes.
3260 * This is the maximal number of linearly independent schedule
3261 * rows that we need to compute.
3262 * Just in case we end up in a part of the dependence graph
3263 * with only lower-dimensional domains, we make sure we will
3264 * compute the required amount of extra linearly independent rows.
3266 static int compute_maxvar(struct isl_sched_graph
*graph
)
3271 for (i
= 0; i
< graph
->n
; ++i
) {
3272 struct isl_sched_node
*node
= &graph
->node
[i
];
3275 if (node_update_vmap(node
) < 0)
3277 nvar
= node
->nvar
+ graph
->n_row
- node
->rank
;
3278 if (nvar
> graph
->maxvar
)
3279 graph
->maxvar
= nvar
;
3285 /* Extract the subgraph of "graph" that consists of the node satisfying
3286 * "node_pred" and the edges satisfying "edge_pred" and store
3287 * the result in "sub".
3289 static int extract_sub_graph(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
3290 int (*node_pred
)(struct isl_sched_node
*node
, int data
),
3291 int (*edge_pred
)(struct isl_sched_edge
*edge
, int data
),
3292 int data
, struct isl_sched_graph
*sub
)
3294 int i
, n
= 0, n_edge
= 0;
3297 for (i
= 0; i
< graph
->n
; ++i
)
3298 if (node_pred(&graph
->node
[i
], data
))
3300 for (i
= 0; i
< graph
->n_edge
; ++i
)
3301 if (edge_pred(&graph
->edge
[i
], data
))
3303 if (graph_alloc(ctx
, sub
, n
, n_edge
) < 0)
3305 if (copy_nodes(sub
, graph
, node_pred
, data
) < 0)
3307 if (graph_init_table(ctx
, sub
) < 0)
3309 for (t
= 0; t
<= isl_edge_last
; ++t
)
3310 sub
->max_edge
[t
] = graph
->max_edge
[t
];
3311 if (graph_init_edge_tables(ctx
, sub
) < 0)
3313 if (copy_edges(ctx
, sub
, graph
, edge_pred
, data
) < 0)
3315 sub
->n_row
= graph
->n_row
;
3316 sub
->max_row
= graph
->max_row
;
3317 sub
->n_total_row
= graph
->n_total_row
;
3318 sub
->band_start
= graph
->band_start
;
3323 static __isl_give isl_schedule_node
*compute_schedule(isl_schedule_node
*node
,
3324 struct isl_sched_graph
*graph
);
3325 static __isl_give isl_schedule_node
*compute_schedule_wcc(
3326 isl_schedule_node
*node
, struct isl_sched_graph
*graph
);
3328 /* Compute a schedule for a subgraph of "graph". In particular, for
3329 * the graph composed of nodes that satisfy node_pred and edges that
3330 * that satisfy edge_pred.
3331 * If the subgraph is known to consist of a single component, then wcc should
3332 * be set and then we call compute_schedule_wcc on the constructed subgraph.
3333 * Otherwise, we call compute_schedule, which will check whether the subgraph
3336 * The schedule is inserted at "node" and the updated schedule node
3339 static __isl_give isl_schedule_node
*compute_sub_schedule(
3340 __isl_take isl_schedule_node
*node
, isl_ctx
*ctx
,
3341 struct isl_sched_graph
*graph
,
3342 int (*node_pred
)(struct isl_sched_node
*node
, int data
),
3343 int (*edge_pred
)(struct isl_sched_edge
*edge
, int data
),
3346 struct isl_sched_graph split
= { 0 };
3348 if (extract_sub_graph(ctx
, graph
, node_pred
, edge_pred
, data
,
3353 node
= compute_schedule_wcc(node
, &split
);
3355 node
= compute_schedule(node
, &split
);
3357 graph_free(ctx
, &split
);
3360 graph_free(ctx
, &split
);
3361 return isl_schedule_node_free(node
);
3364 static int edge_scc_exactly(struct isl_sched_edge
*edge
, int scc
)
3366 return edge
->src
->scc
== scc
&& edge
->dst
->scc
== scc
;
3369 static int edge_dst_scc_at_most(struct isl_sched_edge
*edge
, int scc
)
3371 return edge
->dst
->scc
<= scc
;
3374 static int edge_src_scc_at_least(struct isl_sched_edge
*edge
, int scc
)
3376 return edge
->src
->scc
>= scc
;
3379 /* Reset the current band by dropping all its schedule rows.
3381 static int reset_band(struct isl_sched_graph
*graph
)
3386 drop
= graph
->n_total_row
- graph
->band_start
;
3387 graph
->n_total_row
-= drop
;
3388 graph
->n_row
-= drop
;
3390 for (i
= 0; i
< graph
->n
; ++i
) {
3391 struct isl_sched_node
*node
= &graph
->node
[i
];
3393 isl_map_free(node
->sched_map
);
3394 node
->sched_map
= NULL
;
3396 node
->sched
= isl_mat_drop_rows(node
->sched
,
3397 graph
->band_start
, drop
);
3406 /* Split the current graph into two parts and compute a schedule for each
3407 * part individually. In particular, one part consists of all SCCs up
3408 * to and including graph->src_scc, while the other part contains the other
3409 * SCCs. The split is enforced by a sequence node inserted at position "node"
3410 * in the schedule tree. Return the updated schedule node.
3411 * If either of these two parts consists of a sequence, then it is spliced
3412 * into the sequence containing the two parts.
3414 * The current band is reset. It would be possible to reuse
3415 * the previously computed rows as the first rows in the next
3416 * band, but recomputing them may result in better rows as we are looking
3417 * at a smaller part of the dependence graph.
3419 static __isl_give isl_schedule_node
*compute_split_schedule(
3420 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
3424 isl_union_set_list
*filters
;
3429 if (reset_band(graph
) < 0)
3430 return isl_schedule_node_free(node
);
3434 ctx
= isl_schedule_node_get_ctx(node
);
3435 filters
= extract_split(ctx
, graph
);
3436 node
= isl_schedule_node_insert_sequence(node
, filters
);
3437 node
= isl_schedule_node_child(node
, 1);
3438 node
= isl_schedule_node_child(node
, 0);
3440 node
= compute_sub_schedule(node
, ctx
, graph
,
3441 &node_scc_at_least
, &edge_src_scc_at_least
,
3442 graph
->src_scc
+ 1, 0);
3443 is_seq
= isl_schedule_node_get_type(node
) == isl_schedule_node_sequence
;
3444 node
= isl_schedule_node_parent(node
);
3445 node
= isl_schedule_node_parent(node
);
3447 node
= isl_schedule_node_sequence_splice_child(node
, 1);
3448 node
= isl_schedule_node_child(node
, 0);
3449 node
= isl_schedule_node_child(node
, 0);
3450 node
= compute_sub_schedule(node
, ctx
, graph
,
3451 &node_scc_at_most
, &edge_dst_scc_at_most
,
3453 is_seq
= isl_schedule_node_get_type(node
) == isl_schedule_node_sequence
;
3454 node
= isl_schedule_node_parent(node
);
3455 node
= isl_schedule_node_parent(node
);
3457 node
= isl_schedule_node_sequence_splice_child(node
, 0);
3462 /* Insert a band node at position "node" in the schedule tree corresponding
3463 * to the current band in "graph". Mark the band node permutable
3464 * if "permutable" is set.
3465 * The partial schedules and the coincidence property are extracted
3466 * from the graph nodes.
3467 * Return the updated schedule node.
3469 static __isl_give isl_schedule_node
*insert_current_band(
3470 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
3476 isl_multi_pw_aff
*mpa
;
3477 isl_multi_union_pw_aff
*mupa
;
3483 isl_die(isl_schedule_node_get_ctx(node
), isl_error_internal
,
3484 "graph should have at least one node",
3485 return isl_schedule_node_free(node
));
3487 start
= graph
->band_start
;
3488 end
= graph
->n_total_row
;
3491 ma
= node_extract_partial_schedule_multi_aff(&graph
->node
[0], start
, n
);
3492 mpa
= isl_multi_pw_aff_from_multi_aff(ma
);
3493 mupa
= isl_multi_union_pw_aff_from_multi_pw_aff(mpa
);
3495 for (i
= 1; i
< graph
->n
; ++i
) {
3496 isl_multi_union_pw_aff
*mupa_i
;
3498 ma
= node_extract_partial_schedule_multi_aff(&graph
->node
[i
],
3500 mpa
= isl_multi_pw_aff_from_multi_aff(ma
);
3501 mupa_i
= isl_multi_union_pw_aff_from_multi_pw_aff(mpa
);
3502 mupa
= isl_multi_union_pw_aff_union_add(mupa
, mupa_i
);
3504 node
= isl_schedule_node_insert_partial_schedule(node
, mupa
);
3506 for (i
= 0; i
< n
; ++i
)
3507 node
= isl_schedule_node_band_member_set_coincident(node
, i
,
3508 graph
->node
[0].coincident
[start
+ i
]);
3509 node
= isl_schedule_node_band_set_permutable(node
, permutable
);
3514 /* Update the dependence relations based on the current schedule,
3515 * add the current band to "node" and then continue with the computation
3517 * Return the updated schedule node.
3519 static __isl_give isl_schedule_node
*compute_next_band(
3520 __isl_take isl_schedule_node
*node
,
3521 struct isl_sched_graph
*graph
, int permutable
)
3528 ctx
= isl_schedule_node_get_ctx(node
);
3529 if (update_edges(ctx
, graph
) < 0)
3530 return isl_schedule_node_free(node
);
3531 node
= insert_current_band(node
, graph
, permutable
);
3534 node
= isl_schedule_node_child(node
, 0);
3535 node
= compute_schedule(node
, graph
);
3536 node
= isl_schedule_node_parent(node
);
3541 /* Add the constraints "coef" derived from an edge from "node" to itself
3542 * to graph->lp in order to respect the dependences and to try and carry them.
3543 * "pos" is the sequence number of the edge that needs to be carried.
3544 * "coef" represents general constraints on coefficients (c_0, c_n, c_x)
3545 * of valid constraints for (y - x) with x and y instances of the node.
3547 * The constraints added to graph->lp need to enforce
3549 * (c_j_0 + c_j_n n + c_j_x y) - (c_j_0 + c_j_n n + c_j_x x)
3550 * = c_j_x (y - x) >= e_i
3552 * for each (x,y) in the dependence relation of the edge.
3553 * That is, (-e_i, 0, c_j_x) needs to be plugged in for (c_0, c_n, c_x),
3554 * taking into account that each coefficient in c_j_x is represented
3555 * as a pair of non-negative coefficients.
3557 static isl_stat
add_intra_constraints(struct isl_sched_graph
*graph
,
3558 struct isl_sched_node
*node
, __isl_take isl_basic_set
*coef
, int pos
)
3562 isl_dim_map
*dim_map
;
3565 return isl_stat_error
;
3567 ctx
= isl_basic_set_get_ctx(coef
);
3568 offset
= coef_var_offset(coef
);
3569 dim_map
= intra_dim_map(ctx
, graph
, node
, offset
, 1);
3570 isl_dim_map_range(dim_map
, 3 + pos
, 0, 0, 0, 1, -1);
3571 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
3576 /* Add the constraints "coef" derived from an edge from "src" to "dst"
3577 * to graph->lp in order to respect the dependences and to try and carry them.
3578 * "pos" is the sequence number of the edge that needs to be carried.
3579 * "coef" represents general constraints on coefficients (c_0, c_n, c_x, c_y)
3580 * of valid constraints for (x, y) with x and y instances of "src" and "dst".
3582 * The constraints added to graph->lp need to enforce
3584 * (c_k_0 + c_k_n n + c_k_x y) - (c_j_0 + c_j_n n + c_j_x x) >= e_i
3586 * for each (x,y) in the dependence relation of the edge.
3588 * (-e_i + c_k_0 - c_j_0, c_k_n - c_j_n, -c_j_x, c_k_x)
3589 * needs to be plugged in for (c_0, c_n, c_x, c_y),
3590 * taking into account that each coefficient in c_j_x and c_k_x is represented
3591 * as a pair of non-negative coefficients.
3593 static isl_stat
add_inter_constraints(struct isl_sched_graph
*graph
,
3594 struct isl_sched_node
*src
, struct isl_sched_node
*dst
,
3595 __isl_take isl_basic_set
*coef
, int pos
)
3599 isl_dim_map
*dim_map
;
3602 return isl_stat_error
;
3604 ctx
= isl_basic_set_get_ctx(coef
);
3605 offset
= coef_var_offset(coef
);
3606 dim_map
= inter_dim_map(ctx
, graph
, src
, dst
, offset
, 1);
3607 isl_dim_map_range(dim_map
, 3 + pos
, 0, 0, 0, 1, -1);
3608 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
3613 /* Data structure collecting information used during the construction
3614 * of an LP for carrying dependences.
3616 * "intra" is a sequence of coefficient constraints for intra-node edges.
3617 * "inter" is a sequence of coefficient constraints for inter-node edges.
3620 isl_basic_set_list
*intra
;
3621 isl_basic_set_list
*inter
;
3624 /* Free all the data stored in "carry".
3626 static void isl_carry_clear(struct isl_carry
*carry
)
3628 isl_basic_set_list_free(carry
->intra
);
3629 isl_basic_set_list_free(carry
->inter
);
3632 /* Return a pointer to the node in "graph" that lives in "space".
3633 * If the requested node has been compressed, then "space"
3634 * corresponds to the compressed space.
3636 * First try and see if "space" is the space of an uncompressed node.
3637 * If so, return that node.
3638 * Otherwise, "space" was constructed by construct_compressed_id and
3639 * contains a user pointer pointing to the node in the tuple id.
3641 static struct isl_sched_node
*graph_find_compressed_node(isl_ctx
*ctx
,
3642 struct isl_sched_graph
*graph
, __isl_keep isl_space
*space
)
3645 struct isl_sched_node
*node
;
3650 node
= graph_find_node(ctx
, graph
, space
);
3654 id
= isl_space_get_tuple_id(space
, isl_dim_set
);
3655 node
= isl_id_get_user(id
);
3661 if (!(node
>= &graph
->node
[0] && node
< &graph
->node
[graph
->n
]))
3662 isl_die(ctx
, isl_error_internal
,
3663 "space points to invalid node", return NULL
);
3668 /* Internal data structure for add_all_constraints.
3670 * "graph" is the schedule constraint graph for which an LP problem
3671 * is being constructed.
3672 * "pos" is the position of the next edge that needs to be carried.
3674 struct isl_add_all_constraints_data
{
3676 struct isl_sched_graph
*graph
;
3680 /* Add the constraints "coef" derived from an edge from a node to itself
3681 * to data->graph->lp in order to respect the dependences and
3682 * to try and carry them.
3684 * The space of "coef" is of the form
3686 * coefficients[[c_cst, c_n] -> S[c_x]]
3688 * with S[c_x] the (compressed) space of the node.
3689 * Extract the node from the space and call add_intra_constraints.
3691 static isl_stat
lp_add_intra(__isl_take isl_basic_set
*coef
, void *user
)
3693 struct isl_add_all_constraints_data
*data
= user
;
3695 struct isl_sched_node
*node
;
3697 space
= isl_basic_set_get_space(coef
);
3698 space
= isl_space_range(isl_space_unwrap(space
));
3699 node
= graph_find_compressed_node(data
->ctx
, data
->graph
, space
);
3700 isl_space_free(space
);
3701 return add_intra_constraints(data
->graph
, node
, coef
, data
->pos
++);
3704 /* Add the constraints "coef" derived from an edge from a node j
3705 * to a node k to data->graph->lp in order to respect the dependences and
3706 * to try and carry them.
3708 * The space of "coef" is of the form
3710 * coefficients[[c_cst, c_n] -> [S_j[c_x] -> S_k[c_y]]]
3712 * with S_j[c_x] and S_k[c_y] the (compressed) spaces of the nodes.
3713 * Extract the nodes from the space and call add_inter_constraints.
3715 static isl_stat
lp_add_inter(__isl_take isl_basic_set
*coef
, void *user
)
3717 struct isl_add_all_constraints_data
*data
= user
;
3718 isl_space
*space
, *dom
;
3719 struct isl_sched_node
*src
, *dst
;
3721 space
= isl_basic_set_get_space(coef
);
3722 space
= isl_space_unwrap(isl_space_range(isl_space_unwrap(space
)));
3723 dom
= isl_space_domain(isl_space_copy(space
));
3724 src
= graph_find_compressed_node(data
->ctx
, data
->graph
, dom
);
3725 isl_space_free(dom
);
3726 space
= isl_space_range(space
);
3727 dst
= graph_find_compressed_node(data
->ctx
, data
->graph
, space
);
3728 isl_space_free(space
);
3730 return add_inter_constraints(data
->graph
, src
, dst
, coef
, data
->pos
++);
3733 /* Add constraints to graph->lp that force all (conditional) validity
3734 * dependences to be respected and attempt to carry them.
3735 * "intra" is the sequence of coefficient constraints for intra-node edges.
3736 * "inter" is the sequence of coefficient constraints for inter-node edges.
3738 static isl_stat
add_all_constraints(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
3739 __isl_keep isl_basic_set_list
*intra
,
3740 __isl_keep isl_basic_set_list
*inter
)
3742 struct isl_add_all_constraints_data data
= { ctx
, graph
};
3745 if (isl_basic_set_list_foreach(intra
, &lp_add_intra
, &data
) < 0)
3746 return isl_stat_error
;
3747 if (isl_basic_set_list_foreach(inter
, &lp_add_inter
, &data
) < 0)
3748 return isl_stat_error
;
3752 /* Internal data structure for count_all_constraints
3753 * for keeping track of the number of equality and inequality constraints.
3755 struct isl_sched_count
{
3760 /* Add the number of equality and inequality constraints of "bset"
3761 * to data->n_eq and data->n_ineq.
3763 static isl_stat
bset_update_count(__isl_take isl_basic_set
*bset
, void *user
)
3765 struct isl_sched_count
*data
= user
;
3767 data
->n_eq
+= isl_basic_set_n_equality(bset
);
3768 data
->n_ineq
+= isl_basic_set_n_inequality(bset
);
3769 isl_basic_set_free(bset
);
3774 /* Count the number of equality and inequality constraints
3775 * that will be added to the carry_lp problem.
3776 * We count each edge exactly once.
3777 * "intra" is the sequence of coefficient constraints for intra-node edges.
3778 * "inter" is the sequence of coefficient constraints for inter-node edges.
3780 static isl_stat
count_all_constraints(__isl_keep isl_basic_set_list
*intra
,
3781 __isl_keep isl_basic_set_list
*inter
, int *n_eq
, int *n_ineq
)
3783 struct isl_sched_count data
;
3785 data
.n_eq
= data
.n_ineq
= 0;
3786 if (isl_basic_set_list_foreach(inter
, &bset_update_count
, &data
) < 0)
3787 return isl_stat_error
;
3788 if (isl_basic_set_list_foreach(intra
, &bset_update_count
, &data
) < 0)
3789 return isl_stat_error
;
3792 *n_ineq
= data
.n_ineq
;
3797 /* Construct an LP problem for finding schedule coefficients
3798 * such that the schedule carries as many validity dependences as possible.
3799 * In particular, for each dependence i, we bound the dependence distance
3800 * from below by e_i, with 0 <= e_i <= 1 and then maximize the sum
3801 * of all e_i's. Dependences with e_i = 0 in the solution are simply
3802 * respected, while those with e_i > 0 (in practice e_i = 1) are carried.
3803 * "intra" is the sequence of coefficient constraints for intra-node edges.
3804 * "inter" is the sequence of coefficient constraints for inter-node edges.
3805 * "n_edge" is the total number of edges.
3807 * All variables of the LP are non-negative. The actual coefficients
3808 * may be negative, so each coefficient is represented as the difference
3809 * of two non-negative variables. The negative part always appears
3810 * immediately before the positive part.
3811 * Other than that, the variables have the following order
3813 * - sum of (1 - e_i) over all edges
3814 * - sum of all c_n coefficients
3815 * (unconstrained when computing non-parametric schedules)
3816 * - sum of positive and negative parts of all c_x coefficients
3821 * - c_i_n (if parametric)
3822 * - positive and negative parts of c_i_x, in opposite order
3824 * The constraints are those from the (validity) edges plus three equalities
3825 * to express the sums and n_edge inequalities to express e_i <= 1.
3827 static isl_stat
setup_carry_lp(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
3828 int n_edge
, __isl_keep isl_basic_set_list
*intra
,
3829 __isl_keep isl_basic_set_list
*inter
)
3838 for (i
= 0; i
< graph
->n
; ++i
) {
3839 struct isl_sched_node
*node
= &graph
->node
[graph
->sorted
[i
]];
3840 node
->start
= total
;
3841 total
+= 1 + node
->nparam
+ 2 * node
->nvar
;
3844 if (count_all_constraints(intra
, inter
, &n_eq
, &n_ineq
) < 0)
3845 return isl_stat_error
;
3847 dim
= isl_space_set_alloc(ctx
, 0, total
);
3848 isl_basic_set_free(graph
->lp
);
3851 graph
->lp
= isl_basic_set_alloc_space(dim
, 0, n_eq
, n_ineq
);
3852 graph
->lp
= isl_basic_set_set_rational(graph
->lp
);
3854 k
= isl_basic_set_alloc_equality(graph
->lp
);
3856 return isl_stat_error
;
3857 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
3858 isl_int_set_si(graph
->lp
->eq
[k
][0], -n_edge
);
3859 isl_int_set_si(graph
->lp
->eq
[k
][1], 1);
3860 for (i
= 0; i
< n_edge
; ++i
)
3861 isl_int_set_si(graph
->lp
->eq
[k
][4 + i
], 1);
3863 if (add_param_sum_constraint(graph
, 1) < 0)
3864 return isl_stat_error
;
3865 if (add_var_sum_constraint(graph
, 2) < 0)
3866 return isl_stat_error
;
3868 for (i
= 0; i
< n_edge
; ++i
) {
3869 k
= isl_basic_set_alloc_inequality(graph
->lp
);
3871 return isl_stat_error
;
3872 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
3873 isl_int_set_si(graph
->lp
->ineq
[k
][4 + i
], -1);
3874 isl_int_set_si(graph
->lp
->ineq
[k
][0], 1);
3877 if (add_all_constraints(ctx
, graph
, intra
, inter
) < 0)
3878 return isl_stat_error
;
3883 static __isl_give isl_schedule_node
*compute_component_schedule(
3884 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
3887 /* Comparison function for sorting the statements based on
3888 * the corresponding value in "r".
3890 static int smaller_value(const void *a
, const void *b
, void *data
)
3896 return isl_int_cmp(r
->el
[*i1
], r
->el
[*i2
]);
3899 /* If the schedule_split_scaled option is set and if the linear
3900 * parts of the scheduling rows for all nodes in the graphs have
3901 * a non-trivial common divisor, then split off the remainder of the
3902 * constant term modulo this common divisor from the linear part.
3903 * Otherwise, insert a band node directly and continue with
3904 * the construction of the schedule.
3906 * If a non-trivial common divisor is found, then
3907 * the linear part is reduced and the remainder is enforced
3908 * by a sequence node with the children placed in the order
3909 * of this remainder.
3910 * In particular, we assign an scc index based on the remainder and
3911 * then rely on compute_component_schedule to insert the sequence and
3912 * to continue the schedule construction on each part.
3914 static __isl_give isl_schedule_node
*split_scaled(
3915 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
3928 ctx
= isl_schedule_node_get_ctx(node
);
3929 if (!ctx
->opt
->schedule_split_scaled
)
3930 return compute_next_band(node
, graph
, 0);
3932 return compute_next_band(node
, graph
, 0);
3935 isl_int_init(gcd_i
);
3937 isl_int_set_si(gcd
, 0);
3939 row
= isl_mat_rows(graph
->node
[0].sched
) - 1;
3941 for (i
= 0; i
< graph
->n
; ++i
) {
3942 struct isl_sched_node
*node
= &graph
->node
[i
];
3943 int cols
= isl_mat_cols(node
->sched
);
3945 isl_seq_gcd(node
->sched
->row
[row
] + 1, cols
- 1, &gcd_i
);
3946 isl_int_gcd(gcd
, gcd
, gcd_i
);
3949 isl_int_clear(gcd_i
);
3951 if (isl_int_cmp_si(gcd
, 1) <= 0) {
3953 return compute_next_band(node
, graph
, 0);
3956 r
= isl_vec_alloc(ctx
, graph
->n
);
3957 order
= isl_calloc_array(ctx
, int, graph
->n
);
3961 for (i
= 0; i
< graph
->n
; ++i
) {
3962 struct isl_sched_node
*node
= &graph
->node
[i
];
3965 isl_int_fdiv_r(r
->el
[i
], node
->sched
->row
[row
][0], gcd
);
3966 isl_int_fdiv_q(node
->sched
->row
[row
][0],
3967 node
->sched
->row
[row
][0], gcd
);
3968 isl_int_mul(node
->sched
->row
[row
][0],
3969 node
->sched
->row
[row
][0], gcd
);
3970 node
->sched
= isl_mat_scale_down_row(node
->sched
, row
, gcd
);
3975 if (isl_sort(order
, graph
->n
, sizeof(order
[0]), &smaller_value
, r
) < 0)
3979 for (i
= 0; i
< graph
->n
; ++i
) {
3980 if (i
> 0 && isl_int_ne(r
->el
[order
[i
- 1]], r
->el
[order
[i
]]))
3982 graph
->node
[order
[i
]].scc
= scc
;
3991 if (update_edges(ctx
, graph
) < 0)
3992 return isl_schedule_node_free(node
);
3993 node
= insert_current_band(node
, graph
, 0);
3996 node
= isl_schedule_node_child(node
, 0);
3997 node
= compute_component_schedule(node
, graph
, 0);
3998 node
= isl_schedule_node_parent(node
);
4005 return isl_schedule_node_free(node
);
4008 /* Is the schedule row "sol" trivial on node "node"?
4009 * That is, is the solution zero on the dimensions linearly independent of
4010 * the previously found solutions?
4011 * Return 1 if the solution is trivial, 0 if it is not and -1 on error.
4013 * Each coefficient is represented as the difference between
4014 * two non-negative values in "sol".
4015 * We construct the schedule row s and check if it is linearly
4016 * independent of previously computed schedule rows
4017 * by computing T s, with T the linear combinations that are zero
4018 * on linearly dependent schedule rows.
4019 * If the result consists of all zeros, then the solution is trivial.
4021 static int is_trivial(struct isl_sched_node
*node
, __isl_keep isl_vec
*sol
)
4028 if (node
->nvar
== node
->rank
)
4031 node_sol
= extract_var_coef(node
, sol
);
4032 node_sol
= isl_mat_vec_product(isl_mat_copy(node
->indep
), node_sol
);
4036 trivial
= isl_seq_first_non_zero(node_sol
->el
,
4037 node
->nvar
- node
->rank
) == -1;
4039 isl_vec_free(node_sol
);
4044 /* Is the schedule row "sol" trivial on any node where it should
4046 * Return 1 if any solution is trivial, 0 if they are not and -1 on error.
4048 static int is_any_trivial(struct isl_sched_graph
*graph
,
4049 __isl_keep isl_vec
*sol
)
4053 for (i
= 0; i
< graph
->n
; ++i
) {
4054 struct isl_sched_node
*node
= &graph
->node
[i
];
4057 if (!needs_row(graph
, node
))
4059 trivial
= is_trivial(node
, sol
);
4060 if (trivial
< 0 || trivial
)
4067 /* Does the schedule represented by "sol" perform loop coalescing on "node"?
4068 * If so, return the position of the coalesced dimension.
4069 * Otherwise, return node->nvar or -1 on error.
4071 * In particular, look for pairs of coefficients c_i and c_j such that
4072 * |c_j/c_i| >= size_i, i.e., |c_j| >= |c_i * size_i|.
4073 * If any such pair is found, then return i.
4074 * If size_i is infinity, then no check on c_i needs to be performed.
4076 static int find_node_coalescing(struct isl_sched_node
*node
,
4077 __isl_keep isl_vec
*sol
)
4083 if (node
->nvar
<= 1)
4086 csol
= extract_var_coef(node
, sol
);
4090 for (i
= 0; i
< node
->nvar
; ++i
) {
4093 if (isl_int_is_zero(csol
->el
[i
]))
4095 v
= isl_multi_val_get_val(node
->sizes
, i
);
4098 if (!isl_val_is_int(v
)) {
4102 isl_int_mul(max
, v
->n
, csol
->el
[i
]);
4105 for (j
= 0; j
< node
->nvar
; ++j
) {
4108 if (isl_int_abs_ge(csol
->el
[j
], max
))
4124 /* Force the schedule coefficient at position "pos" of "node" to be zero
4126 * The coefficient is encoded as the difference between two non-negative
4127 * variables. Force these two variables to have the same value.
4129 static __isl_give isl_tab_lexmin
*zero_out_node_coef(
4130 __isl_take isl_tab_lexmin
*tl
, struct isl_sched_node
*node
, int pos
)
4136 ctx
= isl_space_get_ctx(node
->space
);
4137 dim
= isl_tab_lexmin_dim(tl
);
4139 return isl_tab_lexmin_free(tl
);
4140 eq
= isl_vec_alloc(ctx
, 1 + dim
);
4141 eq
= isl_vec_clr(eq
);
4143 return isl_tab_lexmin_free(tl
);
4145 pos
= 1 + node_var_coef_pos(node
, pos
);
4146 isl_int_set_si(eq
->el
[pos
], 1);
4147 isl_int_set_si(eq
->el
[pos
+ 1], -1);
4148 tl
= isl_tab_lexmin_add_eq(tl
, eq
->el
);
4154 /* Return the lexicographically smallest rational point in the basic set
4155 * from which "tl" was constructed, double checking that this input set
4158 static __isl_give isl_vec
*non_empty_solution(__isl_keep isl_tab_lexmin
*tl
)
4162 sol
= isl_tab_lexmin_get_solution(tl
);
4166 isl_die(isl_vec_get_ctx(sol
), isl_error_internal
,
4167 "error in schedule construction",
4168 return isl_vec_free(sol
));
4172 /* Does the solution "sol" of the LP problem constructed by setup_carry_lp
4173 * carry any of the "n_edge" groups of dependences?
4174 * The value in the first position is the sum of (1 - e_i) over all "n_edge"
4175 * edges, with 0 <= e_i <= 1 equal to 1 when the dependences represented
4176 * by the edge are carried by the solution.
4177 * If the sum of the (1 - e_i) is smaller than "n_edge" then at least
4178 * one of those is carried.
4180 * Note that despite the fact that the problem is solved using a rational
4181 * solver, the solution is guaranteed to be integral.
4182 * Specifically, the dependence distance lower bounds e_i (and therefore
4183 * also their sum) are integers. See Lemma 5 of [1].
4185 * Any potential denominator of the sum is cleared by this function.
4186 * The denominator is not relevant for any of the other elements
4189 * [1] P. Feautrier, Some Efficient Solutions to the Affine Scheduling
4190 * Problem, Part II: Multi-Dimensional Time.
4191 * In Intl. Journal of Parallel Programming, 1992.
4193 static int carries_dependences(__isl_keep isl_vec
*sol
, int n_edge
)
4195 isl_int_divexact(sol
->el
[1], sol
->el
[1], sol
->el
[0]);
4196 isl_int_set_si(sol
->el
[0], 1);
4197 return isl_int_cmp_si(sol
->el
[1], n_edge
) < 0;
4200 /* Return the lexicographically smallest rational point in "lp",
4201 * assuming that all variables are non-negative and performing some
4202 * additional sanity checks.
4203 * If "want_integral" is set, then compute the lexicographically smallest
4204 * integer point instead.
4205 * In particular, "lp" should not be empty by construction.
4206 * Double check that this is the case.
4207 * If dependences are not carried for any of the "n_edge" edges,
4208 * then return an empty vector.
4210 * If the schedule_treat_coalescing option is set and
4211 * if the computed schedule performs loop coalescing on a given node,
4212 * i.e., if it is of the form
4214 * c_i i + c_j j + ...
4216 * with |c_j/c_i| >= size_i, then force the coefficient c_i to be zero
4217 * to cut out this solution. Repeat this process until no more loop
4218 * coalescing occurs or until no more dependences can be carried.
4219 * In the latter case, revert to the previously computed solution.
4221 * If the caller requests an integral solution and if coalescing should
4222 * be treated, then perform the coalescing treatment first as
4223 * an integral solution computed before coalescing treatment
4224 * would carry the same number of edges and would therefore probably
4225 * also be coalescing.
4227 * To allow the coalescing treatment to be performed first,
4228 * the initial solution is allowed to be rational and it is only
4229 * cut out (if needed) in the next iteration, if no coalescing measures
4232 static __isl_give isl_vec
*non_neg_lexmin(struct isl_sched_graph
*graph
,
4233 __isl_take isl_basic_set
*lp
, int n_edge
, int want_integral
)
4238 isl_vec
*sol
, *prev
= NULL
;
4239 int treat_coalescing
;
4243 ctx
= isl_basic_set_get_ctx(lp
);
4244 treat_coalescing
= isl_options_get_schedule_treat_coalescing(ctx
);
4245 tl
= isl_tab_lexmin_from_basic_set(lp
);
4252 tl
= isl_tab_lexmin_cut_to_integer(tl
);
4253 sol
= non_empty_solution(tl
);
4257 integral
= isl_int_is_one(sol
->el
[0]);
4258 if (!carries_dependences(sol
, n_edge
)) {
4260 prev
= isl_vec_alloc(ctx
, 0);
4265 prev
= isl_vec_free(prev
);
4266 cut
= want_integral
&& !integral
;
4269 if (!treat_coalescing
)
4271 for (i
= 0; i
< graph
->n
; ++i
) {
4272 struct isl_sched_node
*node
= &graph
->node
[i
];
4274 pos
= find_node_coalescing(node
, sol
);
4277 if (pos
< node
->nvar
)
4282 tl
= zero_out_node_coef(tl
, &graph
->node
[i
], pos
);
4287 isl_tab_lexmin_free(tl
);
4291 isl_tab_lexmin_free(tl
);
4297 /* If "edge" is an edge from a node to itself, then add the corresponding
4298 * dependence relation to "umap".
4299 * If "node" has been compressed, then the dependence relation
4300 * is also compressed first.
4302 static __isl_give isl_union_map
*add_intra(__isl_take isl_union_map
*umap
,
4303 struct isl_sched_edge
*edge
)
4306 struct isl_sched_node
*node
= edge
->src
;
4308 if (edge
->src
!= edge
->dst
)
4311 map
= isl_map_copy(edge
->map
);
4312 if (node
->compressed
) {
4313 map
= isl_map_preimage_domain_multi_aff(map
,
4314 isl_multi_aff_copy(node
->decompress
));
4315 map
= isl_map_preimage_range_multi_aff(map
,
4316 isl_multi_aff_copy(node
->decompress
));
4318 umap
= isl_union_map_add_map(umap
, map
);
4322 /* If "edge" is an edge from a node to another node, then add the corresponding
4323 * dependence relation to "umap".
4324 * If the source or destination nodes of "edge" have been compressed,
4325 * then the dependence relation is also compressed first.
4327 static __isl_give isl_union_map
*add_inter(__isl_take isl_union_map
*umap
,
4328 struct isl_sched_edge
*edge
)
4332 if (edge
->src
== edge
->dst
)
4335 map
= isl_map_copy(edge
->map
);
4336 if (edge
->src
->compressed
)
4337 map
= isl_map_preimage_domain_multi_aff(map
,
4338 isl_multi_aff_copy(edge
->src
->decompress
));
4339 if (edge
->dst
->compressed
)
4340 map
= isl_map_preimage_range_multi_aff(map
,
4341 isl_multi_aff_copy(edge
->dst
->decompress
));
4342 umap
= isl_union_map_add_map(umap
, map
);
4346 /* For each (conditional) validity edge in "graph",
4347 * add the corresponding dependence relation using "add"
4348 * to a collection of dependence relations and return the result.
4349 * If "coincidence" is set, then coincidence edges are considered as well.
4351 static __isl_give isl_union_map
*collect_validity(struct isl_sched_graph
*graph
,
4352 __isl_give isl_union_map
*(*add
)(__isl_take isl_union_map
*umap
,
4353 struct isl_sched_edge
*edge
), int coincidence
)
4357 isl_union_map
*umap
;
4359 space
= isl_space_copy(graph
->node
[0].space
);
4360 umap
= isl_union_map_empty(space
);
4362 for (i
= 0; i
< graph
->n_edge
; ++i
) {
4363 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
4365 if (!is_any_validity(edge
) &&
4366 (!coincidence
|| !is_coincidence(edge
)))
4369 umap
= add(umap
, edge
);
4375 /* For each dependence relation on a (conditional) validity edge
4376 * from a node to itself,
4377 * construct the set of coefficients of valid constraints for elements
4378 * in that dependence relation and collect the results.
4379 * If "coincidence" is set, then coincidence edges are considered as well.
4381 * In particular, for each dependence relation R, constraints
4382 * on coefficients (c_0, c_n, c_x) are constructed such that
4384 * c_0 + c_n n + c_x d >= 0 for each d in delta R = { y - x | (x,y) in R }
4386 * This computation is essentially the same as that performed
4387 * by intra_coefficients, except that it operates on multiple
4390 * Note that if a dependence relation is a union of basic maps,
4391 * then each basic map needs to be treated individually as it may only
4392 * be possible to carry the dependences expressed by some of those
4393 * basic maps and not all of them.
4394 * The collected validity constraints are therefore not coalesced and
4395 * it is assumed that they are not coalesced automatically.
4396 * Duplicate basic maps can be removed, however.
4397 * In particular, if the same basic map appears as a disjunct
4398 * in multiple edges, then it only needs to be carried once.
4400 static __isl_give isl_basic_set_list
*collect_intra_validity(
4401 struct isl_sched_graph
*graph
, int coincidence
)
4403 isl_union_map
*intra
;
4404 isl_union_set
*delta
;
4405 isl_basic_set_list
*list
;
4407 intra
= collect_validity(graph
, &add_intra
, coincidence
);
4408 delta
= isl_union_map_deltas(intra
);
4409 delta
= isl_union_set_remove_divs(delta
);
4410 list
= isl_union_set_get_basic_set_list(delta
);
4411 isl_union_set_free(delta
);
4413 return isl_basic_set_list_coefficients(list
);
4416 /* For each dependence relation on a (conditional) validity edge
4417 * from a node to some other node,
4418 * construct the set of coefficients of valid constraints for elements
4419 * in that dependence relation and collect the results.
4420 * If "coincidence" is set, then coincidence edges are considered as well.
4422 * In particular, for each dependence relation R, constraints
4423 * on coefficients (c_0, c_n, c_x, c_y) are constructed such that
4425 * c_0 + c_n n + c_x x + c_y y >= 0 for each (x,y) in R
4427 * This computation is essentially the same as that performed
4428 * by inter_coefficients, except that it operates on multiple
4431 * Note that if a dependence relation is a union of basic maps,
4432 * then each basic map needs to be treated individually as it may only
4433 * be possible to carry the dependences expressed by some of those
4434 * basic maps and not all of them.
4435 * The collected validity constraints are therefore not coalesced and
4436 * it is assumed that they are not coalesced automatically.
4437 * Duplicate basic maps can be removed, however.
4438 * In particular, if the same basic map appears as a disjunct
4439 * in multiple edges, then it only needs to be carried once.
4441 static __isl_give isl_basic_set_list
*collect_inter_validity(
4442 struct isl_sched_graph
*graph
, int coincidence
)
4444 isl_union_map
*inter
;
4445 isl_union_set
*wrap
;
4446 isl_basic_set_list
*list
;
4448 inter
= collect_validity(graph
, &add_inter
, coincidence
);
4449 inter
= isl_union_map_remove_divs(inter
);
4450 wrap
= isl_union_map_wrap(inter
);
4451 list
= isl_union_set_get_basic_set_list(wrap
);
4452 isl_union_set_free(wrap
);
4453 return isl_basic_set_list_coefficients(list
);
4456 /* Construct an LP problem for finding schedule coefficients
4457 * such that the schedule carries as many of the validity dependences
4459 * return the lexicographically smallest non-trivial solution.
4460 * If "fallback" is set, then the carrying is performed as a fallback
4461 * for the Pluto-like scheduler.
4462 * If "coincidence" is set, then try and carry coincidence edges as well.
4464 * The variable "n_edge" stores the number of groups that should be carried.
4465 * If none of the "n_edge" groups can be carried
4466 * then return an empty vector.
4467 * If, moreover, "n_edge" is zero, then the LP problem does not even
4468 * need to be constructed.
4470 * If a fallback solution is being computed, then compute an integral solution
4471 * for the coefficients rather than using the numerators
4472 * of a rational solution.
4474 static __isl_give isl_vec
*compute_carrying_sol(isl_ctx
*ctx
,
4475 struct isl_sched_graph
*graph
, int fallback
, int coincidence
)
4477 int n_intra
, n_inter
;
4480 struct isl_carry carry
= { 0 };
4482 carry
.intra
= collect_intra_validity(graph
, coincidence
);
4483 carry
.inter
= collect_inter_validity(graph
, coincidence
);
4484 if (!carry
.intra
|| !carry
.inter
)
4486 n_intra
= isl_basic_set_list_n_basic_set(carry
.intra
);
4487 n_inter
= isl_basic_set_list_n_basic_set(carry
.inter
);
4488 n_edge
= n_intra
+ n_inter
;
4490 isl_carry_clear(&carry
);
4491 return isl_vec_alloc(ctx
, 0);
4494 if (setup_carry_lp(ctx
, graph
, n_edge
, carry
.intra
, carry
.inter
) < 0)
4497 isl_carry_clear(&carry
);
4498 lp
= isl_basic_set_copy(graph
->lp
);
4499 return non_neg_lexmin(graph
, lp
, n_edge
, fallback
);
4501 isl_carry_clear(&carry
);
4505 /* Construct a schedule row for each node such that as many validity dependences
4506 * as possible are carried and then continue with the next band.
4507 * If "fallback" is set, then the carrying is performed as a fallback
4508 * for the Pluto-like scheduler.
4509 * If "coincidence" is set, then try and carry coincidence edges as well.
4511 * If there are no validity dependences, then no dependence can be carried and
4512 * the procedure is guaranteed to fail. If there is more than one component,
4513 * then try computing a schedule on each component separately
4514 * to prevent or at least postpone this failure.
4516 * If a schedule row is computed, then check that dependences are carried
4517 * for at least one of the edges.
4519 * If the computed schedule row turns out to be trivial on one or
4520 * more nodes where it should not be trivial, then we throw it away
4521 * and try again on each component separately.
4523 * If there is only one component, then we accept the schedule row anyway,
4524 * but we do not consider it as a complete row and therefore do not
4525 * increment graph->n_row. Note that the ranks of the nodes that
4526 * do get a non-trivial schedule part will get updated regardless and
4527 * graph->maxvar is computed based on these ranks. The test for
4528 * whether more schedule rows are required in compute_schedule_wcc
4529 * is therefore not affected.
4531 * Insert a band corresponding to the schedule row at position "node"
4532 * of the schedule tree and continue with the construction of the schedule.
4533 * This insertion and the continued construction is performed by split_scaled
4534 * after optionally checking for non-trivial common divisors.
4536 static __isl_give isl_schedule_node
*carry(__isl_take isl_schedule_node
*node
,
4537 struct isl_sched_graph
*graph
, int fallback
, int coincidence
)
4546 ctx
= isl_schedule_node_get_ctx(node
);
4547 sol
= compute_carrying_sol(ctx
, graph
, fallback
, coincidence
);
4549 return isl_schedule_node_free(node
);
4550 if (sol
->size
== 0) {
4553 return compute_component_schedule(node
, graph
, 1);
4554 isl_die(ctx
, isl_error_unknown
, "unable to carry dependences",
4555 return isl_schedule_node_free(node
));
4558 trivial
= is_any_trivial(graph
, sol
);
4560 sol
= isl_vec_free(sol
);
4561 } else if (trivial
&& graph
->scc
> 1) {
4563 return compute_component_schedule(node
, graph
, 1);
4566 if (update_schedule(graph
, sol
, 0) < 0)
4567 return isl_schedule_node_free(node
);
4571 return split_scaled(node
, graph
);
4574 /* Construct a schedule row for each node such that as many validity dependences
4575 * as possible are carried and then continue with the next band.
4576 * Do so as a fallback for the Pluto-like scheduler.
4577 * If "coincidence" is set, then try and carry coincidence edges as well.
4579 static __isl_give isl_schedule_node
*carry_fallback(
4580 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
4583 return carry(node
, graph
, 1, coincidence
);
4586 /* Construct a schedule row for each node such that as many validity dependences
4587 * as possible are carried and then continue with the next band.
4588 * Do so for the case where the Feautrier scheduler was selected
4591 static __isl_give isl_schedule_node
*carry_feautrier(
4592 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
4594 return carry(node
, graph
, 0, 0);
4597 /* Construct a schedule row for each node such that as many validity dependences
4598 * as possible are carried and then continue with the next band.
4599 * Do so as a fallback for the Pluto-like scheduler.
4601 static __isl_give isl_schedule_node
*carry_dependences(
4602 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
4604 return carry_fallback(node
, graph
, 0);
4607 /* Construct a schedule row for each node such that as many validity or
4608 * coincidence dependences as possible are carried and
4609 * then continue with the next band.
4610 * Do so as a fallback for the Pluto-like scheduler.
4612 static __isl_give isl_schedule_node
*carry_coincidence(
4613 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
4615 return carry_fallback(node
, graph
, 1);
4618 /* Topologically sort statements mapped to the same schedule iteration
4619 * and add insert a sequence node in front of "node"
4620 * corresponding to this order.
4621 * If "initialized" is set, then it may be assumed that compute_maxvar
4622 * has been called on the current band. Otherwise, call
4623 * compute_maxvar if and before carry_dependences gets called.
4625 * If it turns out to be impossible to sort the statements apart,
4626 * because different dependences impose different orderings
4627 * on the statements, then we extend the schedule such that
4628 * it carries at least one more dependence.
4630 static __isl_give isl_schedule_node
*sort_statements(
4631 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
4635 isl_union_set_list
*filters
;
4640 ctx
= isl_schedule_node_get_ctx(node
);
4642 isl_die(ctx
, isl_error_internal
,
4643 "graph should have at least one node",
4644 return isl_schedule_node_free(node
));
4649 if (update_edges(ctx
, graph
) < 0)
4650 return isl_schedule_node_free(node
);
4652 if (graph
->n_edge
== 0)
4655 if (detect_sccs(ctx
, graph
) < 0)
4656 return isl_schedule_node_free(node
);
4659 if (graph
->scc
< graph
->n
) {
4660 if (!initialized
&& compute_maxvar(graph
) < 0)
4661 return isl_schedule_node_free(node
);
4662 return carry_dependences(node
, graph
);
4665 filters
= extract_sccs(ctx
, graph
);
4666 node
= isl_schedule_node_insert_sequence(node
, filters
);
4671 /* Are there any (non-empty) (conditional) validity edges in the graph?
4673 static int has_validity_edges(struct isl_sched_graph
*graph
)
4677 for (i
= 0; i
< graph
->n_edge
; ++i
) {
4680 empty
= isl_map_plain_is_empty(graph
->edge
[i
].map
);
4685 if (is_any_validity(&graph
->edge
[i
]))
4692 /* Should we apply a Feautrier step?
4693 * That is, did the user request the Feautrier algorithm and are
4694 * there any validity dependences (left)?
4696 static int need_feautrier_step(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
4698 if (ctx
->opt
->schedule_algorithm
!= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
)
4701 return has_validity_edges(graph
);
4704 /* Compute a schedule for a connected dependence graph using Feautrier's
4705 * multi-dimensional scheduling algorithm and return the updated schedule node.
4707 * The original algorithm is described in [1].
4708 * The main idea is to minimize the number of scheduling dimensions, by
4709 * trying to satisfy as many dependences as possible per scheduling dimension.
4711 * [1] P. Feautrier, Some Efficient Solutions to the Affine Scheduling
4712 * Problem, Part II: Multi-Dimensional Time.
4713 * In Intl. Journal of Parallel Programming, 1992.
4715 static __isl_give isl_schedule_node
*compute_schedule_wcc_feautrier(
4716 isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
4718 return carry_feautrier(node
, graph
);
4721 /* Turn off the "local" bit on all (condition) edges.
4723 static void clear_local_edges(struct isl_sched_graph
*graph
)
4727 for (i
= 0; i
< graph
->n_edge
; ++i
)
4728 if (is_condition(&graph
->edge
[i
]))
4729 clear_local(&graph
->edge
[i
]);
4732 /* Does "graph" have both condition and conditional validity edges?
4734 static int need_condition_check(struct isl_sched_graph
*graph
)
4737 int any_condition
= 0;
4738 int any_conditional_validity
= 0;
4740 for (i
= 0; i
< graph
->n_edge
; ++i
) {
4741 if (is_condition(&graph
->edge
[i
]))
4743 if (is_conditional_validity(&graph
->edge
[i
]))
4744 any_conditional_validity
= 1;
4747 return any_condition
&& any_conditional_validity
;
4750 /* Does "graph" contain any coincidence edge?
4752 static int has_any_coincidence(struct isl_sched_graph
*graph
)
4756 for (i
= 0; i
< graph
->n_edge
; ++i
)
4757 if (is_coincidence(&graph
->edge
[i
]))
4763 /* Extract the final schedule row as a map with the iteration domain
4764 * of "node" as domain.
4766 static __isl_give isl_map
*final_row(struct isl_sched_node
*node
)
4771 row
= isl_mat_rows(node
->sched
) - 1;
4772 ma
= node_extract_partial_schedule_multi_aff(node
, row
, 1);
4773 return isl_map_from_multi_aff(ma
);
4776 /* Is the conditional validity dependence in the edge with index "edge_index"
4777 * violated by the latest (i.e., final) row of the schedule?
4778 * That is, is i scheduled after j
4779 * for any conditional validity dependence i -> j?
4781 static int is_violated(struct isl_sched_graph
*graph
, int edge_index
)
4783 isl_map
*src_sched
, *dst_sched
, *map
;
4784 struct isl_sched_edge
*edge
= &graph
->edge
[edge_index
];
4787 src_sched
= final_row(edge
->src
);
4788 dst_sched
= final_row(edge
->dst
);
4789 map
= isl_map_copy(edge
->map
);
4790 map
= isl_map_apply_domain(map
, src_sched
);
4791 map
= isl_map_apply_range(map
, dst_sched
);
4792 map
= isl_map_order_gt(map
, isl_dim_in
, 0, isl_dim_out
, 0);
4793 empty
= isl_map_is_empty(map
);
4802 /* Does "graph" have any satisfied condition edges that
4803 * are adjacent to the conditional validity constraint with
4804 * domain "conditional_source" and range "conditional_sink"?
4806 * A satisfied condition is one that is not local.
4807 * If a condition was forced to be local already (i.e., marked as local)
4808 * then there is no need to check if it is in fact local.
4810 * Additionally, mark all adjacent condition edges found as local.
4812 static int has_adjacent_true_conditions(struct isl_sched_graph
*graph
,
4813 __isl_keep isl_union_set
*conditional_source
,
4814 __isl_keep isl_union_set
*conditional_sink
)
4819 for (i
= 0; i
< graph
->n_edge
; ++i
) {
4820 int adjacent
, local
;
4821 isl_union_map
*condition
;
4823 if (!is_condition(&graph
->edge
[i
]))
4825 if (is_local(&graph
->edge
[i
]))
4828 condition
= graph
->edge
[i
].tagged_condition
;
4829 adjacent
= domain_intersects(condition
, conditional_sink
);
4830 if (adjacent
>= 0 && !adjacent
)
4831 adjacent
= range_intersects(condition
,
4832 conditional_source
);
4838 set_local(&graph
->edge
[i
]);
4840 local
= is_condition_false(&graph
->edge
[i
]);
4850 /* Are there any violated conditional validity dependences with
4851 * adjacent condition dependences that are not local with respect
4852 * to the current schedule?
4853 * That is, is the conditional validity constraint violated?
4855 * Additionally, mark all those adjacent condition dependences as local.
4856 * We also mark those adjacent condition dependences that were not marked
4857 * as local before, but just happened to be local already. This ensures
4858 * that they remain local if the schedule is recomputed.
4860 * We first collect domain and range of all violated conditional validity
4861 * dependences and then check if there are any adjacent non-local
4862 * condition dependences.
4864 static int has_violated_conditional_constraint(isl_ctx
*ctx
,
4865 struct isl_sched_graph
*graph
)
4869 isl_union_set
*source
, *sink
;
4871 source
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
4872 sink
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
4873 for (i
= 0; i
< graph
->n_edge
; ++i
) {
4874 isl_union_set
*uset
;
4875 isl_union_map
*umap
;
4878 if (!is_conditional_validity(&graph
->edge
[i
]))
4881 violated
= is_violated(graph
, i
);
4889 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_validity
);
4890 uset
= isl_union_map_domain(umap
);
4891 source
= isl_union_set_union(source
, uset
);
4892 source
= isl_union_set_coalesce(source
);
4894 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_validity
);
4895 uset
= isl_union_map_range(umap
);
4896 sink
= isl_union_set_union(sink
, uset
);
4897 sink
= isl_union_set_coalesce(sink
);
4901 any
= has_adjacent_true_conditions(graph
, source
, sink
);
4903 isl_union_set_free(source
);
4904 isl_union_set_free(sink
);
4907 isl_union_set_free(source
);
4908 isl_union_set_free(sink
);
4912 /* Examine the current band (the rows between graph->band_start and
4913 * graph->n_total_row), deciding whether to drop it or add it to "node"
4914 * and then continue with the computation of the next band, if any.
4915 * If "initialized" is set, then it may be assumed that compute_maxvar
4916 * has been called on the current band. Otherwise, call
4917 * compute_maxvar if and before carry_dependences gets called.
4919 * The caller keeps looking for a new row as long as
4920 * graph->n_row < graph->maxvar. If the latest attempt to find
4921 * such a row failed (i.e., we still have graph->n_row < graph->maxvar),
4923 * - split between SCCs and start over (assuming we found an interesting
4924 * pair of SCCs between which to split)
4925 * - continue with the next band (assuming the current band has at least
4927 * - if outer coincidence needs to be enforced, then try to carry as many
4928 * validity or coincidence dependences as possible and
4929 * continue with the next band
4930 * - try to carry as many validity dependences as possible and
4931 * continue with the next band
4932 * In each case, we first insert a band node in the schedule tree
4933 * if any rows have been computed.
4935 * If the caller managed to complete the schedule, we insert a band node
4936 * (if any schedule rows were computed) and we finish off by topologically
4937 * sorting the statements based on the remaining dependences.
4939 static __isl_give isl_schedule_node
*compute_schedule_finish_band(
4940 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
4948 if (graph
->n_row
< graph
->maxvar
) {
4950 int empty
= graph
->n_total_row
== graph
->band_start
;
4952 ctx
= isl_schedule_node_get_ctx(node
);
4953 if (!ctx
->opt
->schedule_maximize_band_depth
&& !empty
)
4954 return compute_next_band(node
, graph
, 1);
4955 if (graph
->src_scc
>= 0)
4956 return compute_split_schedule(node
, graph
);
4958 return compute_next_band(node
, graph
, 1);
4959 if (!initialized
&& compute_maxvar(graph
) < 0)
4960 return isl_schedule_node_free(node
);
4961 if (isl_options_get_schedule_outer_coincidence(ctx
))
4962 return carry_coincidence(node
, graph
);
4963 return carry_dependences(node
, graph
);
4966 insert
= graph
->n_total_row
> graph
->band_start
;
4968 node
= insert_current_band(node
, graph
, 1);
4969 node
= isl_schedule_node_child(node
, 0);
4971 node
= sort_statements(node
, graph
, initialized
);
4973 node
= isl_schedule_node_parent(node
);
4978 /* Construct a band of schedule rows for a connected dependence graph.
4979 * The caller is responsible for determining the strongly connected
4980 * components and calling compute_maxvar first.
4982 * We try to find a sequence of as many schedule rows as possible that result
4983 * in non-negative dependence distances (independent of the previous rows
4984 * in the sequence, i.e., such that the sequence is tilable), with as
4985 * many of the initial rows as possible satisfying the coincidence constraints.
4986 * The computation stops if we can't find any more rows or if we have found
4987 * all the rows we wanted to find.
4989 * If ctx->opt->schedule_outer_coincidence is set, then we force the
4990 * outermost dimension to satisfy the coincidence constraints. If this
4991 * turns out to be impossible, we fall back on the general scheme above
4992 * and try to carry as many dependences as possible.
4994 * If "graph" contains both condition and conditional validity dependences,
4995 * then we need to check that that the conditional schedule constraint
4996 * is satisfied, i.e., there are no violated conditional validity dependences
4997 * that are adjacent to any non-local condition dependences.
4998 * If there are, then we mark all those adjacent condition dependences
4999 * as local and recompute the current band. Those dependences that
5000 * are marked local will then be forced to be local.
5001 * The initial computation is performed with no dependences marked as local.
5002 * If we are lucky, then there will be no violated conditional validity
5003 * dependences adjacent to any non-local condition dependences.
5004 * Otherwise, we mark some additional condition dependences as local and
5005 * recompute. We continue this process until there are no violations left or
5006 * until we are no longer able to compute a schedule.
5007 * Since there are only a finite number of dependences,
5008 * there will only be a finite number of iterations.
5010 static isl_stat
compute_schedule_wcc_band(isl_ctx
*ctx
,
5011 struct isl_sched_graph
*graph
)
5013 int has_coincidence
;
5014 int use_coincidence
;
5015 int force_coincidence
= 0;
5016 int check_conditional
;
5018 if (sort_sccs(graph
) < 0)
5019 return isl_stat_error
;
5021 clear_local_edges(graph
);
5022 check_conditional
= need_condition_check(graph
);
5023 has_coincidence
= has_any_coincidence(graph
);
5025 if (ctx
->opt
->schedule_outer_coincidence
)
5026 force_coincidence
= 1;
5028 use_coincidence
= has_coincidence
;
5029 while (graph
->n_row
< graph
->maxvar
) {
5034 graph
->src_scc
= -1;
5035 graph
->dst_scc
= -1;
5037 if (setup_lp(ctx
, graph
, use_coincidence
) < 0)
5038 return isl_stat_error
;
5039 sol
= solve_lp(ctx
, graph
);
5041 return isl_stat_error
;
5042 if (sol
->size
== 0) {
5043 int empty
= graph
->n_total_row
== graph
->band_start
;
5046 if (use_coincidence
&& (!force_coincidence
|| !empty
)) {
5047 use_coincidence
= 0;
5052 coincident
= !has_coincidence
|| use_coincidence
;
5053 if (update_schedule(graph
, sol
, coincident
) < 0)
5054 return isl_stat_error
;
5056 if (!check_conditional
)
5058 violated
= has_violated_conditional_constraint(ctx
, graph
);
5060 return isl_stat_error
;
5063 if (reset_band(graph
) < 0)
5064 return isl_stat_error
;
5065 use_coincidence
= has_coincidence
;
5071 /* Compute a schedule for a connected dependence graph by considering
5072 * the graph as a whole and return the updated schedule node.
5074 * The actual schedule rows of the current band are computed by
5075 * compute_schedule_wcc_band. compute_schedule_finish_band takes
5076 * care of integrating the band into "node" and continuing
5079 static __isl_give isl_schedule_node
*compute_schedule_wcc_whole(
5080 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
5087 ctx
= isl_schedule_node_get_ctx(node
);
5088 if (compute_schedule_wcc_band(ctx
, graph
) < 0)
5089 return isl_schedule_node_free(node
);
5091 return compute_schedule_finish_band(node
, graph
, 1);
5094 /* Clustering information used by compute_schedule_wcc_clustering.
5096 * "n" is the number of SCCs in the original dependence graph
5097 * "scc" is an array of "n" elements, each representing an SCC
5098 * of the original dependence graph. All entries in the same cluster
5099 * have the same number of schedule rows.
5100 * "scc_cluster" maps each SCC index to the cluster to which it belongs,
5101 * where each cluster is represented by the index of the first SCC
5102 * in the cluster. Initially, each SCC belongs to a cluster containing
5105 * "scc_in_merge" is used by merge_clusters_along_edge to keep
5106 * track of which SCCs need to be merged.
5108 * "cluster" contains the merged clusters of SCCs after the clustering
5111 * "scc_node" is a temporary data structure used inside copy_partial.
5112 * For each SCC, it keeps track of the number of nodes in the SCC
5113 * that have already been copied.
5115 struct isl_clustering
{
5117 struct isl_sched_graph
*scc
;
5118 struct isl_sched_graph
*cluster
;
5124 /* Initialize the clustering data structure "c" from "graph".
5126 * In particular, allocate memory, extract the SCCs from "graph"
5127 * into c->scc, initialize scc_cluster and construct
5128 * a band of schedule rows for each SCC.
5129 * Within each SCC, there is only one SCC by definition.
5130 * Each SCC initially belongs to a cluster containing only that SCC.
5132 static isl_stat
clustering_init(isl_ctx
*ctx
, struct isl_clustering
*c
,
5133 struct isl_sched_graph
*graph
)
5138 c
->scc
= isl_calloc_array(ctx
, struct isl_sched_graph
, c
->n
);
5139 c
->cluster
= isl_calloc_array(ctx
, struct isl_sched_graph
, c
->n
);
5140 c
->scc_cluster
= isl_calloc_array(ctx
, int, c
->n
);
5141 c
->scc_node
= isl_calloc_array(ctx
, int, c
->n
);
5142 c
->scc_in_merge
= isl_calloc_array(ctx
, int, c
->n
);
5143 if (!c
->scc
|| !c
->cluster
||
5144 !c
->scc_cluster
|| !c
->scc_node
|| !c
->scc_in_merge
)
5145 return isl_stat_error
;
5147 for (i
= 0; i
< c
->n
; ++i
) {
5148 if (extract_sub_graph(ctx
, graph
, &node_scc_exactly
,
5149 &edge_scc_exactly
, i
, &c
->scc
[i
]) < 0)
5150 return isl_stat_error
;
5152 if (compute_maxvar(&c
->scc
[i
]) < 0)
5153 return isl_stat_error
;
5154 if (compute_schedule_wcc_band(ctx
, &c
->scc
[i
]) < 0)
5155 return isl_stat_error
;
5156 c
->scc_cluster
[i
] = i
;
5162 /* Free all memory allocated for "c".
5164 static void clustering_free(isl_ctx
*ctx
, struct isl_clustering
*c
)
5169 for (i
= 0; i
< c
->n
; ++i
)
5170 graph_free(ctx
, &c
->scc
[i
]);
5173 for (i
= 0; i
< c
->n
; ++i
)
5174 graph_free(ctx
, &c
->cluster
[i
]);
5176 free(c
->scc_cluster
);
5178 free(c
->scc_in_merge
);
5181 /* Should we refrain from merging the cluster in "graph" with
5182 * any other cluster?
5183 * In particular, is its current schedule band empty and incomplete.
5185 static int bad_cluster(struct isl_sched_graph
*graph
)
5187 return graph
->n_row
< graph
->maxvar
&&
5188 graph
->n_total_row
== graph
->band_start
;
5191 /* Is "edge" a proximity edge with a non-empty dependence relation?
5193 static isl_bool
is_non_empty_proximity(struct isl_sched_edge
*edge
)
5195 if (!is_proximity(edge
))
5196 return isl_bool_false
;
5197 return isl_bool_not(isl_map_plain_is_empty(edge
->map
));
5200 /* Return the index of an edge in "graph" that can be used to merge
5201 * two clusters in "c".
5202 * Return graph->n_edge if no such edge can be found.
5203 * Return -1 on error.
5205 * In particular, return a proximity edge between two clusters
5206 * that is not marked "no_merge" and such that neither of the
5207 * two clusters has an incomplete, empty band.
5209 * If there are multiple such edges, then try and find the most
5210 * appropriate edge to use for merging. In particular, pick the edge
5211 * with the greatest weight. If there are multiple of those,
5212 * then pick one with the shortest distance between
5213 * the two cluster representatives.
5215 static int find_proximity(struct isl_sched_graph
*graph
,
5216 struct isl_clustering
*c
)
5218 int i
, best
= graph
->n_edge
, best_dist
, best_weight
;
5220 for (i
= 0; i
< graph
->n_edge
; ++i
) {
5221 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
5225 prox
= is_non_empty_proximity(edge
);
5232 if (bad_cluster(&c
->scc
[edge
->src
->scc
]) ||
5233 bad_cluster(&c
->scc
[edge
->dst
->scc
]))
5235 dist
= c
->scc_cluster
[edge
->dst
->scc
] -
5236 c
->scc_cluster
[edge
->src
->scc
];
5239 weight
= edge
->weight
;
5240 if (best
< graph
->n_edge
) {
5241 if (best_weight
> weight
)
5243 if (best_weight
== weight
&& best_dist
<= dist
)
5248 best_weight
= weight
;
5254 /* Internal data structure used in mark_merge_sccs.
5256 * "graph" is the dependence graph in which a strongly connected
5257 * component is constructed.
5258 * "scc_cluster" maps each SCC index to the cluster to which it belongs.
5259 * "src" and "dst" are the indices of the nodes that are being merged.
5261 struct isl_mark_merge_sccs_data
{
5262 struct isl_sched_graph
*graph
;
5268 /* Check whether the cluster containing node "i" depends on the cluster
5269 * containing node "j". If "i" and "j" belong to the same cluster,
5270 * then they are taken to depend on each other to ensure that
5271 * the resulting strongly connected component consists of complete
5272 * clusters. Furthermore, if "i" and "j" are the two nodes that
5273 * are being merged, then they are taken to depend on each other as well.
5274 * Otherwise, check if there is a (conditional) validity dependence
5275 * from node[j] to node[i], forcing node[i] to follow node[j].
5277 static isl_bool
cluster_follows(int i
, int j
, void *user
)
5279 struct isl_mark_merge_sccs_data
*data
= user
;
5280 struct isl_sched_graph
*graph
= data
->graph
;
5281 int *scc_cluster
= data
->scc_cluster
;
5283 if (data
->src
== i
&& data
->dst
== j
)
5284 return isl_bool_true
;
5285 if (data
->src
== j
&& data
->dst
== i
)
5286 return isl_bool_true
;
5287 if (scc_cluster
[graph
->node
[i
].scc
] == scc_cluster
[graph
->node
[j
].scc
])
5288 return isl_bool_true
;
5290 return graph_has_validity_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
5293 /* Mark all SCCs that belong to either of the two clusters in "c"
5294 * connected by the edge in "graph" with index "edge", or to any
5295 * of the intermediate clusters.
5296 * The marking is recorded in c->scc_in_merge.
5298 * The given edge has been selected for merging two clusters,
5299 * meaning that there is at least a proximity edge between the two nodes.
5300 * However, there may also be (indirect) validity dependences
5301 * between the two nodes. When merging the two clusters, all clusters
5302 * containing one or more of the intermediate nodes along the
5303 * indirect validity dependences need to be merged in as well.
5305 * First collect all such nodes by computing the strongly connected
5306 * component (SCC) containing the two nodes connected by the edge, where
5307 * the two nodes are considered to depend on each other to make
5308 * sure they end up in the same SCC. Similarly, each node is considered
5309 * to depend on every other node in the same cluster to ensure
5310 * that the SCC consists of complete clusters.
5312 * Then the original SCCs that contain any of these nodes are marked
5313 * in c->scc_in_merge.
5315 static isl_stat
mark_merge_sccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
5316 int edge
, struct isl_clustering
*c
)
5318 struct isl_mark_merge_sccs_data data
;
5319 struct isl_tarjan_graph
*g
;
5322 for (i
= 0; i
< c
->n
; ++i
)
5323 c
->scc_in_merge
[i
] = 0;
5326 data
.scc_cluster
= c
->scc_cluster
;
5327 data
.src
= graph
->edge
[edge
].src
- graph
->node
;
5328 data
.dst
= graph
->edge
[edge
].dst
- graph
->node
;
5330 g
= isl_tarjan_graph_component(ctx
, graph
->n
, data
.dst
,
5331 &cluster_follows
, &data
);
5337 isl_die(ctx
, isl_error_internal
,
5338 "expecting at least two nodes in component",
5340 if (g
->order
[--i
] != -1)
5341 isl_die(ctx
, isl_error_internal
,
5342 "expecting end of component marker", goto error
);
5344 for (--i
; i
>= 0 && g
->order
[i
] != -1; --i
) {
5345 int scc
= graph
->node
[g
->order
[i
]].scc
;
5346 c
->scc_in_merge
[scc
] = 1;
5349 isl_tarjan_graph_free(g
);
5352 isl_tarjan_graph_free(g
);
5353 return isl_stat_error
;
5356 /* Construct the identifier "cluster_i".
5358 static __isl_give isl_id
*cluster_id(isl_ctx
*ctx
, int i
)
5362 snprintf(name
, sizeof(name
), "cluster_%d", i
);
5363 return isl_id_alloc(ctx
, name
, NULL
);
5366 /* Construct the space of the cluster with index "i" containing
5367 * the strongly connected component "scc".
5369 * In particular, construct a space called cluster_i with dimension equal
5370 * to the number of schedule rows in the current band of "scc".
5372 static __isl_give isl_space
*cluster_space(struct isl_sched_graph
*scc
, int i
)
5378 nvar
= scc
->n_total_row
- scc
->band_start
;
5379 space
= isl_space_copy(scc
->node
[0].space
);
5380 space
= isl_space_params(space
);
5381 space
= isl_space_set_from_params(space
);
5382 space
= isl_space_add_dims(space
, isl_dim_set
, nvar
);
5383 id
= cluster_id(isl_space_get_ctx(space
), i
);
5384 space
= isl_space_set_tuple_id(space
, isl_dim_set
, id
);
5389 /* Collect the domain of the graph for merging clusters.
5391 * In particular, for each cluster with first SCC "i", construct
5392 * a set in the space called cluster_i with dimension equal
5393 * to the number of schedule rows in the current band of the cluster.
5395 static __isl_give isl_union_set
*collect_domain(isl_ctx
*ctx
,
5396 struct isl_sched_graph
*graph
, struct isl_clustering
*c
)
5400 isl_union_set
*domain
;
5402 space
= isl_space_params_alloc(ctx
, 0);
5403 domain
= isl_union_set_empty(space
);
5405 for (i
= 0; i
< graph
->scc
; ++i
) {
5408 if (!c
->scc_in_merge
[i
])
5410 if (c
->scc_cluster
[i
] != i
)
5412 space
= cluster_space(&c
->scc
[i
], i
);
5413 domain
= isl_union_set_add_set(domain
, isl_set_universe(space
));
5419 /* Construct a map from the original instances to the corresponding
5420 * cluster instance in the current bands of the clusters in "c".
5422 static __isl_give isl_union_map
*collect_cluster_map(isl_ctx
*ctx
,
5423 struct isl_sched_graph
*graph
, struct isl_clustering
*c
)
5427 isl_union_map
*cluster_map
;
5429 space
= isl_space_params_alloc(ctx
, 0);
5430 cluster_map
= isl_union_map_empty(space
);
5431 for (i
= 0; i
< graph
->scc
; ++i
) {
5435 if (!c
->scc_in_merge
[i
])
5438 id
= cluster_id(ctx
, c
->scc_cluster
[i
]);
5439 start
= c
->scc
[i
].band_start
;
5440 n
= c
->scc
[i
].n_total_row
- start
;
5441 for (j
= 0; j
< c
->scc
[i
].n
; ++j
) {
5444 struct isl_sched_node
*node
= &c
->scc
[i
].node
[j
];
5446 ma
= node_extract_partial_schedule_multi_aff(node
,
5448 ma
= isl_multi_aff_set_tuple_id(ma
, isl_dim_out
,
5450 map
= isl_map_from_multi_aff(ma
);
5451 cluster_map
= isl_union_map_add_map(cluster_map
, map
);
5459 /* Add "umap" to the schedule constraints "sc" of all types of "edge"
5460 * that are not isl_edge_condition or isl_edge_conditional_validity.
5462 static __isl_give isl_schedule_constraints
*add_non_conditional_constraints(
5463 struct isl_sched_edge
*edge
, __isl_keep isl_union_map
*umap
,
5464 __isl_take isl_schedule_constraints
*sc
)
5466 enum isl_edge_type t
;
5471 for (t
= isl_edge_first
; t
<= isl_edge_last
; ++t
) {
5472 if (t
== isl_edge_condition
||
5473 t
== isl_edge_conditional_validity
)
5475 if (!is_type(edge
, t
))
5477 sc
= isl_schedule_constraints_add(sc
, t
,
5478 isl_union_map_copy(umap
));
5484 /* Add schedule constraints of types isl_edge_condition and
5485 * isl_edge_conditional_validity to "sc" by applying "umap" to
5486 * the domains of the wrapped relations in domain and range
5487 * of the corresponding tagged constraints of "edge".
5489 static __isl_give isl_schedule_constraints
*add_conditional_constraints(
5490 struct isl_sched_edge
*edge
, __isl_keep isl_union_map
*umap
,
5491 __isl_take isl_schedule_constraints
*sc
)
5493 enum isl_edge_type t
;
5494 isl_union_map
*tagged
;
5496 for (t
= isl_edge_condition
; t
<= isl_edge_conditional_validity
; ++t
) {
5497 if (!is_type(edge
, t
))
5499 if (t
== isl_edge_condition
)
5500 tagged
= isl_union_map_copy(edge
->tagged_condition
);
5502 tagged
= isl_union_map_copy(edge
->tagged_validity
);
5503 tagged
= isl_union_map_zip(tagged
);
5504 tagged
= isl_union_map_apply_domain(tagged
,
5505 isl_union_map_copy(umap
));
5506 tagged
= isl_union_map_zip(tagged
);
5507 sc
= isl_schedule_constraints_add(sc
, t
, tagged
);
5515 /* Given a mapping "cluster_map" from the original instances to
5516 * the cluster instances, add schedule constraints on the clusters
5517 * to "sc" corresponding to the original constraints represented by "edge".
5519 * For non-tagged dependence constraints, the cluster constraints
5520 * are obtained by applying "cluster_map" to the edge->map.
5522 * For tagged dependence constraints, "cluster_map" needs to be applied
5523 * to the domains of the wrapped relations in domain and range
5524 * of the tagged dependence constraints. Pick out the mappings
5525 * from these domains from "cluster_map" and construct their product.
5526 * This mapping can then be applied to the pair of domains.
5528 static __isl_give isl_schedule_constraints
*collect_edge_constraints(
5529 struct isl_sched_edge
*edge
, __isl_keep isl_union_map
*cluster_map
,
5530 __isl_take isl_schedule_constraints
*sc
)
5532 isl_union_map
*umap
;
5534 isl_union_set
*uset
;
5535 isl_union_map
*umap1
, *umap2
;
5540 umap
= isl_union_map_from_map(isl_map_copy(edge
->map
));
5541 umap
= isl_union_map_apply_domain(umap
,
5542 isl_union_map_copy(cluster_map
));
5543 umap
= isl_union_map_apply_range(umap
,
5544 isl_union_map_copy(cluster_map
));
5545 sc
= add_non_conditional_constraints(edge
, umap
, sc
);
5546 isl_union_map_free(umap
);
5548 if (!sc
|| (!is_condition(edge
) && !is_conditional_validity(edge
)))
5551 space
= isl_space_domain(isl_map_get_space(edge
->map
));
5552 uset
= isl_union_set_from_set(isl_set_universe(space
));
5553 umap1
= isl_union_map_copy(cluster_map
);
5554 umap1
= isl_union_map_intersect_domain(umap1
, uset
);
5555 space
= isl_space_range(isl_map_get_space(edge
->map
));
5556 uset
= isl_union_set_from_set(isl_set_universe(space
));
5557 umap2
= isl_union_map_copy(cluster_map
);
5558 umap2
= isl_union_map_intersect_domain(umap2
, uset
);
5559 umap
= isl_union_map_product(umap1
, umap2
);
5561 sc
= add_conditional_constraints(edge
, umap
, sc
);
5563 isl_union_map_free(umap
);
5567 /* Given a mapping "cluster_map" from the original instances to
5568 * the cluster instances, add schedule constraints on the clusters
5569 * to "sc" corresponding to all edges in "graph" between nodes that
5570 * belong to SCCs that are marked for merging in "scc_in_merge".
5572 static __isl_give isl_schedule_constraints
*collect_constraints(
5573 struct isl_sched_graph
*graph
, int *scc_in_merge
,
5574 __isl_keep isl_union_map
*cluster_map
,
5575 __isl_take isl_schedule_constraints
*sc
)
5579 for (i
= 0; i
< graph
->n_edge
; ++i
) {
5580 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
5582 if (!scc_in_merge
[edge
->src
->scc
])
5584 if (!scc_in_merge
[edge
->dst
->scc
])
5586 sc
= collect_edge_constraints(edge
, cluster_map
, sc
);
5592 /* Construct a dependence graph for scheduling clusters with respect
5593 * to each other and store the result in "merge_graph".
5594 * In particular, the nodes of the graph correspond to the schedule
5595 * dimensions of the current bands of those clusters that have been
5596 * marked for merging in "c".
5598 * First construct an isl_schedule_constraints object for this domain
5599 * by transforming the edges in "graph" to the domain.
5600 * Then initialize a dependence graph for scheduling from these
5603 static isl_stat
init_merge_graph(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
5604 struct isl_clustering
*c
, struct isl_sched_graph
*merge_graph
)
5606 isl_union_set
*domain
;
5607 isl_union_map
*cluster_map
;
5608 isl_schedule_constraints
*sc
;
5611 domain
= collect_domain(ctx
, graph
, c
);
5612 sc
= isl_schedule_constraints_on_domain(domain
);
5614 return isl_stat_error
;
5615 cluster_map
= collect_cluster_map(ctx
, graph
, c
);
5616 sc
= collect_constraints(graph
, c
->scc_in_merge
, cluster_map
, sc
);
5617 isl_union_map_free(cluster_map
);
5619 r
= graph_init(merge_graph
, sc
);
5621 isl_schedule_constraints_free(sc
);
5626 /* Compute the maximal number of remaining schedule rows that still need
5627 * to be computed for the nodes that belong to clusters with the maximal
5628 * dimension for the current band (i.e., the band that is to be merged).
5629 * Only clusters that are about to be merged are considered.
5630 * "maxvar" is the maximal dimension for the current band.
5631 * "c" contains information about the clusters.
5633 * Return the maximal number of remaining schedule rows or -1 on error.
5635 static int compute_maxvar_max_slack(int maxvar
, struct isl_clustering
*c
)
5641 for (i
= 0; i
< c
->n
; ++i
) {
5643 struct isl_sched_graph
*scc
;
5645 if (!c
->scc_in_merge
[i
])
5648 nvar
= scc
->n_total_row
- scc
->band_start
;
5651 for (j
= 0; j
< scc
->n
; ++j
) {
5652 struct isl_sched_node
*node
= &scc
->node
[j
];
5655 if (node_update_vmap(node
) < 0)
5657 slack
= node
->nvar
- node
->rank
;
5658 if (slack
> max_slack
)
5666 /* If there are any clusters where the dimension of the current band
5667 * (i.e., the band that is to be merged) is smaller than "maxvar" and
5668 * if there are any nodes in such a cluster where the number
5669 * of remaining schedule rows that still need to be computed
5670 * is greater than "max_slack", then return the smallest current band
5671 * dimension of all these clusters. Otherwise return the original value
5672 * of "maxvar". Return -1 in case of any error.
5673 * Only clusters that are about to be merged are considered.
5674 * "c" contains information about the clusters.
5676 static int limit_maxvar_to_slack(int maxvar
, int max_slack
,
5677 struct isl_clustering
*c
)
5681 for (i
= 0; i
< c
->n
; ++i
) {
5683 struct isl_sched_graph
*scc
;
5685 if (!c
->scc_in_merge
[i
])
5688 nvar
= scc
->n_total_row
- scc
->band_start
;
5691 for (j
= 0; j
< scc
->n
; ++j
) {
5692 struct isl_sched_node
*node
= &scc
->node
[j
];
5695 if (node_update_vmap(node
) < 0)
5697 slack
= node
->nvar
- node
->rank
;
5698 if (slack
> max_slack
) {
5708 /* Adjust merge_graph->maxvar based on the number of remaining schedule rows
5709 * that still need to be computed. In particular, if there is a node
5710 * in a cluster where the dimension of the current band is smaller
5711 * than merge_graph->maxvar, but the number of remaining schedule rows
5712 * is greater than that of any node in a cluster with the maximal
5713 * dimension for the current band (i.e., merge_graph->maxvar),
5714 * then adjust merge_graph->maxvar to the (smallest) current band dimension
5715 * of those clusters. Without this adjustment, the total number of
5716 * schedule dimensions would be increased, resulting in a skewed view
5717 * of the number of coincident dimensions.
5718 * "c" contains information about the clusters.
5720 * If the maximize_band_depth option is set and merge_graph->maxvar is reduced,
5721 * then there is no point in attempting any merge since it will be rejected
5722 * anyway. Set merge_graph->maxvar to zero in such cases.
5724 static isl_stat
adjust_maxvar_to_slack(isl_ctx
*ctx
,
5725 struct isl_sched_graph
*merge_graph
, struct isl_clustering
*c
)
5727 int max_slack
, maxvar
;
5729 max_slack
= compute_maxvar_max_slack(merge_graph
->maxvar
, c
);
5731 return isl_stat_error
;
5732 maxvar
= limit_maxvar_to_slack(merge_graph
->maxvar
, max_slack
, c
);
5734 return isl_stat_error
;
5736 if (maxvar
< merge_graph
->maxvar
) {
5737 if (isl_options_get_schedule_maximize_band_depth(ctx
))
5738 merge_graph
->maxvar
= 0;
5740 merge_graph
->maxvar
= maxvar
;
5746 /* Return the number of coincident dimensions in the current band of "graph",
5747 * where the nodes of "graph" are assumed to be scheduled by a single band.
5749 static int get_n_coincident(struct isl_sched_graph
*graph
)
5753 for (i
= graph
->band_start
; i
< graph
->n_total_row
; ++i
)
5754 if (!graph
->node
[0].coincident
[i
])
5757 return i
- graph
->band_start
;
5760 /* Should the clusters be merged based on the cluster schedule
5761 * in the current (and only) band of "merge_graph", given that
5762 * coincidence should be maximized?
5764 * If the number of coincident schedule dimensions in the merged band
5765 * would be less than the maximal number of coincident schedule dimensions
5766 * in any of the merged clusters, then the clusters should not be merged.
5768 static isl_bool
ok_to_merge_coincident(struct isl_clustering
*c
,
5769 struct isl_sched_graph
*merge_graph
)
5776 for (i
= 0; i
< c
->n
; ++i
) {
5777 if (!c
->scc_in_merge
[i
])
5779 n_coincident
= get_n_coincident(&c
->scc
[i
]);
5780 if (n_coincident
> max_coincident
)
5781 max_coincident
= n_coincident
;
5784 n_coincident
= get_n_coincident(merge_graph
);
5786 return n_coincident
>= max_coincident
;
5789 /* Return the transformation on "node" expressed by the current (and only)
5790 * band of "merge_graph" applied to the clusters in "c".
5792 * First find the representation of "node" in its SCC in "c" and
5793 * extract the transformation expressed by the current band.
5794 * Then extract the transformation applied by "merge_graph"
5795 * to the cluster to which this SCC belongs.
5796 * Combine the two to obtain the complete transformation on the node.
5798 * Note that the range of the first transformation is an anonymous space,
5799 * while the domain of the second is named "cluster_X". The range
5800 * of the former therefore needs to be adjusted before the two
5803 static __isl_give isl_map
*extract_node_transformation(isl_ctx
*ctx
,
5804 struct isl_sched_node
*node
, struct isl_clustering
*c
,
5805 struct isl_sched_graph
*merge_graph
)
5807 struct isl_sched_node
*scc_node
, *cluster_node
;
5811 isl_multi_aff
*ma
, *ma2
;
5813 scc_node
= graph_find_node(ctx
, &c
->scc
[node
->scc
], node
->space
);
5814 start
= c
->scc
[node
->scc
].band_start
;
5815 n
= c
->scc
[node
->scc
].n_total_row
- start
;
5816 ma
= node_extract_partial_schedule_multi_aff(scc_node
, start
, n
);
5817 space
= cluster_space(&c
->scc
[node
->scc
], c
->scc_cluster
[node
->scc
]);
5818 cluster_node
= graph_find_node(ctx
, merge_graph
, space
);
5819 if (space
&& !cluster_node
)
5820 isl_die(ctx
, isl_error_internal
, "unable to find cluster",
5821 space
= isl_space_free(space
));
5822 id
= isl_space_get_tuple_id(space
, isl_dim_set
);
5823 ma
= isl_multi_aff_set_tuple_id(ma
, isl_dim_out
, id
);
5824 isl_space_free(space
);
5825 n
= merge_graph
->n_total_row
;
5826 ma2
= node_extract_partial_schedule_multi_aff(cluster_node
, 0, n
);
5827 ma
= isl_multi_aff_pullback_multi_aff(ma2
, ma
);
5829 return isl_map_from_multi_aff(ma
);
5832 /* Give a set of distances "set", are they bounded by a small constant
5833 * in direction "pos"?
5834 * In practice, check if they are bounded by 2 by checking that there
5835 * are no elements with a value greater than or equal to 3 or
5836 * smaller than or equal to -3.
5838 static isl_bool
distance_is_bounded(__isl_keep isl_set
*set
, int pos
)
5844 return isl_bool_error
;
5846 test
= isl_set_copy(set
);
5847 test
= isl_set_lower_bound_si(test
, isl_dim_set
, pos
, 3);
5848 bounded
= isl_set_is_empty(test
);
5851 if (bounded
< 0 || !bounded
)
5854 test
= isl_set_copy(set
);
5855 test
= isl_set_upper_bound_si(test
, isl_dim_set
, pos
, -3);
5856 bounded
= isl_set_is_empty(test
);
5862 /* Does the set "set" have a fixed (but possible parametric) value
5863 * at dimension "pos"?
5865 static isl_bool
has_single_value(__isl_keep isl_set
*set
, int pos
)
5871 return isl_bool_error
;
5872 set
= isl_set_copy(set
);
5873 n
= isl_set_dim(set
, isl_dim_set
);
5874 set
= isl_set_project_out(set
, isl_dim_set
, pos
+ 1, n
- (pos
+ 1));
5875 set
= isl_set_project_out(set
, isl_dim_set
, 0, pos
);
5876 single
= isl_set_is_singleton(set
);
5882 /* Does "map" have a fixed (but possible parametric) value
5883 * at dimension "pos" of either its domain or its range?
5885 static isl_bool
has_singular_src_or_dst(__isl_keep isl_map
*map
, int pos
)
5890 set
= isl_map_domain(isl_map_copy(map
));
5891 single
= has_single_value(set
, pos
);
5894 if (single
< 0 || single
)
5897 set
= isl_map_range(isl_map_copy(map
));
5898 single
= has_single_value(set
, pos
);
5904 /* Does the edge "edge" from "graph" have bounded dependence distances
5905 * in the merged graph "merge_graph" of a selection of clusters in "c"?
5907 * Extract the complete transformations of the source and destination
5908 * nodes of the edge, apply them to the edge constraints and
5909 * compute the differences. Finally, check if these differences are bounded
5910 * in each direction.
5912 * If the dimension of the band is greater than the number of
5913 * dimensions that can be expected to be optimized by the edge
5914 * (based on its weight), then also allow the differences to be unbounded
5915 * in the remaining dimensions, but only if either the source or
5916 * the destination has a fixed value in that direction.
5917 * This allows a statement that produces values that are used by
5918 * several instances of another statement to be merged with that
5920 * However, merging such clusters will introduce an inherently
5921 * large proximity distance inside the merged cluster, meaning
5922 * that proximity distances will no longer be optimized in
5923 * subsequent merges. These merges are therefore only allowed
5924 * after all other possible merges have been tried.
5925 * The first time such a merge is encountered, the weight of the edge
5926 * is replaced by a negative weight. The second time (i.e., after
5927 * all merges over edges with a non-negative weight have been tried),
5928 * the merge is allowed.
5930 static isl_bool
has_bounded_distances(isl_ctx
*ctx
, struct isl_sched_edge
*edge
,
5931 struct isl_sched_graph
*graph
, struct isl_clustering
*c
,
5932 struct isl_sched_graph
*merge_graph
)
5939 map
= isl_map_copy(edge
->map
);
5940 t
= extract_node_transformation(ctx
, edge
->src
, c
, merge_graph
);
5941 map
= isl_map_apply_domain(map
, t
);
5942 t
= extract_node_transformation(ctx
, edge
->dst
, c
, merge_graph
);
5943 map
= isl_map_apply_range(map
, t
);
5944 dist
= isl_map_deltas(isl_map_copy(map
));
5946 bounded
= isl_bool_true
;
5947 n
= isl_set_dim(dist
, isl_dim_set
);
5948 n_slack
= n
- edge
->weight
;
5949 if (edge
->weight
< 0)
5950 n_slack
-= graph
->max_weight
+ 1;
5951 for (i
= 0; i
< n
; ++i
) {
5952 isl_bool bounded_i
, singular_i
;
5954 bounded_i
= distance_is_bounded(dist
, i
);
5959 if (edge
->weight
>= 0)
5960 bounded
= isl_bool_false
;
5964 singular_i
= has_singular_src_or_dst(map
, i
);
5969 bounded
= isl_bool_false
;
5972 if (!bounded
&& i
>= n
&& edge
->weight
>= 0)
5973 edge
->weight
-= graph
->max_weight
+ 1;
5981 return isl_bool_error
;
5984 /* Should the clusters be merged based on the cluster schedule
5985 * in the current (and only) band of "merge_graph"?
5986 * "graph" is the original dependence graph, while "c" records
5987 * which SCCs are involved in the latest merge.
5989 * In particular, is there at least one proximity constraint
5990 * that is optimized by the merge?
5992 * A proximity constraint is considered to be optimized
5993 * if the dependence distances are small.
5995 static isl_bool
ok_to_merge_proximity(isl_ctx
*ctx
,
5996 struct isl_sched_graph
*graph
, struct isl_clustering
*c
,
5997 struct isl_sched_graph
*merge_graph
)
6001 for (i
= 0; i
< graph
->n_edge
; ++i
) {
6002 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
6005 if (!is_proximity(edge
))
6007 if (!c
->scc_in_merge
[edge
->src
->scc
])
6009 if (!c
->scc_in_merge
[edge
->dst
->scc
])
6011 if (c
->scc_cluster
[edge
->dst
->scc
] ==
6012 c
->scc_cluster
[edge
->src
->scc
])
6014 bounded
= has_bounded_distances(ctx
, edge
, graph
, c
,
6016 if (bounded
< 0 || bounded
)
6020 return isl_bool_false
;
6023 /* Should the clusters be merged based on the cluster schedule
6024 * in the current (and only) band of "merge_graph"?
6025 * "graph" is the original dependence graph, while "c" records
6026 * which SCCs are involved in the latest merge.
6028 * If the current band is empty, then the clusters should not be merged.
6030 * If the band depth should be maximized and the merge schedule
6031 * is incomplete (meaning that the dimension of some of the schedule
6032 * bands in the original schedule will be reduced), then the clusters
6033 * should not be merged.
6035 * If the schedule_maximize_coincidence option is set, then check that
6036 * the number of coincident schedule dimensions is not reduced.
6038 * Finally, only allow the merge if at least one proximity
6039 * constraint is optimized.
6041 static isl_bool
ok_to_merge(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
6042 struct isl_clustering
*c
, struct isl_sched_graph
*merge_graph
)
6044 if (merge_graph
->n_total_row
== merge_graph
->band_start
)
6045 return isl_bool_false
;
6047 if (isl_options_get_schedule_maximize_band_depth(ctx
) &&
6048 merge_graph
->n_total_row
< merge_graph
->maxvar
)
6049 return isl_bool_false
;
6051 if (isl_options_get_schedule_maximize_coincidence(ctx
)) {
6054 ok
= ok_to_merge_coincident(c
, merge_graph
);
6059 return ok_to_merge_proximity(ctx
, graph
, c
, merge_graph
);
6062 /* Apply the schedule in "t_node" to the "n" rows starting at "first"
6063 * of the schedule in "node" and return the result.
6065 * That is, essentially compute
6067 * T * N(first:first+n-1)
6069 * taking into account the constant term and the parameter coefficients
6072 static __isl_give isl_mat
*node_transformation(isl_ctx
*ctx
,
6073 struct isl_sched_node
*t_node
, struct isl_sched_node
*node
,
6078 int n_row
, n_col
, n_param
, n_var
;
6080 n_param
= node
->nparam
;
6082 n_row
= isl_mat_rows(t_node
->sched
);
6083 n_col
= isl_mat_cols(node
->sched
);
6084 t
= isl_mat_alloc(ctx
, n_row
, n_col
);
6087 for (i
= 0; i
< n_row
; ++i
) {
6088 isl_seq_cpy(t
->row
[i
], t_node
->sched
->row
[i
], 1 + n_param
);
6089 isl_seq_clr(t
->row
[i
] + 1 + n_param
, n_var
);
6090 for (j
= 0; j
< n
; ++j
)
6091 isl_seq_addmul(t
->row
[i
],
6092 t_node
->sched
->row
[i
][1 + n_param
+ j
],
6093 node
->sched
->row
[first
+ j
],
6094 1 + n_param
+ n_var
);
6099 /* Apply the cluster schedule in "t_node" to the current band
6100 * schedule of the nodes in "graph".
6102 * In particular, replace the rows starting at band_start
6103 * by the result of applying the cluster schedule in "t_node"
6104 * to the original rows.
6106 * The coincidence of the schedule is determined by the coincidence
6107 * of the cluster schedule.
6109 static isl_stat
transform(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
6110 struct isl_sched_node
*t_node
)
6116 start
= graph
->band_start
;
6117 n
= graph
->n_total_row
- start
;
6119 n_new
= isl_mat_rows(t_node
->sched
);
6120 for (i
= 0; i
< graph
->n
; ++i
) {
6121 struct isl_sched_node
*node
= &graph
->node
[i
];
6124 t
= node_transformation(ctx
, t_node
, node
, start
, n
);
6125 node
->sched
= isl_mat_drop_rows(node
->sched
, start
, n
);
6126 node
->sched
= isl_mat_concat(node
->sched
, t
);
6127 node
->sched_map
= isl_map_free(node
->sched_map
);
6129 return isl_stat_error
;
6130 for (j
= 0; j
< n_new
; ++j
)
6131 node
->coincident
[start
+ j
] = t_node
->coincident
[j
];
6133 graph
->n_total_row
-= n
;
6135 graph
->n_total_row
+= n_new
;
6136 graph
->n_row
+= n_new
;
6141 /* Merge the clusters marked for merging in "c" into a single
6142 * cluster using the cluster schedule in the current band of "merge_graph".
6143 * The representative SCC for the new cluster is the SCC with
6144 * the smallest index.
6146 * The current band schedule of each SCC in the new cluster is obtained
6147 * by applying the schedule of the corresponding original cluster
6148 * to the original band schedule.
6149 * All SCCs in the new cluster have the same number of schedule rows.
6151 static isl_stat
merge(isl_ctx
*ctx
, struct isl_clustering
*c
,
6152 struct isl_sched_graph
*merge_graph
)
6158 for (i
= 0; i
< c
->n
; ++i
) {
6159 struct isl_sched_node
*node
;
6161 if (!c
->scc_in_merge
[i
])
6165 space
= cluster_space(&c
->scc
[i
], c
->scc_cluster
[i
]);
6167 return isl_stat_error
;
6168 node
= graph_find_node(ctx
, merge_graph
, space
);
6169 isl_space_free(space
);
6171 isl_die(ctx
, isl_error_internal
,
6172 "unable to find cluster",
6173 return isl_stat_error
);
6174 if (transform(ctx
, &c
->scc
[i
], node
) < 0)
6175 return isl_stat_error
;
6176 c
->scc_cluster
[i
] = cluster
;
6182 /* Try and merge the clusters of SCCs marked in c->scc_in_merge
6183 * by scheduling the current cluster bands with respect to each other.
6185 * Construct a dependence graph with a space for each cluster and
6186 * with the coordinates of each space corresponding to the schedule
6187 * dimensions of the current band of that cluster.
6188 * Construct a cluster schedule in this cluster dependence graph and
6189 * apply it to the current cluster bands if it is applicable
6190 * according to ok_to_merge.
6192 * If the number of remaining schedule dimensions in a cluster
6193 * with a non-maximal current schedule dimension is greater than
6194 * the number of remaining schedule dimensions in clusters
6195 * with a maximal current schedule dimension, then restrict
6196 * the number of rows to be computed in the cluster schedule
6197 * to the minimal such non-maximal current schedule dimension.
6198 * Do this by adjusting merge_graph.maxvar.
6200 * Return isl_bool_true if the clusters have effectively been merged
6201 * into a single cluster.
6203 * Note that since the standard scheduling algorithm minimizes the maximal
6204 * distance over proximity constraints, the proximity constraints between
6205 * the merged clusters may not be optimized any further than what is
6206 * sufficient to bring the distances within the limits of the internal
6207 * proximity constraints inside the individual clusters.
6208 * It may therefore make sense to perform an additional translation step
6209 * to bring the clusters closer to each other, while maintaining
6210 * the linear part of the merging schedule found using the standard
6211 * scheduling algorithm.
6213 static isl_bool
try_merge(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
6214 struct isl_clustering
*c
)
6216 struct isl_sched_graph merge_graph
= { 0 };
6219 if (init_merge_graph(ctx
, graph
, c
, &merge_graph
) < 0)
6222 if (compute_maxvar(&merge_graph
) < 0)
6224 if (adjust_maxvar_to_slack(ctx
, &merge_graph
,c
) < 0)
6226 if (compute_schedule_wcc_band(ctx
, &merge_graph
) < 0)
6228 merged
= ok_to_merge(ctx
, graph
, c
, &merge_graph
);
6229 if (merged
&& merge(ctx
, c
, &merge_graph
) < 0)
6232 graph_free(ctx
, &merge_graph
);
6235 graph_free(ctx
, &merge_graph
);
6236 return isl_bool_error
;
6239 /* Is there any edge marked "no_merge" between two SCCs that are
6240 * about to be merged (i.e., that are set in "scc_in_merge")?
6241 * "merge_edge" is the proximity edge along which the clusters of SCCs
6242 * are going to be merged.
6244 * If there is any edge between two SCCs with a negative weight,
6245 * while the weight of "merge_edge" is non-negative, then this
6246 * means that the edge was postponed. "merge_edge" should then
6247 * also be postponed since merging along the edge with negative weight should
6248 * be postponed until all edges with non-negative weight have been tried.
6249 * Replace the weight of "merge_edge" by a negative weight as well and
6250 * tell the caller not to attempt a merge.
6252 static int any_no_merge(struct isl_sched_graph
*graph
, int *scc_in_merge
,
6253 struct isl_sched_edge
*merge_edge
)
6257 for (i
= 0; i
< graph
->n_edge
; ++i
) {
6258 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
6260 if (!scc_in_merge
[edge
->src
->scc
])
6262 if (!scc_in_merge
[edge
->dst
->scc
])
6266 if (merge_edge
->weight
>= 0 && edge
->weight
< 0) {
6267 merge_edge
->weight
-= graph
->max_weight
+ 1;
6275 /* Merge the two clusters in "c" connected by the edge in "graph"
6276 * with index "edge" into a single cluster.
6277 * If it turns out to be impossible to merge these two clusters,
6278 * then mark the edge as "no_merge" such that it will not be
6281 * First mark all SCCs that need to be merged. This includes the SCCs
6282 * in the two clusters, but it may also include the SCCs
6283 * of intermediate clusters.
6284 * If there is already a no_merge edge between any pair of such SCCs,
6285 * then simply mark the current edge as no_merge as well.
6286 * Likewise, if any of those edges was postponed by has_bounded_distances,
6287 * then postpone the current edge as well.
6288 * Otherwise, try and merge the clusters and mark "edge" as "no_merge"
6289 * if the clusters did not end up getting merged, unless the non-merge
6290 * is due to the fact that the edge was postponed. This postponement
6291 * can be recognized by a change in weight (from non-negative to negative).
6293 static isl_stat
merge_clusters_along_edge(isl_ctx
*ctx
,
6294 struct isl_sched_graph
*graph
, int edge
, struct isl_clustering
*c
)
6297 int edge_weight
= graph
->edge
[edge
].weight
;
6299 if (mark_merge_sccs(ctx
, graph
, edge
, c
) < 0)
6300 return isl_stat_error
;
6302 if (any_no_merge(graph
, c
->scc_in_merge
, &graph
->edge
[edge
]))
6303 merged
= isl_bool_false
;
6305 merged
= try_merge(ctx
, graph
, c
);
6307 return isl_stat_error
;
6308 if (!merged
&& edge_weight
== graph
->edge
[edge
].weight
)
6309 graph
->edge
[edge
].no_merge
= 1;
6314 /* Does "node" belong to the cluster identified by "cluster"?
6316 static int node_cluster_exactly(struct isl_sched_node
*node
, int cluster
)
6318 return node
->cluster
== cluster
;
6321 /* Does "edge" connect two nodes belonging to the cluster
6322 * identified by "cluster"?
6324 static int edge_cluster_exactly(struct isl_sched_edge
*edge
, int cluster
)
6326 return edge
->src
->cluster
== cluster
&& edge
->dst
->cluster
== cluster
;
6329 /* Swap the schedule of "node1" and "node2".
6330 * Both nodes have been derived from the same node in a common parent graph.
6331 * Since the "coincident" field is shared with that node
6332 * in the parent graph, there is no need to also swap this field.
6334 static void swap_sched(struct isl_sched_node
*node1
,
6335 struct isl_sched_node
*node2
)
6340 sched
= node1
->sched
;
6341 node1
->sched
= node2
->sched
;
6342 node2
->sched
= sched
;
6344 sched_map
= node1
->sched_map
;
6345 node1
->sched_map
= node2
->sched_map
;
6346 node2
->sched_map
= sched_map
;
6349 /* Copy the current band schedule from the SCCs that form the cluster
6350 * with index "pos" to the actual cluster at position "pos".
6351 * By construction, the index of the first SCC that belongs to the cluster
6354 * The order of the nodes inside both the SCCs and the cluster
6355 * is assumed to be same as the order in the original "graph".
6357 * Since the SCC graphs will no longer be used after this function,
6358 * the schedules are actually swapped rather than copied.
6360 static isl_stat
copy_partial(struct isl_sched_graph
*graph
,
6361 struct isl_clustering
*c
, int pos
)
6365 c
->cluster
[pos
].n_total_row
= c
->scc
[pos
].n_total_row
;
6366 c
->cluster
[pos
].n_row
= c
->scc
[pos
].n_row
;
6367 c
->cluster
[pos
].maxvar
= c
->scc
[pos
].maxvar
;
6369 for (i
= 0; i
< graph
->n
; ++i
) {
6373 if (graph
->node
[i
].cluster
!= pos
)
6375 s
= graph
->node
[i
].scc
;
6376 k
= c
->scc_node
[s
]++;
6377 swap_sched(&c
->cluster
[pos
].node
[j
], &c
->scc
[s
].node
[k
]);
6378 if (c
->scc
[s
].maxvar
> c
->cluster
[pos
].maxvar
)
6379 c
->cluster
[pos
].maxvar
= c
->scc
[s
].maxvar
;
6386 /* Is there a (conditional) validity dependence from node[j] to node[i],
6387 * forcing node[i] to follow node[j] or do the nodes belong to the same
6390 static isl_bool
node_follows_strong_or_same_cluster(int i
, int j
, void *user
)
6392 struct isl_sched_graph
*graph
= user
;
6394 if (graph
->node
[i
].cluster
== graph
->node
[j
].cluster
)
6395 return isl_bool_true
;
6396 return graph_has_validity_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
6399 /* Extract the merged clusters of SCCs in "graph", sort them, and
6400 * store them in c->clusters. Update c->scc_cluster accordingly.
6402 * First keep track of the cluster containing the SCC to which a node
6403 * belongs in the node itself.
6404 * Then extract the clusters into c->clusters, copying the current
6405 * band schedule from the SCCs that belong to the cluster.
6406 * Do this only once per cluster.
6408 * Finally, topologically sort the clusters and update c->scc_cluster
6409 * to match the new scc numbering. While the SCCs were originally
6410 * sorted already, some SCCs that depend on some other SCCs may
6411 * have been merged with SCCs that appear before these other SCCs.
6412 * A reordering may therefore be required.
6414 static isl_stat
extract_clusters(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
6415 struct isl_clustering
*c
)
6419 for (i
= 0; i
< graph
->n
; ++i
)
6420 graph
->node
[i
].cluster
= c
->scc_cluster
[graph
->node
[i
].scc
];
6422 for (i
= 0; i
< graph
->scc
; ++i
) {
6423 if (c
->scc_cluster
[i
] != i
)
6425 if (extract_sub_graph(ctx
, graph
, &node_cluster_exactly
,
6426 &edge_cluster_exactly
, i
, &c
->cluster
[i
]) < 0)
6427 return isl_stat_error
;
6428 c
->cluster
[i
].src_scc
= -1;
6429 c
->cluster
[i
].dst_scc
= -1;
6430 if (copy_partial(graph
, c
, i
) < 0)
6431 return isl_stat_error
;
6434 if (detect_ccs(ctx
, graph
, &node_follows_strong_or_same_cluster
) < 0)
6435 return isl_stat_error
;
6436 for (i
= 0; i
< graph
->n
; ++i
)
6437 c
->scc_cluster
[graph
->node
[i
].scc
] = graph
->node
[i
].cluster
;
6442 /* Compute weights on the proximity edges of "graph" that can
6443 * be used by find_proximity to find the most appropriate
6444 * proximity edge to use to merge two clusters in "c".
6445 * The weights are also used by has_bounded_distances to determine
6446 * whether the merge should be allowed.
6447 * Store the maximum of the computed weights in graph->max_weight.
6449 * The computed weight is a measure for the number of remaining schedule
6450 * dimensions that can still be completely aligned.
6451 * In particular, compute the number of equalities between
6452 * input dimensions and output dimensions in the proximity constraints.
6453 * The directions that are already handled by outer schedule bands
6454 * are projected out prior to determining this number.
6456 * Edges that will never be considered by find_proximity are ignored.
6458 static isl_stat
compute_weights(struct isl_sched_graph
*graph
,
6459 struct isl_clustering
*c
)
6463 graph
->max_weight
= 0;
6465 for (i
= 0; i
< graph
->n_edge
; ++i
) {
6466 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
6467 struct isl_sched_node
*src
= edge
->src
;
6468 struct isl_sched_node
*dst
= edge
->dst
;
6469 isl_basic_map
*hull
;
6473 prox
= is_non_empty_proximity(edge
);
6475 return isl_stat_error
;
6478 if (bad_cluster(&c
->scc
[edge
->src
->scc
]) ||
6479 bad_cluster(&c
->scc
[edge
->dst
->scc
]))
6481 if (c
->scc_cluster
[edge
->dst
->scc
] ==
6482 c
->scc_cluster
[edge
->src
->scc
])
6485 hull
= isl_map_affine_hull(isl_map_copy(edge
->map
));
6486 hull
= isl_basic_map_transform_dims(hull
, isl_dim_in
, 0,
6487 isl_mat_copy(src
->vmap
));
6488 hull
= isl_basic_map_transform_dims(hull
, isl_dim_out
, 0,
6489 isl_mat_copy(dst
->vmap
));
6490 hull
= isl_basic_map_project_out(hull
,
6491 isl_dim_in
, 0, src
->rank
);
6492 hull
= isl_basic_map_project_out(hull
,
6493 isl_dim_out
, 0, dst
->rank
);
6494 hull
= isl_basic_map_remove_divs(hull
);
6495 n_in
= isl_basic_map_dim(hull
, isl_dim_in
);
6496 n_out
= isl_basic_map_dim(hull
, isl_dim_out
);
6497 hull
= isl_basic_map_drop_constraints_not_involving_dims(hull
,
6498 isl_dim_in
, 0, n_in
);
6499 hull
= isl_basic_map_drop_constraints_not_involving_dims(hull
,
6500 isl_dim_out
, 0, n_out
);
6502 return isl_stat_error
;
6503 edge
->weight
= isl_basic_map_n_equality(hull
);
6504 isl_basic_map_free(hull
);
6506 if (edge
->weight
> graph
->max_weight
)
6507 graph
->max_weight
= edge
->weight
;
6513 /* Call compute_schedule_finish_band on each of the clusters in "c"
6514 * in their topological order. This order is determined by the scc
6515 * fields of the nodes in "graph".
6516 * Combine the results in a sequence expressing the topological order.
6518 * If there is only one cluster left, then there is no need to introduce
6519 * a sequence node. Also, in this case, the cluster necessarily contains
6520 * the SCC at position 0 in the original graph and is therefore also
6521 * stored in the first cluster of "c".
6523 static __isl_give isl_schedule_node
*finish_bands_clustering(
6524 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
6525 struct isl_clustering
*c
)
6529 isl_union_set_list
*filters
;
6531 if (graph
->scc
== 1)
6532 return compute_schedule_finish_band(node
, &c
->cluster
[0], 0);
6534 ctx
= isl_schedule_node_get_ctx(node
);
6536 filters
= extract_sccs(ctx
, graph
);
6537 node
= isl_schedule_node_insert_sequence(node
, filters
);
6539 for (i
= 0; i
< graph
->scc
; ++i
) {
6540 int j
= c
->scc_cluster
[i
];
6541 node
= isl_schedule_node_child(node
, i
);
6542 node
= isl_schedule_node_child(node
, 0);
6543 node
= compute_schedule_finish_band(node
, &c
->cluster
[j
], 0);
6544 node
= isl_schedule_node_parent(node
);
6545 node
= isl_schedule_node_parent(node
);
6551 /* Compute a schedule for a connected dependence graph by first considering
6552 * each strongly connected component (SCC) in the graph separately and then
6553 * incrementally combining them into clusters.
6554 * Return the updated schedule node.
6556 * Initially, each cluster consists of a single SCC, each with its
6557 * own band schedule. The algorithm then tries to merge pairs
6558 * of clusters along a proximity edge until no more suitable
6559 * proximity edges can be found. During this merging, the schedule
6560 * is maintained in the individual SCCs.
6561 * After the merging is completed, the full resulting clusters
6562 * are extracted and in finish_bands_clustering,
6563 * compute_schedule_finish_band is called on each of them to integrate
6564 * the band into "node" and to continue the computation.
6566 * compute_weights initializes the weights that are used by find_proximity.
6568 static __isl_give isl_schedule_node
*compute_schedule_wcc_clustering(
6569 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
6572 struct isl_clustering c
;
6575 ctx
= isl_schedule_node_get_ctx(node
);
6577 if (clustering_init(ctx
, &c
, graph
) < 0)
6580 if (compute_weights(graph
, &c
) < 0)
6584 i
= find_proximity(graph
, &c
);
6587 if (i
>= graph
->n_edge
)
6589 if (merge_clusters_along_edge(ctx
, graph
, i
, &c
) < 0)
6593 if (extract_clusters(ctx
, graph
, &c
) < 0)
6596 node
= finish_bands_clustering(node
, graph
, &c
);
6598 clustering_free(ctx
, &c
);
6601 clustering_free(ctx
, &c
);
6602 return isl_schedule_node_free(node
);
6605 /* Compute a schedule for a connected dependence graph and return
6606 * the updated schedule node.
6608 * If Feautrier's algorithm is selected, we first recursively try to satisfy
6609 * as many validity dependences as possible. When all validity dependences
6610 * are satisfied we extend the schedule to a full-dimensional schedule.
6612 * Call compute_schedule_wcc_whole or compute_schedule_wcc_clustering
6613 * depending on whether the user has selected the option to try and
6614 * compute a schedule for the entire (weakly connected) component first.
6615 * If there is only a single strongly connected component (SCC), then
6616 * there is no point in trying to combine SCCs
6617 * in compute_schedule_wcc_clustering, so compute_schedule_wcc_whole
6618 * is called instead.
6620 static __isl_give isl_schedule_node
*compute_schedule_wcc(
6621 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
6628 ctx
= isl_schedule_node_get_ctx(node
);
6629 if (detect_sccs(ctx
, graph
) < 0)
6630 return isl_schedule_node_free(node
);
6632 if (compute_maxvar(graph
) < 0)
6633 return isl_schedule_node_free(node
);
6635 if (need_feautrier_step(ctx
, graph
))
6636 return compute_schedule_wcc_feautrier(node
, graph
);
6638 if (graph
->scc
<= 1 || isl_options_get_schedule_whole_component(ctx
))
6639 return compute_schedule_wcc_whole(node
, graph
);
6641 return compute_schedule_wcc_clustering(node
, graph
);
6644 /* Compute a schedule for each group of nodes identified by node->scc
6645 * separately and then combine them in a sequence node (or as set node
6646 * if graph->weak is set) inserted at position "node" of the schedule tree.
6647 * Return the updated schedule node.
6649 * If "wcc" is set then each of the groups belongs to a single
6650 * weakly connected component in the dependence graph so that
6651 * there is no need for compute_sub_schedule to look for weakly
6652 * connected components.
6654 static __isl_give isl_schedule_node
*compute_component_schedule(
6655 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
6660 isl_union_set_list
*filters
;
6664 ctx
= isl_schedule_node_get_ctx(node
);
6666 filters
= extract_sccs(ctx
, graph
);
6668 node
= isl_schedule_node_insert_set(node
, filters
);
6670 node
= isl_schedule_node_insert_sequence(node
, filters
);
6672 for (component
= 0; component
< graph
->scc
; ++component
) {
6673 node
= isl_schedule_node_child(node
, component
);
6674 node
= isl_schedule_node_child(node
, 0);
6675 node
= compute_sub_schedule(node
, ctx
, graph
,
6677 &edge_scc_exactly
, component
, wcc
);
6678 node
= isl_schedule_node_parent(node
);
6679 node
= isl_schedule_node_parent(node
);
6685 /* Compute a schedule for the given dependence graph and insert it at "node".
6686 * Return the updated schedule node.
6688 * We first check if the graph is connected (through validity and conditional
6689 * validity dependences) and, if not, compute a schedule
6690 * for each component separately.
6691 * If the schedule_serialize_sccs option is set, then we check for strongly
6692 * connected components instead and compute a separate schedule for
6693 * each such strongly connected component.
6695 static __isl_give isl_schedule_node
*compute_schedule(isl_schedule_node
*node
,
6696 struct isl_sched_graph
*graph
)
6703 ctx
= isl_schedule_node_get_ctx(node
);
6704 if (isl_options_get_schedule_serialize_sccs(ctx
)) {
6705 if (detect_sccs(ctx
, graph
) < 0)
6706 return isl_schedule_node_free(node
);
6708 if (detect_wccs(ctx
, graph
) < 0)
6709 return isl_schedule_node_free(node
);
6713 return compute_component_schedule(node
, graph
, 1);
6715 return compute_schedule_wcc(node
, graph
);
6718 /* Compute a schedule on sc->domain that respects the given schedule
6721 * In particular, the schedule respects all the validity dependences.
6722 * If the default isl scheduling algorithm is used, it tries to minimize
6723 * the dependence distances over the proximity dependences.
6724 * If Feautrier's scheduling algorithm is used, the proximity dependence
6725 * distances are only minimized during the extension to a full-dimensional
6728 * If there are any condition and conditional validity dependences,
6729 * then the conditional validity dependences may be violated inside
6730 * a tilable band, provided they have no adjacent non-local
6731 * condition dependences.
6733 __isl_give isl_schedule
*isl_schedule_constraints_compute_schedule(
6734 __isl_take isl_schedule_constraints
*sc
)
6736 isl_ctx
*ctx
= isl_schedule_constraints_get_ctx(sc
);
6737 struct isl_sched_graph graph
= { 0 };
6738 isl_schedule
*sched
;
6739 isl_schedule_node
*node
;
6740 isl_union_set
*domain
;
6742 sc
= isl_schedule_constraints_align_params(sc
);
6744 domain
= isl_schedule_constraints_get_domain(sc
);
6745 if (isl_union_set_n_set(domain
) == 0) {
6746 isl_schedule_constraints_free(sc
);
6747 return isl_schedule_from_domain(domain
);
6750 if (graph_init(&graph
, sc
) < 0)
6751 domain
= isl_union_set_free(domain
);
6753 node
= isl_schedule_node_from_domain(domain
);
6754 node
= isl_schedule_node_child(node
, 0);
6756 node
= compute_schedule(node
, &graph
);
6757 sched
= isl_schedule_node_get_schedule(node
);
6758 isl_schedule_node_free(node
);
6760 graph_free(ctx
, &graph
);
6761 isl_schedule_constraints_free(sc
);
6766 /* Compute a schedule for the given union of domains that respects
6767 * all the validity dependences and minimizes
6768 * the dependence distances over the proximity dependences.
6770 * This function is kept for backward compatibility.
6772 __isl_give isl_schedule
*isl_union_set_compute_schedule(
6773 __isl_take isl_union_set
*domain
,
6774 __isl_take isl_union_map
*validity
,
6775 __isl_take isl_union_map
*proximity
)
6777 isl_schedule_constraints
*sc
;
6779 sc
= isl_schedule_constraints_on_domain(domain
);
6780 sc
= isl_schedule_constraints_set_validity(sc
, validity
);
6781 sc
= isl_schedule_constraints_set_proximity(sc
, proximity
);
6783 return isl_schedule_constraints_compute_schedule(sc
);