2 * Copyright 2011 INRIA Saclay
3 * Copyright 2012-2014 Ecole Normale Superieure
4 * Copyright 2015-2016 Sven Verdoolaege
5 * Copyright 2016 INRIA Paris
7 * Use of this software is governed by the MIT license
9 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
10 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
12 * and Ecole Normale Superieure, 45 rue d'Ulm, 75230 Paris, France
13 * and Centre de Recherche Inria de Paris, 2 rue Simone Iff - Voie DQ12,
14 * CS 42112, 75589 Paris Cedex 12, France
17 #include <isl_ctx_private.h>
18 #include <isl_map_private.h>
19 #include <isl_space_private.h>
20 #include <isl_aff_private.h>
22 #include <isl/constraint.h>
23 #include <isl/schedule.h>
24 #include <isl_schedule_constraints.h>
25 #include <isl/schedule_node.h>
26 #include <isl_mat_private.h>
27 #include <isl_vec_private.h>
29 #include <isl/union_set.h>
32 #include <isl_dim_map.h>
33 #include <isl/map_to_basic_set.h>
35 #include <isl_options_private.h>
36 #include <isl_tarjan.h>
37 #include <isl_morph.h>
39 #include <isl_val_private.h>
42 * The scheduling algorithm implemented in this file was inspired by
43 * Bondhugula et al., "Automatic Transformations for Communication-Minimized
44 * Parallelization and Locality Optimization in the Polyhedral Model".
48 /* Internal information about a node that is used during the construction
50 * space represents the original space in which the domain lives;
51 * that is, the space is not affected by compression
52 * sched is a matrix representation of the schedule being constructed
53 * for this node; if compressed is set, then this schedule is
54 * defined over the compressed domain space
55 * sched_map is an isl_map representation of the same (partial) schedule
56 * sched_map may be NULL; if compressed is set, then this map
57 * is defined over the uncompressed domain space
58 * rank is the number of linearly independent rows in the linear part
60 * the columns of cmap represent a change of basis for the schedule
61 * coefficients; the first rank columns span the linear part of
63 * cinv is the inverse of cmap.
64 * ctrans is the transpose of cmap.
65 * start is the first variable in the LP problem in the sequences that
66 * represents the schedule coefficients of this node
67 * nvar is the dimension of the domain
68 * nparam is the number of parameters or 0 if we are not constructing
69 * a parametric schedule
71 * If compressed is set, then hull represents the constraints
72 * that were used to derive the compression, while compress and
73 * decompress map the original space to the compressed space and
76 * scc is the index of SCC (or WCC) this node belongs to
78 * "cluster" is only used inside extract_clusters and identifies
79 * the cluster of SCCs that the node belongs to.
81 * coincident contains a boolean for each of the rows of the schedule,
82 * indicating whether the corresponding scheduling dimension satisfies
83 * the coincidence constraints in the sense that the corresponding
84 * dependence distances are zero.
86 * If the schedule_treat_coalescing option is set, then
87 * "sizes" contains the sizes of the (compressed) instance set
88 * in each direction. If there is no fixed size in a given direction,
89 * then the corresponding size value is set to infinity.
90 * If the schedule_treat_coalescing option or the schedule_max_coefficient
91 * option is set, then "max" contains the maximal values for
92 * schedule coefficients of the (compressed) variables. If no bound
93 * needs to be imposed on a particular variable, then the corresponding
96 struct isl_sched_node
{
100 isl_multi_aff
*compress
;
101 isl_multi_aff
*decompress
;
117 isl_multi_val
*sizes
;
121 static int node_has_space(const void *entry
, const void *val
)
123 struct isl_sched_node
*node
= (struct isl_sched_node
*)entry
;
124 isl_space
*dim
= (isl_space
*)val
;
126 return isl_space_is_equal(node
->space
, dim
);
129 static int node_scc_exactly(struct isl_sched_node
*node
, int scc
)
131 return node
->scc
== scc
;
134 static int node_scc_at_most(struct isl_sched_node
*node
, int scc
)
136 return node
->scc
<= scc
;
139 static int node_scc_at_least(struct isl_sched_node
*node
, int scc
)
141 return node
->scc
>= scc
;
144 /* An edge in the dependence graph. An edge may be used to
145 * ensure validity of the generated schedule, to minimize the dependence
148 * map is the dependence relation, with i -> j in the map if j depends on i
149 * tagged_condition and tagged_validity contain the union of all tagged
150 * condition or conditional validity dependence relations that
151 * specialize the dependence relation "map"; that is,
152 * if (i -> a) -> (j -> b) is an element of "tagged_condition"
153 * or "tagged_validity", then i -> j is an element of "map".
154 * If these fields are NULL, then they represent the empty relation.
155 * src is the source node
156 * dst is the sink node
158 * types is a bit vector containing the types of this edge.
159 * validity is set if the edge is used to ensure correctness
160 * coincidence is used to enforce zero dependence distances
161 * proximity is set if the edge is used to minimize dependence distances
162 * condition is set if the edge represents a condition
163 * for a conditional validity schedule constraint
164 * local can only be set for condition edges and indicates that
165 * the dependence distance over the edge should be zero
166 * conditional_validity is set if the edge is used to conditionally
169 * For validity edges, start and end mark the sequence of inequality
170 * constraints in the LP problem that encode the validity constraint
171 * corresponding to this edge.
173 * During clustering, an edge may be marked "no_merge" if it should
174 * not be used to merge clusters.
175 * The weight is also only used during clustering and it is
176 * an indication of how many schedule dimensions on either side
177 * of the schedule constraints can be aligned.
178 * If the weight is negative, then this means that this edge was postponed
179 * by has_bounded_distances or any_no_merge. The original weight can
180 * be retrieved by adding 1 + graph->max_weight, with "graph"
181 * the graph containing this edge.
183 struct isl_sched_edge
{
185 isl_union_map
*tagged_condition
;
186 isl_union_map
*tagged_validity
;
188 struct isl_sched_node
*src
;
189 struct isl_sched_node
*dst
;
200 /* Is "edge" marked as being of type "type"?
202 static int is_type(struct isl_sched_edge
*edge
, enum isl_edge_type type
)
204 return ISL_FL_ISSET(edge
->types
, 1 << type
);
207 /* Mark "edge" as being of type "type".
209 static void set_type(struct isl_sched_edge
*edge
, enum isl_edge_type type
)
211 ISL_FL_SET(edge
->types
, 1 << type
);
214 /* No longer mark "edge" as being of type "type"?
216 static void clear_type(struct isl_sched_edge
*edge
, enum isl_edge_type type
)
218 ISL_FL_CLR(edge
->types
, 1 << type
);
221 /* Is "edge" marked as a validity edge?
223 static int is_validity(struct isl_sched_edge
*edge
)
225 return is_type(edge
, isl_edge_validity
);
228 /* Mark "edge" as a validity edge.
230 static void set_validity(struct isl_sched_edge
*edge
)
232 set_type(edge
, isl_edge_validity
);
235 /* Is "edge" marked as a proximity edge?
237 static int is_proximity(struct isl_sched_edge
*edge
)
239 return is_type(edge
, isl_edge_proximity
);
242 /* Is "edge" marked as a local edge?
244 static int is_local(struct isl_sched_edge
*edge
)
246 return is_type(edge
, isl_edge_local
);
249 /* Mark "edge" as a local edge.
251 static void set_local(struct isl_sched_edge
*edge
)
253 set_type(edge
, isl_edge_local
);
256 /* No longer mark "edge" as a local edge.
258 static void clear_local(struct isl_sched_edge
*edge
)
260 clear_type(edge
, isl_edge_local
);
263 /* Is "edge" marked as a coincidence edge?
265 static int is_coincidence(struct isl_sched_edge
*edge
)
267 return is_type(edge
, isl_edge_coincidence
);
270 /* Is "edge" marked as a condition edge?
272 static int is_condition(struct isl_sched_edge
*edge
)
274 return is_type(edge
, isl_edge_condition
);
277 /* Is "edge" marked as a conditional validity edge?
279 static int is_conditional_validity(struct isl_sched_edge
*edge
)
281 return is_type(edge
, isl_edge_conditional_validity
);
284 /* Internal information about the dependence graph used during
285 * the construction of the schedule.
287 * intra_hmap is a cache, mapping dependence relations to their dual,
288 * for dependences from a node to itself
289 * inter_hmap is a cache, mapping dependence relations to their dual,
290 * for dependences between distinct nodes
291 * if compression is involved then the key for these maps
292 * is the original, uncompressed dependence relation, while
293 * the value is the dual of the compressed dependence relation.
295 * n is the number of nodes
296 * node is the list of nodes
297 * maxvar is the maximal number of variables over all nodes
298 * max_row is the allocated number of rows in the schedule
299 * n_row is the current (maximal) number of linearly independent
300 * rows in the node schedules
301 * n_total_row is the current number of rows in the node schedules
302 * band_start is the starting row in the node schedules of the current band
303 * root is set if this graph is the original dependence graph,
304 * without any splitting
306 * sorted contains a list of node indices sorted according to the
307 * SCC to which a node belongs
309 * n_edge is the number of edges
310 * edge is the list of edges
311 * max_edge contains the maximal number of edges of each type;
312 * in particular, it contains the number of edges in the inital graph.
313 * edge_table contains pointers into the edge array, hashed on the source
314 * and sink spaces; there is one such table for each type;
315 * a given edge may be referenced from more than one table
316 * if the corresponding relation appears in more than one of the
317 * sets of dependences; however, for each type there is only
318 * a single edge between a given pair of source and sink space
319 * in the entire graph
321 * node_table contains pointers into the node array, hashed on the space
323 * region contains a list of variable sequences that should be non-trivial
325 * lp contains the (I)LP problem used to obtain new schedule rows
327 * src_scc and dst_scc are the source and sink SCCs of an edge with
328 * conflicting constraints
330 * scc represents the number of components
331 * weak is set if the components are weakly connected
333 * max_weight is used during clustering and represents the maximal
334 * weight of the relevant proximity edges.
336 struct isl_sched_graph
{
337 isl_map_to_basic_set
*intra_hmap
;
338 isl_map_to_basic_set
*inter_hmap
;
340 struct isl_sched_node
*node
;
353 struct isl_sched_edge
*edge
;
355 int max_edge
[isl_edge_last
+ 1];
356 struct isl_hash_table
*edge_table
[isl_edge_last
+ 1];
358 struct isl_hash_table
*node_table
;
359 struct isl_region
*region
;
372 /* Initialize node_table based on the list of nodes.
374 static int graph_init_table(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
378 graph
->node_table
= isl_hash_table_alloc(ctx
, graph
->n
);
379 if (!graph
->node_table
)
382 for (i
= 0; i
< graph
->n
; ++i
) {
383 struct isl_hash_table_entry
*entry
;
386 hash
= isl_space_get_hash(graph
->node
[i
].space
);
387 entry
= isl_hash_table_find(ctx
, graph
->node_table
, hash
,
389 graph
->node
[i
].space
, 1);
392 entry
->data
= &graph
->node
[i
];
398 /* Return a pointer to the node that lives within the given space,
399 * or NULL if there is no such node.
401 static struct isl_sched_node
*graph_find_node(isl_ctx
*ctx
,
402 struct isl_sched_graph
*graph
, __isl_keep isl_space
*dim
)
404 struct isl_hash_table_entry
*entry
;
407 hash
= isl_space_get_hash(dim
);
408 entry
= isl_hash_table_find(ctx
, graph
->node_table
, hash
,
409 &node_has_space
, dim
, 0);
411 return entry
? entry
->data
: NULL
;
414 static int edge_has_src_and_dst(const void *entry
, const void *val
)
416 const struct isl_sched_edge
*edge
= entry
;
417 const struct isl_sched_edge
*temp
= val
;
419 return edge
->src
== temp
->src
&& edge
->dst
== temp
->dst
;
422 /* Add the given edge to graph->edge_table[type].
424 static isl_stat
graph_edge_table_add(isl_ctx
*ctx
,
425 struct isl_sched_graph
*graph
, enum isl_edge_type type
,
426 struct isl_sched_edge
*edge
)
428 struct isl_hash_table_entry
*entry
;
431 hash
= isl_hash_init();
432 hash
= isl_hash_builtin(hash
, edge
->src
);
433 hash
= isl_hash_builtin(hash
, edge
->dst
);
434 entry
= isl_hash_table_find(ctx
, graph
->edge_table
[type
], hash
,
435 &edge_has_src_and_dst
, edge
, 1);
437 return isl_stat_error
;
443 /* Allocate the edge_tables based on the maximal number of edges of
446 static int graph_init_edge_tables(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
450 for (i
= 0; i
<= isl_edge_last
; ++i
) {
451 graph
->edge_table
[i
] = isl_hash_table_alloc(ctx
,
453 if (!graph
->edge_table
[i
])
460 /* If graph->edge_table[type] contains an edge from the given source
461 * to the given destination, then return the hash table entry of this edge.
462 * Otherwise, return NULL.
464 static struct isl_hash_table_entry
*graph_find_edge_entry(
465 struct isl_sched_graph
*graph
,
466 enum isl_edge_type type
,
467 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
469 isl_ctx
*ctx
= isl_space_get_ctx(src
->space
);
471 struct isl_sched_edge temp
= { .src
= src
, .dst
= dst
};
473 hash
= isl_hash_init();
474 hash
= isl_hash_builtin(hash
, temp
.src
);
475 hash
= isl_hash_builtin(hash
, temp
.dst
);
476 return isl_hash_table_find(ctx
, graph
->edge_table
[type
], hash
,
477 &edge_has_src_and_dst
, &temp
, 0);
481 /* If graph->edge_table[type] contains an edge from the given source
482 * to the given destination, then return this edge.
483 * Otherwise, return NULL.
485 static struct isl_sched_edge
*graph_find_edge(struct isl_sched_graph
*graph
,
486 enum isl_edge_type type
,
487 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
489 struct isl_hash_table_entry
*entry
;
491 entry
= graph_find_edge_entry(graph
, type
, src
, dst
);
498 /* Check whether the dependence graph has an edge of the given type
499 * between the given two nodes.
501 static isl_bool
graph_has_edge(struct isl_sched_graph
*graph
,
502 enum isl_edge_type type
,
503 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
505 struct isl_sched_edge
*edge
;
508 edge
= graph_find_edge(graph
, type
, src
, dst
);
512 empty
= isl_map_plain_is_empty(edge
->map
);
514 return isl_bool_error
;
519 /* Look for any edge with the same src, dst and map fields as "model".
521 * Return the matching edge if one can be found.
522 * Return "model" if no matching edge is found.
523 * Return NULL on error.
525 static struct isl_sched_edge
*graph_find_matching_edge(
526 struct isl_sched_graph
*graph
, struct isl_sched_edge
*model
)
528 enum isl_edge_type i
;
529 struct isl_sched_edge
*edge
;
531 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
534 edge
= graph_find_edge(graph
, i
, model
->src
, model
->dst
);
537 is_equal
= isl_map_plain_is_equal(model
->map
, edge
->map
);
547 /* Remove the given edge from all the edge_tables that refer to it.
549 static void graph_remove_edge(struct isl_sched_graph
*graph
,
550 struct isl_sched_edge
*edge
)
552 isl_ctx
*ctx
= isl_map_get_ctx(edge
->map
);
553 enum isl_edge_type i
;
555 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
556 struct isl_hash_table_entry
*entry
;
558 entry
= graph_find_edge_entry(graph
, i
, edge
->src
, edge
->dst
);
561 if (entry
->data
!= edge
)
563 isl_hash_table_remove(ctx
, graph
->edge_table
[i
], entry
);
567 /* Check whether the dependence graph has any edge
568 * between the given two nodes.
570 static isl_bool
graph_has_any_edge(struct isl_sched_graph
*graph
,
571 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
573 enum isl_edge_type i
;
576 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
577 r
= graph_has_edge(graph
, i
, src
, dst
);
585 /* Check whether the dependence graph has a validity edge
586 * between the given two nodes.
588 * Conditional validity edges are essentially validity edges that
589 * can be ignored if the corresponding condition edges are iteration private.
590 * Here, we are only checking for the presence of validity
591 * edges, so we need to consider the conditional validity edges too.
592 * In particular, this function is used during the detection
593 * of strongly connected components and we cannot ignore
594 * conditional validity edges during this detection.
596 static isl_bool
graph_has_validity_edge(struct isl_sched_graph
*graph
,
597 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
601 r
= graph_has_edge(graph
, isl_edge_validity
, src
, dst
);
605 return graph_has_edge(graph
, isl_edge_conditional_validity
, src
, dst
);
608 static int graph_alloc(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
609 int n_node
, int n_edge
)
614 graph
->n_edge
= n_edge
;
615 graph
->node
= isl_calloc_array(ctx
, struct isl_sched_node
, graph
->n
);
616 graph
->sorted
= isl_calloc_array(ctx
, int, graph
->n
);
617 graph
->region
= isl_alloc_array(ctx
, struct isl_region
, graph
->n
);
618 graph
->edge
= isl_calloc_array(ctx
,
619 struct isl_sched_edge
, graph
->n_edge
);
621 graph
->intra_hmap
= isl_map_to_basic_set_alloc(ctx
, 2 * n_edge
);
622 graph
->inter_hmap
= isl_map_to_basic_set_alloc(ctx
, 2 * n_edge
);
624 if (!graph
->node
|| !graph
->region
|| (graph
->n_edge
&& !graph
->edge
) ||
628 for(i
= 0; i
< graph
->n
; ++i
)
629 graph
->sorted
[i
] = i
;
634 static void graph_free(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
638 isl_map_to_basic_set_free(graph
->intra_hmap
);
639 isl_map_to_basic_set_free(graph
->inter_hmap
);
642 for (i
= 0; i
< graph
->n
; ++i
) {
643 isl_space_free(graph
->node
[i
].space
);
644 isl_set_free(graph
->node
[i
].hull
);
645 isl_multi_aff_free(graph
->node
[i
].compress
);
646 isl_multi_aff_free(graph
->node
[i
].decompress
);
647 isl_mat_free(graph
->node
[i
].sched
);
648 isl_map_free(graph
->node
[i
].sched_map
);
649 isl_mat_free(graph
->node
[i
].cmap
);
650 isl_mat_free(graph
->node
[i
].cinv
);
651 isl_mat_free(graph
->node
[i
].ctrans
);
653 free(graph
->node
[i
].coincident
);
654 isl_multi_val_free(graph
->node
[i
].sizes
);
655 isl_vec_free(graph
->node
[i
].max
);
660 for (i
= 0; i
< graph
->n_edge
; ++i
) {
661 isl_map_free(graph
->edge
[i
].map
);
662 isl_union_map_free(graph
->edge
[i
].tagged_condition
);
663 isl_union_map_free(graph
->edge
[i
].tagged_validity
);
667 for (i
= 0; i
<= isl_edge_last
; ++i
)
668 isl_hash_table_free(ctx
, graph
->edge_table
[i
]);
669 isl_hash_table_free(ctx
, graph
->node_table
);
670 isl_basic_set_free(graph
->lp
);
673 /* For each "set" on which this function is called, increment
674 * graph->n by one and update graph->maxvar.
676 static isl_stat
init_n_maxvar(__isl_take isl_set
*set
, void *user
)
678 struct isl_sched_graph
*graph
= user
;
679 int nvar
= isl_set_dim(set
, isl_dim_set
);
682 if (nvar
> graph
->maxvar
)
683 graph
->maxvar
= nvar
;
690 /* Compute the number of rows that should be allocated for the schedule.
691 * In particular, we need one row for each variable or one row
692 * for each basic map in the dependences.
693 * Note that it is practically impossible to exhaust both
694 * the number of dependences and the number of variables.
696 static isl_stat
compute_max_row(struct isl_sched_graph
*graph
,
697 __isl_keep isl_schedule_constraints
*sc
)
701 isl_union_set
*domain
;
705 domain
= isl_schedule_constraints_get_domain(sc
);
706 r
= isl_union_set_foreach_set(domain
, &init_n_maxvar
, graph
);
707 isl_union_set_free(domain
);
709 return isl_stat_error
;
710 n_edge
= isl_schedule_constraints_n_basic_map(sc
);
712 return isl_stat_error
;
713 graph
->max_row
= n_edge
+ graph
->maxvar
;
718 /* Does "bset" have any defining equalities for its set variables?
720 static isl_bool
has_any_defining_equality(__isl_keep isl_basic_set
*bset
)
725 return isl_bool_error
;
727 n
= isl_basic_set_dim(bset
, isl_dim_set
);
728 for (i
= 0; i
< n
; ++i
) {
731 has
= isl_basic_set_has_defining_equality(bset
, isl_dim_set
, i
,
737 return isl_bool_false
;
740 /* Set the entries of node->max to the value of the schedule_max_coefficient
743 static isl_stat
set_max_coefficient(isl_ctx
*ctx
, struct isl_sched_node
*node
)
747 max
= isl_options_get_schedule_max_coefficient(ctx
);
751 node
->max
= isl_vec_alloc(ctx
, node
->nvar
);
752 node
->max
= isl_vec_set_si(node
->max
, max
);
754 return isl_stat_error
;
759 /* Set the entries of node->max to the minimum of the schedule_max_coefficient
760 * option (if set) and half of the minimum of the sizes in the other
761 * dimensions. If the minimum of the sizes is one, half of the size
762 * is zero and this value is reset to one.
763 * If the global minimum is unbounded (i.e., if both
764 * the schedule_max_coefficient is not set and the sizes in the other
765 * dimensions are unbounded), then store a negative value.
766 * If the schedule coefficient is close to the size of the instance set
767 * in another dimension, then the schedule may represent a loop
768 * coalescing transformation (especially if the coefficient
769 * in that other dimension is one). Forcing the coefficient to be
770 * smaller than or equal to half the minimal size should avoid this
773 static isl_stat
compute_max_coefficient(isl_ctx
*ctx
,
774 struct isl_sched_node
*node
)
780 max
= isl_options_get_schedule_max_coefficient(ctx
);
781 v
= isl_vec_alloc(ctx
, node
->nvar
);
783 return isl_stat_error
;
785 for (i
= 0; i
< node
->nvar
; ++i
) {
786 isl_int_set_si(v
->el
[i
], max
);
787 isl_int_mul_si(v
->el
[i
], v
->el
[i
], 2);
790 for (i
= 0; i
< node
->nvar
; ++i
) {
793 size
= isl_multi_val_get_val(node
->sizes
, i
);
796 if (!isl_val_is_int(size
)) {
800 for (j
= 0; j
< node
->nvar
; ++j
) {
803 if (isl_int_is_neg(v
->el
[j
]) ||
804 isl_int_gt(v
->el
[j
], size
->n
))
805 isl_int_set(v
->el
[j
], size
->n
);
810 for (i
= 0; i
< node
->nvar
; ++i
) {
811 isl_int_fdiv_q_ui(v
->el
[i
], v
->el
[i
], 2);
812 if (isl_int_is_zero(v
->el
[i
]))
813 isl_int_set_si(v
->el
[i
], 1);
820 return isl_stat_error
;
823 /* Compute and return the size of "set" in dimension "dim".
824 * The size is taken to be the difference in values for that variable
825 * for fixed values of the other variables.
826 * In particular, the variable is first isolated from the other variables
827 * in the range of a map
829 * [i_0, ..., i_dim-1, i_dim+1, ...] -> [i_dim]
831 * and then duplicated
833 * [i_0, ..., i_dim-1, i_dim+1, ...] -> [[i_dim] -> [i_dim']]
835 * The shared variables are then projected out and the maximal value
836 * of i_dim' - i_dim is computed.
838 static __isl_give isl_val
*compute_size(__isl_take isl_set
*set
, int dim
)
845 map
= isl_set_project_onto_map(set
, isl_dim_set
, dim
, 1);
846 map
= isl_map_project_out(map
, isl_dim_in
, dim
, 1);
847 map
= isl_map_range_product(map
, isl_map_copy(map
));
848 map
= isl_set_unwrap(isl_map_range(map
));
849 set
= isl_map_deltas(map
);
850 ls
= isl_local_space_from_space(isl_set_get_space(set
));
851 obj
= isl_aff_var_on_domain(ls
, isl_dim_set
, 0);
852 v
= isl_set_max_val(set
, obj
);
859 /* Compute the size of the instance set "set" of "node", after compression,
860 * as well as bounds on the corresponding coefficients, if needed.
862 * The sizes are needed when the schedule_treat_coalescing option is set.
863 * The bounds are needed when the schedule_treat_coalescing option or
864 * the schedule_max_coefficient option is set.
866 * If the schedule_treat_coalescing option is not set, then at most
867 * the bounds need to be set and this is done in set_max_coefficient.
868 * Otherwise, compress the domain if needed, compute the size
869 * in each direction and store the results in node->size.
870 * Finally, set the bounds on the coefficients based on the sizes
871 * and the schedule_max_coefficient option in compute_max_coefficient.
873 static isl_stat
compute_sizes_and_max(isl_ctx
*ctx
, struct isl_sched_node
*node
,
874 __isl_take isl_set
*set
)
879 if (!isl_options_get_schedule_treat_coalescing(ctx
)) {
881 return set_max_coefficient(ctx
, node
);
884 if (node
->compressed
)
885 set
= isl_set_preimage_multi_aff(set
,
886 isl_multi_aff_copy(node
->decompress
));
887 mv
= isl_multi_val_zero(isl_set_get_space(set
));
888 n
= isl_set_dim(set
, isl_dim_set
);
889 for (j
= 0; j
< n
; ++j
) {
892 v
= compute_size(isl_set_copy(set
), j
);
893 mv
= isl_multi_val_set_val(mv
, j
, v
);
898 return isl_stat_error
;
899 return compute_max_coefficient(ctx
, node
);
902 /* Add a new node to the graph representing the given instance set.
903 * "nvar" is the (possibly compressed) number of variables and
904 * may be smaller than then number of set variables in "set"
905 * if "compressed" is set.
906 * If "compressed" is set, then "hull" represents the constraints
907 * that were used to derive the compression, while "compress" and
908 * "decompress" map the original space to the compressed space and
910 * If "compressed" is not set, then "hull", "compress" and "decompress"
913 * Compute the size of the instance set and bounds on the coefficients,
916 static isl_stat
add_node(struct isl_sched_graph
*graph
,
917 __isl_take isl_set
*set
, int nvar
, int compressed
,
918 __isl_take isl_set
*hull
, __isl_take isl_multi_aff
*compress
,
919 __isl_take isl_multi_aff
*decompress
)
926 struct isl_sched_node
*node
;
929 return isl_stat_error
;
931 ctx
= isl_set_get_ctx(set
);
932 nparam
= isl_set_dim(set
, isl_dim_param
);
933 if (!ctx
->opt
->schedule_parametric
)
935 sched
= isl_mat_alloc(ctx
, 0, 1 + nparam
+ nvar
);
936 node
= &graph
->node
[graph
->n
];
938 space
= isl_set_get_space(set
);
941 node
->nparam
= nparam
;
943 node
->sched_map
= NULL
;
944 coincident
= isl_calloc_array(ctx
, int, graph
->max_row
);
945 node
->coincident
= coincident
;
946 node
->compressed
= compressed
;
948 node
->compress
= compress
;
949 node
->decompress
= decompress
;
950 if (compute_sizes_and_max(ctx
, node
, set
) < 0)
951 return isl_stat_error
;
953 if (!space
|| !sched
|| (graph
->max_row
&& !coincident
))
954 return isl_stat_error
;
955 if (compressed
&& (!hull
|| !compress
|| !decompress
))
956 return isl_stat_error
;
961 /* Add a new node to the graph representing the given set.
963 * If any of the set variables is defined by an equality, then
964 * we perform variable compression such that we can perform
965 * the scheduling on the compressed domain.
967 static isl_stat
extract_node(__isl_take isl_set
*set
, void *user
)
970 isl_bool has_equality
;
974 isl_multi_aff
*compress
, *decompress
;
975 struct isl_sched_graph
*graph
= user
;
977 hull
= isl_set_affine_hull(isl_set_copy(set
));
978 hull
= isl_basic_set_remove_divs(hull
);
979 nvar
= isl_set_dim(set
, isl_dim_set
);
980 has_equality
= has_any_defining_equality(hull
);
982 if (has_equality
< 0)
985 isl_basic_set_free(hull
);
986 return add_node(graph
, set
, nvar
, 0, NULL
, NULL
, NULL
);
989 morph
= isl_basic_set_variable_compression(hull
, isl_dim_set
);
990 nvar
= isl_morph_ran_dim(morph
, isl_dim_set
);
991 compress
= isl_morph_get_var_multi_aff(morph
);
992 morph
= isl_morph_inverse(morph
);
993 decompress
= isl_morph_get_var_multi_aff(morph
);
994 isl_morph_free(morph
);
996 hull_set
= isl_set_from_basic_set(hull
);
997 return add_node(graph
, set
, nvar
, 1, hull_set
, compress
, decompress
);
999 isl_basic_set_free(hull
);
1001 return isl_stat_error
;
1004 struct isl_extract_edge_data
{
1005 enum isl_edge_type type
;
1006 struct isl_sched_graph
*graph
;
1009 /* Merge edge2 into edge1, freeing the contents of edge2.
1010 * Return 0 on success and -1 on failure.
1012 * edge1 and edge2 are assumed to have the same value for the map field.
1014 static int merge_edge(struct isl_sched_edge
*edge1
,
1015 struct isl_sched_edge
*edge2
)
1017 edge1
->types
|= edge2
->types
;
1018 isl_map_free(edge2
->map
);
1020 if (is_condition(edge2
)) {
1021 if (!edge1
->tagged_condition
)
1022 edge1
->tagged_condition
= edge2
->tagged_condition
;
1024 edge1
->tagged_condition
=
1025 isl_union_map_union(edge1
->tagged_condition
,
1026 edge2
->tagged_condition
);
1029 if (is_conditional_validity(edge2
)) {
1030 if (!edge1
->tagged_validity
)
1031 edge1
->tagged_validity
= edge2
->tagged_validity
;
1033 edge1
->tagged_validity
=
1034 isl_union_map_union(edge1
->tagged_validity
,
1035 edge2
->tagged_validity
);
1038 if (is_condition(edge2
) && !edge1
->tagged_condition
)
1040 if (is_conditional_validity(edge2
) && !edge1
->tagged_validity
)
1046 /* Insert dummy tags in domain and range of "map".
1048 * In particular, if "map" is of the form
1054 * [A -> dummy_tag] -> [B -> dummy_tag]
1056 * where the dummy_tags are identical and equal to any dummy tags
1057 * introduced by any other call to this function.
1059 static __isl_give isl_map
*insert_dummy_tags(__isl_take isl_map
*map
)
1065 isl_set
*domain
, *range
;
1067 ctx
= isl_map_get_ctx(map
);
1069 id
= isl_id_alloc(ctx
, NULL
, &dummy
);
1070 space
= isl_space_params(isl_map_get_space(map
));
1071 space
= isl_space_set_from_params(space
);
1072 space
= isl_space_set_tuple_id(space
, isl_dim_set
, id
);
1073 space
= isl_space_map_from_set(space
);
1075 domain
= isl_map_wrap(map
);
1076 range
= isl_map_wrap(isl_map_universe(space
));
1077 map
= isl_map_from_domain_and_range(domain
, range
);
1078 map
= isl_map_zip(map
);
1083 /* Given that at least one of "src" or "dst" is compressed, return
1084 * a map between the spaces of these nodes restricted to the affine
1085 * hull that was used in the compression.
1087 static __isl_give isl_map
*extract_hull(struct isl_sched_node
*src
,
1088 struct isl_sched_node
*dst
)
1092 if (src
->compressed
)
1093 dom
= isl_set_copy(src
->hull
);
1095 dom
= isl_set_universe(isl_space_copy(src
->space
));
1096 if (dst
->compressed
)
1097 ran
= isl_set_copy(dst
->hull
);
1099 ran
= isl_set_universe(isl_space_copy(dst
->space
));
1101 return isl_map_from_domain_and_range(dom
, ran
);
1104 /* Intersect the domains of the nested relations in domain and range
1105 * of "tagged" with "map".
1107 static __isl_give isl_map
*map_intersect_domains(__isl_take isl_map
*tagged
,
1108 __isl_keep isl_map
*map
)
1112 tagged
= isl_map_zip(tagged
);
1113 set
= isl_map_wrap(isl_map_copy(map
));
1114 tagged
= isl_map_intersect_domain(tagged
, set
);
1115 tagged
= isl_map_zip(tagged
);
1119 /* Return a pointer to the node that lives in the domain space of "map"
1120 * or NULL if there is no such node.
1122 static struct isl_sched_node
*find_domain_node(isl_ctx
*ctx
,
1123 struct isl_sched_graph
*graph
, __isl_keep isl_map
*map
)
1125 struct isl_sched_node
*node
;
1128 space
= isl_space_domain(isl_map_get_space(map
));
1129 node
= graph_find_node(ctx
, graph
, space
);
1130 isl_space_free(space
);
1135 /* Return a pointer to the node that lives in the range space of "map"
1136 * or NULL if there is no such node.
1138 static struct isl_sched_node
*find_range_node(isl_ctx
*ctx
,
1139 struct isl_sched_graph
*graph
, __isl_keep isl_map
*map
)
1141 struct isl_sched_node
*node
;
1144 space
= isl_space_range(isl_map_get_space(map
));
1145 node
= graph_find_node(ctx
, graph
, space
);
1146 isl_space_free(space
);
1151 /* Add a new edge to the graph based on the given map
1152 * and add it to data->graph->edge_table[data->type].
1153 * If a dependence relation of a given type happens to be identical
1154 * to one of the dependence relations of a type that was added before,
1155 * then we don't create a new edge, but instead mark the original edge
1156 * as also representing a dependence of the current type.
1158 * Edges of type isl_edge_condition or isl_edge_conditional_validity
1159 * may be specified as "tagged" dependence relations. That is, "map"
1160 * may contain elements (i -> a) -> (j -> b), where i -> j denotes
1161 * the dependence on iterations and a and b are tags.
1162 * edge->map is set to the relation containing the elements i -> j,
1163 * while edge->tagged_condition and edge->tagged_validity contain
1164 * the union of all the "map" relations
1165 * for which extract_edge is called that result in the same edge->map.
1167 * If the source or the destination node is compressed, then
1168 * intersect both "map" and "tagged" with the constraints that
1169 * were used to construct the compression.
1170 * This ensures that there are no schedule constraints defined
1171 * outside of these domains, while the scheduler no longer has
1172 * any control over those outside parts.
1174 static isl_stat
extract_edge(__isl_take isl_map
*map
, void *user
)
1176 isl_ctx
*ctx
= isl_map_get_ctx(map
);
1177 struct isl_extract_edge_data
*data
= user
;
1178 struct isl_sched_graph
*graph
= data
->graph
;
1179 struct isl_sched_node
*src
, *dst
;
1180 struct isl_sched_edge
*edge
;
1181 isl_map
*tagged
= NULL
;
1183 if (data
->type
== isl_edge_condition
||
1184 data
->type
== isl_edge_conditional_validity
) {
1185 if (isl_map_can_zip(map
)) {
1186 tagged
= isl_map_copy(map
);
1187 map
= isl_set_unwrap(isl_map_domain(isl_map_zip(map
)));
1189 tagged
= insert_dummy_tags(isl_map_copy(map
));
1193 src
= find_domain_node(ctx
, graph
, map
);
1194 dst
= find_range_node(ctx
, graph
, map
);
1198 isl_map_free(tagged
);
1202 if (src
->compressed
|| dst
->compressed
) {
1204 hull
= extract_hull(src
, dst
);
1206 tagged
= map_intersect_domains(tagged
, hull
);
1207 map
= isl_map_intersect(map
, hull
);
1210 graph
->edge
[graph
->n_edge
].src
= src
;
1211 graph
->edge
[graph
->n_edge
].dst
= dst
;
1212 graph
->edge
[graph
->n_edge
].map
= map
;
1213 graph
->edge
[graph
->n_edge
].types
= 0;
1214 graph
->edge
[graph
->n_edge
].tagged_condition
= NULL
;
1215 graph
->edge
[graph
->n_edge
].tagged_validity
= NULL
;
1216 set_type(&graph
->edge
[graph
->n_edge
], data
->type
);
1217 if (data
->type
== isl_edge_condition
)
1218 graph
->edge
[graph
->n_edge
].tagged_condition
=
1219 isl_union_map_from_map(tagged
);
1220 if (data
->type
== isl_edge_conditional_validity
)
1221 graph
->edge
[graph
->n_edge
].tagged_validity
=
1222 isl_union_map_from_map(tagged
);
1224 edge
= graph_find_matching_edge(graph
, &graph
->edge
[graph
->n_edge
]);
1227 return isl_stat_error
;
1229 if (edge
== &graph
->edge
[graph
->n_edge
])
1230 return graph_edge_table_add(ctx
, graph
, data
->type
,
1231 &graph
->edge
[graph
->n_edge
++]);
1233 if (merge_edge(edge
, &graph
->edge
[graph
->n_edge
]) < 0)
1236 return graph_edge_table_add(ctx
, graph
, data
->type
, edge
);
1239 /* Initialize the schedule graph "graph" from the schedule constraints "sc".
1241 * The context is included in the domain before the nodes of
1242 * the graphs are extracted in order to be able to exploit
1243 * any possible additional equalities.
1244 * Note that this intersection is only performed locally here.
1246 static isl_stat
graph_init(struct isl_sched_graph
*graph
,
1247 __isl_keep isl_schedule_constraints
*sc
)
1250 isl_union_set
*domain
;
1252 struct isl_extract_edge_data data
;
1253 enum isl_edge_type i
;
1257 return isl_stat_error
;
1259 ctx
= isl_schedule_constraints_get_ctx(sc
);
1261 domain
= isl_schedule_constraints_get_domain(sc
);
1262 graph
->n
= isl_union_set_n_set(domain
);
1263 isl_union_set_free(domain
);
1265 if (graph_alloc(ctx
, graph
, graph
->n
,
1266 isl_schedule_constraints_n_map(sc
)) < 0)
1267 return isl_stat_error
;
1269 if (compute_max_row(graph
, sc
) < 0)
1270 return isl_stat_error
;
1273 domain
= isl_schedule_constraints_get_domain(sc
);
1274 domain
= isl_union_set_intersect_params(domain
,
1275 isl_schedule_constraints_get_context(sc
));
1276 r
= isl_union_set_foreach_set(domain
, &extract_node
, graph
);
1277 isl_union_set_free(domain
);
1279 return isl_stat_error
;
1280 if (graph_init_table(ctx
, graph
) < 0)
1281 return isl_stat_error
;
1282 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
1283 c
= isl_schedule_constraints_get(sc
, i
);
1284 graph
->max_edge
[i
] = isl_union_map_n_map(c
);
1285 isl_union_map_free(c
);
1287 return isl_stat_error
;
1289 if (graph_init_edge_tables(ctx
, graph
) < 0)
1290 return isl_stat_error
;
1293 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
1297 c
= isl_schedule_constraints_get(sc
, i
);
1298 r
= isl_union_map_foreach_map(c
, &extract_edge
, &data
);
1299 isl_union_map_free(c
);
1301 return isl_stat_error
;
1307 /* Check whether there is any dependence from node[j] to node[i]
1308 * or from node[i] to node[j].
1310 static isl_bool
node_follows_weak(int i
, int j
, void *user
)
1313 struct isl_sched_graph
*graph
= user
;
1315 f
= graph_has_any_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
1318 return graph_has_any_edge(graph
, &graph
->node
[i
], &graph
->node
[j
]);
1321 /* Check whether there is a (conditional) validity dependence from node[j]
1322 * to node[i], forcing node[i] to follow node[j].
1324 static isl_bool
node_follows_strong(int i
, int j
, void *user
)
1326 struct isl_sched_graph
*graph
= user
;
1328 return graph_has_validity_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
1331 /* Use Tarjan's algorithm for computing the strongly connected components
1332 * in the dependence graph only considering those edges defined by "follows".
1334 static int detect_ccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
1335 isl_bool (*follows
)(int i
, int j
, void *user
))
1338 struct isl_tarjan_graph
*g
= NULL
;
1340 g
= isl_tarjan_graph_init(ctx
, graph
->n
, follows
, graph
);
1348 while (g
->order
[i
] != -1) {
1349 graph
->node
[g
->order
[i
]].scc
= graph
->scc
;
1357 isl_tarjan_graph_free(g
);
1362 /* Apply Tarjan's algorithm to detect the strongly connected components
1363 * in the dependence graph.
1364 * Only consider the (conditional) validity dependences and clear "weak".
1366 static int detect_sccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
1369 return detect_ccs(ctx
, graph
, &node_follows_strong
);
1372 /* Apply Tarjan's algorithm to detect the (weakly) connected components
1373 * in the dependence graph.
1374 * Consider all dependences and set "weak".
1376 static int detect_wccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
1379 return detect_ccs(ctx
, graph
, &node_follows_weak
);
1382 static int cmp_scc(const void *a
, const void *b
, void *data
)
1384 struct isl_sched_graph
*graph
= data
;
1388 return graph
->node
[*i1
].scc
- graph
->node
[*i2
].scc
;
1391 /* Sort the elements of graph->sorted according to the corresponding SCCs.
1393 static int sort_sccs(struct isl_sched_graph
*graph
)
1395 return isl_sort(graph
->sorted
, graph
->n
, sizeof(int), &cmp_scc
, graph
);
1398 /* Given a dependence relation R from "node" to itself,
1399 * construct the set of coefficients of valid constraints for elements
1400 * in that dependence relation.
1401 * In particular, the result contains tuples of coefficients
1402 * c_0, c_n, c_x such that
1404 * c_0 + c_n n + c_x y - c_x x >= 0 for each (x,y) in R
1408 * c_0 + c_n n + c_x d >= 0 for each d in delta R = { y - x | (x,y) in R }
1410 * We choose here to compute the dual of delta R.
1411 * Alternatively, we could have computed the dual of R, resulting
1412 * in a set of tuples c_0, c_n, c_x, c_y, and then
1413 * plugged in (c_0, c_n, c_x, -c_x).
1415 * If "node" has been compressed, then the dependence relation
1416 * is also compressed before the set of coefficients is computed.
1418 static __isl_give isl_basic_set
*intra_coefficients(
1419 struct isl_sched_graph
*graph
, struct isl_sched_node
*node
,
1420 __isl_take isl_map
*map
)
1424 isl_basic_set
*coef
;
1425 isl_maybe_isl_basic_set m
;
1427 m
= isl_map_to_basic_set_try_get(graph
->intra_hmap
, map
);
1428 if (m
.valid
< 0 || m
.valid
) {
1433 key
= isl_map_copy(map
);
1434 if (node
->compressed
) {
1435 map
= isl_map_preimage_domain_multi_aff(map
,
1436 isl_multi_aff_copy(node
->decompress
));
1437 map
= isl_map_preimage_range_multi_aff(map
,
1438 isl_multi_aff_copy(node
->decompress
));
1440 delta
= isl_set_remove_divs(isl_map_deltas(map
));
1441 coef
= isl_set_coefficients(delta
);
1442 graph
->intra_hmap
= isl_map_to_basic_set_set(graph
->intra_hmap
, key
,
1443 isl_basic_set_copy(coef
));
1448 /* Given a dependence relation R, construct the set of coefficients
1449 * of valid constraints for elements in that dependence relation.
1450 * In particular, the result contains tuples of coefficients
1451 * c_0, c_n, c_x, c_y such that
1453 * c_0 + c_n n + c_x x + c_y y >= 0 for each (x,y) in R
1455 * If the source or destination nodes of "edge" have been compressed,
1456 * then the dependence relation is also compressed before
1457 * the set of coefficients is computed.
1459 static __isl_give isl_basic_set
*inter_coefficients(
1460 struct isl_sched_graph
*graph
, struct isl_sched_edge
*edge
,
1461 __isl_take isl_map
*map
)
1465 isl_basic_set
*coef
;
1466 isl_maybe_isl_basic_set m
;
1468 m
= isl_map_to_basic_set_try_get(graph
->inter_hmap
, map
);
1469 if (m
.valid
< 0 || m
.valid
) {
1474 key
= isl_map_copy(map
);
1475 if (edge
->src
->compressed
)
1476 map
= isl_map_preimage_domain_multi_aff(map
,
1477 isl_multi_aff_copy(edge
->src
->decompress
));
1478 if (edge
->dst
->compressed
)
1479 map
= isl_map_preimage_range_multi_aff(map
,
1480 isl_multi_aff_copy(edge
->dst
->decompress
));
1481 set
= isl_map_wrap(isl_map_remove_divs(map
));
1482 coef
= isl_set_coefficients(set
);
1483 graph
->inter_hmap
= isl_map_to_basic_set_set(graph
->inter_hmap
, key
,
1484 isl_basic_set_copy(coef
));
1489 /* Return the position of the coefficients of the variables in
1490 * the coefficients constraints "coef".
1492 * The space of "coef" is of the form
1494 * { coefficients[[cst, params] -> S] }
1496 * Return the position of S.
1498 static int coef_var_offset(__isl_keep isl_basic_set
*coef
)
1503 space
= isl_space_unwrap(isl_basic_set_get_space(coef
));
1504 offset
= isl_space_dim(space
, isl_dim_in
);
1505 isl_space_free(space
);
1510 /* Return the offset of the coefficients of the variables of "node"
1513 * Within each node, the coefficients have the following order:
1515 * - c_i_n (if parametric)
1516 * - positive and negative parts of c_i_x
1518 static int node_var_coef_offset(struct isl_sched_node
*node
)
1520 return node
->start
+ 1 + node
->nparam
;
1523 /* Construct an isl_dim_map for mapping constraints on coefficients
1524 * for "node" to the corresponding positions in graph->lp.
1525 * "offset" is the offset of the coefficients for the variables
1526 * in the input constraints.
1527 * "s" is the sign of the mapping.
1529 * The input constraints are given in terms of the coefficients (c_0, c_n, c_x).
1530 * The mapping produced by this function essentially plugs in
1531 * (0, 0, c_i_x^+ - c_i_x^-) if s = 1 and
1532 * (0, 0, -c_i_x^+ + c_i_x^-) if s = -1.
1533 * In graph->lp, the c_i_x^- appear before their c_i_x^+ counterpart.
1535 * The caller can extend the mapping to also map the other coefficients
1536 * (and therefore not plug in 0).
1538 static __isl_give isl_dim_map
*intra_dim_map(isl_ctx
*ctx
,
1539 struct isl_sched_graph
*graph
, struct isl_sched_node
*node
,
1544 isl_dim_map
*dim_map
;
1546 total
= isl_basic_set_total_dim(graph
->lp
);
1547 pos
= node_var_coef_offset(node
);
1548 dim_map
= isl_dim_map_alloc(ctx
, total
);
1549 isl_dim_map_range(dim_map
, pos
, 2, offset
, 1, node
->nvar
, -s
);
1550 isl_dim_map_range(dim_map
, pos
+ 1, 2, offset
, 1, node
->nvar
, s
);
1555 /* Construct an isl_dim_map for mapping constraints on coefficients
1556 * for "src" (node i) and "dst" (node j) to the corresponding positions
1558 * "offset" is the offset of the coefficients for the variables of "src"
1559 * in the input constraints.
1560 * "s" is the sign of the mapping.
1562 * The input constraints are given in terms of the coefficients
1563 * (c_0, c_n, c_x, c_y).
1564 * The mapping produced by this function essentially plugs in
1565 * (c_j_0 - c_i_0, c_j_n - c_i_n,
1566 * -(c_i_x^+ - c_i_x^-), c_j_x^+ - c_j_x^-) if s = 1 and
1567 * (-c_j_0 + c_i_0, -c_j_n + c_i_n,
1568 * c_i_x^+ - c_i_x^-, -(c_j_x^+ - c_j_x^-)) if s = -1.
1569 * In graph->lp, the c_*^- appear before their c_*^+ counterpart.
1571 * The caller can further extend the mapping.
1573 static __isl_give isl_dim_map
*inter_dim_map(isl_ctx
*ctx
,
1574 struct isl_sched_graph
*graph
, struct isl_sched_node
*src
,
1575 struct isl_sched_node
*dst
, int offset
, int s
)
1579 isl_dim_map
*dim_map
;
1581 total
= isl_basic_set_total_dim(graph
->lp
);
1582 dim_map
= isl_dim_map_alloc(ctx
, total
);
1584 isl_dim_map_range(dim_map
, dst
->start
, 0, 0, 0, 1, s
);
1585 isl_dim_map_range(dim_map
, dst
->start
+ 1, 1, 1, 1, dst
->nparam
, s
);
1586 pos
= node_var_coef_offset(dst
);
1587 isl_dim_map_range(dim_map
, pos
, 2, offset
+ src
->nvar
, 1,
1589 isl_dim_map_range(dim_map
, pos
+ 1, 2, offset
+ src
->nvar
, 1,
1592 isl_dim_map_range(dim_map
, src
->start
, 0, 0, 0, 1, -s
);
1593 isl_dim_map_range(dim_map
, src
->start
+ 1, 1, 1, 1, src
->nparam
, -s
);
1594 pos
= node_var_coef_offset(src
);
1595 isl_dim_map_range(dim_map
, pos
, 2, offset
, 1, src
->nvar
, s
);
1596 isl_dim_map_range(dim_map
, pos
+ 1, 2, offset
, 1, src
->nvar
, -s
);
1601 /* Add constraints to graph->lp that force validity for the given
1602 * dependence from a node i to itself.
1603 * That is, add constraints that enforce
1605 * (c_i_0 + c_i_n n + c_i_x y) - (c_i_0 + c_i_n n + c_i_x x)
1606 * = c_i_x (y - x) >= 0
1608 * for each (x,y) in R.
1609 * We obtain general constraints on coefficients (c_0, c_n, c_x)
1610 * of valid constraints for (y - x) and then plug in (0, 0, c_i_x^+ - c_i_x^-),
1611 * where c_i_x = c_i_x^+ - c_i_x^-, with c_i_x^+ and c_i_x^- non-negative.
1612 * In graph->lp, the c_i_x^- appear before their c_i_x^+ counterpart.
1614 * Actually, we do not construct constraints for the c_i_x themselves,
1615 * but for the coefficients of c_i_x written as a linear combination
1616 * of the columns in node->cmap.
1618 static isl_stat
add_intra_validity_constraints(struct isl_sched_graph
*graph
,
1619 struct isl_sched_edge
*edge
)
1622 isl_map
*map
= isl_map_copy(edge
->map
);
1623 isl_ctx
*ctx
= isl_map_get_ctx(map
);
1624 isl_dim_map
*dim_map
;
1625 isl_basic_set
*coef
;
1626 struct isl_sched_node
*node
= edge
->src
;
1628 coef
= intra_coefficients(graph
, node
, map
);
1630 offset
= coef_var_offset(coef
);
1632 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
1633 offset
, isl_mat_copy(node
->cmap
));
1635 return isl_stat_error
;
1637 dim_map
= intra_dim_map(ctx
, graph
, node
, offset
, 1);
1638 graph
->lp
= isl_basic_set_extend_constraints(graph
->lp
,
1639 coef
->n_eq
, coef
->n_ineq
);
1640 graph
->lp
= isl_basic_set_add_constraints_dim_map(graph
->lp
,
1646 /* Add constraints to graph->lp that force validity for the given
1647 * dependence from node i to node j.
1648 * That is, add constraints that enforce
1650 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) >= 0
1652 * for each (x,y) in R.
1653 * We obtain general constraints on coefficients (c_0, c_n, c_x, c_y)
1654 * of valid constraints for R and then plug in
1655 * (c_j_0 - c_i_0, c_j_n - c_i_n, -(c_i_x^+ - c_i_x^-), c_j_x^+ - c_j_x^-),
1656 * where c_* = c_*^+ - c_*^-, with c_*^+ and c_*^- non-negative.
1657 * In graph->lp, the c_*^- appear before their c_*^+ counterpart.
1659 * Actually, we do not construct constraints for the c_*_x themselves,
1660 * but for the coefficients of c_*_x written as a linear combination
1661 * of the columns in node->cmap.
1663 static isl_stat
add_inter_validity_constraints(struct isl_sched_graph
*graph
,
1664 struct isl_sched_edge
*edge
)
1669 isl_dim_map
*dim_map
;
1670 isl_basic_set
*coef
;
1671 struct isl_sched_node
*src
= edge
->src
;
1672 struct isl_sched_node
*dst
= edge
->dst
;
1675 return isl_stat_error
;
1677 map
= isl_map_copy(edge
->map
);
1678 ctx
= isl_map_get_ctx(map
);
1679 coef
= inter_coefficients(graph
, edge
, map
);
1681 offset
= coef_var_offset(coef
);
1683 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
1684 offset
, isl_mat_copy(src
->cmap
));
1685 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
1686 offset
+ src
->nvar
, isl_mat_copy(dst
->cmap
));
1688 return isl_stat_error
;
1690 dim_map
= inter_dim_map(ctx
, graph
, src
, dst
, offset
, 1);
1692 edge
->start
= graph
->lp
->n_ineq
;
1693 graph
->lp
= isl_basic_set_extend_constraints(graph
->lp
,
1694 coef
->n_eq
, coef
->n_ineq
);
1695 graph
->lp
= isl_basic_set_add_constraints_dim_map(graph
->lp
,
1698 return isl_stat_error
;
1699 edge
->end
= graph
->lp
->n_ineq
;
1704 /* Add constraints to graph->lp that bound the dependence distance for the given
1705 * dependence from a node i to itself.
1706 * If s = 1, we add the constraint
1708 * c_i_x (y - x) <= m_0 + m_n n
1712 * -c_i_x (y - x) + m_0 + m_n n >= 0
1714 * for each (x,y) in R.
1715 * If s = -1, we add the constraint
1717 * -c_i_x (y - x) <= m_0 + m_n n
1721 * c_i_x (y - x) + m_0 + m_n n >= 0
1723 * for each (x,y) in R.
1724 * We obtain general constraints on coefficients (c_0, c_n, c_x)
1725 * of valid constraints for (y - x) and then plug in (m_0, m_n, -s * c_i_x),
1726 * with each coefficient (except m_0) represented as a pair of non-negative
1729 * Actually, we do not construct constraints for the c_i_x themselves,
1730 * but for the coefficients of c_i_x written as a linear combination
1731 * of the columns in node->cmap.
1734 * If "local" is set, then we add constraints
1736 * c_i_x (y - x) <= 0
1740 * -c_i_x (y - x) <= 0
1742 * instead, forcing the dependence distance to be (less than or) equal to 0.
1743 * That is, we plug in (0, 0, -s * c_i_x),
1744 * Note that dependences marked local are treated as validity constraints
1745 * by add_all_validity_constraints and therefore also have
1746 * their distances bounded by 0 from below.
1748 static isl_stat
add_intra_proximity_constraints(struct isl_sched_graph
*graph
,
1749 struct isl_sched_edge
*edge
, int s
, int local
)
1753 isl_map
*map
= isl_map_copy(edge
->map
);
1754 isl_ctx
*ctx
= isl_map_get_ctx(map
);
1755 isl_dim_map
*dim_map
;
1756 isl_basic_set
*coef
;
1757 struct isl_sched_node
*node
= edge
->src
;
1759 coef
= intra_coefficients(graph
, node
, map
);
1761 offset
= coef_var_offset(coef
);
1763 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
1764 offset
, isl_mat_copy(node
->cmap
));
1766 return isl_stat_error
;
1768 nparam
= isl_space_dim(node
->space
, isl_dim_param
);
1769 dim_map
= intra_dim_map(ctx
, graph
, node
, offset
, -s
);
1772 isl_dim_map_range(dim_map
, 1, 0, 0, 0, 1, 1);
1773 isl_dim_map_range(dim_map
, 4, 2, 1, 1, nparam
, -1);
1774 isl_dim_map_range(dim_map
, 5, 2, 1, 1, nparam
, 1);
1776 graph
->lp
= isl_basic_set_extend_constraints(graph
->lp
,
1777 coef
->n_eq
, coef
->n_ineq
);
1778 graph
->lp
= isl_basic_set_add_constraints_dim_map(graph
->lp
,
1784 /* Add constraints to graph->lp that bound the dependence distance for the given
1785 * dependence from node i to node j.
1786 * If s = 1, we add the constraint
1788 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x)
1793 * -(c_j_0 + c_j_n n + c_j_x y) + (c_i_0 + c_i_n n + c_i_x x) +
1796 * for each (x,y) in R.
1797 * If s = -1, we add the constraint
1799 * -((c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x))
1804 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) +
1807 * for each (x,y) in R.
1808 * We obtain general constraints on coefficients (c_0, c_n, c_x, c_y)
1809 * of valid constraints for R and then plug in
1810 * (m_0 - s*c_j_0 + s*c_i_0, m_n - s*c_j_n + s*c_i_n,
1811 * s*c_i_x, -s*c_j_x)
1812 * with each coefficient (except m_0, c_*_0 and c_*_n)
1813 * represented as a pair of non-negative coefficients.
1815 * Actually, we do not construct constraints for the c_*_x themselves,
1816 * but for the coefficients of c_*_x written as a linear combination
1817 * of the columns in node->cmap.
1820 * If "local" is set (and s = 1), then we add constraints
1822 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) <= 0
1826 * -((c_j_0 + c_j_n n + c_j_x y) + (c_i_0 + c_i_n n + c_i_x x)) >= 0
1828 * instead, forcing the dependence distance to be (less than or) equal to 0.
1829 * That is, we plug in
1830 * (-s*c_j_0 + s*c_i_0, -s*c_j_n + s*c_i_n, s*c_i_x, -s*c_j_x).
1831 * Note that dependences marked local are treated as validity constraints
1832 * by add_all_validity_constraints and therefore also have
1833 * their distances bounded by 0 from below.
1835 static isl_stat
add_inter_proximity_constraints(struct isl_sched_graph
*graph
,
1836 struct isl_sched_edge
*edge
, int s
, int local
)
1840 isl_map
*map
= isl_map_copy(edge
->map
);
1841 isl_ctx
*ctx
= isl_map_get_ctx(map
);
1842 isl_dim_map
*dim_map
;
1843 isl_basic_set
*coef
;
1844 struct isl_sched_node
*src
= edge
->src
;
1845 struct isl_sched_node
*dst
= edge
->dst
;
1847 coef
= inter_coefficients(graph
, edge
, map
);
1849 offset
= coef_var_offset(coef
);
1851 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
1852 offset
, isl_mat_copy(src
->cmap
));
1853 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
1854 offset
+ src
->nvar
, isl_mat_copy(dst
->cmap
));
1856 return isl_stat_error
;
1858 nparam
= isl_space_dim(src
->space
, isl_dim_param
);
1859 dim_map
= inter_dim_map(ctx
, graph
, src
, dst
, offset
, -s
);
1862 isl_dim_map_range(dim_map
, 1, 0, 0, 0, 1, 1);
1863 isl_dim_map_range(dim_map
, 4, 2, 1, 1, nparam
, -1);
1864 isl_dim_map_range(dim_map
, 5, 2, 1, 1, nparam
, 1);
1867 graph
->lp
= isl_basic_set_extend_constraints(graph
->lp
,
1868 coef
->n_eq
, coef
->n_ineq
);
1869 graph
->lp
= isl_basic_set_add_constraints_dim_map(graph
->lp
,
1875 /* Add all validity constraints to graph->lp.
1877 * An edge that is forced to be local needs to have its dependence
1878 * distances equal to zero. We take care of bounding them by 0 from below
1879 * here. add_all_proximity_constraints takes care of bounding them by 0
1882 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
1883 * Otherwise, we ignore them.
1885 static int add_all_validity_constraints(struct isl_sched_graph
*graph
,
1886 int use_coincidence
)
1890 for (i
= 0; i
< graph
->n_edge
; ++i
) {
1891 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
1894 local
= is_local(edge
) ||
1895 (is_coincidence(edge
) && use_coincidence
);
1896 if (!is_validity(edge
) && !local
)
1898 if (edge
->src
!= edge
->dst
)
1900 if (add_intra_validity_constraints(graph
, edge
) < 0)
1904 for (i
= 0; i
< graph
->n_edge
; ++i
) {
1905 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
1908 local
= is_local(edge
) ||
1909 (is_coincidence(edge
) && use_coincidence
);
1910 if (!is_validity(edge
) && !local
)
1912 if (edge
->src
== edge
->dst
)
1914 if (add_inter_validity_constraints(graph
, edge
) < 0)
1921 /* Add constraints to graph->lp that bound the dependence distance
1922 * for all dependence relations.
1923 * If a given proximity dependence is identical to a validity
1924 * dependence, then the dependence distance is already bounded
1925 * from below (by zero), so we only need to bound the distance
1926 * from above. (This includes the case of "local" dependences
1927 * which are treated as validity dependence by add_all_validity_constraints.)
1928 * Otherwise, we need to bound the distance both from above and from below.
1930 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
1931 * Otherwise, we ignore them.
1933 static int add_all_proximity_constraints(struct isl_sched_graph
*graph
,
1934 int use_coincidence
)
1938 for (i
= 0; i
< graph
->n_edge
; ++i
) {
1939 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
1942 local
= is_local(edge
) ||
1943 (is_coincidence(edge
) && use_coincidence
);
1944 if (!is_proximity(edge
) && !local
)
1946 if (edge
->src
== edge
->dst
&&
1947 add_intra_proximity_constraints(graph
, edge
, 1, local
) < 0)
1949 if (edge
->src
!= edge
->dst
&&
1950 add_inter_proximity_constraints(graph
, edge
, 1, local
) < 0)
1952 if (is_validity(edge
) || local
)
1954 if (edge
->src
== edge
->dst
&&
1955 add_intra_proximity_constraints(graph
, edge
, -1, 0) < 0)
1957 if (edge
->src
!= edge
->dst
&&
1958 add_inter_proximity_constraints(graph
, edge
, -1, 0) < 0)
1965 /* Compute a basis for the rows in the linear part of the schedule
1966 * and extend this basis to a full basis. The remaining rows
1967 * can then be used to force linear independence from the rows
1970 * In particular, given the schedule rows S, we compute
1975 * with H the Hermite normal form of S. That is, all but the
1976 * first rank columns of H are zero and so each row in S is
1977 * a linear combination of the first rank rows of Q.
1978 * The matrix Q is then transposed because we will write the
1979 * coefficients of the next schedule row as a column vector s
1980 * and express this s as a linear combination s = Q c of the
1982 * Similarly, the matrix U is transposed such that we can
1983 * compute the coefficients c = U s from a schedule row s.
1985 static int node_update_cmap(struct isl_sched_node
*node
)
1988 int n_row
= isl_mat_rows(node
->sched
);
1990 H
= isl_mat_sub_alloc(node
->sched
, 0, n_row
,
1991 1 + node
->nparam
, node
->nvar
);
1993 H
= isl_mat_left_hermite(H
, 0, &U
, &Q
);
1994 isl_mat_free(node
->cmap
);
1995 isl_mat_free(node
->cinv
);
1996 isl_mat_free(node
->ctrans
);
1997 node
->ctrans
= isl_mat_copy(Q
);
1998 node
->cmap
= isl_mat_transpose(Q
);
1999 node
->cinv
= isl_mat_transpose(U
);
2000 node
->rank
= isl_mat_initial_non_zero_cols(H
);
2003 if (!node
->cmap
|| !node
->cinv
|| !node
->ctrans
|| node
->rank
< 0)
2008 /* Is "edge" marked as a validity or a conditional validity edge?
2010 static int is_any_validity(struct isl_sched_edge
*edge
)
2012 return is_validity(edge
) || is_conditional_validity(edge
);
2015 /* How many times should we count the constraints in "edge"?
2017 * If carry is set, then we are counting the number of
2018 * (validity or conditional validity) constraints that will be added
2019 * in setup_carry_lp and we count each edge exactly once.
2021 * Otherwise, we count as follows
2022 * validity -> 1 (>= 0)
2023 * validity+proximity -> 2 (>= 0 and upper bound)
2024 * proximity -> 2 (lower and upper bound)
2025 * local(+any) -> 2 (>= 0 and <= 0)
2027 * If an edge is only marked conditional_validity then it counts
2028 * as zero since it is only checked afterwards.
2030 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2031 * Otherwise, we ignore them.
2033 static int edge_multiplicity(struct isl_sched_edge
*edge
, int carry
,
2034 int use_coincidence
)
2038 if (is_proximity(edge
) || is_local(edge
))
2040 if (use_coincidence
&& is_coincidence(edge
))
2042 if (is_validity(edge
))
2047 /* Count the number of equality and inequality constraints
2048 * that will be added for the given map.
2050 * "use_coincidence" is set if we should take into account coincidence edges.
2052 static isl_stat
count_map_constraints(struct isl_sched_graph
*graph
,
2053 struct isl_sched_edge
*edge
, __isl_take isl_map
*map
,
2054 int *n_eq
, int *n_ineq
, int carry
, int use_coincidence
)
2056 isl_basic_set
*coef
;
2057 int f
= edge_multiplicity(edge
, carry
, use_coincidence
);
2064 if (edge
->src
== edge
->dst
)
2065 coef
= intra_coefficients(graph
, edge
->src
, map
);
2067 coef
= inter_coefficients(graph
, edge
, map
);
2069 return isl_stat_error
;
2070 *n_eq
+= f
* coef
->n_eq
;
2071 *n_ineq
+= f
* coef
->n_ineq
;
2072 isl_basic_set_free(coef
);
2077 /* Count the number of equality and inequality constraints
2078 * that will be added to the main lp problem.
2079 * We count as follows
2080 * validity -> 1 (>= 0)
2081 * validity+proximity -> 2 (>= 0 and upper bound)
2082 * proximity -> 2 (lower and upper bound)
2083 * local(+any) -> 2 (>= 0 and <= 0)
2085 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2086 * Otherwise, we ignore them.
2088 static int count_constraints(struct isl_sched_graph
*graph
,
2089 int *n_eq
, int *n_ineq
, int use_coincidence
)
2093 *n_eq
= *n_ineq
= 0;
2094 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2095 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
2096 isl_map
*map
= isl_map_copy(edge
->map
);
2098 if (count_map_constraints(graph
, edge
, map
, n_eq
, n_ineq
,
2099 0, use_coincidence
) < 0)
2106 /* Count the number of constraints that will be added by
2107 * add_bound_constant_constraints to bound the values of the constant terms
2108 * and increment *n_eq and *n_ineq accordingly.
2110 * In practice, add_bound_constant_constraints only adds inequalities.
2112 static isl_stat
count_bound_constant_constraints(isl_ctx
*ctx
,
2113 struct isl_sched_graph
*graph
, int *n_eq
, int *n_ineq
)
2115 if (isl_options_get_schedule_max_constant_term(ctx
) == -1)
2118 *n_ineq
+= graph
->n
;
2123 /* Add constraints to bound the values of the constant terms in the schedule,
2124 * if requested by the user.
2126 * The maximal value of the constant terms is defined by the option
2127 * "schedule_max_constant_term".
2129 * Within each node, the coefficients have the following order:
2131 * - c_i_n (if parametric)
2132 * - positive and negative parts of c_i_x
2134 static isl_stat
add_bound_constant_constraints(isl_ctx
*ctx
,
2135 struct isl_sched_graph
*graph
)
2141 max
= isl_options_get_schedule_max_constant_term(ctx
);
2145 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2147 for (i
= 0; i
< graph
->n
; ++i
) {
2148 struct isl_sched_node
*node
= &graph
->node
[i
];
2149 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2151 return isl_stat_error
;
2152 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
2153 isl_int_set_si(graph
->lp
->ineq
[k
][1 + node
->start
], -1);
2154 isl_int_set_si(graph
->lp
->ineq
[k
][0], max
);
2160 /* Count the number of constraints that will be added by
2161 * add_bound_coefficient_constraints and increment *n_eq and *n_ineq
2164 * In practice, add_bound_coefficient_constraints only adds inequalities.
2166 static int count_bound_coefficient_constraints(isl_ctx
*ctx
,
2167 struct isl_sched_graph
*graph
, int *n_eq
, int *n_ineq
)
2171 if (isl_options_get_schedule_max_coefficient(ctx
) == -1 &&
2172 !isl_options_get_schedule_treat_coalescing(ctx
))
2175 for (i
= 0; i
< graph
->n
; ++i
)
2176 *n_ineq
+= graph
->node
[i
].nparam
+ 2 * graph
->node
[i
].nvar
;
2181 /* Add constraints to graph->lp that bound the values of
2182 * the parameter schedule coefficients of "node" to "max" and
2183 * the variable schedule coefficients to the corresponding entry
2185 * In either case, a negative value means that no bound needs to be imposed.
2187 * For parameter coefficients, this amounts to adding a constraint
2195 * The variables coefficients are, however, not represented directly.
2196 * Instead, the variables coefficients c_x are written as a linear
2197 * combination c_x = cmap c_z of some other coefficients c_z,
2198 * which are in turn encoded as c_z = c_z^+ - c_z^-.
2199 * Let a_j be the elements of row i of node->cmap, then
2201 * -max_i <= c_x_i <= max_i
2205 * -max_i <= \sum_j a_j (c_z_j^+ - c_z_j^-) <= max_i
2209 * -\sum_j a_j (c_z_j^+ - c_z_j^-) + max_i >= 0
2210 * \sum_j a_j (c_z_j^+ - c_z_j^-) + max_i >= 0
2212 static isl_stat
node_add_coefficient_constraints(isl_ctx
*ctx
,
2213 struct isl_sched_graph
*graph
, struct isl_sched_node
*node
, int max
)
2219 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2221 for (j
= 0; j
< node
->nparam
; ++j
) {
2227 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2229 return isl_stat_error
;
2230 dim
= 1 + node
->start
+ 1 + j
;
2231 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
2232 isl_int_set_si(graph
->lp
->ineq
[k
][dim
], -1);
2233 isl_int_set_si(graph
->lp
->ineq
[k
][0], max
);
2236 ineq
= isl_vec_alloc(ctx
, 1 + total
);
2237 ineq
= isl_vec_clr(ineq
);
2239 return isl_stat_error
;
2240 for (i
= 0; i
< node
->nvar
; ++i
) {
2241 int pos
= 1 + node_var_coef_offset(node
);
2243 if (isl_int_is_neg(node
->max
->el
[i
]))
2246 for (j
= 0; j
< node
->nvar
; ++j
) {
2247 isl_int_set(ineq
->el
[pos
+ 2 * j
],
2248 node
->cmap
->row
[i
][j
]);
2249 isl_int_neg(ineq
->el
[pos
+ 2 * j
+ 1],
2250 node
->cmap
->row
[i
][j
]);
2252 isl_int_set(ineq
->el
[0], node
->max
->el
[i
]);
2254 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2257 isl_seq_cpy(graph
->lp
->ineq
[k
], ineq
->el
, 1 + total
);
2259 isl_seq_neg(ineq
->el
+ pos
, ineq
->el
+ pos
, 2 * node
->nvar
);
2260 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2263 isl_seq_cpy(graph
->lp
->ineq
[k
], ineq
->el
, 1 + total
);
2270 return isl_stat_error
;
2273 /* Add constraints that bound the values of the variable and parameter
2274 * coefficients of the schedule.
2276 * The maximal value of the coefficients is defined by the option
2277 * 'schedule_max_coefficient' and the entries in node->max.
2278 * These latter entries are only set if either the schedule_max_coefficient
2279 * option or the schedule_treat_coalescing option is set.
2281 static isl_stat
add_bound_coefficient_constraints(isl_ctx
*ctx
,
2282 struct isl_sched_graph
*graph
)
2287 max
= isl_options_get_schedule_max_coefficient(ctx
);
2289 if (max
== -1 && !isl_options_get_schedule_treat_coalescing(ctx
))
2292 for (i
= 0; i
< graph
->n
; ++i
) {
2293 struct isl_sched_node
*node
= &graph
->node
[i
];
2295 if (node_add_coefficient_constraints(ctx
, graph
, node
, max
) < 0)
2296 return isl_stat_error
;
2302 /* Add a constraint to graph->lp that equates the value at position
2303 * "sum_pos" to the sum of the "n" values starting at "first".
2305 static isl_stat
add_sum_constraint(struct isl_sched_graph
*graph
,
2306 int sum_pos
, int first
, int n
)
2311 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2313 k
= isl_basic_set_alloc_equality(graph
->lp
);
2315 return isl_stat_error
;
2316 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2317 isl_int_set_si(graph
->lp
->eq
[k
][1 + sum_pos
], -1);
2318 for (i
= 0; i
< n
; ++i
)
2319 isl_int_set_si(graph
->lp
->eq
[k
][1 + first
+ i
], 1);
2324 /* Add a constraint to graph->lp that equates the value at position
2325 * "sum_pos" to the sum of the parameter coefficients of all nodes.
2327 * Within each node, the coefficients have the following order:
2329 * - c_i_n (if parametric)
2330 * - positive and negative parts of c_i_x
2332 static isl_stat
add_param_sum_constraint(struct isl_sched_graph
*graph
,
2338 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2340 k
= isl_basic_set_alloc_equality(graph
->lp
);
2342 return isl_stat_error
;
2343 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2344 isl_int_set_si(graph
->lp
->eq
[k
][1 + sum_pos
], -1);
2345 for (i
= 0; i
< graph
->n
; ++i
) {
2346 int pos
= 1 + graph
->node
[i
].start
+ 1;
2348 for (j
= 0; j
< graph
->node
[i
].nparam
; ++j
)
2349 isl_int_set_si(graph
->lp
->eq
[k
][pos
+ j
], 1);
2355 /* Add a constraint to graph->lp that equates the value at position
2356 * "sum_pos" to the sum of the variable coefficients of all nodes.
2358 * Within each node, the coefficients have the following order:
2360 * - c_i_n (if parametric)
2361 * - positive and negative parts of c_i_x
2363 static isl_stat
add_var_sum_constraint(struct isl_sched_graph
*graph
,
2369 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2371 k
= isl_basic_set_alloc_equality(graph
->lp
);
2373 return isl_stat_error
;
2374 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2375 isl_int_set_si(graph
->lp
->eq
[k
][1 + sum_pos
], -1);
2376 for (i
= 0; i
< graph
->n
; ++i
) {
2377 struct isl_sched_node
*node
= &graph
->node
[i
];
2378 int pos
= 1 + node_var_coef_offset(node
);
2380 for (j
= 0; j
< 2 * node
->nvar
; ++j
)
2381 isl_int_set_si(graph
->lp
->eq
[k
][pos
+ j
], 1);
2387 /* Construct an ILP problem for finding schedule coefficients
2388 * that result in non-negative, but small dependence distances
2389 * over all dependences.
2390 * In particular, the dependence distances over proximity edges
2391 * are bounded by m_0 + m_n n and we compute schedule coefficients
2392 * with small values (preferably zero) of m_n and m_0.
2394 * All variables of the ILP are non-negative. The actual coefficients
2395 * may be negative, so each coefficient is represented as the difference
2396 * of two non-negative variables. The negative part always appears
2397 * immediately before the positive part.
2398 * Other than that, the variables have the following order
2400 * - sum of positive and negative parts of m_n coefficients
2402 * - sum of all c_n coefficients
2403 * (unconstrained when computing non-parametric schedules)
2404 * - sum of positive and negative parts of all c_x coefficients
2405 * - positive and negative parts of m_n coefficients
2408 * - c_i_n (if parametric)
2409 * - positive and negative parts of c_i_x
2411 * The c_i_x are not represented directly, but through the columns of
2412 * node->cmap. That is, the computed values are for variable t_i_x
2413 * such that c_i_x = Q t_i_x with Q equal to node->cmap.
2415 * The constraints are those from the edges plus two or three equalities
2416 * to express the sums.
2418 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2419 * Otherwise, we ignore them.
2421 static isl_stat
setup_lp(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
2422 int use_coincidence
)
2432 parametric
= ctx
->opt
->schedule_parametric
;
2433 nparam
= isl_space_dim(graph
->node
[0].space
, isl_dim_param
);
2435 total
= param_pos
+ 2 * nparam
;
2436 for (i
= 0; i
< graph
->n
; ++i
) {
2437 struct isl_sched_node
*node
= &graph
->node
[graph
->sorted
[i
]];
2438 if (node_update_cmap(node
) < 0)
2439 return isl_stat_error
;
2440 node
->start
= total
;
2441 total
+= 1 + node
->nparam
+ 2 * node
->nvar
;
2444 if (count_constraints(graph
, &n_eq
, &n_ineq
, use_coincidence
) < 0)
2445 return isl_stat_error
;
2446 if (count_bound_constant_constraints(ctx
, graph
, &n_eq
, &n_ineq
) < 0)
2447 return isl_stat_error
;
2448 if (count_bound_coefficient_constraints(ctx
, graph
, &n_eq
, &n_ineq
) < 0)
2449 return isl_stat_error
;
2451 space
= isl_space_set_alloc(ctx
, 0, total
);
2452 isl_basic_set_free(graph
->lp
);
2453 n_eq
+= 2 + parametric
;
2455 graph
->lp
= isl_basic_set_alloc_space(space
, 0, n_eq
, n_ineq
);
2457 if (add_sum_constraint(graph
, 0, param_pos
, 2 * nparam
) < 0)
2458 return isl_stat_error
;
2459 if (parametric
&& add_param_sum_constraint(graph
, 2) < 0)
2460 return isl_stat_error
;
2461 if (add_var_sum_constraint(graph
, 3) < 0)
2462 return isl_stat_error
;
2463 if (add_bound_constant_constraints(ctx
, graph
) < 0)
2464 return isl_stat_error
;
2465 if (add_bound_coefficient_constraints(ctx
, graph
) < 0)
2466 return isl_stat_error
;
2467 if (add_all_validity_constraints(graph
, use_coincidence
) < 0)
2468 return isl_stat_error
;
2469 if (add_all_proximity_constraints(graph
, use_coincidence
) < 0)
2470 return isl_stat_error
;
2475 /* Analyze the conflicting constraint found by
2476 * isl_tab_basic_set_non_trivial_lexmin. If it corresponds to the validity
2477 * constraint of one of the edges between distinct nodes, living, moreover
2478 * in distinct SCCs, then record the source and sink SCC as this may
2479 * be a good place to cut between SCCs.
2481 static int check_conflict(int con
, void *user
)
2484 struct isl_sched_graph
*graph
= user
;
2486 if (graph
->src_scc
>= 0)
2489 con
-= graph
->lp
->n_eq
;
2491 if (con
>= graph
->lp
->n_ineq
)
2494 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2495 if (!is_validity(&graph
->edge
[i
]))
2497 if (graph
->edge
[i
].src
== graph
->edge
[i
].dst
)
2499 if (graph
->edge
[i
].src
->scc
== graph
->edge
[i
].dst
->scc
)
2501 if (graph
->edge
[i
].start
> con
)
2503 if (graph
->edge
[i
].end
<= con
)
2505 graph
->src_scc
= graph
->edge
[i
].src
->scc
;
2506 graph
->dst_scc
= graph
->edge
[i
].dst
->scc
;
2512 /* Check whether the next schedule row of the given node needs to be
2513 * non-trivial. Lower-dimensional domains may have some trivial rows,
2514 * but as soon as the number of remaining required non-trivial rows
2515 * is as large as the number or remaining rows to be computed,
2516 * all remaining rows need to be non-trivial.
2518 static int needs_row(struct isl_sched_graph
*graph
, struct isl_sched_node
*node
)
2520 return node
->nvar
- node
->rank
>= graph
->maxvar
- graph
->n_row
;
2523 /* Solve the ILP problem constructed in setup_lp.
2524 * For each node such that all the remaining rows of its schedule
2525 * need to be non-trivial, we construct a non-triviality region.
2526 * This region imposes that the next row is independent of previous rows.
2527 * In particular the coefficients c_i_x are represented by t_i_x
2528 * variables with c_i_x = Q t_i_x and Q a unimodular matrix such that
2529 * its first columns span the rows of the previously computed part
2530 * of the schedule. The non-triviality region enforces that at least
2531 * one of the remaining components of t_i_x is non-zero, i.e.,
2532 * that the new schedule row depends on at least one of the remaining
2535 static __isl_give isl_vec
*solve_lp(struct isl_sched_graph
*graph
)
2541 for (i
= 0; i
< graph
->n
; ++i
) {
2542 struct isl_sched_node
*node
= &graph
->node
[i
];
2543 int skip
= node
->rank
;
2544 graph
->region
[i
].pos
= node_var_coef_offset(node
) + 2 * skip
;
2545 if (needs_row(graph
, node
))
2546 graph
->region
[i
].len
= 2 * (node
->nvar
- skip
);
2548 graph
->region
[i
].len
= 0;
2550 lp
= isl_basic_set_copy(graph
->lp
);
2551 sol
= isl_tab_basic_set_non_trivial_lexmin(lp
, 2, graph
->n
,
2552 graph
->region
, &check_conflict
, graph
);
2556 /* Extract the coefficients for the variables of "node" from "sol".
2558 * Within each node, the coefficients have the following order:
2560 * - c_i_n (if parametric)
2561 * - positive and negative parts of c_i_x
2563 * The c_i_x^- appear before their c_i_x^+ counterpart.
2565 * Return c_i_x = c_i_x^+ - c_i_x^-
2567 static __isl_give isl_vec
*extract_var_coef(struct isl_sched_node
*node
,
2568 __isl_keep isl_vec
*sol
)
2576 csol
= isl_vec_alloc(isl_vec_get_ctx(sol
), node
->nvar
);
2580 pos
= 1 + node_var_coef_offset(node
);
2581 for (i
= 0; i
< node
->nvar
; ++i
)
2582 isl_int_sub(csol
->el
[i
],
2583 sol
->el
[pos
+ 2 * i
+ 1], sol
->el
[pos
+ 2 * i
]);
2588 /* Update the schedules of all nodes based on the given solution
2589 * of the LP problem.
2590 * The new row is added to the current band.
2591 * All possibly negative coefficients are encoded as a difference
2592 * of two non-negative variables, so we need to perform the subtraction
2593 * here. Moreover, if use_cmap is set, then the solution does
2594 * not refer to the actual coefficients c_i_x, but instead to variables
2595 * t_i_x such that c_i_x = Q t_i_x and Q is equal to node->cmap.
2596 * In this case, we then also need to perform this multiplication
2597 * to obtain the values of c_i_x.
2599 * If coincident is set, then the caller guarantees that the new
2600 * row satisfies the coincidence constraints.
2602 static int update_schedule(struct isl_sched_graph
*graph
,
2603 __isl_take isl_vec
*sol
, int use_cmap
, int coincident
)
2606 isl_vec
*csol
= NULL
;
2611 isl_die(sol
->ctx
, isl_error_internal
,
2612 "no solution found", goto error
);
2613 if (graph
->n_total_row
>= graph
->max_row
)
2614 isl_die(sol
->ctx
, isl_error_internal
,
2615 "too many schedule rows", goto error
);
2617 for (i
= 0; i
< graph
->n
; ++i
) {
2618 struct isl_sched_node
*node
= &graph
->node
[i
];
2619 int pos
= node
->start
;
2620 int row
= isl_mat_rows(node
->sched
);
2623 csol
= extract_var_coef(node
, sol
);
2627 isl_map_free(node
->sched_map
);
2628 node
->sched_map
= NULL
;
2629 node
->sched
= isl_mat_add_rows(node
->sched
, 1);
2632 for (j
= 0; j
< 1 + node
->nparam
; ++j
)
2633 node
->sched
= isl_mat_set_element(node
->sched
,
2634 row
, j
, sol
->el
[1 + pos
+ j
]);
2636 csol
= isl_mat_vec_product(isl_mat_copy(node
->cmap
),
2640 for (j
= 0; j
< node
->nvar
; ++j
)
2641 node
->sched
= isl_mat_set_element(node
->sched
,
2642 row
, 1 + node
->nparam
+ j
, csol
->el
[j
]);
2643 node
->coincident
[graph
->n_total_row
] = coincident
;
2649 graph
->n_total_row
++;
2658 /* Convert row "row" of node->sched into an isl_aff living in "ls"
2659 * and return this isl_aff.
2661 static __isl_give isl_aff
*extract_schedule_row(__isl_take isl_local_space
*ls
,
2662 struct isl_sched_node
*node
, int row
)
2670 aff
= isl_aff_zero_on_domain(ls
);
2671 isl_mat_get_element(node
->sched
, row
, 0, &v
);
2672 aff
= isl_aff_set_constant(aff
, v
);
2673 for (j
= 0; j
< node
->nparam
; ++j
) {
2674 isl_mat_get_element(node
->sched
, row
, 1 + j
, &v
);
2675 aff
= isl_aff_set_coefficient(aff
, isl_dim_param
, j
, v
);
2677 for (j
= 0; j
< node
->nvar
; ++j
) {
2678 isl_mat_get_element(node
->sched
, row
, 1 + node
->nparam
+ j
, &v
);
2679 aff
= isl_aff_set_coefficient(aff
, isl_dim_in
, j
, v
);
2687 /* Convert the "n" rows starting at "first" of node->sched into a multi_aff
2688 * and return this multi_aff.
2690 * The result is defined over the uncompressed node domain.
2692 static __isl_give isl_multi_aff
*node_extract_partial_schedule_multi_aff(
2693 struct isl_sched_node
*node
, int first
, int n
)
2697 isl_local_space
*ls
;
2704 nrow
= isl_mat_rows(node
->sched
);
2705 if (node
->compressed
)
2706 space
= isl_multi_aff_get_domain_space(node
->decompress
);
2708 space
= isl_space_copy(node
->space
);
2709 ls
= isl_local_space_from_space(isl_space_copy(space
));
2710 space
= isl_space_from_domain(space
);
2711 space
= isl_space_add_dims(space
, isl_dim_out
, n
);
2712 ma
= isl_multi_aff_zero(space
);
2714 for (i
= first
; i
< first
+ n
; ++i
) {
2715 aff
= extract_schedule_row(isl_local_space_copy(ls
), node
, i
);
2716 ma
= isl_multi_aff_set_aff(ma
, i
- first
, aff
);
2719 isl_local_space_free(ls
);
2721 if (node
->compressed
)
2722 ma
= isl_multi_aff_pullback_multi_aff(ma
,
2723 isl_multi_aff_copy(node
->compress
));
2728 /* Convert node->sched into a multi_aff and return this multi_aff.
2730 * The result is defined over the uncompressed node domain.
2732 static __isl_give isl_multi_aff
*node_extract_schedule_multi_aff(
2733 struct isl_sched_node
*node
)
2737 nrow
= isl_mat_rows(node
->sched
);
2738 return node_extract_partial_schedule_multi_aff(node
, 0, nrow
);
2741 /* Convert node->sched into a map and return this map.
2743 * The result is cached in node->sched_map, which needs to be released
2744 * whenever node->sched is updated.
2745 * It is defined over the uncompressed node domain.
2747 static __isl_give isl_map
*node_extract_schedule(struct isl_sched_node
*node
)
2749 if (!node
->sched_map
) {
2752 ma
= node_extract_schedule_multi_aff(node
);
2753 node
->sched_map
= isl_map_from_multi_aff(ma
);
2756 return isl_map_copy(node
->sched_map
);
2759 /* Construct a map that can be used to update a dependence relation
2760 * based on the current schedule.
2761 * That is, construct a map expressing that source and sink
2762 * are executed within the same iteration of the current schedule.
2763 * This map can then be intersected with the dependence relation.
2764 * This is not the most efficient way, but this shouldn't be a critical
2767 static __isl_give isl_map
*specializer(struct isl_sched_node
*src
,
2768 struct isl_sched_node
*dst
)
2770 isl_map
*src_sched
, *dst_sched
;
2772 src_sched
= node_extract_schedule(src
);
2773 dst_sched
= node_extract_schedule(dst
);
2774 return isl_map_apply_range(src_sched
, isl_map_reverse(dst_sched
));
2777 /* Intersect the domains of the nested relations in domain and range
2778 * of "umap" with "map".
2780 static __isl_give isl_union_map
*intersect_domains(
2781 __isl_take isl_union_map
*umap
, __isl_keep isl_map
*map
)
2783 isl_union_set
*uset
;
2785 umap
= isl_union_map_zip(umap
);
2786 uset
= isl_union_set_from_set(isl_map_wrap(isl_map_copy(map
)));
2787 umap
= isl_union_map_intersect_domain(umap
, uset
);
2788 umap
= isl_union_map_zip(umap
);
2792 /* Update the dependence relation of the given edge based
2793 * on the current schedule.
2794 * If the dependence is carried completely by the current schedule, then
2795 * it is removed from the edge_tables. It is kept in the list of edges
2796 * as otherwise all edge_tables would have to be recomputed.
2798 static int update_edge(struct isl_sched_graph
*graph
,
2799 struct isl_sched_edge
*edge
)
2804 id
= specializer(edge
->src
, edge
->dst
);
2805 edge
->map
= isl_map_intersect(edge
->map
, isl_map_copy(id
));
2809 if (edge
->tagged_condition
) {
2810 edge
->tagged_condition
=
2811 intersect_domains(edge
->tagged_condition
, id
);
2812 if (!edge
->tagged_condition
)
2815 if (edge
->tagged_validity
) {
2816 edge
->tagged_validity
=
2817 intersect_domains(edge
->tagged_validity
, id
);
2818 if (!edge
->tagged_validity
)
2822 empty
= isl_map_plain_is_empty(edge
->map
);
2826 graph_remove_edge(graph
, edge
);
2835 /* Does the domain of "umap" intersect "uset"?
2837 static int domain_intersects(__isl_keep isl_union_map
*umap
,
2838 __isl_keep isl_union_set
*uset
)
2842 umap
= isl_union_map_copy(umap
);
2843 umap
= isl_union_map_intersect_domain(umap
, isl_union_set_copy(uset
));
2844 empty
= isl_union_map_is_empty(umap
);
2845 isl_union_map_free(umap
);
2847 return empty
< 0 ? -1 : !empty
;
2850 /* Does the range of "umap" intersect "uset"?
2852 static int range_intersects(__isl_keep isl_union_map
*umap
,
2853 __isl_keep isl_union_set
*uset
)
2857 umap
= isl_union_map_copy(umap
);
2858 umap
= isl_union_map_intersect_range(umap
, isl_union_set_copy(uset
));
2859 empty
= isl_union_map_is_empty(umap
);
2860 isl_union_map_free(umap
);
2862 return empty
< 0 ? -1 : !empty
;
2865 /* Are the condition dependences of "edge" local with respect to
2866 * the current schedule?
2868 * That is, are domain and range of the condition dependences mapped
2869 * to the same point?
2871 * In other words, is the condition false?
2873 static int is_condition_false(struct isl_sched_edge
*edge
)
2875 isl_union_map
*umap
;
2876 isl_map
*map
, *sched
, *test
;
2879 empty
= isl_union_map_is_empty(edge
->tagged_condition
);
2880 if (empty
< 0 || empty
)
2883 umap
= isl_union_map_copy(edge
->tagged_condition
);
2884 umap
= isl_union_map_zip(umap
);
2885 umap
= isl_union_set_unwrap(isl_union_map_domain(umap
));
2886 map
= isl_map_from_union_map(umap
);
2888 sched
= node_extract_schedule(edge
->src
);
2889 map
= isl_map_apply_domain(map
, sched
);
2890 sched
= node_extract_schedule(edge
->dst
);
2891 map
= isl_map_apply_range(map
, sched
);
2893 test
= isl_map_identity(isl_map_get_space(map
));
2894 local
= isl_map_is_subset(map
, test
);
2901 /* For each conditional validity constraint that is adjacent
2902 * to a condition with domain in condition_source or range in condition_sink,
2903 * turn it into an unconditional validity constraint.
2905 static int unconditionalize_adjacent_validity(struct isl_sched_graph
*graph
,
2906 __isl_take isl_union_set
*condition_source
,
2907 __isl_take isl_union_set
*condition_sink
)
2911 condition_source
= isl_union_set_coalesce(condition_source
);
2912 condition_sink
= isl_union_set_coalesce(condition_sink
);
2914 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2916 isl_union_map
*validity
;
2918 if (!is_conditional_validity(&graph
->edge
[i
]))
2920 if (is_validity(&graph
->edge
[i
]))
2923 validity
= graph
->edge
[i
].tagged_validity
;
2924 adjacent
= domain_intersects(validity
, condition_sink
);
2925 if (adjacent
>= 0 && !adjacent
)
2926 adjacent
= range_intersects(validity
, condition_source
);
2932 set_validity(&graph
->edge
[i
]);
2935 isl_union_set_free(condition_source
);
2936 isl_union_set_free(condition_sink
);
2939 isl_union_set_free(condition_source
);
2940 isl_union_set_free(condition_sink
);
2944 /* Update the dependence relations of all edges based on the current schedule
2945 * and enforce conditional validity constraints that are adjacent
2946 * to satisfied condition constraints.
2948 * First check if any of the condition constraints are satisfied
2949 * (i.e., not local to the outer schedule) and keep track of
2950 * their domain and range.
2951 * Then update all dependence relations (which removes the non-local
2953 * Finally, if any condition constraints turned out to be satisfied,
2954 * then turn all adjacent conditional validity constraints into
2955 * unconditional validity constraints.
2957 static int update_edges(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2961 isl_union_set
*source
, *sink
;
2963 source
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
2964 sink
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
2965 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2967 isl_union_set
*uset
;
2968 isl_union_map
*umap
;
2970 if (!is_condition(&graph
->edge
[i
]))
2972 if (is_local(&graph
->edge
[i
]))
2974 local
= is_condition_false(&graph
->edge
[i
]);
2982 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_condition
);
2983 uset
= isl_union_map_domain(umap
);
2984 source
= isl_union_set_union(source
, uset
);
2986 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_condition
);
2987 uset
= isl_union_map_range(umap
);
2988 sink
= isl_union_set_union(sink
, uset
);
2991 for (i
= graph
->n_edge
- 1; i
>= 0; --i
) {
2992 if (update_edge(graph
, &graph
->edge
[i
]) < 0)
2997 return unconditionalize_adjacent_validity(graph
, source
, sink
);
2999 isl_union_set_free(source
);
3000 isl_union_set_free(sink
);
3003 isl_union_set_free(source
);
3004 isl_union_set_free(sink
);
3008 static void next_band(struct isl_sched_graph
*graph
)
3010 graph
->band_start
= graph
->n_total_row
;
3013 /* Return the union of the universe domains of the nodes in "graph"
3014 * that satisfy "pred".
3016 static __isl_give isl_union_set
*isl_sched_graph_domain(isl_ctx
*ctx
,
3017 struct isl_sched_graph
*graph
,
3018 int (*pred
)(struct isl_sched_node
*node
, int data
), int data
)
3024 for (i
= 0; i
< graph
->n
; ++i
)
3025 if (pred(&graph
->node
[i
], data
))
3029 isl_die(ctx
, isl_error_internal
,
3030 "empty component", return NULL
);
3032 set
= isl_set_universe(isl_space_copy(graph
->node
[i
].space
));
3033 dom
= isl_union_set_from_set(set
);
3035 for (i
= i
+ 1; i
< graph
->n
; ++i
) {
3036 if (!pred(&graph
->node
[i
], data
))
3038 set
= isl_set_universe(isl_space_copy(graph
->node
[i
].space
));
3039 dom
= isl_union_set_union(dom
, isl_union_set_from_set(set
));
3045 /* Return a list of unions of universe domains, where each element
3046 * in the list corresponds to an SCC (or WCC) indexed by node->scc.
3048 static __isl_give isl_union_set_list
*extract_sccs(isl_ctx
*ctx
,
3049 struct isl_sched_graph
*graph
)
3052 isl_union_set_list
*filters
;
3054 filters
= isl_union_set_list_alloc(ctx
, graph
->scc
);
3055 for (i
= 0; i
< graph
->scc
; ++i
) {
3058 dom
= isl_sched_graph_domain(ctx
, graph
, &node_scc_exactly
, i
);
3059 filters
= isl_union_set_list_add(filters
, dom
);
3065 /* Return a list of two unions of universe domains, one for the SCCs up
3066 * to and including graph->src_scc and another for the other SCCs.
3068 static __isl_give isl_union_set_list
*extract_split(isl_ctx
*ctx
,
3069 struct isl_sched_graph
*graph
)
3072 isl_union_set_list
*filters
;
3074 filters
= isl_union_set_list_alloc(ctx
, 2);
3075 dom
= isl_sched_graph_domain(ctx
, graph
,
3076 &node_scc_at_most
, graph
->src_scc
);
3077 filters
= isl_union_set_list_add(filters
, dom
);
3078 dom
= isl_sched_graph_domain(ctx
, graph
,
3079 &node_scc_at_least
, graph
->src_scc
+ 1);
3080 filters
= isl_union_set_list_add(filters
, dom
);
3085 /* Copy nodes that satisfy node_pred from the src dependence graph
3086 * to the dst dependence graph.
3088 static int copy_nodes(struct isl_sched_graph
*dst
, struct isl_sched_graph
*src
,
3089 int (*node_pred
)(struct isl_sched_node
*node
, int data
), int data
)
3094 for (i
= 0; i
< src
->n
; ++i
) {
3097 if (!node_pred(&src
->node
[i
], data
))
3101 dst
->node
[j
].space
= isl_space_copy(src
->node
[i
].space
);
3102 dst
->node
[j
].compressed
= src
->node
[i
].compressed
;
3103 dst
->node
[j
].hull
= isl_set_copy(src
->node
[i
].hull
);
3104 dst
->node
[j
].compress
=
3105 isl_multi_aff_copy(src
->node
[i
].compress
);
3106 dst
->node
[j
].decompress
=
3107 isl_multi_aff_copy(src
->node
[i
].decompress
);
3108 dst
->node
[j
].nvar
= src
->node
[i
].nvar
;
3109 dst
->node
[j
].nparam
= src
->node
[i
].nparam
;
3110 dst
->node
[j
].sched
= isl_mat_copy(src
->node
[i
].sched
);
3111 dst
->node
[j
].sched_map
= isl_map_copy(src
->node
[i
].sched_map
);
3112 dst
->node
[j
].coincident
= src
->node
[i
].coincident
;
3113 dst
->node
[j
].sizes
= isl_multi_val_copy(src
->node
[i
].sizes
);
3114 dst
->node
[j
].max
= isl_vec_copy(src
->node
[i
].max
);
3117 if (!dst
->node
[j
].space
|| !dst
->node
[j
].sched
)
3119 if (dst
->node
[j
].compressed
&&
3120 (!dst
->node
[j
].hull
|| !dst
->node
[j
].compress
||
3121 !dst
->node
[j
].decompress
))
3128 /* Copy non-empty edges that satisfy edge_pred from the src dependence graph
3129 * to the dst dependence graph.
3130 * If the source or destination node of the edge is not in the destination
3131 * graph, then it must be a backward proximity edge and it should simply
3134 static int copy_edges(isl_ctx
*ctx
, struct isl_sched_graph
*dst
,
3135 struct isl_sched_graph
*src
,
3136 int (*edge_pred
)(struct isl_sched_edge
*edge
, int data
), int data
)
3139 enum isl_edge_type t
;
3142 for (i
= 0; i
< src
->n_edge
; ++i
) {
3143 struct isl_sched_edge
*edge
= &src
->edge
[i
];
3145 isl_union_map
*tagged_condition
;
3146 isl_union_map
*tagged_validity
;
3147 struct isl_sched_node
*dst_src
, *dst_dst
;
3149 if (!edge_pred(edge
, data
))
3152 if (isl_map_plain_is_empty(edge
->map
))
3155 dst_src
= graph_find_node(ctx
, dst
, edge
->src
->space
);
3156 dst_dst
= graph_find_node(ctx
, dst
, edge
->dst
->space
);
3157 if (!dst_src
|| !dst_dst
) {
3158 if (is_validity(edge
) || is_conditional_validity(edge
))
3159 isl_die(ctx
, isl_error_internal
,
3160 "backward (conditional) validity edge",
3165 map
= isl_map_copy(edge
->map
);
3166 tagged_condition
= isl_union_map_copy(edge
->tagged_condition
);
3167 tagged_validity
= isl_union_map_copy(edge
->tagged_validity
);
3169 dst
->edge
[dst
->n_edge
].src
= dst_src
;
3170 dst
->edge
[dst
->n_edge
].dst
= dst_dst
;
3171 dst
->edge
[dst
->n_edge
].map
= map
;
3172 dst
->edge
[dst
->n_edge
].tagged_condition
= tagged_condition
;
3173 dst
->edge
[dst
->n_edge
].tagged_validity
= tagged_validity
;
3174 dst
->edge
[dst
->n_edge
].types
= edge
->types
;
3177 if (edge
->tagged_condition
&& !tagged_condition
)
3179 if (edge
->tagged_validity
&& !tagged_validity
)
3182 for (t
= isl_edge_first
; t
<= isl_edge_last
; ++t
) {
3184 graph_find_edge(src
, t
, edge
->src
, edge
->dst
))
3186 if (graph_edge_table_add(ctx
, dst
, t
,
3187 &dst
->edge
[dst
->n_edge
- 1]) < 0)
3195 /* Compute the maximal number of variables over all nodes.
3196 * This is the maximal number of linearly independent schedule
3197 * rows that we need to compute.
3198 * Just in case we end up in a part of the dependence graph
3199 * with only lower-dimensional domains, we make sure we will
3200 * compute the required amount of extra linearly independent rows.
3202 static int compute_maxvar(struct isl_sched_graph
*graph
)
3207 for (i
= 0; i
< graph
->n
; ++i
) {
3208 struct isl_sched_node
*node
= &graph
->node
[i
];
3211 if (node_update_cmap(node
) < 0)
3213 nvar
= node
->nvar
+ graph
->n_row
- node
->rank
;
3214 if (nvar
> graph
->maxvar
)
3215 graph
->maxvar
= nvar
;
3221 /* Extract the subgraph of "graph" that consists of the node satisfying
3222 * "node_pred" and the edges satisfying "edge_pred" and store
3223 * the result in "sub".
3225 static int extract_sub_graph(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
3226 int (*node_pred
)(struct isl_sched_node
*node
, int data
),
3227 int (*edge_pred
)(struct isl_sched_edge
*edge
, int data
),
3228 int data
, struct isl_sched_graph
*sub
)
3230 int i
, n
= 0, n_edge
= 0;
3233 for (i
= 0; i
< graph
->n
; ++i
)
3234 if (node_pred(&graph
->node
[i
], data
))
3236 for (i
= 0; i
< graph
->n_edge
; ++i
)
3237 if (edge_pred(&graph
->edge
[i
], data
))
3239 if (graph_alloc(ctx
, sub
, n
, n_edge
) < 0)
3241 if (copy_nodes(sub
, graph
, node_pred
, data
) < 0)
3243 if (graph_init_table(ctx
, sub
) < 0)
3245 for (t
= 0; t
<= isl_edge_last
; ++t
)
3246 sub
->max_edge
[t
] = graph
->max_edge
[t
];
3247 if (graph_init_edge_tables(ctx
, sub
) < 0)
3249 if (copy_edges(ctx
, sub
, graph
, edge_pred
, data
) < 0)
3251 sub
->n_row
= graph
->n_row
;
3252 sub
->max_row
= graph
->max_row
;
3253 sub
->n_total_row
= graph
->n_total_row
;
3254 sub
->band_start
= graph
->band_start
;
3259 static __isl_give isl_schedule_node
*compute_schedule(isl_schedule_node
*node
,
3260 struct isl_sched_graph
*graph
);
3261 static __isl_give isl_schedule_node
*compute_schedule_wcc(
3262 isl_schedule_node
*node
, struct isl_sched_graph
*graph
);
3264 /* Compute a schedule for a subgraph of "graph". In particular, for
3265 * the graph composed of nodes that satisfy node_pred and edges that
3266 * that satisfy edge_pred.
3267 * If the subgraph is known to consist of a single component, then wcc should
3268 * be set and then we call compute_schedule_wcc on the constructed subgraph.
3269 * Otherwise, we call compute_schedule, which will check whether the subgraph
3272 * The schedule is inserted at "node" and the updated schedule node
3275 static __isl_give isl_schedule_node
*compute_sub_schedule(
3276 __isl_take isl_schedule_node
*node
, isl_ctx
*ctx
,
3277 struct isl_sched_graph
*graph
,
3278 int (*node_pred
)(struct isl_sched_node
*node
, int data
),
3279 int (*edge_pred
)(struct isl_sched_edge
*edge
, int data
),
3282 struct isl_sched_graph split
= { 0 };
3284 if (extract_sub_graph(ctx
, graph
, node_pred
, edge_pred
, data
,
3289 node
= compute_schedule_wcc(node
, &split
);
3291 node
= compute_schedule(node
, &split
);
3293 graph_free(ctx
, &split
);
3296 graph_free(ctx
, &split
);
3297 return isl_schedule_node_free(node
);
3300 static int edge_scc_exactly(struct isl_sched_edge
*edge
, int scc
)
3302 return edge
->src
->scc
== scc
&& edge
->dst
->scc
== scc
;
3305 static int edge_dst_scc_at_most(struct isl_sched_edge
*edge
, int scc
)
3307 return edge
->dst
->scc
<= scc
;
3310 static int edge_src_scc_at_least(struct isl_sched_edge
*edge
, int scc
)
3312 return edge
->src
->scc
>= scc
;
3315 /* Reset the current band by dropping all its schedule rows.
3317 static int reset_band(struct isl_sched_graph
*graph
)
3322 drop
= graph
->n_total_row
- graph
->band_start
;
3323 graph
->n_total_row
-= drop
;
3324 graph
->n_row
-= drop
;
3326 for (i
= 0; i
< graph
->n
; ++i
) {
3327 struct isl_sched_node
*node
= &graph
->node
[i
];
3329 isl_map_free(node
->sched_map
);
3330 node
->sched_map
= NULL
;
3332 node
->sched
= isl_mat_drop_rows(node
->sched
,
3333 graph
->band_start
, drop
);
3342 /* Split the current graph into two parts and compute a schedule for each
3343 * part individually. In particular, one part consists of all SCCs up
3344 * to and including graph->src_scc, while the other part contains the other
3345 * SCCs. The split is enforced by a sequence node inserted at position "node"
3346 * in the schedule tree. Return the updated schedule node.
3347 * If either of these two parts consists of a sequence, then it is spliced
3348 * into the sequence containing the two parts.
3350 * The current band is reset. It would be possible to reuse
3351 * the previously computed rows as the first rows in the next
3352 * band, but recomputing them may result in better rows as we are looking
3353 * at a smaller part of the dependence graph.
3355 static __isl_give isl_schedule_node
*compute_split_schedule(
3356 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
3360 isl_union_set_list
*filters
;
3365 if (reset_band(graph
) < 0)
3366 return isl_schedule_node_free(node
);
3370 ctx
= isl_schedule_node_get_ctx(node
);
3371 filters
= extract_split(ctx
, graph
);
3372 node
= isl_schedule_node_insert_sequence(node
, filters
);
3373 node
= isl_schedule_node_child(node
, 1);
3374 node
= isl_schedule_node_child(node
, 0);
3376 node
= compute_sub_schedule(node
, ctx
, graph
,
3377 &node_scc_at_least
, &edge_src_scc_at_least
,
3378 graph
->src_scc
+ 1, 0);
3379 is_seq
= isl_schedule_node_get_type(node
) == isl_schedule_node_sequence
;
3380 node
= isl_schedule_node_parent(node
);
3381 node
= isl_schedule_node_parent(node
);
3383 node
= isl_schedule_node_sequence_splice_child(node
, 1);
3384 node
= isl_schedule_node_child(node
, 0);
3385 node
= isl_schedule_node_child(node
, 0);
3386 node
= compute_sub_schedule(node
, ctx
, graph
,
3387 &node_scc_at_most
, &edge_dst_scc_at_most
,
3389 is_seq
= isl_schedule_node_get_type(node
) == isl_schedule_node_sequence
;
3390 node
= isl_schedule_node_parent(node
);
3391 node
= isl_schedule_node_parent(node
);
3393 node
= isl_schedule_node_sequence_splice_child(node
, 0);
3398 /* Insert a band node at position "node" in the schedule tree corresponding
3399 * to the current band in "graph". Mark the band node permutable
3400 * if "permutable" is set.
3401 * The partial schedules and the coincidence property are extracted
3402 * from the graph nodes.
3403 * Return the updated schedule node.
3405 static __isl_give isl_schedule_node
*insert_current_band(
3406 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
3412 isl_multi_pw_aff
*mpa
;
3413 isl_multi_union_pw_aff
*mupa
;
3419 isl_die(isl_schedule_node_get_ctx(node
), isl_error_internal
,
3420 "graph should have at least one node",
3421 return isl_schedule_node_free(node
));
3423 start
= graph
->band_start
;
3424 end
= graph
->n_total_row
;
3427 ma
= node_extract_partial_schedule_multi_aff(&graph
->node
[0], start
, n
);
3428 mpa
= isl_multi_pw_aff_from_multi_aff(ma
);
3429 mupa
= isl_multi_union_pw_aff_from_multi_pw_aff(mpa
);
3431 for (i
= 1; i
< graph
->n
; ++i
) {
3432 isl_multi_union_pw_aff
*mupa_i
;
3434 ma
= node_extract_partial_schedule_multi_aff(&graph
->node
[i
],
3436 mpa
= isl_multi_pw_aff_from_multi_aff(ma
);
3437 mupa_i
= isl_multi_union_pw_aff_from_multi_pw_aff(mpa
);
3438 mupa
= isl_multi_union_pw_aff_union_add(mupa
, mupa_i
);
3440 node
= isl_schedule_node_insert_partial_schedule(node
, mupa
);
3442 for (i
= 0; i
< n
; ++i
)
3443 node
= isl_schedule_node_band_member_set_coincident(node
, i
,
3444 graph
->node
[0].coincident
[start
+ i
]);
3445 node
= isl_schedule_node_band_set_permutable(node
, permutable
);
3450 /* Update the dependence relations based on the current schedule,
3451 * add the current band to "node" and then continue with the computation
3453 * Return the updated schedule node.
3455 static __isl_give isl_schedule_node
*compute_next_band(
3456 __isl_take isl_schedule_node
*node
,
3457 struct isl_sched_graph
*graph
, int permutable
)
3464 ctx
= isl_schedule_node_get_ctx(node
);
3465 if (update_edges(ctx
, graph
) < 0)
3466 return isl_schedule_node_free(node
);
3467 node
= insert_current_band(node
, graph
, permutable
);
3470 node
= isl_schedule_node_child(node
, 0);
3471 node
= compute_schedule(node
, graph
);
3472 node
= isl_schedule_node_parent(node
);
3477 /* Add constraints to graph->lp that force the dependence "map" (which
3478 * is part of the dependence relation of "edge")
3479 * to be respected and attempt to carry it, where the edge is one from
3480 * a node j to itself. "pos" is the sequence number of the given map.
3481 * That is, add constraints that enforce
3483 * (c_j_0 + c_j_n n + c_j_x y) - (c_j_0 + c_j_n n + c_j_x x)
3484 * = c_j_x (y - x) >= e_i
3486 * for each (x,y) in R.
3487 * We obtain general constraints on coefficients (c_0, c_n, c_x)
3488 * of valid constraints for (y - x) and then plug in (-e_i, 0, c_j_x),
3489 * with each coefficient in c_j_x represented as a pair of non-negative
3492 static int add_intra_constraints(struct isl_sched_graph
*graph
,
3493 struct isl_sched_edge
*edge
, __isl_take isl_map
*map
, int pos
)
3496 isl_ctx
*ctx
= isl_map_get_ctx(map
);
3497 isl_dim_map
*dim_map
;
3498 isl_basic_set
*coef
;
3499 struct isl_sched_node
*node
= edge
->src
;
3501 coef
= intra_coefficients(graph
, node
, map
);
3505 offset
= coef_var_offset(coef
);
3506 dim_map
= intra_dim_map(ctx
, graph
, node
, offset
, 1);
3507 isl_dim_map_range(dim_map
, 3 + pos
, 0, 0, 0, 1, -1);
3508 graph
->lp
= isl_basic_set_extend_constraints(graph
->lp
,
3509 coef
->n_eq
, coef
->n_ineq
);
3510 graph
->lp
= isl_basic_set_add_constraints_dim_map(graph
->lp
,
3516 /* Add constraints to graph->lp that force the dependence "map" (which
3517 * is part of the dependence relation of "edge")
3518 * to be respected and attempt to carry it, where the edge is one from
3519 * node j to node k. "pos" is the sequence number of the given map.
3520 * That is, add constraints that enforce
3522 * (c_k_0 + c_k_n n + c_k_x y) - (c_j_0 + c_j_n n + c_j_x x) >= e_i
3524 * for each (x,y) in R.
3525 * We obtain general constraints on coefficients (c_0, c_n, c_x, c_y)
3526 * of valid constraints for R and then plug in
3527 * (-e_i + c_k_0 - c_j_0, c_k_n - c_j_n, -c_j_x, c_k_x)
3528 * with each coefficient (except e_i, c_*_0 and c_*_n)
3529 * represented as a pair of non-negative coefficients.
3531 static int add_inter_constraints(struct isl_sched_graph
*graph
,
3532 struct isl_sched_edge
*edge
, __isl_take isl_map
*map
, int pos
)
3535 isl_ctx
*ctx
= isl_map_get_ctx(map
);
3536 isl_dim_map
*dim_map
;
3537 isl_basic_set
*coef
;
3538 struct isl_sched_node
*src
= edge
->src
;
3539 struct isl_sched_node
*dst
= edge
->dst
;
3541 coef
= inter_coefficients(graph
, edge
, map
);
3545 offset
= coef_var_offset(coef
);
3546 dim_map
= inter_dim_map(ctx
, graph
, src
, dst
, offset
, 1);
3547 isl_dim_map_range(dim_map
, 3 + pos
, 0, 0, 0, 1, -1);
3548 graph
->lp
= isl_basic_set_extend_constraints(graph
->lp
,
3549 coef
->n_eq
, coef
->n_ineq
);
3550 graph
->lp
= isl_basic_set_add_constraints_dim_map(graph
->lp
,
3556 /* Add constraints to graph->lp that force all (conditional) validity
3557 * dependences to be respected and attempt to carry them.
3559 static isl_stat
add_all_constraints(struct isl_sched_graph
*graph
)
3565 for (i
= 0; i
< graph
->n_edge
; ++i
) {
3566 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
3568 if (!is_any_validity(edge
))
3571 for (j
= 0; j
< edge
->map
->n
; ++j
) {
3572 isl_basic_map
*bmap
;
3575 bmap
= isl_basic_map_copy(edge
->map
->p
[j
]);
3576 map
= isl_map_from_basic_map(bmap
);
3578 if (edge
->src
== edge
->dst
&&
3579 add_intra_constraints(graph
, edge
, map
, pos
) < 0)
3580 return isl_stat_error
;
3581 if (edge
->src
!= edge
->dst
&&
3582 add_inter_constraints(graph
, edge
, map
, pos
) < 0)
3583 return isl_stat_error
;
3591 /* Count the number of equality and inequality constraints
3592 * that will be added to the carry_lp problem.
3593 * We count each edge exactly once.
3595 static isl_stat
count_all_constraints(struct isl_sched_graph
*graph
,
3596 int *n_eq
, int *n_ineq
)
3600 *n_eq
= *n_ineq
= 0;
3601 for (i
= 0; i
< graph
->n_edge
; ++i
) {
3602 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
3604 if (!is_any_validity(edge
))
3607 for (j
= 0; j
< edge
->map
->n
; ++j
) {
3608 isl_basic_map
*bmap
;
3611 bmap
= isl_basic_map_copy(edge
->map
->p
[j
]);
3612 map
= isl_map_from_basic_map(bmap
);
3614 if (count_map_constraints(graph
, edge
, map
,
3615 n_eq
, n_ineq
, 1, 0) < 0)
3616 return isl_stat_error
;
3623 /* Return the total number of (validity) edges that carry_dependences will
3626 static int count_carry_edges(struct isl_sched_graph
*graph
)
3632 for (i
= 0; i
< graph
->n_edge
; ++i
) {
3633 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
3635 if (!is_any_validity(edge
))
3638 n_edge
+= isl_map_n_basic_map(edge
->map
);
3644 /* Construct an LP problem for finding schedule coefficients
3645 * such that the schedule carries as many validity dependences as possible.
3646 * In particular, for each dependence i, we bound the dependence distance
3647 * from below by e_i, with 0 <= e_i <= 1 and then maximize the sum
3648 * of all e_i's. Dependences with e_i = 0 in the solution are simply
3649 * respected, while those with e_i > 0 (in practice e_i = 1) are carried.
3650 * Note that if the dependence relation is a union of basic maps,
3651 * then we have to consider each basic map individually as it may only
3652 * be possible to carry the dependences expressed by some of those
3653 * basic maps and not all of them.
3654 * Below, we consider each of those basic maps as a separate "edge".
3655 * "n_edge" is the number of these edges.
3657 * All variables of the LP are non-negative. The actual coefficients
3658 * may be negative, so each coefficient is represented as the difference
3659 * of two non-negative variables. The negative part always appears
3660 * immediately before the positive part.
3661 * Other than that, the variables have the following order
3663 * - sum of (1 - e_i) over all edges
3664 * - sum of all c_n coefficients
3665 * (unconstrained when computing non-parametric schedules)
3666 * - sum of positive and negative parts of all c_x coefficients
3671 * - c_i_n (if parametric)
3672 * - positive and negative parts of c_i_x
3674 * The constraints are those from the (validity) edges plus three equalities
3675 * to express the sums and n_edge inequalities to express e_i <= 1.
3677 static isl_stat
setup_carry_lp(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
3687 for (i
= 0; i
< graph
->n
; ++i
) {
3688 struct isl_sched_node
*node
= &graph
->node
[graph
->sorted
[i
]];
3689 node
->start
= total
;
3690 total
+= 1 + node
->nparam
+ 2 * node
->nvar
;
3693 if (count_all_constraints(graph
, &n_eq
, &n_ineq
) < 0)
3694 return isl_stat_error
;
3696 dim
= isl_space_set_alloc(ctx
, 0, total
);
3697 isl_basic_set_free(graph
->lp
);
3700 graph
->lp
= isl_basic_set_alloc_space(dim
, 0, n_eq
, n_ineq
);
3701 graph
->lp
= isl_basic_set_set_rational(graph
->lp
);
3703 k
= isl_basic_set_alloc_equality(graph
->lp
);
3705 return isl_stat_error
;
3706 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
3707 isl_int_set_si(graph
->lp
->eq
[k
][0], -n_edge
);
3708 isl_int_set_si(graph
->lp
->eq
[k
][1], 1);
3709 for (i
= 0; i
< n_edge
; ++i
)
3710 isl_int_set_si(graph
->lp
->eq
[k
][4 + i
], 1);
3712 if (add_param_sum_constraint(graph
, 1) < 0)
3713 return isl_stat_error
;
3714 if (add_var_sum_constraint(graph
, 2) < 0)
3715 return isl_stat_error
;
3717 for (i
= 0; i
< n_edge
; ++i
) {
3718 k
= isl_basic_set_alloc_inequality(graph
->lp
);
3720 return isl_stat_error
;
3721 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
3722 isl_int_set_si(graph
->lp
->ineq
[k
][4 + i
], -1);
3723 isl_int_set_si(graph
->lp
->ineq
[k
][0], 1);
3726 if (add_all_constraints(graph
) < 0)
3727 return isl_stat_error
;
3732 static __isl_give isl_schedule_node
*compute_component_schedule(
3733 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
3736 /* Comparison function for sorting the statements based on
3737 * the corresponding value in "r".
3739 static int smaller_value(const void *a
, const void *b
, void *data
)
3745 return isl_int_cmp(r
->el
[*i1
], r
->el
[*i2
]);
3748 /* If the schedule_split_scaled option is set and if the linear
3749 * parts of the scheduling rows for all nodes in the graphs have
3750 * a non-trivial common divisor, then split off the remainder of the
3751 * constant term modulo this common divisor from the linear part.
3752 * Otherwise, insert a band node directly and continue with
3753 * the construction of the schedule.
3755 * If a non-trivial common divisor is found, then
3756 * the linear part is reduced and the remainder is enforced
3757 * by a sequence node with the children placed in the order
3758 * of this remainder.
3759 * In particular, we assign an scc index based on the remainder and
3760 * then rely on compute_component_schedule to insert the sequence and
3761 * to continue the schedule construction on each part.
3763 static __isl_give isl_schedule_node
*split_scaled(
3764 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
3777 ctx
= isl_schedule_node_get_ctx(node
);
3778 if (!ctx
->opt
->schedule_split_scaled
)
3779 return compute_next_band(node
, graph
, 0);
3781 return compute_next_band(node
, graph
, 0);
3784 isl_int_init(gcd_i
);
3786 isl_int_set_si(gcd
, 0);
3788 row
= isl_mat_rows(graph
->node
[0].sched
) - 1;
3790 for (i
= 0; i
< graph
->n
; ++i
) {
3791 struct isl_sched_node
*node
= &graph
->node
[i
];
3792 int cols
= isl_mat_cols(node
->sched
);
3794 isl_seq_gcd(node
->sched
->row
[row
] + 1, cols
- 1, &gcd_i
);
3795 isl_int_gcd(gcd
, gcd
, gcd_i
);
3798 isl_int_clear(gcd_i
);
3800 if (isl_int_cmp_si(gcd
, 1) <= 0) {
3802 return compute_next_band(node
, graph
, 0);
3805 r
= isl_vec_alloc(ctx
, graph
->n
);
3806 order
= isl_calloc_array(ctx
, int, graph
->n
);
3810 for (i
= 0; i
< graph
->n
; ++i
) {
3811 struct isl_sched_node
*node
= &graph
->node
[i
];
3814 isl_int_fdiv_r(r
->el
[i
], node
->sched
->row
[row
][0], gcd
);
3815 isl_int_fdiv_q(node
->sched
->row
[row
][0],
3816 node
->sched
->row
[row
][0], gcd
);
3817 isl_int_mul(node
->sched
->row
[row
][0],
3818 node
->sched
->row
[row
][0], gcd
);
3819 node
->sched
= isl_mat_scale_down_row(node
->sched
, row
, gcd
);
3824 if (isl_sort(order
, graph
->n
, sizeof(order
[0]), &smaller_value
, r
) < 0)
3828 for (i
= 0; i
< graph
->n
; ++i
) {
3829 if (i
> 0 && isl_int_ne(r
->el
[order
[i
- 1]], r
->el
[order
[i
]]))
3831 graph
->node
[order
[i
]].scc
= scc
;
3840 if (update_edges(ctx
, graph
) < 0)
3841 return isl_schedule_node_free(node
);
3842 node
= insert_current_band(node
, graph
, 0);
3845 node
= isl_schedule_node_child(node
, 0);
3846 node
= compute_component_schedule(node
, graph
, 0);
3847 node
= isl_schedule_node_parent(node
);
3854 return isl_schedule_node_free(node
);
3857 /* Is the schedule row "sol" trivial on node "node"?
3858 * That is, is the solution zero on the dimensions linearly independent of
3859 * the previously found solutions?
3860 * Return 1 if the solution is trivial, 0 if it is not and -1 on error.
3862 * Each coefficient is represented as the difference between
3863 * two non-negative values in "sol". "sol" has been computed
3864 * in terms of the original iterators (i.e., without use of cmap).
3865 * We construct the schedule row s and write it as a linear
3866 * combination of (linear combinations of) previously computed schedule rows.
3867 * s = Q c or c = U s.
3868 * If the final entries of c are all zero, then the solution is trivial.
3870 static int is_trivial(struct isl_sched_node
*node
, __isl_keep isl_vec
*sol
)
3877 if (node
->nvar
== node
->rank
)
3880 node_sol
= extract_var_coef(node
, sol
);
3881 node_sol
= isl_mat_vec_product(isl_mat_copy(node
->cinv
), node_sol
);
3885 trivial
= isl_seq_first_non_zero(node_sol
->el
+ node
->rank
,
3886 node
->nvar
- node
->rank
) == -1;
3888 isl_vec_free(node_sol
);
3893 /* Is the schedule row "sol" trivial on any node where it should
3895 * "sol" has been computed in terms of the original iterators
3896 * (i.e., without use of cmap).
3897 * Return 1 if any solution is trivial, 0 if they are not and -1 on error.
3899 static int is_any_trivial(struct isl_sched_graph
*graph
,
3900 __isl_keep isl_vec
*sol
)
3904 for (i
= 0; i
< graph
->n
; ++i
) {
3905 struct isl_sched_node
*node
= &graph
->node
[i
];
3908 if (!needs_row(graph
, node
))
3910 trivial
= is_trivial(node
, sol
);
3911 if (trivial
< 0 || trivial
)
3918 /* Does the schedule represented by "sol" perform loop coalescing on "node"?
3919 * If so, return the position of the coalesced dimension.
3920 * Otherwise, return node->nvar or -1 on error.
3922 * In particular, look for pairs of coefficients c_i and c_j such that
3923 * |c_j/c_i| >= size_i, i.e., |c_j| >= |c_i * size_i|.
3924 * If any such pair is found, then return i.
3925 * If size_i is infinity, then no check on c_i needs to be performed.
3927 static int find_node_coalescing(struct isl_sched_node
*node
,
3928 __isl_keep isl_vec
*sol
)
3934 if (node
->nvar
<= 1)
3937 csol
= extract_var_coef(node
, sol
);
3941 for (i
= 0; i
< node
->nvar
; ++i
) {
3944 if (isl_int_is_zero(csol
->el
[i
]))
3946 v
= isl_multi_val_get_val(node
->sizes
, i
);
3949 if (!isl_val_is_int(v
)) {
3953 isl_int_mul(max
, v
->n
, csol
->el
[i
]);
3956 for (j
= 0; j
< node
->nvar
; ++j
) {
3959 if (isl_int_abs_ge(csol
->el
[j
], max
))
3975 /* Force the schedule coefficient at position "pos" of "node" to be zero
3977 * The coefficient is encoded as the difference between two non-negative
3978 * variables. Force these two variables to have the same value.
3980 static __isl_give isl_tab_lexmin
*zero_out_node_coef(
3981 __isl_take isl_tab_lexmin
*tl
, struct isl_sched_node
*node
, int pos
)
3987 ctx
= isl_space_get_ctx(node
->space
);
3988 dim
= isl_tab_lexmin_dim(tl
);
3990 return isl_tab_lexmin_free(tl
);
3991 eq
= isl_vec_alloc(ctx
, 1 + dim
);
3992 eq
= isl_vec_clr(eq
);
3994 return isl_tab_lexmin_free(tl
);
3996 pos
= 1 + node_var_coef_offset(node
) + 2 * pos
;
3997 isl_int_set_si(eq
->el
[pos
], 1);
3998 isl_int_set_si(eq
->el
[pos
+ 1], -1);
3999 tl
= isl_tab_lexmin_add_eq(tl
, eq
->el
);
4005 /* Return the lexicographically smallest rational point in the basic set
4006 * from which "tl" was constructed, double checking that this input set
4009 static __isl_give isl_vec
*non_empty_solution(__isl_keep isl_tab_lexmin
*tl
)
4013 sol
= isl_tab_lexmin_get_solution(tl
);
4017 isl_die(isl_vec_get_ctx(sol
), isl_error_internal
,
4018 "error in schedule construction",
4019 return isl_vec_free(sol
));
4023 /* Does the solution "sol" of the LP problem constructed by setup_carry_lp
4024 * carry any of the "n_edge" groups of dependences?
4025 * The value in the first position is the sum of (1 - e_i) over all "n_edge"
4026 * edges, with 0 <= e_i <= 1 equal to 1 when the dependences represented
4027 * by the edge are carried by the solution.
4028 * If the sum of the (1 - e_i) is smaller than "n_edge" then at least
4029 * one of those is carried.
4031 * Note that despite the fact that the problem is solved using a rational
4032 * solver, the solution is guaranteed to be integral.
4033 * Specifically, the dependence distance lower bounds e_i (and therefore
4034 * also their sum) are integers. See Lemma 5 of [1].
4036 * Any potential denominator of the sum is cleared by this function.
4037 * The denominator is not relevant for any of the other elements
4040 * [1] P. Feautrier, Some Efficient Solutions to the Affine Scheduling
4041 * Problem, Part II: Multi-Dimensional Time.
4042 * In Intl. Journal of Parallel Programming, 1992.
4044 static int carries_dependences(__isl_keep isl_vec
*sol
, int n_edge
)
4046 isl_int_divexact(sol
->el
[1], sol
->el
[1], sol
->el
[0]);
4047 isl_int_set_si(sol
->el
[0], 1);
4048 return isl_int_cmp_si(sol
->el
[1], n_edge
) < 0;
4051 /* Return the lexicographically smallest rational point in "lp",
4052 * assuming that all variables are non-negative and performing some
4053 * additional sanity checks.
4054 * In particular, "lp" should not be empty by construction.
4055 * Double check that this is the case.
4056 * Also, check that dependences are carried for at least one of
4057 * the "n_edge" edges.
4059 * If the schedule_treat_coalescing option is set and
4060 * if the computed schedule performs loop coalescing on a given node,
4061 * i.e., if it is of the form
4063 * c_i i + c_j j + ...
4065 * with |c_j/c_i| >= size_i, then force the coefficient c_i to be zero
4066 * to cut out this solution. Repeat this process until no more loop
4067 * coalescing occurs or until no more dependences can be carried.
4068 * In the latter case, revert to the previously computed solution.
4070 static __isl_give isl_vec
*non_neg_lexmin(struct isl_sched_graph
*graph
,
4071 __isl_take isl_basic_set
*lp
, int n_edge
)
4076 isl_vec
*sol
, *prev
= NULL
;
4077 int treat_coalescing
;
4081 ctx
= isl_basic_set_get_ctx(lp
);
4082 treat_coalescing
= isl_options_get_schedule_treat_coalescing(ctx
);
4083 tl
= isl_tab_lexmin_from_basic_set(lp
);
4086 sol
= non_empty_solution(tl
);
4090 if (!carries_dependences(sol
, n_edge
)) {
4092 isl_die(ctx
, isl_error_unknown
,
4093 "unable to carry dependences",
4099 prev
= isl_vec_free(prev
);
4100 if (!treat_coalescing
)
4102 for (i
= 0; i
< graph
->n
; ++i
) {
4103 struct isl_sched_node
*node
= &graph
->node
[i
];
4105 pos
= find_node_coalescing(node
, sol
);
4108 if (pos
< node
->nvar
)
4113 tl
= zero_out_node_coef(tl
, &graph
->node
[i
], pos
);
4115 } while (i
< graph
->n
);
4117 isl_tab_lexmin_free(tl
);
4121 isl_tab_lexmin_free(tl
);
4127 /* Construct a schedule row for each node such that as many validity dependences
4128 * as possible are carried and then continue with the next band.
4130 * If there are no validity dependences, then no dependence can be carried and
4131 * the procedure is guaranteed to fail. If there is more than one component,
4132 * then try computing a schedule on each component separately
4133 * to prevent or at least postpone this failure.
4135 * If the computed schedule row turns out to be trivial on one or
4136 * more nodes where it should not be trivial, then we throw it away
4137 * and try again on each component separately.
4139 * If there is only one component, then we accept the schedule row anyway,
4140 * but we do not consider it as a complete row and therefore do not
4141 * increment graph->n_row. Note that the ranks of the nodes that
4142 * do get a non-trivial schedule part will get updated regardless and
4143 * graph->maxvar is computed based on these ranks. The test for
4144 * whether more schedule rows are required in compute_schedule_wcc
4145 * is therefore not affected.
4147 * Insert a band corresponding to the schedule row at position "node"
4148 * of the schedule tree and continue with the construction of the schedule.
4149 * This insertion and the continued construction is performed by split_scaled
4150 * after optionally checking for non-trivial common divisors.
4152 static __isl_give isl_schedule_node
*carry_dependences(
4153 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
4164 n_edge
= count_carry_edges(graph
);
4165 if (n_edge
== 0 && graph
->scc
> 1)
4166 return compute_component_schedule(node
, graph
, 1);
4168 ctx
= isl_schedule_node_get_ctx(node
);
4169 if (setup_carry_lp(ctx
, graph
, n_edge
) < 0)
4170 return isl_schedule_node_free(node
);
4172 lp
= isl_basic_set_copy(graph
->lp
);
4173 sol
= non_neg_lexmin(graph
, lp
, n_edge
);
4175 return isl_schedule_node_free(node
);
4177 trivial
= is_any_trivial(graph
, sol
);
4179 sol
= isl_vec_free(sol
);
4180 } else if (trivial
&& graph
->scc
> 1) {
4182 return compute_component_schedule(node
, graph
, 1);
4185 if (update_schedule(graph
, sol
, 0, 0) < 0)
4186 return isl_schedule_node_free(node
);
4190 return split_scaled(node
, graph
);
4193 /* Topologically sort statements mapped to the same schedule iteration
4194 * and add insert a sequence node in front of "node"
4195 * corresponding to this order.
4196 * If "initialized" is set, then it may be assumed that compute_maxvar
4197 * has been called on the current band. Otherwise, call
4198 * compute_maxvar if and before carry_dependences gets called.
4200 * If it turns out to be impossible to sort the statements apart,
4201 * because different dependences impose different orderings
4202 * on the statements, then we extend the schedule such that
4203 * it carries at least one more dependence.
4205 static __isl_give isl_schedule_node
*sort_statements(
4206 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
4210 isl_union_set_list
*filters
;
4215 ctx
= isl_schedule_node_get_ctx(node
);
4217 isl_die(ctx
, isl_error_internal
,
4218 "graph should have at least one node",
4219 return isl_schedule_node_free(node
));
4224 if (update_edges(ctx
, graph
) < 0)
4225 return isl_schedule_node_free(node
);
4227 if (graph
->n_edge
== 0)
4230 if (detect_sccs(ctx
, graph
) < 0)
4231 return isl_schedule_node_free(node
);
4234 if (graph
->scc
< graph
->n
) {
4235 if (!initialized
&& compute_maxvar(graph
) < 0)
4236 return isl_schedule_node_free(node
);
4237 return carry_dependences(node
, graph
);
4240 filters
= extract_sccs(ctx
, graph
);
4241 node
= isl_schedule_node_insert_sequence(node
, filters
);
4246 /* Are there any (non-empty) (conditional) validity edges in the graph?
4248 static int has_validity_edges(struct isl_sched_graph
*graph
)
4252 for (i
= 0; i
< graph
->n_edge
; ++i
) {
4255 empty
= isl_map_plain_is_empty(graph
->edge
[i
].map
);
4260 if (is_any_validity(&graph
->edge
[i
]))
4267 /* Should we apply a Feautrier step?
4268 * That is, did the user request the Feautrier algorithm and are
4269 * there any validity dependences (left)?
4271 static int need_feautrier_step(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
4273 if (ctx
->opt
->schedule_algorithm
!= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
)
4276 return has_validity_edges(graph
);
4279 /* Compute a schedule for a connected dependence graph using Feautrier's
4280 * multi-dimensional scheduling algorithm and return the updated schedule node.
4282 * The original algorithm is described in [1].
4283 * The main idea is to minimize the number of scheduling dimensions, by
4284 * trying to satisfy as many dependences as possible per scheduling dimension.
4286 * [1] P. Feautrier, Some Efficient Solutions to the Affine Scheduling
4287 * Problem, Part II: Multi-Dimensional Time.
4288 * In Intl. Journal of Parallel Programming, 1992.
4290 static __isl_give isl_schedule_node
*compute_schedule_wcc_feautrier(
4291 isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
4293 return carry_dependences(node
, graph
);
4296 /* Turn off the "local" bit on all (condition) edges.
4298 static void clear_local_edges(struct isl_sched_graph
*graph
)
4302 for (i
= 0; i
< graph
->n_edge
; ++i
)
4303 if (is_condition(&graph
->edge
[i
]))
4304 clear_local(&graph
->edge
[i
]);
4307 /* Does "graph" have both condition and conditional validity edges?
4309 static int need_condition_check(struct isl_sched_graph
*graph
)
4312 int any_condition
= 0;
4313 int any_conditional_validity
= 0;
4315 for (i
= 0; i
< graph
->n_edge
; ++i
) {
4316 if (is_condition(&graph
->edge
[i
]))
4318 if (is_conditional_validity(&graph
->edge
[i
]))
4319 any_conditional_validity
= 1;
4322 return any_condition
&& any_conditional_validity
;
4325 /* Does "graph" contain any coincidence edge?
4327 static int has_any_coincidence(struct isl_sched_graph
*graph
)
4331 for (i
= 0; i
< graph
->n_edge
; ++i
)
4332 if (is_coincidence(&graph
->edge
[i
]))
4338 /* Extract the final schedule row as a map with the iteration domain
4339 * of "node" as domain.
4341 static __isl_give isl_map
*final_row(struct isl_sched_node
*node
)
4346 row
= isl_mat_rows(node
->sched
) - 1;
4347 ma
= node_extract_partial_schedule_multi_aff(node
, row
, 1);
4348 return isl_map_from_multi_aff(ma
);
4351 /* Is the conditional validity dependence in the edge with index "edge_index"
4352 * violated by the latest (i.e., final) row of the schedule?
4353 * That is, is i scheduled after j
4354 * for any conditional validity dependence i -> j?
4356 static int is_violated(struct isl_sched_graph
*graph
, int edge_index
)
4358 isl_map
*src_sched
, *dst_sched
, *map
;
4359 struct isl_sched_edge
*edge
= &graph
->edge
[edge_index
];
4362 src_sched
= final_row(edge
->src
);
4363 dst_sched
= final_row(edge
->dst
);
4364 map
= isl_map_copy(edge
->map
);
4365 map
= isl_map_apply_domain(map
, src_sched
);
4366 map
= isl_map_apply_range(map
, dst_sched
);
4367 map
= isl_map_order_gt(map
, isl_dim_in
, 0, isl_dim_out
, 0);
4368 empty
= isl_map_is_empty(map
);
4377 /* Does "graph" have any satisfied condition edges that
4378 * are adjacent to the conditional validity constraint with
4379 * domain "conditional_source" and range "conditional_sink"?
4381 * A satisfied condition is one that is not local.
4382 * If a condition was forced to be local already (i.e., marked as local)
4383 * then there is no need to check if it is in fact local.
4385 * Additionally, mark all adjacent condition edges found as local.
4387 static int has_adjacent_true_conditions(struct isl_sched_graph
*graph
,
4388 __isl_keep isl_union_set
*conditional_source
,
4389 __isl_keep isl_union_set
*conditional_sink
)
4394 for (i
= 0; i
< graph
->n_edge
; ++i
) {
4395 int adjacent
, local
;
4396 isl_union_map
*condition
;
4398 if (!is_condition(&graph
->edge
[i
]))
4400 if (is_local(&graph
->edge
[i
]))
4403 condition
= graph
->edge
[i
].tagged_condition
;
4404 adjacent
= domain_intersects(condition
, conditional_sink
);
4405 if (adjacent
>= 0 && !adjacent
)
4406 adjacent
= range_intersects(condition
,
4407 conditional_source
);
4413 set_local(&graph
->edge
[i
]);
4415 local
= is_condition_false(&graph
->edge
[i
]);
4425 /* Are there any violated conditional validity dependences with
4426 * adjacent condition dependences that are not local with respect
4427 * to the current schedule?
4428 * That is, is the conditional validity constraint violated?
4430 * Additionally, mark all those adjacent condition dependences as local.
4431 * We also mark those adjacent condition dependences that were not marked
4432 * as local before, but just happened to be local already. This ensures
4433 * that they remain local if the schedule is recomputed.
4435 * We first collect domain and range of all violated conditional validity
4436 * dependences and then check if there are any adjacent non-local
4437 * condition dependences.
4439 static int has_violated_conditional_constraint(isl_ctx
*ctx
,
4440 struct isl_sched_graph
*graph
)
4444 isl_union_set
*source
, *sink
;
4446 source
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
4447 sink
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
4448 for (i
= 0; i
< graph
->n_edge
; ++i
) {
4449 isl_union_set
*uset
;
4450 isl_union_map
*umap
;
4453 if (!is_conditional_validity(&graph
->edge
[i
]))
4456 violated
= is_violated(graph
, i
);
4464 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_validity
);
4465 uset
= isl_union_map_domain(umap
);
4466 source
= isl_union_set_union(source
, uset
);
4467 source
= isl_union_set_coalesce(source
);
4469 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_validity
);
4470 uset
= isl_union_map_range(umap
);
4471 sink
= isl_union_set_union(sink
, uset
);
4472 sink
= isl_union_set_coalesce(sink
);
4476 any
= has_adjacent_true_conditions(graph
, source
, sink
);
4478 isl_union_set_free(source
);
4479 isl_union_set_free(sink
);
4482 isl_union_set_free(source
);
4483 isl_union_set_free(sink
);
4487 /* Examine the current band (the rows between graph->band_start and
4488 * graph->n_total_row), deciding whether to drop it or add it to "node"
4489 * and then continue with the computation of the next band, if any.
4490 * If "initialized" is set, then it may be assumed that compute_maxvar
4491 * has been called on the current band. Otherwise, call
4492 * compute_maxvar if and before carry_dependences gets called.
4494 * The caller keeps looking for a new row as long as
4495 * graph->n_row < graph->maxvar. If the latest attempt to find
4496 * such a row failed (i.e., we still have graph->n_row < graph->maxvar),
4498 * - split between SCCs and start over (assuming we found an interesting
4499 * pair of SCCs between which to split)
4500 * - continue with the next band (assuming the current band has at least
4502 * - try to carry as many dependences as possible and continue with the next
4504 * In each case, we first insert a band node in the schedule tree
4505 * if any rows have been computed.
4507 * If the caller managed to complete the schedule, we insert a band node
4508 * (if any schedule rows were computed) and we finish off by topologically
4509 * sorting the statements based on the remaining dependences.
4511 static __isl_give isl_schedule_node
*compute_schedule_finish_band(
4512 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
4520 if (graph
->n_row
< graph
->maxvar
) {
4522 int empty
= graph
->n_total_row
== graph
->band_start
;
4524 ctx
= isl_schedule_node_get_ctx(node
);
4525 if (!ctx
->opt
->schedule_maximize_band_depth
&& !empty
)
4526 return compute_next_band(node
, graph
, 1);
4527 if (graph
->src_scc
>= 0)
4528 return compute_split_schedule(node
, graph
);
4530 return compute_next_band(node
, graph
, 1);
4531 if (!initialized
&& compute_maxvar(graph
) < 0)
4532 return isl_schedule_node_free(node
);
4533 return carry_dependences(node
, graph
);
4536 insert
= graph
->n_total_row
> graph
->band_start
;
4538 node
= insert_current_band(node
, graph
, 1);
4539 node
= isl_schedule_node_child(node
, 0);
4541 node
= sort_statements(node
, graph
, initialized
);
4543 node
= isl_schedule_node_parent(node
);
4548 /* Construct a band of schedule rows for a connected dependence graph.
4549 * The caller is responsible for determining the strongly connected
4550 * components and calling compute_maxvar first.
4552 * We try to find a sequence of as many schedule rows as possible that result
4553 * in non-negative dependence distances (independent of the previous rows
4554 * in the sequence, i.e., such that the sequence is tilable), with as
4555 * many of the initial rows as possible satisfying the coincidence constraints.
4556 * The computation stops if we can't find any more rows or if we have found
4557 * all the rows we wanted to find.
4559 * If ctx->opt->schedule_outer_coincidence is set, then we force the
4560 * outermost dimension to satisfy the coincidence constraints. If this
4561 * turns out to be impossible, we fall back on the general scheme above
4562 * and try to carry as many dependences as possible.
4564 * If "graph" contains both condition and conditional validity dependences,
4565 * then we need to check that that the conditional schedule constraint
4566 * is satisfied, i.e., there are no violated conditional validity dependences
4567 * that are adjacent to any non-local condition dependences.
4568 * If there are, then we mark all those adjacent condition dependences
4569 * as local and recompute the current band. Those dependences that
4570 * are marked local will then be forced to be local.
4571 * The initial computation is performed with no dependences marked as local.
4572 * If we are lucky, then there will be no violated conditional validity
4573 * dependences adjacent to any non-local condition dependences.
4574 * Otherwise, we mark some additional condition dependences as local and
4575 * recompute. We continue this process until there are no violations left or
4576 * until we are no longer able to compute a schedule.
4577 * Since there are only a finite number of dependences,
4578 * there will only be a finite number of iterations.
4580 static isl_stat
compute_schedule_wcc_band(isl_ctx
*ctx
,
4581 struct isl_sched_graph
*graph
)
4583 int has_coincidence
;
4584 int use_coincidence
;
4585 int force_coincidence
= 0;
4586 int check_conditional
;
4588 if (sort_sccs(graph
) < 0)
4589 return isl_stat_error
;
4591 clear_local_edges(graph
);
4592 check_conditional
= need_condition_check(graph
);
4593 has_coincidence
= has_any_coincidence(graph
);
4595 if (ctx
->opt
->schedule_outer_coincidence
)
4596 force_coincidence
= 1;
4598 use_coincidence
= has_coincidence
;
4599 while (graph
->n_row
< graph
->maxvar
) {
4604 graph
->src_scc
= -1;
4605 graph
->dst_scc
= -1;
4607 if (setup_lp(ctx
, graph
, use_coincidence
) < 0)
4608 return isl_stat_error
;
4609 sol
= solve_lp(graph
);
4611 return isl_stat_error
;
4612 if (sol
->size
== 0) {
4613 int empty
= graph
->n_total_row
== graph
->band_start
;
4616 if (use_coincidence
&& (!force_coincidence
|| !empty
)) {
4617 use_coincidence
= 0;
4622 coincident
= !has_coincidence
|| use_coincidence
;
4623 if (update_schedule(graph
, sol
, 1, coincident
) < 0)
4624 return isl_stat_error
;
4626 if (!check_conditional
)
4628 violated
= has_violated_conditional_constraint(ctx
, graph
);
4630 return isl_stat_error
;
4633 if (reset_band(graph
) < 0)
4634 return isl_stat_error
;
4635 use_coincidence
= has_coincidence
;
4641 /* Compute a schedule for a connected dependence graph by considering
4642 * the graph as a whole and return the updated schedule node.
4644 * The actual schedule rows of the current band are computed by
4645 * compute_schedule_wcc_band. compute_schedule_finish_band takes
4646 * care of integrating the band into "node" and continuing
4649 static __isl_give isl_schedule_node
*compute_schedule_wcc_whole(
4650 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
4657 ctx
= isl_schedule_node_get_ctx(node
);
4658 if (compute_schedule_wcc_band(ctx
, graph
) < 0)
4659 return isl_schedule_node_free(node
);
4661 return compute_schedule_finish_band(node
, graph
, 1);
4664 /* Clustering information used by compute_schedule_wcc_clustering.
4666 * "n" is the number of SCCs in the original dependence graph
4667 * "scc" is an array of "n" elements, each representing an SCC
4668 * of the original dependence graph. All entries in the same cluster
4669 * have the same number of schedule rows.
4670 * "scc_cluster" maps each SCC index to the cluster to which it belongs,
4671 * where each cluster is represented by the index of the first SCC
4672 * in the cluster. Initially, each SCC belongs to a cluster containing
4675 * "scc_in_merge" is used by merge_clusters_along_edge to keep
4676 * track of which SCCs need to be merged.
4678 * "cluster" contains the merged clusters of SCCs after the clustering
4681 * "scc_node" is a temporary data structure used inside copy_partial.
4682 * For each SCC, it keeps track of the number of nodes in the SCC
4683 * that have already been copied.
4685 struct isl_clustering
{
4687 struct isl_sched_graph
*scc
;
4688 struct isl_sched_graph
*cluster
;
4694 /* Initialize the clustering data structure "c" from "graph".
4696 * In particular, allocate memory, extract the SCCs from "graph"
4697 * into c->scc, initialize scc_cluster and construct
4698 * a band of schedule rows for each SCC.
4699 * Within each SCC, there is only one SCC by definition.
4700 * Each SCC initially belongs to a cluster containing only that SCC.
4702 static isl_stat
clustering_init(isl_ctx
*ctx
, struct isl_clustering
*c
,
4703 struct isl_sched_graph
*graph
)
4708 c
->scc
= isl_calloc_array(ctx
, struct isl_sched_graph
, c
->n
);
4709 c
->cluster
= isl_calloc_array(ctx
, struct isl_sched_graph
, c
->n
);
4710 c
->scc_cluster
= isl_calloc_array(ctx
, int, c
->n
);
4711 c
->scc_node
= isl_calloc_array(ctx
, int, c
->n
);
4712 c
->scc_in_merge
= isl_calloc_array(ctx
, int, c
->n
);
4713 if (!c
->scc
|| !c
->cluster
||
4714 !c
->scc_cluster
|| !c
->scc_node
|| !c
->scc_in_merge
)
4715 return isl_stat_error
;
4717 for (i
= 0; i
< c
->n
; ++i
) {
4718 if (extract_sub_graph(ctx
, graph
, &node_scc_exactly
,
4719 &edge_scc_exactly
, i
, &c
->scc
[i
]) < 0)
4720 return isl_stat_error
;
4722 if (compute_maxvar(&c
->scc
[i
]) < 0)
4723 return isl_stat_error
;
4724 if (compute_schedule_wcc_band(ctx
, &c
->scc
[i
]) < 0)
4725 return isl_stat_error
;
4726 c
->scc_cluster
[i
] = i
;
4732 /* Free all memory allocated for "c".
4734 static void clustering_free(isl_ctx
*ctx
, struct isl_clustering
*c
)
4739 for (i
= 0; i
< c
->n
; ++i
)
4740 graph_free(ctx
, &c
->scc
[i
]);
4743 for (i
= 0; i
< c
->n
; ++i
)
4744 graph_free(ctx
, &c
->cluster
[i
]);
4746 free(c
->scc_cluster
);
4748 free(c
->scc_in_merge
);
4751 /* Should we refrain from merging the cluster in "graph" with
4752 * any other cluster?
4753 * In particular, is its current schedule band empty and incomplete.
4755 static int bad_cluster(struct isl_sched_graph
*graph
)
4757 return graph
->n_row
< graph
->maxvar
&&
4758 graph
->n_total_row
== graph
->band_start
;
4761 /* Return the index of an edge in "graph" that can be used to merge
4762 * two clusters in "c".
4763 * Return graph->n_edge if no such edge can be found.
4764 * Return -1 on error.
4766 * In particular, return a proximity edge between two clusters
4767 * that is not marked "no_merge" and such that neither of the
4768 * two clusters has an incomplete, empty band.
4770 * If there are multiple such edges, then try and find the most
4771 * appropriate edge to use for merging. In particular, pick the edge
4772 * with the greatest weight. If there are multiple of those,
4773 * then pick one with the shortest distance between
4774 * the two cluster representatives.
4776 static int find_proximity(struct isl_sched_graph
*graph
,
4777 struct isl_clustering
*c
)
4779 int i
, best
= graph
->n_edge
, best_dist
, best_weight
;
4781 for (i
= 0; i
< graph
->n_edge
; ++i
) {
4782 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
4785 if (!is_proximity(edge
))
4789 if (bad_cluster(&c
->scc
[edge
->src
->scc
]) ||
4790 bad_cluster(&c
->scc
[edge
->dst
->scc
]))
4792 dist
= c
->scc_cluster
[edge
->dst
->scc
] -
4793 c
->scc_cluster
[edge
->src
->scc
];
4796 weight
= edge
->weight
;
4797 if (best
< graph
->n_edge
) {
4798 if (best_weight
> weight
)
4800 if (best_weight
== weight
&& best_dist
<= dist
)
4805 best_weight
= weight
;
4811 /* Internal data structure used in mark_merge_sccs.
4813 * "graph" is the dependence graph in which a strongly connected
4814 * component is constructed.
4815 * "scc_cluster" maps each SCC index to the cluster to which it belongs.
4816 * "src" and "dst" are the indices of the nodes that are being merged.
4818 struct isl_mark_merge_sccs_data
{
4819 struct isl_sched_graph
*graph
;
4825 /* Check whether the cluster containing node "i" depends on the cluster
4826 * containing node "j". If "i" and "j" belong to the same cluster,
4827 * then they are taken to depend on each other to ensure that
4828 * the resulting strongly connected component consists of complete
4829 * clusters. Furthermore, if "i" and "j" are the two nodes that
4830 * are being merged, then they are taken to depend on each other as well.
4831 * Otherwise, check if there is a (conditional) validity dependence
4832 * from node[j] to node[i], forcing node[i] to follow node[j].
4834 static isl_bool
cluster_follows(int i
, int j
, void *user
)
4836 struct isl_mark_merge_sccs_data
*data
= user
;
4837 struct isl_sched_graph
*graph
= data
->graph
;
4838 int *scc_cluster
= data
->scc_cluster
;
4840 if (data
->src
== i
&& data
->dst
== j
)
4841 return isl_bool_true
;
4842 if (data
->src
== j
&& data
->dst
== i
)
4843 return isl_bool_true
;
4844 if (scc_cluster
[graph
->node
[i
].scc
] == scc_cluster
[graph
->node
[j
].scc
])
4845 return isl_bool_true
;
4847 return graph_has_validity_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
4850 /* Mark all SCCs that belong to either of the two clusters in "c"
4851 * connected by the edge in "graph" with index "edge", or to any
4852 * of the intermediate clusters.
4853 * The marking is recorded in c->scc_in_merge.
4855 * The given edge has been selected for merging two clusters,
4856 * meaning that there is at least a proximity edge between the two nodes.
4857 * However, there may also be (indirect) validity dependences
4858 * between the two nodes. When merging the two clusters, all clusters
4859 * containing one or more of the intermediate nodes along the
4860 * indirect validity dependences need to be merged in as well.
4862 * First collect all such nodes by computing the strongly connected
4863 * component (SCC) containing the two nodes connected by the edge, where
4864 * the two nodes are considered to depend on each other to make
4865 * sure they end up in the same SCC. Similarly, each node is considered
4866 * to depend on every other node in the same cluster to ensure
4867 * that the SCC consists of complete clusters.
4869 * Then the original SCCs that contain any of these nodes are marked
4870 * in c->scc_in_merge.
4872 static isl_stat
mark_merge_sccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
4873 int edge
, struct isl_clustering
*c
)
4875 struct isl_mark_merge_sccs_data data
;
4876 struct isl_tarjan_graph
*g
;
4879 for (i
= 0; i
< c
->n
; ++i
)
4880 c
->scc_in_merge
[i
] = 0;
4883 data
.scc_cluster
= c
->scc_cluster
;
4884 data
.src
= graph
->edge
[edge
].src
- graph
->node
;
4885 data
.dst
= graph
->edge
[edge
].dst
- graph
->node
;
4887 g
= isl_tarjan_graph_component(ctx
, graph
->n
, data
.dst
,
4888 &cluster_follows
, &data
);
4894 isl_die(ctx
, isl_error_internal
,
4895 "expecting at least two nodes in component",
4897 if (g
->order
[--i
] != -1)
4898 isl_die(ctx
, isl_error_internal
,
4899 "expecting end of component marker", goto error
);
4901 for (--i
; i
>= 0 && g
->order
[i
] != -1; --i
) {
4902 int scc
= graph
->node
[g
->order
[i
]].scc
;
4903 c
->scc_in_merge
[scc
] = 1;
4906 isl_tarjan_graph_free(g
);
4909 isl_tarjan_graph_free(g
);
4910 return isl_stat_error
;
4913 /* Construct the identifier "cluster_i".
4915 static __isl_give isl_id
*cluster_id(isl_ctx
*ctx
, int i
)
4919 snprintf(name
, sizeof(name
), "cluster_%d", i
);
4920 return isl_id_alloc(ctx
, name
, NULL
);
4923 /* Construct the space of the cluster with index "i" containing
4924 * the strongly connected component "scc".
4926 * In particular, construct a space called cluster_i with dimension equal
4927 * to the number of schedule rows in the current band of "scc".
4929 static __isl_give isl_space
*cluster_space(struct isl_sched_graph
*scc
, int i
)
4935 nvar
= scc
->n_total_row
- scc
->band_start
;
4936 space
= isl_space_copy(scc
->node
[0].space
);
4937 space
= isl_space_params(space
);
4938 space
= isl_space_set_from_params(space
);
4939 space
= isl_space_add_dims(space
, isl_dim_set
, nvar
);
4940 id
= cluster_id(isl_space_get_ctx(space
), i
);
4941 space
= isl_space_set_tuple_id(space
, isl_dim_set
, id
);
4946 /* Collect the domain of the graph for merging clusters.
4948 * In particular, for each cluster with first SCC "i", construct
4949 * a set in the space called cluster_i with dimension equal
4950 * to the number of schedule rows in the current band of the cluster.
4952 static __isl_give isl_union_set
*collect_domain(isl_ctx
*ctx
,
4953 struct isl_sched_graph
*graph
, struct isl_clustering
*c
)
4957 isl_union_set
*domain
;
4959 space
= isl_space_params_alloc(ctx
, 0);
4960 domain
= isl_union_set_empty(space
);
4962 for (i
= 0; i
< graph
->scc
; ++i
) {
4965 if (!c
->scc_in_merge
[i
])
4967 if (c
->scc_cluster
[i
] != i
)
4969 space
= cluster_space(&c
->scc
[i
], i
);
4970 domain
= isl_union_set_add_set(domain
, isl_set_universe(space
));
4976 /* Construct a map from the original instances to the corresponding
4977 * cluster instance in the current bands of the clusters in "c".
4979 static __isl_give isl_union_map
*collect_cluster_map(isl_ctx
*ctx
,
4980 struct isl_sched_graph
*graph
, struct isl_clustering
*c
)
4984 isl_union_map
*cluster_map
;
4986 space
= isl_space_params_alloc(ctx
, 0);
4987 cluster_map
= isl_union_map_empty(space
);
4988 for (i
= 0; i
< graph
->scc
; ++i
) {
4992 if (!c
->scc_in_merge
[i
])
4995 id
= cluster_id(ctx
, c
->scc_cluster
[i
]);
4996 start
= c
->scc
[i
].band_start
;
4997 n
= c
->scc
[i
].n_total_row
- start
;
4998 for (j
= 0; j
< c
->scc
[i
].n
; ++j
) {
5001 struct isl_sched_node
*node
= &c
->scc
[i
].node
[j
];
5003 ma
= node_extract_partial_schedule_multi_aff(node
,
5005 ma
= isl_multi_aff_set_tuple_id(ma
, isl_dim_out
,
5007 map
= isl_map_from_multi_aff(ma
);
5008 cluster_map
= isl_union_map_add_map(cluster_map
, map
);
5016 /* Add "umap" to the schedule constraints "sc" of all types of "edge"
5017 * that are not isl_edge_condition or isl_edge_conditional_validity.
5019 static __isl_give isl_schedule_constraints
*add_non_conditional_constraints(
5020 struct isl_sched_edge
*edge
, __isl_keep isl_union_map
*umap
,
5021 __isl_take isl_schedule_constraints
*sc
)
5023 enum isl_edge_type t
;
5028 for (t
= isl_edge_first
; t
<= isl_edge_last
; ++t
) {
5029 if (t
== isl_edge_condition
||
5030 t
== isl_edge_conditional_validity
)
5032 if (!is_type(edge
, t
))
5034 sc
= isl_schedule_constraints_add(sc
, t
,
5035 isl_union_map_copy(umap
));
5041 /* Add schedule constraints of types isl_edge_condition and
5042 * isl_edge_conditional_validity to "sc" by applying "umap" to
5043 * the domains of the wrapped relations in domain and range
5044 * of the corresponding tagged constraints of "edge".
5046 static __isl_give isl_schedule_constraints
*add_conditional_constraints(
5047 struct isl_sched_edge
*edge
, __isl_keep isl_union_map
*umap
,
5048 __isl_take isl_schedule_constraints
*sc
)
5050 enum isl_edge_type t
;
5051 isl_union_map
*tagged
;
5053 for (t
= isl_edge_condition
; t
<= isl_edge_conditional_validity
; ++t
) {
5054 if (!is_type(edge
, t
))
5056 if (t
== isl_edge_condition
)
5057 tagged
= isl_union_map_copy(edge
->tagged_condition
);
5059 tagged
= isl_union_map_copy(edge
->tagged_validity
);
5060 tagged
= isl_union_map_zip(tagged
);
5061 tagged
= isl_union_map_apply_domain(tagged
,
5062 isl_union_map_copy(umap
));
5063 tagged
= isl_union_map_zip(tagged
);
5064 sc
= isl_schedule_constraints_add(sc
, t
, tagged
);
5072 /* Given a mapping "cluster_map" from the original instances to
5073 * the cluster instances, add schedule constraints on the clusters
5074 * to "sc" corresponding to the original constraints represented by "edge".
5076 * For non-tagged dependence constraints, the cluster constraints
5077 * are obtained by applying "cluster_map" to the edge->map.
5079 * For tagged dependence constraints, "cluster_map" needs to be applied
5080 * to the domains of the wrapped relations in domain and range
5081 * of the tagged dependence constraints. Pick out the mappings
5082 * from these domains from "cluster_map" and construct their product.
5083 * This mapping can then be applied to the pair of domains.
5085 static __isl_give isl_schedule_constraints
*collect_edge_constraints(
5086 struct isl_sched_edge
*edge
, __isl_keep isl_union_map
*cluster_map
,
5087 __isl_take isl_schedule_constraints
*sc
)
5089 isl_union_map
*umap
;
5091 isl_union_set
*uset
;
5092 isl_union_map
*umap1
, *umap2
;
5097 umap
= isl_union_map_from_map(isl_map_copy(edge
->map
));
5098 umap
= isl_union_map_apply_domain(umap
,
5099 isl_union_map_copy(cluster_map
));
5100 umap
= isl_union_map_apply_range(umap
,
5101 isl_union_map_copy(cluster_map
));
5102 sc
= add_non_conditional_constraints(edge
, umap
, sc
);
5103 isl_union_map_free(umap
);
5105 if (!sc
|| (!is_condition(edge
) && !is_conditional_validity(edge
)))
5108 space
= isl_space_domain(isl_map_get_space(edge
->map
));
5109 uset
= isl_union_set_from_set(isl_set_universe(space
));
5110 umap1
= isl_union_map_copy(cluster_map
);
5111 umap1
= isl_union_map_intersect_domain(umap1
, uset
);
5112 space
= isl_space_range(isl_map_get_space(edge
->map
));
5113 uset
= isl_union_set_from_set(isl_set_universe(space
));
5114 umap2
= isl_union_map_copy(cluster_map
);
5115 umap2
= isl_union_map_intersect_domain(umap2
, uset
);
5116 umap
= isl_union_map_product(umap1
, umap2
);
5118 sc
= add_conditional_constraints(edge
, umap
, sc
);
5120 isl_union_map_free(umap
);
5124 /* Given a mapping "cluster_map" from the original instances to
5125 * the cluster instances, add schedule constraints on the clusters
5126 * to "sc" corresponding to all edges in "graph" between nodes that
5127 * belong to SCCs that are marked for merging in "scc_in_merge".
5129 static __isl_give isl_schedule_constraints
*collect_constraints(
5130 struct isl_sched_graph
*graph
, int *scc_in_merge
,
5131 __isl_keep isl_union_map
*cluster_map
,
5132 __isl_take isl_schedule_constraints
*sc
)
5136 for (i
= 0; i
< graph
->n_edge
; ++i
) {
5137 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
5139 if (!scc_in_merge
[edge
->src
->scc
])
5141 if (!scc_in_merge
[edge
->dst
->scc
])
5143 sc
= collect_edge_constraints(edge
, cluster_map
, sc
);
5149 /* Construct a dependence graph for scheduling clusters with respect
5150 * to each other and store the result in "merge_graph".
5151 * In particular, the nodes of the graph correspond to the schedule
5152 * dimensions of the current bands of those clusters that have been
5153 * marked for merging in "c".
5155 * First construct an isl_schedule_constraints object for this domain
5156 * by transforming the edges in "graph" to the domain.
5157 * Then initialize a dependence graph for scheduling from these
5160 static isl_stat
init_merge_graph(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
5161 struct isl_clustering
*c
, struct isl_sched_graph
*merge_graph
)
5163 isl_union_set
*domain
;
5164 isl_union_map
*cluster_map
;
5165 isl_schedule_constraints
*sc
;
5168 domain
= collect_domain(ctx
, graph
, c
);
5169 sc
= isl_schedule_constraints_on_domain(domain
);
5171 return isl_stat_error
;
5172 cluster_map
= collect_cluster_map(ctx
, graph
, c
);
5173 sc
= collect_constraints(graph
, c
->scc_in_merge
, cluster_map
, sc
);
5174 isl_union_map_free(cluster_map
);
5176 r
= graph_init(merge_graph
, sc
);
5178 isl_schedule_constraints_free(sc
);
5183 /* Compute the maximal number of remaining schedule rows that still need
5184 * to be computed for the nodes that belong to clusters with the maximal
5185 * dimension for the current band (i.e., the band that is to be merged).
5186 * Only clusters that are about to be merged are considered.
5187 * "maxvar" is the maximal dimension for the current band.
5188 * "c" contains information about the clusters.
5190 * Return the maximal number of remaining schedule rows or -1 on error.
5192 static int compute_maxvar_max_slack(int maxvar
, struct isl_clustering
*c
)
5198 for (i
= 0; i
< c
->n
; ++i
) {
5200 struct isl_sched_graph
*scc
;
5202 if (!c
->scc_in_merge
[i
])
5205 nvar
= scc
->n_total_row
- scc
->band_start
;
5208 for (j
= 0; j
< scc
->n
; ++j
) {
5209 struct isl_sched_node
*node
= &scc
->node
[j
];
5212 if (node_update_cmap(node
) < 0)
5214 slack
= node
->nvar
- node
->rank
;
5215 if (slack
> max_slack
)
5223 /* If there are any clusters where the dimension of the current band
5224 * (i.e., the band that is to be merged) is smaller than "maxvar" and
5225 * if there are any nodes in such a cluster where the number
5226 * of remaining schedule rows that still need to be computed
5227 * is greater than "max_slack", then return the smallest current band
5228 * dimension of all these clusters. Otherwise return the original value
5229 * of "maxvar". Return -1 in case of any error.
5230 * Only clusters that are about to be merged are considered.
5231 * "c" contains information about the clusters.
5233 static int limit_maxvar_to_slack(int maxvar
, int max_slack
,
5234 struct isl_clustering
*c
)
5238 for (i
= 0; i
< c
->n
; ++i
) {
5240 struct isl_sched_graph
*scc
;
5242 if (!c
->scc_in_merge
[i
])
5245 nvar
= scc
->n_total_row
- scc
->band_start
;
5248 for (j
= 0; j
< scc
->n
; ++j
) {
5249 struct isl_sched_node
*node
= &scc
->node
[j
];
5252 if (node_update_cmap(node
) < 0)
5254 slack
= node
->nvar
- node
->rank
;
5255 if (slack
> max_slack
) {
5265 /* Adjust merge_graph->maxvar based on the number of remaining schedule rows
5266 * that still need to be computed. In particular, if there is a node
5267 * in a cluster where the dimension of the current band is smaller
5268 * than merge_graph->maxvar, but the number of remaining schedule rows
5269 * is greater than that of any node in a cluster with the maximal
5270 * dimension for the current band (i.e., merge_graph->maxvar),
5271 * then adjust merge_graph->maxvar to the (smallest) current band dimension
5272 * of those clusters. Without this adjustment, the total number of
5273 * schedule dimensions would be increased, resulting in a skewed view
5274 * of the number of coincident dimensions.
5275 * "c" contains information about the clusters.
5277 * If the maximize_band_depth option is set and merge_graph->maxvar is reduced,
5278 * then there is no point in attempting any merge since it will be rejected
5279 * anyway. Set merge_graph->maxvar to zero in such cases.
5281 static isl_stat
adjust_maxvar_to_slack(isl_ctx
*ctx
,
5282 struct isl_sched_graph
*merge_graph
, struct isl_clustering
*c
)
5284 int max_slack
, maxvar
;
5286 max_slack
= compute_maxvar_max_slack(merge_graph
->maxvar
, c
);
5288 return isl_stat_error
;
5289 maxvar
= limit_maxvar_to_slack(merge_graph
->maxvar
, max_slack
, c
);
5291 return isl_stat_error
;
5293 if (maxvar
< merge_graph
->maxvar
) {
5294 if (isl_options_get_schedule_maximize_band_depth(ctx
))
5295 merge_graph
->maxvar
= 0;
5297 merge_graph
->maxvar
= maxvar
;
5303 /* Return the number of coincident dimensions in the current band of "graph",
5304 * where the nodes of "graph" are assumed to be scheduled by a single band.
5306 static int get_n_coincident(struct isl_sched_graph
*graph
)
5310 for (i
= graph
->band_start
; i
< graph
->n_total_row
; ++i
)
5311 if (!graph
->node
[0].coincident
[i
])
5314 return i
- graph
->band_start
;
5317 /* Should the clusters be merged based on the cluster schedule
5318 * in the current (and only) band of "merge_graph", given that
5319 * coincidence should be maximized?
5321 * If the number of coincident schedule dimensions in the merged band
5322 * would be less than the maximal number of coincident schedule dimensions
5323 * in any of the merged clusters, then the clusters should not be merged.
5325 static isl_bool
ok_to_merge_coincident(struct isl_clustering
*c
,
5326 struct isl_sched_graph
*merge_graph
)
5333 for (i
= 0; i
< c
->n
; ++i
) {
5334 if (!c
->scc_in_merge
[i
])
5336 n_coincident
= get_n_coincident(&c
->scc
[i
]);
5337 if (n_coincident
> max_coincident
)
5338 max_coincident
= n_coincident
;
5341 n_coincident
= get_n_coincident(merge_graph
);
5343 return n_coincident
>= max_coincident
;
5346 /* Return the transformation on "node" expressed by the current (and only)
5347 * band of "merge_graph" applied to the clusters in "c".
5349 * First find the representation of "node" in its SCC in "c" and
5350 * extract the transformation expressed by the current band.
5351 * Then extract the transformation applied by "merge_graph"
5352 * to the cluster to which this SCC belongs.
5353 * Combine the two to obtain the complete transformation on the node.
5355 * Note that the range of the first transformation is an anonymous space,
5356 * while the domain of the second is named "cluster_X". The range
5357 * of the former therefore needs to be adjusted before the two
5360 static __isl_give isl_map
*extract_node_transformation(isl_ctx
*ctx
,
5361 struct isl_sched_node
*node
, struct isl_clustering
*c
,
5362 struct isl_sched_graph
*merge_graph
)
5364 struct isl_sched_node
*scc_node
, *cluster_node
;
5368 isl_multi_aff
*ma
, *ma2
;
5370 scc_node
= graph_find_node(ctx
, &c
->scc
[node
->scc
], node
->space
);
5371 start
= c
->scc
[node
->scc
].band_start
;
5372 n
= c
->scc
[node
->scc
].n_total_row
- start
;
5373 ma
= node_extract_partial_schedule_multi_aff(scc_node
, start
, n
);
5374 space
= cluster_space(&c
->scc
[node
->scc
], c
->scc_cluster
[node
->scc
]);
5375 cluster_node
= graph_find_node(ctx
, merge_graph
, space
);
5376 if (space
&& !cluster_node
)
5377 isl_die(ctx
, isl_error_internal
, "unable to find cluster",
5378 space
= isl_space_free(space
));
5379 id
= isl_space_get_tuple_id(space
, isl_dim_set
);
5380 ma
= isl_multi_aff_set_tuple_id(ma
, isl_dim_out
, id
);
5381 isl_space_free(space
);
5382 n
= merge_graph
->n_total_row
;
5383 ma2
= node_extract_partial_schedule_multi_aff(cluster_node
, 0, n
);
5384 ma
= isl_multi_aff_pullback_multi_aff(ma2
, ma
);
5386 return isl_map_from_multi_aff(ma
);
5389 /* Give a set of distances "set", are they bounded by a small constant
5390 * in direction "pos"?
5391 * In practice, check if they are bounded by 2 by checking that there
5392 * are no elements with a value greater than or equal to 3 or
5393 * smaller than or equal to -3.
5395 static isl_bool
distance_is_bounded(__isl_keep isl_set
*set
, int pos
)
5401 return isl_bool_error
;
5403 test
= isl_set_copy(set
);
5404 test
= isl_set_lower_bound_si(test
, isl_dim_set
, pos
, 3);
5405 bounded
= isl_set_is_empty(test
);
5408 if (bounded
< 0 || !bounded
)
5411 test
= isl_set_copy(set
);
5412 test
= isl_set_upper_bound_si(test
, isl_dim_set
, pos
, -3);
5413 bounded
= isl_set_is_empty(test
);
5419 /* Does the set "set" have a fixed (but possible parametric) value
5420 * at dimension "pos"?
5422 static isl_bool
has_single_value(__isl_keep isl_set
*set
, int pos
)
5428 return isl_bool_error
;
5429 set
= isl_set_copy(set
);
5430 n
= isl_set_dim(set
, isl_dim_set
);
5431 set
= isl_set_project_out(set
, isl_dim_set
, pos
+ 1, n
- (pos
+ 1));
5432 set
= isl_set_project_out(set
, isl_dim_set
, 0, pos
);
5433 single
= isl_set_is_singleton(set
);
5439 /* Does "map" have a fixed (but possible parametric) value
5440 * at dimension "pos" of either its domain or its range?
5442 static isl_bool
has_singular_src_or_dst(__isl_keep isl_map
*map
, int pos
)
5447 set
= isl_map_domain(isl_map_copy(map
));
5448 single
= has_single_value(set
, pos
);
5451 if (single
< 0 || single
)
5454 set
= isl_map_range(isl_map_copy(map
));
5455 single
= has_single_value(set
, pos
);
5461 /* Does the edge "edge" from "graph" have bounded dependence distances
5462 * in the merged graph "merge_graph" of a selection of clusters in "c"?
5464 * Extract the complete transformations of the source and destination
5465 * nodes of the edge, apply them to the edge constraints and
5466 * compute the differences. Finally, check if these differences are bounded
5467 * in each direction.
5469 * If the dimension of the band is greater than the number of
5470 * dimensions that can be expected to be optimized by the edge
5471 * (based on its weight), then also allow the differences to be unbounded
5472 * in the remaining dimensions, but only if either the source or
5473 * the destination has a fixed value in that direction.
5474 * This allows a statement that produces values that are used by
5475 * several instances of another statement to be merged with that
5477 * However, merging such clusters will introduce an inherently
5478 * large proximity distance inside the merged cluster, meaning
5479 * that proximity distances will no longer be optimized in
5480 * subsequent merges. These merges are therefore only allowed
5481 * after all other possible merges have been tried.
5482 * The first time such a merge is encountered, the weight of the edge
5483 * is replaced by a negative weight. The second time (i.e., after
5484 * all merges over edges with a non-negative weight have been tried),
5485 * the merge is allowed.
5487 static isl_bool
has_bounded_distances(isl_ctx
*ctx
, struct isl_sched_edge
*edge
,
5488 struct isl_sched_graph
*graph
, struct isl_clustering
*c
,
5489 struct isl_sched_graph
*merge_graph
)
5496 map
= isl_map_copy(edge
->map
);
5497 t
= extract_node_transformation(ctx
, edge
->src
, c
, merge_graph
);
5498 map
= isl_map_apply_domain(map
, t
);
5499 t
= extract_node_transformation(ctx
, edge
->dst
, c
, merge_graph
);
5500 map
= isl_map_apply_range(map
, t
);
5501 dist
= isl_map_deltas(isl_map_copy(map
));
5503 bounded
= isl_bool_true
;
5504 n
= isl_set_dim(dist
, isl_dim_set
);
5505 n_slack
= n
- edge
->weight
;
5506 if (edge
->weight
< 0)
5507 n_slack
-= graph
->max_weight
+ 1;
5508 for (i
= 0; i
< n
; ++i
) {
5509 isl_bool bounded_i
, singular_i
;
5511 bounded_i
= distance_is_bounded(dist
, i
);
5516 if (edge
->weight
>= 0)
5517 bounded
= isl_bool_false
;
5521 singular_i
= has_singular_src_or_dst(map
, i
);
5526 bounded
= isl_bool_false
;
5529 if (!bounded
&& i
>= n
&& edge
->weight
>= 0)
5530 edge
->weight
-= graph
->max_weight
+ 1;
5538 return isl_bool_error
;
5541 /* Should the clusters be merged based on the cluster schedule
5542 * in the current (and only) band of "merge_graph"?
5543 * "graph" is the original dependence graph, while "c" records
5544 * which SCCs are involved in the latest merge.
5546 * In particular, is there at least one proximity constraint
5547 * that is optimized by the merge?
5549 * A proximity constraint is considered to be optimized
5550 * if the dependence distances are small.
5552 static isl_bool
ok_to_merge_proximity(isl_ctx
*ctx
,
5553 struct isl_sched_graph
*graph
, struct isl_clustering
*c
,
5554 struct isl_sched_graph
*merge_graph
)
5558 for (i
= 0; i
< graph
->n_edge
; ++i
) {
5559 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
5562 if (!is_proximity(edge
))
5564 if (!c
->scc_in_merge
[edge
->src
->scc
])
5566 if (!c
->scc_in_merge
[edge
->dst
->scc
])
5568 if (c
->scc_cluster
[edge
->dst
->scc
] ==
5569 c
->scc_cluster
[edge
->src
->scc
])
5571 bounded
= has_bounded_distances(ctx
, edge
, graph
, c
,
5573 if (bounded
< 0 || bounded
)
5577 return isl_bool_false
;
5580 /* Should the clusters be merged based on the cluster schedule
5581 * in the current (and only) band of "merge_graph"?
5582 * "graph" is the original dependence graph, while "c" records
5583 * which SCCs are involved in the latest merge.
5585 * If the current band is empty, then the clusters should not be merged.
5587 * If the band depth should be maximized and the merge schedule
5588 * is incomplete (meaning that the dimension of some of the schedule
5589 * bands in the original schedule will be reduced), then the clusters
5590 * should not be merged.
5592 * If the schedule_maximize_coincidence option is set, then check that
5593 * the number of coincident schedule dimensions is not reduced.
5595 * Finally, only allow the merge if at least one proximity
5596 * constraint is optimized.
5598 static isl_bool
ok_to_merge(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
5599 struct isl_clustering
*c
, struct isl_sched_graph
*merge_graph
)
5601 if (merge_graph
->n_total_row
== merge_graph
->band_start
)
5602 return isl_bool_false
;
5604 if (isl_options_get_schedule_maximize_band_depth(ctx
) &&
5605 merge_graph
->n_total_row
< merge_graph
->maxvar
)
5606 return isl_bool_false
;
5608 if (isl_options_get_schedule_maximize_coincidence(ctx
)) {
5611 ok
= ok_to_merge_coincident(c
, merge_graph
);
5616 return ok_to_merge_proximity(ctx
, graph
, c
, merge_graph
);
5619 /* Apply the schedule in "t_node" to the "n" rows starting at "first"
5620 * of the schedule in "node" and return the result.
5622 * That is, essentially compute
5624 * T * N(first:first+n-1)
5626 * taking into account the constant term and the parameter coefficients
5629 static __isl_give isl_mat
*node_transformation(isl_ctx
*ctx
,
5630 struct isl_sched_node
*t_node
, struct isl_sched_node
*node
,
5635 int n_row
, n_col
, n_param
, n_var
;
5637 n_param
= node
->nparam
;
5639 n_row
= isl_mat_rows(t_node
->sched
);
5640 n_col
= isl_mat_cols(node
->sched
);
5641 t
= isl_mat_alloc(ctx
, n_row
, n_col
);
5644 for (i
= 0; i
< n_row
; ++i
) {
5645 isl_seq_cpy(t
->row
[i
], t_node
->sched
->row
[i
], 1 + n_param
);
5646 isl_seq_clr(t
->row
[i
] + 1 + n_param
, n_var
);
5647 for (j
= 0; j
< n
; ++j
)
5648 isl_seq_addmul(t
->row
[i
],
5649 t_node
->sched
->row
[i
][1 + n_param
+ j
],
5650 node
->sched
->row
[first
+ j
],
5651 1 + n_param
+ n_var
);
5656 /* Apply the cluster schedule in "t_node" to the current band
5657 * schedule of the nodes in "graph".
5659 * In particular, replace the rows starting at band_start
5660 * by the result of applying the cluster schedule in "t_node"
5661 * to the original rows.
5663 * The coincidence of the schedule is determined by the coincidence
5664 * of the cluster schedule.
5666 static isl_stat
transform(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
5667 struct isl_sched_node
*t_node
)
5673 start
= graph
->band_start
;
5674 n
= graph
->n_total_row
- start
;
5676 n_new
= isl_mat_rows(t_node
->sched
);
5677 for (i
= 0; i
< graph
->n
; ++i
) {
5678 struct isl_sched_node
*node
= &graph
->node
[i
];
5681 t
= node_transformation(ctx
, t_node
, node
, start
, n
);
5682 node
->sched
= isl_mat_drop_rows(node
->sched
, start
, n
);
5683 node
->sched
= isl_mat_concat(node
->sched
, t
);
5684 node
->sched_map
= isl_map_free(node
->sched_map
);
5686 return isl_stat_error
;
5687 for (j
= 0; j
< n_new
; ++j
)
5688 node
->coincident
[start
+ j
] = t_node
->coincident
[j
];
5690 graph
->n_total_row
-= n
;
5692 graph
->n_total_row
+= n_new
;
5693 graph
->n_row
+= n_new
;
5698 /* Merge the clusters marked for merging in "c" into a single
5699 * cluster using the cluster schedule in the current band of "merge_graph".
5700 * The representative SCC for the new cluster is the SCC with
5701 * the smallest index.
5703 * The current band schedule of each SCC in the new cluster is obtained
5704 * by applying the schedule of the corresponding original cluster
5705 * to the original band schedule.
5706 * All SCCs in the new cluster have the same number of schedule rows.
5708 static isl_stat
merge(isl_ctx
*ctx
, struct isl_clustering
*c
,
5709 struct isl_sched_graph
*merge_graph
)
5715 for (i
= 0; i
< c
->n
; ++i
) {
5716 struct isl_sched_node
*node
;
5718 if (!c
->scc_in_merge
[i
])
5722 space
= cluster_space(&c
->scc
[i
], c
->scc_cluster
[i
]);
5724 return isl_stat_error
;
5725 node
= graph_find_node(ctx
, merge_graph
, space
);
5726 isl_space_free(space
);
5728 isl_die(ctx
, isl_error_internal
,
5729 "unable to find cluster",
5730 return isl_stat_error
);
5731 if (transform(ctx
, &c
->scc
[i
], node
) < 0)
5732 return isl_stat_error
;
5733 c
->scc_cluster
[i
] = cluster
;
5739 /* Try and merge the clusters of SCCs marked in c->scc_in_merge
5740 * by scheduling the current cluster bands with respect to each other.
5742 * Construct a dependence graph with a space for each cluster and
5743 * with the coordinates of each space corresponding to the schedule
5744 * dimensions of the current band of that cluster.
5745 * Construct a cluster schedule in this cluster dependence graph and
5746 * apply it to the current cluster bands if it is applicable
5747 * according to ok_to_merge.
5749 * If the number of remaining schedule dimensions in a cluster
5750 * with a non-maximal current schedule dimension is greater than
5751 * the number of remaining schedule dimensions in clusters
5752 * with a maximal current schedule dimension, then restrict
5753 * the number of rows to be computed in the cluster schedule
5754 * to the minimal such non-maximal current schedule dimension.
5755 * Do this by adjusting merge_graph.maxvar.
5757 * Return isl_bool_true if the clusters have effectively been merged
5758 * into a single cluster.
5760 * Note that since the standard scheduling algorithm minimizes the maximal
5761 * distance over proximity constraints, the proximity constraints between
5762 * the merged clusters may not be optimized any further than what is
5763 * sufficient to bring the distances within the limits of the internal
5764 * proximity constraints inside the individual clusters.
5765 * It may therefore make sense to perform an additional translation step
5766 * to bring the clusters closer to each other, while maintaining
5767 * the linear part of the merging schedule found using the standard
5768 * scheduling algorithm.
5770 static isl_bool
try_merge(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
5771 struct isl_clustering
*c
)
5773 struct isl_sched_graph merge_graph
= { 0 };
5776 if (init_merge_graph(ctx
, graph
, c
, &merge_graph
) < 0)
5779 if (compute_maxvar(&merge_graph
) < 0)
5781 if (adjust_maxvar_to_slack(ctx
, &merge_graph
,c
) < 0)
5783 if (compute_schedule_wcc_band(ctx
, &merge_graph
) < 0)
5785 merged
= ok_to_merge(ctx
, graph
, c
, &merge_graph
);
5786 if (merged
&& merge(ctx
, c
, &merge_graph
) < 0)
5789 graph_free(ctx
, &merge_graph
);
5792 graph_free(ctx
, &merge_graph
);
5793 return isl_bool_error
;
5796 /* Is there any edge marked "no_merge" between two SCCs that are
5797 * about to be merged (i.e., that are set in "scc_in_merge")?
5798 * "merge_edge" is the proximity edge along which the clusters of SCCs
5799 * are going to be merged.
5801 * If there is any edge between two SCCs with a negative weight,
5802 * while the weight of "merge_edge" is non-negative, then this
5803 * means that the edge was postponed. "merge_edge" should then
5804 * also be postponed since merging along the edge with negative weight should
5805 * be postponed until all edges with non-negative weight have been tried.
5806 * Replace the weight of "merge_edge" by a negative weight as well and
5807 * tell the caller not to attempt a merge.
5809 static int any_no_merge(struct isl_sched_graph
*graph
, int *scc_in_merge
,
5810 struct isl_sched_edge
*merge_edge
)
5814 for (i
= 0; i
< graph
->n_edge
; ++i
) {
5815 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
5817 if (!scc_in_merge
[edge
->src
->scc
])
5819 if (!scc_in_merge
[edge
->dst
->scc
])
5823 if (merge_edge
->weight
>= 0 && edge
->weight
< 0) {
5824 merge_edge
->weight
-= graph
->max_weight
+ 1;
5832 /* Merge the two clusters in "c" connected by the edge in "graph"
5833 * with index "edge" into a single cluster.
5834 * If it turns out to be impossible to merge these two clusters,
5835 * then mark the edge as "no_merge" such that it will not be
5838 * First mark all SCCs that need to be merged. This includes the SCCs
5839 * in the two clusters, but it may also include the SCCs
5840 * of intermediate clusters.
5841 * If there is already a no_merge edge between any pair of such SCCs,
5842 * then simply mark the current edge as no_merge as well.
5843 * Likewise, if any of those edges was postponed by has_bounded_distances,
5844 * then postpone the current edge as well.
5845 * Otherwise, try and merge the clusters and mark "edge" as "no_merge"
5846 * if the clusters did not end up getting merged, unless the non-merge
5847 * is due to the fact that the edge was postponed. This postponement
5848 * can be recognized by a change in weight (from non-negative to negative).
5850 static isl_stat
merge_clusters_along_edge(isl_ctx
*ctx
,
5851 struct isl_sched_graph
*graph
, int edge
, struct isl_clustering
*c
)
5854 int edge_weight
= graph
->edge
[edge
].weight
;
5856 if (mark_merge_sccs(ctx
, graph
, edge
, c
) < 0)
5857 return isl_stat_error
;
5859 if (any_no_merge(graph
, c
->scc_in_merge
, &graph
->edge
[edge
]))
5860 merged
= isl_bool_false
;
5862 merged
= try_merge(ctx
, graph
, c
);
5864 return isl_stat_error
;
5865 if (!merged
&& edge_weight
== graph
->edge
[edge
].weight
)
5866 graph
->edge
[edge
].no_merge
= 1;
5871 /* Does "node" belong to the cluster identified by "cluster"?
5873 static int node_cluster_exactly(struct isl_sched_node
*node
, int cluster
)
5875 return node
->cluster
== cluster
;
5878 /* Does "edge" connect two nodes belonging to the cluster
5879 * identified by "cluster"?
5881 static int edge_cluster_exactly(struct isl_sched_edge
*edge
, int cluster
)
5883 return edge
->src
->cluster
== cluster
&& edge
->dst
->cluster
== cluster
;
5886 /* Swap the schedule of "node1" and "node2".
5887 * Both nodes have been derived from the same node in a common parent graph.
5888 * Since the "coincident" field is shared with that node
5889 * in the parent graph, there is no need to also swap this field.
5891 static void swap_sched(struct isl_sched_node
*node1
,
5892 struct isl_sched_node
*node2
)
5897 sched
= node1
->sched
;
5898 node1
->sched
= node2
->sched
;
5899 node2
->sched
= sched
;
5901 sched_map
= node1
->sched_map
;
5902 node1
->sched_map
= node2
->sched_map
;
5903 node2
->sched_map
= sched_map
;
5906 /* Copy the current band schedule from the SCCs that form the cluster
5907 * with index "pos" to the actual cluster at position "pos".
5908 * By construction, the index of the first SCC that belongs to the cluster
5911 * The order of the nodes inside both the SCCs and the cluster
5912 * is assumed to be same as the order in the original "graph".
5914 * Since the SCC graphs will no longer be used after this function,
5915 * the schedules are actually swapped rather than copied.
5917 static isl_stat
copy_partial(struct isl_sched_graph
*graph
,
5918 struct isl_clustering
*c
, int pos
)
5922 c
->cluster
[pos
].n_total_row
= c
->scc
[pos
].n_total_row
;
5923 c
->cluster
[pos
].n_row
= c
->scc
[pos
].n_row
;
5924 c
->cluster
[pos
].maxvar
= c
->scc
[pos
].maxvar
;
5926 for (i
= 0; i
< graph
->n
; ++i
) {
5930 if (graph
->node
[i
].cluster
!= pos
)
5932 s
= graph
->node
[i
].scc
;
5933 k
= c
->scc_node
[s
]++;
5934 swap_sched(&c
->cluster
[pos
].node
[j
], &c
->scc
[s
].node
[k
]);
5935 if (c
->scc
[s
].maxvar
> c
->cluster
[pos
].maxvar
)
5936 c
->cluster
[pos
].maxvar
= c
->scc
[s
].maxvar
;
5943 /* Is there a (conditional) validity dependence from node[j] to node[i],
5944 * forcing node[i] to follow node[j] or do the nodes belong to the same
5947 static isl_bool
node_follows_strong_or_same_cluster(int i
, int j
, void *user
)
5949 struct isl_sched_graph
*graph
= user
;
5951 if (graph
->node
[i
].cluster
== graph
->node
[j
].cluster
)
5952 return isl_bool_true
;
5953 return graph_has_validity_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
5956 /* Extract the merged clusters of SCCs in "graph", sort them, and
5957 * store them in c->clusters. Update c->scc_cluster accordingly.
5959 * First keep track of the cluster containing the SCC to which a node
5960 * belongs in the node itself.
5961 * Then extract the clusters into c->clusters, copying the current
5962 * band schedule from the SCCs that belong to the cluster.
5963 * Do this only once per cluster.
5965 * Finally, topologically sort the clusters and update c->scc_cluster
5966 * to match the new scc numbering. While the SCCs were originally
5967 * sorted already, some SCCs that depend on some other SCCs may
5968 * have been merged with SCCs that appear before these other SCCs.
5969 * A reordering may therefore be required.
5971 static isl_stat
extract_clusters(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
5972 struct isl_clustering
*c
)
5976 for (i
= 0; i
< graph
->n
; ++i
)
5977 graph
->node
[i
].cluster
= c
->scc_cluster
[graph
->node
[i
].scc
];
5979 for (i
= 0; i
< graph
->scc
; ++i
) {
5980 if (c
->scc_cluster
[i
] != i
)
5982 if (extract_sub_graph(ctx
, graph
, &node_cluster_exactly
,
5983 &edge_cluster_exactly
, i
, &c
->cluster
[i
]) < 0)
5984 return isl_stat_error
;
5985 c
->cluster
[i
].src_scc
= -1;
5986 c
->cluster
[i
].dst_scc
= -1;
5987 if (copy_partial(graph
, c
, i
) < 0)
5988 return isl_stat_error
;
5991 if (detect_ccs(ctx
, graph
, &node_follows_strong_or_same_cluster
) < 0)
5992 return isl_stat_error
;
5993 for (i
= 0; i
< graph
->n
; ++i
)
5994 c
->scc_cluster
[graph
->node
[i
].scc
] = graph
->node
[i
].cluster
;
5999 /* Compute weights on the proximity edges of "graph" that can
6000 * be used by find_proximity to find the most appropriate
6001 * proximity edge to use to merge two clusters in "c".
6002 * The weights are also used by has_bounded_distances to determine
6003 * whether the merge should be allowed.
6004 * Store the maximum of the computed weights in graph->max_weight.
6006 * The computed weight is a measure for the number of remaining schedule
6007 * dimensions that can still be completely aligned.
6008 * In particular, compute the number of equalities between
6009 * input dimensions and output dimensions in the proximity constraints.
6010 * The directions that are already handled by outer schedule bands
6011 * are projected out prior to determining this number.
6013 * Edges that will never be considered by find_proximity are ignored.
6015 static isl_stat
compute_weights(struct isl_sched_graph
*graph
,
6016 struct isl_clustering
*c
)
6020 graph
->max_weight
= 0;
6022 for (i
= 0; i
< graph
->n_edge
; ++i
) {
6023 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
6024 struct isl_sched_node
*src
= edge
->src
;
6025 struct isl_sched_node
*dst
= edge
->dst
;
6026 isl_basic_map
*hull
;
6029 if (!is_proximity(edge
))
6031 if (bad_cluster(&c
->scc
[edge
->src
->scc
]) ||
6032 bad_cluster(&c
->scc
[edge
->dst
->scc
]))
6034 if (c
->scc_cluster
[edge
->dst
->scc
] ==
6035 c
->scc_cluster
[edge
->src
->scc
])
6038 hull
= isl_map_affine_hull(isl_map_copy(edge
->map
));
6039 hull
= isl_basic_map_transform_dims(hull
, isl_dim_in
, 0,
6040 isl_mat_copy(src
->ctrans
));
6041 hull
= isl_basic_map_transform_dims(hull
, isl_dim_out
, 0,
6042 isl_mat_copy(dst
->ctrans
));
6043 hull
= isl_basic_map_project_out(hull
,
6044 isl_dim_in
, 0, src
->rank
);
6045 hull
= isl_basic_map_project_out(hull
,
6046 isl_dim_out
, 0, dst
->rank
);
6047 hull
= isl_basic_map_remove_divs(hull
);
6048 n_in
= isl_basic_map_dim(hull
, isl_dim_in
);
6049 n_out
= isl_basic_map_dim(hull
, isl_dim_out
);
6050 hull
= isl_basic_map_drop_constraints_not_involving_dims(hull
,
6051 isl_dim_in
, 0, n_in
);
6052 hull
= isl_basic_map_drop_constraints_not_involving_dims(hull
,
6053 isl_dim_out
, 0, n_out
);
6055 return isl_stat_error
;
6056 edge
->weight
= hull
->n_eq
;
6057 isl_basic_map_free(hull
);
6059 if (edge
->weight
> graph
->max_weight
)
6060 graph
->max_weight
= edge
->weight
;
6066 /* Call compute_schedule_finish_band on each of the clusters in "c"
6067 * in their topological order. This order is determined by the scc
6068 * fields of the nodes in "graph".
6069 * Combine the results in a sequence expressing the topological order.
6071 * If there is only one cluster left, then there is no need to introduce
6072 * a sequence node. Also, in this case, the cluster necessarily contains
6073 * the SCC at position 0 in the original graph and is therefore also
6074 * stored in the first cluster of "c".
6076 static __isl_give isl_schedule_node
*finish_bands_clustering(
6077 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
6078 struct isl_clustering
*c
)
6082 isl_union_set_list
*filters
;
6084 if (graph
->scc
== 1)
6085 return compute_schedule_finish_band(node
, &c
->cluster
[0], 0);
6087 ctx
= isl_schedule_node_get_ctx(node
);
6089 filters
= extract_sccs(ctx
, graph
);
6090 node
= isl_schedule_node_insert_sequence(node
, filters
);
6092 for (i
= 0; i
< graph
->scc
; ++i
) {
6093 int j
= c
->scc_cluster
[i
];
6094 node
= isl_schedule_node_child(node
, i
);
6095 node
= isl_schedule_node_child(node
, 0);
6096 node
= compute_schedule_finish_band(node
, &c
->cluster
[j
], 0);
6097 node
= isl_schedule_node_parent(node
);
6098 node
= isl_schedule_node_parent(node
);
6104 /* Compute a schedule for a connected dependence graph by first considering
6105 * each strongly connected component (SCC) in the graph separately and then
6106 * incrementally combining them into clusters.
6107 * Return the updated schedule node.
6109 * Initially, each cluster consists of a single SCC, each with its
6110 * own band schedule. The algorithm then tries to merge pairs
6111 * of clusters along a proximity edge until no more suitable
6112 * proximity edges can be found. During this merging, the schedule
6113 * is maintained in the individual SCCs.
6114 * After the merging is completed, the full resulting clusters
6115 * are extracted and in finish_bands_clustering,
6116 * compute_schedule_finish_band is called on each of them to integrate
6117 * the band into "node" and to continue the computation.
6119 * compute_weights initializes the weights that are used by find_proximity.
6121 static __isl_give isl_schedule_node
*compute_schedule_wcc_clustering(
6122 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
6125 struct isl_clustering c
;
6128 ctx
= isl_schedule_node_get_ctx(node
);
6130 if (clustering_init(ctx
, &c
, graph
) < 0)
6133 if (compute_weights(graph
, &c
) < 0)
6137 i
= find_proximity(graph
, &c
);
6140 if (i
>= graph
->n_edge
)
6142 if (merge_clusters_along_edge(ctx
, graph
, i
, &c
) < 0)
6146 if (extract_clusters(ctx
, graph
, &c
) < 0)
6149 node
= finish_bands_clustering(node
, graph
, &c
);
6151 clustering_free(ctx
, &c
);
6154 clustering_free(ctx
, &c
);
6155 return isl_schedule_node_free(node
);
6158 /* Compute a schedule for a connected dependence graph and return
6159 * the updated schedule node.
6161 * If Feautrier's algorithm is selected, we first recursively try to satisfy
6162 * as many validity dependences as possible. When all validity dependences
6163 * are satisfied we extend the schedule to a full-dimensional schedule.
6165 * Call compute_schedule_wcc_whole or compute_schedule_wcc_clustering
6166 * depending on whether the user has selected the option to try and
6167 * compute a schedule for the entire (weakly connected) component first.
6168 * If there is only a single strongly connected component (SCC), then
6169 * there is no point in trying to combine SCCs
6170 * in compute_schedule_wcc_clustering, so compute_schedule_wcc_whole
6171 * is called instead.
6173 static __isl_give isl_schedule_node
*compute_schedule_wcc(
6174 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
6181 ctx
= isl_schedule_node_get_ctx(node
);
6182 if (detect_sccs(ctx
, graph
) < 0)
6183 return isl_schedule_node_free(node
);
6185 if (compute_maxvar(graph
) < 0)
6186 return isl_schedule_node_free(node
);
6188 if (need_feautrier_step(ctx
, graph
))
6189 return compute_schedule_wcc_feautrier(node
, graph
);
6191 if (graph
->scc
<= 1 || isl_options_get_schedule_whole_component(ctx
))
6192 return compute_schedule_wcc_whole(node
, graph
);
6194 return compute_schedule_wcc_clustering(node
, graph
);
6197 /* Compute a schedule for each group of nodes identified by node->scc
6198 * separately and then combine them in a sequence node (or as set node
6199 * if graph->weak is set) inserted at position "node" of the schedule tree.
6200 * Return the updated schedule node.
6202 * If "wcc" is set then each of the groups belongs to a single
6203 * weakly connected component in the dependence graph so that
6204 * there is no need for compute_sub_schedule to look for weakly
6205 * connected components.
6207 static __isl_give isl_schedule_node
*compute_component_schedule(
6208 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
6213 isl_union_set_list
*filters
;
6217 ctx
= isl_schedule_node_get_ctx(node
);
6219 filters
= extract_sccs(ctx
, graph
);
6221 node
= isl_schedule_node_insert_set(node
, filters
);
6223 node
= isl_schedule_node_insert_sequence(node
, filters
);
6225 for (component
= 0; component
< graph
->scc
; ++component
) {
6226 node
= isl_schedule_node_child(node
, component
);
6227 node
= isl_schedule_node_child(node
, 0);
6228 node
= compute_sub_schedule(node
, ctx
, graph
,
6230 &edge_scc_exactly
, component
, wcc
);
6231 node
= isl_schedule_node_parent(node
);
6232 node
= isl_schedule_node_parent(node
);
6238 /* Compute a schedule for the given dependence graph and insert it at "node".
6239 * Return the updated schedule node.
6241 * We first check if the graph is connected (through validity and conditional
6242 * validity dependences) and, if not, compute a schedule
6243 * for each component separately.
6244 * If the schedule_serialize_sccs option is set, then we check for strongly
6245 * connected components instead and compute a separate schedule for
6246 * each such strongly connected component.
6248 static __isl_give isl_schedule_node
*compute_schedule(isl_schedule_node
*node
,
6249 struct isl_sched_graph
*graph
)
6256 ctx
= isl_schedule_node_get_ctx(node
);
6257 if (isl_options_get_schedule_serialize_sccs(ctx
)) {
6258 if (detect_sccs(ctx
, graph
) < 0)
6259 return isl_schedule_node_free(node
);
6261 if (detect_wccs(ctx
, graph
) < 0)
6262 return isl_schedule_node_free(node
);
6266 return compute_component_schedule(node
, graph
, 1);
6268 return compute_schedule_wcc(node
, graph
);
6271 /* Compute a schedule on sc->domain that respects the given schedule
6274 * In particular, the schedule respects all the validity dependences.
6275 * If the default isl scheduling algorithm is used, it tries to minimize
6276 * the dependence distances over the proximity dependences.
6277 * If Feautrier's scheduling algorithm is used, the proximity dependence
6278 * distances are only minimized during the extension to a full-dimensional
6281 * If there are any condition and conditional validity dependences,
6282 * then the conditional validity dependences may be violated inside
6283 * a tilable band, provided they have no adjacent non-local
6284 * condition dependences.
6286 __isl_give isl_schedule
*isl_schedule_constraints_compute_schedule(
6287 __isl_take isl_schedule_constraints
*sc
)
6289 isl_ctx
*ctx
= isl_schedule_constraints_get_ctx(sc
);
6290 struct isl_sched_graph graph
= { 0 };
6291 isl_schedule
*sched
;
6292 isl_schedule_node
*node
;
6293 isl_union_set
*domain
;
6295 sc
= isl_schedule_constraints_align_params(sc
);
6297 domain
= isl_schedule_constraints_get_domain(sc
);
6298 if (isl_union_set_n_set(domain
) == 0) {
6299 isl_schedule_constraints_free(sc
);
6300 return isl_schedule_from_domain(domain
);
6303 if (graph_init(&graph
, sc
) < 0)
6304 domain
= isl_union_set_free(domain
);
6306 node
= isl_schedule_node_from_domain(domain
);
6307 node
= isl_schedule_node_child(node
, 0);
6309 node
= compute_schedule(node
, &graph
);
6310 sched
= isl_schedule_node_get_schedule(node
);
6311 isl_schedule_node_free(node
);
6313 graph_free(ctx
, &graph
);
6314 isl_schedule_constraints_free(sc
);
6319 /* Compute a schedule for the given union of domains that respects
6320 * all the validity dependences and minimizes
6321 * the dependence distances over the proximity dependences.
6323 * This function is kept for backward compatibility.
6325 __isl_give isl_schedule
*isl_union_set_compute_schedule(
6326 __isl_take isl_union_set
*domain
,
6327 __isl_take isl_union_map
*validity
,
6328 __isl_take isl_union_map
*proximity
)
6330 isl_schedule_constraints
*sc
;
6332 sc
= isl_schedule_constraints_on_domain(domain
);
6333 sc
= isl_schedule_constraints_set_validity(sc
, validity
);
6334 sc
= isl_schedule_constraints_set_proximity(sc
, proximity
);
6336 return isl_schedule_constraints_compute_schedule(sc
);