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 space in which the domain lives
51 * sched is a matrix representation of the schedule being constructed
52 * for this node; if compressed is set, then this schedule is
53 * defined over the compressed domain space
54 * sched_map is an isl_map representation of the same (partial) schedule
55 * sched_map may be NULL; if compressed is set, then this map
56 * is defined over the uncompressed domain space
57 * rank is the number of linearly independent rows in the linear part
59 * the columns of cmap represent a change of basis for the schedule
60 * coefficients; the first rank columns span the linear part of
62 * cinv is the inverse of cmap.
63 * ctrans is the transpose of cmap.
64 * start is the first variable in the LP problem in the sequences that
65 * represents the schedule coefficients of this node
66 * nvar is the dimension of the domain
67 * nparam is the number of parameters or 0 if we are not constructing
68 * a parametric schedule
70 * If compressed is set, then hull represents the constraints
71 * that were used to derive the compression, while compress and
72 * decompress map the original space to the compressed space and
75 * scc is the index of SCC (or WCC) this node belongs to
77 * "cluster" is only used inside extract_clusters and identifies
78 * the cluster of SCCs that the node belongs to.
80 * coincident contains a boolean for each of the rows of the schedule,
81 * indicating whether the corresponding scheduling dimension satisfies
82 * the coincidence constraints in the sense that the corresponding
83 * dependence distances are zero.
85 * If the schedule_treat_coalescing option is set, then
86 * "sizes" contains the sizes of the (compressed) instance set
87 * in each direction. If there is no fixed size in a given direction,
88 * then the corresponding size value is set to infinity.
89 * If the schedule_treat_coalescing option or the schedule_max_coefficient
90 * option is set, then "max" contains the maximal values for
91 * schedule coefficients of the (compressed) variables. If no bound
92 * needs to be imposed on a particular variable, then the corresponding
95 struct isl_sched_node
{
99 isl_multi_aff
*compress
;
100 isl_multi_aff
*decompress
;
116 isl_multi_val
*sizes
;
120 static int node_has_space(const void *entry
, const void *val
)
122 struct isl_sched_node
*node
= (struct isl_sched_node
*)entry
;
123 isl_space
*dim
= (isl_space
*)val
;
125 return isl_space_is_equal(node
->space
, dim
);
128 static int node_scc_exactly(struct isl_sched_node
*node
, int scc
)
130 return node
->scc
== scc
;
133 static int node_scc_at_most(struct isl_sched_node
*node
, int scc
)
135 return node
->scc
<= scc
;
138 static int node_scc_at_least(struct isl_sched_node
*node
, int scc
)
140 return node
->scc
>= scc
;
143 /* An edge in the dependence graph. An edge may be used to
144 * ensure validity of the generated schedule, to minimize the dependence
147 * map is the dependence relation, with i -> j in the map if j depends on i
148 * tagged_condition and tagged_validity contain the union of all tagged
149 * condition or conditional validity dependence relations that
150 * specialize the dependence relation "map"; that is,
151 * if (i -> a) -> (j -> b) is an element of "tagged_condition"
152 * or "tagged_validity", then i -> j is an element of "map".
153 * If these fields are NULL, then they represent the empty relation.
154 * src is the source node
155 * dst is the sink node
157 * types is a bit vector containing the types of this edge.
158 * validity is set if the edge is used to ensure correctness
159 * coincidence is used to enforce zero dependence distances
160 * proximity is set if the edge is used to minimize dependence distances
161 * condition is set if the edge represents a condition
162 * for a conditional validity schedule constraint
163 * local can only be set for condition edges and indicates that
164 * the dependence distance over the edge should be zero
165 * conditional_validity is set if the edge is used to conditionally
168 * For validity edges, start and end mark the sequence of inequality
169 * constraints in the LP problem that encode the validity constraint
170 * corresponding to this edge.
172 * During clustering, an edge may be marked "no_merge" if it should
173 * not be used to merge clusters.
174 * The weight is also only used during clustering and it is
175 * an indication of how many schedule dimensions on either side
176 * of the schedule constraints can be aligned.
177 * If the weight is negative, then this means that this edge was postponed
178 * by has_bounded_distances or any_no_merge. The original weight can
179 * be retrieved by adding 1 + graph->max_weight, with "graph"
180 * the graph containing this edge.
182 struct isl_sched_edge
{
184 isl_union_map
*tagged_condition
;
185 isl_union_map
*tagged_validity
;
187 struct isl_sched_node
*src
;
188 struct isl_sched_node
*dst
;
199 /* Is "edge" marked as being of type "type"?
201 static int is_type(struct isl_sched_edge
*edge
, enum isl_edge_type type
)
203 return ISL_FL_ISSET(edge
->types
, 1 << type
);
206 /* Mark "edge" as being of type "type".
208 static void set_type(struct isl_sched_edge
*edge
, enum isl_edge_type type
)
210 ISL_FL_SET(edge
->types
, 1 << type
);
213 /* No longer mark "edge" as being of type "type"?
215 static void clear_type(struct isl_sched_edge
*edge
, enum isl_edge_type type
)
217 ISL_FL_CLR(edge
->types
, 1 << type
);
220 /* Is "edge" marked as a validity edge?
222 static int is_validity(struct isl_sched_edge
*edge
)
224 return is_type(edge
, isl_edge_validity
);
227 /* Mark "edge" as a validity edge.
229 static void set_validity(struct isl_sched_edge
*edge
)
231 set_type(edge
, isl_edge_validity
);
234 /* Is "edge" marked as a proximity edge?
236 static int is_proximity(struct isl_sched_edge
*edge
)
238 return is_type(edge
, isl_edge_proximity
);
241 /* Is "edge" marked as a local edge?
243 static int is_local(struct isl_sched_edge
*edge
)
245 return is_type(edge
, isl_edge_local
);
248 /* Mark "edge" as a local edge.
250 static void set_local(struct isl_sched_edge
*edge
)
252 set_type(edge
, isl_edge_local
);
255 /* No longer mark "edge" as a local edge.
257 static void clear_local(struct isl_sched_edge
*edge
)
259 clear_type(edge
, isl_edge_local
);
262 /* Is "edge" marked as a coincidence edge?
264 static int is_coincidence(struct isl_sched_edge
*edge
)
266 return is_type(edge
, isl_edge_coincidence
);
269 /* Is "edge" marked as a condition edge?
271 static int is_condition(struct isl_sched_edge
*edge
)
273 return is_type(edge
, isl_edge_condition
);
276 /* Is "edge" marked as a conditional validity edge?
278 static int is_conditional_validity(struct isl_sched_edge
*edge
)
280 return is_type(edge
, isl_edge_conditional_validity
);
283 /* Is "edge" of a type that can appear multiple times between
284 * the same pair of nodes?
286 * Condition edges and conditional validity edges may have tagged
287 * dependence relations, in which case an edge is added for each
290 static int is_multi_edge_type(struct isl_sched_edge
*edge
)
292 return is_condition(edge
) || is_conditional_validity(edge
);
295 /* Internal information about the dependence graph used during
296 * the construction of the schedule.
298 * intra_hmap is a cache, mapping dependence relations to their dual,
299 * for dependences from a node to itself
300 * inter_hmap is a cache, mapping dependence relations to their dual,
301 * for dependences between distinct nodes
302 * if compression is involved then the key for these maps
303 * is the original, uncompressed dependence relation, while
304 * the value is the dual of the compressed dependence relation.
306 * n is the number of nodes
307 * node is the list of nodes
308 * maxvar is the maximal number of variables over all nodes
309 * max_row is the allocated number of rows in the schedule
310 * n_row is the current (maximal) number of linearly independent
311 * rows in the node schedules
312 * n_total_row is the current number of rows in the node schedules
313 * band_start is the starting row in the node schedules of the current band
314 * root is set if this graph is the original dependence graph,
315 * without any splitting
317 * sorted contains a list of node indices sorted according to the
318 * SCC to which a node belongs
320 * n_edge is the number of edges
321 * edge is the list of edges
322 * max_edge contains the maximal number of edges of each type;
323 * in particular, it contains the number of edges in the inital graph.
324 * edge_table contains pointers into the edge array, hashed on the source
325 * and sink spaces; there is one such table for each type;
326 * a given edge may be referenced from more than one table
327 * if the corresponding relation appears in more than one of the
328 * sets of dependences; however, for each type there is only
329 * a single edge between a given pair of source and sink space
330 * in the entire graph
332 * node_table contains pointers into the node array, hashed on the space
334 * region contains a list of variable sequences that should be non-trivial
336 * lp contains the (I)LP problem used to obtain new schedule rows
338 * src_scc and dst_scc are the source and sink SCCs of an edge with
339 * conflicting constraints
341 * scc represents the number of components
342 * weak is set if the components are weakly connected
344 * max_weight is used during clustering and represents the maximal
345 * weight of the relevant proximity edges.
347 struct isl_sched_graph
{
348 isl_map_to_basic_set
*intra_hmap
;
349 isl_map_to_basic_set
*inter_hmap
;
351 struct isl_sched_node
*node
;
364 struct isl_sched_edge
*edge
;
366 int max_edge
[isl_edge_last
+ 1];
367 struct isl_hash_table
*edge_table
[isl_edge_last
+ 1];
369 struct isl_hash_table
*node_table
;
370 struct isl_region
*region
;
383 /* Initialize node_table based on the list of nodes.
385 static int graph_init_table(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
389 graph
->node_table
= isl_hash_table_alloc(ctx
, graph
->n
);
390 if (!graph
->node_table
)
393 for (i
= 0; i
< graph
->n
; ++i
) {
394 struct isl_hash_table_entry
*entry
;
397 hash
= isl_space_get_hash(graph
->node
[i
].space
);
398 entry
= isl_hash_table_find(ctx
, graph
->node_table
, hash
,
400 graph
->node
[i
].space
, 1);
403 entry
->data
= &graph
->node
[i
];
409 /* Return a pointer to the node that lives within the given space,
410 * or NULL if there is no such node.
412 static struct isl_sched_node
*graph_find_node(isl_ctx
*ctx
,
413 struct isl_sched_graph
*graph
, __isl_keep isl_space
*dim
)
415 struct isl_hash_table_entry
*entry
;
418 hash
= isl_space_get_hash(dim
);
419 entry
= isl_hash_table_find(ctx
, graph
->node_table
, hash
,
420 &node_has_space
, dim
, 0);
422 return entry
? entry
->data
: NULL
;
425 static int edge_has_src_and_dst(const void *entry
, const void *val
)
427 const struct isl_sched_edge
*edge
= entry
;
428 const struct isl_sched_edge
*temp
= val
;
430 return edge
->src
== temp
->src
&& edge
->dst
== temp
->dst
;
433 /* Add the given edge to graph->edge_table[type].
435 static isl_stat
graph_edge_table_add(isl_ctx
*ctx
,
436 struct isl_sched_graph
*graph
, enum isl_edge_type type
,
437 struct isl_sched_edge
*edge
)
439 struct isl_hash_table_entry
*entry
;
442 hash
= isl_hash_init();
443 hash
= isl_hash_builtin(hash
, edge
->src
);
444 hash
= isl_hash_builtin(hash
, edge
->dst
);
445 entry
= isl_hash_table_find(ctx
, graph
->edge_table
[type
], hash
,
446 &edge_has_src_and_dst
, edge
, 1);
448 return isl_stat_error
;
454 /* Add "edge" to all relevant edge tables.
455 * That is, for every type of the edge, add it to the corresponding table.
457 static isl_stat
graph_edge_tables_add(isl_ctx
*ctx
,
458 struct isl_sched_graph
*graph
, struct isl_sched_edge
*edge
)
460 enum isl_edge_type t
;
462 for (t
= isl_edge_first
; t
<= isl_edge_last
; ++t
) {
463 if (!is_type(edge
, t
))
465 if (graph_edge_table_add(ctx
, graph
, t
, edge
) < 0)
466 return isl_stat_error
;
472 /* Allocate the edge_tables based on the maximal number of edges of
475 static int graph_init_edge_tables(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
479 for (i
= 0; i
<= isl_edge_last
; ++i
) {
480 graph
->edge_table
[i
] = isl_hash_table_alloc(ctx
,
482 if (!graph
->edge_table
[i
])
489 /* If graph->edge_table[type] contains an edge from the given source
490 * to the given destination, then return the hash table entry of this edge.
491 * Otherwise, return NULL.
493 static struct isl_hash_table_entry
*graph_find_edge_entry(
494 struct isl_sched_graph
*graph
,
495 enum isl_edge_type type
,
496 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
498 isl_ctx
*ctx
= isl_space_get_ctx(src
->space
);
500 struct isl_sched_edge temp
= { .src
= src
, .dst
= dst
};
502 hash
= isl_hash_init();
503 hash
= isl_hash_builtin(hash
, temp
.src
);
504 hash
= isl_hash_builtin(hash
, temp
.dst
);
505 return isl_hash_table_find(ctx
, graph
->edge_table
[type
], hash
,
506 &edge_has_src_and_dst
, &temp
, 0);
510 /* If graph->edge_table[type] contains an edge from the given source
511 * to the given destination, then return this edge.
512 * Otherwise, return NULL.
514 static struct isl_sched_edge
*graph_find_edge(struct isl_sched_graph
*graph
,
515 enum isl_edge_type type
,
516 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
518 struct isl_hash_table_entry
*entry
;
520 entry
= graph_find_edge_entry(graph
, type
, src
, dst
);
527 /* Check whether the dependence graph has an edge of the given type
528 * between the given two nodes.
530 static isl_bool
graph_has_edge(struct isl_sched_graph
*graph
,
531 enum isl_edge_type type
,
532 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
534 struct isl_sched_edge
*edge
;
537 edge
= graph_find_edge(graph
, type
, src
, dst
);
541 empty
= isl_map_plain_is_empty(edge
->map
);
543 return isl_bool_error
;
548 /* Look for any edge with the same src, dst and map fields as "model".
550 * Return the matching edge if one can be found.
551 * Return "model" if no matching edge is found.
552 * Return NULL on error.
554 static struct isl_sched_edge
*graph_find_matching_edge(
555 struct isl_sched_graph
*graph
, struct isl_sched_edge
*model
)
557 enum isl_edge_type i
;
558 struct isl_sched_edge
*edge
;
560 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
563 edge
= graph_find_edge(graph
, i
, model
->src
, model
->dst
);
566 is_equal
= isl_map_plain_is_equal(model
->map
, edge
->map
);
576 /* Remove the given edge from all the edge_tables that refer to it.
578 static void graph_remove_edge(struct isl_sched_graph
*graph
,
579 struct isl_sched_edge
*edge
)
581 isl_ctx
*ctx
= isl_map_get_ctx(edge
->map
);
582 enum isl_edge_type i
;
584 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
585 struct isl_hash_table_entry
*entry
;
587 entry
= graph_find_edge_entry(graph
, i
, edge
->src
, edge
->dst
);
590 if (entry
->data
!= edge
)
592 isl_hash_table_remove(ctx
, graph
->edge_table
[i
], entry
);
596 /* Check whether the dependence graph has any edge
597 * between the given two nodes.
599 static isl_bool
graph_has_any_edge(struct isl_sched_graph
*graph
,
600 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
602 enum isl_edge_type i
;
605 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
606 r
= graph_has_edge(graph
, i
, src
, dst
);
614 /* Check whether the dependence graph has a validity edge
615 * between the given two nodes.
617 * Conditional validity edges are essentially validity edges that
618 * can be ignored if the corresponding condition edges are iteration private.
619 * Here, we are only checking for the presence of validity
620 * edges, so we need to consider the conditional validity edges too.
621 * In particular, this function is used during the detection
622 * of strongly connected components and we cannot ignore
623 * conditional validity edges during this detection.
625 static isl_bool
graph_has_validity_edge(struct isl_sched_graph
*graph
,
626 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
630 r
= graph_has_edge(graph
, isl_edge_validity
, src
, dst
);
634 return graph_has_edge(graph
, isl_edge_conditional_validity
, src
, dst
);
637 static int graph_alloc(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
638 int n_node
, int n_edge
)
643 graph
->n_edge
= n_edge
;
644 graph
->node
= isl_calloc_array(ctx
, struct isl_sched_node
, graph
->n
);
645 graph
->sorted
= isl_calloc_array(ctx
, int, graph
->n
);
646 graph
->region
= isl_alloc_array(ctx
, struct isl_region
, graph
->n
);
647 graph
->edge
= isl_calloc_array(ctx
,
648 struct isl_sched_edge
, graph
->n_edge
);
650 graph
->intra_hmap
= isl_map_to_basic_set_alloc(ctx
, 2 * n_edge
);
651 graph
->inter_hmap
= isl_map_to_basic_set_alloc(ctx
, 2 * n_edge
);
653 if (!graph
->node
|| !graph
->region
|| (graph
->n_edge
&& !graph
->edge
) ||
657 for(i
= 0; i
< graph
->n
; ++i
)
658 graph
->sorted
[i
] = i
;
663 static void graph_free(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
667 isl_map_to_basic_set_free(graph
->intra_hmap
);
668 isl_map_to_basic_set_free(graph
->inter_hmap
);
671 for (i
= 0; i
< graph
->n
; ++i
) {
672 isl_space_free(graph
->node
[i
].space
);
673 isl_set_free(graph
->node
[i
].hull
);
674 isl_multi_aff_free(graph
->node
[i
].compress
);
675 isl_multi_aff_free(graph
->node
[i
].decompress
);
676 isl_mat_free(graph
->node
[i
].sched
);
677 isl_map_free(graph
->node
[i
].sched_map
);
678 isl_mat_free(graph
->node
[i
].cmap
);
679 isl_mat_free(graph
->node
[i
].cinv
);
680 isl_mat_free(graph
->node
[i
].ctrans
);
682 free(graph
->node
[i
].coincident
);
683 isl_multi_val_free(graph
->node
[i
].sizes
);
684 isl_vec_free(graph
->node
[i
].max
);
689 for (i
= 0; i
< graph
->n_edge
; ++i
) {
690 isl_map_free(graph
->edge
[i
].map
);
691 isl_union_map_free(graph
->edge
[i
].tagged_condition
);
692 isl_union_map_free(graph
->edge
[i
].tagged_validity
);
696 for (i
= 0; i
<= isl_edge_last
; ++i
)
697 isl_hash_table_free(ctx
, graph
->edge_table
[i
]);
698 isl_hash_table_free(ctx
, graph
->node_table
);
699 isl_basic_set_free(graph
->lp
);
702 /* For each "set" on which this function is called, increment
703 * graph->n by one and update graph->maxvar.
705 static isl_stat
init_n_maxvar(__isl_take isl_set
*set
, void *user
)
707 struct isl_sched_graph
*graph
= user
;
708 int nvar
= isl_set_dim(set
, isl_dim_set
);
711 if (nvar
> graph
->maxvar
)
712 graph
->maxvar
= nvar
;
719 /* Compute the number of rows that should be allocated for the schedule.
720 * In particular, we need one row for each variable or one row
721 * for each basic map in the dependences.
722 * Note that it is practically impossible to exhaust both
723 * the number of dependences and the number of variables.
725 static isl_stat
compute_max_row(struct isl_sched_graph
*graph
,
726 __isl_keep isl_schedule_constraints
*sc
)
730 isl_union_set
*domain
;
734 domain
= isl_schedule_constraints_get_domain(sc
);
735 r
= isl_union_set_foreach_set(domain
, &init_n_maxvar
, graph
);
736 isl_union_set_free(domain
);
738 return isl_stat_error
;
739 n_edge
= isl_schedule_constraints_n_basic_map(sc
);
741 return isl_stat_error
;
742 graph
->max_row
= n_edge
+ graph
->maxvar
;
747 /* Does "bset" have any defining equalities for its set variables?
749 static int has_any_defining_equality(__isl_keep isl_basic_set
*bset
)
756 n
= isl_basic_set_dim(bset
, isl_dim_set
);
757 for (i
= 0; i
< n
; ++i
) {
760 has
= isl_basic_set_has_defining_equality(bset
, isl_dim_set
, i
,
769 /* Set the entries of node->max to the value of the schedule_max_coefficient
772 static isl_stat
set_max_coefficient(isl_ctx
*ctx
, struct isl_sched_node
*node
)
776 max
= isl_options_get_schedule_max_coefficient(ctx
);
780 node
->max
= isl_vec_alloc(ctx
, node
->nvar
);
781 node
->max
= isl_vec_set_si(node
->max
, max
);
783 return isl_stat_error
;
788 /* Set the entries of node->max to the minimum of the schedule_max_coefficient
789 * option (if set) and half of the minimum of the sizes in the other
790 * dimensions. If the minimum of the sizes is one, half of the size
791 * is zero and this value is reset to one.
792 * If the global minimum is unbounded (i.e., if both
793 * the schedule_max_coefficient is not set and the sizes in the other
794 * dimensions are unbounded), then store a negative value.
795 * If the schedule coefficient is close to the size of the instance set
796 * in another dimension, then the schedule may represent a loop
797 * coalescing transformation (especially if the coefficient
798 * in that other dimension is one). Forcing the coefficient to be
799 * smaller than or equal to half the minimal size should avoid this
802 static isl_stat
compute_max_coefficient(isl_ctx
*ctx
,
803 struct isl_sched_node
*node
)
809 max
= isl_options_get_schedule_max_coefficient(ctx
);
810 v
= isl_vec_alloc(ctx
, node
->nvar
);
812 return isl_stat_error
;
814 for (i
= 0; i
< node
->nvar
; ++i
) {
815 isl_int_set_si(v
->el
[i
], max
);
816 isl_int_mul_si(v
->el
[i
], v
->el
[i
], 2);
819 for (i
= 0; i
< node
->nvar
; ++i
) {
822 size
= isl_multi_val_get_val(node
->sizes
, i
);
825 if (!isl_val_is_int(size
)) {
829 for (j
= 0; j
< node
->nvar
; ++j
) {
832 if (isl_int_is_neg(v
->el
[j
]) ||
833 isl_int_gt(v
->el
[j
], size
->n
))
834 isl_int_set(v
->el
[j
], size
->n
);
839 for (i
= 0; i
< node
->nvar
; ++i
) {
840 isl_int_fdiv_q_ui(v
->el
[i
], v
->el
[i
], 2);
841 if (isl_int_is_zero(v
->el
[i
]))
842 isl_int_set_si(v
->el
[i
], 1);
849 return isl_stat_error
;
852 /* Compute and return the size of "set" in dimension "dim".
853 * The size is taken to be the difference in values for that variable
854 * for fixed values of the other variables.
855 * In particular, the variable is first isolated from the other variables
856 * in the range of a map
858 * [i_0, ..., i_dim-1, i_dim+1, ...] -> [i_dim]
860 * and then duplicated
862 * [i_0, ..., i_dim-1, i_dim+1, ...] -> [[i_dim] -> [i_dim']]
864 * The shared variables are then projected out and the maximal value
865 * of i_dim' - i_dim is computed.
867 static __isl_give isl_val
*compute_size(__isl_take isl_set
*set
, int dim
)
874 map
= isl_set_project_onto_map(set
, isl_dim_set
, dim
, 1);
875 map
= isl_map_project_out(map
, isl_dim_in
, dim
, 1);
876 map
= isl_map_range_product(map
, isl_map_copy(map
));
877 map
= isl_set_unwrap(isl_map_range(map
));
878 set
= isl_map_deltas(map
);
879 ls
= isl_local_space_from_space(isl_set_get_space(set
));
880 obj
= isl_aff_var_on_domain(ls
, isl_dim_set
, 0);
881 v
= isl_set_max_val(set
, obj
);
888 /* Compute the size of the instance set "set" of "node", after compression,
889 * as well as bounds on the corresponding coefficients, if needed.
891 * The sizes are needed when the schedule_treat_coalescing option is set.
892 * The bounds are needed when the schedule_treat_coalescing option or
893 * the schedule_max_coefficient option is set.
895 * If the schedule_treat_coalescing option is not set, then at most
896 * the bounds need to be set and this is done in set_max_coefficient.
897 * Otherwise, compress the domain if needed, compute the size
898 * in each direction and store the results in node->size.
899 * Finally, set the bounds on the coefficients based on the sizes
900 * and the schedule_max_coefficient option in compute_max_coefficient.
902 static isl_stat
compute_sizes_and_max(isl_ctx
*ctx
, struct isl_sched_node
*node
,
903 __isl_take isl_set
*set
)
908 if (!isl_options_get_schedule_treat_coalescing(ctx
)) {
910 return set_max_coefficient(ctx
, node
);
913 if (node
->compressed
)
914 set
= isl_set_preimage_multi_aff(set
,
915 isl_multi_aff_copy(node
->decompress
));
916 mv
= isl_multi_val_zero(isl_set_get_space(set
));
917 n
= isl_set_dim(set
, isl_dim_set
);
918 for (j
= 0; j
< n
; ++j
) {
921 v
= compute_size(isl_set_copy(set
), j
);
922 mv
= isl_multi_val_set_val(mv
, j
, v
);
927 return isl_stat_error
;
928 return compute_max_coefficient(ctx
, node
);
931 /* Add a new node to the graph representing the given instance set.
932 * "nvar" is the (possibly compressed) number of variables and
933 * may be smaller than then number of set variables in "set"
934 * if "compressed" is set.
935 * If "compressed" is set, then "hull" represents the constraints
936 * that were used to derive the compression, while "compress" and
937 * "decompress" map the original space to the compressed space and
939 * If "compressed" is not set, then "hull", "compress" and "decompress"
942 * Compute the size of the instance set and bounds on the coefficients,
945 static isl_stat
add_node(struct isl_sched_graph
*graph
,
946 __isl_take isl_set
*set
, int nvar
, int compressed
,
947 __isl_take isl_set
*hull
, __isl_take isl_multi_aff
*compress
,
948 __isl_take isl_multi_aff
*decompress
)
955 struct isl_sched_node
*node
;
958 return isl_stat_error
;
960 ctx
= isl_set_get_ctx(set
);
961 nparam
= isl_set_dim(set
, isl_dim_param
);
962 if (!ctx
->opt
->schedule_parametric
)
964 sched
= isl_mat_alloc(ctx
, 0, 1 + nparam
+ nvar
);
965 node
= &graph
->node
[graph
->n
];
967 space
= isl_set_get_space(set
);
970 node
->nparam
= nparam
;
972 node
->sched_map
= NULL
;
973 coincident
= isl_calloc_array(ctx
, int, graph
->max_row
);
974 node
->coincident
= coincident
;
975 node
->compressed
= compressed
;
977 node
->compress
= compress
;
978 node
->decompress
= decompress
;
979 if (compute_sizes_and_max(ctx
, node
, set
) < 0)
980 return isl_stat_error
;
982 if (!space
|| !sched
|| (graph
->max_row
&& !coincident
))
983 return isl_stat_error
;
984 if (compressed
&& (!hull
|| !compress
|| !decompress
))
985 return isl_stat_error
;
990 /* Add a new node to the graph representing the given set.
992 * If any of the set variables is defined by an equality, then
993 * we perform variable compression such that we can perform
994 * the scheduling on the compressed domain.
996 static isl_stat
extract_node(__isl_take isl_set
*set
, void *user
)
1000 isl_basic_set
*hull
;
1003 isl_multi_aff
*compress
, *decompress
;
1004 struct isl_sched_graph
*graph
= user
;
1006 hull
= isl_set_affine_hull(isl_set_copy(set
));
1007 hull
= isl_basic_set_remove_divs(hull
);
1008 nvar
= isl_set_dim(set
, isl_dim_set
);
1009 has_equality
= has_any_defining_equality(hull
);
1011 if (has_equality
< 0)
1013 if (!has_equality
) {
1014 isl_basic_set_free(hull
);
1015 return add_node(graph
, set
, nvar
, 0, NULL
, NULL
, NULL
);
1018 morph
= isl_basic_set_variable_compression(hull
, isl_dim_set
);
1019 nvar
= isl_morph_ran_dim(morph
, isl_dim_set
);
1020 compress
= isl_morph_get_var_multi_aff(morph
);
1021 morph
= isl_morph_inverse(morph
);
1022 decompress
= isl_morph_get_var_multi_aff(morph
);
1023 isl_morph_free(morph
);
1025 hull_set
= isl_set_from_basic_set(hull
);
1026 return add_node(graph
, set
, nvar
, 1, hull_set
, compress
, decompress
);
1028 isl_basic_set_free(hull
);
1030 return isl_stat_error
;
1033 struct isl_extract_edge_data
{
1034 enum isl_edge_type type
;
1035 struct isl_sched_graph
*graph
;
1038 /* Merge edge2 into edge1, freeing the contents of edge2.
1039 * Return 0 on success and -1 on failure.
1041 * edge1 and edge2 are assumed to have the same value for the map field.
1043 static int merge_edge(struct isl_sched_edge
*edge1
,
1044 struct isl_sched_edge
*edge2
)
1046 edge1
->types
|= edge2
->types
;
1047 isl_map_free(edge2
->map
);
1049 if (is_condition(edge2
)) {
1050 if (!edge1
->tagged_condition
)
1051 edge1
->tagged_condition
= edge2
->tagged_condition
;
1053 edge1
->tagged_condition
=
1054 isl_union_map_union(edge1
->tagged_condition
,
1055 edge2
->tagged_condition
);
1058 if (is_conditional_validity(edge2
)) {
1059 if (!edge1
->tagged_validity
)
1060 edge1
->tagged_validity
= edge2
->tagged_validity
;
1062 edge1
->tagged_validity
=
1063 isl_union_map_union(edge1
->tagged_validity
,
1064 edge2
->tagged_validity
);
1067 if (is_condition(edge2
) && !edge1
->tagged_condition
)
1069 if (is_conditional_validity(edge2
) && !edge1
->tagged_validity
)
1075 /* Insert dummy tags in domain and range of "map".
1077 * In particular, if "map" is of the form
1083 * [A -> dummy_tag] -> [B -> dummy_tag]
1085 * where the dummy_tags are identical and equal to any dummy tags
1086 * introduced by any other call to this function.
1088 static __isl_give isl_map
*insert_dummy_tags(__isl_take isl_map
*map
)
1094 isl_set
*domain
, *range
;
1096 ctx
= isl_map_get_ctx(map
);
1098 id
= isl_id_alloc(ctx
, NULL
, &dummy
);
1099 space
= isl_space_params(isl_map_get_space(map
));
1100 space
= isl_space_set_from_params(space
);
1101 space
= isl_space_set_tuple_id(space
, isl_dim_set
, id
);
1102 space
= isl_space_map_from_set(space
);
1104 domain
= isl_map_wrap(map
);
1105 range
= isl_map_wrap(isl_map_universe(space
));
1106 map
= isl_map_from_domain_and_range(domain
, range
);
1107 map
= isl_map_zip(map
);
1112 /* Given that at least one of "src" or "dst" is compressed, return
1113 * a map between the spaces of these nodes restricted to the affine
1114 * hull that was used in the compression.
1116 static __isl_give isl_map
*extract_hull(struct isl_sched_node
*src
,
1117 struct isl_sched_node
*dst
)
1121 if (src
->compressed
)
1122 dom
= isl_set_copy(src
->hull
);
1124 dom
= isl_set_universe(isl_space_copy(src
->space
));
1125 if (dst
->compressed
)
1126 ran
= isl_set_copy(dst
->hull
);
1128 ran
= isl_set_universe(isl_space_copy(dst
->space
));
1130 return isl_map_from_domain_and_range(dom
, ran
);
1133 /* Intersect the domains of the nested relations in domain and range
1134 * of "tagged" with "map".
1136 static __isl_give isl_map
*map_intersect_domains(__isl_take isl_map
*tagged
,
1137 __isl_keep isl_map
*map
)
1141 tagged
= isl_map_zip(tagged
);
1142 set
= isl_map_wrap(isl_map_copy(map
));
1143 tagged
= isl_map_intersect_domain(tagged
, set
);
1144 tagged
= isl_map_zip(tagged
);
1148 /* Return a pointer to the node that lives in the domain space of "map"
1149 * or NULL if there is no such node.
1151 static struct isl_sched_node
*find_domain_node(isl_ctx
*ctx
,
1152 struct isl_sched_graph
*graph
, __isl_keep isl_map
*map
)
1154 struct isl_sched_node
*node
;
1157 space
= isl_space_domain(isl_map_get_space(map
));
1158 node
= graph_find_node(ctx
, graph
, space
);
1159 isl_space_free(space
);
1164 /* Return a pointer to the node that lives in the range space of "map"
1165 * or NULL if there is no such node.
1167 static struct isl_sched_node
*find_range_node(isl_ctx
*ctx
,
1168 struct isl_sched_graph
*graph
, __isl_keep isl_map
*map
)
1170 struct isl_sched_node
*node
;
1173 space
= isl_space_range(isl_map_get_space(map
));
1174 node
= graph_find_node(ctx
, graph
, space
);
1175 isl_space_free(space
);
1180 /* Refrain from adding a new edge based on "map".
1181 * Instead, just free the map.
1182 * "tagged" is either a copy of "map" with additional tags or NULL.
1184 static isl_stat
skip_edge(__isl_take isl_map
*map
, __isl_take isl_map
*tagged
)
1187 isl_map_free(tagged
);
1192 /* Add a new edge to the graph based on the given map
1193 * and add it to data->graph->edge_table[data->type].
1194 * If a dependence relation of a given type happens to be identical
1195 * to one of the dependence relations of a type that was added before,
1196 * then we don't create a new edge, but instead mark the original edge
1197 * as also representing a dependence of the current type.
1199 * Edges of type isl_edge_condition or isl_edge_conditional_validity
1200 * may be specified as "tagged" dependence relations. That is, "map"
1201 * may contain elements (i -> a) -> (j -> b), where i -> j denotes
1202 * the dependence on iterations and a and b are tags.
1203 * edge->map is set to the relation containing the elements i -> j,
1204 * while edge->tagged_condition and edge->tagged_validity contain
1205 * the union of all the "map" relations
1206 * for which extract_edge is called that result in the same edge->map.
1208 * If the source or the destination node is compressed, then
1209 * intersect both "map" and "tagged" with the constraints that
1210 * were used to construct the compression.
1211 * This ensures that there are no schedule constraints defined
1212 * outside of these domains, while the scheduler no longer has
1213 * any control over those outside parts.
1215 static isl_stat
extract_edge(__isl_take isl_map
*map
, void *user
)
1217 isl_ctx
*ctx
= isl_map_get_ctx(map
);
1218 struct isl_extract_edge_data
*data
= user
;
1219 struct isl_sched_graph
*graph
= data
->graph
;
1220 struct isl_sched_node
*src
, *dst
;
1221 struct isl_sched_edge
*edge
;
1222 isl_map
*tagged
= NULL
;
1224 if (data
->type
== isl_edge_condition
||
1225 data
->type
== isl_edge_conditional_validity
) {
1226 if (isl_map_can_zip(map
)) {
1227 tagged
= isl_map_copy(map
);
1228 map
= isl_set_unwrap(isl_map_domain(isl_map_zip(map
)));
1230 tagged
= insert_dummy_tags(isl_map_copy(map
));
1234 src
= find_domain_node(ctx
, graph
, map
);
1235 dst
= find_range_node(ctx
, graph
, map
);
1238 return skip_edge(map
, tagged
);
1240 if (src
->compressed
|| dst
->compressed
) {
1242 hull
= extract_hull(src
, dst
);
1244 tagged
= map_intersect_domains(tagged
, hull
);
1245 map
= isl_map_intersect(map
, hull
);
1248 graph
->edge
[graph
->n_edge
].src
= src
;
1249 graph
->edge
[graph
->n_edge
].dst
= dst
;
1250 graph
->edge
[graph
->n_edge
].map
= map
;
1251 graph
->edge
[graph
->n_edge
].types
= 0;
1252 graph
->edge
[graph
->n_edge
].tagged_condition
= NULL
;
1253 graph
->edge
[graph
->n_edge
].tagged_validity
= NULL
;
1254 set_type(&graph
->edge
[graph
->n_edge
], data
->type
);
1255 if (data
->type
== isl_edge_condition
)
1256 graph
->edge
[graph
->n_edge
].tagged_condition
=
1257 isl_union_map_from_map(tagged
);
1258 if (data
->type
== isl_edge_conditional_validity
)
1259 graph
->edge
[graph
->n_edge
].tagged_validity
=
1260 isl_union_map_from_map(tagged
);
1262 edge
= graph_find_matching_edge(graph
, &graph
->edge
[graph
->n_edge
]);
1265 return isl_stat_error
;
1267 if (edge
== &graph
->edge
[graph
->n_edge
])
1268 return graph_edge_table_add(ctx
, graph
, data
->type
,
1269 &graph
->edge
[graph
->n_edge
++]);
1271 if (merge_edge(edge
, &graph
->edge
[graph
->n_edge
]) < 0)
1274 return graph_edge_table_add(ctx
, graph
, data
->type
, edge
);
1277 /* Initialize the schedule graph "graph" from the schedule constraints "sc".
1279 * The context is included in the domain before the nodes of
1280 * the graphs are extracted in order to be able to exploit
1281 * any possible additional equalities.
1282 * Note that this intersection is only performed locally here.
1284 static isl_stat
graph_init(struct isl_sched_graph
*graph
,
1285 __isl_keep isl_schedule_constraints
*sc
)
1288 isl_union_set
*domain
;
1290 struct isl_extract_edge_data data
;
1291 enum isl_edge_type i
;
1295 return isl_stat_error
;
1297 ctx
= isl_schedule_constraints_get_ctx(sc
);
1299 domain
= isl_schedule_constraints_get_domain(sc
);
1300 graph
->n
= isl_union_set_n_set(domain
);
1301 isl_union_set_free(domain
);
1303 if (graph_alloc(ctx
, graph
, graph
->n
,
1304 isl_schedule_constraints_n_map(sc
)) < 0)
1305 return isl_stat_error
;
1307 if (compute_max_row(graph
, sc
) < 0)
1308 return isl_stat_error
;
1311 domain
= isl_schedule_constraints_get_domain(sc
);
1312 domain
= isl_union_set_intersect_params(domain
,
1313 isl_schedule_constraints_get_context(sc
));
1314 r
= isl_union_set_foreach_set(domain
, &extract_node
, graph
);
1315 isl_union_set_free(domain
);
1317 return isl_stat_error
;
1318 if (graph_init_table(ctx
, graph
) < 0)
1319 return isl_stat_error
;
1320 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
1321 c
= isl_schedule_constraints_get(sc
, i
);
1322 graph
->max_edge
[i
] = isl_union_map_n_map(c
);
1323 isl_union_map_free(c
);
1325 return isl_stat_error
;
1327 if (graph_init_edge_tables(ctx
, graph
) < 0)
1328 return isl_stat_error
;
1331 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
1335 c
= isl_schedule_constraints_get(sc
, i
);
1336 r
= isl_union_map_foreach_map(c
, &extract_edge
, &data
);
1337 isl_union_map_free(c
);
1339 return isl_stat_error
;
1345 /* Check whether there is any dependence from node[j] to node[i]
1346 * or from node[i] to node[j].
1348 static isl_bool
node_follows_weak(int i
, int j
, void *user
)
1351 struct isl_sched_graph
*graph
= user
;
1353 f
= graph_has_any_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
1356 return graph_has_any_edge(graph
, &graph
->node
[i
], &graph
->node
[j
]);
1359 /* Check whether there is a (conditional) validity dependence from node[j]
1360 * to node[i], forcing node[i] to follow node[j].
1362 static isl_bool
node_follows_strong(int i
, int j
, void *user
)
1364 struct isl_sched_graph
*graph
= user
;
1366 return graph_has_validity_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
1369 /* Use Tarjan's algorithm for computing the strongly connected components
1370 * in the dependence graph only considering those edges defined by "follows".
1372 static int detect_ccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
1373 isl_bool (*follows
)(int i
, int j
, void *user
))
1376 struct isl_tarjan_graph
*g
= NULL
;
1378 g
= isl_tarjan_graph_init(ctx
, graph
->n
, follows
, graph
);
1386 while (g
->order
[i
] != -1) {
1387 graph
->node
[g
->order
[i
]].scc
= graph
->scc
;
1395 isl_tarjan_graph_free(g
);
1400 /* Apply Tarjan's algorithm to detect the strongly connected components
1401 * in the dependence graph.
1402 * Only consider the (conditional) validity dependences and clear "weak".
1404 static int detect_sccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
1407 return detect_ccs(ctx
, graph
, &node_follows_strong
);
1410 /* Apply Tarjan's algorithm to detect the (weakly) connected components
1411 * in the dependence graph.
1412 * Consider all dependences and set "weak".
1414 static int detect_wccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
1417 return detect_ccs(ctx
, graph
, &node_follows_weak
);
1420 static int cmp_scc(const void *a
, const void *b
, void *data
)
1422 struct isl_sched_graph
*graph
= data
;
1426 return graph
->node
[*i1
].scc
- graph
->node
[*i2
].scc
;
1429 /* Sort the elements of graph->sorted according to the corresponding SCCs.
1431 static int sort_sccs(struct isl_sched_graph
*graph
)
1433 return isl_sort(graph
->sorted
, graph
->n
, sizeof(int), &cmp_scc
, graph
);
1436 /* Given a dependence relation R from "node" to itself,
1437 * construct the set of coefficients of valid constraints for elements
1438 * in that dependence relation.
1439 * In particular, the result contains tuples of coefficients
1440 * c_0, c_n, c_x such that
1442 * c_0 + c_n n + c_x y - c_x x >= 0 for each (x,y) in R
1446 * c_0 + c_n n + c_x d >= 0 for each d in delta R = { y - x | (x,y) in R }
1448 * We choose here to compute the dual of delta R.
1449 * Alternatively, we could have computed the dual of R, resulting
1450 * in a set of tuples c_0, c_n, c_x, c_y, and then
1451 * plugged in (c_0, c_n, c_x, -c_x).
1453 * If "node" has been compressed, then the dependence relation
1454 * is also compressed before the set of coefficients is computed.
1456 static __isl_give isl_basic_set
*intra_coefficients(
1457 struct isl_sched_graph
*graph
, struct isl_sched_node
*node
,
1458 __isl_take isl_map
*map
)
1462 isl_basic_set
*coef
;
1463 isl_maybe_isl_basic_set m
;
1465 m
= isl_map_to_basic_set_try_get(graph
->intra_hmap
, map
);
1466 if (m
.valid
< 0 || m
.valid
) {
1471 key
= isl_map_copy(map
);
1472 if (node
->compressed
) {
1473 map
= isl_map_preimage_domain_multi_aff(map
,
1474 isl_multi_aff_copy(node
->decompress
));
1475 map
= isl_map_preimage_range_multi_aff(map
,
1476 isl_multi_aff_copy(node
->decompress
));
1478 delta
= isl_set_remove_divs(isl_map_deltas(map
));
1479 coef
= isl_set_coefficients(delta
);
1480 graph
->intra_hmap
= isl_map_to_basic_set_set(graph
->intra_hmap
, key
,
1481 isl_basic_set_copy(coef
));
1486 /* Given a dependence relation R, construct the set of coefficients
1487 * of valid constraints for elements in that dependence relation.
1488 * In particular, the result contains tuples of coefficients
1489 * c_0, c_n, c_x, c_y such that
1491 * c_0 + c_n n + c_x x + c_y y >= 0 for each (x,y) in R
1493 * If the source or destination nodes of "edge" have been compressed,
1494 * then the dependence relation is also compressed before
1495 * the set of coefficients is computed.
1497 static __isl_give isl_basic_set
*inter_coefficients(
1498 struct isl_sched_graph
*graph
, struct isl_sched_edge
*edge
,
1499 __isl_take isl_map
*map
)
1503 isl_basic_set
*coef
;
1504 isl_maybe_isl_basic_set m
;
1506 m
= isl_map_to_basic_set_try_get(graph
->inter_hmap
, map
);
1507 if (m
.valid
< 0 || m
.valid
) {
1512 key
= isl_map_copy(map
);
1513 if (edge
->src
->compressed
)
1514 map
= isl_map_preimage_domain_multi_aff(map
,
1515 isl_multi_aff_copy(edge
->src
->decompress
));
1516 if (edge
->dst
->compressed
)
1517 map
= isl_map_preimage_range_multi_aff(map
,
1518 isl_multi_aff_copy(edge
->dst
->decompress
));
1519 set
= isl_map_wrap(isl_map_remove_divs(map
));
1520 coef
= isl_set_coefficients(set
);
1521 graph
->inter_hmap
= isl_map_to_basic_set_set(graph
->inter_hmap
, key
,
1522 isl_basic_set_copy(coef
));
1527 /* Return the position of the coefficients of the variables in
1528 * the coefficients constraints "coef".
1530 * The space of "coef" is of the form
1532 * { coefficients[[cst, params] -> S] }
1534 * Return the position of S.
1536 static int coef_var_offset(__isl_keep isl_basic_set
*coef
)
1541 space
= isl_space_unwrap(isl_basic_set_get_space(coef
));
1542 offset
= isl_space_dim(space
, isl_dim_in
);
1543 isl_space_free(space
);
1548 /* Return the offset of the coefficients of the variables of "node"
1551 * Within each node, the coefficients have the following order:
1553 * - c_i_n (if parametric)
1554 * - positive and negative parts of c_i_x
1556 static int node_var_coef_offset(struct isl_sched_node
*node
)
1558 return node
->start
+ 1 + node
->nparam
;
1561 /* Construct an isl_dim_map for mapping constraints on coefficients
1562 * for "node" to the corresponding positions in graph->lp.
1563 * "offset" is the offset of the coefficients for the variables
1564 * in the input constraints.
1565 * "s" is the sign of the mapping.
1567 * The input constraints are given in terms of the coefficients (c_0, c_n, c_x).
1568 * The mapping produced by this function essentially plugs in
1569 * (0, 0, c_i_x^+ - c_i_x^-) if s = 1 and
1570 * (0, 0, -c_i_x^+ + c_i_x^-) if s = -1.
1571 * In graph->lp, the c_i_x^- appear before their c_i_x^+ counterpart.
1573 * The caller can extend the mapping to also map the other coefficients
1574 * (and therefore not plug in 0).
1576 static __isl_give isl_dim_map
*intra_dim_map(isl_ctx
*ctx
,
1577 struct isl_sched_graph
*graph
, struct isl_sched_node
*node
,
1582 isl_dim_map
*dim_map
;
1584 if (!node
|| !graph
->lp
)
1587 total
= isl_basic_set_total_dim(graph
->lp
);
1588 pos
= node_var_coef_offset(node
);
1589 dim_map
= isl_dim_map_alloc(ctx
, total
);
1590 isl_dim_map_range(dim_map
, pos
, 2, offset
, 1, node
->nvar
, -s
);
1591 isl_dim_map_range(dim_map
, pos
+ 1, 2, offset
, 1, node
->nvar
, s
);
1596 /* Construct an isl_dim_map for mapping constraints on coefficients
1597 * for "src" (node i) and "dst" (node j) to the corresponding positions
1599 * "offset" is the offset of the coefficients for the variables of "src"
1600 * in the input constraints.
1601 * "s" is the sign of the mapping.
1603 * The input constraints are given in terms of the coefficients
1604 * (c_0, c_n, c_x, c_y).
1605 * The mapping produced by this function essentially plugs in
1606 * (c_j_0 - c_i_0, c_j_n - c_i_n,
1607 * c_j_x^+ - c_j_x^-, -(c_i_x^+ - c_i_x^-)) if s = 1 and
1608 * (-c_j_0 + c_i_0, -c_j_n + c_i_n,
1609 * - (c_j_x^+ - c_j_x^-), c_i_x^+ - c_i_x^-) if s = -1.
1610 * In graph->lp, the c_*^- appear before their c_*^+ counterpart.
1612 * The caller can further extend the mapping.
1614 static __isl_give isl_dim_map
*inter_dim_map(isl_ctx
*ctx
,
1615 struct isl_sched_graph
*graph
, struct isl_sched_node
*src
,
1616 struct isl_sched_node
*dst
, int offset
, int s
)
1620 isl_dim_map
*dim_map
;
1622 if (!src
|| !dst
|| !graph
->lp
)
1625 total
= isl_basic_set_total_dim(graph
->lp
);
1626 dim_map
= isl_dim_map_alloc(ctx
, total
);
1628 isl_dim_map_range(dim_map
, dst
->start
, 0, 0, 0, 1, s
);
1629 isl_dim_map_range(dim_map
, dst
->start
+ 1, 1, 1, 1, dst
->nparam
, s
);
1630 pos
= node_var_coef_offset(dst
);
1631 isl_dim_map_range(dim_map
, pos
, 2, offset
+ src
->nvar
, 1,
1633 isl_dim_map_range(dim_map
, pos
+ 1, 2, offset
+ src
->nvar
, 1,
1636 isl_dim_map_range(dim_map
, src
->start
, 0, 0, 0, 1, -s
);
1637 isl_dim_map_range(dim_map
, src
->start
+ 1, 1, 1, 1, src
->nparam
, -s
);
1638 pos
= node_var_coef_offset(src
);
1639 isl_dim_map_range(dim_map
, pos
, 2, offset
, 1, src
->nvar
, s
);
1640 isl_dim_map_range(dim_map
, pos
+ 1, 2, offset
, 1, src
->nvar
, -s
);
1645 /* Add constraints to graph->lp that force validity for the given
1646 * dependence from a node i to itself.
1647 * That is, add constraints that enforce
1649 * (c_i_0 + c_i_n n + c_i_x y) - (c_i_0 + c_i_n n + c_i_x x)
1650 * = c_i_x (y - x) >= 0
1652 * for each (x,y) in R.
1653 * We obtain general constraints on coefficients (c_0, c_n, c_x)
1654 * of valid constraints for (y - x) and then plug in (0, 0, c_i_x^+ - c_i_x^-),
1655 * where c_i_x = c_i_x^+ - c_i_x^-, with c_i_x^+ and c_i_x^- non-negative.
1656 * In graph->lp, the c_i_x^- appear before their c_i_x^+ counterpart.
1658 * Actually, we do not construct constraints for the c_i_x themselves,
1659 * but for the coefficients of c_i_x written as a linear combination
1660 * of the columns in node->cmap.
1662 static isl_stat
add_intra_validity_constraints(struct isl_sched_graph
*graph
,
1663 struct isl_sched_edge
*edge
)
1666 isl_map
*map
= isl_map_copy(edge
->map
);
1667 isl_ctx
*ctx
= isl_map_get_ctx(map
);
1668 isl_dim_map
*dim_map
;
1669 isl_basic_set
*coef
;
1670 struct isl_sched_node
*node
= edge
->src
;
1672 coef
= intra_coefficients(graph
, node
, map
);
1674 offset
= coef_var_offset(coef
);
1676 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
1677 offset
, isl_mat_copy(node
->cmap
));
1679 return isl_stat_error
;
1681 dim_map
= intra_dim_map(ctx
, graph
, node
, offset
, 1);
1682 graph
->lp
= isl_basic_set_extend_constraints(graph
->lp
,
1683 coef
->n_eq
, coef
->n_ineq
);
1684 graph
->lp
= isl_basic_set_add_constraints_dim_map(graph
->lp
,
1690 /* Add constraints to graph->lp that force validity for the given
1691 * dependence from node i to node j.
1692 * That is, add constraints that enforce
1694 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) >= 0
1696 * for each (x,y) in R.
1697 * We obtain general constraints on coefficients (c_0, c_n, c_x, c_y)
1698 * of valid constraints for R and then plug in
1699 * (c_j_0 - c_i_0, c_j_n - c_i_n, c_j_x^+ - c_j_x^- - (c_i_x^+ - c_i_x^-)),
1700 * where c_* = c_*^+ - c_*^-, with c_*^+ and c_*^- non-negative.
1701 * In graph->lp, the c_*^- appear before their c_*^+ counterpart.
1703 * Actually, we do not construct constraints for the c_*_x themselves,
1704 * but for the coefficients of c_*_x written as a linear combination
1705 * of the columns in node->cmap.
1707 static isl_stat
add_inter_validity_constraints(struct isl_sched_graph
*graph
,
1708 struct isl_sched_edge
*edge
)
1713 isl_dim_map
*dim_map
;
1714 isl_basic_set
*coef
;
1715 struct isl_sched_node
*src
= edge
->src
;
1716 struct isl_sched_node
*dst
= edge
->dst
;
1719 return isl_stat_error
;
1721 map
= isl_map_copy(edge
->map
);
1722 ctx
= isl_map_get_ctx(map
);
1723 coef
= inter_coefficients(graph
, edge
, map
);
1725 offset
= coef_var_offset(coef
);
1727 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
1728 offset
, isl_mat_copy(src
->cmap
));
1729 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
1730 offset
+ src
->nvar
, isl_mat_copy(dst
->cmap
));
1732 return isl_stat_error
;
1734 dim_map
= inter_dim_map(ctx
, graph
, src
, dst
, offset
, 1);
1736 edge
->start
= graph
->lp
->n_ineq
;
1737 graph
->lp
= isl_basic_set_extend_constraints(graph
->lp
,
1738 coef
->n_eq
, coef
->n_ineq
);
1739 graph
->lp
= isl_basic_set_add_constraints_dim_map(graph
->lp
,
1742 return isl_stat_error
;
1743 edge
->end
= graph
->lp
->n_ineq
;
1748 /* Add constraints to graph->lp that bound the dependence distance for the given
1749 * dependence from a node i to itself.
1750 * If s = 1, we add the constraint
1752 * c_i_x (y - x) <= m_0 + m_n n
1756 * -c_i_x (y - x) + m_0 + m_n n >= 0
1758 * for each (x,y) in R.
1759 * If s = -1, we add the constraint
1761 * -c_i_x (y - x) <= m_0 + m_n n
1765 * c_i_x (y - x) + m_0 + m_n n >= 0
1767 * for each (x,y) in R.
1768 * We obtain general constraints on coefficients (c_0, c_n, c_x)
1769 * of valid constraints for (y - x) and then plug in (m_0, m_n, -s * c_i_x),
1770 * with each coefficient (except m_0) represented as a pair of non-negative
1773 * Actually, we do not construct constraints for the c_i_x themselves,
1774 * but for the coefficients of c_i_x written as a linear combination
1775 * of the columns in node->cmap.
1778 * If "local" is set, then we add constraints
1780 * c_i_x (y - x) <= 0
1784 * -c_i_x (y - x) <= 0
1786 * instead, forcing the dependence distance to be (less than or) equal to 0.
1787 * That is, we plug in (0, 0, -s * c_i_x),
1788 * Note that dependences marked local are treated as validity constraints
1789 * by add_all_validity_constraints and therefore also have
1790 * their distances bounded by 0 from below.
1792 static isl_stat
add_intra_proximity_constraints(struct isl_sched_graph
*graph
,
1793 struct isl_sched_edge
*edge
, int s
, int local
)
1797 isl_map
*map
= isl_map_copy(edge
->map
);
1798 isl_ctx
*ctx
= isl_map_get_ctx(map
);
1799 isl_dim_map
*dim_map
;
1800 isl_basic_set
*coef
;
1801 struct isl_sched_node
*node
= edge
->src
;
1803 coef
= intra_coefficients(graph
, node
, map
);
1805 offset
= coef_var_offset(coef
);
1807 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
1808 offset
, isl_mat_copy(node
->cmap
));
1810 return isl_stat_error
;
1812 nparam
= isl_space_dim(node
->space
, isl_dim_param
);
1813 dim_map
= intra_dim_map(ctx
, graph
, node
, offset
, -s
);
1816 isl_dim_map_range(dim_map
, 1, 0, 0, 0, 1, 1);
1817 isl_dim_map_range(dim_map
, 4, 2, 1, 1, nparam
, -1);
1818 isl_dim_map_range(dim_map
, 5, 2, 1, 1, nparam
, 1);
1820 graph
->lp
= isl_basic_set_extend_constraints(graph
->lp
,
1821 coef
->n_eq
, coef
->n_ineq
);
1822 graph
->lp
= isl_basic_set_add_constraints_dim_map(graph
->lp
,
1828 /* Add constraints to graph->lp that bound the dependence distance for the given
1829 * dependence from node i to node j.
1830 * If s = 1, we add the constraint
1832 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x)
1837 * -(c_j_0 + c_j_n n + c_j_x y) + (c_i_0 + c_i_n n + c_i_x x) +
1840 * for each (x,y) in R.
1841 * If s = -1, we add the constraint
1843 * -((c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x))
1848 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) +
1851 * for each (x,y) in R.
1852 * We obtain general constraints on coefficients (c_0, c_n, c_x, c_y)
1853 * of valid constraints for R and then plug in
1854 * (m_0 - s*c_j_0 + s*c_i_0, m_n - s*c_j_n + s*c_i_n,
1856 * with each coefficient (except m_0, c_*_0 and c_*_n)
1857 * represented as a pair of non-negative coefficients.
1859 * Actually, we do not construct constraints for the c_*_x themselves,
1860 * but for the coefficients of c_*_x written as a linear combination
1861 * of the columns in node->cmap.
1864 * If "local" is set, then we add constraints
1866 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) <= 0
1870 * -((c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x)) <= 0
1872 * instead, forcing the dependence distance to be (less than or) equal to 0.
1873 * That is, we plug in
1874 * (-s*c_j_0 + s*c_i_0, -s*c_j_n + s*c_i_n, -s*c_j_x+s*c_i_x).
1875 * Note that dependences marked local are treated as validity constraints
1876 * by add_all_validity_constraints and therefore also have
1877 * their distances bounded by 0 from below.
1879 static isl_stat
add_inter_proximity_constraints(struct isl_sched_graph
*graph
,
1880 struct isl_sched_edge
*edge
, int s
, int local
)
1884 isl_map
*map
= isl_map_copy(edge
->map
);
1885 isl_ctx
*ctx
= isl_map_get_ctx(map
);
1886 isl_dim_map
*dim_map
;
1887 isl_basic_set
*coef
;
1888 struct isl_sched_node
*src
= edge
->src
;
1889 struct isl_sched_node
*dst
= edge
->dst
;
1891 coef
= inter_coefficients(graph
, edge
, map
);
1893 offset
= coef_var_offset(coef
);
1895 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
1896 offset
, isl_mat_copy(src
->cmap
));
1897 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
1898 offset
+ src
->nvar
, isl_mat_copy(dst
->cmap
));
1900 return isl_stat_error
;
1902 nparam
= isl_space_dim(src
->space
, isl_dim_param
);
1903 dim_map
= inter_dim_map(ctx
, graph
, src
, dst
, offset
, -s
);
1906 isl_dim_map_range(dim_map
, 1, 0, 0, 0, 1, 1);
1907 isl_dim_map_range(dim_map
, 4, 2, 1, 1, nparam
, -1);
1908 isl_dim_map_range(dim_map
, 5, 2, 1, 1, nparam
, 1);
1911 graph
->lp
= isl_basic_set_extend_constraints(graph
->lp
,
1912 coef
->n_eq
, coef
->n_ineq
);
1913 graph
->lp
= isl_basic_set_add_constraints_dim_map(graph
->lp
,
1919 /* Add all validity constraints to graph->lp.
1921 * An edge that is forced to be local needs to have its dependence
1922 * distances equal to zero. We take care of bounding them by 0 from below
1923 * here. add_all_proximity_constraints takes care of bounding them by 0
1926 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
1927 * Otherwise, we ignore them.
1929 static int add_all_validity_constraints(struct isl_sched_graph
*graph
,
1930 int use_coincidence
)
1934 for (i
= 0; i
< graph
->n_edge
; ++i
) {
1935 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
1938 local
= is_local(edge
) ||
1939 (is_coincidence(edge
) && use_coincidence
);
1940 if (!is_validity(edge
) && !local
)
1942 if (edge
->src
!= edge
->dst
)
1944 if (add_intra_validity_constraints(graph
, edge
) < 0)
1948 for (i
= 0; i
< graph
->n_edge
; ++i
) {
1949 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
1952 local
= is_local(edge
) ||
1953 (is_coincidence(edge
) && use_coincidence
);
1954 if (!is_validity(edge
) && !local
)
1956 if (edge
->src
== edge
->dst
)
1958 if (add_inter_validity_constraints(graph
, edge
) < 0)
1965 /* Add constraints to graph->lp that bound the dependence distance
1966 * for all dependence relations.
1967 * If a given proximity dependence is identical to a validity
1968 * dependence, then the dependence distance is already bounded
1969 * from below (by zero), so we only need to bound the distance
1970 * from above. (This includes the case of "local" dependences
1971 * which are treated as validity dependence by add_all_validity_constraints.)
1972 * Otherwise, we need to bound the distance both from above and from below.
1974 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
1975 * Otherwise, we ignore them.
1977 static int add_all_proximity_constraints(struct isl_sched_graph
*graph
,
1978 int use_coincidence
)
1982 for (i
= 0; i
< graph
->n_edge
; ++i
) {
1983 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
1986 local
= is_local(edge
) ||
1987 (is_coincidence(edge
) && use_coincidence
);
1988 if (!is_proximity(edge
) && !local
)
1990 if (edge
->src
== edge
->dst
&&
1991 add_intra_proximity_constraints(graph
, edge
, 1, local
) < 0)
1993 if (edge
->src
!= edge
->dst
&&
1994 add_inter_proximity_constraints(graph
, edge
, 1, local
) < 0)
1996 if (is_validity(edge
) || local
)
1998 if (edge
->src
== edge
->dst
&&
1999 add_intra_proximity_constraints(graph
, edge
, -1, 0) < 0)
2001 if (edge
->src
!= edge
->dst
&&
2002 add_inter_proximity_constraints(graph
, edge
, -1, 0) < 0)
2009 /* Compute a basis for the rows in the linear part of the schedule
2010 * and extend this basis to a full basis. The remaining rows
2011 * can then be used to force linear independence from the rows
2014 * In particular, given the schedule rows S, we compute
2019 * with H the Hermite normal form of S. That is, all but the
2020 * first rank columns of H are zero and so each row in S is
2021 * a linear combination of the first rank rows of Q.
2022 * The matrix Q is then transposed because we will write the
2023 * coefficients of the next schedule row as a column vector s
2024 * and express this s as a linear combination s = Q c of the
2026 * Similarly, the matrix U is transposed such that we can
2027 * compute the coefficients c = U s from a schedule row s.
2029 static int node_update_cmap(struct isl_sched_node
*node
)
2032 int n_row
= isl_mat_rows(node
->sched
);
2034 H
= isl_mat_sub_alloc(node
->sched
, 0, n_row
,
2035 1 + node
->nparam
, node
->nvar
);
2037 H
= isl_mat_left_hermite(H
, 0, &U
, &Q
);
2038 isl_mat_free(node
->cmap
);
2039 isl_mat_free(node
->cinv
);
2040 isl_mat_free(node
->ctrans
);
2041 node
->ctrans
= isl_mat_copy(Q
);
2042 node
->cmap
= isl_mat_transpose(Q
);
2043 node
->cinv
= isl_mat_transpose(U
);
2044 node
->rank
= isl_mat_initial_non_zero_cols(H
);
2047 if (!node
->cmap
|| !node
->cinv
|| !node
->ctrans
|| node
->rank
< 0)
2052 /* Is "edge" marked as a validity or a conditional validity edge?
2054 static int is_any_validity(struct isl_sched_edge
*edge
)
2056 return is_validity(edge
) || is_conditional_validity(edge
);
2059 /* How many times should we count the constraints in "edge"?
2061 * If carry is set, then we are counting the number of
2062 * (validity or conditional validity) constraints that will be added
2063 * in setup_carry_lp and we count each edge exactly once.
2065 * Otherwise, we count as follows
2066 * validity -> 1 (>= 0)
2067 * validity+proximity -> 2 (>= 0 and upper bound)
2068 * proximity -> 2 (lower and upper bound)
2069 * local(+any) -> 2 (>= 0 and <= 0)
2071 * If an edge is only marked conditional_validity then it counts
2072 * as zero since it is only checked afterwards.
2074 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2075 * Otherwise, we ignore them.
2077 static int edge_multiplicity(struct isl_sched_edge
*edge
, int carry
,
2078 int use_coincidence
)
2082 if (is_proximity(edge
) || is_local(edge
))
2084 if (use_coincidence
&& is_coincidence(edge
))
2086 if (is_validity(edge
))
2091 /* Count the number of equality and inequality constraints
2092 * that will be added for the given map.
2094 * "use_coincidence" is set if we should take into account coincidence edges.
2096 static int count_map_constraints(struct isl_sched_graph
*graph
,
2097 struct isl_sched_edge
*edge
, __isl_take isl_map
*map
,
2098 int *n_eq
, int *n_ineq
, int carry
, int use_coincidence
)
2100 isl_basic_set
*coef
;
2101 int f
= edge_multiplicity(edge
, carry
, use_coincidence
);
2108 if (edge
->src
== edge
->dst
)
2109 coef
= intra_coefficients(graph
, edge
->src
, map
);
2111 coef
= inter_coefficients(graph
, edge
, map
);
2114 *n_eq
+= f
* coef
->n_eq
;
2115 *n_ineq
+= f
* coef
->n_ineq
;
2116 isl_basic_set_free(coef
);
2121 /* Count the number of equality and inequality constraints
2122 * that will be added to the main lp problem.
2123 * We count as follows
2124 * validity -> 1 (>= 0)
2125 * validity+proximity -> 2 (>= 0 and upper bound)
2126 * proximity -> 2 (lower and upper bound)
2127 * local(+any) -> 2 (>= 0 and <= 0)
2129 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2130 * Otherwise, we ignore them.
2132 static int count_constraints(struct isl_sched_graph
*graph
,
2133 int *n_eq
, int *n_ineq
, int use_coincidence
)
2137 *n_eq
= *n_ineq
= 0;
2138 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2139 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
2140 isl_map
*map
= isl_map_copy(edge
->map
);
2142 if (count_map_constraints(graph
, edge
, map
, n_eq
, n_ineq
,
2143 0, use_coincidence
) < 0)
2150 /* Count the number of constraints that will be added by
2151 * add_bound_constant_constraints to bound the values of the constant terms
2152 * and increment *n_eq and *n_ineq accordingly.
2154 * In practice, add_bound_constant_constraints only adds inequalities.
2156 static isl_stat
count_bound_constant_constraints(isl_ctx
*ctx
,
2157 struct isl_sched_graph
*graph
, int *n_eq
, int *n_ineq
)
2159 if (isl_options_get_schedule_max_constant_term(ctx
) == -1)
2162 *n_ineq
+= graph
->n
;
2167 /* Add constraints to bound the values of the constant terms in the schedule,
2168 * if requested by the user.
2170 * The maximal value of the constant terms is defined by the option
2171 * "schedule_max_constant_term".
2173 * Within each node, the coefficients have the following order:
2175 * - c_i_n (if parametric)
2176 * - positive and negative parts of c_i_x
2178 static isl_stat
add_bound_constant_constraints(isl_ctx
*ctx
,
2179 struct isl_sched_graph
*graph
)
2185 max
= isl_options_get_schedule_max_constant_term(ctx
);
2189 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2191 for (i
= 0; i
< graph
->n
; ++i
) {
2192 struct isl_sched_node
*node
= &graph
->node
[i
];
2193 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2195 return isl_stat_error
;
2196 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
2197 isl_int_set_si(graph
->lp
->ineq
[k
][1 + node
->start
], -1);
2198 isl_int_set_si(graph
->lp
->ineq
[k
][0], max
);
2204 /* Count the number of constraints that will be added by
2205 * add_bound_coefficient_constraints and increment *n_eq and *n_ineq
2208 * In practice, add_bound_coefficient_constraints only adds inequalities.
2210 static int count_bound_coefficient_constraints(isl_ctx
*ctx
,
2211 struct isl_sched_graph
*graph
, int *n_eq
, int *n_ineq
)
2215 if (isl_options_get_schedule_max_coefficient(ctx
) == -1 &&
2216 !isl_options_get_schedule_treat_coalescing(ctx
))
2219 for (i
= 0; i
< graph
->n
; ++i
)
2220 *n_ineq
+= graph
->node
[i
].nparam
+ 2 * graph
->node
[i
].nvar
;
2225 /* Add constraints to graph->lp that bound the values of
2226 * the parameter schedule coefficients of "node" to "max" and
2227 * the variable schedule coefficients to the corresponding entry
2229 * In either case, a negative value means that no bound needs to be imposed.
2231 * For parameter coefficients, this amounts to adding a constraint
2239 * The variables coefficients are, however, not represented directly.
2240 * Instead, the variables coefficients c_x are written as a linear
2241 * combination c_x = cmap c_z of some other coefficients c_z,
2242 * which are in turn encoded as c_z = c_z^+ - c_z^-.
2243 * Let a_j be the elements of row i of node->cmap, then
2245 * -max_i <= c_x_i <= max_i
2249 * -max_i <= \sum_j a_j (c_z_j^+ - c_z_j^-) <= max_i
2253 * -\sum_j a_j (c_z_j^+ - c_z_j^-) + max_i >= 0
2254 * \sum_j a_j (c_z_j^+ - c_z_j^-) + max_i >= 0
2256 static isl_stat
node_add_coefficient_constraints(isl_ctx
*ctx
,
2257 struct isl_sched_graph
*graph
, struct isl_sched_node
*node
, int max
)
2263 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2265 for (j
= 0; j
< node
->nparam
; ++j
) {
2271 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2273 return isl_stat_error
;
2274 dim
= 1 + node
->start
+ 1 + j
;
2275 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
2276 isl_int_set_si(graph
->lp
->ineq
[k
][dim
], -1);
2277 isl_int_set_si(graph
->lp
->ineq
[k
][0], max
);
2280 ineq
= isl_vec_alloc(ctx
, 1 + total
);
2281 ineq
= isl_vec_clr(ineq
);
2283 return isl_stat_error
;
2284 for (i
= 0; i
< node
->nvar
; ++i
) {
2285 int pos
= 1 + node_var_coef_offset(node
);
2287 if (isl_int_is_neg(node
->max
->el
[i
]))
2290 for (j
= 0; j
< node
->nvar
; ++j
) {
2291 isl_int_set(ineq
->el
[pos
+ 2 * j
],
2292 node
->cmap
->row
[i
][j
]);
2293 isl_int_neg(ineq
->el
[pos
+ 2 * j
+ 1],
2294 node
->cmap
->row
[i
][j
]);
2296 isl_int_set(ineq
->el
[0], node
->max
->el
[i
]);
2298 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2301 isl_seq_cpy(graph
->lp
->ineq
[k
], ineq
->el
, 1 + total
);
2303 isl_seq_neg(ineq
->el
+ pos
, ineq
->el
+ pos
, 2 * node
->nvar
);
2304 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2307 isl_seq_cpy(graph
->lp
->ineq
[k
], ineq
->el
, 1 + total
);
2314 return isl_stat_error
;
2317 /* Add constraints that bound the values of the variable and parameter
2318 * coefficients of the schedule.
2320 * The maximal value of the coefficients is defined by the option
2321 * 'schedule_max_coefficient' and the entries in node->max.
2322 * These latter entries are only set if either the schedule_max_coefficient
2323 * option or the schedule_treat_coalescing option is set.
2325 static isl_stat
add_bound_coefficient_constraints(isl_ctx
*ctx
,
2326 struct isl_sched_graph
*graph
)
2331 max
= isl_options_get_schedule_max_coefficient(ctx
);
2333 if (max
== -1 && !isl_options_get_schedule_treat_coalescing(ctx
))
2336 for (i
= 0; i
< graph
->n
; ++i
) {
2337 struct isl_sched_node
*node
= &graph
->node
[i
];
2339 if (node_add_coefficient_constraints(ctx
, graph
, node
, max
) < 0)
2340 return isl_stat_error
;
2346 /* Add a constraint to graph->lp that equates the value at position
2347 * "sum_pos" to the sum of the "n" values starting at "first".
2349 static isl_stat
add_sum_constraint(struct isl_sched_graph
*graph
,
2350 int sum_pos
, int first
, int n
)
2355 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2357 k
= isl_basic_set_alloc_equality(graph
->lp
);
2359 return isl_stat_error
;
2360 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2361 isl_int_set_si(graph
->lp
->eq
[k
][1 + sum_pos
], -1);
2362 for (i
= 0; i
< n
; ++i
)
2363 isl_int_set_si(graph
->lp
->eq
[k
][1 + first
+ i
], 1);
2368 /* Add a constraint to graph->lp that equates the value at position
2369 * "sum_pos" to the sum of the parameter coefficients of all nodes.
2371 * Within each node, the coefficients have the following order:
2373 * - c_i_n (if parametric)
2374 * - positive and negative parts of c_i_x
2376 static isl_stat
add_param_sum_constraint(struct isl_sched_graph
*graph
,
2382 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2384 k
= isl_basic_set_alloc_equality(graph
->lp
);
2386 return isl_stat_error
;
2387 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2388 isl_int_set_si(graph
->lp
->eq
[k
][1 + sum_pos
], -1);
2389 for (i
= 0; i
< graph
->n
; ++i
) {
2390 int pos
= 1 + graph
->node
[i
].start
+ 1;
2392 for (j
= 0; j
< graph
->node
[i
].nparam
; ++j
)
2393 isl_int_set_si(graph
->lp
->eq
[k
][pos
+ j
], 1);
2399 /* Add a constraint to graph->lp that equates the value at position
2400 * "sum_pos" to the sum of the variable coefficients of all nodes.
2402 * Within each node, the coefficients have the following order:
2404 * - c_i_n (if parametric)
2405 * - positive and negative parts of c_i_x
2407 static isl_stat
add_var_sum_constraint(struct isl_sched_graph
*graph
,
2413 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2415 k
= isl_basic_set_alloc_equality(graph
->lp
);
2417 return isl_stat_error
;
2418 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2419 isl_int_set_si(graph
->lp
->eq
[k
][1 + sum_pos
], -1);
2420 for (i
= 0; i
< graph
->n
; ++i
) {
2421 struct isl_sched_node
*node
= &graph
->node
[i
];
2422 int pos
= 1 + node_var_coef_offset(node
);
2424 for (j
= 0; j
< 2 * node
->nvar
; ++j
)
2425 isl_int_set_si(graph
->lp
->eq
[k
][pos
+ j
], 1);
2431 /* Construct an ILP problem for finding schedule coefficients
2432 * that result in non-negative, but small dependence distances
2433 * over all dependences.
2434 * In particular, the dependence distances over proximity edges
2435 * are bounded by m_0 + m_n n and we compute schedule coefficients
2436 * with small values (preferably zero) of m_n and m_0.
2438 * All variables of the ILP are non-negative. The actual coefficients
2439 * may be negative, so each coefficient is represented as the difference
2440 * of two non-negative variables. The negative part always appears
2441 * immediately before the positive part.
2442 * Other than that, the variables have the following order
2444 * - sum of positive and negative parts of m_n coefficients
2446 * - sum of all c_n coefficients
2447 * (unconstrained when computing non-parametric schedules)
2448 * - sum of positive and negative parts of all c_x coefficients
2449 * - positive and negative parts of m_n coefficients
2452 * - c_i_n (if parametric)
2453 * - positive and negative parts of c_i_x
2455 * The c_i_x are not represented directly, but through the columns of
2456 * node->cmap. That is, the computed values are for variable t_i_x
2457 * such that c_i_x = Q t_i_x with Q equal to node->cmap.
2459 * The constraints are those from the edges plus two or three equalities
2460 * to express the sums.
2462 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2463 * Otherwise, we ignore them.
2465 static isl_stat
setup_lp(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
2466 int use_coincidence
)
2476 parametric
= ctx
->opt
->schedule_parametric
;
2477 nparam
= isl_space_dim(graph
->node
[0].space
, isl_dim_param
);
2479 total
= param_pos
+ 2 * nparam
;
2480 for (i
= 0; i
< graph
->n
; ++i
) {
2481 struct isl_sched_node
*node
= &graph
->node
[graph
->sorted
[i
]];
2482 if (node_update_cmap(node
) < 0)
2483 return isl_stat_error
;
2484 node
->start
= total
;
2485 total
+= 1 + node
->nparam
+ 2 * node
->nvar
;
2488 if (count_constraints(graph
, &n_eq
, &n_ineq
, use_coincidence
) < 0)
2489 return isl_stat_error
;
2490 if (count_bound_constant_constraints(ctx
, graph
, &n_eq
, &n_ineq
) < 0)
2491 return isl_stat_error
;
2492 if (count_bound_coefficient_constraints(ctx
, graph
, &n_eq
, &n_ineq
) < 0)
2493 return isl_stat_error
;
2495 space
= isl_space_set_alloc(ctx
, 0, total
);
2496 isl_basic_set_free(graph
->lp
);
2497 n_eq
+= 2 + parametric
;
2499 graph
->lp
= isl_basic_set_alloc_space(space
, 0, n_eq
, n_ineq
);
2501 if (add_sum_constraint(graph
, 0, param_pos
, 2 * nparam
) < 0)
2502 return isl_stat_error
;
2503 if (parametric
&& add_param_sum_constraint(graph
, 2) < 0)
2504 return isl_stat_error
;
2505 if (add_var_sum_constraint(graph
, 3) < 0)
2506 return isl_stat_error
;
2507 if (add_bound_constant_constraints(ctx
, graph
) < 0)
2508 return isl_stat_error
;
2509 if (add_bound_coefficient_constraints(ctx
, graph
) < 0)
2510 return isl_stat_error
;
2511 if (add_all_validity_constraints(graph
, use_coincidence
) < 0)
2512 return isl_stat_error
;
2513 if (add_all_proximity_constraints(graph
, use_coincidence
) < 0)
2514 return isl_stat_error
;
2519 /* Analyze the conflicting constraint found by
2520 * isl_tab_basic_set_non_trivial_lexmin. If it corresponds to the validity
2521 * constraint of one of the edges between distinct nodes, living, moreover
2522 * in distinct SCCs, then record the source and sink SCC as this may
2523 * be a good place to cut between SCCs.
2525 static int check_conflict(int con
, void *user
)
2528 struct isl_sched_graph
*graph
= user
;
2530 if (graph
->src_scc
>= 0)
2533 con
-= graph
->lp
->n_eq
;
2535 if (con
>= graph
->lp
->n_ineq
)
2538 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2539 if (!is_validity(&graph
->edge
[i
]))
2541 if (graph
->edge
[i
].src
== graph
->edge
[i
].dst
)
2543 if (graph
->edge
[i
].src
->scc
== graph
->edge
[i
].dst
->scc
)
2545 if (graph
->edge
[i
].start
> con
)
2547 if (graph
->edge
[i
].end
<= con
)
2549 graph
->src_scc
= graph
->edge
[i
].src
->scc
;
2550 graph
->dst_scc
= graph
->edge
[i
].dst
->scc
;
2556 /* Check whether the next schedule row of the given node needs to be
2557 * non-trivial. Lower-dimensional domains may have some trivial rows,
2558 * but as soon as the number of remaining required non-trivial rows
2559 * is as large as the number or remaining rows to be computed,
2560 * all remaining rows need to be non-trivial.
2562 static int needs_row(struct isl_sched_graph
*graph
, struct isl_sched_node
*node
)
2564 return node
->nvar
- node
->rank
>= graph
->maxvar
- graph
->n_row
;
2567 /* Solve the ILP problem constructed in setup_lp.
2568 * For each node such that all the remaining rows of its schedule
2569 * need to be non-trivial, we construct a non-triviality region.
2570 * This region imposes that the next row is independent of previous rows.
2571 * In particular the coefficients c_i_x are represented by t_i_x
2572 * variables with c_i_x = Q t_i_x and Q a unimodular matrix such that
2573 * its first columns span the rows of the previously computed part
2574 * of the schedule. The non-triviality region enforces that at least
2575 * one of the remaining components of t_i_x is non-zero, i.e.,
2576 * that the new schedule row depends on at least one of the remaining
2579 static __isl_give isl_vec
*solve_lp(struct isl_sched_graph
*graph
)
2585 for (i
= 0; i
< graph
->n
; ++i
) {
2586 struct isl_sched_node
*node
= &graph
->node
[i
];
2587 int skip
= node
->rank
;
2588 graph
->region
[i
].pos
= node_var_coef_offset(node
) + 2 * skip
;
2589 if (needs_row(graph
, node
))
2590 graph
->region
[i
].len
= 2 * (node
->nvar
- skip
);
2592 graph
->region
[i
].len
= 0;
2594 lp
= isl_basic_set_copy(graph
->lp
);
2595 sol
= isl_tab_basic_set_non_trivial_lexmin(lp
, 2, graph
->n
,
2596 graph
->region
, &check_conflict
, graph
);
2600 /* Extract the coefficients for the variables of "node" from "sol".
2602 * Within each node, the coefficients have the following order:
2604 * - c_i_n (if parametric)
2605 * - positive and negative parts of c_i_x
2607 * The c_i_x^- appear before their c_i_x^+ counterpart.
2609 * Return c_i_x = c_i_x^+ - c_i_x^-
2611 static __isl_give isl_vec
*extract_var_coef(struct isl_sched_node
*node
,
2612 __isl_keep isl_vec
*sol
)
2620 csol
= isl_vec_alloc(isl_vec_get_ctx(sol
), node
->nvar
);
2624 pos
= 1 + node_var_coef_offset(node
);
2625 for (i
= 0; i
< node
->nvar
; ++i
)
2626 isl_int_sub(csol
->el
[i
],
2627 sol
->el
[pos
+ 2 * i
+ 1], sol
->el
[pos
+ 2 * i
]);
2632 /* Update the schedules of all nodes based on the given solution
2633 * of the LP problem.
2634 * The new row is added to the current band.
2635 * All possibly negative coefficients are encoded as a difference
2636 * of two non-negative variables, so we need to perform the subtraction
2637 * here. Moreover, if use_cmap is set, then the solution does
2638 * not refer to the actual coefficients c_i_x, but instead to variables
2639 * t_i_x such that c_i_x = Q t_i_x and Q is equal to node->cmap.
2640 * In this case, we then also need to perform this multiplication
2641 * to obtain the values of c_i_x.
2643 * If coincident is set, then the caller guarantees that the new
2644 * row satisfies the coincidence constraints.
2646 static int update_schedule(struct isl_sched_graph
*graph
,
2647 __isl_take isl_vec
*sol
, int use_cmap
, int coincident
)
2650 isl_vec
*csol
= NULL
;
2655 isl_die(sol
->ctx
, isl_error_internal
,
2656 "no solution found", goto error
);
2657 if (graph
->n_total_row
>= graph
->max_row
)
2658 isl_die(sol
->ctx
, isl_error_internal
,
2659 "too many schedule rows", goto error
);
2661 for (i
= 0; i
< graph
->n
; ++i
) {
2662 struct isl_sched_node
*node
= &graph
->node
[i
];
2663 int pos
= node
->start
;
2664 int row
= isl_mat_rows(node
->sched
);
2667 csol
= extract_var_coef(node
, sol
);
2671 isl_map_free(node
->sched_map
);
2672 node
->sched_map
= NULL
;
2673 node
->sched
= isl_mat_add_rows(node
->sched
, 1);
2676 for (j
= 0; j
< 1 + node
->nparam
; ++j
)
2677 node
->sched
= isl_mat_set_element(node
->sched
,
2678 row
, j
, sol
->el
[1 + pos
+ j
]);
2680 csol
= isl_mat_vec_product(isl_mat_copy(node
->cmap
),
2684 for (j
= 0; j
< node
->nvar
; ++j
)
2685 node
->sched
= isl_mat_set_element(node
->sched
,
2686 row
, 1 + node
->nparam
+ j
, csol
->el
[j
]);
2687 node
->coincident
[graph
->n_total_row
] = coincident
;
2693 graph
->n_total_row
++;
2702 /* Convert row "row" of node->sched into an isl_aff living in "ls"
2703 * and return this isl_aff.
2705 static __isl_give isl_aff
*extract_schedule_row(__isl_take isl_local_space
*ls
,
2706 struct isl_sched_node
*node
, int row
)
2714 aff
= isl_aff_zero_on_domain(ls
);
2715 isl_mat_get_element(node
->sched
, row
, 0, &v
);
2716 aff
= isl_aff_set_constant(aff
, v
);
2717 for (j
= 0; j
< node
->nparam
; ++j
) {
2718 isl_mat_get_element(node
->sched
, row
, 1 + j
, &v
);
2719 aff
= isl_aff_set_coefficient(aff
, isl_dim_param
, j
, v
);
2721 for (j
= 0; j
< node
->nvar
; ++j
) {
2722 isl_mat_get_element(node
->sched
, row
, 1 + node
->nparam
+ j
, &v
);
2723 aff
= isl_aff_set_coefficient(aff
, isl_dim_in
, j
, v
);
2731 /* Convert the "n" rows starting at "first" of node->sched into a multi_aff
2732 * and return this multi_aff.
2734 * The result is defined over the uncompressed node domain.
2736 static __isl_give isl_multi_aff
*node_extract_partial_schedule_multi_aff(
2737 struct isl_sched_node
*node
, int first
, int n
)
2741 isl_local_space
*ls
;
2748 nrow
= isl_mat_rows(node
->sched
);
2749 if (node
->compressed
)
2750 space
= isl_multi_aff_get_domain_space(node
->decompress
);
2752 space
= isl_space_copy(node
->space
);
2753 ls
= isl_local_space_from_space(isl_space_copy(space
));
2754 space
= isl_space_from_domain(space
);
2755 space
= isl_space_add_dims(space
, isl_dim_out
, n
);
2756 ma
= isl_multi_aff_zero(space
);
2758 for (i
= first
; i
< first
+ n
; ++i
) {
2759 aff
= extract_schedule_row(isl_local_space_copy(ls
), node
, i
);
2760 ma
= isl_multi_aff_set_aff(ma
, i
- first
, aff
);
2763 isl_local_space_free(ls
);
2765 if (node
->compressed
)
2766 ma
= isl_multi_aff_pullback_multi_aff(ma
,
2767 isl_multi_aff_copy(node
->compress
));
2772 /* Convert node->sched into a multi_aff and return this multi_aff.
2774 * The result is defined over the uncompressed node domain.
2776 static __isl_give isl_multi_aff
*node_extract_schedule_multi_aff(
2777 struct isl_sched_node
*node
)
2781 nrow
= isl_mat_rows(node
->sched
);
2782 return node_extract_partial_schedule_multi_aff(node
, 0, nrow
);
2785 /* Convert node->sched into a map and return this map.
2787 * The result is cached in node->sched_map, which needs to be released
2788 * whenever node->sched is updated.
2789 * It is defined over the uncompressed node domain.
2791 static __isl_give isl_map
*node_extract_schedule(struct isl_sched_node
*node
)
2793 if (!node
->sched_map
) {
2796 ma
= node_extract_schedule_multi_aff(node
);
2797 node
->sched_map
= isl_map_from_multi_aff(ma
);
2800 return isl_map_copy(node
->sched_map
);
2803 /* Construct a map that can be used to update a dependence relation
2804 * based on the current schedule.
2805 * That is, construct a map expressing that source and sink
2806 * are executed within the same iteration of the current schedule.
2807 * This map can then be intersected with the dependence relation.
2808 * This is not the most efficient way, but this shouldn't be a critical
2811 static __isl_give isl_map
*specializer(struct isl_sched_node
*src
,
2812 struct isl_sched_node
*dst
)
2814 isl_map
*src_sched
, *dst_sched
;
2816 src_sched
= node_extract_schedule(src
);
2817 dst_sched
= node_extract_schedule(dst
);
2818 return isl_map_apply_range(src_sched
, isl_map_reverse(dst_sched
));
2821 /* Intersect the domains of the nested relations in domain and range
2822 * of "umap" with "map".
2824 static __isl_give isl_union_map
*intersect_domains(
2825 __isl_take isl_union_map
*umap
, __isl_keep isl_map
*map
)
2827 isl_union_set
*uset
;
2829 umap
= isl_union_map_zip(umap
);
2830 uset
= isl_union_set_from_set(isl_map_wrap(isl_map_copy(map
)));
2831 umap
= isl_union_map_intersect_domain(umap
, uset
);
2832 umap
= isl_union_map_zip(umap
);
2836 /* Update the dependence relation of the given edge based
2837 * on the current schedule.
2838 * If the dependence is carried completely by the current schedule, then
2839 * it is removed from the edge_tables. It is kept in the list of edges
2840 * as otherwise all edge_tables would have to be recomputed.
2842 * If the edge is of a type that can appear multiple times
2843 * between the same pair of nodes, then it is added to
2844 * the edge table (again). This prevents the situation
2845 * where none of these edges is referenced from the edge table
2846 * because the one that was referenced turned out to be empty and
2847 * was therefore removed from the table.
2849 static int update_edge(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
2850 struct isl_sched_edge
*edge
)
2855 id
= specializer(edge
->src
, edge
->dst
);
2856 edge
->map
= isl_map_intersect(edge
->map
, isl_map_copy(id
));
2860 if (edge
->tagged_condition
) {
2861 edge
->tagged_condition
=
2862 intersect_domains(edge
->tagged_condition
, id
);
2863 if (!edge
->tagged_condition
)
2866 if (edge
->tagged_validity
) {
2867 edge
->tagged_validity
=
2868 intersect_domains(edge
->tagged_validity
, id
);
2869 if (!edge
->tagged_validity
)
2873 empty
= isl_map_plain_is_empty(edge
->map
);
2877 graph_remove_edge(graph
, edge
);
2878 } else if (is_multi_edge_type(edge
)) {
2879 if (graph_edge_tables_add(ctx
, graph
, edge
) < 0)
2890 /* Does the domain of "umap" intersect "uset"?
2892 static int domain_intersects(__isl_keep isl_union_map
*umap
,
2893 __isl_keep isl_union_set
*uset
)
2897 umap
= isl_union_map_copy(umap
);
2898 umap
= isl_union_map_intersect_domain(umap
, isl_union_set_copy(uset
));
2899 empty
= isl_union_map_is_empty(umap
);
2900 isl_union_map_free(umap
);
2902 return empty
< 0 ? -1 : !empty
;
2905 /* Does the range of "umap" intersect "uset"?
2907 static int range_intersects(__isl_keep isl_union_map
*umap
,
2908 __isl_keep isl_union_set
*uset
)
2912 umap
= isl_union_map_copy(umap
);
2913 umap
= isl_union_map_intersect_range(umap
, isl_union_set_copy(uset
));
2914 empty
= isl_union_map_is_empty(umap
);
2915 isl_union_map_free(umap
);
2917 return empty
< 0 ? -1 : !empty
;
2920 /* Are the condition dependences of "edge" local with respect to
2921 * the current schedule?
2923 * That is, are domain and range of the condition dependences mapped
2924 * to the same point?
2926 * In other words, is the condition false?
2928 static int is_condition_false(struct isl_sched_edge
*edge
)
2930 isl_union_map
*umap
;
2931 isl_map
*map
, *sched
, *test
;
2934 empty
= isl_union_map_is_empty(edge
->tagged_condition
);
2935 if (empty
< 0 || empty
)
2938 umap
= isl_union_map_copy(edge
->tagged_condition
);
2939 umap
= isl_union_map_zip(umap
);
2940 umap
= isl_union_set_unwrap(isl_union_map_domain(umap
));
2941 map
= isl_map_from_union_map(umap
);
2943 sched
= node_extract_schedule(edge
->src
);
2944 map
= isl_map_apply_domain(map
, sched
);
2945 sched
= node_extract_schedule(edge
->dst
);
2946 map
= isl_map_apply_range(map
, sched
);
2948 test
= isl_map_identity(isl_map_get_space(map
));
2949 local
= isl_map_is_subset(map
, test
);
2956 /* For each conditional validity constraint that is adjacent
2957 * to a condition with domain in condition_source or range in condition_sink,
2958 * turn it into an unconditional validity constraint.
2960 static int unconditionalize_adjacent_validity(struct isl_sched_graph
*graph
,
2961 __isl_take isl_union_set
*condition_source
,
2962 __isl_take isl_union_set
*condition_sink
)
2966 condition_source
= isl_union_set_coalesce(condition_source
);
2967 condition_sink
= isl_union_set_coalesce(condition_sink
);
2969 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2971 isl_union_map
*validity
;
2973 if (!is_conditional_validity(&graph
->edge
[i
]))
2975 if (is_validity(&graph
->edge
[i
]))
2978 validity
= graph
->edge
[i
].tagged_validity
;
2979 adjacent
= domain_intersects(validity
, condition_sink
);
2980 if (adjacent
>= 0 && !adjacent
)
2981 adjacent
= range_intersects(validity
, condition_source
);
2987 set_validity(&graph
->edge
[i
]);
2990 isl_union_set_free(condition_source
);
2991 isl_union_set_free(condition_sink
);
2994 isl_union_set_free(condition_source
);
2995 isl_union_set_free(condition_sink
);
2999 /* Update the dependence relations of all edges based on the current schedule
3000 * and enforce conditional validity constraints that are adjacent
3001 * to satisfied condition constraints.
3003 * First check if any of the condition constraints are satisfied
3004 * (i.e., not local to the outer schedule) and keep track of
3005 * their domain and range.
3006 * Then update all dependence relations (which removes the non-local
3008 * Finally, if any condition constraints turned out to be satisfied,
3009 * then turn all adjacent conditional validity constraints into
3010 * unconditional validity constraints.
3012 static int update_edges(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
3016 isl_union_set
*source
, *sink
;
3018 source
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
3019 sink
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
3020 for (i
= 0; i
< graph
->n_edge
; ++i
) {
3022 isl_union_set
*uset
;
3023 isl_union_map
*umap
;
3025 if (!is_condition(&graph
->edge
[i
]))
3027 if (is_local(&graph
->edge
[i
]))
3029 local
= is_condition_false(&graph
->edge
[i
]);
3037 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_condition
);
3038 uset
= isl_union_map_domain(umap
);
3039 source
= isl_union_set_union(source
, uset
);
3041 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_condition
);
3042 uset
= isl_union_map_range(umap
);
3043 sink
= isl_union_set_union(sink
, uset
);
3046 for (i
= 0; i
< graph
->n_edge
; ++i
) {
3047 if (update_edge(ctx
, graph
, &graph
->edge
[i
]) < 0)
3052 return unconditionalize_adjacent_validity(graph
, source
, sink
);
3054 isl_union_set_free(source
);
3055 isl_union_set_free(sink
);
3058 isl_union_set_free(source
);
3059 isl_union_set_free(sink
);
3063 static void next_band(struct isl_sched_graph
*graph
)
3065 graph
->band_start
= graph
->n_total_row
;
3068 /* Return the union of the universe domains of the nodes in "graph"
3069 * that satisfy "pred".
3071 static __isl_give isl_union_set
*isl_sched_graph_domain(isl_ctx
*ctx
,
3072 struct isl_sched_graph
*graph
,
3073 int (*pred
)(struct isl_sched_node
*node
, int data
), int data
)
3079 for (i
= 0; i
< graph
->n
; ++i
)
3080 if (pred(&graph
->node
[i
], data
))
3084 isl_die(ctx
, isl_error_internal
,
3085 "empty component", return NULL
);
3087 set
= isl_set_universe(isl_space_copy(graph
->node
[i
].space
));
3088 dom
= isl_union_set_from_set(set
);
3090 for (i
= i
+ 1; i
< graph
->n
; ++i
) {
3091 if (!pred(&graph
->node
[i
], data
))
3093 set
= isl_set_universe(isl_space_copy(graph
->node
[i
].space
));
3094 dom
= isl_union_set_union(dom
, isl_union_set_from_set(set
));
3100 /* Return a list of unions of universe domains, where each element
3101 * in the list corresponds to an SCC (or WCC) indexed by node->scc.
3103 static __isl_give isl_union_set_list
*extract_sccs(isl_ctx
*ctx
,
3104 struct isl_sched_graph
*graph
)
3107 isl_union_set_list
*filters
;
3109 filters
= isl_union_set_list_alloc(ctx
, graph
->scc
);
3110 for (i
= 0; i
< graph
->scc
; ++i
) {
3113 dom
= isl_sched_graph_domain(ctx
, graph
, &node_scc_exactly
, i
);
3114 filters
= isl_union_set_list_add(filters
, dom
);
3120 /* Return a list of two unions of universe domains, one for the SCCs up
3121 * to and including graph->src_scc and another for the other SCCs.
3123 static __isl_give isl_union_set_list
*extract_split(isl_ctx
*ctx
,
3124 struct isl_sched_graph
*graph
)
3127 isl_union_set_list
*filters
;
3129 filters
= isl_union_set_list_alloc(ctx
, 2);
3130 dom
= isl_sched_graph_domain(ctx
, graph
,
3131 &node_scc_at_most
, graph
->src_scc
);
3132 filters
= isl_union_set_list_add(filters
, dom
);
3133 dom
= isl_sched_graph_domain(ctx
, graph
,
3134 &node_scc_at_least
, graph
->src_scc
+ 1);
3135 filters
= isl_union_set_list_add(filters
, dom
);
3140 /* Copy nodes that satisfy node_pred from the src dependence graph
3141 * to the dst dependence graph.
3143 static int copy_nodes(struct isl_sched_graph
*dst
, struct isl_sched_graph
*src
,
3144 int (*node_pred
)(struct isl_sched_node
*node
, int data
), int data
)
3149 for (i
= 0; i
< src
->n
; ++i
) {
3152 if (!node_pred(&src
->node
[i
], data
))
3156 dst
->node
[j
].space
= isl_space_copy(src
->node
[i
].space
);
3157 dst
->node
[j
].compressed
= src
->node
[i
].compressed
;
3158 dst
->node
[j
].hull
= isl_set_copy(src
->node
[i
].hull
);
3159 dst
->node
[j
].compress
=
3160 isl_multi_aff_copy(src
->node
[i
].compress
);
3161 dst
->node
[j
].decompress
=
3162 isl_multi_aff_copy(src
->node
[i
].decompress
);
3163 dst
->node
[j
].nvar
= src
->node
[i
].nvar
;
3164 dst
->node
[j
].nparam
= src
->node
[i
].nparam
;
3165 dst
->node
[j
].sched
= isl_mat_copy(src
->node
[i
].sched
);
3166 dst
->node
[j
].sched_map
= isl_map_copy(src
->node
[i
].sched_map
);
3167 dst
->node
[j
].coincident
= src
->node
[i
].coincident
;
3168 dst
->node
[j
].sizes
= isl_multi_val_copy(src
->node
[i
].sizes
);
3169 dst
->node
[j
].max
= isl_vec_copy(src
->node
[i
].max
);
3172 if (!dst
->node
[j
].space
|| !dst
->node
[j
].sched
)
3174 if (dst
->node
[j
].compressed
&&
3175 (!dst
->node
[j
].hull
|| !dst
->node
[j
].compress
||
3176 !dst
->node
[j
].decompress
))
3183 /* Copy non-empty edges that satisfy edge_pred from the src dependence graph
3184 * to the dst dependence graph.
3185 * If the source or destination node of the edge is not in the destination
3186 * graph, then it must be a backward proximity edge and it should simply
3189 static int copy_edges(isl_ctx
*ctx
, struct isl_sched_graph
*dst
,
3190 struct isl_sched_graph
*src
,
3191 int (*edge_pred
)(struct isl_sched_edge
*edge
, int data
), int data
)
3196 for (i
= 0; i
< src
->n_edge
; ++i
) {
3197 struct isl_sched_edge
*edge
= &src
->edge
[i
];
3199 isl_union_map
*tagged_condition
;
3200 isl_union_map
*tagged_validity
;
3201 struct isl_sched_node
*dst_src
, *dst_dst
;
3203 if (!edge_pred(edge
, data
))
3206 if (isl_map_plain_is_empty(edge
->map
))
3209 dst_src
= graph_find_node(ctx
, dst
, edge
->src
->space
);
3210 dst_dst
= graph_find_node(ctx
, dst
, edge
->dst
->space
);
3211 if (!dst_src
|| !dst_dst
) {
3212 if (is_validity(edge
) || is_conditional_validity(edge
))
3213 isl_die(ctx
, isl_error_internal
,
3214 "backward (conditional) validity edge",
3219 map
= isl_map_copy(edge
->map
);
3220 tagged_condition
= isl_union_map_copy(edge
->tagged_condition
);
3221 tagged_validity
= isl_union_map_copy(edge
->tagged_validity
);
3223 dst
->edge
[dst
->n_edge
].src
= dst_src
;
3224 dst
->edge
[dst
->n_edge
].dst
= dst_dst
;
3225 dst
->edge
[dst
->n_edge
].map
= map
;
3226 dst
->edge
[dst
->n_edge
].tagged_condition
= tagged_condition
;
3227 dst
->edge
[dst
->n_edge
].tagged_validity
= tagged_validity
;
3228 dst
->edge
[dst
->n_edge
].types
= edge
->types
;
3231 if (edge
->tagged_condition
&& !tagged_condition
)
3233 if (edge
->tagged_validity
&& !tagged_validity
)
3236 if (graph_edge_tables_add(ctx
, dst
,
3237 &dst
->edge
[dst
->n_edge
- 1]) < 0)
3244 /* Compute the maximal number of variables over all nodes.
3245 * This is the maximal number of linearly independent schedule
3246 * rows that we need to compute.
3247 * Just in case we end up in a part of the dependence graph
3248 * with only lower-dimensional domains, we make sure we will
3249 * compute the required amount of extra linearly independent rows.
3251 static int compute_maxvar(struct isl_sched_graph
*graph
)
3256 for (i
= 0; i
< graph
->n
; ++i
) {
3257 struct isl_sched_node
*node
= &graph
->node
[i
];
3260 if (node_update_cmap(node
) < 0)
3262 nvar
= node
->nvar
+ graph
->n_row
- node
->rank
;
3263 if (nvar
> graph
->maxvar
)
3264 graph
->maxvar
= nvar
;
3270 /* Extract the subgraph of "graph" that consists of the node satisfying
3271 * "node_pred" and the edges satisfying "edge_pred" and store
3272 * the result in "sub".
3274 static int extract_sub_graph(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
3275 int (*node_pred
)(struct isl_sched_node
*node
, int data
),
3276 int (*edge_pred
)(struct isl_sched_edge
*edge
, int data
),
3277 int data
, struct isl_sched_graph
*sub
)
3279 int i
, n
= 0, n_edge
= 0;
3282 for (i
= 0; i
< graph
->n
; ++i
)
3283 if (node_pred(&graph
->node
[i
], data
))
3285 for (i
= 0; i
< graph
->n_edge
; ++i
)
3286 if (edge_pred(&graph
->edge
[i
], data
))
3288 if (graph_alloc(ctx
, sub
, n
, n_edge
) < 0)
3290 if (copy_nodes(sub
, graph
, node_pred
, data
) < 0)
3292 if (graph_init_table(ctx
, sub
) < 0)
3294 for (t
= 0; t
<= isl_edge_last
; ++t
)
3295 sub
->max_edge
[t
] = graph
->max_edge
[t
];
3296 if (graph_init_edge_tables(ctx
, sub
) < 0)
3298 if (copy_edges(ctx
, sub
, graph
, edge_pred
, data
) < 0)
3300 sub
->n_row
= graph
->n_row
;
3301 sub
->max_row
= graph
->max_row
;
3302 sub
->n_total_row
= graph
->n_total_row
;
3303 sub
->band_start
= graph
->band_start
;
3308 static __isl_give isl_schedule_node
*compute_schedule(isl_schedule_node
*node
,
3309 struct isl_sched_graph
*graph
);
3310 static __isl_give isl_schedule_node
*compute_schedule_wcc(
3311 isl_schedule_node
*node
, struct isl_sched_graph
*graph
);
3313 /* Compute a schedule for a subgraph of "graph". In particular, for
3314 * the graph composed of nodes that satisfy node_pred and edges that
3315 * that satisfy edge_pred.
3316 * If the subgraph is known to consist of a single component, then wcc should
3317 * be set and then we call compute_schedule_wcc on the constructed subgraph.
3318 * Otherwise, we call compute_schedule, which will check whether the subgraph
3321 * The schedule is inserted at "node" and the updated schedule node
3324 static __isl_give isl_schedule_node
*compute_sub_schedule(
3325 __isl_take isl_schedule_node
*node
, isl_ctx
*ctx
,
3326 struct isl_sched_graph
*graph
,
3327 int (*node_pred
)(struct isl_sched_node
*node
, int data
),
3328 int (*edge_pred
)(struct isl_sched_edge
*edge
, int data
),
3331 struct isl_sched_graph split
= { 0 };
3333 if (extract_sub_graph(ctx
, graph
, node_pred
, edge_pred
, data
,
3338 node
= compute_schedule_wcc(node
, &split
);
3340 node
= compute_schedule(node
, &split
);
3342 graph_free(ctx
, &split
);
3345 graph_free(ctx
, &split
);
3346 return isl_schedule_node_free(node
);
3349 static int edge_scc_exactly(struct isl_sched_edge
*edge
, int scc
)
3351 return edge
->src
->scc
== scc
&& edge
->dst
->scc
== scc
;
3354 static int edge_dst_scc_at_most(struct isl_sched_edge
*edge
, int scc
)
3356 return edge
->dst
->scc
<= scc
;
3359 static int edge_src_scc_at_least(struct isl_sched_edge
*edge
, int scc
)
3361 return edge
->src
->scc
>= scc
;
3364 /* Reset the current band by dropping all its schedule rows.
3366 static int reset_band(struct isl_sched_graph
*graph
)
3371 drop
= graph
->n_total_row
- graph
->band_start
;
3372 graph
->n_total_row
-= drop
;
3373 graph
->n_row
-= drop
;
3375 for (i
= 0; i
< graph
->n
; ++i
) {
3376 struct isl_sched_node
*node
= &graph
->node
[i
];
3378 isl_map_free(node
->sched_map
);
3379 node
->sched_map
= NULL
;
3381 node
->sched
= isl_mat_drop_rows(node
->sched
,
3382 graph
->band_start
, drop
);
3391 /* Split the current graph into two parts and compute a schedule for each
3392 * part individually. In particular, one part consists of all SCCs up
3393 * to and including graph->src_scc, while the other part contains the other
3394 * SCCs. The split is enforced by a sequence node inserted at position "node"
3395 * in the schedule tree. Return the updated schedule node.
3396 * If either of these two parts consists of a sequence, then it is spliced
3397 * into the sequence containing the two parts.
3399 * The current band is reset. It would be possible to reuse
3400 * the previously computed rows as the first rows in the next
3401 * band, but recomputing them may result in better rows as we are looking
3402 * at a smaller part of the dependence graph.
3404 static __isl_give isl_schedule_node
*compute_split_schedule(
3405 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
3409 isl_union_set_list
*filters
;
3414 if (reset_band(graph
) < 0)
3415 return isl_schedule_node_free(node
);
3419 ctx
= isl_schedule_node_get_ctx(node
);
3420 filters
= extract_split(ctx
, graph
);
3421 node
= isl_schedule_node_insert_sequence(node
, filters
);
3422 node
= isl_schedule_node_child(node
, 1);
3423 node
= isl_schedule_node_child(node
, 0);
3425 node
= compute_sub_schedule(node
, ctx
, graph
,
3426 &node_scc_at_least
, &edge_src_scc_at_least
,
3427 graph
->src_scc
+ 1, 0);
3428 is_seq
= isl_schedule_node_get_type(node
) == isl_schedule_node_sequence
;
3429 node
= isl_schedule_node_parent(node
);
3430 node
= isl_schedule_node_parent(node
);
3432 node
= isl_schedule_node_sequence_splice_child(node
, 1);
3433 node
= isl_schedule_node_child(node
, 0);
3434 node
= isl_schedule_node_child(node
, 0);
3435 node
= compute_sub_schedule(node
, ctx
, graph
,
3436 &node_scc_at_most
, &edge_dst_scc_at_most
,
3438 is_seq
= isl_schedule_node_get_type(node
) == isl_schedule_node_sequence
;
3439 node
= isl_schedule_node_parent(node
);
3440 node
= isl_schedule_node_parent(node
);
3442 node
= isl_schedule_node_sequence_splice_child(node
, 0);
3447 /* Insert a band node at position "node" in the schedule tree corresponding
3448 * to the current band in "graph". Mark the band node permutable
3449 * if "permutable" is set.
3450 * The partial schedules and the coincidence property are extracted
3451 * from the graph nodes.
3452 * Return the updated schedule node.
3454 static __isl_give isl_schedule_node
*insert_current_band(
3455 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
3461 isl_multi_pw_aff
*mpa
;
3462 isl_multi_union_pw_aff
*mupa
;
3468 isl_die(isl_schedule_node_get_ctx(node
), isl_error_internal
,
3469 "graph should have at least one node",
3470 return isl_schedule_node_free(node
));
3472 start
= graph
->band_start
;
3473 end
= graph
->n_total_row
;
3476 ma
= node_extract_partial_schedule_multi_aff(&graph
->node
[0], start
, n
);
3477 mpa
= isl_multi_pw_aff_from_multi_aff(ma
);
3478 mupa
= isl_multi_union_pw_aff_from_multi_pw_aff(mpa
);
3480 for (i
= 1; i
< graph
->n
; ++i
) {
3481 isl_multi_union_pw_aff
*mupa_i
;
3483 ma
= node_extract_partial_schedule_multi_aff(&graph
->node
[i
],
3485 mpa
= isl_multi_pw_aff_from_multi_aff(ma
);
3486 mupa_i
= isl_multi_union_pw_aff_from_multi_pw_aff(mpa
);
3487 mupa
= isl_multi_union_pw_aff_union_add(mupa
, mupa_i
);
3489 node
= isl_schedule_node_insert_partial_schedule(node
, mupa
);
3491 for (i
= 0; i
< n
; ++i
)
3492 node
= isl_schedule_node_band_member_set_coincident(node
, i
,
3493 graph
->node
[0].coincident
[start
+ i
]);
3494 node
= isl_schedule_node_band_set_permutable(node
, permutable
);
3499 /* Update the dependence relations based on the current schedule,
3500 * add the current band to "node" and then continue with the computation
3502 * Return the updated schedule node.
3504 static __isl_give isl_schedule_node
*compute_next_band(
3505 __isl_take isl_schedule_node
*node
,
3506 struct isl_sched_graph
*graph
, int permutable
)
3513 ctx
= isl_schedule_node_get_ctx(node
);
3514 if (update_edges(ctx
, graph
) < 0)
3515 return isl_schedule_node_free(node
);
3516 node
= insert_current_band(node
, graph
, permutable
);
3519 node
= isl_schedule_node_child(node
, 0);
3520 node
= compute_schedule(node
, graph
);
3521 node
= isl_schedule_node_parent(node
);
3526 /* Add constraints to graph->lp that force the dependence "map" (which
3527 * is part of the dependence relation of "edge")
3528 * to be respected and attempt to carry it, where the edge is one from
3529 * a node j to itself. "pos" is the sequence number of the given map.
3530 * That is, add constraints that enforce
3532 * (c_j_0 + c_j_n n + c_j_x y) - (c_j_0 + c_j_n n + c_j_x x)
3533 * = c_j_x (y - x) >= e_i
3535 * for each (x,y) in R.
3536 * We obtain general constraints on coefficients (c_0, c_n, c_x)
3537 * of valid constraints for (y - x) and then plug in (-e_i, 0, c_j_x),
3538 * with each coefficient in c_j_x represented as a pair of non-negative
3541 static int add_intra_constraints(struct isl_sched_graph
*graph
,
3542 struct isl_sched_edge
*edge
, __isl_take isl_map
*map
, int pos
)
3545 isl_ctx
*ctx
= isl_map_get_ctx(map
);
3546 isl_dim_map
*dim_map
;
3547 isl_basic_set
*coef
;
3548 struct isl_sched_node
*node
= edge
->src
;
3550 coef
= intra_coefficients(graph
, node
, map
);
3554 offset
= coef_var_offset(coef
);
3555 dim_map
= intra_dim_map(ctx
, graph
, node
, offset
, 1);
3556 isl_dim_map_range(dim_map
, 3 + pos
, 0, 0, 0, 1, -1);
3557 graph
->lp
= isl_basic_set_extend_constraints(graph
->lp
,
3558 coef
->n_eq
, coef
->n_ineq
);
3559 graph
->lp
= isl_basic_set_add_constraints_dim_map(graph
->lp
,
3565 /* Add constraints to graph->lp that force the dependence "map" (which
3566 * is part of the dependence relation of "edge")
3567 * to be respected and attempt to carry it, where the edge is one from
3568 * node j to node k. "pos" is the sequence number of the given map.
3569 * That is, add constraints that enforce
3571 * (c_k_0 + c_k_n n + c_k_x y) - (c_j_0 + c_j_n n + c_j_x x) >= e_i
3573 * for each (x,y) in R.
3574 * We obtain general constraints on coefficients (c_0, c_n, c_x)
3575 * of valid constraints for R and then plug in
3576 * (-e_i + c_k_0 - c_j_0, c_k_n - c_j_n, c_k_x - c_j_x)
3577 * with each coefficient (except e_i, c_*_0 and c_*_n)
3578 * represented as a pair of non-negative coefficients.
3580 static int add_inter_constraints(struct isl_sched_graph
*graph
,
3581 struct isl_sched_edge
*edge
, __isl_take isl_map
*map
, int pos
)
3584 isl_ctx
*ctx
= isl_map_get_ctx(map
);
3585 isl_dim_map
*dim_map
;
3586 isl_basic_set
*coef
;
3587 struct isl_sched_node
*src
= edge
->src
;
3588 struct isl_sched_node
*dst
= edge
->dst
;
3590 coef
= inter_coefficients(graph
, edge
, map
);
3594 offset
= coef_var_offset(coef
);
3595 dim_map
= inter_dim_map(ctx
, graph
, src
, dst
, offset
, 1);
3596 isl_dim_map_range(dim_map
, 3 + pos
, 0, 0, 0, 1, -1);
3597 graph
->lp
= isl_basic_set_extend_constraints(graph
->lp
,
3598 coef
->n_eq
, coef
->n_ineq
);
3599 graph
->lp
= isl_basic_set_add_constraints_dim_map(graph
->lp
,
3605 /* Add constraints to graph->lp that force all (conditional) validity
3606 * dependences to be respected and attempt to carry them.
3608 static int add_all_constraints(struct isl_sched_graph
*graph
)
3614 for (i
= 0; i
< graph
->n_edge
; ++i
) {
3615 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
3617 if (!is_any_validity(edge
))
3620 for (j
= 0; j
< edge
->map
->n
; ++j
) {
3621 isl_basic_map
*bmap
;
3624 bmap
= isl_basic_map_copy(edge
->map
->p
[j
]);
3625 map
= isl_map_from_basic_map(bmap
);
3627 if (edge
->src
== edge
->dst
&&
3628 add_intra_constraints(graph
, edge
, map
, pos
) < 0)
3630 if (edge
->src
!= edge
->dst
&&
3631 add_inter_constraints(graph
, edge
, map
, pos
) < 0)
3640 /* Count the number of equality and inequality constraints
3641 * that will be added to the carry_lp problem.
3642 * We count each edge exactly once.
3644 static int count_all_constraints(struct isl_sched_graph
*graph
,
3645 int *n_eq
, int *n_ineq
)
3649 *n_eq
= *n_ineq
= 0;
3650 for (i
= 0; i
< graph
->n_edge
; ++i
) {
3651 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
3653 if (!is_any_validity(edge
))
3656 for (j
= 0; j
< edge
->map
->n
; ++j
) {
3657 isl_basic_map
*bmap
;
3660 bmap
= isl_basic_map_copy(edge
->map
->p
[j
]);
3661 map
= isl_map_from_basic_map(bmap
);
3663 if (count_map_constraints(graph
, edge
, map
,
3664 n_eq
, n_ineq
, 1, 0) < 0)
3672 /* Return the total number of (validity) edges that carry_dependences will
3675 static int count_carry_edges(struct isl_sched_graph
*graph
)
3681 for (i
= 0; i
< graph
->n_edge
; ++i
) {
3682 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
3684 if (!is_any_validity(edge
))
3687 n_edge
+= isl_map_n_basic_map(edge
->map
);
3693 /* Construct an LP problem for finding schedule coefficients
3694 * such that the schedule carries as many validity dependences as possible.
3695 * In particular, for each dependence i, we bound the dependence distance
3696 * from below by e_i, with 0 <= e_i <= 1 and then maximize the sum
3697 * of all e_i's. Dependences with e_i = 0 in the solution are simply
3698 * respected, while those with e_i > 0 (in practice e_i = 1) are carried.
3699 * Note that if the dependence relation is a union of basic maps,
3700 * then we have to consider each basic map individually as it may only
3701 * be possible to carry the dependences expressed by some of those
3702 * basic maps and not all of them.
3703 * Below, we consider each of those basic maps as a separate "edge".
3705 * All variables of the LP are non-negative. The actual coefficients
3706 * may be negative, so each coefficient is represented as the difference
3707 * of two non-negative variables. The negative part always appears
3708 * immediately before the positive part.
3709 * Other than that, the variables have the following order
3711 * - sum of (1 - e_i) over all edges
3712 * - sum of all c_n coefficients
3713 * (unconstrained when computing non-parametric schedules)
3714 * - sum of positive and negative parts of all c_x coefficients
3719 * - c_i_n (if parametric)
3720 * - positive and negative parts of c_i_x
3722 * The constraints are those from the (validity) edges plus three equalities
3723 * to express the sums and n_edge inequalities to express e_i <= 1.
3725 static isl_stat
setup_carry_lp(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
3734 n_edge
= count_carry_edges(graph
);
3737 for (i
= 0; i
< graph
->n
; ++i
) {
3738 struct isl_sched_node
*node
= &graph
->node
[graph
->sorted
[i
]];
3739 node
->start
= total
;
3740 total
+= 1 + node
->nparam
+ 2 * node
->nvar
;
3743 if (count_all_constraints(graph
, &n_eq
, &n_ineq
) < 0)
3744 return isl_stat_error
;
3746 dim
= isl_space_set_alloc(ctx
, 0, total
);
3747 isl_basic_set_free(graph
->lp
);
3750 graph
->lp
= isl_basic_set_alloc_space(dim
, 0, n_eq
, n_ineq
);
3751 graph
->lp
= isl_basic_set_set_rational(graph
->lp
);
3753 k
= isl_basic_set_alloc_equality(graph
->lp
);
3755 return isl_stat_error
;
3756 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
3757 isl_int_set_si(graph
->lp
->eq
[k
][0], -n_edge
);
3758 isl_int_set_si(graph
->lp
->eq
[k
][1], 1);
3759 for (i
= 0; i
< n_edge
; ++i
)
3760 isl_int_set_si(graph
->lp
->eq
[k
][4 + i
], 1);
3762 if (add_param_sum_constraint(graph
, 1) < 0)
3763 return isl_stat_error
;
3764 if (add_var_sum_constraint(graph
, 2) < 0)
3765 return isl_stat_error
;
3767 for (i
= 0; i
< n_edge
; ++i
) {
3768 k
= isl_basic_set_alloc_inequality(graph
->lp
);
3770 return isl_stat_error
;
3771 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
3772 isl_int_set_si(graph
->lp
->ineq
[k
][4 + i
], -1);
3773 isl_int_set_si(graph
->lp
->ineq
[k
][0], 1);
3776 if (add_all_constraints(graph
) < 0)
3777 return isl_stat_error
;
3782 static __isl_give isl_schedule_node
*compute_component_schedule(
3783 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
3786 /* Comparison function for sorting the statements based on
3787 * the corresponding value in "r".
3789 static int smaller_value(const void *a
, const void *b
, void *data
)
3795 return isl_int_cmp(r
->el
[*i1
], r
->el
[*i2
]);
3798 /* If the schedule_split_scaled option is set and if the linear
3799 * parts of the scheduling rows for all nodes in the graphs have
3800 * a non-trivial common divisor, then split off the remainder of the
3801 * constant term modulo this common divisor from the linear part.
3802 * Otherwise, insert a band node directly and continue with
3803 * the construction of the schedule.
3805 * If a non-trivial common divisor is found, then
3806 * the linear part is reduced and the remainder is enforced
3807 * by a sequence node with the children placed in the order
3808 * of this remainder.
3809 * In particular, we assign an scc index based on the remainder and
3810 * then rely on compute_component_schedule to insert the sequence and
3811 * to continue the schedule construction on each part.
3813 static __isl_give isl_schedule_node
*split_scaled(
3814 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
3827 ctx
= isl_schedule_node_get_ctx(node
);
3828 if (!ctx
->opt
->schedule_split_scaled
)
3829 return compute_next_band(node
, graph
, 0);
3831 return compute_next_band(node
, graph
, 0);
3834 isl_int_init(gcd_i
);
3836 isl_int_set_si(gcd
, 0);
3838 row
= isl_mat_rows(graph
->node
[0].sched
) - 1;
3840 for (i
= 0; i
< graph
->n
; ++i
) {
3841 struct isl_sched_node
*node
= &graph
->node
[i
];
3842 int cols
= isl_mat_cols(node
->sched
);
3844 isl_seq_gcd(node
->sched
->row
[row
] + 1, cols
- 1, &gcd_i
);
3845 isl_int_gcd(gcd
, gcd
, gcd_i
);
3848 isl_int_clear(gcd_i
);
3850 if (isl_int_cmp_si(gcd
, 1) <= 0) {
3852 return compute_next_band(node
, graph
, 0);
3855 r
= isl_vec_alloc(ctx
, graph
->n
);
3856 order
= isl_calloc_array(ctx
, int, graph
->n
);
3860 for (i
= 0; i
< graph
->n
; ++i
) {
3861 struct isl_sched_node
*node
= &graph
->node
[i
];
3864 isl_int_fdiv_r(r
->el
[i
], node
->sched
->row
[row
][0], gcd
);
3865 isl_int_fdiv_q(node
->sched
->row
[row
][0],
3866 node
->sched
->row
[row
][0], gcd
);
3867 isl_int_mul(node
->sched
->row
[row
][0],
3868 node
->sched
->row
[row
][0], gcd
);
3869 node
->sched
= isl_mat_scale_down_row(node
->sched
, row
, gcd
);
3874 if (isl_sort(order
, graph
->n
, sizeof(order
[0]), &smaller_value
, r
) < 0)
3878 for (i
= 0; i
< graph
->n
; ++i
) {
3879 if (i
> 0 && isl_int_ne(r
->el
[order
[i
- 1]], r
->el
[order
[i
]]))
3881 graph
->node
[order
[i
]].scc
= scc
;
3890 if (update_edges(ctx
, graph
) < 0)
3891 return isl_schedule_node_free(node
);
3892 node
= insert_current_band(node
, graph
, 0);
3895 node
= isl_schedule_node_child(node
, 0);
3896 node
= compute_component_schedule(node
, graph
, 0);
3897 node
= isl_schedule_node_parent(node
);
3904 return isl_schedule_node_free(node
);
3907 /* Is the schedule row "sol" trivial on node "node"?
3908 * That is, is the solution zero on the dimensions orthogonal to
3909 * the previously found solutions?
3910 * Return 1 if the solution is trivial, 0 if it is not and -1 on error.
3912 * Each coefficient is represented as the difference between
3913 * two non-negative values in "sol". "sol" has been computed
3914 * in terms of the original iterators (i.e., without use of cmap).
3915 * We construct the schedule row s and write it as a linear
3916 * combination of (linear combinations of) previously computed schedule rows.
3917 * s = Q c or c = U s.
3918 * If the final entries of c are all zero, then the solution is trivial.
3920 static int is_trivial(struct isl_sched_node
*node
, __isl_keep isl_vec
*sol
)
3927 if (node
->nvar
== node
->rank
)
3930 node_sol
= extract_var_coef(node
, sol
);
3931 node_sol
= isl_mat_vec_product(isl_mat_copy(node
->cinv
), node_sol
);
3935 trivial
= isl_seq_first_non_zero(node_sol
->el
+ node
->rank
,
3936 node
->nvar
- node
->rank
) == -1;
3938 isl_vec_free(node_sol
);
3943 /* Is the schedule row "sol" trivial on any node where it should
3945 * "sol" has been computed in terms of the original iterators
3946 * (i.e., without use of cmap).
3947 * Return 1 if any solution is trivial, 0 if they are not and -1 on error.
3949 static int is_any_trivial(struct isl_sched_graph
*graph
,
3950 __isl_keep isl_vec
*sol
)
3954 for (i
= 0; i
< graph
->n
; ++i
) {
3955 struct isl_sched_node
*node
= &graph
->node
[i
];
3958 if (!needs_row(graph
, node
))
3960 trivial
= is_trivial(node
, sol
);
3961 if (trivial
< 0 || trivial
)
3968 /* Does the schedule represented by "sol" perform loop coalescing on "node"?
3969 * If so, return the position of the coalesced dimension.
3970 * Otherwise, return node->nvar or -1 on error.
3972 * In particular, look for pairs of coefficients c_i and c_j such that
3973 * |c_j/c_i| >= size_i, i.e., |c_j| >= |c_i * size_i|.
3974 * If any such pair is found, then return i.
3975 * If size_i is infinity, then no check on c_i needs to be performed.
3977 static int find_node_coalescing(struct isl_sched_node
*node
,
3978 __isl_keep isl_vec
*sol
)
3984 if (node
->nvar
<= 1)
3987 csol
= extract_var_coef(node
, sol
);
3991 for (i
= 0; i
< node
->nvar
; ++i
) {
3994 if (isl_int_is_zero(csol
->el
[i
]))
3996 v
= isl_multi_val_get_val(node
->sizes
, i
);
3999 if (!isl_val_is_int(v
)) {
4003 isl_int_mul(max
, v
->n
, csol
->el
[i
]);
4006 for (j
= 0; j
< node
->nvar
; ++j
) {
4009 if (isl_int_abs_ge(csol
->el
[j
], max
))
4025 /* Force the schedule coefficient at position "pos" of "node" to be zero
4027 * The coefficient is encoded as the difference between two non-negative
4028 * variables. Force these two variables to have the same value.
4030 static __isl_give isl_tab_lexmin
*zero_out_node_coef(
4031 __isl_take isl_tab_lexmin
*tl
, struct isl_sched_node
*node
, int pos
)
4037 ctx
= isl_space_get_ctx(node
->space
);
4038 dim
= isl_tab_lexmin_dim(tl
);
4040 return isl_tab_lexmin_free(tl
);
4041 eq
= isl_vec_alloc(ctx
, 1 + dim
);
4042 eq
= isl_vec_clr(eq
);
4044 return isl_tab_lexmin_free(tl
);
4046 pos
= 1 + node_var_coef_offset(node
) + 2 * pos
;
4047 isl_int_set_si(eq
->el
[pos
], 1);
4048 isl_int_set_si(eq
->el
[pos
+ 1], -1);
4049 tl
= isl_tab_lexmin_add_eq(tl
, eq
->el
);
4055 /* Return the lexicographically smallest rational point in the basic set
4056 * from which "tl" was constructed, double checking that this input set
4059 static __isl_give isl_vec
*non_empty_solution(__isl_keep isl_tab_lexmin
*tl
)
4063 sol
= isl_tab_lexmin_get_solution(tl
);
4067 isl_die(isl_vec_get_ctx(sol
), isl_error_internal
,
4068 "error in schedule construction",
4069 return isl_vec_free(sol
));
4073 /* Does the solution "sol" of the LP problem constructed by setup_carry_lp
4074 * carry any of the "n_edge" groups of dependences?
4075 * The value in the first position is the sum of (1 - e_i) over all "n_edge"
4076 * edges, with 0 <= e_i <= 1 equal to 1 when the dependences represented
4077 * by the edge are carried by the solution.
4078 * If the sum of the (1 - e_i) is smaller than "n_edge" then at least
4079 * one of those is carried.
4081 * Note that despite the fact that the problem is solved using a rational
4082 * solver, the solution is guaranteed to be integral.
4083 * Specifically, the dependence distance lower bounds e_i (and therefore
4084 * also their sum) are integers. See Lemma 5 of [1].
4086 * Any potential denominator of the sum is cleared by this function.
4087 * The denominator is not relevant for any of the other elements
4090 * [1] P. Feautrier, Some Efficient Solutions to the Affine Scheduling
4091 * Problem, Part II: Multi-Dimensional Time.
4092 * In Intl. Journal of Parallel Programming, 1992.
4094 static int carries_dependences(__isl_keep isl_vec
*sol
, int n_edge
)
4096 isl_int_divexact(sol
->el
[1], sol
->el
[1], sol
->el
[0]);
4097 isl_int_set_si(sol
->el
[0], 1);
4098 return isl_int_cmp_si(sol
->el
[1], n_edge
) < 0;
4101 /* Return the lexicographically smallest rational point in "lp",
4102 * assuming that all variables are non-negative and performing some
4103 * additional sanity checks.
4104 * In particular, "lp" should not be empty by construction.
4105 * Double check that this is the case.
4106 * Also, check that dependences are carried for at least one of
4107 * the "n_edge" edges.
4109 * If the computed schedule performs loop coalescing on a given node,
4110 * i.e., if it is of the form
4112 * c_i i + c_j j + ...
4114 * with |c_j/c_i| >= size_i, then force the coefficient c_i to be zero
4115 * to cut out this solution. Repeat this process until no more loop
4116 * coalescing occurs or until no more dependences can be carried.
4117 * In the latter case, revert to the previously computed solution.
4119 static __isl_give isl_vec
*non_neg_lexmin(struct isl_sched_graph
*graph
,
4120 __isl_take isl_basic_set
*lp
, int n_edge
)
4125 isl_vec
*sol
, *prev
= NULL
;
4126 int treat_coalescing
;
4130 ctx
= isl_basic_set_get_ctx(lp
);
4131 treat_coalescing
= isl_options_get_schedule_treat_coalescing(ctx
);
4132 tl
= isl_tab_lexmin_from_basic_set(lp
);
4135 sol
= non_empty_solution(tl
);
4139 if (!carries_dependences(sol
, n_edge
)) {
4141 isl_die(ctx
, isl_error_unknown
,
4142 "unable to carry dependences",
4148 prev
= isl_vec_free(prev
);
4149 if (!treat_coalescing
)
4151 for (i
= 0; i
< graph
->n
; ++i
) {
4152 struct isl_sched_node
*node
= &graph
->node
[i
];
4154 pos
= find_node_coalescing(node
, sol
);
4157 if (pos
< node
->nvar
)
4162 tl
= zero_out_node_coef(tl
, &graph
->node
[i
], pos
);
4164 } while (i
< graph
->n
);
4166 isl_tab_lexmin_free(tl
);
4170 isl_tab_lexmin_free(tl
);
4176 /* Construct a schedule row for each node such that as many validity dependences
4177 * as possible are carried and then continue with the next band.
4179 * If there are no validity dependences, then no dependence can be carried and
4180 * the procedure is guaranteed to fail. If there is more than one component,
4181 * then try computing a schedule on each component separately
4182 * to prevent or at least postpone this failure.
4184 * If the computed schedule row turns out to be trivial on one or
4185 * more nodes where it should not be trivial, then we throw it away
4186 * and try again on each component separately.
4188 * If there is only one component, then we accept the schedule row anyway,
4189 * but we do not consider it as a complete row and therefore do not
4190 * increment graph->n_row. Note that the ranks of the nodes that
4191 * do get a non-trivial schedule part will get updated regardless and
4192 * graph->maxvar is computed based on these ranks. The test for
4193 * whether more schedule rows are required in compute_schedule_wcc
4194 * is therefore not affected.
4196 * Insert a band corresponding to the schedule row at position "node"
4197 * of the schedule tree and continue with the construction of the schedule.
4198 * This insertion and the continued construction is performed by split_scaled
4199 * after optionally checking for non-trivial common divisors.
4201 static __isl_give isl_schedule_node
*carry_dependences(
4202 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
4213 n_edge
= count_carry_edges(graph
);
4214 if (n_edge
== 0 && graph
->scc
> 1)
4215 return compute_component_schedule(node
, graph
, 1);
4217 ctx
= isl_schedule_node_get_ctx(node
);
4218 if (setup_carry_lp(ctx
, graph
) < 0)
4219 return isl_schedule_node_free(node
);
4221 lp
= isl_basic_set_copy(graph
->lp
);
4222 sol
= non_neg_lexmin(graph
, lp
, n_edge
);
4224 return isl_schedule_node_free(node
);
4226 trivial
= is_any_trivial(graph
, sol
);
4228 sol
= isl_vec_free(sol
);
4229 } else if (trivial
&& graph
->scc
> 1) {
4231 return compute_component_schedule(node
, graph
, 1);
4234 if (update_schedule(graph
, sol
, 0, 0) < 0)
4235 return isl_schedule_node_free(node
);
4239 return split_scaled(node
, graph
);
4242 /* Topologically sort statements mapped to the same schedule iteration
4243 * and add insert a sequence node in front of "node"
4244 * corresponding to this order.
4245 * If "initialized" is set, then it may be assumed that compute_maxvar
4246 * has been called on the current band. Otherwise, call
4247 * compute_maxvar if and before carry_dependences gets called.
4249 * If it turns out to be impossible to sort the statements apart,
4250 * because different dependences impose different orderings
4251 * on the statements, then we extend the schedule such that
4252 * it carries at least one more dependence.
4254 static __isl_give isl_schedule_node
*sort_statements(
4255 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
4259 isl_union_set_list
*filters
;
4264 ctx
= isl_schedule_node_get_ctx(node
);
4266 isl_die(ctx
, isl_error_internal
,
4267 "graph should have at least one node",
4268 return isl_schedule_node_free(node
));
4273 if (update_edges(ctx
, graph
) < 0)
4274 return isl_schedule_node_free(node
);
4276 if (graph
->n_edge
== 0)
4279 if (detect_sccs(ctx
, graph
) < 0)
4280 return isl_schedule_node_free(node
);
4283 if (graph
->scc
< graph
->n
) {
4284 if (!initialized
&& compute_maxvar(graph
) < 0)
4285 return isl_schedule_node_free(node
);
4286 return carry_dependences(node
, graph
);
4289 filters
= extract_sccs(ctx
, graph
);
4290 node
= isl_schedule_node_insert_sequence(node
, filters
);
4295 /* Are there any (non-empty) (conditional) validity edges in the graph?
4297 static int has_validity_edges(struct isl_sched_graph
*graph
)
4301 for (i
= 0; i
< graph
->n_edge
; ++i
) {
4304 empty
= isl_map_plain_is_empty(graph
->edge
[i
].map
);
4309 if (is_any_validity(&graph
->edge
[i
]))
4316 /* Should we apply a Feautrier step?
4317 * That is, did the user request the Feautrier algorithm and are
4318 * there any validity dependences (left)?
4320 static int need_feautrier_step(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
4322 if (ctx
->opt
->schedule_algorithm
!= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
)
4325 return has_validity_edges(graph
);
4328 /* Compute a schedule for a connected dependence graph using Feautrier's
4329 * multi-dimensional scheduling algorithm and return the updated schedule node.
4331 * The original algorithm is described in [1].
4332 * The main idea is to minimize the number of scheduling dimensions, by
4333 * trying to satisfy as many dependences as possible per scheduling dimension.
4335 * [1] P. Feautrier, Some Efficient Solutions to the Affine Scheduling
4336 * Problem, Part II: Multi-Dimensional Time.
4337 * In Intl. Journal of Parallel Programming, 1992.
4339 static __isl_give isl_schedule_node
*compute_schedule_wcc_feautrier(
4340 isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
4342 return carry_dependences(node
, graph
);
4345 /* Turn off the "local" bit on all (condition) edges.
4347 static void clear_local_edges(struct isl_sched_graph
*graph
)
4351 for (i
= 0; i
< graph
->n_edge
; ++i
)
4352 if (is_condition(&graph
->edge
[i
]))
4353 clear_local(&graph
->edge
[i
]);
4356 /* Does "graph" have both condition and conditional validity edges?
4358 static int need_condition_check(struct isl_sched_graph
*graph
)
4361 int any_condition
= 0;
4362 int any_conditional_validity
= 0;
4364 for (i
= 0; i
< graph
->n_edge
; ++i
) {
4365 if (is_condition(&graph
->edge
[i
]))
4367 if (is_conditional_validity(&graph
->edge
[i
]))
4368 any_conditional_validity
= 1;
4371 return any_condition
&& any_conditional_validity
;
4374 /* Does "graph" contain any coincidence edge?
4376 static int has_any_coincidence(struct isl_sched_graph
*graph
)
4380 for (i
= 0; i
< graph
->n_edge
; ++i
)
4381 if (is_coincidence(&graph
->edge
[i
]))
4387 /* Extract the final schedule row as a map with the iteration domain
4388 * of "node" as domain.
4390 static __isl_give isl_map
*final_row(struct isl_sched_node
*node
)
4395 row
= isl_mat_rows(node
->sched
) - 1;
4396 ma
= node_extract_partial_schedule_multi_aff(node
, row
, 1);
4397 return isl_map_from_multi_aff(ma
);
4400 /* Is the conditional validity dependence in the edge with index "edge_index"
4401 * violated by the latest (i.e., final) row of the schedule?
4402 * That is, is i scheduled after j
4403 * for any conditional validity dependence i -> j?
4405 static int is_violated(struct isl_sched_graph
*graph
, int edge_index
)
4407 isl_map
*src_sched
, *dst_sched
, *map
;
4408 struct isl_sched_edge
*edge
= &graph
->edge
[edge_index
];
4411 src_sched
= final_row(edge
->src
);
4412 dst_sched
= final_row(edge
->dst
);
4413 map
= isl_map_copy(edge
->map
);
4414 map
= isl_map_apply_domain(map
, src_sched
);
4415 map
= isl_map_apply_range(map
, dst_sched
);
4416 map
= isl_map_order_gt(map
, isl_dim_in
, 0, isl_dim_out
, 0);
4417 empty
= isl_map_is_empty(map
);
4426 /* Does "graph" have any satisfied condition edges that
4427 * are adjacent to the conditional validity constraint with
4428 * domain "conditional_source" and range "conditional_sink"?
4430 * A satisfied condition is one that is not local.
4431 * If a condition was forced to be local already (i.e., marked as local)
4432 * then there is no need to check if it is in fact local.
4434 * Additionally, mark all adjacent condition edges found as local.
4436 static int has_adjacent_true_conditions(struct isl_sched_graph
*graph
,
4437 __isl_keep isl_union_set
*conditional_source
,
4438 __isl_keep isl_union_set
*conditional_sink
)
4443 for (i
= 0; i
< graph
->n_edge
; ++i
) {
4444 int adjacent
, local
;
4445 isl_union_map
*condition
;
4447 if (!is_condition(&graph
->edge
[i
]))
4449 if (is_local(&graph
->edge
[i
]))
4452 condition
= graph
->edge
[i
].tagged_condition
;
4453 adjacent
= domain_intersects(condition
, conditional_sink
);
4454 if (adjacent
>= 0 && !adjacent
)
4455 adjacent
= range_intersects(condition
,
4456 conditional_source
);
4462 set_local(&graph
->edge
[i
]);
4464 local
= is_condition_false(&graph
->edge
[i
]);
4474 /* Are there any violated conditional validity dependences with
4475 * adjacent condition dependences that are not local with respect
4476 * to the current schedule?
4477 * That is, is the conditional validity constraint violated?
4479 * Additionally, mark all those adjacent condition dependences as local.
4480 * We also mark those adjacent condition dependences that were not marked
4481 * as local before, but just happened to be local already. This ensures
4482 * that they remain local if the schedule is recomputed.
4484 * We first collect domain and range of all violated conditional validity
4485 * dependences and then check if there are any adjacent non-local
4486 * condition dependences.
4488 static int has_violated_conditional_constraint(isl_ctx
*ctx
,
4489 struct isl_sched_graph
*graph
)
4493 isl_union_set
*source
, *sink
;
4495 source
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
4496 sink
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
4497 for (i
= 0; i
< graph
->n_edge
; ++i
) {
4498 isl_union_set
*uset
;
4499 isl_union_map
*umap
;
4502 if (!is_conditional_validity(&graph
->edge
[i
]))
4505 violated
= is_violated(graph
, i
);
4513 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_validity
);
4514 uset
= isl_union_map_domain(umap
);
4515 source
= isl_union_set_union(source
, uset
);
4516 source
= isl_union_set_coalesce(source
);
4518 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_validity
);
4519 uset
= isl_union_map_range(umap
);
4520 sink
= isl_union_set_union(sink
, uset
);
4521 sink
= isl_union_set_coalesce(sink
);
4525 any
= has_adjacent_true_conditions(graph
, source
, sink
);
4527 isl_union_set_free(source
);
4528 isl_union_set_free(sink
);
4531 isl_union_set_free(source
);
4532 isl_union_set_free(sink
);
4536 /* Examine the current band (the rows between graph->band_start and
4537 * graph->n_total_row), deciding whether to drop it or add it to "node"
4538 * and then continue with the computation of the next band, if any.
4539 * If "initialized" is set, then it may be assumed that compute_maxvar
4540 * has been called on the current band. Otherwise, call
4541 * compute_maxvar if and before carry_dependences gets called.
4543 * The caller keeps looking for a new row as long as
4544 * graph->n_row < graph->maxvar. If the latest attempt to find
4545 * such a row failed (i.e., we still have graph->n_row < graph->maxvar),
4547 * - split between SCCs and start over (assuming we found an interesting
4548 * pair of SCCs between which to split)
4549 * - continue with the next band (assuming the current band has at least
4551 * - try to carry as many dependences as possible and continue with the next
4553 * In each case, we first insert a band node in the schedule tree
4554 * if any rows have been computed.
4556 * If the caller managed to complete the schedule, we insert a band node
4557 * (if any schedule rows were computed) and we finish off by topologically
4558 * sorting the statements based on the remaining dependences.
4560 static __isl_give isl_schedule_node
*compute_schedule_finish_band(
4561 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
4569 if (graph
->n_row
< graph
->maxvar
) {
4571 int empty
= graph
->n_total_row
== graph
->band_start
;
4573 ctx
= isl_schedule_node_get_ctx(node
);
4574 if (!ctx
->opt
->schedule_maximize_band_depth
&& !empty
)
4575 return compute_next_band(node
, graph
, 1);
4576 if (graph
->src_scc
>= 0)
4577 return compute_split_schedule(node
, graph
);
4579 return compute_next_band(node
, graph
, 1);
4580 if (!initialized
&& compute_maxvar(graph
) < 0)
4581 return isl_schedule_node_free(node
);
4582 return carry_dependences(node
, graph
);
4585 insert
= graph
->n_total_row
> graph
->band_start
;
4587 node
= insert_current_band(node
, graph
, 1);
4588 node
= isl_schedule_node_child(node
, 0);
4590 node
= sort_statements(node
, graph
, initialized
);
4592 node
= isl_schedule_node_parent(node
);
4597 /* Construct a band of schedule rows for a connected dependence graph.
4598 * The caller is responsible for determining the strongly connected
4599 * components and calling compute_maxvar first.
4601 * We try to find a sequence of as many schedule rows as possible that result
4602 * in non-negative dependence distances (independent of the previous rows
4603 * in the sequence, i.e., such that the sequence is tilable), with as
4604 * many of the initial rows as possible satisfying the coincidence constraints.
4605 * The computation stops if we can't find any more rows or if we have found
4606 * all the rows we wanted to find.
4608 * If ctx->opt->schedule_outer_coincidence is set, then we force the
4609 * outermost dimension to satisfy the coincidence constraints. If this
4610 * turns out to be impossible, we fall back on the general scheme above
4611 * and try to carry as many dependences as possible.
4613 * If "graph" contains both condition and conditional validity dependences,
4614 * then we need to check that that the conditional schedule constraint
4615 * is satisfied, i.e., there are no violated conditional validity dependences
4616 * that are adjacent to any non-local condition dependences.
4617 * If there are, then we mark all those adjacent condition dependences
4618 * as local and recompute the current band. Those dependences that
4619 * are marked local will then be forced to be local.
4620 * The initial computation is performed with no dependences marked as local.
4621 * If we are lucky, then there will be no violated conditional validity
4622 * dependences adjacent to any non-local condition dependences.
4623 * Otherwise, we mark some additional condition dependences as local and
4624 * recompute. We continue this process until there are no violations left or
4625 * until we are no longer able to compute a schedule.
4626 * Since there are only a finite number of dependences,
4627 * there will only be a finite number of iterations.
4629 static isl_stat
compute_schedule_wcc_band(isl_ctx
*ctx
,
4630 struct isl_sched_graph
*graph
)
4632 int has_coincidence
;
4633 int use_coincidence
;
4634 int force_coincidence
= 0;
4635 int check_conditional
;
4637 if (sort_sccs(graph
) < 0)
4638 return isl_stat_error
;
4640 clear_local_edges(graph
);
4641 check_conditional
= need_condition_check(graph
);
4642 has_coincidence
= has_any_coincidence(graph
);
4644 if (ctx
->opt
->schedule_outer_coincidence
)
4645 force_coincidence
= 1;
4647 use_coincidence
= has_coincidence
;
4648 while (graph
->n_row
< graph
->maxvar
) {
4653 graph
->src_scc
= -1;
4654 graph
->dst_scc
= -1;
4656 if (setup_lp(ctx
, graph
, use_coincidence
) < 0)
4657 return isl_stat_error
;
4658 sol
= solve_lp(graph
);
4660 return isl_stat_error
;
4661 if (sol
->size
== 0) {
4662 int empty
= graph
->n_total_row
== graph
->band_start
;
4665 if (use_coincidence
&& (!force_coincidence
|| !empty
)) {
4666 use_coincidence
= 0;
4671 coincident
= !has_coincidence
|| use_coincidence
;
4672 if (update_schedule(graph
, sol
, 1, coincident
) < 0)
4673 return isl_stat_error
;
4675 if (!check_conditional
)
4677 violated
= has_violated_conditional_constraint(ctx
, graph
);
4679 return isl_stat_error
;
4682 if (reset_band(graph
) < 0)
4683 return isl_stat_error
;
4684 use_coincidence
= has_coincidence
;
4690 /* Compute a schedule for a connected dependence graph by considering
4691 * the graph as a whole and return the updated schedule node.
4693 * The actual schedule rows of the current band are computed by
4694 * compute_schedule_wcc_band. compute_schedule_finish_band takes
4695 * care of integrating the band into "node" and continuing
4698 static __isl_give isl_schedule_node
*compute_schedule_wcc_whole(
4699 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
4706 ctx
= isl_schedule_node_get_ctx(node
);
4707 if (compute_schedule_wcc_band(ctx
, graph
) < 0)
4708 return isl_schedule_node_free(node
);
4710 return compute_schedule_finish_band(node
, graph
, 1);
4713 /* Clustering information used by compute_schedule_wcc_clustering.
4715 * "n" is the number of SCCs in the original dependence graph
4716 * "scc" is an array of "n" elements, each representing an SCC
4717 * of the original dependence graph. All entries in the same cluster
4718 * have the same number of schedule rows.
4719 * "scc_cluster" maps each SCC index to the cluster to which it belongs,
4720 * where each cluster is represented by the index of the first SCC
4721 * in the cluster. Initially, each SCC belongs to a cluster containing
4724 * "scc_in_merge" is used by merge_clusters_along_edge to keep
4725 * track of which SCCs need to be merged.
4727 * "cluster" contains the merged clusters of SCCs after the clustering
4730 * "scc_node" is a temporary data structure used inside copy_partial.
4731 * For each SCC, it keeps track of the number of nodes in the SCC
4732 * that have already been copied.
4734 struct isl_clustering
{
4736 struct isl_sched_graph
*scc
;
4737 struct isl_sched_graph
*cluster
;
4743 /* Initialize the clustering data structure "c" from "graph".
4745 * In particular, allocate memory, extract the SCCs from "graph"
4746 * into c->scc, initialize scc_cluster and construct
4747 * a band of schedule rows for each SCC.
4748 * Within each SCC, there is only one SCC by definition.
4749 * Each SCC initially belongs to a cluster containing only that SCC.
4751 static isl_stat
clustering_init(isl_ctx
*ctx
, struct isl_clustering
*c
,
4752 struct isl_sched_graph
*graph
)
4757 c
->scc
= isl_calloc_array(ctx
, struct isl_sched_graph
, c
->n
);
4758 c
->cluster
= isl_calloc_array(ctx
, struct isl_sched_graph
, c
->n
);
4759 c
->scc_cluster
= isl_calloc_array(ctx
, int, c
->n
);
4760 c
->scc_node
= isl_calloc_array(ctx
, int, c
->n
);
4761 c
->scc_in_merge
= isl_calloc_array(ctx
, int, c
->n
);
4762 if (!c
->scc
|| !c
->cluster
||
4763 !c
->scc_cluster
|| !c
->scc_node
|| !c
->scc_in_merge
)
4764 return isl_stat_error
;
4766 for (i
= 0; i
< c
->n
; ++i
) {
4767 if (extract_sub_graph(ctx
, graph
, &node_scc_exactly
,
4768 &edge_scc_exactly
, i
, &c
->scc
[i
]) < 0)
4769 return isl_stat_error
;
4771 if (compute_maxvar(&c
->scc
[i
]) < 0)
4772 return isl_stat_error
;
4773 if (compute_schedule_wcc_band(ctx
, &c
->scc
[i
]) < 0)
4774 return isl_stat_error
;
4775 c
->scc_cluster
[i
] = i
;
4781 /* Free all memory allocated for "c".
4783 static void clustering_free(isl_ctx
*ctx
, struct isl_clustering
*c
)
4788 for (i
= 0; i
< c
->n
; ++i
)
4789 graph_free(ctx
, &c
->scc
[i
]);
4792 for (i
= 0; i
< c
->n
; ++i
)
4793 graph_free(ctx
, &c
->cluster
[i
]);
4795 free(c
->scc_cluster
);
4797 free(c
->scc_in_merge
);
4800 /* Should we refrain from merging the cluster in "graph" with
4801 * any other cluster?
4802 * In particular, is its current schedule band empty and incomplete.
4804 static int bad_cluster(struct isl_sched_graph
*graph
)
4806 return graph
->n_row
< graph
->maxvar
&&
4807 graph
->n_total_row
== graph
->band_start
;
4810 /* Return the index of an edge in "graph" that can be used to merge
4811 * two clusters in "c".
4812 * Return graph->n_edge if no such edge can be found.
4813 * Return -1 on error.
4815 * In particular, return a proximity edge between two clusters
4816 * that is not marked "no_merge" and such that neither of the
4817 * two clusters has an incomplete, empty band.
4819 * If there are multiple such edges, then try and find the most
4820 * appropriate edge to use for merging. In particular, pick the edge
4821 * with the greatest weight. If there are multiple of those,
4822 * then pick one with the shortest distance between
4823 * the two cluster representatives.
4825 static int find_proximity(struct isl_sched_graph
*graph
,
4826 struct isl_clustering
*c
)
4828 int i
, best
= graph
->n_edge
, best_dist
, best_weight
;
4830 for (i
= 0; i
< graph
->n_edge
; ++i
) {
4831 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
4834 if (!is_proximity(edge
))
4838 if (bad_cluster(&c
->scc
[edge
->src
->scc
]) ||
4839 bad_cluster(&c
->scc
[edge
->dst
->scc
]))
4841 dist
= c
->scc_cluster
[edge
->dst
->scc
] -
4842 c
->scc_cluster
[edge
->src
->scc
];
4845 weight
= edge
->weight
;
4846 if (best
< graph
->n_edge
) {
4847 if (best_weight
> weight
)
4849 if (best_weight
== weight
&& best_dist
<= dist
)
4854 best_weight
= weight
;
4860 /* Internal data structure used in mark_merge_sccs.
4862 * "graph" is the dependence graph in which a strongly connected
4863 * component is constructed.
4864 * "scc_cluster" maps each SCC index to the cluster to which it belongs.
4865 * "src" and "dst" are the indices of the nodes that are being merged.
4867 struct isl_mark_merge_sccs_data
{
4868 struct isl_sched_graph
*graph
;
4874 /* Check whether the cluster containing node "i" depends on the cluster
4875 * containing node "j". If "i" and "j" belong to the same cluster,
4876 * then they are taken to depend on each other to ensure that
4877 * the resulting strongly connected component consists of complete
4878 * clusters. Furthermore, if "i" and "j" are the two nodes that
4879 * are being merged, then they are taken to depend on each other as well.
4880 * Otherwise, check if there is a (conditional) validity dependence
4881 * from node[j] to node[i], forcing node[i] to follow node[j].
4883 static isl_bool
cluster_follows(int i
, int j
, void *user
)
4885 struct isl_mark_merge_sccs_data
*data
= user
;
4886 struct isl_sched_graph
*graph
= data
->graph
;
4887 int *scc_cluster
= data
->scc_cluster
;
4889 if (data
->src
== i
&& data
->dst
== j
)
4890 return isl_bool_true
;
4891 if (data
->src
== j
&& data
->dst
== i
)
4892 return isl_bool_true
;
4893 if (scc_cluster
[graph
->node
[i
].scc
] == scc_cluster
[graph
->node
[j
].scc
])
4894 return isl_bool_true
;
4896 return graph_has_validity_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
4899 /* Mark all SCCs that belong to either of the two clusters in "c"
4900 * connected by the edge in "graph" with index "edge", or to any
4901 * of the intermediate clusters.
4902 * The marking is recorded in c->scc_in_merge.
4904 * The given edge has been selected for merging two clusters,
4905 * meaning that there is at least a proximity edge between the two nodes.
4906 * However, there may also be (indirect) validity dependences
4907 * between the two nodes. When merging the two clusters, all clusters
4908 * containing one or more of the intermediate nodes along the
4909 * indirect validity dependences need to be merged in as well.
4911 * First collect all such nodes by computing the strongly connected
4912 * component (SCC) containing the two nodes connected by the edge, where
4913 * the two nodes are considered to depend on each other to make
4914 * sure they end up in the same SCC. Similarly, each node is considered
4915 * to depend on every other node in the same cluster to ensure
4916 * that the SCC consists of complete clusters.
4918 * Then the original SCCs that contain any of these nodes are marked
4919 * in c->scc_in_merge.
4921 static isl_stat
mark_merge_sccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
4922 int edge
, struct isl_clustering
*c
)
4924 struct isl_mark_merge_sccs_data data
;
4925 struct isl_tarjan_graph
*g
;
4928 for (i
= 0; i
< c
->n
; ++i
)
4929 c
->scc_in_merge
[i
] = 0;
4932 data
.scc_cluster
= c
->scc_cluster
;
4933 data
.src
= graph
->edge
[edge
].src
- graph
->node
;
4934 data
.dst
= graph
->edge
[edge
].dst
- graph
->node
;
4936 g
= isl_tarjan_graph_component(ctx
, graph
->n
, data
.dst
,
4937 &cluster_follows
, &data
);
4943 isl_die(ctx
, isl_error_internal
,
4944 "expecting at least two nodes in component",
4946 if (g
->order
[--i
] != -1)
4947 isl_die(ctx
, isl_error_internal
,
4948 "expecting end of component marker", goto error
);
4950 for (--i
; i
>= 0 && g
->order
[i
] != -1; --i
) {
4951 int scc
= graph
->node
[g
->order
[i
]].scc
;
4952 c
->scc_in_merge
[scc
] = 1;
4955 isl_tarjan_graph_free(g
);
4958 isl_tarjan_graph_free(g
);
4959 return isl_stat_error
;
4962 /* Construct the identifier "cluster_i".
4964 static __isl_give isl_id
*cluster_id(isl_ctx
*ctx
, int i
)
4968 snprintf(name
, sizeof(name
), "cluster_%d", i
);
4969 return isl_id_alloc(ctx
, name
, NULL
);
4972 /* Construct the space of the cluster with index "i" containing
4973 * the strongly connected component "scc".
4975 * In particular, construct a space called cluster_i with dimension equal
4976 * to the number of schedule rows in the current band of "scc".
4978 static __isl_give isl_space
*cluster_space(struct isl_sched_graph
*scc
, int i
)
4984 nvar
= scc
->n_total_row
- scc
->band_start
;
4985 space
= isl_space_copy(scc
->node
[0].space
);
4986 space
= isl_space_params(space
);
4987 space
= isl_space_set_from_params(space
);
4988 space
= isl_space_add_dims(space
, isl_dim_set
, nvar
);
4989 id
= cluster_id(isl_space_get_ctx(space
), i
);
4990 space
= isl_space_set_tuple_id(space
, isl_dim_set
, id
);
4995 /* Collect the domain of the graph for merging clusters.
4997 * In particular, for each cluster with first SCC "i", construct
4998 * a set in the space called cluster_i with dimension equal
4999 * to the number of schedule rows in the current band of the cluster.
5001 static __isl_give isl_union_set
*collect_domain(isl_ctx
*ctx
,
5002 struct isl_sched_graph
*graph
, struct isl_clustering
*c
)
5006 isl_union_set
*domain
;
5008 space
= isl_space_params_alloc(ctx
, 0);
5009 domain
= isl_union_set_empty(space
);
5011 for (i
= 0; i
< graph
->scc
; ++i
) {
5014 if (!c
->scc_in_merge
[i
])
5016 if (c
->scc_cluster
[i
] != i
)
5018 space
= cluster_space(&c
->scc
[i
], i
);
5019 domain
= isl_union_set_add_set(domain
, isl_set_universe(space
));
5025 /* Construct a map from the original instances to the corresponding
5026 * cluster instance in the current bands of the clusters in "c".
5028 static __isl_give isl_union_map
*collect_cluster_map(isl_ctx
*ctx
,
5029 struct isl_sched_graph
*graph
, struct isl_clustering
*c
)
5033 isl_union_map
*cluster_map
;
5035 space
= isl_space_params_alloc(ctx
, 0);
5036 cluster_map
= isl_union_map_empty(space
);
5037 for (i
= 0; i
< graph
->scc
; ++i
) {
5041 if (!c
->scc_in_merge
[i
])
5044 id
= cluster_id(ctx
, c
->scc_cluster
[i
]);
5045 start
= c
->scc
[i
].band_start
;
5046 n
= c
->scc
[i
].n_total_row
- start
;
5047 for (j
= 0; j
< c
->scc
[i
].n
; ++j
) {
5050 struct isl_sched_node
*node
= &c
->scc
[i
].node
[j
];
5052 ma
= node_extract_partial_schedule_multi_aff(node
,
5054 ma
= isl_multi_aff_set_tuple_id(ma
, isl_dim_out
,
5056 map
= isl_map_from_multi_aff(ma
);
5057 cluster_map
= isl_union_map_add_map(cluster_map
, map
);
5065 /* Add "umap" to the schedule constraints "sc" of all types of "edge"
5066 * that are not isl_edge_condition or isl_edge_conditional_validity.
5068 static __isl_give isl_schedule_constraints
*add_non_conditional_constraints(
5069 struct isl_sched_edge
*edge
, __isl_keep isl_union_map
*umap
,
5070 __isl_take isl_schedule_constraints
*sc
)
5072 enum isl_edge_type t
;
5077 for (t
= isl_edge_first
; t
<= isl_edge_last
; ++t
) {
5078 if (t
== isl_edge_condition
||
5079 t
== isl_edge_conditional_validity
)
5081 if (!is_type(edge
, t
))
5083 sc
= isl_schedule_constraints_add(sc
, t
,
5084 isl_union_map_copy(umap
));
5090 /* Add schedule constraints of types isl_edge_condition and
5091 * isl_edge_conditional_validity to "sc" by applying "umap" to
5092 * the domains of the wrapped relations in domain and range
5093 * of the corresponding tagged constraints of "edge".
5095 static __isl_give isl_schedule_constraints
*add_conditional_constraints(
5096 struct isl_sched_edge
*edge
, __isl_keep isl_union_map
*umap
,
5097 __isl_take isl_schedule_constraints
*sc
)
5099 enum isl_edge_type t
;
5100 isl_union_map
*tagged
;
5102 for (t
= isl_edge_condition
; t
<= isl_edge_conditional_validity
; ++t
) {
5103 if (!is_type(edge
, t
))
5105 if (t
== isl_edge_condition
)
5106 tagged
= isl_union_map_copy(edge
->tagged_condition
);
5108 tagged
= isl_union_map_copy(edge
->tagged_validity
);
5109 tagged
= isl_union_map_zip(tagged
);
5110 tagged
= isl_union_map_apply_domain(tagged
,
5111 isl_union_map_copy(umap
));
5112 tagged
= isl_union_map_zip(tagged
);
5113 sc
= isl_schedule_constraints_add(sc
, t
, tagged
);
5121 /* Given a mapping "cluster_map" from the original instances to
5122 * the cluster instances, add schedule constraints on the clusters
5123 * to "sc" corresponding to the original constraints represented by "edge".
5125 * For non-tagged dependence constraints, the cluster constraints
5126 * are obtained by applying "cluster_map" to the edge->map.
5128 * For tagged dependence constraints, "cluster_map" needs to be applied
5129 * to the domains of the wrapped relations in domain and range
5130 * of the tagged dependence constraints. Pick out the mappings
5131 * from these domains from "cluster_map" and construct their product.
5132 * This mapping can then be applied to the pair of domains.
5134 static __isl_give isl_schedule_constraints
*collect_edge_constraints(
5135 struct isl_sched_edge
*edge
, __isl_keep isl_union_map
*cluster_map
,
5136 __isl_take isl_schedule_constraints
*sc
)
5138 isl_union_map
*umap
;
5140 isl_union_set
*uset
;
5141 isl_union_map
*umap1
, *umap2
;
5146 umap
= isl_union_map_from_map(isl_map_copy(edge
->map
));
5147 umap
= isl_union_map_apply_domain(umap
,
5148 isl_union_map_copy(cluster_map
));
5149 umap
= isl_union_map_apply_range(umap
,
5150 isl_union_map_copy(cluster_map
));
5151 sc
= add_non_conditional_constraints(edge
, umap
, sc
);
5152 isl_union_map_free(umap
);
5154 if (!sc
|| (!is_condition(edge
) && !is_conditional_validity(edge
)))
5157 space
= isl_space_domain(isl_map_get_space(edge
->map
));
5158 uset
= isl_union_set_from_set(isl_set_universe(space
));
5159 umap1
= isl_union_map_copy(cluster_map
);
5160 umap1
= isl_union_map_intersect_domain(umap1
, uset
);
5161 space
= isl_space_range(isl_map_get_space(edge
->map
));
5162 uset
= isl_union_set_from_set(isl_set_universe(space
));
5163 umap2
= isl_union_map_copy(cluster_map
);
5164 umap2
= isl_union_map_intersect_domain(umap2
, uset
);
5165 umap
= isl_union_map_product(umap1
, umap2
);
5167 sc
= add_conditional_constraints(edge
, umap
, sc
);
5169 isl_union_map_free(umap
);
5173 /* Given a mapping "cluster_map" from the original instances to
5174 * the cluster instances, add schedule constraints on the clusters
5175 * to "sc" corresponding to all edges in "graph" between nodes that
5176 * belong to SCCs that are marked for merging in "scc_in_merge".
5178 static __isl_give isl_schedule_constraints
*collect_constraints(
5179 struct isl_sched_graph
*graph
, int *scc_in_merge
,
5180 __isl_keep isl_union_map
*cluster_map
,
5181 __isl_take isl_schedule_constraints
*sc
)
5185 for (i
= 0; i
< graph
->n_edge
; ++i
) {
5186 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
5188 if (!scc_in_merge
[edge
->src
->scc
])
5190 if (!scc_in_merge
[edge
->dst
->scc
])
5192 sc
= collect_edge_constraints(edge
, cluster_map
, sc
);
5198 /* Construct a dependence graph for scheduling clusters with respect
5199 * to each other and store the result in "merge_graph".
5200 * In particular, the nodes of the graph correspond to the schedule
5201 * dimensions of the current bands of those clusters that have been
5202 * marked for merging in "c".
5204 * First construct an isl_schedule_constraints object for this domain
5205 * by transforming the edges in "graph" to the domain.
5206 * Then initialize a dependence graph for scheduling from these
5209 static isl_stat
init_merge_graph(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
5210 struct isl_clustering
*c
, struct isl_sched_graph
*merge_graph
)
5212 isl_union_set
*domain
;
5213 isl_union_map
*cluster_map
;
5214 isl_schedule_constraints
*sc
;
5217 domain
= collect_domain(ctx
, graph
, c
);
5218 sc
= isl_schedule_constraints_on_domain(domain
);
5220 return isl_stat_error
;
5221 cluster_map
= collect_cluster_map(ctx
, graph
, c
);
5222 sc
= collect_constraints(graph
, c
->scc_in_merge
, cluster_map
, sc
);
5223 isl_union_map_free(cluster_map
);
5225 r
= graph_init(merge_graph
, sc
);
5227 isl_schedule_constraints_free(sc
);
5232 /* Compute the maximal number of remaining schedule rows that still need
5233 * to be computed for the nodes that belong to clusters with the maximal
5234 * dimension for the current band (i.e., the band that is to be merged).
5235 * Only clusters that are about to be merged are considered.
5236 * "maxvar" is the maximal dimension for the current band.
5237 * "c" contains information about the clusters.
5239 * Return the maximal number of remaining schedule rows or -1 on error.
5241 static int compute_maxvar_max_slack(int maxvar
, struct isl_clustering
*c
)
5247 for (i
= 0; i
< c
->n
; ++i
) {
5249 struct isl_sched_graph
*scc
;
5251 if (!c
->scc_in_merge
[i
])
5254 nvar
= scc
->n_total_row
- scc
->band_start
;
5257 for (j
= 0; j
< scc
->n
; ++j
) {
5258 struct isl_sched_node
*node
= &scc
->node
[j
];
5261 if (node_update_cmap(node
) < 0)
5263 slack
= node
->nvar
- node
->rank
;
5264 if (slack
> max_slack
)
5272 /* If there are any clusters where the dimension of the current band
5273 * (i.e., the band that is to be merged) is smaller than "maxvar" and
5274 * if there are any nodes in such a cluster where the number
5275 * of remaining schedule rows that still need to be computed
5276 * is greater than "max_slack", then return the smallest current band
5277 * dimension of all these clusters. Otherwise return the original value
5278 * of "maxvar". Return -1 in case of any error.
5279 * Only clusters that are about to be merged are considered.
5280 * "c" contains information about the clusters.
5282 static int limit_maxvar_to_slack(int maxvar
, int max_slack
,
5283 struct isl_clustering
*c
)
5287 for (i
= 0; i
< c
->n
; ++i
) {
5289 struct isl_sched_graph
*scc
;
5291 if (!c
->scc_in_merge
[i
])
5294 nvar
= scc
->n_total_row
- scc
->band_start
;
5297 for (j
= 0; j
< scc
->n
; ++j
) {
5298 struct isl_sched_node
*node
= &scc
->node
[j
];
5301 if (node_update_cmap(node
) < 0)
5303 slack
= node
->nvar
- node
->rank
;
5304 if (slack
> max_slack
) {
5314 /* Adjust merge_graph->maxvar based on the number of remaining schedule rows
5315 * that still need to be computed. In particular, if there is a node
5316 * in a cluster where the dimension of the current band is smaller
5317 * than merge_graph->maxvar, but the number of remaining schedule rows
5318 * is greater than that of any node in a cluster with the maximal
5319 * dimension for the current band (i.e., merge_graph->maxvar),
5320 * then adjust merge_graph->maxvar to the (smallest) current band dimension
5321 * of those clusters. Without this adjustment, the total number of
5322 * schedule dimensions would be increased, resulting in a skewed view
5323 * of the number of coincident dimensions.
5324 * "c" contains information about the clusters.
5326 * If the maximize_band_depth option is set and merge_graph->maxvar is reduced,
5327 * then there is no point in attempting any merge since it will be rejected
5328 * anyway. Set merge_graph->maxvar to zero in such cases.
5330 static isl_stat
adjust_maxvar_to_slack(isl_ctx
*ctx
,
5331 struct isl_sched_graph
*merge_graph
, struct isl_clustering
*c
)
5333 int max_slack
, maxvar
;
5335 max_slack
= compute_maxvar_max_slack(merge_graph
->maxvar
, c
);
5337 return isl_stat_error
;
5338 maxvar
= limit_maxvar_to_slack(merge_graph
->maxvar
, max_slack
, c
);
5340 return isl_stat_error
;
5342 if (maxvar
< merge_graph
->maxvar
) {
5343 if (isl_options_get_schedule_maximize_band_depth(ctx
))
5344 merge_graph
->maxvar
= 0;
5346 merge_graph
->maxvar
= maxvar
;
5352 /* Return the number of coincident dimensions in the current band of "graph",
5353 * where the nodes of "graph" are assumed to be scheduled by a single band.
5355 static int get_n_coincident(struct isl_sched_graph
*graph
)
5359 for (i
= graph
->band_start
; i
< graph
->n_total_row
; ++i
)
5360 if (!graph
->node
[0].coincident
[i
])
5363 return i
- graph
->band_start
;
5366 /* Should the clusters be merged based on the cluster schedule
5367 * in the current (and only) band of "merge_graph", given that
5368 * coincidence should be maximized?
5370 * If the number of coincident schedule dimensions in the merged band
5371 * would be less than the maximal number of coincident schedule dimensions
5372 * in any of the merged clusters, then the clusters should not be merged.
5374 static isl_bool
ok_to_merge_coincident(struct isl_clustering
*c
,
5375 struct isl_sched_graph
*merge_graph
)
5382 for (i
= 0; i
< c
->n
; ++i
) {
5383 if (!c
->scc_in_merge
[i
])
5385 n_coincident
= get_n_coincident(&c
->scc
[i
]);
5386 if (n_coincident
> max_coincident
)
5387 max_coincident
= n_coincident
;
5390 n_coincident
= get_n_coincident(merge_graph
);
5392 return n_coincident
>= max_coincident
;
5395 /* Return the transformation on "node" expressed by the current (and only)
5396 * band of "merge_graph" applied to the clusters in "c".
5398 * First find the representation of "node" in its SCC in "c" and
5399 * extract the transformation expressed by the current band.
5400 * Then extract the transformation applied by "merge_graph"
5401 * to the cluster to which this SCC belongs.
5402 * Combine the two to obtain the complete transformation on the node.
5404 * Note that the range of the first transformation is an anonymous space,
5405 * while the domain of the second is named "cluster_X". The range
5406 * of the former therefore needs to be adjusted before the two
5409 static __isl_give isl_map
*extract_node_transformation(isl_ctx
*ctx
,
5410 struct isl_sched_node
*node
, struct isl_clustering
*c
,
5411 struct isl_sched_graph
*merge_graph
)
5413 struct isl_sched_node
*scc_node
, *cluster_node
;
5417 isl_multi_aff
*ma
, *ma2
;
5419 scc_node
= graph_find_node(ctx
, &c
->scc
[node
->scc
], node
->space
);
5420 start
= c
->scc
[node
->scc
].band_start
;
5421 n
= c
->scc
[node
->scc
].n_total_row
- start
;
5422 ma
= node_extract_partial_schedule_multi_aff(scc_node
, start
, n
);
5423 space
= cluster_space(&c
->scc
[node
->scc
], c
->scc_cluster
[node
->scc
]);
5424 cluster_node
= graph_find_node(ctx
, merge_graph
, space
);
5425 if (space
&& !cluster_node
)
5426 isl_die(ctx
, isl_error_internal
, "unable to find cluster",
5427 space
= isl_space_free(space
));
5428 id
= isl_space_get_tuple_id(space
, isl_dim_set
);
5429 ma
= isl_multi_aff_set_tuple_id(ma
, isl_dim_out
, id
);
5430 isl_space_free(space
);
5431 n
= merge_graph
->n_total_row
;
5432 ma2
= node_extract_partial_schedule_multi_aff(cluster_node
, 0, n
);
5433 ma
= isl_multi_aff_pullback_multi_aff(ma2
, ma
);
5435 return isl_map_from_multi_aff(ma
);
5438 /* Give a set of distances "set", are they bounded by a small constant
5439 * in direction "pos"?
5440 * In practice, check if they are bounded by 2 by checking that there
5441 * are no elements with a value greater than or equal to 3 or
5442 * smaller than or equal to -3.
5444 static isl_bool
distance_is_bounded(__isl_keep isl_set
*set
, int pos
)
5450 return isl_bool_error
;
5452 test
= isl_set_copy(set
);
5453 test
= isl_set_lower_bound_si(test
, isl_dim_set
, pos
, 3);
5454 bounded
= isl_set_is_empty(test
);
5457 if (bounded
< 0 || !bounded
)
5460 test
= isl_set_copy(set
);
5461 test
= isl_set_upper_bound_si(test
, isl_dim_set
, pos
, -3);
5462 bounded
= isl_set_is_empty(test
);
5468 /* Does the set "set" have a fixed (but possible parametric) value
5469 * at dimension "pos"?
5471 static isl_bool
has_single_value(__isl_keep isl_set
*set
, int pos
)
5477 return isl_bool_error
;
5478 set
= isl_set_copy(set
);
5479 n
= isl_set_dim(set
, isl_dim_set
);
5480 set
= isl_set_project_out(set
, isl_dim_set
, pos
+ 1, n
- (pos
+ 1));
5481 set
= isl_set_project_out(set
, isl_dim_set
, 0, pos
);
5482 single
= isl_set_is_singleton(set
);
5488 /* Does "map" have a fixed (but possible parametric) value
5489 * at dimension "pos" of either its domain or its range?
5491 static isl_bool
has_singular_src_or_dst(__isl_keep isl_map
*map
, int pos
)
5496 set
= isl_map_domain(isl_map_copy(map
));
5497 single
= has_single_value(set
, pos
);
5500 if (single
< 0 || single
)
5503 set
= isl_map_range(isl_map_copy(map
));
5504 single
= has_single_value(set
, pos
);
5510 /* Does the edge "edge" from "graph" have bounded dependence distances
5511 * in the merged graph "merge_graph" of a selection of clusters in "c"?
5513 * Extract the complete transformations of the source and destination
5514 * nodes of the edge, apply them to the edge constraints and
5515 * compute the differences. Finally, check if these differences are bounded
5516 * in each direction.
5518 * If the dimension of the band is greater than the number of
5519 * dimensions that can be expected to be optimized by the edge
5520 * (based on its weight), then also allow the differences to be unbounded
5521 * in the remaining dimensions, but only if either the source or
5522 * the destination has a fixed value in that direction.
5523 * This allows a statement that produces values that are used by
5524 * several instances of another statement to be merged with that
5526 * However, merging such clusters will introduce an inherently
5527 * large proximity distance inside the merged cluster, meaning
5528 * that proximity distances will no longer be optimized in
5529 * subsequent merges. These merges are therefore only allowed
5530 * after all other possible merges have been tried.
5531 * The first time such a merge is encountered, the weight of the edge
5532 * is replaced by a negative weight. The second time (i.e., after
5533 * all merges over edges with a non-negative weight have been tried),
5534 * the merge is allowed.
5536 static isl_bool
has_bounded_distances(isl_ctx
*ctx
, struct isl_sched_edge
*edge
,
5537 struct isl_sched_graph
*graph
, struct isl_clustering
*c
,
5538 struct isl_sched_graph
*merge_graph
)
5545 map
= isl_map_copy(edge
->map
);
5546 t
= extract_node_transformation(ctx
, edge
->src
, c
, merge_graph
);
5547 map
= isl_map_apply_domain(map
, t
);
5548 t
= extract_node_transformation(ctx
, edge
->dst
, c
, merge_graph
);
5549 map
= isl_map_apply_range(map
, t
);
5550 dist
= isl_map_deltas(isl_map_copy(map
));
5552 bounded
= isl_bool_true
;
5553 n
= isl_set_dim(dist
, isl_dim_set
);
5554 n_slack
= n
- edge
->weight
;
5555 if (edge
->weight
< 0)
5556 n_slack
-= graph
->max_weight
+ 1;
5557 for (i
= 0; i
< n
; ++i
) {
5558 isl_bool bounded_i
, singular_i
;
5560 bounded_i
= distance_is_bounded(dist
, i
);
5565 if (edge
->weight
>= 0)
5566 bounded
= isl_bool_false
;
5570 singular_i
= has_singular_src_or_dst(map
, i
);
5575 bounded
= isl_bool_false
;
5578 if (!bounded
&& i
>= n
&& edge
->weight
>= 0)
5579 edge
->weight
-= graph
->max_weight
+ 1;
5587 return isl_bool_error
;
5590 /* Should the clusters be merged based on the cluster schedule
5591 * in the current (and only) band of "merge_graph"?
5592 * "graph" is the original dependence graph, while "c" records
5593 * which SCCs are involved in the latest merge.
5595 * In particular, is there at least one proximity constraint
5596 * that is optimized by the merge?
5598 * A proximity constraint is considered to be optimized
5599 * if the dependence distances are small.
5601 static isl_bool
ok_to_merge_proximity(isl_ctx
*ctx
,
5602 struct isl_sched_graph
*graph
, struct isl_clustering
*c
,
5603 struct isl_sched_graph
*merge_graph
)
5607 for (i
= 0; i
< graph
->n_edge
; ++i
) {
5608 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
5611 if (!is_proximity(edge
))
5613 if (!c
->scc_in_merge
[edge
->src
->scc
])
5615 if (!c
->scc_in_merge
[edge
->dst
->scc
])
5617 if (c
->scc_cluster
[edge
->dst
->scc
] ==
5618 c
->scc_cluster
[edge
->src
->scc
])
5620 bounded
= has_bounded_distances(ctx
, edge
, graph
, c
,
5622 if (bounded
< 0 || bounded
)
5626 return isl_bool_false
;
5629 /* Should the clusters be merged based on the cluster schedule
5630 * in the current (and only) band of "merge_graph"?
5631 * "graph" is the original dependence graph, while "c" records
5632 * which SCCs are involved in the latest merge.
5634 * If the current band is empty, then the clusters should not be merged.
5636 * If the band depth should be maximized and the merge schedule
5637 * is incomplete (meaning that the dimension of some of the schedule
5638 * bands in the original schedule will be reduced), then the clusters
5639 * should not be merged.
5641 * If the schedule_maximize_coincidence option is set, then check that
5642 * the number of coincident schedule dimensions is not reduced.
5644 * Finally, only allow the merge if at least one proximity
5645 * constraint is optimized.
5647 static isl_bool
ok_to_merge(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
5648 struct isl_clustering
*c
, struct isl_sched_graph
*merge_graph
)
5650 if (merge_graph
->n_total_row
== merge_graph
->band_start
)
5651 return isl_bool_false
;
5653 if (isl_options_get_schedule_maximize_band_depth(ctx
) &&
5654 merge_graph
->n_total_row
< merge_graph
->maxvar
)
5655 return isl_bool_false
;
5657 if (isl_options_get_schedule_maximize_coincidence(ctx
)) {
5660 ok
= ok_to_merge_coincident(c
, merge_graph
);
5665 return ok_to_merge_proximity(ctx
, graph
, c
, merge_graph
);
5668 /* Apply the schedule in "t_node" to the "n" rows starting at "first"
5669 * of the schedule in "node" and return the result.
5671 * That is, essentially compute
5673 * T * N(first:first+n-1)
5675 * taking into account the constant term and the parameter coefficients
5678 static __isl_give isl_mat
*node_transformation(isl_ctx
*ctx
,
5679 struct isl_sched_node
*t_node
, struct isl_sched_node
*node
,
5684 int n_row
, n_col
, n_param
, n_var
;
5686 n_param
= node
->nparam
;
5688 n_row
= isl_mat_rows(t_node
->sched
);
5689 n_col
= isl_mat_cols(node
->sched
);
5690 t
= isl_mat_alloc(ctx
, n_row
, n_col
);
5693 for (i
= 0; i
< n_row
; ++i
) {
5694 isl_seq_cpy(t
->row
[i
], t_node
->sched
->row
[i
], 1 + n_param
);
5695 isl_seq_clr(t
->row
[i
] + 1 + n_param
, n_var
);
5696 for (j
= 0; j
< n
; ++j
)
5697 isl_seq_addmul(t
->row
[i
],
5698 t_node
->sched
->row
[i
][1 + n_param
+ j
],
5699 node
->sched
->row
[first
+ j
],
5700 1 + n_param
+ n_var
);
5705 /* Apply the cluster schedule in "t_node" to the current band
5706 * schedule of the nodes in "graph".
5708 * In particular, replace the rows starting at band_start
5709 * by the result of applying the cluster schedule in "t_node"
5710 * to the original rows.
5712 * The coincidence of the schedule is determined by the coincidence
5713 * of the cluster schedule.
5715 static isl_stat
transform(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
5716 struct isl_sched_node
*t_node
)
5722 start
= graph
->band_start
;
5723 n
= graph
->n_total_row
- start
;
5725 n_new
= isl_mat_rows(t_node
->sched
);
5726 for (i
= 0; i
< graph
->n
; ++i
) {
5727 struct isl_sched_node
*node
= &graph
->node
[i
];
5730 t
= node_transformation(ctx
, t_node
, node
, start
, n
);
5731 node
->sched
= isl_mat_drop_rows(node
->sched
, start
, n
);
5732 node
->sched
= isl_mat_concat(node
->sched
, t
);
5733 node
->sched_map
= isl_map_free(node
->sched_map
);
5735 return isl_stat_error
;
5736 for (j
= 0; j
< n_new
; ++j
)
5737 node
->coincident
[start
+ j
] = t_node
->coincident
[j
];
5739 graph
->n_total_row
-= n
;
5741 graph
->n_total_row
+= n_new
;
5742 graph
->n_row
+= n_new
;
5747 /* Merge the clusters marked for merging in "c" into a single
5748 * cluster using the cluster schedule in the current band of "merge_graph".
5749 * The representative SCC for the new cluster is the SCC with
5750 * the smallest index.
5752 * The current band schedule of each SCC in the new cluster is obtained
5753 * by applying the schedule of the corresponding original cluster
5754 * to the original band schedule.
5755 * All SCCs in the new cluster have the same number of schedule rows.
5757 static isl_stat
merge(isl_ctx
*ctx
, struct isl_clustering
*c
,
5758 struct isl_sched_graph
*merge_graph
)
5764 for (i
= 0; i
< c
->n
; ++i
) {
5765 struct isl_sched_node
*node
;
5767 if (!c
->scc_in_merge
[i
])
5771 space
= cluster_space(&c
->scc
[i
], c
->scc_cluster
[i
]);
5773 return isl_stat_error
;
5774 node
= graph_find_node(ctx
, merge_graph
, space
);
5775 isl_space_free(space
);
5777 isl_die(ctx
, isl_error_internal
,
5778 "unable to find cluster",
5779 return isl_stat_error
);
5780 if (transform(ctx
, &c
->scc
[i
], node
) < 0)
5781 return isl_stat_error
;
5782 c
->scc_cluster
[i
] = cluster
;
5788 /* Try and merge the clusters of SCCs marked in c->scc_in_merge
5789 * by scheduling the current cluster bands with respect to each other.
5791 * Construct a dependence graph with a space for each cluster and
5792 * with the coordinates of each space corresponding to the schedule
5793 * dimensions of the current band of that cluster.
5794 * Construct a cluster schedule in this cluster dependence graph and
5795 * apply it to the current cluster bands if it is applicable
5796 * according to ok_to_merge.
5798 * If the number of remaining schedule dimensions in a cluster
5799 * with a non-maximal current schedule dimension is greater than
5800 * the number of remaining schedule dimensions in clusters
5801 * with a maximal current schedule dimension, then restrict
5802 * the number of rows to be computed in the cluster schedule
5803 * to the minimal such non-maximal current schedule dimension.
5804 * Do this by adjusting merge_graph.maxvar.
5806 * Return isl_bool_true if the clusters have effectively been merged
5807 * into a single cluster.
5809 * Note that since the standard scheduling algorithm minimizes the maximal
5810 * distance over proximity constraints, the proximity constraints between
5811 * the merged clusters may not be optimized any further than what is
5812 * sufficient to bring the distances within the limits of the internal
5813 * proximity constraints inside the individual clusters.
5814 * It may therefore make sense to perform an additional translation step
5815 * to bring the clusters closer to each other, while maintaining
5816 * the linear part of the merging schedule found using the standard
5817 * scheduling algorithm.
5819 static isl_bool
try_merge(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
5820 struct isl_clustering
*c
)
5822 struct isl_sched_graph merge_graph
= { 0 };
5825 if (init_merge_graph(ctx
, graph
, c
, &merge_graph
) < 0)
5828 if (compute_maxvar(&merge_graph
) < 0)
5830 if (adjust_maxvar_to_slack(ctx
, &merge_graph
,c
) < 0)
5832 if (compute_schedule_wcc_band(ctx
, &merge_graph
) < 0)
5834 merged
= ok_to_merge(ctx
, graph
, c
, &merge_graph
);
5835 if (merged
&& merge(ctx
, c
, &merge_graph
) < 0)
5838 graph_free(ctx
, &merge_graph
);
5841 graph_free(ctx
, &merge_graph
);
5842 return isl_bool_error
;
5845 /* Is there any edge marked "no_merge" between two SCCs that are
5846 * about to be merged (i.e., that are set in "scc_in_merge")?
5847 * "merge_edge" is the proximity edge along which the clusters of SCCs
5848 * are going to be merged.
5850 * If there is any edge between two SCCs with a negative weight,
5851 * while the weight of "merge_edge" is non-negative, then this
5852 * means that the edge was postponed. "merge_edge" should then
5853 * also be postponed since merging along the edge with negative weight should
5854 * be postponed until all edges with non-negative weight have been tried.
5855 * Replace the weight of "merge_edge" by a negative weight as well and
5856 * tell the caller not to attempt a merge.
5858 static int any_no_merge(struct isl_sched_graph
*graph
, int *scc_in_merge
,
5859 struct isl_sched_edge
*merge_edge
)
5863 for (i
= 0; i
< graph
->n_edge
; ++i
) {
5864 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
5866 if (!scc_in_merge
[edge
->src
->scc
])
5868 if (!scc_in_merge
[edge
->dst
->scc
])
5872 if (merge_edge
->weight
>= 0 && edge
->weight
< 0) {
5873 merge_edge
->weight
-= graph
->max_weight
+ 1;
5881 /* Merge the two clusters in "c" connected by the edge in "graph"
5882 * with index "edge" into a single cluster.
5883 * If it turns out to be impossible to merge these two clusters,
5884 * then mark the edge as "no_merge" such that it will not be
5887 * First mark all SCCs that need to be merged. This includes the SCCs
5888 * in the two clusters, but it may also include the SCCs
5889 * of intermediate clusters.
5890 * If there is already a no_merge edge between any pair of such SCCs,
5891 * then simply mark the current edge as no_merge as well.
5892 * Likewise, if any of those edges was postponed by has_bounded_distances,
5893 * then postpone the current edge as well.
5894 * Otherwise, try and merge the clusters and mark "edge" as "no_merge"
5895 * if the clusters did not end up getting merged, unless the non-merge
5896 * is due to the fact that the edge was postponed. This postponement
5897 * can be recognized by a change in weight (from non-negative to negative).
5899 static isl_stat
merge_clusters_along_edge(isl_ctx
*ctx
,
5900 struct isl_sched_graph
*graph
, int edge
, struct isl_clustering
*c
)
5903 int edge_weight
= graph
->edge
[edge
].weight
;
5905 if (mark_merge_sccs(ctx
, graph
, edge
, c
) < 0)
5906 return isl_stat_error
;
5908 if (any_no_merge(graph
, c
->scc_in_merge
, &graph
->edge
[edge
]))
5909 merged
= isl_bool_false
;
5911 merged
= try_merge(ctx
, graph
, c
);
5913 return isl_stat_error
;
5914 if (!merged
&& edge_weight
== graph
->edge
[edge
].weight
)
5915 graph
->edge
[edge
].no_merge
= 1;
5920 /* Does "node" belong to the cluster identified by "cluster"?
5922 static int node_cluster_exactly(struct isl_sched_node
*node
, int cluster
)
5924 return node
->cluster
== cluster
;
5927 /* Does "edge" connect two nodes belonging to the cluster
5928 * identified by "cluster"?
5930 static int edge_cluster_exactly(struct isl_sched_edge
*edge
, int cluster
)
5932 return edge
->src
->cluster
== cluster
&& edge
->dst
->cluster
== cluster
;
5935 /* Swap the schedule of "node1" and "node2".
5936 * Both nodes have been derived from the same node in a common parent graph.
5937 * Since the "coincident" field is shared with that node
5938 * in the parent graph, there is no need to also swap this field.
5940 static void swap_sched(struct isl_sched_node
*node1
,
5941 struct isl_sched_node
*node2
)
5946 sched
= node1
->sched
;
5947 node1
->sched
= node2
->sched
;
5948 node2
->sched
= sched
;
5950 sched_map
= node1
->sched_map
;
5951 node1
->sched_map
= node2
->sched_map
;
5952 node2
->sched_map
= sched_map
;
5955 /* Copy the current band schedule from the SCCs that form the cluster
5956 * with index "pos" to the actual cluster at position "pos".
5957 * By construction, the index of the first SCC that belongs to the cluster
5960 * The order of the nodes inside both the SCCs and the cluster
5961 * is assumed to be same as the order in the original "graph".
5963 * Since the SCC graphs will no longer be used after this function,
5964 * the schedules are actually swapped rather than copied.
5966 static isl_stat
copy_partial(struct isl_sched_graph
*graph
,
5967 struct isl_clustering
*c
, int pos
)
5971 c
->cluster
[pos
].n_total_row
= c
->scc
[pos
].n_total_row
;
5972 c
->cluster
[pos
].n_row
= c
->scc
[pos
].n_row
;
5973 c
->cluster
[pos
].maxvar
= c
->scc
[pos
].maxvar
;
5975 for (i
= 0; i
< graph
->n
; ++i
) {
5979 if (graph
->node
[i
].cluster
!= pos
)
5981 s
= graph
->node
[i
].scc
;
5982 k
= c
->scc_node
[s
]++;
5983 swap_sched(&c
->cluster
[pos
].node
[j
], &c
->scc
[s
].node
[k
]);
5984 if (c
->scc
[s
].maxvar
> c
->cluster
[pos
].maxvar
)
5985 c
->cluster
[pos
].maxvar
= c
->scc
[s
].maxvar
;
5992 /* Is there a (conditional) validity dependence from node[j] to node[i],
5993 * forcing node[i] to follow node[j] or do the nodes belong to the same
5996 static isl_bool
node_follows_strong_or_same_cluster(int i
, int j
, void *user
)
5998 struct isl_sched_graph
*graph
= user
;
6000 if (graph
->node
[i
].cluster
== graph
->node
[j
].cluster
)
6001 return isl_bool_true
;
6002 return graph_has_validity_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
6005 /* Extract the merged clusters of SCCs in "graph", sort them, and
6006 * store them in c->clusters. Update c->scc_cluster accordingly.
6008 * First keep track of the cluster containing the SCC to which a node
6009 * belongs in the node itself.
6010 * Then extract the clusters into c->clusters, copying the current
6011 * band schedule from the SCCs that belong to the cluster.
6012 * Do this only once per cluster.
6014 * Finally, topologically sort the clusters and update c->scc_cluster
6015 * to match the new scc numbering. While the SCCs were originally
6016 * sorted already, some SCCs that depend on some other SCCs may
6017 * have been merged with SCCs that appear before these other SCCs.
6018 * A reordering may therefore be required.
6020 static isl_stat
extract_clusters(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
6021 struct isl_clustering
*c
)
6025 for (i
= 0; i
< graph
->n
; ++i
)
6026 graph
->node
[i
].cluster
= c
->scc_cluster
[graph
->node
[i
].scc
];
6028 for (i
= 0; i
< graph
->scc
; ++i
) {
6029 if (c
->scc_cluster
[i
] != i
)
6031 if (extract_sub_graph(ctx
, graph
, &node_cluster_exactly
,
6032 &edge_cluster_exactly
, i
, &c
->cluster
[i
]) < 0)
6033 return isl_stat_error
;
6034 c
->cluster
[i
].src_scc
= -1;
6035 c
->cluster
[i
].dst_scc
= -1;
6036 if (copy_partial(graph
, c
, i
) < 0)
6037 return isl_stat_error
;
6040 if (detect_ccs(ctx
, graph
, &node_follows_strong_or_same_cluster
) < 0)
6041 return isl_stat_error
;
6042 for (i
= 0; i
< graph
->n
; ++i
)
6043 c
->scc_cluster
[graph
->node
[i
].scc
] = graph
->node
[i
].cluster
;
6048 /* Compute weights on the proximity edges of "graph" that can
6049 * be used by find_proximity to find the most appropriate
6050 * proximity edge to use to merge two clusters in "c".
6051 * The weights are also used by has_bounded_distances to determine
6052 * whether the merge should be allowed.
6053 * Store the maximum of the computed weights in graph->max_weight.
6055 * The computed weight is a measure for the number of remaining schedule
6056 * dimensions that can still be completely aligned.
6057 * In particular, compute the number of equalities between
6058 * input dimensions and output dimensions in the proximity constraints.
6059 * The directions that are already handled by outer schedule bands
6060 * are projected out prior to determining this number.
6062 * Edges that will never be considered by find_proximity are ignored.
6064 static isl_stat
compute_weights(struct isl_sched_graph
*graph
,
6065 struct isl_clustering
*c
)
6069 graph
->max_weight
= 0;
6071 for (i
= 0; i
< graph
->n_edge
; ++i
) {
6072 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
6073 struct isl_sched_node
*src
= edge
->src
;
6074 struct isl_sched_node
*dst
= edge
->dst
;
6075 isl_basic_map
*hull
;
6078 if (!is_proximity(edge
))
6080 if (bad_cluster(&c
->scc
[edge
->src
->scc
]) ||
6081 bad_cluster(&c
->scc
[edge
->dst
->scc
]))
6083 if (c
->scc_cluster
[edge
->dst
->scc
] ==
6084 c
->scc_cluster
[edge
->src
->scc
])
6087 hull
= isl_map_affine_hull(isl_map_copy(edge
->map
));
6088 hull
= isl_basic_map_transform_dims(hull
, isl_dim_in
, 0,
6089 isl_mat_copy(src
->ctrans
));
6090 hull
= isl_basic_map_transform_dims(hull
, isl_dim_out
, 0,
6091 isl_mat_copy(dst
->ctrans
));
6092 hull
= isl_basic_map_project_out(hull
,
6093 isl_dim_in
, 0, src
->rank
);
6094 hull
= isl_basic_map_project_out(hull
,
6095 isl_dim_out
, 0, dst
->rank
);
6096 hull
= isl_basic_map_remove_divs(hull
);
6097 n_in
= isl_basic_map_dim(hull
, isl_dim_in
);
6098 n_out
= isl_basic_map_dim(hull
, isl_dim_out
);
6099 hull
= isl_basic_map_drop_constraints_not_involving_dims(hull
,
6100 isl_dim_in
, 0, n_in
);
6101 hull
= isl_basic_map_drop_constraints_not_involving_dims(hull
,
6102 isl_dim_out
, 0, n_out
);
6104 return isl_stat_error
;
6105 edge
->weight
= hull
->n_eq
;
6106 isl_basic_map_free(hull
);
6108 if (edge
->weight
> graph
->max_weight
)
6109 graph
->max_weight
= edge
->weight
;
6115 /* Call compute_schedule_finish_band on each of the clusters in "c"
6116 * in their topological order. This order is determined by the scc
6117 * fields of the nodes in "graph".
6118 * Combine the results in a sequence expressing the topological order.
6120 * If there is only one cluster left, then there is no need to introduce
6121 * a sequence node. Also, in this case, the cluster necessarily contains
6122 * the SCC at position 0 in the original graph and is therefore also
6123 * stored in the first cluster of "c".
6125 static __isl_give isl_schedule_node
*finish_bands_clustering(
6126 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
6127 struct isl_clustering
*c
)
6131 isl_union_set_list
*filters
;
6133 if (graph
->scc
== 1)
6134 return compute_schedule_finish_band(node
, &c
->cluster
[0], 0);
6136 ctx
= isl_schedule_node_get_ctx(node
);
6138 filters
= extract_sccs(ctx
, graph
);
6139 node
= isl_schedule_node_insert_sequence(node
, filters
);
6141 for (i
= 0; i
< graph
->scc
; ++i
) {
6142 int j
= c
->scc_cluster
[i
];
6143 node
= isl_schedule_node_child(node
, i
);
6144 node
= isl_schedule_node_child(node
, 0);
6145 node
= compute_schedule_finish_band(node
, &c
->cluster
[j
], 0);
6146 node
= isl_schedule_node_parent(node
);
6147 node
= isl_schedule_node_parent(node
);
6153 /* Compute a schedule for a connected dependence graph by first considering
6154 * each strongly connected component (SCC) in the graph separately and then
6155 * incrementally combining them into clusters.
6156 * Return the updated schedule node.
6158 * Initially, each cluster consists of a single SCC, each with its
6159 * own band schedule. The algorithm then tries to merge pairs
6160 * of clusters along a proximity edge until no more suitable
6161 * proximity edges can be found. During this merging, the schedule
6162 * is maintained in the individual SCCs.
6163 * After the merging is completed, the full resulting clusters
6164 * are extracted and in finish_bands_clustering,
6165 * compute_schedule_finish_band is called on each of them to integrate
6166 * the band into "node" and to continue the computation.
6168 * compute_weights initializes the weights that are used by find_proximity.
6170 static __isl_give isl_schedule_node
*compute_schedule_wcc_clustering(
6171 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
6174 struct isl_clustering c
;
6177 ctx
= isl_schedule_node_get_ctx(node
);
6179 if (clustering_init(ctx
, &c
, graph
) < 0)
6182 if (compute_weights(graph
, &c
) < 0)
6186 i
= find_proximity(graph
, &c
);
6189 if (i
>= graph
->n_edge
)
6191 if (merge_clusters_along_edge(ctx
, graph
, i
, &c
) < 0)
6195 if (extract_clusters(ctx
, graph
, &c
) < 0)
6198 node
= finish_bands_clustering(node
, graph
, &c
);
6200 clustering_free(ctx
, &c
);
6203 clustering_free(ctx
, &c
);
6204 return isl_schedule_node_free(node
);
6207 /* Compute a schedule for a connected dependence graph and return
6208 * the updated schedule node.
6210 * If Feautrier's algorithm is selected, we first recursively try to satisfy
6211 * as many validity dependences as possible. When all validity dependences
6212 * are satisfied we extend the schedule to a full-dimensional schedule.
6214 * Call compute_schedule_wcc_whole or compute_schedule_wcc_clustering
6215 * depending on whether the user has selected the option to try and
6216 * compute a schedule for the entire (weakly connected) component first.
6217 * If there is only a single strongly connected component (SCC), then
6218 * there is no point in trying to combine SCCs
6219 * in compute_schedule_wcc_clustering, so compute_schedule_wcc_whole
6220 * is called instead.
6222 static __isl_give isl_schedule_node
*compute_schedule_wcc(
6223 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
6230 ctx
= isl_schedule_node_get_ctx(node
);
6231 if (detect_sccs(ctx
, graph
) < 0)
6232 return isl_schedule_node_free(node
);
6234 if (compute_maxvar(graph
) < 0)
6235 return isl_schedule_node_free(node
);
6237 if (need_feautrier_step(ctx
, graph
))
6238 return compute_schedule_wcc_feautrier(node
, graph
);
6240 if (graph
->scc
<= 1 || isl_options_get_schedule_whole_component(ctx
))
6241 return compute_schedule_wcc_whole(node
, graph
);
6243 return compute_schedule_wcc_clustering(node
, graph
);
6246 /* Compute a schedule for each group of nodes identified by node->scc
6247 * separately and then combine them in a sequence node (or as set node
6248 * if graph->weak is set) inserted at position "node" of the schedule tree.
6249 * Return the updated schedule node.
6251 * If "wcc" is set then each of the groups belongs to a single
6252 * weakly connected component in the dependence graph so that
6253 * there is no need for compute_sub_schedule to look for weakly
6254 * connected components.
6256 static __isl_give isl_schedule_node
*compute_component_schedule(
6257 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
6262 isl_union_set_list
*filters
;
6266 ctx
= isl_schedule_node_get_ctx(node
);
6268 filters
= extract_sccs(ctx
, graph
);
6270 node
= isl_schedule_node_insert_set(node
, filters
);
6272 node
= isl_schedule_node_insert_sequence(node
, filters
);
6274 for (component
= 0; component
< graph
->scc
; ++component
) {
6275 node
= isl_schedule_node_child(node
, component
);
6276 node
= isl_schedule_node_child(node
, 0);
6277 node
= compute_sub_schedule(node
, ctx
, graph
,
6279 &edge_scc_exactly
, component
, wcc
);
6280 node
= isl_schedule_node_parent(node
);
6281 node
= isl_schedule_node_parent(node
);
6287 /* Compute a schedule for the given dependence graph and insert it at "node".
6288 * Return the updated schedule node.
6290 * We first check if the graph is connected (through validity and conditional
6291 * validity dependences) and, if not, compute a schedule
6292 * for each component separately.
6293 * If the schedule_serialize_sccs option is set, then we check for strongly
6294 * connected components instead and compute a separate schedule for
6295 * each such strongly connected component.
6297 static __isl_give isl_schedule_node
*compute_schedule(isl_schedule_node
*node
,
6298 struct isl_sched_graph
*graph
)
6305 ctx
= isl_schedule_node_get_ctx(node
);
6306 if (isl_options_get_schedule_serialize_sccs(ctx
)) {
6307 if (detect_sccs(ctx
, graph
) < 0)
6308 return isl_schedule_node_free(node
);
6310 if (detect_wccs(ctx
, graph
) < 0)
6311 return isl_schedule_node_free(node
);
6315 return compute_component_schedule(node
, graph
, 1);
6317 return compute_schedule_wcc(node
, graph
);
6320 /* Compute a schedule on sc->domain that respects the given schedule
6323 * In particular, the schedule respects all the validity dependences.
6324 * If the default isl scheduling algorithm is used, it tries to minimize
6325 * the dependence distances over the proximity dependences.
6326 * If Feautrier's scheduling algorithm is used, the proximity dependence
6327 * distances are only minimized during the extension to a full-dimensional
6330 * If there are any condition and conditional validity dependences,
6331 * then the conditional validity dependences may be violated inside
6332 * a tilable band, provided they have no adjacent non-local
6333 * condition dependences.
6335 __isl_give isl_schedule
*isl_schedule_constraints_compute_schedule(
6336 __isl_take isl_schedule_constraints
*sc
)
6338 isl_ctx
*ctx
= isl_schedule_constraints_get_ctx(sc
);
6339 struct isl_sched_graph graph
= { 0 };
6340 isl_schedule
*sched
;
6341 isl_schedule_node
*node
;
6342 isl_union_set
*domain
;
6344 sc
= isl_schedule_constraints_align_params(sc
);
6346 domain
= isl_schedule_constraints_get_domain(sc
);
6347 if (isl_union_set_n_set(domain
) == 0) {
6348 isl_schedule_constraints_free(sc
);
6349 return isl_schedule_from_domain(domain
);
6352 if (graph_init(&graph
, sc
) < 0)
6353 domain
= isl_union_set_free(domain
);
6355 node
= isl_schedule_node_from_domain(domain
);
6356 node
= isl_schedule_node_child(node
, 0);
6358 node
= compute_schedule(node
, &graph
);
6359 sched
= isl_schedule_node_get_schedule(node
);
6360 isl_schedule_node_free(node
);
6362 graph_free(ctx
, &graph
);
6363 isl_schedule_constraints_free(sc
);
6368 /* Compute a schedule for the given union of domains that respects
6369 * all the validity dependences and minimizes
6370 * the dependence distances over the proximity dependences.
6372 * This function is kept for backward compatibility.
6374 __isl_give isl_schedule
*isl_union_set_compute_schedule(
6375 __isl_take isl_union_set
*domain
,
6376 __isl_take isl_union_map
*validity
,
6377 __isl_take isl_union_map
*proximity
)
6379 isl_schedule_constraints
*sc
;
6381 sc
= isl_schedule_constraints_on_domain(domain
);
6382 sc
= isl_schedule_constraints_set_validity(sc
, validity
);
6383 sc
= isl_schedule_constraints_set_proximity(sc
, proximity
);
6385 return isl_schedule_constraints_compute_schedule(sc
);