2 * Copyright 2011 INRIA Saclay
3 * Copyright 2012-2014 Ecole Normale Superieure
4 * Copyright 2015-2016 Sven Verdoolaege
5 * Copyright 2016 INRIA Paris
6 * Copyright 2017 Sven Verdoolaege
8 * Use of this software is governed by the MIT license
10 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
11 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
13 * and Ecole Normale Superieure, 45 rue d'Ulm, 75230 Paris, France
14 * and Centre de Recherche Inria de Paris, 2 rue Simone Iff - Voie DQ12,
15 * CS 42112, 75589 Paris Cedex 12, France
18 #include <isl_ctx_private.h>
19 #include <isl_map_private.h>
20 #include <isl_space_private.h>
21 #include <isl_aff_private.h>
23 #include <isl/constraint.h>
24 #include <isl/schedule.h>
25 #include <isl_schedule_constraints.h>
26 #include <isl/schedule_node.h>
27 #include <isl_mat_private.h>
28 #include <isl_vec_private.h>
30 #include <isl/union_set.h>
33 #include <isl_dim_map.h>
34 #include <isl/map_to_basic_set.h>
36 #include <isl_options_private.h>
37 #include <isl_tarjan.h>
38 #include <isl_morph.h>
40 #include <isl_val_private.h>
43 * The scheduling algorithm implemented in this file was inspired by
44 * Bondhugula et al., "Automatic Transformations for Communication-Minimized
45 * Parallelization and Locality Optimization in the Polyhedral Model".
49 /* Internal information about a node that is used during the construction
51 * space represents the original space in which the domain lives;
52 * that is, the space is not affected by compression
53 * sched is a matrix representation of the schedule being constructed
54 * for this node; if compressed is set, then this schedule is
55 * defined over the compressed domain space
56 * sched_map is an isl_map representation of the same (partial) schedule
57 * sched_map may be NULL; if compressed is set, then this map
58 * is defined over the uncompressed domain space
59 * rank is the number of linearly independent rows in the linear part
61 * the columns of cmap represent a change of basis for the schedule
62 * coefficients; the first rank columns span the linear part of
64 * the rows of "indep" represent linear combinations of the schedule
65 * coefficients that are non-zero when the schedule coefficients are
66 * linearly independent of previously computed schedule rows.
67 * ctrans is the transpose of cmap.
68 * start is the first variable in the LP problem in the sequences that
69 * represents the schedule coefficients of this node
70 * nvar is the dimension of the domain
71 * nparam is the number of parameters or 0 if we are not constructing
72 * a parametric schedule
74 * If compressed is set, then hull represents the constraints
75 * that were used to derive the compression, while compress and
76 * decompress map the original space to the compressed space and
79 * scc is the index of SCC (or WCC) this node belongs to
81 * "cluster" is only used inside extract_clusters and identifies
82 * the cluster of SCCs that the node belongs to.
84 * coincident contains a boolean for each of the rows of the schedule,
85 * indicating whether the corresponding scheduling dimension satisfies
86 * the coincidence constraints in the sense that the corresponding
87 * dependence distances are zero.
89 * If the schedule_treat_coalescing option is set, then
90 * "sizes" contains the sizes of the (compressed) instance set
91 * in each direction. If there is no fixed size in a given direction,
92 * then the corresponding size value is set to infinity.
93 * If the schedule_treat_coalescing option or the schedule_max_coefficient
94 * option is set, then "max" contains the maximal values for
95 * schedule coefficients of the (compressed) variables. If no bound
96 * needs to be imposed on a particular variable, then the corresponding
99 struct isl_sched_node
{
103 isl_multi_aff
*compress
;
104 isl_multi_aff
*decompress
;
120 isl_multi_val
*sizes
;
124 static int node_has_tuples(const void *entry
, const void *val
)
126 struct isl_sched_node
*node
= (struct isl_sched_node
*)entry
;
127 isl_space
*space
= (isl_space
*) val
;
129 return isl_space_has_equal_tuples(node
->space
, space
);
132 static int node_scc_exactly(struct isl_sched_node
*node
, int scc
)
134 return node
->scc
== scc
;
137 static int node_scc_at_most(struct isl_sched_node
*node
, int scc
)
139 return node
->scc
<= scc
;
142 static int node_scc_at_least(struct isl_sched_node
*node
, int scc
)
144 return node
->scc
>= scc
;
147 /* An edge in the dependence graph. An edge may be used to
148 * ensure validity of the generated schedule, to minimize the dependence
151 * map is the dependence relation, with i -> j in the map if j depends on i
152 * tagged_condition and tagged_validity contain the union of all tagged
153 * condition or conditional validity dependence relations that
154 * specialize the dependence relation "map"; that is,
155 * if (i -> a) -> (j -> b) is an element of "tagged_condition"
156 * or "tagged_validity", then i -> j is an element of "map".
157 * If these fields are NULL, then they represent the empty relation.
158 * src is the source node
159 * dst is the sink node
161 * types is a bit vector containing the types of this edge.
162 * validity is set if the edge is used to ensure correctness
163 * coincidence is used to enforce zero dependence distances
164 * proximity is set if the edge is used to minimize dependence distances
165 * condition is set if the edge represents a condition
166 * for a conditional validity schedule constraint
167 * local can only be set for condition edges and indicates that
168 * the dependence distance over the edge should be zero
169 * conditional_validity is set if the edge is used to conditionally
172 * For validity edges, start and end mark the sequence of inequality
173 * constraints in the LP problem that encode the validity constraint
174 * corresponding to this edge.
176 * During clustering, an edge may be marked "no_merge" if it should
177 * not be used to merge clusters.
178 * The weight is also only used during clustering and it is
179 * an indication of how many schedule dimensions on either side
180 * of the schedule constraints can be aligned.
181 * If the weight is negative, then this means that this edge was postponed
182 * by has_bounded_distances or any_no_merge. The original weight can
183 * be retrieved by adding 1 + graph->max_weight, with "graph"
184 * the graph containing this edge.
186 struct isl_sched_edge
{
188 isl_union_map
*tagged_condition
;
189 isl_union_map
*tagged_validity
;
191 struct isl_sched_node
*src
;
192 struct isl_sched_node
*dst
;
203 /* Is "edge" marked as being of type "type"?
205 static int is_type(struct isl_sched_edge
*edge
, enum isl_edge_type type
)
207 return ISL_FL_ISSET(edge
->types
, 1 << type
);
210 /* Mark "edge" as being of type "type".
212 static void set_type(struct isl_sched_edge
*edge
, enum isl_edge_type type
)
214 ISL_FL_SET(edge
->types
, 1 << type
);
217 /* No longer mark "edge" as being of type "type"?
219 static void clear_type(struct isl_sched_edge
*edge
, enum isl_edge_type type
)
221 ISL_FL_CLR(edge
->types
, 1 << type
);
224 /* Is "edge" marked as a validity edge?
226 static int is_validity(struct isl_sched_edge
*edge
)
228 return is_type(edge
, isl_edge_validity
);
231 /* Mark "edge" as a validity edge.
233 static void set_validity(struct isl_sched_edge
*edge
)
235 set_type(edge
, isl_edge_validity
);
238 /* Is "edge" marked as a proximity edge?
240 static int is_proximity(struct isl_sched_edge
*edge
)
242 return is_type(edge
, isl_edge_proximity
);
245 /* Is "edge" marked as a local edge?
247 static int is_local(struct isl_sched_edge
*edge
)
249 return is_type(edge
, isl_edge_local
);
252 /* Mark "edge" as a local edge.
254 static void set_local(struct isl_sched_edge
*edge
)
256 set_type(edge
, isl_edge_local
);
259 /* No longer mark "edge" as a local edge.
261 static void clear_local(struct isl_sched_edge
*edge
)
263 clear_type(edge
, isl_edge_local
);
266 /* Is "edge" marked as a coincidence edge?
268 static int is_coincidence(struct isl_sched_edge
*edge
)
270 return is_type(edge
, isl_edge_coincidence
);
273 /* Is "edge" marked as a condition edge?
275 static int is_condition(struct isl_sched_edge
*edge
)
277 return is_type(edge
, isl_edge_condition
);
280 /* Is "edge" marked as a conditional validity edge?
282 static int is_conditional_validity(struct isl_sched_edge
*edge
)
284 return is_type(edge
, isl_edge_conditional_validity
);
287 /* Internal information about the dependence graph used during
288 * the construction of the schedule.
290 * intra_hmap is a cache, mapping dependence relations to their dual,
291 * for dependences from a node to itself
292 * inter_hmap is a cache, mapping dependence relations to their dual,
293 * for dependences between distinct nodes
294 * if compression is involved then the key for these maps
295 * is the original, uncompressed dependence relation, while
296 * the value is the dual of the compressed dependence relation.
298 * n is the number of nodes
299 * node is the list of nodes
300 * maxvar is the maximal number of variables over all nodes
301 * max_row is the allocated number of rows in the schedule
302 * n_row is the current (maximal) number of linearly independent
303 * rows in the node schedules
304 * n_total_row is the current number of rows in the node schedules
305 * band_start is the starting row in the node schedules of the current band
306 * root is set if this graph is the original dependence graph,
307 * without any splitting
309 * sorted contains a list of node indices sorted according to the
310 * SCC to which a node belongs
312 * n_edge is the number of edges
313 * edge is the list of edges
314 * max_edge contains the maximal number of edges of each type;
315 * in particular, it contains the number of edges in the inital graph.
316 * edge_table contains pointers into the edge array, hashed on the source
317 * and sink spaces; there is one such table for each type;
318 * a given edge may be referenced from more than one table
319 * if the corresponding relation appears in more than one of the
320 * sets of dependences; however, for each type there is only
321 * a single edge between a given pair of source and sink space
322 * in the entire graph
324 * node_table contains pointers into the node array, hashed on the space tuples
326 * region contains a list of variable sequences that should be non-trivial
328 * lp contains the (I)LP problem used to obtain new schedule rows
330 * src_scc and dst_scc are the source and sink SCCs of an edge with
331 * conflicting constraints
333 * scc represents the number of components
334 * weak is set if the components are weakly connected
336 * max_weight is used during clustering and represents the maximal
337 * weight of the relevant proximity edges.
339 struct isl_sched_graph
{
340 isl_map_to_basic_set
*intra_hmap
;
341 isl_map_to_basic_set
*inter_hmap
;
343 struct isl_sched_node
*node
;
356 struct isl_sched_edge
*edge
;
358 int max_edge
[isl_edge_last
+ 1];
359 struct isl_hash_table
*edge_table
[isl_edge_last
+ 1];
361 struct isl_hash_table
*node_table
;
362 struct isl_trivial_region
*region
;
375 /* Initialize node_table based on the list of nodes.
377 static int graph_init_table(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
381 graph
->node_table
= isl_hash_table_alloc(ctx
, graph
->n
);
382 if (!graph
->node_table
)
385 for (i
= 0; i
< graph
->n
; ++i
) {
386 struct isl_hash_table_entry
*entry
;
389 hash
= isl_space_get_tuple_hash(graph
->node
[i
].space
);
390 entry
= isl_hash_table_find(ctx
, graph
->node_table
, hash
,
392 graph
->node
[i
].space
, 1);
395 entry
->data
= &graph
->node
[i
];
401 /* Return a pointer to the node that lives within the given space,
402 * or NULL if there is no such node.
404 static struct isl_sched_node
*graph_find_node(isl_ctx
*ctx
,
405 struct isl_sched_graph
*graph
, __isl_keep isl_space
*space
)
407 struct isl_hash_table_entry
*entry
;
410 hash
= isl_space_get_tuple_hash(space
);
411 entry
= isl_hash_table_find(ctx
, graph
->node_table
, hash
,
412 &node_has_tuples
, space
, 0);
414 return entry
? entry
->data
: NULL
;
417 static int edge_has_src_and_dst(const void *entry
, const void *val
)
419 const struct isl_sched_edge
*edge
= entry
;
420 const struct isl_sched_edge
*temp
= val
;
422 return edge
->src
== temp
->src
&& edge
->dst
== temp
->dst
;
425 /* Add the given edge to graph->edge_table[type].
427 static isl_stat
graph_edge_table_add(isl_ctx
*ctx
,
428 struct isl_sched_graph
*graph
, enum isl_edge_type type
,
429 struct isl_sched_edge
*edge
)
431 struct isl_hash_table_entry
*entry
;
434 hash
= isl_hash_init();
435 hash
= isl_hash_builtin(hash
, edge
->src
);
436 hash
= isl_hash_builtin(hash
, edge
->dst
);
437 entry
= isl_hash_table_find(ctx
, graph
->edge_table
[type
], hash
,
438 &edge_has_src_and_dst
, edge
, 1);
440 return isl_stat_error
;
446 /* Allocate the edge_tables based on the maximal number of edges of
449 static int graph_init_edge_tables(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
453 for (i
= 0; i
<= isl_edge_last
; ++i
) {
454 graph
->edge_table
[i
] = isl_hash_table_alloc(ctx
,
456 if (!graph
->edge_table
[i
])
463 /* If graph->edge_table[type] contains an edge from the given source
464 * to the given destination, then return the hash table entry of this edge.
465 * Otherwise, return NULL.
467 static struct isl_hash_table_entry
*graph_find_edge_entry(
468 struct isl_sched_graph
*graph
,
469 enum isl_edge_type type
,
470 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
472 isl_ctx
*ctx
= isl_space_get_ctx(src
->space
);
474 struct isl_sched_edge temp
= { .src
= src
, .dst
= dst
};
476 hash
= isl_hash_init();
477 hash
= isl_hash_builtin(hash
, temp
.src
);
478 hash
= isl_hash_builtin(hash
, temp
.dst
);
479 return isl_hash_table_find(ctx
, graph
->edge_table
[type
], hash
,
480 &edge_has_src_and_dst
, &temp
, 0);
484 /* If graph->edge_table[type] contains an edge from the given source
485 * to the given destination, then return this edge.
486 * Otherwise, return NULL.
488 static struct isl_sched_edge
*graph_find_edge(struct isl_sched_graph
*graph
,
489 enum isl_edge_type type
,
490 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
492 struct isl_hash_table_entry
*entry
;
494 entry
= graph_find_edge_entry(graph
, type
, src
, dst
);
501 /* Check whether the dependence graph has an edge of the given type
502 * between the given two nodes.
504 static isl_bool
graph_has_edge(struct isl_sched_graph
*graph
,
505 enum isl_edge_type type
,
506 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
508 struct isl_sched_edge
*edge
;
511 edge
= graph_find_edge(graph
, type
, src
, dst
);
515 empty
= isl_map_plain_is_empty(edge
->map
);
517 return isl_bool_error
;
522 /* Look for any edge with the same src, dst and map fields as "model".
524 * Return the matching edge if one can be found.
525 * Return "model" if no matching edge is found.
526 * Return NULL on error.
528 static struct isl_sched_edge
*graph_find_matching_edge(
529 struct isl_sched_graph
*graph
, struct isl_sched_edge
*model
)
531 enum isl_edge_type i
;
532 struct isl_sched_edge
*edge
;
534 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
537 edge
= graph_find_edge(graph
, i
, model
->src
, model
->dst
);
540 is_equal
= isl_map_plain_is_equal(model
->map
, edge
->map
);
550 /* Remove the given edge from all the edge_tables that refer to it.
552 static void graph_remove_edge(struct isl_sched_graph
*graph
,
553 struct isl_sched_edge
*edge
)
555 isl_ctx
*ctx
= isl_map_get_ctx(edge
->map
);
556 enum isl_edge_type i
;
558 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
559 struct isl_hash_table_entry
*entry
;
561 entry
= graph_find_edge_entry(graph
, i
, edge
->src
, edge
->dst
);
564 if (entry
->data
!= edge
)
566 isl_hash_table_remove(ctx
, graph
->edge_table
[i
], entry
);
570 /* Check whether the dependence graph has any edge
571 * between the given two nodes.
573 static isl_bool
graph_has_any_edge(struct isl_sched_graph
*graph
,
574 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
576 enum isl_edge_type i
;
579 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
580 r
= graph_has_edge(graph
, i
, src
, dst
);
588 /* Check whether the dependence graph has a validity edge
589 * between the given two nodes.
591 * Conditional validity edges are essentially validity edges that
592 * can be ignored if the corresponding condition edges are iteration private.
593 * Here, we are only checking for the presence of validity
594 * edges, so we need to consider the conditional validity edges too.
595 * In particular, this function is used during the detection
596 * of strongly connected components and we cannot ignore
597 * conditional validity edges during this detection.
599 static isl_bool
graph_has_validity_edge(struct isl_sched_graph
*graph
,
600 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
604 r
= graph_has_edge(graph
, isl_edge_validity
, src
, dst
);
608 return graph_has_edge(graph
, isl_edge_conditional_validity
, src
, dst
);
611 static int graph_alloc(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
612 int n_node
, int n_edge
)
617 graph
->n_edge
= n_edge
;
618 graph
->node
= isl_calloc_array(ctx
, struct isl_sched_node
, graph
->n
);
619 graph
->sorted
= isl_calloc_array(ctx
, int, graph
->n
);
620 graph
->region
= isl_alloc_array(ctx
,
621 struct isl_trivial_region
, graph
->n
);
622 graph
->edge
= isl_calloc_array(ctx
,
623 struct isl_sched_edge
, graph
->n_edge
);
625 graph
->intra_hmap
= isl_map_to_basic_set_alloc(ctx
, 2 * n_edge
);
626 graph
->inter_hmap
= isl_map_to_basic_set_alloc(ctx
, 2 * n_edge
);
628 if (!graph
->node
|| !graph
->region
|| (graph
->n_edge
&& !graph
->edge
) ||
632 for(i
= 0; i
< graph
->n
; ++i
)
633 graph
->sorted
[i
] = i
;
638 static void graph_free(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
642 isl_map_to_basic_set_free(graph
->intra_hmap
);
643 isl_map_to_basic_set_free(graph
->inter_hmap
);
646 for (i
= 0; i
< graph
->n
; ++i
) {
647 isl_space_free(graph
->node
[i
].space
);
648 isl_set_free(graph
->node
[i
].hull
);
649 isl_multi_aff_free(graph
->node
[i
].compress
);
650 isl_multi_aff_free(graph
->node
[i
].decompress
);
651 isl_mat_free(graph
->node
[i
].sched
);
652 isl_map_free(graph
->node
[i
].sched_map
);
653 isl_mat_free(graph
->node
[i
].cmap
);
654 isl_mat_free(graph
->node
[i
].indep
);
655 isl_mat_free(graph
->node
[i
].ctrans
);
657 free(graph
->node
[i
].coincident
);
658 isl_multi_val_free(graph
->node
[i
].sizes
);
659 isl_vec_free(graph
->node
[i
].max
);
664 for (i
= 0; i
< graph
->n_edge
; ++i
) {
665 isl_map_free(graph
->edge
[i
].map
);
666 isl_union_map_free(graph
->edge
[i
].tagged_condition
);
667 isl_union_map_free(graph
->edge
[i
].tagged_validity
);
671 for (i
= 0; i
<= isl_edge_last
; ++i
)
672 isl_hash_table_free(ctx
, graph
->edge_table
[i
]);
673 isl_hash_table_free(ctx
, graph
->node_table
);
674 isl_basic_set_free(graph
->lp
);
677 /* For each "set" on which this function is called, increment
678 * graph->n by one and update graph->maxvar.
680 static isl_stat
init_n_maxvar(__isl_take isl_set
*set
, void *user
)
682 struct isl_sched_graph
*graph
= user
;
683 int nvar
= isl_set_dim(set
, isl_dim_set
);
686 if (nvar
> graph
->maxvar
)
687 graph
->maxvar
= nvar
;
694 /* Compute the number of rows that should be allocated for the schedule.
695 * In particular, we need one row for each variable or one row
696 * for each basic map in the dependences.
697 * Note that it is practically impossible to exhaust both
698 * the number of dependences and the number of variables.
700 static isl_stat
compute_max_row(struct isl_sched_graph
*graph
,
701 __isl_keep isl_schedule_constraints
*sc
)
705 isl_union_set
*domain
;
709 domain
= isl_schedule_constraints_get_domain(sc
);
710 r
= isl_union_set_foreach_set(domain
, &init_n_maxvar
, graph
);
711 isl_union_set_free(domain
);
713 return isl_stat_error
;
714 n_edge
= isl_schedule_constraints_n_basic_map(sc
);
716 return isl_stat_error
;
717 graph
->max_row
= n_edge
+ graph
->maxvar
;
722 /* Does "bset" have any defining equalities for its set variables?
724 static isl_bool
has_any_defining_equality(__isl_keep isl_basic_set
*bset
)
729 return isl_bool_error
;
731 n
= isl_basic_set_dim(bset
, isl_dim_set
);
732 for (i
= 0; i
< n
; ++i
) {
735 has
= isl_basic_set_has_defining_equality(bset
, isl_dim_set
, i
,
741 return isl_bool_false
;
744 /* Set the entries of node->max to the value of the schedule_max_coefficient
747 static isl_stat
set_max_coefficient(isl_ctx
*ctx
, struct isl_sched_node
*node
)
751 max
= isl_options_get_schedule_max_coefficient(ctx
);
755 node
->max
= isl_vec_alloc(ctx
, node
->nvar
);
756 node
->max
= isl_vec_set_si(node
->max
, max
);
758 return isl_stat_error
;
763 /* Set the entries of node->max to the minimum of the schedule_max_coefficient
764 * option (if set) and half of the minimum of the sizes in the other
765 * dimensions. If the minimum of the sizes is one, half of the size
766 * is zero and this value is reset to one.
767 * If the global minimum is unbounded (i.e., if both
768 * the schedule_max_coefficient is not set and the sizes in the other
769 * dimensions are unbounded), then store a negative value.
770 * If the schedule coefficient is close to the size of the instance set
771 * in another dimension, then the schedule may represent a loop
772 * coalescing transformation (especially if the coefficient
773 * in that other dimension is one). Forcing the coefficient to be
774 * smaller than or equal to half the minimal size should avoid this
777 static isl_stat
compute_max_coefficient(isl_ctx
*ctx
,
778 struct isl_sched_node
*node
)
784 max
= isl_options_get_schedule_max_coefficient(ctx
);
785 v
= isl_vec_alloc(ctx
, node
->nvar
);
787 return isl_stat_error
;
789 for (i
= 0; i
< node
->nvar
; ++i
) {
790 isl_int_set_si(v
->el
[i
], max
);
791 isl_int_mul_si(v
->el
[i
], v
->el
[i
], 2);
794 for (i
= 0; i
< node
->nvar
; ++i
) {
797 size
= isl_multi_val_get_val(node
->sizes
, i
);
800 if (!isl_val_is_int(size
)) {
804 for (j
= 0; j
< node
->nvar
; ++j
) {
807 if (isl_int_is_neg(v
->el
[j
]) ||
808 isl_int_gt(v
->el
[j
], size
->n
))
809 isl_int_set(v
->el
[j
], size
->n
);
814 for (i
= 0; i
< node
->nvar
; ++i
) {
815 isl_int_fdiv_q_ui(v
->el
[i
], v
->el
[i
], 2);
816 if (isl_int_is_zero(v
->el
[i
]))
817 isl_int_set_si(v
->el
[i
], 1);
824 return isl_stat_error
;
827 /* Compute and return the size of "set" in dimension "dim".
828 * The size is taken to be the difference in values for that variable
829 * for fixed values of the other variables.
830 * In particular, the variable is first isolated from the other variables
831 * in the range of a map
833 * [i_0, ..., i_dim-1, i_dim+1, ...] -> [i_dim]
835 * and then duplicated
837 * [i_0, ..., i_dim-1, i_dim+1, ...] -> [[i_dim] -> [i_dim']]
839 * The shared variables are then projected out and the maximal value
840 * of i_dim' - i_dim is computed.
842 static __isl_give isl_val
*compute_size(__isl_take isl_set
*set
, int dim
)
849 map
= isl_set_project_onto_map(set
, isl_dim_set
, dim
, 1);
850 map
= isl_map_project_out(map
, isl_dim_in
, dim
, 1);
851 map
= isl_map_range_product(map
, isl_map_copy(map
));
852 map
= isl_set_unwrap(isl_map_range(map
));
853 set
= isl_map_deltas(map
);
854 ls
= isl_local_space_from_space(isl_set_get_space(set
));
855 obj
= isl_aff_var_on_domain(ls
, isl_dim_set
, 0);
856 v
= isl_set_max_val(set
, obj
);
863 /* Compute the size of the instance set "set" of "node", after compression,
864 * as well as bounds on the corresponding coefficients, if needed.
866 * The sizes are needed when the schedule_treat_coalescing option is set.
867 * The bounds are needed when the schedule_treat_coalescing option or
868 * the schedule_max_coefficient option is set.
870 * If the schedule_treat_coalescing option is not set, then at most
871 * the bounds need to be set and this is done in set_max_coefficient.
872 * Otherwise, compress the domain if needed, compute the size
873 * in each direction and store the results in node->size.
874 * Finally, set the bounds on the coefficients based on the sizes
875 * and the schedule_max_coefficient option in compute_max_coefficient.
877 static isl_stat
compute_sizes_and_max(isl_ctx
*ctx
, struct isl_sched_node
*node
,
878 __isl_take isl_set
*set
)
883 if (!isl_options_get_schedule_treat_coalescing(ctx
)) {
885 return set_max_coefficient(ctx
, node
);
888 if (node
->compressed
)
889 set
= isl_set_preimage_multi_aff(set
,
890 isl_multi_aff_copy(node
->decompress
));
891 mv
= isl_multi_val_zero(isl_set_get_space(set
));
892 n
= isl_set_dim(set
, isl_dim_set
);
893 for (j
= 0; j
< n
; ++j
) {
896 v
= compute_size(isl_set_copy(set
), j
);
897 mv
= isl_multi_val_set_val(mv
, j
, v
);
902 return isl_stat_error
;
903 return compute_max_coefficient(ctx
, node
);
906 /* Add a new node to the graph representing the given instance set.
907 * "nvar" is the (possibly compressed) number of variables and
908 * may be smaller than then number of set variables in "set"
909 * if "compressed" is set.
910 * If "compressed" is set, then "hull" represents the constraints
911 * that were used to derive the compression, while "compress" and
912 * "decompress" map the original space to the compressed space and
914 * If "compressed" is not set, then "hull", "compress" and "decompress"
917 * Compute the size of the instance set and bounds on the coefficients,
920 static isl_stat
add_node(struct isl_sched_graph
*graph
,
921 __isl_take isl_set
*set
, int nvar
, int compressed
,
922 __isl_take isl_set
*hull
, __isl_take isl_multi_aff
*compress
,
923 __isl_take isl_multi_aff
*decompress
)
930 struct isl_sched_node
*node
;
933 return isl_stat_error
;
935 ctx
= isl_set_get_ctx(set
);
936 nparam
= isl_set_dim(set
, isl_dim_param
);
937 if (!ctx
->opt
->schedule_parametric
)
939 sched
= isl_mat_alloc(ctx
, 0, 1 + nparam
+ nvar
);
940 node
= &graph
->node
[graph
->n
];
942 space
= isl_set_get_space(set
);
945 node
->nparam
= nparam
;
947 node
->sched_map
= NULL
;
948 coincident
= isl_calloc_array(ctx
, int, graph
->max_row
);
949 node
->coincident
= coincident
;
950 node
->compressed
= compressed
;
952 node
->compress
= compress
;
953 node
->decompress
= decompress
;
954 if (compute_sizes_and_max(ctx
, node
, set
) < 0)
955 return isl_stat_error
;
957 if (!space
|| !sched
|| (graph
->max_row
&& !coincident
))
958 return isl_stat_error
;
959 if (compressed
&& (!hull
|| !compress
|| !decompress
))
960 return isl_stat_error
;
965 /* Construct an identifier for node "node", which will represent "set".
966 * The name of the identifier is either "compressed" or
967 * "compressed_<name>", with <name> the name of the space of "set".
968 * The user pointer of the identifier points to "node".
970 static __isl_give isl_id
*construct_compressed_id(__isl_keep isl_set
*set
,
971 struct isl_sched_node
*node
)
980 has_name
= isl_set_has_tuple_name(set
);
984 ctx
= isl_set_get_ctx(set
);
986 return isl_id_alloc(ctx
, "compressed", node
);
988 p
= isl_printer_to_str(ctx
);
989 name
= isl_set_get_tuple_name(set
);
990 p
= isl_printer_print_str(p
, "compressed_");
991 p
= isl_printer_print_str(p
, name
);
992 id_name
= isl_printer_get_str(p
);
995 id
= isl_id_alloc(ctx
, id_name
, node
);
1001 /* Add a new node to the graph representing the given set.
1003 * If any of the set variables is defined by an equality, then
1004 * we perform variable compression such that we can perform
1005 * the scheduling on the compressed domain.
1006 * In this case, an identifier is used that references the new node
1007 * such that each compressed space is unique and
1008 * such that the node can be recovered from the compressed space.
1010 static isl_stat
extract_node(__isl_take isl_set
*set
, void *user
)
1013 isl_bool has_equality
;
1015 isl_basic_set
*hull
;
1018 isl_multi_aff
*compress
, *decompress
;
1019 struct isl_sched_graph
*graph
= user
;
1021 hull
= isl_set_affine_hull(isl_set_copy(set
));
1022 hull
= isl_basic_set_remove_divs(hull
);
1023 nvar
= isl_set_dim(set
, isl_dim_set
);
1024 has_equality
= has_any_defining_equality(hull
);
1026 if (has_equality
< 0)
1028 if (!has_equality
) {
1029 isl_basic_set_free(hull
);
1030 return add_node(graph
, set
, nvar
, 0, NULL
, NULL
, NULL
);
1033 id
= construct_compressed_id(set
, &graph
->node
[graph
->n
]);
1034 morph
= isl_basic_set_variable_compression_with_id(hull
,
1037 nvar
= isl_morph_ran_dim(morph
, isl_dim_set
);
1038 compress
= isl_morph_get_var_multi_aff(morph
);
1039 morph
= isl_morph_inverse(morph
);
1040 decompress
= isl_morph_get_var_multi_aff(morph
);
1041 isl_morph_free(morph
);
1043 hull_set
= isl_set_from_basic_set(hull
);
1044 return add_node(graph
, set
, nvar
, 1, hull_set
, compress
, decompress
);
1046 isl_basic_set_free(hull
);
1048 return isl_stat_error
;
1051 struct isl_extract_edge_data
{
1052 enum isl_edge_type type
;
1053 struct isl_sched_graph
*graph
;
1056 /* Merge edge2 into edge1, freeing the contents of edge2.
1057 * Return 0 on success and -1 on failure.
1059 * edge1 and edge2 are assumed to have the same value for the map field.
1061 static int merge_edge(struct isl_sched_edge
*edge1
,
1062 struct isl_sched_edge
*edge2
)
1064 edge1
->types
|= edge2
->types
;
1065 isl_map_free(edge2
->map
);
1067 if (is_condition(edge2
)) {
1068 if (!edge1
->tagged_condition
)
1069 edge1
->tagged_condition
= edge2
->tagged_condition
;
1071 edge1
->tagged_condition
=
1072 isl_union_map_union(edge1
->tagged_condition
,
1073 edge2
->tagged_condition
);
1076 if (is_conditional_validity(edge2
)) {
1077 if (!edge1
->tagged_validity
)
1078 edge1
->tagged_validity
= edge2
->tagged_validity
;
1080 edge1
->tagged_validity
=
1081 isl_union_map_union(edge1
->tagged_validity
,
1082 edge2
->tagged_validity
);
1085 if (is_condition(edge2
) && !edge1
->tagged_condition
)
1087 if (is_conditional_validity(edge2
) && !edge1
->tagged_validity
)
1093 /* Insert dummy tags in domain and range of "map".
1095 * In particular, if "map" is of the form
1101 * [A -> dummy_tag] -> [B -> dummy_tag]
1103 * where the dummy_tags are identical and equal to any dummy tags
1104 * introduced by any other call to this function.
1106 static __isl_give isl_map
*insert_dummy_tags(__isl_take isl_map
*map
)
1112 isl_set
*domain
, *range
;
1114 ctx
= isl_map_get_ctx(map
);
1116 id
= isl_id_alloc(ctx
, NULL
, &dummy
);
1117 space
= isl_space_params(isl_map_get_space(map
));
1118 space
= isl_space_set_from_params(space
);
1119 space
= isl_space_set_tuple_id(space
, isl_dim_set
, id
);
1120 space
= isl_space_map_from_set(space
);
1122 domain
= isl_map_wrap(map
);
1123 range
= isl_map_wrap(isl_map_universe(space
));
1124 map
= isl_map_from_domain_and_range(domain
, range
);
1125 map
= isl_map_zip(map
);
1130 /* Given that at least one of "src" or "dst" is compressed, return
1131 * a map between the spaces of these nodes restricted to the affine
1132 * hull that was used in the compression.
1134 static __isl_give isl_map
*extract_hull(struct isl_sched_node
*src
,
1135 struct isl_sched_node
*dst
)
1139 if (src
->compressed
)
1140 dom
= isl_set_copy(src
->hull
);
1142 dom
= isl_set_universe(isl_space_copy(src
->space
));
1143 if (dst
->compressed
)
1144 ran
= isl_set_copy(dst
->hull
);
1146 ran
= isl_set_universe(isl_space_copy(dst
->space
));
1148 return isl_map_from_domain_and_range(dom
, ran
);
1151 /* Intersect the domains of the nested relations in domain and range
1152 * of "tagged" with "map".
1154 static __isl_give isl_map
*map_intersect_domains(__isl_take isl_map
*tagged
,
1155 __isl_keep isl_map
*map
)
1159 tagged
= isl_map_zip(tagged
);
1160 set
= isl_map_wrap(isl_map_copy(map
));
1161 tagged
= isl_map_intersect_domain(tagged
, set
);
1162 tagged
= isl_map_zip(tagged
);
1166 /* Return a pointer to the node that lives in the domain space of "map"
1167 * or NULL if there is no such node.
1169 static struct isl_sched_node
*find_domain_node(isl_ctx
*ctx
,
1170 struct isl_sched_graph
*graph
, __isl_keep isl_map
*map
)
1172 struct isl_sched_node
*node
;
1175 space
= isl_space_domain(isl_map_get_space(map
));
1176 node
= graph_find_node(ctx
, graph
, space
);
1177 isl_space_free(space
);
1182 /* Return a pointer to the node that lives in the range space of "map"
1183 * or NULL if there is no such node.
1185 static struct isl_sched_node
*find_range_node(isl_ctx
*ctx
,
1186 struct isl_sched_graph
*graph
, __isl_keep isl_map
*map
)
1188 struct isl_sched_node
*node
;
1191 space
= isl_space_range(isl_map_get_space(map
));
1192 node
= graph_find_node(ctx
, graph
, space
);
1193 isl_space_free(space
);
1198 /* Add a new edge to the graph based on the given map
1199 * and add it to data->graph->edge_table[data->type].
1200 * If a dependence relation of a given type happens to be identical
1201 * to one of the dependence relations of a type that was added before,
1202 * then we don't create a new edge, but instead mark the original edge
1203 * as also representing a dependence of the current type.
1205 * Edges of type isl_edge_condition or isl_edge_conditional_validity
1206 * may be specified as "tagged" dependence relations. That is, "map"
1207 * may contain elements (i -> a) -> (j -> b), where i -> j denotes
1208 * the dependence on iterations and a and b are tags.
1209 * edge->map is set to the relation containing the elements i -> j,
1210 * while edge->tagged_condition and edge->tagged_validity contain
1211 * the union of all the "map" relations
1212 * for which extract_edge is called that result in the same edge->map.
1214 * If the source or the destination node is compressed, then
1215 * intersect both "map" and "tagged" with the constraints that
1216 * were used to construct the compression.
1217 * This ensures that there are no schedule constraints defined
1218 * outside of these domains, while the scheduler no longer has
1219 * any control over those outside parts.
1221 static isl_stat
extract_edge(__isl_take isl_map
*map
, void *user
)
1223 isl_ctx
*ctx
= isl_map_get_ctx(map
);
1224 struct isl_extract_edge_data
*data
= user
;
1225 struct isl_sched_graph
*graph
= data
->graph
;
1226 struct isl_sched_node
*src
, *dst
;
1227 struct isl_sched_edge
*edge
;
1228 isl_map
*tagged
= NULL
;
1230 if (data
->type
== isl_edge_condition
||
1231 data
->type
== isl_edge_conditional_validity
) {
1232 if (isl_map_can_zip(map
)) {
1233 tagged
= isl_map_copy(map
);
1234 map
= isl_set_unwrap(isl_map_domain(isl_map_zip(map
)));
1236 tagged
= insert_dummy_tags(isl_map_copy(map
));
1240 src
= find_domain_node(ctx
, graph
, map
);
1241 dst
= find_range_node(ctx
, graph
, map
);
1245 isl_map_free(tagged
);
1249 if (src
->compressed
|| dst
->compressed
) {
1251 hull
= extract_hull(src
, dst
);
1253 tagged
= map_intersect_domains(tagged
, hull
);
1254 map
= isl_map_intersect(map
, hull
);
1257 graph
->edge
[graph
->n_edge
].src
= src
;
1258 graph
->edge
[graph
->n_edge
].dst
= dst
;
1259 graph
->edge
[graph
->n_edge
].map
= map
;
1260 graph
->edge
[graph
->n_edge
].types
= 0;
1261 graph
->edge
[graph
->n_edge
].tagged_condition
= NULL
;
1262 graph
->edge
[graph
->n_edge
].tagged_validity
= NULL
;
1263 set_type(&graph
->edge
[graph
->n_edge
], data
->type
);
1264 if (data
->type
== isl_edge_condition
)
1265 graph
->edge
[graph
->n_edge
].tagged_condition
=
1266 isl_union_map_from_map(tagged
);
1267 if (data
->type
== isl_edge_conditional_validity
)
1268 graph
->edge
[graph
->n_edge
].tagged_validity
=
1269 isl_union_map_from_map(tagged
);
1271 edge
= graph_find_matching_edge(graph
, &graph
->edge
[graph
->n_edge
]);
1274 return isl_stat_error
;
1276 if (edge
== &graph
->edge
[graph
->n_edge
])
1277 return graph_edge_table_add(ctx
, graph
, data
->type
,
1278 &graph
->edge
[graph
->n_edge
++]);
1280 if (merge_edge(edge
, &graph
->edge
[graph
->n_edge
]) < 0)
1283 return graph_edge_table_add(ctx
, graph
, data
->type
, edge
);
1286 /* Initialize the schedule graph "graph" from the schedule constraints "sc".
1288 * The context is included in the domain before the nodes of
1289 * the graphs are extracted in order to be able to exploit
1290 * any possible additional equalities.
1291 * Note that this intersection is only performed locally here.
1293 static isl_stat
graph_init(struct isl_sched_graph
*graph
,
1294 __isl_keep isl_schedule_constraints
*sc
)
1297 isl_union_set
*domain
;
1299 struct isl_extract_edge_data data
;
1300 enum isl_edge_type i
;
1304 return isl_stat_error
;
1306 ctx
= isl_schedule_constraints_get_ctx(sc
);
1308 domain
= isl_schedule_constraints_get_domain(sc
);
1309 graph
->n
= isl_union_set_n_set(domain
);
1310 isl_union_set_free(domain
);
1312 if (graph_alloc(ctx
, graph
, graph
->n
,
1313 isl_schedule_constraints_n_map(sc
)) < 0)
1314 return isl_stat_error
;
1316 if (compute_max_row(graph
, sc
) < 0)
1317 return isl_stat_error
;
1320 domain
= isl_schedule_constraints_get_domain(sc
);
1321 domain
= isl_union_set_intersect_params(domain
,
1322 isl_schedule_constraints_get_context(sc
));
1323 r
= isl_union_set_foreach_set(domain
, &extract_node
, graph
);
1324 isl_union_set_free(domain
);
1326 return isl_stat_error
;
1327 if (graph_init_table(ctx
, graph
) < 0)
1328 return isl_stat_error
;
1329 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
1330 c
= isl_schedule_constraints_get(sc
, i
);
1331 graph
->max_edge
[i
] = isl_union_map_n_map(c
);
1332 isl_union_map_free(c
);
1334 return isl_stat_error
;
1336 if (graph_init_edge_tables(ctx
, graph
) < 0)
1337 return isl_stat_error
;
1340 for (i
= isl_edge_first
; i
<= isl_edge_last
; ++i
) {
1344 c
= isl_schedule_constraints_get(sc
, i
);
1345 r
= isl_union_map_foreach_map(c
, &extract_edge
, &data
);
1346 isl_union_map_free(c
);
1348 return isl_stat_error
;
1354 /* Check whether there is any dependence from node[j] to node[i]
1355 * or from node[i] to node[j].
1357 static isl_bool
node_follows_weak(int i
, int j
, void *user
)
1360 struct isl_sched_graph
*graph
= user
;
1362 f
= graph_has_any_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
1365 return graph_has_any_edge(graph
, &graph
->node
[i
], &graph
->node
[j
]);
1368 /* Check whether there is a (conditional) validity dependence from node[j]
1369 * to node[i], forcing node[i] to follow node[j].
1371 static isl_bool
node_follows_strong(int i
, int j
, void *user
)
1373 struct isl_sched_graph
*graph
= user
;
1375 return graph_has_validity_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
1378 /* Use Tarjan's algorithm for computing the strongly connected components
1379 * in the dependence graph only considering those edges defined by "follows".
1381 static int detect_ccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
1382 isl_bool (*follows
)(int i
, int j
, void *user
))
1385 struct isl_tarjan_graph
*g
= NULL
;
1387 g
= isl_tarjan_graph_init(ctx
, graph
->n
, follows
, graph
);
1395 while (g
->order
[i
] != -1) {
1396 graph
->node
[g
->order
[i
]].scc
= graph
->scc
;
1404 isl_tarjan_graph_free(g
);
1409 /* Apply Tarjan's algorithm to detect the strongly connected components
1410 * in the dependence graph.
1411 * Only consider the (conditional) validity dependences and clear "weak".
1413 static int detect_sccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
1416 return detect_ccs(ctx
, graph
, &node_follows_strong
);
1419 /* Apply Tarjan's algorithm to detect the (weakly) connected components
1420 * in the dependence graph.
1421 * Consider all dependences and set "weak".
1423 static int detect_wccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
1426 return detect_ccs(ctx
, graph
, &node_follows_weak
);
1429 static int cmp_scc(const void *a
, const void *b
, void *data
)
1431 struct isl_sched_graph
*graph
= data
;
1435 return graph
->node
[*i1
].scc
- graph
->node
[*i2
].scc
;
1438 /* Sort the elements of graph->sorted according to the corresponding SCCs.
1440 static int sort_sccs(struct isl_sched_graph
*graph
)
1442 return isl_sort(graph
->sorted
, graph
->n
, sizeof(int), &cmp_scc
, graph
);
1445 /* Given a dependence relation R from "node" to itself,
1446 * construct the set of coefficients of valid constraints for elements
1447 * in that dependence relation.
1448 * In particular, the result contains tuples of coefficients
1449 * c_0, c_n, c_x such that
1451 * c_0 + c_n n + c_x y - c_x x >= 0 for each (x,y) in R
1455 * c_0 + c_n n + c_x d >= 0 for each d in delta R = { y - x | (x,y) in R }
1457 * We choose here to compute the dual of delta R.
1458 * Alternatively, we could have computed the dual of R, resulting
1459 * in a set of tuples c_0, c_n, c_x, c_y, and then
1460 * plugged in (c_0, c_n, c_x, -c_x).
1462 * If "node" has been compressed, then the dependence relation
1463 * is also compressed before the set of coefficients is computed.
1465 static __isl_give isl_basic_set
*intra_coefficients(
1466 struct isl_sched_graph
*graph
, struct isl_sched_node
*node
,
1467 __isl_take isl_map
*map
)
1471 isl_basic_set
*coef
;
1472 isl_maybe_isl_basic_set m
;
1474 m
= isl_map_to_basic_set_try_get(graph
->intra_hmap
, map
);
1475 if (m
.valid
< 0 || m
.valid
) {
1480 key
= isl_map_copy(map
);
1481 if (node
->compressed
) {
1482 map
= isl_map_preimage_domain_multi_aff(map
,
1483 isl_multi_aff_copy(node
->decompress
));
1484 map
= isl_map_preimage_range_multi_aff(map
,
1485 isl_multi_aff_copy(node
->decompress
));
1487 delta
= isl_set_remove_divs(isl_map_deltas(map
));
1488 coef
= isl_set_coefficients(delta
);
1489 graph
->intra_hmap
= isl_map_to_basic_set_set(graph
->intra_hmap
, key
,
1490 isl_basic_set_copy(coef
));
1495 /* Given a dependence relation R, construct the set of coefficients
1496 * of valid constraints for elements in that dependence relation.
1497 * In particular, the result contains tuples of coefficients
1498 * c_0, c_n, c_x, c_y such that
1500 * c_0 + c_n n + c_x x + c_y y >= 0 for each (x,y) in R
1502 * If the source or destination nodes of "edge" have been compressed,
1503 * then the dependence relation is also compressed before
1504 * the set of coefficients is computed.
1506 static __isl_give isl_basic_set
*inter_coefficients(
1507 struct isl_sched_graph
*graph
, struct isl_sched_edge
*edge
,
1508 __isl_take isl_map
*map
)
1512 isl_basic_set
*coef
;
1513 isl_maybe_isl_basic_set m
;
1515 m
= isl_map_to_basic_set_try_get(graph
->inter_hmap
, map
);
1516 if (m
.valid
< 0 || m
.valid
) {
1521 key
= isl_map_copy(map
);
1522 if (edge
->src
->compressed
)
1523 map
= isl_map_preimage_domain_multi_aff(map
,
1524 isl_multi_aff_copy(edge
->src
->decompress
));
1525 if (edge
->dst
->compressed
)
1526 map
= isl_map_preimage_range_multi_aff(map
,
1527 isl_multi_aff_copy(edge
->dst
->decompress
));
1528 set
= isl_map_wrap(isl_map_remove_divs(map
));
1529 coef
= isl_set_coefficients(set
);
1530 graph
->inter_hmap
= isl_map_to_basic_set_set(graph
->inter_hmap
, key
,
1531 isl_basic_set_copy(coef
));
1536 /* Return the position of the coefficients of the variables in
1537 * the coefficients constraints "coef".
1539 * The space of "coef" is of the form
1541 * { coefficients[[cst, params] -> S] }
1543 * Return the position of S.
1545 static int coef_var_offset(__isl_keep isl_basic_set
*coef
)
1550 space
= isl_space_unwrap(isl_basic_set_get_space(coef
));
1551 offset
= isl_space_dim(space
, isl_dim_in
);
1552 isl_space_free(space
);
1557 /* Return the offset of the coefficients of the variables of "node"
1560 * Within each node, the coefficients have the following order:
1562 * - c_i_n (if parametric)
1563 * - positive and negative parts of c_i_x
1565 static int node_var_coef_offset(struct isl_sched_node
*node
)
1567 return node
->start
+ 1 + node
->nparam
;
1570 /* Return the position of the pair of variables encoding
1571 * coefficient "i" of "node".
1573 * The order of these variable pairs is the opposite of
1574 * that of the coefficients, with 2 variables per coefficient.
1576 static int node_var_coef_pos(struct isl_sched_node
*node
, int i
)
1578 return node_var_coef_offset(node
) + 2 * (node
->nvar
- 1 - i
);
1581 /* Construct an isl_dim_map for mapping constraints on coefficients
1582 * for "node" to the corresponding positions in graph->lp.
1583 * "offset" is the offset of the coefficients for the variables
1584 * in the input constraints.
1585 * "s" is the sign of the mapping.
1587 * The input constraints are given in terms of the coefficients (c_0, c_n, c_x).
1588 * The mapping produced by this function essentially plugs in
1589 * (0, 0, c_i_x^+ - c_i_x^-) if s = 1 and
1590 * (0, 0, -c_i_x^+ + c_i_x^-) if s = -1.
1591 * In graph->lp, the c_i_x^- appear before their c_i_x^+ counterpart.
1592 * Furthermore, the order of these pairs is the opposite of that
1593 * of the corresponding coefficients.
1595 * The caller can extend the mapping to also map the other coefficients
1596 * (and therefore not plug in 0).
1598 static __isl_give isl_dim_map
*intra_dim_map(isl_ctx
*ctx
,
1599 struct isl_sched_graph
*graph
, struct isl_sched_node
*node
,
1604 isl_dim_map
*dim_map
;
1609 total
= isl_basic_set_total_dim(graph
->lp
);
1610 pos
= node_var_coef_pos(node
, 0);
1611 dim_map
= isl_dim_map_alloc(ctx
, total
);
1612 isl_dim_map_range(dim_map
, pos
, -2, offset
, 1, node
->nvar
, -s
);
1613 isl_dim_map_range(dim_map
, pos
+ 1, -2, offset
, 1, node
->nvar
, s
);
1618 /* Construct an isl_dim_map for mapping constraints on coefficients
1619 * for "src" (node i) and "dst" (node j) to the corresponding positions
1621 * "offset" is the offset of the coefficients for the variables of "src"
1622 * in the input constraints.
1623 * "s" is the sign of the mapping.
1625 * The input constraints are given in terms of the coefficients
1626 * (c_0, c_n, c_x, c_y).
1627 * The mapping produced by this function essentially plugs in
1628 * (c_j_0 - c_i_0, c_j_n - c_i_n,
1629 * -(c_i_x^+ - c_i_x^-), c_j_x^+ - c_j_x^-) if s = 1 and
1630 * (-c_j_0 + c_i_0, -c_j_n + c_i_n,
1631 * c_i_x^+ - c_i_x^-, -(c_j_x^+ - c_j_x^-)) if s = -1.
1632 * In graph->lp, the c_*^- appear before their c_*^+ counterpart.
1633 * Furthermore, the order of these pairs is the opposite of that
1634 * of the corresponding coefficients.
1636 * The caller can further extend the mapping.
1638 static __isl_give isl_dim_map
*inter_dim_map(isl_ctx
*ctx
,
1639 struct isl_sched_graph
*graph
, struct isl_sched_node
*src
,
1640 struct isl_sched_node
*dst
, int offset
, int s
)
1644 isl_dim_map
*dim_map
;
1649 total
= isl_basic_set_total_dim(graph
->lp
);
1650 dim_map
= isl_dim_map_alloc(ctx
, total
);
1652 isl_dim_map_range(dim_map
, dst
->start
, 0, 0, 0, 1, s
);
1653 isl_dim_map_range(dim_map
, dst
->start
+ 1, 1, 1, 1, dst
->nparam
, s
);
1654 pos
= node_var_coef_pos(dst
, 0);
1655 isl_dim_map_range(dim_map
, pos
, -2, offset
+ src
->nvar
, 1,
1657 isl_dim_map_range(dim_map
, pos
+ 1, -2, offset
+ src
->nvar
, 1,
1660 isl_dim_map_range(dim_map
, src
->start
, 0, 0, 0, 1, -s
);
1661 isl_dim_map_range(dim_map
, src
->start
+ 1, 1, 1, 1, src
->nparam
, -s
);
1662 pos
= node_var_coef_pos(src
, 0);
1663 isl_dim_map_range(dim_map
, pos
, -2, offset
, 1, src
->nvar
, s
);
1664 isl_dim_map_range(dim_map
, pos
+ 1, -2, offset
, 1, src
->nvar
, -s
);
1669 /* Add the constraints from "src" to "dst" using "dim_map",
1670 * after making sure there is enough room in "dst" for the extra constraints.
1672 static __isl_give isl_basic_set
*add_constraints_dim_map(
1673 __isl_take isl_basic_set
*dst
, __isl_take isl_basic_set
*src
,
1674 __isl_take isl_dim_map
*dim_map
)
1678 n_eq
= isl_basic_set_n_equality(src
);
1679 n_ineq
= isl_basic_set_n_inequality(src
);
1680 dst
= isl_basic_set_extend_constraints(dst
, n_eq
, n_ineq
);
1681 dst
= isl_basic_set_add_constraints_dim_map(dst
, src
, dim_map
);
1685 /* Add constraints to graph->lp that force validity for the given
1686 * dependence from a node i to itself.
1687 * That is, add constraints that enforce
1689 * (c_i_0 + c_i_n n + c_i_x y) - (c_i_0 + c_i_n n + c_i_x x)
1690 * = c_i_x (y - x) >= 0
1692 * for each (x,y) in R.
1693 * We obtain general constraints on coefficients (c_0, c_n, c_x)
1694 * of valid constraints for (y - x) and then plug in (0, 0, c_i_x^+ - c_i_x^-),
1695 * where c_i_x = c_i_x^+ - c_i_x^-, with c_i_x^+ and c_i_x^- non-negative.
1696 * In graph->lp, the c_i_x^- appear before their c_i_x^+ counterpart.
1698 * Actually, we do not construct constraints for the c_i_x themselves,
1699 * but for the coefficients of c_i_x written as a linear combination
1700 * of the columns in node->cmap.
1702 static isl_stat
add_intra_validity_constraints(struct isl_sched_graph
*graph
,
1703 struct isl_sched_edge
*edge
)
1706 isl_map
*map
= isl_map_copy(edge
->map
);
1707 isl_ctx
*ctx
= isl_map_get_ctx(map
);
1708 isl_dim_map
*dim_map
;
1709 isl_basic_set
*coef
;
1710 struct isl_sched_node
*node
= edge
->src
;
1712 coef
= intra_coefficients(graph
, node
, map
);
1714 offset
= coef_var_offset(coef
);
1716 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
1717 offset
, isl_mat_copy(node
->cmap
));
1719 return isl_stat_error
;
1721 dim_map
= intra_dim_map(ctx
, graph
, node
, offset
, 1);
1722 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
1727 /* Add constraints to graph->lp that force validity for the given
1728 * dependence from node i to node j.
1729 * That is, add constraints that enforce
1731 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) >= 0
1733 * for each (x,y) in R.
1734 * We obtain general constraints on coefficients (c_0, c_n, c_x, c_y)
1735 * of valid constraints for R and then plug in
1736 * (c_j_0 - c_i_0, c_j_n - c_i_n, -(c_i_x^+ - c_i_x^-), c_j_x^+ - c_j_x^-),
1737 * where c_* = c_*^+ - c_*^-, with c_*^+ and c_*^- non-negative.
1738 * In graph->lp, the c_*^- appear before their c_*^+ counterpart.
1740 * Actually, we do not construct constraints for the c_*_x themselves,
1741 * but for the coefficients of c_*_x written as a linear combination
1742 * of the columns in node->cmap.
1744 static isl_stat
add_inter_validity_constraints(struct isl_sched_graph
*graph
,
1745 struct isl_sched_edge
*edge
)
1750 isl_dim_map
*dim_map
;
1751 isl_basic_set
*coef
;
1752 struct isl_sched_node
*src
= edge
->src
;
1753 struct isl_sched_node
*dst
= edge
->dst
;
1756 return isl_stat_error
;
1758 map
= isl_map_copy(edge
->map
);
1759 ctx
= isl_map_get_ctx(map
);
1760 coef
= inter_coefficients(graph
, edge
, map
);
1762 offset
= coef_var_offset(coef
);
1764 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
1765 offset
, isl_mat_copy(src
->cmap
));
1766 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
1767 offset
+ src
->nvar
, isl_mat_copy(dst
->cmap
));
1769 return isl_stat_error
;
1771 dim_map
= inter_dim_map(ctx
, graph
, src
, dst
, offset
, 1);
1773 edge
->start
= graph
->lp
->n_ineq
;
1774 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
1776 return isl_stat_error
;
1777 edge
->end
= graph
->lp
->n_ineq
;
1782 /* Add constraints to graph->lp that bound the dependence distance for the given
1783 * dependence from a node i to itself.
1784 * If s = 1, we add the constraint
1786 * c_i_x (y - x) <= m_0 + m_n n
1790 * -c_i_x (y - x) + m_0 + m_n n >= 0
1792 * for each (x,y) in R.
1793 * If s = -1, we add the constraint
1795 * -c_i_x (y - x) <= m_0 + m_n n
1799 * c_i_x (y - x) + m_0 + m_n n >= 0
1801 * for each (x,y) in R.
1802 * We obtain general constraints on coefficients (c_0, c_n, c_x)
1803 * of valid constraints for (y - x) and then plug in (m_0, m_n, -s * c_i_x),
1804 * with each coefficient (except m_0) represented as a pair of non-negative
1807 * Actually, we do not construct constraints for the c_i_x themselves,
1808 * but for the coefficients of c_i_x written as a linear combination
1809 * of the columns in node->cmap.
1812 * If "local" is set, then we add constraints
1814 * c_i_x (y - x) <= 0
1818 * -c_i_x (y - x) <= 0
1820 * instead, forcing the dependence distance to be (less than or) equal to 0.
1821 * That is, we plug in (0, 0, -s * c_i_x),
1822 * Note that dependences marked local are treated as validity constraints
1823 * by add_all_validity_constraints and therefore also have
1824 * their distances bounded by 0 from below.
1826 static isl_stat
add_intra_proximity_constraints(struct isl_sched_graph
*graph
,
1827 struct isl_sched_edge
*edge
, int s
, int local
)
1831 isl_map
*map
= isl_map_copy(edge
->map
);
1832 isl_ctx
*ctx
= isl_map_get_ctx(map
);
1833 isl_dim_map
*dim_map
;
1834 isl_basic_set
*coef
;
1835 struct isl_sched_node
*node
= edge
->src
;
1837 coef
= intra_coefficients(graph
, node
, map
);
1839 offset
= coef_var_offset(coef
);
1841 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
1842 offset
, isl_mat_copy(node
->cmap
));
1844 return isl_stat_error
;
1846 nparam
= isl_space_dim(node
->space
, isl_dim_param
);
1847 dim_map
= intra_dim_map(ctx
, graph
, node
, offset
, -s
);
1850 isl_dim_map_range(dim_map
, 1, 0, 0, 0, 1, 1);
1851 isl_dim_map_range(dim_map
, 4, 2, 1, 1, nparam
, -1);
1852 isl_dim_map_range(dim_map
, 5, 2, 1, 1, nparam
, 1);
1854 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
1859 /* Add constraints to graph->lp that bound the dependence distance for the given
1860 * dependence from node i to node j.
1861 * If s = 1, we add the constraint
1863 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x)
1868 * -(c_j_0 + c_j_n n + c_j_x y) + (c_i_0 + c_i_n n + c_i_x x) +
1871 * for each (x,y) in R.
1872 * If s = -1, we add the constraint
1874 * -((c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x))
1879 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) +
1882 * for each (x,y) in R.
1883 * We obtain general constraints on coefficients (c_0, c_n, c_x, c_y)
1884 * of valid constraints for R and then plug in
1885 * (m_0 - s*c_j_0 + s*c_i_0, m_n - s*c_j_n + s*c_i_n,
1886 * s*c_i_x, -s*c_j_x)
1887 * with each coefficient (except m_0, c_*_0 and c_*_n)
1888 * represented as a pair of non-negative coefficients.
1890 * Actually, we do not construct constraints for the c_*_x themselves,
1891 * but for the coefficients of c_*_x written as a linear combination
1892 * of the columns in node->cmap.
1895 * If "local" is set (and s = 1), then we add constraints
1897 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) <= 0
1901 * -((c_j_0 + c_j_n n + c_j_x y) + (c_i_0 + c_i_n n + c_i_x x)) >= 0
1903 * instead, forcing the dependence distance to be (less than or) equal to 0.
1904 * That is, we plug in
1905 * (-s*c_j_0 + s*c_i_0, -s*c_j_n + s*c_i_n, s*c_i_x, -s*c_j_x).
1906 * Note that dependences marked local are treated as validity constraints
1907 * by add_all_validity_constraints and therefore also have
1908 * their distances bounded by 0 from below.
1910 static isl_stat
add_inter_proximity_constraints(struct isl_sched_graph
*graph
,
1911 struct isl_sched_edge
*edge
, int s
, int local
)
1915 isl_map
*map
= isl_map_copy(edge
->map
);
1916 isl_ctx
*ctx
= isl_map_get_ctx(map
);
1917 isl_dim_map
*dim_map
;
1918 isl_basic_set
*coef
;
1919 struct isl_sched_node
*src
= edge
->src
;
1920 struct isl_sched_node
*dst
= edge
->dst
;
1922 coef
= inter_coefficients(graph
, edge
, map
);
1924 offset
= coef_var_offset(coef
);
1926 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
1927 offset
, isl_mat_copy(src
->cmap
));
1928 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
1929 offset
+ src
->nvar
, isl_mat_copy(dst
->cmap
));
1931 return isl_stat_error
;
1933 nparam
= isl_space_dim(src
->space
, isl_dim_param
);
1934 dim_map
= inter_dim_map(ctx
, graph
, src
, dst
, offset
, -s
);
1937 isl_dim_map_range(dim_map
, 1, 0, 0, 0, 1, 1);
1938 isl_dim_map_range(dim_map
, 4, 2, 1, 1, nparam
, -1);
1939 isl_dim_map_range(dim_map
, 5, 2, 1, 1, nparam
, 1);
1942 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
1947 /* Add all validity constraints to graph->lp.
1949 * An edge that is forced to be local needs to have its dependence
1950 * distances equal to zero. We take care of bounding them by 0 from below
1951 * here. add_all_proximity_constraints takes care of bounding them by 0
1954 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
1955 * Otherwise, we ignore them.
1957 static int add_all_validity_constraints(struct isl_sched_graph
*graph
,
1958 int use_coincidence
)
1962 for (i
= 0; i
< graph
->n_edge
; ++i
) {
1963 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
1966 local
= is_local(edge
) ||
1967 (is_coincidence(edge
) && use_coincidence
);
1968 if (!is_validity(edge
) && !local
)
1970 if (edge
->src
!= edge
->dst
)
1972 if (add_intra_validity_constraints(graph
, edge
) < 0)
1976 for (i
= 0; i
< graph
->n_edge
; ++i
) {
1977 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
1980 local
= is_local(edge
) ||
1981 (is_coincidence(edge
) && use_coincidence
);
1982 if (!is_validity(edge
) && !local
)
1984 if (edge
->src
== edge
->dst
)
1986 if (add_inter_validity_constraints(graph
, edge
) < 0)
1993 /* Add constraints to graph->lp that bound the dependence distance
1994 * for all dependence relations.
1995 * If a given proximity dependence is identical to a validity
1996 * dependence, then the dependence distance is already bounded
1997 * from below (by zero), so we only need to bound the distance
1998 * from above. (This includes the case of "local" dependences
1999 * which are treated as validity dependence by add_all_validity_constraints.)
2000 * Otherwise, we need to bound the distance both from above and from below.
2002 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2003 * Otherwise, we ignore them.
2005 static int add_all_proximity_constraints(struct isl_sched_graph
*graph
,
2006 int use_coincidence
)
2010 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2011 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
2014 local
= is_local(edge
) ||
2015 (is_coincidence(edge
) && use_coincidence
);
2016 if (!is_proximity(edge
) && !local
)
2018 if (edge
->src
== edge
->dst
&&
2019 add_intra_proximity_constraints(graph
, edge
, 1, local
) < 0)
2021 if (edge
->src
!= edge
->dst
&&
2022 add_inter_proximity_constraints(graph
, edge
, 1, local
) < 0)
2024 if (is_validity(edge
) || local
)
2026 if (edge
->src
== edge
->dst
&&
2027 add_intra_proximity_constraints(graph
, edge
, -1, 0) < 0)
2029 if (edge
->src
!= edge
->dst
&&
2030 add_inter_proximity_constraints(graph
, edge
, -1, 0) < 0)
2037 /* Normalize the rows of "indep" such that all rows are lexicographically
2038 * positive and such that each row contains as many final zeros as possible,
2039 * given the choice for the previous rows.
2040 * Do this by performing elementary row operations.
2042 static __isl_give isl_mat
*normalize_independent(__isl_take isl_mat
*indep
)
2044 indep
= isl_mat_reverse_gauss(indep
);
2045 indep
= isl_mat_lexnonneg_rows(indep
);
2049 /* Compute a basis for the rows in the linear part of the schedule
2050 * and extend this basis to a full basis. The remaining rows
2051 * can then be used to force linear independence from the rows
2054 * In particular, given the schedule rows S, we compute
2059 * with H the Hermite normal form of S. That is, all but the
2060 * first rank columns of H are zero and so each row in S is
2061 * a linear combination of the first rank rows of Q.
2062 * The matrix Q is then transposed because we will write the
2063 * coefficients of the next schedule row as a column vector s
2064 * and express this s as a linear combination s = Q c of the
2066 * Transposing S U = H yields
2070 * with all but the first rank rows of H^T zero.
2071 * The last rows of U^T are therefore linear combinations
2072 * of schedule coefficients that are all zero on schedule
2073 * coefficients that are linearly dependent on the rows of S.
2074 * At least one of these combinations is non-zero on
2075 * linearly independent schedule coefficients.
2076 * The rows are normalized to involve as few of the last
2077 * coefficients as possible and to have a positive initial value.
2079 static int node_update_cmap(struct isl_sched_node
*node
)
2082 int n_row
= isl_mat_rows(node
->sched
);
2084 H
= isl_mat_sub_alloc(node
->sched
, 0, n_row
,
2085 1 + node
->nparam
, node
->nvar
);
2087 H
= isl_mat_left_hermite(H
, 0, &U
, &Q
);
2088 isl_mat_free(node
->cmap
);
2089 isl_mat_free(node
->indep
);
2090 isl_mat_free(node
->ctrans
);
2091 node
->ctrans
= isl_mat_copy(Q
);
2092 node
->cmap
= isl_mat_transpose(Q
);
2093 node
->indep
= isl_mat_transpose(U
);
2094 node
->rank
= isl_mat_initial_non_zero_cols(H
);
2095 node
->indep
= isl_mat_drop_rows(node
->indep
, 0, node
->rank
);
2096 node
->indep
= normalize_independent(node
->indep
);
2099 if (!node
->cmap
|| !node
->indep
|| !node
->ctrans
|| node
->rank
< 0)
2104 /* Is "edge" marked as a validity or a conditional validity edge?
2106 static int is_any_validity(struct isl_sched_edge
*edge
)
2108 return is_validity(edge
) || is_conditional_validity(edge
);
2111 /* How many times should we count the constraints in "edge"?
2113 * We count as follows
2114 * validity -> 1 (>= 0)
2115 * validity+proximity -> 2 (>= 0 and upper bound)
2116 * proximity -> 2 (lower and upper bound)
2117 * local(+any) -> 2 (>= 0 and <= 0)
2119 * If an edge is only marked conditional_validity then it counts
2120 * as zero since it is only checked afterwards.
2122 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2123 * Otherwise, we ignore them.
2125 static int edge_multiplicity(struct isl_sched_edge
*edge
, int use_coincidence
)
2127 if (is_proximity(edge
) || is_local(edge
))
2129 if (use_coincidence
&& is_coincidence(edge
))
2131 if (is_validity(edge
))
2136 /* Count the number of equality and inequality constraints
2137 * that will be added for the given map.
2139 * "use_coincidence" is set if we should take into account coincidence edges.
2141 static isl_stat
count_map_constraints(struct isl_sched_graph
*graph
,
2142 struct isl_sched_edge
*edge
, __isl_take isl_map
*map
,
2143 int *n_eq
, int *n_ineq
, int use_coincidence
)
2145 isl_basic_set
*coef
;
2146 int f
= edge_multiplicity(edge
, use_coincidence
);
2153 if (edge
->src
== edge
->dst
)
2154 coef
= intra_coefficients(graph
, edge
->src
, map
);
2156 coef
= inter_coefficients(graph
, edge
, map
);
2158 return isl_stat_error
;
2159 *n_eq
+= f
* isl_basic_set_n_equality(coef
);
2160 *n_ineq
+= f
* isl_basic_set_n_inequality(coef
);
2161 isl_basic_set_free(coef
);
2166 /* Count the number of equality and inequality constraints
2167 * that will be added to the main lp problem.
2168 * We count as follows
2169 * validity -> 1 (>= 0)
2170 * validity+proximity -> 2 (>= 0 and upper bound)
2171 * proximity -> 2 (lower and upper bound)
2172 * local(+any) -> 2 (>= 0 and <= 0)
2174 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2175 * Otherwise, we ignore them.
2177 static int count_constraints(struct isl_sched_graph
*graph
,
2178 int *n_eq
, int *n_ineq
, int use_coincidence
)
2182 *n_eq
= *n_ineq
= 0;
2183 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2184 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
2185 isl_map
*map
= isl_map_copy(edge
->map
);
2187 if (count_map_constraints(graph
, edge
, map
, n_eq
, n_ineq
,
2188 use_coincidence
) < 0)
2195 /* Count the number of constraints that will be added by
2196 * add_bound_constant_constraints to bound the values of the constant terms
2197 * and increment *n_eq and *n_ineq accordingly.
2199 * In practice, add_bound_constant_constraints only adds inequalities.
2201 static isl_stat
count_bound_constant_constraints(isl_ctx
*ctx
,
2202 struct isl_sched_graph
*graph
, int *n_eq
, int *n_ineq
)
2204 if (isl_options_get_schedule_max_constant_term(ctx
) == -1)
2207 *n_ineq
+= graph
->n
;
2212 /* Add constraints to bound the values of the constant terms in the schedule,
2213 * if requested by the user.
2215 * The maximal value of the constant terms is defined by the option
2216 * "schedule_max_constant_term".
2218 * Within each node, the coefficients have the following order:
2220 * - c_i_n (if parametric)
2221 * - positive and negative parts of c_i_x
2223 static isl_stat
add_bound_constant_constraints(isl_ctx
*ctx
,
2224 struct isl_sched_graph
*graph
)
2230 max
= isl_options_get_schedule_max_constant_term(ctx
);
2234 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2236 for (i
= 0; i
< graph
->n
; ++i
) {
2237 struct isl_sched_node
*node
= &graph
->node
[i
];
2238 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2240 return isl_stat_error
;
2241 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
2242 isl_int_set_si(graph
->lp
->ineq
[k
][1 + node
->start
], -1);
2243 isl_int_set_si(graph
->lp
->ineq
[k
][0], max
);
2249 /* Count the number of constraints that will be added by
2250 * add_bound_coefficient_constraints and increment *n_eq and *n_ineq
2253 * In practice, add_bound_coefficient_constraints only adds inequalities.
2255 static int count_bound_coefficient_constraints(isl_ctx
*ctx
,
2256 struct isl_sched_graph
*graph
, int *n_eq
, int *n_ineq
)
2260 if (isl_options_get_schedule_max_coefficient(ctx
) == -1 &&
2261 !isl_options_get_schedule_treat_coalescing(ctx
))
2264 for (i
= 0; i
< graph
->n
; ++i
)
2265 *n_ineq
+= graph
->node
[i
].nparam
+ 2 * graph
->node
[i
].nvar
;
2270 /* Add constraints to graph->lp that bound the values of
2271 * the parameter schedule coefficients of "node" to "max" and
2272 * the variable schedule coefficients to the corresponding entry
2274 * In either case, a negative value means that no bound needs to be imposed.
2276 * For parameter coefficients, this amounts to adding a constraint
2284 * The variables coefficients are, however, not represented directly.
2285 * Instead, the variables coefficients c_x are written as a linear
2286 * combination c_x = cmap c_z of some other coefficients c_z,
2287 * which are in turn encoded as c_z = c_z^+ - c_z^-.
2288 * Let a_j be the elements of row i of node->cmap, then
2290 * -max_i <= c_x_i <= max_i
2294 * -max_i <= \sum_j a_j (c_z_j^+ - c_z_j^-) <= max_i
2298 * -\sum_j a_j (c_z_j^+ - c_z_j^-) + max_i >= 0
2299 * \sum_j a_j (c_z_j^+ - c_z_j^-) + max_i >= 0
2301 static isl_stat
node_add_coefficient_constraints(isl_ctx
*ctx
,
2302 struct isl_sched_graph
*graph
, struct isl_sched_node
*node
, int max
)
2308 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2310 for (j
= 0; j
< node
->nparam
; ++j
) {
2316 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2318 return isl_stat_error
;
2319 dim
= 1 + node
->start
+ 1 + j
;
2320 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
2321 isl_int_set_si(graph
->lp
->ineq
[k
][dim
], -1);
2322 isl_int_set_si(graph
->lp
->ineq
[k
][0], max
);
2325 ineq
= isl_vec_alloc(ctx
, 1 + total
);
2326 ineq
= isl_vec_clr(ineq
);
2328 return isl_stat_error
;
2329 for (i
= 0; i
< node
->nvar
; ++i
) {
2330 int pos
= 1 + node_var_coef_offset(node
);
2332 if (isl_int_is_neg(node
->max
->el
[i
]))
2335 for (j
= 0; j
< node
->nvar
; ++j
) {
2336 int pos_j
= 1 + node_var_coef_pos(node
, j
);
2338 isl_int_set(ineq
->el
[pos_j
], node
->cmap
->row
[i
][j
]);
2339 isl_int_neg(ineq
->el
[pos_j
], node
->cmap
->row
[i
][j
]);
2341 isl_int_set(ineq
->el
[0], node
->max
->el
[i
]);
2343 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2346 isl_seq_cpy(graph
->lp
->ineq
[k
], ineq
->el
, 1 + total
);
2348 isl_seq_neg(ineq
->el
+ pos
, ineq
->el
+ pos
, 2 * node
->nvar
);
2349 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2352 isl_seq_cpy(graph
->lp
->ineq
[k
], ineq
->el
, 1 + total
);
2359 return isl_stat_error
;
2362 /* Add constraints that bound the values of the variable and parameter
2363 * coefficients of the schedule.
2365 * The maximal value of the coefficients is defined by the option
2366 * 'schedule_max_coefficient' and the entries in node->max.
2367 * These latter entries are only set if either the schedule_max_coefficient
2368 * option or the schedule_treat_coalescing option is set.
2370 static isl_stat
add_bound_coefficient_constraints(isl_ctx
*ctx
,
2371 struct isl_sched_graph
*graph
)
2376 max
= isl_options_get_schedule_max_coefficient(ctx
);
2378 if (max
== -1 && !isl_options_get_schedule_treat_coalescing(ctx
))
2381 for (i
= 0; i
< graph
->n
; ++i
) {
2382 struct isl_sched_node
*node
= &graph
->node
[i
];
2384 if (node_add_coefficient_constraints(ctx
, graph
, node
, max
) < 0)
2385 return isl_stat_error
;
2391 /* Add a constraint to graph->lp that equates the value at position
2392 * "sum_pos" to the sum of the "n" values starting at "first".
2394 static isl_stat
add_sum_constraint(struct isl_sched_graph
*graph
,
2395 int sum_pos
, int first
, int n
)
2400 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2402 k
= isl_basic_set_alloc_equality(graph
->lp
);
2404 return isl_stat_error
;
2405 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2406 isl_int_set_si(graph
->lp
->eq
[k
][1 + sum_pos
], -1);
2407 for (i
= 0; i
< n
; ++i
)
2408 isl_int_set_si(graph
->lp
->eq
[k
][1 + first
+ i
], 1);
2413 /* Add a constraint to graph->lp that equates the value at position
2414 * "sum_pos" to the sum of the parameter coefficients of all nodes.
2416 * Within each node, the coefficients have the following order:
2418 * - c_i_n (if parametric)
2419 * - positive and negative parts of c_i_x
2421 static isl_stat
add_param_sum_constraint(struct isl_sched_graph
*graph
,
2427 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2429 k
= isl_basic_set_alloc_equality(graph
->lp
);
2431 return isl_stat_error
;
2432 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2433 isl_int_set_si(graph
->lp
->eq
[k
][1 + sum_pos
], -1);
2434 for (i
= 0; i
< graph
->n
; ++i
) {
2435 int pos
= 1 + graph
->node
[i
].start
+ 1;
2437 for (j
= 0; j
< graph
->node
[i
].nparam
; ++j
)
2438 isl_int_set_si(graph
->lp
->eq
[k
][pos
+ j
], 1);
2444 /* Add a constraint to graph->lp that equates the value at position
2445 * "sum_pos" to the sum of the variable coefficients of all nodes.
2447 * Within each node, the coefficients have the following order:
2449 * - c_i_n (if parametric)
2450 * - positive and negative parts of c_i_x
2452 static isl_stat
add_var_sum_constraint(struct isl_sched_graph
*graph
,
2458 total
= isl_basic_set_dim(graph
->lp
, isl_dim_set
);
2460 k
= isl_basic_set_alloc_equality(graph
->lp
);
2462 return isl_stat_error
;
2463 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2464 isl_int_set_si(graph
->lp
->eq
[k
][1 + sum_pos
], -1);
2465 for (i
= 0; i
< graph
->n
; ++i
) {
2466 struct isl_sched_node
*node
= &graph
->node
[i
];
2467 int pos
= 1 + node_var_coef_offset(node
);
2469 for (j
= 0; j
< 2 * node
->nvar
; ++j
)
2470 isl_int_set_si(graph
->lp
->eq
[k
][pos
+ j
], 1);
2476 /* Construct an ILP problem for finding schedule coefficients
2477 * that result in non-negative, but small dependence distances
2478 * over all dependences.
2479 * In particular, the dependence distances over proximity edges
2480 * are bounded by m_0 + m_n n and we compute schedule coefficients
2481 * with small values (preferably zero) of m_n and m_0.
2483 * All variables of the ILP are non-negative. The actual coefficients
2484 * may be negative, so each coefficient is represented as the difference
2485 * of two non-negative variables. The negative part always appears
2486 * immediately before the positive part.
2487 * Other than that, the variables have the following order
2489 * - sum of positive and negative parts of m_n coefficients
2491 * - sum of all c_n coefficients
2492 * (unconstrained when computing non-parametric schedules)
2493 * - sum of positive and negative parts of all c_x coefficients
2494 * - positive and negative parts of m_n coefficients
2497 * - c_i_n (if parametric)
2498 * - positive and negative parts of c_i_x, in opposite order
2500 * The c_i_x are not represented directly, but through the columns of
2501 * node->cmap. That is, the computed values are for variable t_i_x
2502 * such that c_i_x = Q t_i_x with Q equal to node->cmap.
2504 * The constraints are those from the edges plus two or three equalities
2505 * to express the sums.
2507 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2508 * Otherwise, we ignore them.
2510 static isl_stat
setup_lp(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
2511 int use_coincidence
)
2521 parametric
= ctx
->opt
->schedule_parametric
;
2522 nparam
= isl_space_dim(graph
->node
[0].space
, isl_dim_param
);
2524 total
= param_pos
+ 2 * nparam
;
2525 for (i
= 0; i
< graph
->n
; ++i
) {
2526 struct isl_sched_node
*node
= &graph
->node
[graph
->sorted
[i
]];
2527 if (node_update_cmap(node
) < 0)
2528 return isl_stat_error
;
2529 node
->start
= total
;
2530 total
+= 1 + node
->nparam
+ 2 * node
->nvar
;
2533 if (count_constraints(graph
, &n_eq
, &n_ineq
, use_coincidence
) < 0)
2534 return isl_stat_error
;
2535 if (count_bound_constant_constraints(ctx
, graph
, &n_eq
, &n_ineq
) < 0)
2536 return isl_stat_error
;
2537 if (count_bound_coefficient_constraints(ctx
, graph
, &n_eq
, &n_ineq
) < 0)
2538 return isl_stat_error
;
2540 space
= isl_space_set_alloc(ctx
, 0, total
);
2541 isl_basic_set_free(graph
->lp
);
2542 n_eq
+= 2 + parametric
;
2544 graph
->lp
= isl_basic_set_alloc_space(space
, 0, n_eq
, n_ineq
);
2546 if (add_sum_constraint(graph
, 0, param_pos
, 2 * nparam
) < 0)
2547 return isl_stat_error
;
2548 if (parametric
&& add_param_sum_constraint(graph
, 2) < 0)
2549 return isl_stat_error
;
2550 if (add_var_sum_constraint(graph
, 3) < 0)
2551 return isl_stat_error
;
2552 if (add_bound_constant_constraints(ctx
, graph
) < 0)
2553 return isl_stat_error
;
2554 if (add_bound_coefficient_constraints(ctx
, graph
) < 0)
2555 return isl_stat_error
;
2556 if (add_all_validity_constraints(graph
, use_coincidence
) < 0)
2557 return isl_stat_error
;
2558 if (add_all_proximity_constraints(graph
, use_coincidence
) < 0)
2559 return isl_stat_error
;
2564 /* Analyze the conflicting constraint found by
2565 * isl_tab_basic_set_non_trivial_lexmin. If it corresponds to the validity
2566 * constraint of one of the edges between distinct nodes, living, moreover
2567 * in distinct SCCs, then record the source and sink SCC as this may
2568 * be a good place to cut between SCCs.
2570 static int check_conflict(int con
, void *user
)
2573 struct isl_sched_graph
*graph
= user
;
2575 if (graph
->src_scc
>= 0)
2578 con
-= graph
->lp
->n_eq
;
2580 if (con
>= graph
->lp
->n_ineq
)
2583 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2584 if (!is_validity(&graph
->edge
[i
]))
2586 if (graph
->edge
[i
].src
== graph
->edge
[i
].dst
)
2588 if (graph
->edge
[i
].src
->scc
== graph
->edge
[i
].dst
->scc
)
2590 if (graph
->edge
[i
].start
> con
)
2592 if (graph
->edge
[i
].end
<= con
)
2594 graph
->src_scc
= graph
->edge
[i
].src
->scc
;
2595 graph
->dst_scc
= graph
->edge
[i
].dst
->scc
;
2601 /* Check whether the next schedule row of the given node needs to be
2602 * non-trivial. Lower-dimensional domains may have some trivial rows,
2603 * but as soon as the number of remaining required non-trivial rows
2604 * is as large as the number or remaining rows to be computed,
2605 * all remaining rows need to be non-trivial.
2607 static int needs_row(struct isl_sched_graph
*graph
, struct isl_sched_node
*node
)
2609 return node
->nvar
- node
->rank
>= graph
->maxvar
- graph
->n_row
;
2612 /* Construct a non-triviality region with "n" directions
2613 * over "n_var" coefficients.
2614 * Each direction corresponds to a schedule coefficient,
2615 * where each schedule coefficient is encoded as the difference
2616 * of two non-negative variables, c^+_i - c^-_i
2617 * with c^-_i at position 2 * i and c^+_i at position 2 * i + 1.
2618 * The order of the directions is the same as that of the node variables,
2619 * but the pairs of non-negative variables representing the coefficients
2620 * are stored in the opposite order.
2621 * The first direction therefore corresponds to the last such pair.
2622 * Furthermore, if the number of variables is greater than the number
2623 * of directions, then the directions correspond to the last node variables,
2624 * i.e., the first pairs of non-negative variables.
2626 static __isl_give isl_mat
*construct_trivial(isl_ctx
*ctx
, int n
, int n_var
)
2632 mat
= isl_mat_zero(ctx
, n
, 2 * n_var
);
2633 for (i
= 0; i
< n
; ++i
) {
2634 mat
= isl_mat_set_element_si(mat
, i
, 2 * (n
- 1 - i
), -1);
2635 mat
= isl_mat_set_element_si(mat
, i
, 2 * (n
- 1 - i
) + 1, 1);
2641 /* Solve the ILP problem constructed in setup_lp.
2642 * For each node such that all the remaining rows of its schedule
2643 * need to be non-trivial, we construct a non-triviality region.
2644 * This region imposes that the next row is independent of previous rows.
2645 * In particular the coefficients c_i_x are represented by t_i_x
2646 * variables with c_i_x = Q t_i_x and Q a unimodular matrix such that
2647 * its first columns span the rows of the previously computed part
2648 * of the schedule. The non-triviality region enforces that at least
2649 * one of the remaining components of t_i_x is non-zero, i.e.,
2650 * that the new schedule row depends on at least one of the remaining
2653 static __isl_give isl_vec
*solve_lp(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2659 for (i
= 0; i
< graph
->n
; ++i
) {
2660 struct isl_sched_node
*node
= &graph
->node
[i
];
2661 int skip
= node
->rank
;
2664 graph
->region
[i
].pos
= node_var_coef_offset(node
);
2665 if (needs_row(graph
, node
))
2666 trivial
= construct_trivial(ctx
, node
->nvar
- skip
,
2669 trivial
= isl_mat_zero(ctx
, 0, 0);
2670 graph
->region
[i
].trivial
= trivial
;
2672 lp
= isl_basic_set_copy(graph
->lp
);
2673 sol
= isl_tab_basic_set_non_trivial_lexmin(lp
, 2, graph
->n
,
2674 graph
->region
, &check_conflict
, graph
);
2675 for (i
= 0; i
< graph
->n
; ++i
)
2676 isl_mat_free(graph
->region
[i
].trivial
);
2680 /* Extract the coefficients for the variables of "node" from "sol".
2682 * Within each node, the coefficients have the following order:
2684 * - c_i_n (if parametric)
2685 * - positive and negative parts of c_i_x
2687 * The c_i_x^- appear before their c_i_x^+ counterpart.
2688 * Furthermore, the order of these pairs is the opposite of that
2689 * of the corresponding coefficients.
2691 * Return c_i_x = c_i_x^+ - c_i_x^-
2693 static __isl_give isl_vec
*extract_var_coef(struct isl_sched_node
*node
,
2694 __isl_keep isl_vec
*sol
)
2702 csol
= isl_vec_alloc(isl_vec_get_ctx(sol
), node
->nvar
);
2706 pos
= 1 + node_var_coef_offset(node
);
2707 for (i
= 0; i
< node
->nvar
; ++i
)
2708 isl_int_sub(csol
->el
[node
->nvar
- 1 - i
],
2709 sol
->el
[pos
+ 2 * i
+ 1], sol
->el
[pos
+ 2 * i
]);
2714 /* Update the schedules of all nodes based on the given solution
2715 * of the LP problem.
2716 * The new row is added to the current band.
2717 * All possibly negative coefficients are encoded as a difference
2718 * of two non-negative variables, so we need to perform the subtraction
2719 * here. Moreover, if use_cmap is set, then the solution does
2720 * not refer to the actual coefficients c_i_x, but instead to variables
2721 * t_i_x such that c_i_x = Q t_i_x and Q is equal to node->cmap.
2722 * In this case, we then also need to perform this multiplication
2723 * to obtain the values of c_i_x.
2725 * If coincident is set, then the caller guarantees that the new
2726 * row satisfies the coincidence constraints.
2728 static int update_schedule(struct isl_sched_graph
*graph
,
2729 __isl_take isl_vec
*sol
, int use_cmap
, int coincident
)
2732 isl_vec
*csol
= NULL
;
2737 isl_die(sol
->ctx
, isl_error_internal
,
2738 "no solution found", goto error
);
2739 if (graph
->n_total_row
>= graph
->max_row
)
2740 isl_die(sol
->ctx
, isl_error_internal
,
2741 "too many schedule rows", goto error
);
2743 for (i
= 0; i
< graph
->n
; ++i
) {
2744 struct isl_sched_node
*node
= &graph
->node
[i
];
2745 int pos
= node
->start
;
2746 int row
= isl_mat_rows(node
->sched
);
2749 csol
= extract_var_coef(node
, sol
);
2753 isl_map_free(node
->sched_map
);
2754 node
->sched_map
= NULL
;
2755 node
->sched
= isl_mat_add_rows(node
->sched
, 1);
2758 for (j
= 0; j
< 1 + node
->nparam
; ++j
)
2759 node
->sched
= isl_mat_set_element(node
->sched
,
2760 row
, j
, sol
->el
[1 + pos
+ j
]);
2762 csol
= isl_mat_vec_product(isl_mat_copy(node
->cmap
),
2766 for (j
= 0; j
< node
->nvar
; ++j
)
2767 node
->sched
= isl_mat_set_element(node
->sched
,
2768 row
, 1 + node
->nparam
+ j
, csol
->el
[j
]);
2769 node
->coincident
[graph
->n_total_row
] = coincident
;
2775 graph
->n_total_row
++;
2784 /* Convert row "row" of node->sched into an isl_aff living in "ls"
2785 * and return this isl_aff.
2787 static __isl_give isl_aff
*extract_schedule_row(__isl_take isl_local_space
*ls
,
2788 struct isl_sched_node
*node
, int row
)
2796 aff
= isl_aff_zero_on_domain(ls
);
2797 isl_mat_get_element(node
->sched
, row
, 0, &v
);
2798 aff
= isl_aff_set_constant(aff
, v
);
2799 for (j
= 0; j
< node
->nparam
; ++j
) {
2800 isl_mat_get_element(node
->sched
, row
, 1 + j
, &v
);
2801 aff
= isl_aff_set_coefficient(aff
, isl_dim_param
, j
, v
);
2803 for (j
= 0; j
< node
->nvar
; ++j
) {
2804 isl_mat_get_element(node
->sched
, row
, 1 + node
->nparam
+ j
, &v
);
2805 aff
= isl_aff_set_coefficient(aff
, isl_dim_in
, j
, v
);
2813 /* Convert the "n" rows starting at "first" of node->sched into a multi_aff
2814 * and return this multi_aff.
2816 * The result is defined over the uncompressed node domain.
2818 static __isl_give isl_multi_aff
*node_extract_partial_schedule_multi_aff(
2819 struct isl_sched_node
*node
, int first
, int n
)
2823 isl_local_space
*ls
;
2830 nrow
= isl_mat_rows(node
->sched
);
2831 if (node
->compressed
)
2832 space
= isl_multi_aff_get_domain_space(node
->decompress
);
2834 space
= isl_space_copy(node
->space
);
2835 ls
= isl_local_space_from_space(isl_space_copy(space
));
2836 space
= isl_space_from_domain(space
);
2837 space
= isl_space_add_dims(space
, isl_dim_out
, n
);
2838 ma
= isl_multi_aff_zero(space
);
2840 for (i
= first
; i
< first
+ n
; ++i
) {
2841 aff
= extract_schedule_row(isl_local_space_copy(ls
), node
, i
);
2842 ma
= isl_multi_aff_set_aff(ma
, i
- first
, aff
);
2845 isl_local_space_free(ls
);
2847 if (node
->compressed
)
2848 ma
= isl_multi_aff_pullback_multi_aff(ma
,
2849 isl_multi_aff_copy(node
->compress
));
2854 /* Convert node->sched into a multi_aff and return this multi_aff.
2856 * The result is defined over the uncompressed node domain.
2858 static __isl_give isl_multi_aff
*node_extract_schedule_multi_aff(
2859 struct isl_sched_node
*node
)
2863 nrow
= isl_mat_rows(node
->sched
);
2864 return node_extract_partial_schedule_multi_aff(node
, 0, nrow
);
2867 /* Convert node->sched into a map and return this map.
2869 * The result is cached in node->sched_map, which needs to be released
2870 * whenever node->sched is updated.
2871 * It is defined over the uncompressed node domain.
2873 static __isl_give isl_map
*node_extract_schedule(struct isl_sched_node
*node
)
2875 if (!node
->sched_map
) {
2878 ma
= node_extract_schedule_multi_aff(node
);
2879 node
->sched_map
= isl_map_from_multi_aff(ma
);
2882 return isl_map_copy(node
->sched_map
);
2885 /* Construct a map that can be used to update a dependence relation
2886 * based on the current schedule.
2887 * That is, construct a map expressing that source and sink
2888 * are executed within the same iteration of the current schedule.
2889 * This map can then be intersected with the dependence relation.
2890 * This is not the most efficient way, but this shouldn't be a critical
2893 static __isl_give isl_map
*specializer(struct isl_sched_node
*src
,
2894 struct isl_sched_node
*dst
)
2896 isl_map
*src_sched
, *dst_sched
;
2898 src_sched
= node_extract_schedule(src
);
2899 dst_sched
= node_extract_schedule(dst
);
2900 return isl_map_apply_range(src_sched
, isl_map_reverse(dst_sched
));
2903 /* Intersect the domains of the nested relations in domain and range
2904 * of "umap" with "map".
2906 static __isl_give isl_union_map
*intersect_domains(
2907 __isl_take isl_union_map
*umap
, __isl_keep isl_map
*map
)
2909 isl_union_set
*uset
;
2911 umap
= isl_union_map_zip(umap
);
2912 uset
= isl_union_set_from_set(isl_map_wrap(isl_map_copy(map
)));
2913 umap
= isl_union_map_intersect_domain(umap
, uset
);
2914 umap
= isl_union_map_zip(umap
);
2918 /* Update the dependence relation of the given edge based
2919 * on the current schedule.
2920 * If the dependence is carried completely by the current schedule, then
2921 * it is removed from the edge_tables. It is kept in the list of edges
2922 * as otherwise all edge_tables would have to be recomputed.
2924 static int update_edge(struct isl_sched_graph
*graph
,
2925 struct isl_sched_edge
*edge
)
2930 id
= specializer(edge
->src
, edge
->dst
);
2931 edge
->map
= isl_map_intersect(edge
->map
, isl_map_copy(id
));
2935 if (edge
->tagged_condition
) {
2936 edge
->tagged_condition
=
2937 intersect_domains(edge
->tagged_condition
, id
);
2938 if (!edge
->tagged_condition
)
2941 if (edge
->tagged_validity
) {
2942 edge
->tagged_validity
=
2943 intersect_domains(edge
->tagged_validity
, id
);
2944 if (!edge
->tagged_validity
)
2948 empty
= isl_map_plain_is_empty(edge
->map
);
2952 graph_remove_edge(graph
, edge
);
2961 /* Does the domain of "umap" intersect "uset"?
2963 static int domain_intersects(__isl_keep isl_union_map
*umap
,
2964 __isl_keep isl_union_set
*uset
)
2968 umap
= isl_union_map_copy(umap
);
2969 umap
= isl_union_map_intersect_domain(umap
, isl_union_set_copy(uset
));
2970 empty
= isl_union_map_is_empty(umap
);
2971 isl_union_map_free(umap
);
2973 return empty
< 0 ? -1 : !empty
;
2976 /* Does the range of "umap" intersect "uset"?
2978 static int range_intersects(__isl_keep isl_union_map
*umap
,
2979 __isl_keep isl_union_set
*uset
)
2983 umap
= isl_union_map_copy(umap
);
2984 umap
= isl_union_map_intersect_range(umap
, isl_union_set_copy(uset
));
2985 empty
= isl_union_map_is_empty(umap
);
2986 isl_union_map_free(umap
);
2988 return empty
< 0 ? -1 : !empty
;
2991 /* Are the condition dependences of "edge" local with respect to
2992 * the current schedule?
2994 * That is, are domain and range of the condition dependences mapped
2995 * to the same point?
2997 * In other words, is the condition false?
2999 static int is_condition_false(struct isl_sched_edge
*edge
)
3001 isl_union_map
*umap
;
3002 isl_map
*map
, *sched
, *test
;
3005 empty
= isl_union_map_is_empty(edge
->tagged_condition
);
3006 if (empty
< 0 || empty
)
3009 umap
= isl_union_map_copy(edge
->tagged_condition
);
3010 umap
= isl_union_map_zip(umap
);
3011 umap
= isl_union_set_unwrap(isl_union_map_domain(umap
));
3012 map
= isl_map_from_union_map(umap
);
3014 sched
= node_extract_schedule(edge
->src
);
3015 map
= isl_map_apply_domain(map
, sched
);
3016 sched
= node_extract_schedule(edge
->dst
);
3017 map
= isl_map_apply_range(map
, sched
);
3019 test
= isl_map_identity(isl_map_get_space(map
));
3020 local
= isl_map_is_subset(map
, test
);
3027 /* For each conditional validity constraint that is adjacent
3028 * to a condition with domain in condition_source or range in condition_sink,
3029 * turn it into an unconditional validity constraint.
3031 static int unconditionalize_adjacent_validity(struct isl_sched_graph
*graph
,
3032 __isl_take isl_union_set
*condition_source
,
3033 __isl_take isl_union_set
*condition_sink
)
3037 condition_source
= isl_union_set_coalesce(condition_source
);
3038 condition_sink
= isl_union_set_coalesce(condition_sink
);
3040 for (i
= 0; i
< graph
->n_edge
; ++i
) {
3042 isl_union_map
*validity
;
3044 if (!is_conditional_validity(&graph
->edge
[i
]))
3046 if (is_validity(&graph
->edge
[i
]))
3049 validity
= graph
->edge
[i
].tagged_validity
;
3050 adjacent
= domain_intersects(validity
, condition_sink
);
3051 if (adjacent
>= 0 && !adjacent
)
3052 adjacent
= range_intersects(validity
, condition_source
);
3058 set_validity(&graph
->edge
[i
]);
3061 isl_union_set_free(condition_source
);
3062 isl_union_set_free(condition_sink
);
3065 isl_union_set_free(condition_source
);
3066 isl_union_set_free(condition_sink
);
3070 /* Update the dependence relations of all edges based on the current schedule
3071 * and enforce conditional validity constraints that are adjacent
3072 * to satisfied condition constraints.
3074 * First check if any of the condition constraints are satisfied
3075 * (i.e., not local to the outer schedule) and keep track of
3076 * their domain and range.
3077 * Then update all dependence relations (which removes the non-local
3079 * Finally, if any condition constraints turned out to be satisfied,
3080 * then turn all adjacent conditional validity constraints into
3081 * unconditional validity constraints.
3083 static int update_edges(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
3087 isl_union_set
*source
, *sink
;
3089 source
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
3090 sink
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
3091 for (i
= 0; i
< graph
->n_edge
; ++i
) {
3093 isl_union_set
*uset
;
3094 isl_union_map
*umap
;
3096 if (!is_condition(&graph
->edge
[i
]))
3098 if (is_local(&graph
->edge
[i
]))
3100 local
= is_condition_false(&graph
->edge
[i
]);
3108 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_condition
);
3109 uset
= isl_union_map_domain(umap
);
3110 source
= isl_union_set_union(source
, uset
);
3112 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_condition
);
3113 uset
= isl_union_map_range(umap
);
3114 sink
= isl_union_set_union(sink
, uset
);
3117 for (i
= graph
->n_edge
- 1; i
>= 0; --i
) {
3118 if (update_edge(graph
, &graph
->edge
[i
]) < 0)
3123 return unconditionalize_adjacent_validity(graph
, source
, sink
);
3125 isl_union_set_free(source
);
3126 isl_union_set_free(sink
);
3129 isl_union_set_free(source
);
3130 isl_union_set_free(sink
);
3134 static void next_band(struct isl_sched_graph
*graph
)
3136 graph
->band_start
= graph
->n_total_row
;
3139 /* Return the union of the universe domains of the nodes in "graph"
3140 * that satisfy "pred".
3142 static __isl_give isl_union_set
*isl_sched_graph_domain(isl_ctx
*ctx
,
3143 struct isl_sched_graph
*graph
,
3144 int (*pred
)(struct isl_sched_node
*node
, int data
), int data
)
3150 for (i
= 0; i
< graph
->n
; ++i
)
3151 if (pred(&graph
->node
[i
], data
))
3155 isl_die(ctx
, isl_error_internal
,
3156 "empty component", return NULL
);
3158 set
= isl_set_universe(isl_space_copy(graph
->node
[i
].space
));
3159 dom
= isl_union_set_from_set(set
);
3161 for (i
= i
+ 1; i
< graph
->n
; ++i
) {
3162 if (!pred(&graph
->node
[i
], data
))
3164 set
= isl_set_universe(isl_space_copy(graph
->node
[i
].space
));
3165 dom
= isl_union_set_union(dom
, isl_union_set_from_set(set
));
3171 /* Return a list of unions of universe domains, where each element
3172 * in the list corresponds to an SCC (or WCC) indexed by node->scc.
3174 static __isl_give isl_union_set_list
*extract_sccs(isl_ctx
*ctx
,
3175 struct isl_sched_graph
*graph
)
3178 isl_union_set_list
*filters
;
3180 filters
= isl_union_set_list_alloc(ctx
, graph
->scc
);
3181 for (i
= 0; i
< graph
->scc
; ++i
) {
3184 dom
= isl_sched_graph_domain(ctx
, graph
, &node_scc_exactly
, i
);
3185 filters
= isl_union_set_list_add(filters
, dom
);
3191 /* Return a list of two unions of universe domains, one for the SCCs up
3192 * to and including graph->src_scc and another for the other SCCs.
3194 static __isl_give isl_union_set_list
*extract_split(isl_ctx
*ctx
,
3195 struct isl_sched_graph
*graph
)
3198 isl_union_set_list
*filters
;
3200 filters
= isl_union_set_list_alloc(ctx
, 2);
3201 dom
= isl_sched_graph_domain(ctx
, graph
,
3202 &node_scc_at_most
, graph
->src_scc
);
3203 filters
= isl_union_set_list_add(filters
, dom
);
3204 dom
= isl_sched_graph_domain(ctx
, graph
,
3205 &node_scc_at_least
, graph
->src_scc
+ 1);
3206 filters
= isl_union_set_list_add(filters
, dom
);
3211 /* Copy nodes that satisfy node_pred from the src dependence graph
3212 * to the dst dependence graph.
3214 static int copy_nodes(struct isl_sched_graph
*dst
, struct isl_sched_graph
*src
,
3215 int (*node_pred
)(struct isl_sched_node
*node
, int data
), int data
)
3220 for (i
= 0; i
< src
->n
; ++i
) {
3223 if (!node_pred(&src
->node
[i
], data
))
3227 dst
->node
[j
].space
= isl_space_copy(src
->node
[i
].space
);
3228 dst
->node
[j
].compressed
= src
->node
[i
].compressed
;
3229 dst
->node
[j
].hull
= isl_set_copy(src
->node
[i
].hull
);
3230 dst
->node
[j
].compress
=
3231 isl_multi_aff_copy(src
->node
[i
].compress
);
3232 dst
->node
[j
].decompress
=
3233 isl_multi_aff_copy(src
->node
[i
].decompress
);
3234 dst
->node
[j
].nvar
= src
->node
[i
].nvar
;
3235 dst
->node
[j
].nparam
= src
->node
[i
].nparam
;
3236 dst
->node
[j
].sched
= isl_mat_copy(src
->node
[i
].sched
);
3237 dst
->node
[j
].sched_map
= isl_map_copy(src
->node
[i
].sched_map
);
3238 dst
->node
[j
].coincident
= src
->node
[i
].coincident
;
3239 dst
->node
[j
].sizes
= isl_multi_val_copy(src
->node
[i
].sizes
);
3240 dst
->node
[j
].max
= isl_vec_copy(src
->node
[i
].max
);
3243 if (!dst
->node
[j
].space
|| !dst
->node
[j
].sched
)
3245 if (dst
->node
[j
].compressed
&&
3246 (!dst
->node
[j
].hull
|| !dst
->node
[j
].compress
||
3247 !dst
->node
[j
].decompress
))
3254 /* Copy non-empty edges that satisfy edge_pred from the src dependence graph
3255 * to the dst dependence graph.
3256 * If the source or destination node of the edge is not in the destination
3257 * graph, then it must be a backward proximity edge and it should simply
3260 static int copy_edges(isl_ctx
*ctx
, struct isl_sched_graph
*dst
,
3261 struct isl_sched_graph
*src
,
3262 int (*edge_pred
)(struct isl_sched_edge
*edge
, int data
), int data
)
3265 enum isl_edge_type t
;
3268 for (i
= 0; i
< src
->n_edge
; ++i
) {
3269 struct isl_sched_edge
*edge
= &src
->edge
[i
];
3271 isl_union_map
*tagged_condition
;
3272 isl_union_map
*tagged_validity
;
3273 struct isl_sched_node
*dst_src
, *dst_dst
;
3275 if (!edge_pred(edge
, data
))
3278 if (isl_map_plain_is_empty(edge
->map
))
3281 dst_src
= graph_find_node(ctx
, dst
, edge
->src
->space
);
3282 dst_dst
= graph_find_node(ctx
, dst
, edge
->dst
->space
);
3283 if (!dst_src
|| !dst_dst
) {
3284 if (is_validity(edge
) || is_conditional_validity(edge
))
3285 isl_die(ctx
, isl_error_internal
,
3286 "backward (conditional) validity edge",
3291 map
= isl_map_copy(edge
->map
);
3292 tagged_condition
= isl_union_map_copy(edge
->tagged_condition
);
3293 tagged_validity
= isl_union_map_copy(edge
->tagged_validity
);
3295 dst
->edge
[dst
->n_edge
].src
= dst_src
;
3296 dst
->edge
[dst
->n_edge
].dst
= dst_dst
;
3297 dst
->edge
[dst
->n_edge
].map
= map
;
3298 dst
->edge
[dst
->n_edge
].tagged_condition
= tagged_condition
;
3299 dst
->edge
[dst
->n_edge
].tagged_validity
= tagged_validity
;
3300 dst
->edge
[dst
->n_edge
].types
= edge
->types
;
3303 if (edge
->tagged_condition
&& !tagged_condition
)
3305 if (edge
->tagged_validity
&& !tagged_validity
)
3308 for (t
= isl_edge_first
; t
<= isl_edge_last
; ++t
) {
3310 graph_find_edge(src
, t
, edge
->src
, edge
->dst
))
3312 if (graph_edge_table_add(ctx
, dst
, t
,
3313 &dst
->edge
[dst
->n_edge
- 1]) < 0)
3321 /* Compute the maximal number of variables over all nodes.
3322 * This is the maximal number of linearly independent schedule
3323 * rows that we need to compute.
3324 * Just in case we end up in a part of the dependence graph
3325 * with only lower-dimensional domains, we make sure we will
3326 * compute the required amount of extra linearly independent rows.
3328 static int compute_maxvar(struct isl_sched_graph
*graph
)
3333 for (i
= 0; i
< graph
->n
; ++i
) {
3334 struct isl_sched_node
*node
= &graph
->node
[i
];
3337 if (node_update_cmap(node
) < 0)
3339 nvar
= node
->nvar
+ graph
->n_row
- node
->rank
;
3340 if (nvar
> graph
->maxvar
)
3341 graph
->maxvar
= nvar
;
3347 /* Extract the subgraph of "graph" that consists of the node satisfying
3348 * "node_pred" and the edges satisfying "edge_pred" and store
3349 * the result in "sub".
3351 static int extract_sub_graph(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
3352 int (*node_pred
)(struct isl_sched_node
*node
, int data
),
3353 int (*edge_pred
)(struct isl_sched_edge
*edge
, int data
),
3354 int data
, struct isl_sched_graph
*sub
)
3356 int i
, n
= 0, n_edge
= 0;
3359 for (i
= 0; i
< graph
->n
; ++i
)
3360 if (node_pred(&graph
->node
[i
], data
))
3362 for (i
= 0; i
< graph
->n_edge
; ++i
)
3363 if (edge_pred(&graph
->edge
[i
], data
))
3365 if (graph_alloc(ctx
, sub
, n
, n_edge
) < 0)
3367 if (copy_nodes(sub
, graph
, node_pred
, data
) < 0)
3369 if (graph_init_table(ctx
, sub
) < 0)
3371 for (t
= 0; t
<= isl_edge_last
; ++t
)
3372 sub
->max_edge
[t
] = graph
->max_edge
[t
];
3373 if (graph_init_edge_tables(ctx
, sub
) < 0)
3375 if (copy_edges(ctx
, sub
, graph
, edge_pred
, data
) < 0)
3377 sub
->n_row
= graph
->n_row
;
3378 sub
->max_row
= graph
->max_row
;
3379 sub
->n_total_row
= graph
->n_total_row
;
3380 sub
->band_start
= graph
->band_start
;
3385 static __isl_give isl_schedule_node
*compute_schedule(isl_schedule_node
*node
,
3386 struct isl_sched_graph
*graph
);
3387 static __isl_give isl_schedule_node
*compute_schedule_wcc(
3388 isl_schedule_node
*node
, struct isl_sched_graph
*graph
);
3390 /* Compute a schedule for a subgraph of "graph". In particular, for
3391 * the graph composed of nodes that satisfy node_pred and edges that
3392 * that satisfy edge_pred.
3393 * If the subgraph is known to consist of a single component, then wcc should
3394 * be set and then we call compute_schedule_wcc on the constructed subgraph.
3395 * Otherwise, we call compute_schedule, which will check whether the subgraph
3398 * The schedule is inserted at "node" and the updated schedule node
3401 static __isl_give isl_schedule_node
*compute_sub_schedule(
3402 __isl_take isl_schedule_node
*node
, isl_ctx
*ctx
,
3403 struct isl_sched_graph
*graph
,
3404 int (*node_pred
)(struct isl_sched_node
*node
, int data
),
3405 int (*edge_pred
)(struct isl_sched_edge
*edge
, int data
),
3408 struct isl_sched_graph split
= { 0 };
3410 if (extract_sub_graph(ctx
, graph
, node_pred
, edge_pred
, data
,
3415 node
= compute_schedule_wcc(node
, &split
);
3417 node
= compute_schedule(node
, &split
);
3419 graph_free(ctx
, &split
);
3422 graph_free(ctx
, &split
);
3423 return isl_schedule_node_free(node
);
3426 static int edge_scc_exactly(struct isl_sched_edge
*edge
, int scc
)
3428 return edge
->src
->scc
== scc
&& edge
->dst
->scc
== scc
;
3431 static int edge_dst_scc_at_most(struct isl_sched_edge
*edge
, int scc
)
3433 return edge
->dst
->scc
<= scc
;
3436 static int edge_src_scc_at_least(struct isl_sched_edge
*edge
, int scc
)
3438 return edge
->src
->scc
>= scc
;
3441 /* Reset the current band by dropping all its schedule rows.
3443 static int reset_band(struct isl_sched_graph
*graph
)
3448 drop
= graph
->n_total_row
- graph
->band_start
;
3449 graph
->n_total_row
-= drop
;
3450 graph
->n_row
-= drop
;
3452 for (i
= 0; i
< graph
->n
; ++i
) {
3453 struct isl_sched_node
*node
= &graph
->node
[i
];
3455 isl_map_free(node
->sched_map
);
3456 node
->sched_map
= NULL
;
3458 node
->sched
= isl_mat_drop_rows(node
->sched
,
3459 graph
->band_start
, drop
);
3468 /* Split the current graph into two parts and compute a schedule for each
3469 * part individually. In particular, one part consists of all SCCs up
3470 * to and including graph->src_scc, while the other part contains the other
3471 * SCCs. The split is enforced by a sequence node inserted at position "node"
3472 * in the schedule tree. Return the updated schedule node.
3473 * If either of these two parts consists of a sequence, then it is spliced
3474 * into the sequence containing the two parts.
3476 * The current band is reset. It would be possible to reuse
3477 * the previously computed rows as the first rows in the next
3478 * band, but recomputing them may result in better rows as we are looking
3479 * at a smaller part of the dependence graph.
3481 static __isl_give isl_schedule_node
*compute_split_schedule(
3482 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
3486 isl_union_set_list
*filters
;
3491 if (reset_band(graph
) < 0)
3492 return isl_schedule_node_free(node
);
3496 ctx
= isl_schedule_node_get_ctx(node
);
3497 filters
= extract_split(ctx
, graph
);
3498 node
= isl_schedule_node_insert_sequence(node
, filters
);
3499 node
= isl_schedule_node_child(node
, 1);
3500 node
= isl_schedule_node_child(node
, 0);
3502 node
= compute_sub_schedule(node
, ctx
, graph
,
3503 &node_scc_at_least
, &edge_src_scc_at_least
,
3504 graph
->src_scc
+ 1, 0);
3505 is_seq
= isl_schedule_node_get_type(node
) == isl_schedule_node_sequence
;
3506 node
= isl_schedule_node_parent(node
);
3507 node
= isl_schedule_node_parent(node
);
3509 node
= isl_schedule_node_sequence_splice_child(node
, 1);
3510 node
= isl_schedule_node_child(node
, 0);
3511 node
= isl_schedule_node_child(node
, 0);
3512 node
= compute_sub_schedule(node
, ctx
, graph
,
3513 &node_scc_at_most
, &edge_dst_scc_at_most
,
3515 is_seq
= isl_schedule_node_get_type(node
) == isl_schedule_node_sequence
;
3516 node
= isl_schedule_node_parent(node
);
3517 node
= isl_schedule_node_parent(node
);
3519 node
= isl_schedule_node_sequence_splice_child(node
, 0);
3524 /* Insert a band node at position "node" in the schedule tree corresponding
3525 * to the current band in "graph". Mark the band node permutable
3526 * if "permutable" is set.
3527 * The partial schedules and the coincidence property are extracted
3528 * from the graph nodes.
3529 * Return the updated schedule node.
3531 static __isl_give isl_schedule_node
*insert_current_band(
3532 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
3538 isl_multi_pw_aff
*mpa
;
3539 isl_multi_union_pw_aff
*mupa
;
3545 isl_die(isl_schedule_node_get_ctx(node
), isl_error_internal
,
3546 "graph should have at least one node",
3547 return isl_schedule_node_free(node
));
3549 start
= graph
->band_start
;
3550 end
= graph
->n_total_row
;
3553 ma
= node_extract_partial_schedule_multi_aff(&graph
->node
[0], start
, n
);
3554 mpa
= isl_multi_pw_aff_from_multi_aff(ma
);
3555 mupa
= isl_multi_union_pw_aff_from_multi_pw_aff(mpa
);
3557 for (i
= 1; i
< graph
->n
; ++i
) {
3558 isl_multi_union_pw_aff
*mupa_i
;
3560 ma
= node_extract_partial_schedule_multi_aff(&graph
->node
[i
],
3562 mpa
= isl_multi_pw_aff_from_multi_aff(ma
);
3563 mupa_i
= isl_multi_union_pw_aff_from_multi_pw_aff(mpa
);
3564 mupa
= isl_multi_union_pw_aff_union_add(mupa
, mupa_i
);
3566 node
= isl_schedule_node_insert_partial_schedule(node
, mupa
);
3568 for (i
= 0; i
< n
; ++i
)
3569 node
= isl_schedule_node_band_member_set_coincident(node
, i
,
3570 graph
->node
[0].coincident
[start
+ i
]);
3571 node
= isl_schedule_node_band_set_permutable(node
, permutable
);
3576 /* Update the dependence relations based on the current schedule,
3577 * add the current band to "node" and then continue with the computation
3579 * Return the updated schedule node.
3581 static __isl_give isl_schedule_node
*compute_next_band(
3582 __isl_take isl_schedule_node
*node
,
3583 struct isl_sched_graph
*graph
, int permutable
)
3590 ctx
= isl_schedule_node_get_ctx(node
);
3591 if (update_edges(ctx
, graph
) < 0)
3592 return isl_schedule_node_free(node
);
3593 node
= insert_current_band(node
, graph
, permutable
);
3596 node
= isl_schedule_node_child(node
, 0);
3597 node
= compute_schedule(node
, graph
);
3598 node
= isl_schedule_node_parent(node
);
3603 /* Add the constraints "coef" derived from an edge from "node" to itself
3604 * to graph->lp in order to respect the dependences and to try and carry them.
3605 * "pos" is the sequence number of the edge that needs to be carried.
3606 * "coef" represents general constraints on coefficients (c_0, c_n, c_x)
3607 * of valid constraints for (y - x) with x and y instances of the node.
3609 * The constraints added to graph->lp need to enforce
3611 * (c_j_0 + c_j_n n + c_j_x y) - (c_j_0 + c_j_n n + c_j_x x)
3612 * = c_j_x (y - x) >= e_i
3614 * for each (x,y) in the dependence relation of the edge.
3615 * That is, (-e_i, 0, c_j_x) needs to be plugged in for (c_0, c_n, c_x),
3616 * taking into account that each coefficient in c_j_x is represented
3617 * as a pair of non-negative coefficients.
3619 static isl_stat
add_intra_constraints(struct isl_sched_graph
*graph
,
3620 struct isl_sched_node
*node
, __isl_take isl_basic_set
*coef
, int pos
)
3624 isl_dim_map
*dim_map
;
3627 return isl_stat_error
;
3629 ctx
= isl_basic_set_get_ctx(coef
);
3630 offset
= coef_var_offset(coef
);
3631 dim_map
= intra_dim_map(ctx
, graph
, node
, offset
, 1);
3632 isl_dim_map_range(dim_map
, 3 + pos
, 0, 0, 0, 1, -1);
3633 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
3638 /* Add the constraints "coef" derived from an edge from "src" to "dst"
3639 * to graph->lp in order to respect the dependences and to try and carry them.
3640 * "pos" is the sequence number of the edge that needs to be carried.
3641 * "coef" represents general constraints on coefficients (c_0, c_n, c_x, c_y)
3642 * of valid constraints for (x, y) with x and y instances of "src" and "dst".
3644 * The constraints added to graph->lp need to enforce
3646 * (c_k_0 + c_k_n n + c_k_x y) - (c_j_0 + c_j_n n + c_j_x x) >= e_i
3648 * for each (x,y) in the dependence relation of the edge.
3650 * (-e_i + c_k_0 - c_j_0, c_k_n - c_j_n, -c_j_x, c_k_x)
3651 * needs to be plugged in for (c_0, c_n, c_x, c_y),
3652 * taking into account that each coefficient in c_j_x and c_k_x is represented
3653 * as a pair of non-negative coefficients.
3655 static isl_stat
add_inter_constraints(struct isl_sched_graph
*graph
,
3656 struct isl_sched_node
*src
, struct isl_sched_node
*dst
,
3657 __isl_take isl_basic_set
*coef
, int pos
)
3661 isl_dim_map
*dim_map
;
3664 return isl_stat_error
;
3666 ctx
= isl_basic_set_get_ctx(coef
);
3667 offset
= coef_var_offset(coef
);
3668 dim_map
= inter_dim_map(ctx
, graph
, src
, dst
, offset
, 1);
3669 isl_dim_map_range(dim_map
, 3 + pos
, 0, 0, 0, 1, -1);
3670 graph
->lp
= add_constraints_dim_map(graph
->lp
, coef
, dim_map
);
3675 /* Data structure collecting information used during the construction
3676 * of an LP for carrying dependences.
3678 * "intra" is a sequence of coefficient constraints for intra-node edges.
3679 * "inter" is a sequence of coefficient constraints for inter-node edges.
3682 isl_basic_set_list
*intra
;
3683 isl_basic_set_list
*inter
;
3686 /* Free all the data stored in "carry".
3688 static void isl_carry_clear(struct isl_carry
*carry
)
3690 isl_basic_set_list_free(carry
->intra
);
3691 isl_basic_set_list_free(carry
->inter
);
3694 /* Return a pointer to the node in "graph" that lives in "space".
3695 * If the requested node has been compressed, then "space"
3696 * corresponds to the compressed space.
3698 * First try and see if "space" is the space of an uncompressed node.
3699 * If so, return that node.
3700 * Otherwise, "space" was constructed by construct_compressed_id and
3701 * contains a user pointer pointing to the node in the tuple id.
3703 static struct isl_sched_node
*graph_find_compressed_node(isl_ctx
*ctx
,
3704 struct isl_sched_graph
*graph
, __isl_keep isl_space
*space
)
3707 struct isl_sched_node
*node
;
3712 node
= graph_find_node(ctx
, graph
, space
);
3716 id
= isl_space_get_tuple_id(space
, isl_dim_set
);
3717 node
= isl_id_get_user(id
);
3723 if (!(node
>= &graph
->node
[0] && node
< &graph
->node
[graph
->n
]))
3724 isl_die(ctx
, isl_error_internal
,
3725 "space points to invalid node", return NULL
);
3730 /* Internal data structure for add_all_constraints.
3732 * "graph" is the schedule constraint graph for which an LP problem
3733 * is being constructed.
3734 * "pos" is the position of the next edge that needs to be carried.
3736 struct isl_add_all_constraints_data
{
3738 struct isl_sched_graph
*graph
;
3742 /* Add the constraints "coef" derived from an edge from a node to itself
3743 * to data->graph->lp in order to respect the dependences and
3744 * to try and carry them.
3746 * The space of "coef" is of the form
3748 * coefficients[[c_cst, c_n] -> S[c_x]]
3750 * with S[c_x] the (compressed) space of the node.
3751 * Extract the node from the space and call add_intra_constraints.
3753 static isl_stat
lp_add_intra(__isl_take isl_basic_set
*coef
, void *user
)
3755 struct isl_add_all_constraints_data
*data
= user
;
3757 struct isl_sched_node
*node
;
3759 space
= isl_basic_set_get_space(coef
);
3760 space
= isl_space_range(isl_space_unwrap(space
));
3761 node
= graph_find_compressed_node(data
->ctx
, data
->graph
, space
);
3762 isl_space_free(space
);
3763 return add_intra_constraints(data
->graph
, node
, coef
, data
->pos
++);
3766 /* Add the constraints "coef" derived from an edge from a node j
3767 * to a node k to data->graph->lp in order to respect the dependences and
3768 * to try and carry them.
3770 * The space of "coef" is of the form
3772 * coefficients[[c_cst, c_n] -> [S_j[c_x] -> S_k[c_y]]]
3774 * with S_j[c_x] and S_k[c_y] the (compressed) spaces of the nodes.
3775 * Extract the nodes from the space and call add_inter_constraints.
3777 static isl_stat
lp_add_inter(__isl_take isl_basic_set
*coef
, void *user
)
3779 struct isl_add_all_constraints_data
*data
= user
;
3780 isl_space
*space
, *dom
;
3781 struct isl_sched_node
*src
, *dst
;
3783 space
= isl_basic_set_get_space(coef
);
3784 space
= isl_space_unwrap(isl_space_range(isl_space_unwrap(space
)));
3785 dom
= isl_space_domain(isl_space_copy(space
));
3786 src
= graph_find_compressed_node(data
->ctx
, data
->graph
, dom
);
3787 isl_space_free(dom
);
3788 space
= isl_space_range(space
);
3789 dst
= graph_find_compressed_node(data
->ctx
, data
->graph
, space
);
3790 isl_space_free(space
);
3792 return add_inter_constraints(data
->graph
, src
, dst
, coef
, data
->pos
++);
3795 /* Add constraints to graph->lp that force all (conditional) validity
3796 * dependences to be respected and attempt to carry them.
3797 * "intra" is the sequence of coefficient constraints for intra-node edges.
3798 * "inter" is the sequence of coefficient constraints for inter-node edges.
3800 static isl_stat
add_all_constraints(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
3801 __isl_keep isl_basic_set_list
*intra
,
3802 __isl_keep isl_basic_set_list
*inter
)
3804 struct isl_add_all_constraints_data data
= { ctx
, graph
};
3807 if (isl_basic_set_list_foreach(intra
, &lp_add_intra
, &data
) < 0)
3808 return isl_stat_error
;
3809 if (isl_basic_set_list_foreach(inter
, &lp_add_inter
, &data
) < 0)
3810 return isl_stat_error
;
3814 /* Internal data structure for count_all_constraints
3815 * for keeping track of the number of equality and inequality constraints.
3817 struct isl_sched_count
{
3822 /* Add the number of equality and inequality constraints of "bset"
3823 * to data->n_eq and data->n_ineq.
3825 static isl_stat
bset_update_count(__isl_take isl_basic_set
*bset
, void *user
)
3827 struct isl_sched_count
*data
= user
;
3829 data
->n_eq
+= isl_basic_set_n_equality(bset
);
3830 data
->n_ineq
+= isl_basic_set_n_inequality(bset
);
3831 isl_basic_set_free(bset
);
3836 /* Count the number of equality and inequality constraints
3837 * that will be added to the carry_lp problem.
3838 * We count each edge exactly once.
3839 * "intra" is the sequence of coefficient constraints for intra-node edges.
3840 * "inter" is the sequence of coefficient constraints for inter-node edges.
3842 static isl_stat
count_all_constraints(__isl_keep isl_basic_set_list
*intra
,
3843 __isl_keep isl_basic_set_list
*inter
, int *n_eq
, int *n_ineq
)
3845 struct isl_sched_count data
;
3847 data
.n_eq
= data
.n_ineq
= 0;
3848 if (isl_basic_set_list_foreach(inter
, &bset_update_count
, &data
) < 0)
3849 return isl_stat_error
;
3850 if (isl_basic_set_list_foreach(intra
, &bset_update_count
, &data
) < 0)
3851 return isl_stat_error
;
3854 *n_ineq
= data
.n_ineq
;
3859 /* Construct an LP problem for finding schedule coefficients
3860 * such that the schedule carries as many validity dependences as possible.
3861 * In particular, for each dependence i, we bound the dependence distance
3862 * from below by e_i, with 0 <= e_i <= 1 and then maximize the sum
3863 * of all e_i's. Dependences with e_i = 0 in the solution are simply
3864 * respected, while those with e_i > 0 (in practice e_i = 1) are carried.
3865 * "intra" is the sequence of coefficient constraints for intra-node edges.
3866 * "inter" is the sequence of coefficient constraints for inter-node edges.
3867 * "n_edge" is the total number of edges.
3869 * All variables of the LP are non-negative. The actual coefficients
3870 * may be negative, so each coefficient is represented as the difference
3871 * of two non-negative variables. The negative part always appears
3872 * immediately before the positive part.
3873 * Other than that, the variables have the following order
3875 * - sum of (1 - e_i) over all edges
3876 * - sum of all c_n coefficients
3877 * (unconstrained when computing non-parametric schedules)
3878 * - sum of positive and negative parts of all c_x coefficients
3883 * - c_i_n (if parametric)
3884 * - positive and negative parts of c_i_x, in opposite order
3886 * The constraints are those from the (validity) edges plus three equalities
3887 * to express the sums and n_edge inequalities to express e_i <= 1.
3889 static isl_stat
setup_carry_lp(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
3890 int n_edge
, __isl_keep isl_basic_set_list
*intra
,
3891 __isl_keep isl_basic_set_list
*inter
)
3900 for (i
= 0; i
< graph
->n
; ++i
) {
3901 struct isl_sched_node
*node
= &graph
->node
[graph
->sorted
[i
]];
3902 node
->start
= total
;
3903 total
+= 1 + node
->nparam
+ 2 * node
->nvar
;
3906 if (count_all_constraints(intra
, inter
, &n_eq
, &n_ineq
) < 0)
3907 return isl_stat_error
;
3909 dim
= isl_space_set_alloc(ctx
, 0, total
);
3910 isl_basic_set_free(graph
->lp
);
3913 graph
->lp
= isl_basic_set_alloc_space(dim
, 0, n_eq
, n_ineq
);
3914 graph
->lp
= isl_basic_set_set_rational(graph
->lp
);
3916 k
= isl_basic_set_alloc_equality(graph
->lp
);
3918 return isl_stat_error
;
3919 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
3920 isl_int_set_si(graph
->lp
->eq
[k
][0], -n_edge
);
3921 isl_int_set_si(graph
->lp
->eq
[k
][1], 1);
3922 for (i
= 0; i
< n_edge
; ++i
)
3923 isl_int_set_si(graph
->lp
->eq
[k
][4 + i
], 1);
3925 if (add_param_sum_constraint(graph
, 1) < 0)
3926 return isl_stat_error
;
3927 if (add_var_sum_constraint(graph
, 2) < 0)
3928 return isl_stat_error
;
3930 for (i
= 0; i
< n_edge
; ++i
) {
3931 k
= isl_basic_set_alloc_inequality(graph
->lp
);
3933 return isl_stat_error
;
3934 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
3935 isl_int_set_si(graph
->lp
->ineq
[k
][4 + i
], -1);
3936 isl_int_set_si(graph
->lp
->ineq
[k
][0], 1);
3939 if (add_all_constraints(ctx
, graph
, intra
, inter
) < 0)
3940 return isl_stat_error
;
3945 static __isl_give isl_schedule_node
*compute_component_schedule(
3946 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
3949 /* Comparison function for sorting the statements based on
3950 * the corresponding value in "r".
3952 static int smaller_value(const void *a
, const void *b
, void *data
)
3958 return isl_int_cmp(r
->el
[*i1
], r
->el
[*i2
]);
3961 /* If the schedule_split_scaled option is set and if the linear
3962 * parts of the scheduling rows for all nodes in the graphs have
3963 * a non-trivial common divisor, then split off the remainder of the
3964 * constant term modulo this common divisor from the linear part.
3965 * Otherwise, insert a band node directly and continue with
3966 * the construction of the schedule.
3968 * If a non-trivial common divisor is found, then
3969 * the linear part is reduced and the remainder is enforced
3970 * by a sequence node with the children placed in the order
3971 * of this remainder.
3972 * In particular, we assign an scc index based on the remainder and
3973 * then rely on compute_component_schedule to insert the sequence and
3974 * to continue the schedule construction on each part.
3976 static __isl_give isl_schedule_node
*split_scaled(
3977 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
3990 ctx
= isl_schedule_node_get_ctx(node
);
3991 if (!ctx
->opt
->schedule_split_scaled
)
3992 return compute_next_band(node
, graph
, 0);
3994 return compute_next_band(node
, graph
, 0);
3997 isl_int_init(gcd_i
);
3999 isl_int_set_si(gcd
, 0);
4001 row
= isl_mat_rows(graph
->node
[0].sched
) - 1;
4003 for (i
= 0; i
< graph
->n
; ++i
) {
4004 struct isl_sched_node
*node
= &graph
->node
[i
];
4005 int cols
= isl_mat_cols(node
->sched
);
4007 isl_seq_gcd(node
->sched
->row
[row
] + 1, cols
- 1, &gcd_i
);
4008 isl_int_gcd(gcd
, gcd
, gcd_i
);
4011 isl_int_clear(gcd_i
);
4013 if (isl_int_cmp_si(gcd
, 1) <= 0) {
4015 return compute_next_band(node
, graph
, 0);
4018 r
= isl_vec_alloc(ctx
, graph
->n
);
4019 order
= isl_calloc_array(ctx
, int, graph
->n
);
4023 for (i
= 0; i
< graph
->n
; ++i
) {
4024 struct isl_sched_node
*node
= &graph
->node
[i
];
4027 isl_int_fdiv_r(r
->el
[i
], node
->sched
->row
[row
][0], gcd
);
4028 isl_int_fdiv_q(node
->sched
->row
[row
][0],
4029 node
->sched
->row
[row
][0], gcd
);
4030 isl_int_mul(node
->sched
->row
[row
][0],
4031 node
->sched
->row
[row
][0], gcd
);
4032 node
->sched
= isl_mat_scale_down_row(node
->sched
, row
, gcd
);
4037 if (isl_sort(order
, graph
->n
, sizeof(order
[0]), &smaller_value
, r
) < 0)
4041 for (i
= 0; i
< graph
->n
; ++i
) {
4042 if (i
> 0 && isl_int_ne(r
->el
[order
[i
- 1]], r
->el
[order
[i
]]))
4044 graph
->node
[order
[i
]].scc
= scc
;
4053 if (update_edges(ctx
, graph
) < 0)
4054 return isl_schedule_node_free(node
);
4055 node
= insert_current_band(node
, graph
, 0);
4058 node
= isl_schedule_node_child(node
, 0);
4059 node
= compute_component_schedule(node
, graph
, 0);
4060 node
= isl_schedule_node_parent(node
);
4067 return isl_schedule_node_free(node
);
4070 /* Is the schedule row "sol" trivial on node "node"?
4071 * That is, is the solution zero on the dimensions linearly independent of
4072 * the previously found solutions?
4073 * Return 1 if the solution is trivial, 0 if it is not and -1 on error.
4075 * Each coefficient is represented as the difference between
4076 * two non-negative values in "sol". "sol" has been computed
4077 * in terms of the original iterators (i.e., without use of cmap).
4078 * We construct the schedule row s and check if it is linearly
4079 * independent of previously computed schedule rows
4080 * by computing T s, with T the linear combinations that are zero
4081 * on linearly dependent schedule rows.
4082 * If the result consists of all zeros, then the solution is trivial.
4084 static int is_trivial(struct isl_sched_node
*node
, __isl_keep isl_vec
*sol
)
4091 if (node
->nvar
== node
->rank
)
4094 node_sol
= extract_var_coef(node
, sol
);
4095 node_sol
= isl_mat_vec_product(isl_mat_copy(node
->indep
), node_sol
);
4099 trivial
= isl_seq_first_non_zero(node_sol
->el
,
4100 node
->nvar
- node
->rank
) == -1;
4102 isl_vec_free(node_sol
);
4107 /* Is the schedule row "sol" trivial on any node where it should
4109 * "sol" has been computed in terms of the original iterators
4110 * (i.e., without use of cmap).
4111 * Return 1 if any solution is trivial, 0 if they are not and -1 on error.
4113 static int is_any_trivial(struct isl_sched_graph
*graph
,
4114 __isl_keep isl_vec
*sol
)
4118 for (i
= 0; i
< graph
->n
; ++i
) {
4119 struct isl_sched_node
*node
= &graph
->node
[i
];
4122 if (!needs_row(graph
, node
))
4124 trivial
= is_trivial(node
, sol
);
4125 if (trivial
< 0 || trivial
)
4132 /* Does the schedule represented by "sol" perform loop coalescing on "node"?
4133 * If so, return the position of the coalesced dimension.
4134 * Otherwise, return node->nvar or -1 on error.
4136 * In particular, look for pairs of coefficients c_i and c_j such that
4137 * |c_j/c_i| >= size_i, i.e., |c_j| >= |c_i * size_i|.
4138 * If any such pair is found, then return i.
4139 * If size_i is infinity, then no check on c_i needs to be performed.
4141 static int find_node_coalescing(struct isl_sched_node
*node
,
4142 __isl_keep isl_vec
*sol
)
4148 if (node
->nvar
<= 1)
4151 csol
= extract_var_coef(node
, sol
);
4155 for (i
= 0; i
< node
->nvar
; ++i
) {
4158 if (isl_int_is_zero(csol
->el
[i
]))
4160 v
= isl_multi_val_get_val(node
->sizes
, i
);
4163 if (!isl_val_is_int(v
)) {
4167 isl_int_mul(max
, v
->n
, csol
->el
[i
]);
4170 for (j
= 0; j
< node
->nvar
; ++j
) {
4173 if (isl_int_abs_ge(csol
->el
[j
], max
))
4189 /* Force the schedule coefficient at position "pos" of "node" to be zero
4191 * The coefficient is encoded as the difference between two non-negative
4192 * variables. Force these two variables to have the same value.
4194 static __isl_give isl_tab_lexmin
*zero_out_node_coef(
4195 __isl_take isl_tab_lexmin
*tl
, struct isl_sched_node
*node
, int pos
)
4201 ctx
= isl_space_get_ctx(node
->space
);
4202 dim
= isl_tab_lexmin_dim(tl
);
4204 return isl_tab_lexmin_free(tl
);
4205 eq
= isl_vec_alloc(ctx
, 1 + dim
);
4206 eq
= isl_vec_clr(eq
);
4208 return isl_tab_lexmin_free(tl
);
4210 pos
= 1 + node_var_coef_pos(node
, pos
);
4211 isl_int_set_si(eq
->el
[pos
], 1);
4212 isl_int_set_si(eq
->el
[pos
+ 1], -1);
4213 tl
= isl_tab_lexmin_add_eq(tl
, eq
->el
);
4219 /* Return the lexicographically smallest rational point in the basic set
4220 * from which "tl" was constructed, double checking that this input set
4223 static __isl_give isl_vec
*non_empty_solution(__isl_keep isl_tab_lexmin
*tl
)
4227 sol
= isl_tab_lexmin_get_solution(tl
);
4231 isl_die(isl_vec_get_ctx(sol
), isl_error_internal
,
4232 "error in schedule construction",
4233 return isl_vec_free(sol
));
4237 /* Does the solution "sol" of the LP problem constructed by setup_carry_lp
4238 * carry any of the "n_edge" groups of dependences?
4239 * The value in the first position is the sum of (1 - e_i) over all "n_edge"
4240 * edges, with 0 <= e_i <= 1 equal to 1 when the dependences represented
4241 * by the edge are carried by the solution.
4242 * If the sum of the (1 - e_i) is smaller than "n_edge" then at least
4243 * one of those is carried.
4245 * Note that despite the fact that the problem is solved using a rational
4246 * solver, the solution is guaranteed to be integral.
4247 * Specifically, the dependence distance lower bounds e_i (and therefore
4248 * also their sum) are integers. See Lemma 5 of [1].
4250 * Any potential denominator of the sum is cleared by this function.
4251 * The denominator is not relevant for any of the other elements
4254 * [1] P. Feautrier, Some Efficient Solutions to the Affine Scheduling
4255 * Problem, Part II: Multi-Dimensional Time.
4256 * In Intl. Journal of Parallel Programming, 1992.
4258 static int carries_dependences(__isl_keep isl_vec
*sol
, int n_edge
)
4260 isl_int_divexact(sol
->el
[1], sol
->el
[1], sol
->el
[0]);
4261 isl_int_set_si(sol
->el
[0], 1);
4262 return isl_int_cmp_si(sol
->el
[1], n_edge
) < 0;
4265 /* Return the lexicographically smallest rational point in "lp",
4266 * assuming that all variables are non-negative and performing some
4267 * additional sanity checks.
4268 * If "want_integral" is set, then compute the lexicographically smallest
4269 * integer point instead.
4270 * In particular, "lp" should not be empty by construction.
4271 * Double check that this is the case.
4272 * If dependences are not carried for any of the "n_edge" edges,
4273 * then return an empty vector.
4275 * If the schedule_treat_coalescing option is set and
4276 * if the computed schedule performs loop coalescing on a given node,
4277 * i.e., if it is of the form
4279 * c_i i + c_j j + ...
4281 * with |c_j/c_i| >= size_i, then force the coefficient c_i to be zero
4282 * to cut out this solution. Repeat this process until no more loop
4283 * coalescing occurs or until no more dependences can be carried.
4284 * In the latter case, revert to the previously computed solution.
4286 * If the caller requests an integral solution and if coalescing should
4287 * be treated, then perform the coalescing treatment first as
4288 * an integral solution computed before coalescing treatment
4289 * would carry the same number of edges and would therefore probably
4290 * also be coalescing.
4292 * To allow the coalescing treatment to be performed first,
4293 * the initial solution is allowed to be rational and it is only
4294 * cut out (if needed) in the next iteration, if no coalescing measures
4297 static __isl_give isl_vec
*non_neg_lexmin(struct isl_sched_graph
*graph
,
4298 __isl_take isl_basic_set
*lp
, int n_edge
, int want_integral
)
4303 isl_vec
*sol
, *prev
= NULL
;
4304 int treat_coalescing
;
4308 ctx
= isl_basic_set_get_ctx(lp
);
4309 treat_coalescing
= isl_options_get_schedule_treat_coalescing(ctx
);
4310 tl
= isl_tab_lexmin_from_basic_set(lp
);
4317 tl
= isl_tab_lexmin_cut_to_integer(tl
);
4318 sol
= non_empty_solution(tl
);
4322 integral
= isl_int_is_one(sol
->el
[0]);
4323 if (!carries_dependences(sol
, n_edge
)) {
4325 prev
= isl_vec_alloc(ctx
, 0);
4330 prev
= isl_vec_free(prev
);
4331 cut
= want_integral
&& !integral
;
4334 if (!treat_coalescing
)
4336 for (i
= 0; i
< graph
->n
; ++i
) {
4337 struct isl_sched_node
*node
= &graph
->node
[i
];
4339 pos
= find_node_coalescing(node
, sol
);
4342 if (pos
< node
->nvar
)
4347 tl
= zero_out_node_coef(tl
, &graph
->node
[i
], pos
);
4352 isl_tab_lexmin_free(tl
);
4356 isl_tab_lexmin_free(tl
);
4362 /* If "edge" is an edge from a node to itself, then add the corresponding
4363 * dependence relation to "umap".
4364 * If "node" has been compressed, then the dependence relation
4365 * is also compressed first.
4367 static __isl_give isl_union_map
*add_intra(__isl_take isl_union_map
*umap
,
4368 struct isl_sched_edge
*edge
)
4371 struct isl_sched_node
*node
= edge
->src
;
4373 if (edge
->src
!= edge
->dst
)
4376 map
= isl_map_copy(edge
->map
);
4377 if (node
->compressed
) {
4378 map
= isl_map_preimage_domain_multi_aff(map
,
4379 isl_multi_aff_copy(node
->decompress
));
4380 map
= isl_map_preimage_range_multi_aff(map
,
4381 isl_multi_aff_copy(node
->decompress
));
4383 umap
= isl_union_map_add_map(umap
, map
);
4387 /* If "edge" is an edge from a node to another node, then add the corresponding
4388 * dependence relation to "umap".
4389 * If the source or destination nodes of "edge" have been compressed,
4390 * then the dependence relation is also compressed first.
4392 static __isl_give isl_union_map
*add_inter(__isl_take isl_union_map
*umap
,
4393 struct isl_sched_edge
*edge
)
4397 if (edge
->src
== edge
->dst
)
4400 map
= isl_map_copy(edge
->map
);
4401 if (edge
->src
->compressed
)
4402 map
= isl_map_preimage_domain_multi_aff(map
,
4403 isl_multi_aff_copy(edge
->src
->decompress
));
4404 if (edge
->dst
->compressed
)
4405 map
= isl_map_preimage_range_multi_aff(map
,
4406 isl_multi_aff_copy(edge
->dst
->decompress
));
4407 umap
= isl_union_map_add_map(umap
, map
);
4411 /* For each (conditional) validity edge in "graph",
4412 * add the corresponding dependence relation using "add"
4413 * to a collection of dependence relations and return the result.
4414 * If "coincidence" is set, then coincidence edges are considered as well.
4416 static __isl_give isl_union_map
*collect_validity(struct isl_sched_graph
*graph
,
4417 __isl_give isl_union_map
*(*add
)(__isl_take isl_union_map
*umap
,
4418 struct isl_sched_edge
*edge
), int coincidence
)
4422 isl_union_map
*umap
;
4424 space
= isl_space_copy(graph
->node
[0].space
);
4425 umap
= isl_union_map_empty(space
);
4427 for (i
= 0; i
< graph
->n_edge
; ++i
) {
4428 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
4430 if (!is_any_validity(edge
) &&
4431 (!coincidence
|| !is_coincidence(edge
)))
4434 umap
= add(umap
, edge
);
4440 /* For each dependence relation on a (conditional) validity edge
4441 * from a node to itself,
4442 * construct the set of coefficients of valid constraints for elements
4443 * in that dependence relation and collect the results.
4444 * If "coincidence" is set, then coincidence edges are considered as well.
4446 * In particular, for each dependence relation R, constraints
4447 * on coefficients (c_0, c_n, c_x) are constructed such that
4449 * c_0 + c_n n + c_x d >= 0 for each d in delta R = { y - x | (x,y) in R }
4451 * This computation is essentially the same as that performed
4452 * by intra_coefficients, except that it operates on multiple
4455 * Note that if a dependence relation is a union of basic maps,
4456 * then each basic map needs to be treated individually as it may only
4457 * be possible to carry the dependences expressed by some of those
4458 * basic maps and not all of them.
4459 * The collected validity constraints are therefore not coalesced and
4460 * it is assumed that they are not coalesced automatically.
4461 * Duplicate basic maps can be removed, however.
4462 * In particular, if the same basic map appears as a disjunct
4463 * in multiple edges, then it only needs to be carried once.
4465 static __isl_give isl_basic_set_list
*collect_intra_validity(
4466 struct isl_sched_graph
*graph
, int coincidence
)
4468 isl_union_map
*intra
;
4469 isl_union_set
*delta
;
4470 isl_basic_set_list
*list
;
4472 intra
= collect_validity(graph
, &add_intra
, coincidence
);
4473 delta
= isl_union_map_deltas(intra
);
4474 delta
= isl_union_set_remove_divs(delta
);
4475 list
= isl_union_set_get_basic_set_list(delta
);
4476 isl_union_set_free(delta
);
4478 return isl_basic_set_list_coefficients(list
);
4481 /* For each dependence relation on a (conditional) validity edge
4482 * from a node to some other node,
4483 * construct the set of coefficients of valid constraints for elements
4484 * in that dependence relation and collect the results.
4485 * If "coincidence" is set, then coincidence edges are considered as well.
4487 * In particular, for each dependence relation R, constraints
4488 * on coefficients (c_0, c_n, c_x, c_y) are constructed such that
4490 * c_0 + c_n n + c_x x + c_y y >= 0 for each (x,y) in R
4492 * This computation is essentially the same as that performed
4493 * by inter_coefficients, except that it operates on multiple
4496 * Note that if a dependence relation is a union of basic maps,
4497 * then each basic map needs to be treated individually as it may only
4498 * be possible to carry the dependences expressed by some of those
4499 * basic maps and not all of them.
4500 * The collected validity constraints are therefore not coalesced and
4501 * it is assumed that they are not coalesced automatically.
4502 * Duplicate basic maps can be removed, however.
4503 * In particular, if the same basic map appears as a disjunct
4504 * in multiple edges, then it only needs to be carried once.
4506 static __isl_give isl_basic_set_list
*collect_inter_validity(
4507 struct isl_sched_graph
*graph
, int coincidence
)
4509 isl_union_map
*inter
;
4510 isl_union_set
*wrap
;
4511 isl_basic_set_list
*list
;
4513 inter
= collect_validity(graph
, &add_inter
, coincidence
);
4514 inter
= isl_union_map_remove_divs(inter
);
4515 wrap
= isl_union_map_wrap(inter
);
4516 list
= isl_union_set_get_basic_set_list(wrap
);
4517 isl_union_set_free(wrap
);
4518 return isl_basic_set_list_coefficients(list
);
4521 /* Construct an LP problem for finding schedule coefficients
4522 * such that the schedule carries as many of the validity dependences
4524 * return the lexicographically smallest non-trivial solution.
4525 * If "fallback" is set, then the carrying is performed as a fallback
4526 * for the Pluto-like scheduler.
4527 * If "coincidence" is set, then try and carry coincidence edges as well.
4529 * The variable "n_edge" stores the number of groups that should be carried.
4530 * If none of the "n_edge" groups can be carried
4531 * then return an empty vector.
4532 * If, moreover, "n_edge" is zero, then the LP problem does not even
4533 * need to be constructed.
4535 * If a fallback solution is being computed, then compute an integral solution
4536 * for the coefficients rather than using the numerators
4537 * of a rational solution.
4539 static __isl_give isl_vec
*compute_carrying_sol(isl_ctx
*ctx
,
4540 struct isl_sched_graph
*graph
, int fallback
, int coincidence
)
4542 int n_intra
, n_inter
;
4545 struct isl_carry carry
= { 0 };
4547 carry
.intra
= collect_intra_validity(graph
, coincidence
);
4548 carry
.inter
= collect_inter_validity(graph
, coincidence
);
4549 if (!carry
.intra
|| !carry
.inter
)
4551 n_intra
= isl_basic_set_list_n_basic_set(carry
.intra
);
4552 n_inter
= isl_basic_set_list_n_basic_set(carry
.inter
);
4553 n_edge
= n_intra
+ n_inter
;
4555 isl_carry_clear(&carry
);
4556 return isl_vec_alloc(ctx
, 0);
4559 if (setup_carry_lp(ctx
, graph
, n_edge
, carry
.intra
, carry
.inter
) < 0)
4562 isl_carry_clear(&carry
);
4563 lp
= isl_basic_set_copy(graph
->lp
);
4564 return non_neg_lexmin(graph
, lp
, n_edge
, fallback
);
4566 isl_carry_clear(&carry
);
4570 /* Construct a schedule row for each node such that as many validity dependences
4571 * as possible are carried and then continue with the next band.
4572 * If "fallback" is set, then the carrying is performed as a fallback
4573 * for the Pluto-like scheduler.
4574 * If "coincidence" is set, then try and carry coincidence edges as well.
4576 * If there are no validity dependences, then no dependence can be carried and
4577 * the procedure is guaranteed to fail. If there is more than one component,
4578 * then try computing a schedule on each component separately
4579 * to prevent or at least postpone this failure.
4581 * If a schedule row is computed, then check that dependences are carried
4582 * for at least one of the edges.
4584 * If the computed schedule row turns out to be trivial on one or
4585 * more nodes where it should not be trivial, then we throw it away
4586 * and try again on each component separately.
4588 * If there is only one component, then we accept the schedule row anyway,
4589 * but we do not consider it as a complete row and therefore do not
4590 * increment graph->n_row. Note that the ranks of the nodes that
4591 * do get a non-trivial schedule part will get updated regardless and
4592 * graph->maxvar is computed based on these ranks. The test for
4593 * whether more schedule rows are required in compute_schedule_wcc
4594 * is therefore not affected.
4596 * Insert a band corresponding to the schedule row at position "node"
4597 * of the schedule tree and continue with the construction of the schedule.
4598 * This insertion and the continued construction is performed by split_scaled
4599 * after optionally checking for non-trivial common divisors.
4601 static __isl_give isl_schedule_node
*carry(__isl_take isl_schedule_node
*node
,
4602 struct isl_sched_graph
*graph
, int fallback
, int coincidence
)
4611 ctx
= isl_schedule_node_get_ctx(node
);
4612 sol
= compute_carrying_sol(ctx
, graph
, fallback
, coincidence
);
4614 return isl_schedule_node_free(node
);
4615 if (sol
->size
== 0) {
4618 return compute_component_schedule(node
, graph
, 1);
4619 isl_die(ctx
, isl_error_unknown
, "unable to carry dependences",
4620 return isl_schedule_node_free(node
));
4623 trivial
= is_any_trivial(graph
, sol
);
4625 sol
= isl_vec_free(sol
);
4626 } else if (trivial
&& graph
->scc
> 1) {
4628 return compute_component_schedule(node
, graph
, 1);
4631 if (update_schedule(graph
, sol
, 0, 0) < 0)
4632 return isl_schedule_node_free(node
);
4636 return split_scaled(node
, graph
);
4639 /* Construct a schedule row for each node such that as many validity dependences
4640 * as possible are carried and then continue with the next band.
4641 * Do so as a fallback for the Pluto-like scheduler.
4642 * If "coincidence" is set, then try and carry coincidence edges as well.
4644 static __isl_give isl_schedule_node
*carry_fallback(
4645 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
4648 return carry(node
, graph
, 1, coincidence
);
4651 /* Construct a schedule row for each node such that as many validity dependences
4652 * as possible are carried and then continue with the next band.
4653 * Do so for the case where the Feautrier scheduler was selected
4656 static __isl_give isl_schedule_node
*carry_feautrier(
4657 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
4659 return carry(node
, graph
, 0, 0);
4662 /* Construct a schedule row for each node such that as many validity dependences
4663 * as possible are carried and then continue with the next band.
4664 * Do so as a fallback for the Pluto-like scheduler.
4666 static __isl_give isl_schedule_node
*carry_dependences(
4667 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
4669 return carry_fallback(node
, graph
, 0);
4672 /* Construct a schedule row for each node such that as many validity or
4673 * coincidence dependences as possible are carried and
4674 * then continue with the next band.
4675 * Do so as a fallback for the Pluto-like scheduler.
4677 static __isl_give isl_schedule_node
*carry_coincidence(
4678 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
4680 return carry_fallback(node
, graph
, 1);
4683 /* Topologically sort statements mapped to the same schedule iteration
4684 * and add insert a sequence node in front of "node"
4685 * corresponding to this order.
4686 * If "initialized" is set, then it may be assumed that compute_maxvar
4687 * has been called on the current band. Otherwise, call
4688 * compute_maxvar if and before carry_dependences gets called.
4690 * If it turns out to be impossible to sort the statements apart,
4691 * because different dependences impose different orderings
4692 * on the statements, then we extend the schedule such that
4693 * it carries at least one more dependence.
4695 static __isl_give isl_schedule_node
*sort_statements(
4696 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
4700 isl_union_set_list
*filters
;
4705 ctx
= isl_schedule_node_get_ctx(node
);
4707 isl_die(ctx
, isl_error_internal
,
4708 "graph should have at least one node",
4709 return isl_schedule_node_free(node
));
4714 if (update_edges(ctx
, graph
) < 0)
4715 return isl_schedule_node_free(node
);
4717 if (graph
->n_edge
== 0)
4720 if (detect_sccs(ctx
, graph
) < 0)
4721 return isl_schedule_node_free(node
);
4724 if (graph
->scc
< graph
->n
) {
4725 if (!initialized
&& compute_maxvar(graph
) < 0)
4726 return isl_schedule_node_free(node
);
4727 return carry_dependences(node
, graph
);
4730 filters
= extract_sccs(ctx
, graph
);
4731 node
= isl_schedule_node_insert_sequence(node
, filters
);
4736 /* Are there any (non-empty) (conditional) validity edges in the graph?
4738 static int has_validity_edges(struct isl_sched_graph
*graph
)
4742 for (i
= 0; i
< graph
->n_edge
; ++i
) {
4745 empty
= isl_map_plain_is_empty(graph
->edge
[i
].map
);
4750 if (is_any_validity(&graph
->edge
[i
]))
4757 /* Should we apply a Feautrier step?
4758 * That is, did the user request the Feautrier algorithm and are
4759 * there any validity dependences (left)?
4761 static int need_feautrier_step(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
4763 if (ctx
->opt
->schedule_algorithm
!= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
)
4766 return has_validity_edges(graph
);
4769 /* Compute a schedule for a connected dependence graph using Feautrier's
4770 * multi-dimensional scheduling algorithm and return the updated schedule node.
4772 * The original algorithm is described in [1].
4773 * The main idea is to minimize the number of scheduling dimensions, by
4774 * trying to satisfy as many dependences as possible per scheduling dimension.
4776 * [1] P. Feautrier, Some Efficient Solutions to the Affine Scheduling
4777 * Problem, Part II: Multi-Dimensional Time.
4778 * In Intl. Journal of Parallel Programming, 1992.
4780 static __isl_give isl_schedule_node
*compute_schedule_wcc_feautrier(
4781 isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
4783 return carry_feautrier(node
, graph
);
4786 /* Turn off the "local" bit on all (condition) edges.
4788 static void clear_local_edges(struct isl_sched_graph
*graph
)
4792 for (i
= 0; i
< graph
->n_edge
; ++i
)
4793 if (is_condition(&graph
->edge
[i
]))
4794 clear_local(&graph
->edge
[i
]);
4797 /* Does "graph" have both condition and conditional validity edges?
4799 static int need_condition_check(struct isl_sched_graph
*graph
)
4802 int any_condition
= 0;
4803 int any_conditional_validity
= 0;
4805 for (i
= 0; i
< graph
->n_edge
; ++i
) {
4806 if (is_condition(&graph
->edge
[i
]))
4808 if (is_conditional_validity(&graph
->edge
[i
]))
4809 any_conditional_validity
= 1;
4812 return any_condition
&& any_conditional_validity
;
4815 /* Does "graph" contain any coincidence edge?
4817 static int has_any_coincidence(struct isl_sched_graph
*graph
)
4821 for (i
= 0; i
< graph
->n_edge
; ++i
)
4822 if (is_coincidence(&graph
->edge
[i
]))
4828 /* Extract the final schedule row as a map with the iteration domain
4829 * of "node" as domain.
4831 static __isl_give isl_map
*final_row(struct isl_sched_node
*node
)
4836 row
= isl_mat_rows(node
->sched
) - 1;
4837 ma
= node_extract_partial_schedule_multi_aff(node
, row
, 1);
4838 return isl_map_from_multi_aff(ma
);
4841 /* Is the conditional validity dependence in the edge with index "edge_index"
4842 * violated by the latest (i.e., final) row of the schedule?
4843 * That is, is i scheduled after j
4844 * for any conditional validity dependence i -> j?
4846 static int is_violated(struct isl_sched_graph
*graph
, int edge_index
)
4848 isl_map
*src_sched
, *dst_sched
, *map
;
4849 struct isl_sched_edge
*edge
= &graph
->edge
[edge_index
];
4852 src_sched
= final_row(edge
->src
);
4853 dst_sched
= final_row(edge
->dst
);
4854 map
= isl_map_copy(edge
->map
);
4855 map
= isl_map_apply_domain(map
, src_sched
);
4856 map
= isl_map_apply_range(map
, dst_sched
);
4857 map
= isl_map_order_gt(map
, isl_dim_in
, 0, isl_dim_out
, 0);
4858 empty
= isl_map_is_empty(map
);
4867 /* Does "graph" have any satisfied condition edges that
4868 * are adjacent to the conditional validity constraint with
4869 * domain "conditional_source" and range "conditional_sink"?
4871 * A satisfied condition is one that is not local.
4872 * If a condition was forced to be local already (i.e., marked as local)
4873 * then there is no need to check if it is in fact local.
4875 * Additionally, mark all adjacent condition edges found as local.
4877 static int has_adjacent_true_conditions(struct isl_sched_graph
*graph
,
4878 __isl_keep isl_union_set
*conditional_source
,
4879 __isl_keep isl_union_set
*conditional_sink
)
4884 for (i
= 0; i
< graph
->n_edge
; ++i
) {
4885 int adjacent
, local
;
4886 isl_union_map
*condition
;
4888 if (!is_condition(&graph
->edge
[i
]))
4890 if (is_local(&graph
->edge
[i
]))
4893 condition
= graph
->edge
[i
].tagged_condition
;
4894 adjacent
= domain_intersects(condition
, conditional_sink
);
4895 if (adjacent
>= 0 && !adjacent
)
4896 adjacent
= range_intersects(condition
,
4897 conditional_source
);
4903 set_local(&graph
->edge
[i
]);
4905 local
= is_condition_false(&graph
->edge
[i
]);
4915 /* Are there any violated conditional validity dependences with
4916 * adjacent condition dependences that are not local with respect
4917 * to the current schedule?
4918 * That is, is the conditional validity constraint violated?
4920 * Additionally, mark all those adjacent condition dependences as local.
4921 * We also mark those adjacent condition dependences that were not marked
4922 * as local before, but just happened to be local already. This ensures
4923 * that they remain local if the schedule is recomputed.
4925 * We first collect domain and range of all violated conditional validity
4926 * dependences and then check if there are any adjacent non-local
4927 * condition dependences.
4929 static int has_violated_conditional_constraint(isl_ctx
*ctx
,
4930 struct isl_sched_graph
*graph
)
4934 isl_union_set
*source
, *sink
;
4936 source
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
4937 sink
= isl_union_set_empty(isl_space_params_alloc(ctx
, 0));
4938 for (i
= 0; i
< graph
->n_edge
; ++i
) {
4939 isl_union_set
*uset
;
4940 isl_union_map
*umap
;
4943 if (!is_conditional_validity(&graph
->edge
[i
]))
4946 violated
= is_violated(graph
, i
);
4954 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_validity
);
4955 uset
= isl_union_map_domain(umap
);
4956 source
= isl_union_set_union(source
, uset
);
4957 source
= isl_union_set_coalesce(source
);
4959 umap
= isl_union_map_copy(graph
->edge
[i
].tagged_validity
);
4960 uset
= isl_union_map_range(umap
);
4961 sink
= isl_union_set_union(sink
, uset
);
4962 sink
= isl_union_set_coalesce(sink
);
4966 any
= has_adjacent_true_conditions(graph
, source
, sink
);
4968 isl_union_set_free(source
);
4969 isl_union_set_free(sink
);
4972 isl_union_set_free(source
);
4973 isl_union_set_free(sink
);
4977 /* Examine the current band (the rows between graph->band_start and
4978 * graph->n_total_row), deciding whether to drop it or add it to "node"
4979 * and then continue with the computation of the next band, if any.
4980 * If "initialized" is set, then it may be assumed that compute_maxvar
4981 * has been called on the current band. Otherwise, call
4982 * compute_maxvar if and before carry_dependences gets called.
4984 * The caller keeps looking for a new row as long as
4985 * graph->n_row < graph->maxvar. If the latest attempt to find
4986 * such a row failed (i.e., we still have graph->n_row < graph->maxvar),
4988 * - split between SCCs and start over (assuming we found an interesting
4989 * pair of SCCs between which to split)
4990 * - continue with the next band (assuming the current band has at least
4992 * - if outer coincidence needs to be enforced, then try to carry as many
4993 * validity or coincidence dependences as possible and
4994 * continue with the next band
4995 * - try to carry as many validity dependences as possible and
4996 * continue with the next band
4997 * In each case, we first insert a band node in the schedule tree
4998 * if any rows have been computed.
5000 * If the caller managed to complete the schedule, we insert a band node
5001 * (if any schedule rows were computed) and we finish off by topologically
5002 * sorting the statements based on the remaining dependences.
5004 static __isl_give isl_schedule_node
*compute_schedule_finish_band(
5005 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
5013 if (graph
->n_row
< graph
->maxvar
) {
5015 int empty
= graph
->n_total_row
== graph
->band_start
;
5017 ctx
= isl_schedule_node_get_ctx(node
);
5018 if (!ctx
->opt
->schedule_maximize_band_depth
&& !empty
)
5019 return compute_next_band(node
, graph
, 1);
5020 if (graph
->src_scc
>= 0)
5021 return compute_split_schedule(node
, graph
);
5023 return compute_next_band(node
, graph
, 1);
5024 if (!initialized
&& compute_maxvar(graph
) < 0)
5025 return isl_schedule_node_free(node
);
5026 if (isl_options_get_schedule_outer_coincidence(ctx
))
5027 return carry_coincidence(node
, graph
);
5028 return carry_dependences(node
, graph
);
5031 insert
= graph
->n_total_row
> graph
->band_start
;
5033 node
= insert_current_band(node
, graph
, 1);
5034 node
= isl_schedule_node_child(node
, 0);
5036 node
= sort_statements(node
, graph
, initialized
);
5038 node
= isl_schedule_node_parent(node
);
5043 /* Construct a band of schedule rows for a connected dependence graph.
5044 * The caller is responsible for determining the strongly connected
5045 * components and calling compute_maxvar first.
5047 * We try to find a sequence of as many schedule rows as possible that result
5048 * in non-negative dependence distances (independent of the previous rows
5049 * in the sequence, i.e., such that the sequence is tilable), with as
5050 * many of the initial rows as possible satisfying the coincidence constraints.
5051 * The computation stops if we can't find any more rows or if we have found
5052 * all the rows we wanted to find.
5054 * If ctx->opt->schedule_outer_coincidence is set, then we force the
5055 * outermost dimension to satisfy the coincidence constraints. If this
5056 * turns out to be impossible, we fall back on the general scheme above
5057 * and try to carry as many dependences as possible.
5059 * If "graph" contains both condition and conditional validity dependences,
5060 * then we need to check that that the conditional schedule constraint
5061 * is satisfied, i.e., there are no violated conditional validity dependences
5062 * that are adjacent to any non-local condition dependences.
5063 * If there are, then we mark all those adjacent condition dependences
5064 * as local and recompute the current band. Those dependences that
5065 * are marked local will then be forced to be local.
5066 * The initial computation is performed with no dependences marked as local.
5067 * If we are lucky, then there will be no violated conditional validity
5068 * dependences adjacent to any non-local condition dependences.
5069 * Otherwise, we mark some additional condition dependences as local and
5070 * recompute. We continue this process until there are no violations left or
5071 * until we are no longer able to compute a schedule.
5072 * Since there are only a finite number of dependences,
5073 * there will only be a finite number of iterations.
5075 static isl_stat
compute_schedule_wcc_band(isl_ctx
*ctx
,
5076 struct isl_sched_graph
*graph
)
5078 int has_coincidence
;
5079 int use_coincidence
;
5080 int force_coincidence
= 0;
5081 int check_conditional
;
5083 if (sort_sccs(graph
) < 0)
5084 return isl_stat_error
;
5086 clear_local_edges(graph
);
5087 check_conditional
= need_condition_check(graph
);
5088 has_coincidence
= has_any_coincidence(graph
);
5090 if (ctx
->opt
->schedule_outer_coincidence
)
5091 force_coincidence
= 1;
5093 use_coincidence
= has_coincidence
;
5094 while (graph
->n_row
< graph
->maxvar
) {
5099 graph
->src_scc
= -1;
5100 graph
->dst_scc
= -1;
5102 if (setup_lp(ctx
, graph
, use_coincidence
) < 0)
5103 return isl_stat_error
;
5104 sol
= solve_lp(ctx
, graph
);
5106 return isl_stat_error
;
5107 if (sol
->size
== 0) {
5108 int empty
= graph
->n_total_row
== graph
->band_start
;
5111 if (use_coincidence
&& (!force_coincidence
|| !empty
)) {
5112 use_coincidence
= 0;
5117 coincident
= !has_coincidence
|| use_coincidence
;
5118 if (update_schedule(graph
, sol
, 1, coincident
) < 0)
5119 return isl_stat_error
;
5121 if (!check_conditional
)
5123 violated
= has_violated_conditional_constraint(ctx
, graph
);
5125 return isl_stat_error
;
5128 if (reset_band(graph
) < 0)
5129 return isl_stat_error
;
5130 use_coincidence
= has_coincidence
;
5136 /* Compute a schedule for a connected dependence graph by considering
5137 * the graph as a whole and return the updated schedule node.
5139 * The actual schedule rows of the current band are computed by
5140 * compute_schedule_wcc_band. compute_schedule_finish_band takes
5141 * care of integrating the band into "node" and continuing
5144 static __isl_give isl_schedule_node
*compute_schedule_wcc_whole(
5145 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
5152 ctx
= isl_schedule_node_get_ctx(node
);
5153 if (compute_schedule_wcc_band(ctx
, graph
) < 0)
5154 return isl_schedule_node_free(node
);
5156 return compute_schedule_finish_band(node
, graph
, 1);
5159 /* Clustering information used by compute_schedule_wcc_clustering.
5161 * "n" is the number of SCCs in the original dependence graph
5162 * "scc" is an array of "n" elements, each representing an SCC
5163 * of the original dependence graph. All entries in the same cluster
5164 * have the same number of schedule rows.
5165 * "scc_cluster" maps each SCC index to the cluster to which it belongs,
5166 * where each cluster is represented by the index of the first SCC
5167 * in the cluster. Initially, each SCC belongs to a cluster containing
5170 * "scc_in_merge" is used by merge_clusters_along_edge to keep
5171 * track of which SCCs need to be merged.
5173 * "cluster" contains the merged clusters of SCCs after the clustering
5176 * "scc_node" is a temporary data structure used inside copy_partial.
5177 * For each SCC, it keeps track of the number of nodes in the SCC
5178 * that have already been copied.
5180 struct isl_clustering
{
5182 struct isl_sched_graph
*scc
;
5183 struct isl_sched_graph
*cluster
;
5189 /* Initialize the clustering data structure "c" from "graph".
5191 * In particular, allocate memory, extract the SCCs from "graph"
5192 * into c->scc, initialize scc_cluster and construct
5193 * a band of schedule rows for each SCC.
5194 * Within each SCC, there is only one SCC by definition.
5195 * Each SCC initially belongs to a cluster containing only that SCC.
5197 static isl_stat
clustering_init(isl_ctx
*ctx
, struct isl_clustering
*c
,
5198 struct isl_sched_graph
*graph
)
5203 c
->scc
= isl_calloc_array(ctx
, struct isl_sched_graph
, c
->n
);
5204 c
->cluster
= isl_calloc_array(ctx
, struct isl_sched_graph
, c
->n
);
5205 c
->scc_cluster
= isl_calloc_array(ctx
, int, c
->n
);
5206 c
->scc_node
= isl_calloc_array(ctx
, int, c
->n
);
5207 c
->scc_in_merge
= isl_calloc_array(ctx
, int, c
->n
);
5208 if (!c
->scc
|| !c
->cluster
||
5209 !c
->scc_cluster
|| !c
->scc_node
|| !c
->scc_in_merge
)
5210 return isl_stat_error
;
5212 for (i
= 0; i
< c
->n
; ++i
) {
5213 if (extract_sub_graph(ctx
, graph
, &node_scc_exactly
,
5214 &edge_scc_exactly
, i
, &c
->scc
[i
]) < 0)
5215 return isl_stat_error
;
5217 if (compute_maxvar(&c
->scc
[i
]) < 0)
5218 return isl_stat_error
;
5219 if (compute_schedule_wcc_band(ctx
, &c
->scc
[i
]) < 0)
5220 return isl_stat_error
;
5221 c
->scc_cluster
[i
] = i
;
5227 /* Free all memory allocated for "c".
5229 static void clustering_free(isl_ctx
*ctx
, struct isl_clustering
*c
)
5234 for (i
= 0; i
< c
->n
; ++i
)
5235 graph_free(ctx
, &c
->scc
[i
]);
5238 for (i
= 0; i
< c
->n
; ++i
)
5239 graph_free(ctx
, &c
->cluster
[i
]);
5241 free(c
->scc_cluster
);
5243 free(c
->scc_in_merge
);
5246 /* Should we refrain from merging the cluster in "graph" with
5247 * any other cluster?
5248 * In particular, is its current schedule band empty and incomplete.
5250 static int bad_cluster(struct isl_sched_graph
*graph
)
5252 return graph
->n_row
< graph
->maxvar
&&
5253 graph
->n_total_row
== graph
->band_start
;
5256 /* Is "edge" a proximity edge with a non-empty dependence relation?
5258 static isl_bool
is_non_empty_proximity(struct isl_sched_edge
*edge
)
5260 if (!is_proximity(edge
))
5261 return isl_bool_false
;
5262 return isl_bool_not(isl_map_plain_is_empty(edge
->map
));
5265 /* Return the index of an edge in "graph" that can be used to merge
5266 * two clusters in "c".
5267 * Return graph->n_edge if no such edge can be found.
5268 * Return -1 on error.
5270 * In particular, return a proximity edge between two clusters
5271 * that is not marked "no_merge" and such that neither of the
5272 * two clusters has an incomplete, empty band.
5274 * If there are multiple such edges, then try and find the most
5275 * appropriate edge to use for merging. In particular, pick the edge
5276 * with the greatest weight. If there are multiple of those,
5277 * then pick one with the shortest distance between
5278 * the two cluster representatives.
5280 static int find_proximity(struct isl_sched_graph
*graph
,
5281 struct isl_clustering
*c
)
5283 int i
, best
= graph
->n_edge
, best_dist
, best_weight
;
5285 for (i
= 0; i
< graph
->n_edge
; ++i
) {
5286 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
5290 prox
= is_non_empty_proximity(edge
);
5297 if (bad_cluster(&c
->scc
[edge
->src
->scc
]) ||
5298 bad_cluster(&c
->scc
[edge
->dst
->scc
]))
5300 dist
= c
->scc_cluster
[edge
->dst
->scc
] -
5301 c
->scc_cluster
[edge
->src
->scc
];
5304 weight
= edge
->weight
;
5305 if (best
< graph
->n_edge
) {
5306 if (best_weight
> weight
)
5308 if (best_weight
== weight
&& best_dist
<= dist
)
5313 best_weight
= weight
;
5319 /* Internal data structure used in mark_merge_sccs.
5321 * "graph" is the dependence graph in which a strongly connected
5322 * component is constructed.
5323 * "scc_cluster" maps each SCC index to the cluster to which it belongs.
5324 * "src" and "dst" are the indices of the nodes that are being merged.
5326 struct isl_mark_merge_sccs_data
{
5327 struct isl_sched_graph
*graph
;
5333 /* Check whether the cluster containing node "i" depends on the cluster
5334 * containing node "j". If "i" and "j" belong to the same cluster,
5335 * then they are taken to depend on each other to ensure that
5336 * the resulting strongly connected component consists of complete
5337 * clusters. Furthermore, if "i" and "j" are the two nodes that
5338 * are being merged, then they are taken to depend on each other as well.
5339 * Otherwise, check if there is a (conditional) validity dependence
5340 * from node[j] to node[i], forcing node[i] to follow node[j].
5342 static isl_bool
cluster_follows(int i
, int j
, void *user
)
5344 struct isl_mark_merge_sccs_data
*data
= user
;
5345 struct isl_sched_graph
*graph
= data
->graph
;
5346 int *scc_cluster
= data
->scc_cluster
;
5348 if (data
->src
== i
&& data
->dst
== j
)
5349 return isl_bool_true
;
5350 if (data
->src
== j
&& data
->dst
== i
)
5351 return isl_bool_true
;
5352 if (scc_cluster
[graph
->node
[i
].scc
] == scc_cluster
[graph
->node
[j
].scc
])
5353 return isl_bool_true
;
5355 return graph_has_validity_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
5358 /* Mark all SCCs that belong to either of the two clusters in "c"
5359 * connected by the edge in "graph" with index "edge", or to any
5360 * of the intermediate clusters.
5361 * The marking is recorded in c->scc_in_merge.
5363 * The given edge has been selected for merging two clusters,
5364 * meaning that there is at least a proximity edge between the two nodes.
5365 * However, there may also be (indirect) validity dependences
5366 * between the two nodes. When merging the two clusters, all clusters
5367 * containing one or more of the intermediate nodes along the
5368 * indirect validity dependences need to be merged in as well.
5370 * First collect all such nodes by computing the strongly connected
5371 * component (SCC) containing the two nodes connected by the edge, where
5372 * the two nodes are considered to depend on each other to make
5373 * sure they end up in the same SCC. Similarly, each node is considered
5374 * to depend on every other node in the same cluster to ensure
5375 * that the SCC consists of complete clusters.
5377 * Then the original SCCs that contain any of these nodes are marked
5378 * in c->scc_in_merge.
5380 static isl_stat
mark_merge_sccs(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
5381 int edge
, struct isl_clustering
*c
)
5383 struct isl_mark_merge_sccs_data data
;
5384 struct isl_tarjan_graph
*g
;
5387 for (i
= 0; i
< c
->n
; ++i
)
5388 c
->scc_in_merge
[i
] = 0;
5391 data
.scc_cluster
= c
->scc_cluster
;
5392 data
.src
= graph
->edge
[edge
].src
- graph
->node
;
5393 data
.dst
= graph
->edge
[edge
].dst
- graph
->node
;
5395 g
= isl_tarjan_graph_component(ctx
, graph
->n
, data
.dst
,
5396 &cluster_follows
, &data
);
5402 isl_die(ctx
, isl_error_internal
,
5403 "expecting at least two nodes in component",
5405 if (g
->order
[--i
] != -1)
5406 isl_die(ctx
, isl_error_internal
,
5407 "expecting end of component marker", goto error
);
5409 for (--i
; i
>= 0 && g
->order
[i
] != -1; --i
) {
5410 int scc
= graph
->node
[g
->order
[i
]].scc
;
5411 c
->scc_in_merge
[scc
] = 1;
5414 isl_tarjan_graph_free(g
);
5417 isl_tarjan_graph_free(g
);
5418 return isl_stat_error
;
5421 /* Construct the identifier "cluster_i".
5423 static __isl_give isl_id
*cluster_id(isl_ctx
*ctx
, int i
)
5427 snprintf(name
, sizeof(name
), "cluster_%d", i
);
5428 return isl_id_alloc(ctx
, name
, NULL
);
5431 /* Construct the space of the cluster with index "i" containing
5432 * the strongly connected component "scc".
5434 * In particular, construct a space called cluster_i with dimension equal
5435 * to the number of schedule rows in the current band of "scc".
5437 static __isl_give isl_space
*cluster_space(struct isl_sched_graph
*scc
, int i
)
5443 nvar
= scc
->n_total_row
- scc
->band_start
;
5444 space
= isl_space_copy(scc
->node
[0].space
);
5445 space
= isl_space_params(space
);
5446 space
= isl_space_set_from_params(space
);
5447 space
= isl_space_add_dims(space
, isl_dim_set
, nvar
);
5448 id
= cluster_id(isl_space_get_ctx(space
), i
);
5449 space
= isl_space_set_tuple_id(space
, isl_dim_set
, id
);
5454 /* Collect the domain of the graph for merging clusters.
5456 * In particular, for each cluster with first SCC "i", construct
5457 * a set in the space called cluster_i with dimension equal
5458 * to the number of schedule rows in the current band of the cluster.
5460 static __isl_give isl_union_set
*collect_domain(isl_ctx
*ctx
,
5461 struct isl_sched_graph
*graph
, struct isl_clustering
*c
)
5465 isl_union_set
*domain
;
5467 space
= isl_space_params_alloc(ctx
, 0);
5468 domain
= isl_union_set_empty(space
);
5470 for (i
= 0; i
< graph
->scc
; ++i
) {
5473 if (!c
->scc_in_merge
[i
])
5475 if (c
->scc_cluster
[i
] != i
)
5477 space
= cluster_space(&c
->scc
[i
], i
);
5478 domain
= isl_union_set_add_set(domain
, isl_set_universe(space
));
5484 /* Construct a map from the original instances to the corresponding
5485 * cluster instance in the current bands of the clusters in "c".
5487 static __isl_give isl_union_map
*collect_cluster_map(isl_ctx
*ctx
,
5488 struct isl_sched_graph
*graph
, struct isl_clustering
*c
)
5492 isl_union_map
*cluster_map
;
5494 space
= isl_space_params_alloc(ctx
, 0);
5495 cluster_map
= isl_union_map_empty(space
);
5496 for (i
= 0; i
< graph
->scc
; ++i
) {
5500 if (!c
->scc_in_merge
[i
])
5503 id
= cluster_id(ctx
, c
->scc_cluster
[i
]);
5504 start
= c
->scc
[i
].band_start
;
5505 n
= c
->scc
[i
].n_total_row
- start
;
5506 for (j
= 0; j
< c
->scc
[i
].n
; ++j
) {
5509 struct isl_sched_node
*node
= &c
->scc
[i
].node
[j
];
5511 ma
= node_extract_partial_schedule_multi_aff(node
,
5513 ma
= isl_multi_aff_set_tuple_id(ma
, isl_dim_out
,
5515 map
= isl_map_from_multi_aff(ma
);
5516 cluster_map
= isl_union_map_add_map(cluster_map
, map
);
5524 /* Add "umap" to the schedule constraints "sc" of all types of "edge"
5525 * that are not isl_edge_condition or isl_edge_conditional_validity.
5527 static __isl_give isl_schedule_constraints
*add_non_conditional_constraints(
5528 struct isl_sched_edge
*edge
, __isl_keep isl_union_map
*umap
,
5529 __isl_take isl_schedule_constraints
*sc
)
5531 enum isl_edge_type t
;
5536 for (t
= isl_edge_first
; t
<= isl_edge_last
; ++t
) {
5537 if (t
== isl_edge_condition
||
5538 t
== isl_edge_conditional_validity
)
5540 if (!is_type(edge
, t
))
5542 sc
= isl_schedule_constraints_add(sc
, t
,
5543 isl_union_map_copy(umap
));
5549 /* Add schedule constraints of types isl_edge_condition and
5550 * isl_edge_conditional_validity to "sc" by applying "umap" to
5551 * the domains of the wrapped relations in domain and range
5552 * of the corresponding tagged constraints of "edge".
5554 static __isl_give isl_schedule_constraints
*add_conditional_constraints(
5555 struct isl_sched_edge
*edge
, __isl_keep isl_union_map
*umap
,
5556 __isl_take isl_schedule_constraints
*sc
)
5558 enum isl_edge_type t
;
5559 isl_union_map
*tagged
;
5561 for (t
= isl_edge_condition
; t
<= isl_edge_conditional_validity
; ++t
) {
5562 if (!is_type(edge
, t
))
5564 if (t
== isl_edge_condition
)
5565 tagged
= isl_union_map_copy(edge
->tagged_condition
);
5567 tagged
= isl_union_map_copy(edge
->tagged_validity
);
5568 tagged
= isl_union_map_zip(tagged
);
5569 tagged
= isl_union_map_apply_domain(tagged
,
5570 isl_union_map_copy(umap
));
5571 tagged
= isl_union_map_zip(tagged
);
5572 sc
= isl_schedule_constraints_add(sc
, t
, tagged
);
5580 /* Given a mapping "cluster_map" from the original instances to
5581 * the cluster instances, add schedule constraints on the clusters
5582 * to "sc" corresponding to the original constraints represented by "edge".
5584 * For non-tagged dependence constraints, the cluster constraints
5585 * are obtained by applying "cluster_map" to the edge->map.
5587 * For tagged dependence constraints, "cluster_map" needs to be applied
5588 * to the domains of the wrapped relations in domain and range
5589 * of the tagged dependence constraints. Pick out the mappings
5590 * from these domains from "cluster_map" and construct their product.
5591 * This mapping can then be applied to the pair of domains.
5593 static __isl_give isl_schedule_constraints
*collect_edge_constraints(
5594 struct isl_sched_edge
*edge
, __isl_keep isl_union_map
*cluster_map
,
5595 __isl_take isl_schedule_constraints
*sc
)
5597 isl_union_map
*umap
;
5599 isl_union_set
*uset
;
5600 isl_union_map
*umap1
, *umap2
;
5605 umap
= isl_union_map_from_map(isl_map_copy(edge
->map
));
5606 umap
= isl_union_map_apply_domain(umap
,
5607 isl_union_map_copy(cluster_map
));
5608 umap
= isl_union_map_apply_range(umap
,
5609 isl_union_map_copy(cluster_map
));
5610 sc
= add_non_conditional_constraints(edge
, umap
, sc
);
5611 isl_union_map_free(umap
);
5613 if (!sc
|| (!is_condition(edge
) && !is_conditional_validity(edge
)))
5616 space
= isl_space_domain(isl_map_get_space(edge
->map
));
5617 uset
= isl_union_set_from_set(isl_set_universe(space
));
5618 umap1
= isl_union_map_copy(cluster_map
);
5619 umap1
= isl_union_map_intersect_domain(umap1
, uset
);
5620 space
= isl_space_range(isl_map_get_space(edge
->map
));
5621 uset
= isl_union_set_from_set(isl_set_universe(space
));
5622 umap2
= isl_union_map_copy(cluster_map
);
5623 umap2
= isl_union_map_intersect_domain(umap2
, uset
);
5624 umap
= isl_union_map_product(umap1
, umap2
);
5626 sc
= add_conditional_constraints(edge
, umap
, sc
);
5628 isl_union_map_free(umap
);
5632 /* Given a mapping "cluster_map" from the original instances to
5633 * the cluster instances, add schedule constraints on the clusters
5634 * to "sc" corresponding to all edges in "graph" between nodes that
5635 * belong to SCCs that are marked for merging in "scc_in_merge".
5637 static __isl_give isl_schedule_constraints
*collect_constraints(
5638 struct isl_sched_graph
*graph
, int *scc_in_merge
,
5639 __isl_keep isl_union_map
*cluster_map
,
5640 __isl_take isl_schedule_constraints
*sc
)
5644 for (i
= 0; i
< graph
->n_edge
; ++i
) {
5645 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
5647 if (!scc_in_merge
[edge
->src
->scc
])
5649 if (!scc_in_merge
[edge
->dst
->scc
])
5651 sc
= collect_edge_constraints(edge
, cluster_map
, sc
);
5657 /* Construct a dependence graph for scheduling clusters with respect
5658 * to each other and store the result in "merge_graph".
5659 * In particular, the nodes of the graph correspond to the schedule
5660 * dimensions of the current bands of those clusters that have been
5661 * marked for merging in "c".
5663 * First construct an isl_schedule_constraints object for this domain
5664 * by transforming the edges in "graph" to the domain.
5665 * Then initialize a dependence graph for scheduling from these
5668 static isl_stat
init_merge_graph(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
5669 struct isl_clustering
*c
, struct isl_sched_graph
*merge_graph
)
5671 isl_union_set
*domain
;
5672 isl_union_map
*cluster_map
;
5673 isl_schedule_constraints
*sc
;
5676 domain
= collect_domain(ctx
, graph
, c
);
5677 sc
= isl_schedule_constraints_on_domain(domain
);
5679 return isl_stat_error
;
5680 cluster_map
= collect_cluster_map(ctx
, graph
, c
);
5681 sc
= collect_constraints(graph
, c
->scc_in_merge
, cluster_map
, sc
);
5682 isl_union_map_free(cluster_map
);
5684 r
= graph_init(merge_graph
, sc
);
5686 isl_schedule_constraints_free(sc
);
5691 /* Compute the maximal number of remaining schedule rows that still need
5692 * to be computed for the nodes that belong to clusters with the maximal
5693 * dimension for the current band (i.e., the band that is to be merged).
5694 * Only clusters that are about to be merged are considered.
5695 * "maxvar" is the maximal dimension for the current band.
5696 * "c" contains information about the clusters.
5698 * Return the maximal number of remaining schedule rows or -1 on error.
5700 static int compute_maxvar_max_slack(int maxvar
, struct isl_clustering
*c
)
5706 for (i
= 0; i
< c
->n
; ++i
) {
5708 struct isl_sched_graph
*scc
;
5710 if (!c
->scc_in_merge
[i
])
5713 nvar
= scc
->n_total_row
- scc
->band_start
;
5716 for (j
= 0; j
< scc
->n
; ++j
) {
5717 struct isl_sched_node
*node
= &scc
->node
[j
];
5720 if (node_update_cmap(node
) < 0)
5722 slack
= node
->nvar
- node
->rank
;
5723 if (slack
> max_slack
)
5731 /* If there are any clusters where the dimension of the current band
5732 * (i.e., the band that is to be merged) is smaller than "maxvar" and
5733 * if there are any nodes in such a cluster where the number
5734 * of remaining schedule rows that still need to be computed
5735 * is greater than "max_slack", then return the smallest current band
5736 * dimension of all these clusters. Otherwise return the original value
5737 * of "maxvar". Return -1 in case of any error.
5738 * Only clusters that are about to be merged are considered.
5739 * "c" contains information about the clusters.
5741 static int limit_maxvar_to_slack(int maxvar
, int max_slack
,
5742 struct isl_clustering
*c
)
5746 for (i
= 0; i
< c
->n
; ++i
) {
5748 struct isl_sched_graph
*scc
;
5750 if (!c
->scc_in_merge
[i
])
5753 nvar
= scc
->n_total_row
- scc
->band_start
;
5756 for (j
= 0; j
< scc
->n
; ++j
) {
5757 struct isl_sched_node
*node
= &scc
->node
[j
];
5760 if (node_update_cmap(node
) < 0)
5762 slack
= node
->nvar
- node
->rank
;
5763 if (slack
> max_slack
) {
5773 /* Adjust merge_graph->maxvar based on the number of remaining schedule rows
5774 * that still need to be computed. In particular, if there is a node
5775 * in a cluster where the dimension of the current band is smaller
5776 * than merge_graph->maxvar, but the number of remaining schedule rows
5777 * is greater than that of any node in a cluster with the maximal
5778 * dimension for the current band (i.e., merge_graph->maxvar),
5779 * then adjust merge_graph->maxvar to the (smallest) current band dimension
5780 * of those clusters. Without this adjustment, the total number of
5781 * schedule dimensions would be increased, resulting in a skewed view
5782 * of the number of coincident dimensions.
5783 * "c" contains information about the clusters.
5785 * If the maximize_band_depth option is set and merge_graph->maxvar is reduced,
5786 * then there is no point in attempting any merge since it will be rejected
5787 * anyway. Set merge_graph->maxvar to zero in such cases.
5789 static isl_stat
adjust_maxvar_to_slack(isl_ctx
*ctx
,
5790 struct isl_sched_graph
*merge_graph
, struct isl_clustering
*c
)
5792 int max_slack
, maxvar
;
5794 max_slack
= compute_maxvar_max_slack(merge_graph
->maxvar
, c
);
5796 return isl_stat_error
;
5797 maxvar
= limit_maxvar_to_slack(merge_graph
->maxvar
, max_slack
, c
);
5799 return isl_stat_error
;
5801 if (maxvar
< merge_graph
->maxvar
) {
5802 if (isl_options_get_schedule_maximize_band_depth(ctx
))
5803 merge_graph
->maxvar
= 0;
5805 merge_graph
->maxvar
= maxvar
;
5811 /* Return the number of coincident dimensions in the current band of "graph",
5812 * where the nodes of "graph" are assumed to be scheduled by a single band.
5814 static int get_n_coincident(struct isl_sched_graph
*graph
)
5818 for (i
= graph
->band_start
; i
< graph
->n_total_row
; ++i
)
5819 if (!graph
->node
[0].coincident
[i
])
5822 return i
- graph
->band_start
;
5825 /* Should the clusters be merged based on the cluster schedule
5826 * in the current (and only) band of "merge_graph", given that
5827 * coincidence should be maximized?
5829 * If the number of coincident schedule dimensions in the merged band
5830 * would be less than the maximal number of coincident schedule dimensions
5831 * in any of the merged clusters, then the clusters should not be merged.
5833 static isl_bool
ok_to_merge_coincident(struct isl_clustering
*c
,
5834 struct isl_sched_graph
*merge_graph
)
5841 for (i
= 0; i
< c
->n
; ++i
) {
5842 if (!c
->scc_in_merge
[i
])
5844 n_coincident
= get_n_coincident(&c
->scc
[i
]);
5845 if (n_coincident
> max_coincident
)
5846 max_coincident
= n_coincident
;
5849 n_coincident
= get_n_coincident(merge_graph
);
5851 return n_coincident
>= max_coincident
;
5854 /* Return the transformation on "node" expressed by the current (and only)
5855 * band of "merge_graph" applied to the clusters in "c".
5857 * First find the representation of "node" in its SCC in "c" and
5858 * extract the transformation expressed by the current band.
5859 * Then extract the transformation applied by "merge_graph"
5860 * to the cluster to which this SCC belongs.
5861 * Combine the two to obtain the complete transformation on the node.
5863 * Note that the range of the first transformation is an anonymous space,
5864 * while the domain of the second is named "cluster_X". The range
5865 * of the former therefore needs to be adjusted before the two
5868 static __isl_give isl_map
*extract_node_transformation(isl_ctx
*ctx
,
5869 struct isl_sched_node
*node
, struct isl_clustering
*c
,
5870 struct isl_sched_graph
*merge_graph
)
5872 struct isl_sched_node
*scc_node
, *cluster_node
;
5876 isl_multi_aff
*ma
, *ma2
;
5878 scc_node
= graph_find_node(ctx
, &c
->scc
[node
->scc
], node
->space
);
5879 start
= c
->scc
[node
->scc
].band_start
;
5880 n
= c
->scc
[node
->scc
].n_total_row
- start
;
5881 ma
= node_extract_partial_schedule_multi_aff(scc_node
, start
, n
);
5882 space
= cluster_space(&c
->scc
[node
->scc
], c
->scc_cluster
[node
->scc
]);
5883 cluster_node
= graph_find_node(ctx
, merge_graph
, space
);
5884 if (space
&& !cluster_node
)
5885 isl_die(ctx
, isl_error_internal
, "unable to find cluster",
5886 space
= isl_space_free(space
));
5887 id
= isl_space_get_tuple_id(space
, isl_dim_set
);
5888 ma
= isl_multi_aff_set_tuple_id(ma
, isl_dim_out
, id
);
5889 isl_space_free(space
);
5890 n
= merge_graph
->n_total_row
;
5891 ma2
= node_extract_partial_schedule_multi_aff(cluster_node
, 0, n
);
5892 ma
= isl_multi_aff_pullback_multi_aff(ma2
, ma
);
5894 return isl_map_from_multi_aff(ma
);
5897 /* Give a set of distances "set", are they bounded by a small constant
5898 * in direction "pos"?
5899 * In practice, check if they are bounded by 2 by checking that there
5900 * are no elements with a value greater than or equal to 3 or
5901 * smaller than or equal to -3.
5903 static isl_bool
distance_is_bounded(__isl_keep isl_set
*set
, int pos
)
5909 return isl_bool_error
;
5911 test
= isl_set_copy(set
);
5912 test
= isl_set_lower_bound_si(test
, isl_dim_set
, pos
, 3);
5913 bounded
= isl_set_is_empty(test
);
5916 if (bounded
< 0 || !bounded
)
5919 test
= isl_set_copy(set
);
5920 test
= isl_set_upper_bound_si(test
, isl_dim_set
, pos
, -3);
5921 bounded
= isl_set_is_empty(test
);
5927 /* Does the set "set" have a fixed (but possible parametric) value
5928 * at dimension "pos"?
5930 static isl_bool
has_single_value(__isl_keep isl_set
*set
, int pos
)
5936 return isl_bool_error
;
5937 set
= isl_set_copy(set
);
5938 n
= isl_set_dim(set
, isl_dim_set
);
5939 set
= isl_set_project_out(set
, isl_dim_set
, pos
+ 1, n
- (pos
+ 1));
5940 set
= isl_set_project_out(set
, isl_dim_set
, 0, pos
);
5941 single
= isl_set_is_singleton(set
);
5947 /* Does "map" have a fixed (but possible parametric) value
5948 * at dimension "pos" of either its domain or its range?
5950 static isl_bool
has_singular_src_or_dst(__isl_keep isl_map
*map
, int pos
)
5955 set
= isl_map_domain(isl_map_copy(map
));
5956 single
= has_single_value(set
, pos
);
5959 if (single
< 0 || single
)
5962 set
= isl_map_range(isl_map_copy(map
));
5963 single
= has_single_value(set
, pos
);
5969 /* Does the edge "edge" from "graph" have bounded dependence distances
5970 * in the merged graph "merge_graph" of a selection of clusters in "c"?
5972 * Extract the complete transformations of the source and destination
5973 * nodes of the edge, apply them to the edge constraints and
5974 * compute the differences. Finally, check if these differences are bounded
5975 * in each direction.
5977 * If the dimension of the band is greater than the number of
5978 * dimensions that can be expected to be optimized by the edge
5979 * (based on its weight), then also allow the differences to be unbounded
5980 * in the remaining dimensions, but only if either the source or
5981 * the destination has a fixed value in that direction.
5982 * This allows a statement that produces values that are used by
5983 * several instances of another statement to be merged with that
5985 * However, merging such clusters will introduce an inherently
5986 * large proximity distance inside the merged cluster, meaning
5987 * that proximity distances will no longer be optimized in
5988 * subsequent merges. These merges are therefore only allowed
5989 * after all other possible merges have been tried.
5990 * The first time such a merge is encountered, the weight of the edge
5991 * is replaced by a negative weight. The second time (i.e., after
5992 * all merges over edges with a non-negative weight have been tried),
5993 * the merge is allowed.
5995 static isl_bool
has_bounded_distances(isl_ctx
*ctx
, struct isl_sched_edge
*edge
,
5996 struct isl_sched_graph
*graph
, struct isl_clustering
*c
,
5997 struct isl_sched_graph
*merge_graph
)
6004 map
= isl_map_copy(edge
->map
);
6005 t
= extract_node_transformation(ctx
, edge
->src
, c
, merge_graph
);
6006 map
= isl_map_apply_domain(map
, t
);
6007 t
= extract_node_transformation(ctx
, edge
->dst
, c
, merge_graph
);
6008 map
= isl_map_apply_range(map
, t
);
6009 dist
= isl_map_deltas(isl_map_copy(map
));
6011 bounded
= isl_bool_true
;
6012 n
= isl_set_dim(dist
, isl_dim_set
);
6013 n_slack
= n
- edge
->weight
;
6014 if (edge
->weight
< 0)
6015 n_slack
-= graph
->max_weight
+ 1;
6016 for (i
= 0; i
< n
; ++i
) {
6017 isl_bool bounded_i
, singular_i
;
6019 bounded_i
= distance_is_bounded(dist
, i
);
6024 if (edge
->weight
>= 0)
6025 bounded
= isl_bool_false
;
6029 singular_i
= has_singular_src_or_dst(map
, i
);
6034 bounded
= isl_bool_false
;
6037 if (!bounded
&& i
>= n
&& edge
->weight
>= 0)
6038 edge
->weight
-= graph
->max_weight
+ 1;
6046 return isl_bool_error
;
6049 /* Should the clusters be merged based on the cluster schedule
6050 * in the current (and only) band of "merge_graph"?
6051 * "graph" is the original dependence graph, while "c" records
6052 * which SCCs are involved in the latest merge.
6054 * In particular, is there at least one proximity constraint
6055 * that is optimized by the merge?
6057 * A proximity constraint is considered to be optimized
6058 * if the dependence distances are small.
6060 static isl_bool
ok_to_merge_proximity(isl_ctx
*ctx
,
6061 struct isl_sched_graph
*graph
, struct isl_clustering
*c
,
6062 struct isl_sched_graph
*merge_graph
)
6066 for (i
= 0; i
< graph
->n_edge
; ++i
) {
6067 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
6070 if (!is_proximity(edge
))
6072 if (!c
->scc_in_merge
[edge
->src
->scc
])
6074 if (!c
->scc_in_merge
[edge
->dst
->scc
])
6076 if (c
->scc_cluster
[edge
->dst
->scc
] ==
6077 c
->scc_cluster
[edge
->src
->scc
])
6079 bounded
= has_bounded_distances(ctx
, edge
, graph
, c
,
6081 if (bounded
< 0 || bounded
)
6085 return isl_bool_false
;
6088 /* Should the clusters be merged based on the cluster schedule
6089 * in the current (and only) band of "merge_graph"?
6090 * "graph" is the original dependence graph, while "c" records
6091 * which SCCs are involved in the latest merge.
6093 * If the current band is empty, then the clusters should not be merged.
6095 * If the band depth should be maximized and the merge schedule
6096 * is incomplete (meaning that the dimension of some of the schedule
6097 * bands in the original schedule will be reduced), then the clusters
6098 * should not be merged.
6100 * If the schedule_maximize_coincidence option is set, then check that
6101 * the number of coincident schedule dimensions is not reduced.
6103 * Finally, only allow the merge if at least one proximity
6104 * constraint is optimized.
6106 static isl_bool
ok_to_merge(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
6107 struct isl_clustering
*c
, struct isl_sched_graph
*merge_graph
)
6109 if (merge_graph
->n_total_row
== merge_graph
->band_start
)
6110 return isl_bool_false
;
6112 if (isl_options_get_schedule_maximize_band_depth(ctx
) &&
6113 merge_graph
->n_total_row
< merge_graph
->maxvar
)
6114 return isl_bool_false
;
6116 if (isl_options_get_schedule_maximize_coincidence(ctx
)) {
6119 ok
= ok_to_merge_coincident(c
, merge_graph
);
6124 return ok_to_merge_proximity(ctx
, graph
, c
, merge_graph
);
6127 /* Apply the schedule in "t_node" to the "n" rows starting at "first"
6128 * of the schedule in "node" and return the result.
6130 * That is, essentially compute
6132 * T * N(first:first+n-1)
6134 * taking into account the constant term and the parameter coefficients
6137 static __isl_give isl_mat
*node_transformation(isl_ctx
*ctx
,
6138 struct isl_sched_node
*t_node
, struct isl_sched_node
*node
,
6143 int n_row
, n_col
, n_param
, n_var
;
6145 n_param
= node
->nparam
;
6147 n_row
= isl_mat_rows(t_node
->sched
);
6148 n_col
= isl_mat_cols(node
->sched
);
6149 t
= isl_mat_alloc(ctx
, n_row
, n_col
);
6152 for (i
= 0; i
< n_row
; ++i
) {
6153 isl_seq_cpy(t
->row
[i
], t_node
->sched
->row
[i
], 1 + n_param
);
6154 isl_seq_clr(t
->row
[i
] + 1 + n_param
, n_var
);
6155 for (j
= 0; j
< n
; ++j
)
6156 isl_seq_addmul(t
->row
[i
],
6157 t_node
->sched
->row
[i
][1 + n_param
+ j
],
6158 node
->sched
->row
[first
+ j
],
6159 1 + n_param
+ n_var
);
6164 /* Apply the cluster schedule in "t_node" to the current band
6165 * schedule of the nodes in "graph".
6167 * In particular, replace the rows starting at band_start
6168 * by the result of applying the cluster schedule in "t_node"
6169 * to the original rows.
6171 * The coincidence of the schedule is determined by the coincidence
6172 * of the cluster schedule.
6174 static isl_stat
transform(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
6175 struct isl_sched_node
*t_node
)
6181 start
= graph
->band_start
;
6182 n
= graph
->n_total_row
- start
;
6184 n_new
= isl_mat_rows(t_node
->sched
);
6185 for (i
= 0; i
< graph
->n
; ++i
) {
6186 struct isl_sched_node
*node
= &graph
->node
[i
];
6189 t
= node_transformation(ctx
, t_node
, node
, start
, n
);
6190 node
->sched
= isl_mat_drop_rows(node
->sched
, start
, n
);
6191 node
->sched
= isl_mat_concat(node
->sched
, t
);
6192 node
->sched_map
= isl_map_free(node
->sched_map
);
6194 return isl_stat_error
;
6195 for (j
= 0; j
< n_new
; ++j
)
6196 node
->coincident
[start
+ j
] = t_node
->coincident
[j
];
6198 graph
->n_total_row
-= n
;
6200 graph
->n_total_row
+= n_new
;
6201 graph
->n_row
+= n_new
;
6206 /* Merge the clusters marked for merging in "c" into a single
6207 * cluster using the cluster schedule in the current band of "merge_graph".
6208 * The representative SCC for the new cluster is the SCC with
6209 * the smallest index.
6211 * The current band schedule of each SCC in the new cluster is obtained
6212 * by applying the schedule of the corresponding original cluster
6213 * to the original band schedule.
6214 * All SCCs in the new cluster have the same number of schedule rows.
6216 static isl_stat
merge(isl_ctx
*ctx
, struct isl_clustering
*c
,
6217 struct isl_sched_graph
*merge_graph
)
6223 for (i
= 0; i
< c
->n
; ++i
) {
6224 struct isl_sched_node
*node
;
6226 if (!c
->scc_in_merge
[i
])
6230 space
= cluster_space(&c
->scc
[i
], c
->scc_cluster
[i
]);
6232 return isl_stat_error
;
6233 node
= graph_find_node(ctx
, merge_graph
, space
);
6234 isl_space_free(space
);
6236 isl_die(ctx
, isl_error_internal
,
6237 "unable to find cluster",
6238 return isl_stat_error
);
6239 if (transform(ctx
, &c
->scc
[i
], node
) < 0)
6240 return isl_stat_error
;
6241 c
->scc_cluster
[i
] = cluster
;
6247 /* Try and merge the clusters of SCCs marked in c->scc_in_merge
6248 * by scheduling the current cluster bands with respect to each other.
6250 * Construct a dependence graph with a space for each cluster and
6251 * with the coordinates of each space corresponding to the schedule
6252 * dimensions of the current band of that cluster.
6253 * Construct a cluster schedule in this cluster dependence graph and
6254 * apply it to the current cluster bands if it is applicable
6255 * according to ok_to_merge.
6257 * If the number of remaining schedule dimensions in a cluster
6258 * with a non-maximal current schedule dimension is greater than
6259 * the number of remaining schedule dimensions in clusters
6260 * with a maximal current schedule dimension, then restrict
6261 * the number of rows to be computed in the cluster schedule
6262 * to the minimal such non-maximal current schedule dimension.
6263 * Do this by adjusting merge_graph.maxvar.
6265 * Return isl_bool_true if the clusters have effectively been merged
6266 * into a single cluster.
6268 * Note that since the standard scheduling algorithm minimizes the maximal
6269 * distance over proximity constraints, the proximity constraints between
6270 * the merged clusters may not be optimized any further than what is
6271 * sufficient to bring the distances within the limits of the internal
6272 * proximity constraints inside the individual clusters.
6273 * It may therefore make sense to perform an additional translation step
6274 * to bring the clusters closer to each other, while maintaining
6275 * the linear part of the merging schedule found using the standard
6276 * scheduling algorithm.
6278 static isl_bool
try_merge(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
6279 struct isl_clustering
*c
)
6281 struct isl_sched_graph merge_graph
= { 0 };
6284 if (init_merge_graph(ctx
, graph
, c
, &merge_graph
) < 0)
6287 if (compute_maxvar(&merge_graph
) < 0)
6289 if (adjust_maxvar_to_slack(ctx
, &merge_graph
,c
) < 0)
6291 if (compute_schedule_wcc_band(ctx
, &merge_graph
) < 0)
6293 merged
= ok_to_merge(ctx
, graph
, c
, &merge_graph
);
6294 if (merged
&& merge(ctx
, c
, &merge_graph
) < 0)
6297 graph_free(ctx
, &merge_graph
);
6300 graph_free(ctx
, &merge_graph
);
6301 return isl_bool_error
;
6304 /* Is there any edge marked "no_merge" between two SCCs that are
6305 * about to be merged (i.e., that are set in "scc_in_merge")?
6306 * "merge_edge" is the proximity edge along which the clusters of SCCs
6307 * are going to be merged.
6309 * If there is any edge between two SCCs with a negative weight,
6310 * while the weight of "merge_edge" is non-negative, then this
6311 * means that the edge was postponed. "merge_edge" should then
6312 * also be postponed since merging along the edge with negative weight should
6313 * be postponed until all edges with non-negative weight have been tried.
6314 * Replace the weight of "merge_edge" by a negative weight as well and
6315 * tell the caller not to attempt a merge.
6317 static int any_no_merge(struct isl_sched_graph
*graph
, int *scc_in_merge
,
6318 struct isl_sched_edge
*merge_edge
)
6322 for (i
= 0; i
< graph
->n_edge
; ++i
) {
6323 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
6325 if (!scc_in_merge
[edge
->src
->scc
])
6327 if (!scc_in_merge
[edge
->dst
->scc
])
6331 if (merge_edge
->weight
>= 0 && edge
->weight
< 0) {
6332 merge_edge
->weight
-= graph
->max_weight
+ 1;
6340 /* Merge the two clusters in "c" connected by the edge in "graph"
6341 * with index "edge" into a single cluster.
6342 * If it turns out to be impossible to merge these two clusters,
6343 * then mark the edge as "no_merge" such that it will not be
6346 * First mark all SCCs that need to be merged. This includes the SCCs
6347 * in the two clusters, but it may also include the SCCs
6348 * of intermediate clusters.
6349 * If there is already a no_merge edge between any pair of such SCCs,
6350 * then simply mark the current edge as no_merge as well.
6351 * Likewise, if any of those edges was postponed by has_bounded_distances,
6352 * then postpone the current edge as well.
6353 * Otherwise, try and merge the clusters and mark "edge" as "no_merge"
6354 * if the clusters did not end up getting merged, unless the non-merge
6355 * is due to the fact that the edge was postponed. This postponement
6356 * can be recognized by a change in weight (from non-negative to negative).
6358 static isl_stat
merge_clusters_along_edge(isl_ctx
*ctx
,
6359 struct isl_sched_graph
*graph
, int edge
, struct isl_clustering
*c
)
6362 int edge_weight
= graph
->edge
[edge
].weight
;
6364 if (mark_merge_sccs(ctx
, graph
, edge
, c
) < 0)
6365 return isl_stat_error
;
6367 if (any_no_merge(graph
, c
->scc_in_merge
, &graph
->edge
[edge
]))
6368 merged
= isl_bool_false
;
6370 merged
= try_merge(ctx
, graph
, c
);
6372 return isl_stat_error
;
6373 if (!merged
&& edge_weight
== graph
->edge
[edge
].weight
)
6374 graph
->edge
[edge
].no_merge
= 1;
6379 /* Does "node" belong to the cluster identified by "cluster"?
6381 static int node_cluster_exactly(struct isl_sched_node
*node
, int cluster
)
6383 return node
->cluster
== cluster
;
6386 /* Does "edge" connect two nodes belonging to the cluster
6387 * identified by "cluster"?
6389 static int edge_cluster_exactly(struct isl_sched_edge
*edge
, int cluster
)
6391 return edge
->src
->cluster
== cluster
&& edge
->dst
->cluster
== cluster
;
6394 /* Swap the schedule of "node1" and "node2".
6395 * Both nodes have been derived from the same node in a common parent graph.
6396 * Since the "coincident" field is shared with that node
6397 * in the parent graph, there is no need to also swap this field.
6399 static void swap_sched(struct isl_sched_node
*node1
,
6400 struct isl_sched_node
*node2
)
6405 sched
= node1
->sched
;
6406 node1
->sched
= node2
->sched
;
6407 node2
->sched
= sched
;
6409 sched_map
= node1
->sched_map
;
6410 node1
->sched_map
= node2
->sched_map
;
6411 node2
->sched_map
= sched_map
;
6414 /* Copy the current band schedule from the SCCs that form the cluster
6415 * with index "pos" to the actual cluster at position "pos".
6416 * By construction, the index of the first SCC that belongs to the cluster
6419 * The order of the nodes inside both the SCCs and the cluster
6420 * is assumed to be same as the order in the original "graph".
6422 * Since the SCC graphs will no longer be used after this function,
6423 * the schedules are actually swapped rather than copied.
6425 static isl_stat
copy_partial(struct isl_sched_graph
*graph
,
6426 struct isl_clustering
*c
, int pos
)
6430 c
->cluster
[pos
].n_total_row
= c
->scc
[pos
].n_total_row
;
6431 c
->cluster
[pos
].n_row
= c
->scc
[pos
].n_row
;
6432 c
->cluster
[pos
].maxvar
= c
->scc
[pos
].maxvar
;
6434 for (i
= 0; i
< graph
->n
; ++i
) {
6438 if (graph
->node
[i
].cluster
!= pos
)
6440 s
= graph
->node
[i
].scc
;
6441 k
= c
->scc_node
[s
]++;
6442 swap_sched(&c
->cluster
[pos
].node
[j
], &c
->scc
[s
].node
[k
]);
6443 if (c
->scc
[s
].maxvar
> c
->cluster
[pos
].maxvar
)
6444 c
->cluster
[pos
].maxvar
= c
->scc
[s
].maxvar
;
6451 /* Is there a (conditional) validity dependence from node[j] to node[i],
6452 * forcing node[i] to follow node[j] or do the nodes belong to the same
6455 static isl_bool
node_follows_strong_or_same_cluster(int i
, int j
, void *user
)
6457 struct isl_sched_graph
*graph
= user
;
6459 if (graph
->node
[i
].cluster
== graph
->node
[j
].cluster
)
6460 return isl_bool_true
;
6461 return graph_has_validity_edge(graph
, &graph
->node
[j
], &graph
->node
[i
]);
6464 /* Extract the merged clusters of SCCs in "graph", sort them, and
6465 * store them in c->clusters. Update c->scc_cluster accordingly.
6467 * First keep track of the cluster containing the SCC to which a node
6468 * belongs in the node itself.
6469 * Then extract the clusters into c->clusters, copying the current
6470 * band schedule from the SCCs that belong to the cluster.
6471 * Do this only once per cluster.
6473 * Finally, topologically sort the clusters and update c->scc_cluster
6474 * to match the new scc numbering. While the SCCs were originally
6475 * sorted already, some SCCs that depend on some other SCCs may
6476 * have been merged with SCCs that appear before these other SCCs.
6477 * A reordering may therefore be required.
6479 static isl_stat
extract_clusters(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
6480 struct isl_clustering
*c
)
6484 for (i
= 0; i
< graph
->n
; ++i
)
6485 graph
->node
[i
].cluster
= c
->scc_cluster
[graph
->node
[i
].scc
];
6487 for (i
= 0; i
< graph
->scc
; ++i
) {
6488 if (c
->scc_cluster
[i
] != i
)
6490 if (extract_sub_graph(ctx
, graph
, &node_cluster_exactly
,
6491 &edge_cluster_exactly
, i
, &c
->cluster
[i
]) < 0)
6492 return isl_stat_error
;
6493 c
->cluster
[i
].src_scc
= -1;
6494 c
->cluster
[i
].dst_scc
= -1;
6495 if (copy_partial(graph
, c
, i
) < 0)
6496 return isl_stat_error
;
6499 if (detect_ccs(ctx
, graph
, &node_follows_strong_or_same_cluster
) < 0)
6500 return isl_stat_error
;
6501 for (i
= 0; i
< graph
->n
; ++i
)
6502 c
->scc_cluster
[graph
->node
[i
].scc
] = graph
->node
[i
].cluster
;
6507 /* Compute weights on the proximity edges of "graph" that can
6508 * be used by find_proximity to find the most appropriate
6509 * proximity edge to use to merge two clusters in "c".
6510 * The weights are also used by has_bounded_distances to determine
6511 * whether the merge should be allowed.
6512 * Store the maximum of the computed weights in graph->max_weight.
6514 * The computed weight is a measure for the number of remaining schedule
6515 * dimensions that can still be completely aligned.
6516 * In particular, compute the number of equalities between
6517 * input dimensions and output dimensions in the proximity constraints.
6518 * The directions that are already handled by outer schedule bands
6519 * are projected out prior to determining this number.
6521 * Edges that will never be considered by find_proximity are ignored.
6523 static isl_stat
compute_weights(struct isl_sched_graph
*graph
,
6524 struct isl_clustering
*c
)
6528 graph
->max_weight
= 0;
6530 for (i
= 0; i
< graph
->n_edge
; ++i
) {
6531 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
6532 struct isl_sched_node
*src
= edge
->src
;
6533 struct isl_sched_node
*dst
= edge
->dst
;
6534 isl_basic_map
*hull
;
6538 prox
= is_non_empty_proximity(edge
);
6540 return isl_stat_error
;
6543 if (bad_cluster(&c
->scc
[edge
->src
->scc
]) ||
6544 bad_cluster(&c
->scc
[edge
->dst
->scc
]))
6546 if (c
->scc_cluster
[edge
->dst
->scc
] ==
6547 c
->scc_cluster
[edge
->src
->scc
])
6550 hull
= isl_map_affine_hull(isl_map_copy(edge
->map
));
6551 hull
= isl_basic_map_transform_dims(hull
, isl_dim_in
, 0,
6552 isl_mat_copy(src
->ctrans
));
6553 hull
= isl_basic_map_transform_dims(hull
, isl_dim_out
, 0,
6554 isl_mat_copy(dst
->ctrans
));
6555 hull
= isl_basic_map_project_out(hull
,
6556 isl_dim_in
, 0, src
->rank
);
6557 hull
= isl_basic_map_project_out(hull
,
6558 isl_dim_out
, 0, dst
->rank
);
6559 hull
= isl_basic_map_remove_divs(hull
);
6560 n_in
= isl_basic_map_dim(hull
, isl_dim_in
);
6561 n_out
= isl_basic_map_dim(hull
, isl_dim_out
);
6562 hull
= isl_basic_map_drop_constraints_not_involving_dims(hull
,
6563 isl_dim_in
, 0, n_in
);
6564 hull
= isl_basic_map_drop_constraints_not_involving_dims(hull
,
6565 isl_dim_out
, 0, n_out
);
6567 return isl_stat_error
;
6568 edge
->weight
= isl_basic_map_n_equality(hull
);
6569 isl_basic_map_free(hull
);
6571 if (edge
->weight
> graph
->max_weight
)
6572 graph
->max_weight
= edge
->weight
;
6578 /* Call compute_schedule_finish_band on each of the clusters in "c"
6579 * in their topological order. This order is determined by the scc
6580 * fields of the nodes in "graph".
6581 * Combine the results in a sequence expressing the topological order.
6583 * If there is only one cluster left, then there is no need to introduce
6584 * a sequence node. Also, in this case, the cluster necessarily contains
6585 * the SCC at position 0 in the original graph and is therefore also
6586 * stored in the first cluster of "c".
6588 static __isl_give isl_schedule_node
*finish_bands_clustering(
6589 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
6590 struct isl_clustering
*c
)
6594 isl_union_set_list
*filters
;
6596 if (graph
->scc
== 1)
6597 return compute_schedule_finish_band(node
, &c
->cluster
[0], 0);
6599 ctx
= isl_schedule_node_get_ctx(node
);
6601 filters
= extract_sccs(ctx
, graph
);
6602 node
= isl_schedule_node_insert_sequence(node
, filters
);
6604 for (i
= 0; i
< graph
->scc
; ++i
) {
6605 int j
= c
->scc_cluster
[i
];
6606 node
= isl_schedule_node_child(node
, i
);
6607 node
= isl_schedule_node_child(node
, 0);
6608 node
= compute_schedule_finish_band(node
, &c
->cluster
[j
], 0);
6609 node
= isl_schedule_node_parent(node
);
6610 node
= isl_schedule_node_parent(node
);
6616 /* Compute a schedule for a connected dependence graph by first considering
6617 * each strongly connected component (SCC) in the graph separately and then
6618 * incrementally combining them into clusters.
6619 * Return the updated schedule node.
6621 * Initially, each cluster consists of a single SCC, each with its
6622 * own band schedule. The algorithm then tries to merge pairs
6623 * of clusters along a proximity edge until no more suitable
6624 * proximity edges can be found. During this merging, the schedule
6625 * is maintained in the individual SCCs.
6626 * After the merging is completed, the full resulting clusters
6627 * are extracted and in finish_bands_clustering,
6628 * compute_schedule_finish_band is called on each of them to integrate
6629 * the band into "node" and to continue the computation.
6631 * compute_weights initializes the weights that are used by find_proximity.
6633 static __isl_give isl_schedule_node
*compute_schedule_wcc_clustering(
6634 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
6637 struct isl_clustering c
;
6640 ctx
= isl_schedule_node_get_ctx(node
);
6642 if (clustering_init(ctx
, &c
, graph
) < 0)
6645 if (compute_weights(graph
, &c
) < 0)
6649 i
= find_proximity(graph
, &c
);
6652 if (i
>= graph
->n_edge
)
6654 if (merge_clusters_along_edge(ctx
, graph
, i
, &c
) < 0)
6658 if (extract_clusters(ctx
, graph
, &c
) < 0)
6661 node
= finish_bands_clustering(node
, graph
, &c
);
6663 clustering_free(ctx
, &c
);
6666 clustering_free(ctx
, &c
);
6667 return isl_schedule_node_free(node
);
6670 /* Compute a schedule for a connected dependence graph and return
6671 * the updated schedule node.
6673 * If Feautrier's algorithm is selected, we first recursively try to satisfy
6674 * as many validity dependences as possible. When all validity dependences
6675 * are satisfied we extend the schedule to a full-dimensional schedule.
6677 * Call compute_schedule_wcc_whole or compute_schedule_wcc_clustering
6678 * depending on whether the user has selected the option to try and
6679 * compute a schedule for the entire (weakly connected) component first.
6680 * If there is only a single strongly connected component (SCC), then
6681 * there is no point in trying to combine SCCs
6682 * in compute_schedule_wcc_clustering, so compute_schedule_wcc_whole
6683 * is called instead.
6685 static __isl_give isl_schedule_node
*compute_schedule_wcc(
6686 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
)
6693 ctx
= isl_schedule_node_get_ctx(node
);
6694 if (detect_sccs(ctx
, graph
) < 0)
6695 return isl_schedule_node_free(node
);
6697 if (compute_maxvar(graph
) < 0)
6698 return isl_schedule_node_free(node
);
6700 if (need_feautrier_step(ctx
, graph
))
6701 return compute_schedule_wcc_feautrier(node
, graph
);
6703 if (graph
->scc
<= 1 || isl_options_get_schedule_whole_component(ctx
))
6704 return compute_schedule_wcc_whole(node
, graph
);
6706 return compute_schedule_wcc_clustering(node
, graph
);
6709 /* Compute a schedule for each group of nodes identified by node->scc
6710 * separately and then combine them in a sequence node (or as set node
6711 * if graph->weak is set) inserted at position "node" of the schedule tree.
6712 * Return the updated schedule node.
6714 * If "wcc" is set then each of the groups belongs to a single
6715 * weakly connected component in the dependence graph so that
6716 * there is no need for compute_sub_schedule to look for weakly
6717 * connected components.
6719 static __isl_give isl_schedule_node
*compute_component_schedule(
6720 __isl_take isl_schedule_node
*node
, struct isl_sched_graph
*graph
,
6725 isl_union_set_list
*filters
;
6729 ctx
= isl_schedule_node_get_ctx(node
);
6731 filters
= extract_sccs(ctx
, graph
);
6733 node
= isl_schedule_node_insert_set(node
, filters
);
6735 node
= isl_schedule_node_insert_sequence(node
, filters
);
6737 for (component
= 0; component
< graph
->scc
; ++component
) {
6738 node
= isl_schedule_node_child(node
, component
);
6739 node
= isl_schedule_node_child(node
, 0);
6740 node
= compute_sub_schedule(node
, ctx
, graph
,
6742 &edge_scc_exactly
, component
, wcc
);
6743 node
= isl_schedule_node_parent(node
);
6744 node
= isl_schedule_node_parent(node
);
6750 /* Compute a schedule for the given dependence graph and insert it at "node".
6751 * Return the updated schedule node.
6753 * We first check if the graph is connected (through validity and conditional
6754 * validity dependences) and, if not, compute a schedule
6755 * for each component separately.
6756 * If the schedule_serialize_sccs option is set, then we check for strongly
6757 * connected components instead and compute a separate schedule for
6758 * each such strongly connected component.
6760 static __isl_give isl_schedule_node
*compute_schedule(isl_schedule_node
*node
,
6761 struct isl_sched_graph
*graph
)
6768 ctx
= isl_schedule_node_get_ctx(node
);
6769 if (isl_options_get_schedule_serialize_sccs(ctx
)) {
6770 if (detect_sccs(ctx
, graph
) < 0)
6771 return isl_schedule_node_free(node
);
6773 if (detect_wccs(ctx
, graph
) < 0)
6774 return isl_schedule_node_free(node
);
6778 return compute_component_schedule(node
, graph
, 1);
6780 return compute_schedule_wcc(node
, graph
);
6783 /* Compute a schedule on sc->domain that respects the given schedule
6786 * In particular, the schedule respects all the validity dependences.
6787 * If the default isl scheduling algorithm is used, it tries to minimize
6788 * the dependence distances over the proximity dependences.
6789 * If Feautrier's scheduling algorithm is used, the proximity dependence
6790 * distances are only minimized during the extension to a full-dimensional
6793 * If there are any condition and conditional validity dependences,
6794 * then the conditional validity dependences may be violated inside
6795 * a tilable band, provided they have no adjacent non-local
6796 * condition dependences.
6798 __isl_give isl_schedule
*isl_schedule_constraints_compute_schedule(
6799 __isl_take isl_schedule_constraints
*sc
)
6801 isl_ctx
*ctx
= isl_schedule_constraints_get_ctx(sc
);
6802 struct isl_sched_graph graph
= { 0 };
6803 isl_schedule
*sched
;
6804 isl_schedule_node
*node
;
6805 isl_union_set
*domain
;
6807 sc
= isl_schedule_constraints_align_params(sc
);
6809 domain
= isl_schedule_constraints_get_domain(sc
);
6810 if (isl_union_set_n_set(domain
) == 0) {
6811 isl_schedule_constraints_free(sc
);
6812 return isl_schedule_from_domain(domain
);
6815 if (graph_init(&graph
, sc
) < 0)
6816 domain
= isl_union_set_free(domain
);
6818 node
= isl_schedule_node_from_domain(domain
);
6819 node
= isl_schedule_node_child(node
, 0);
6821 node
= compute_schedule(node
, &graph
);
6822 sched
= isl_schedule_node_get_schedule(node
);
6823 isl_schedule_node_free(node
);
6825 graph_free(ctx
, &graph
);
6826 isl_schedule_constraints_free(sc
);
6831 /* Compute a schedule for the given union of domains that respects
6832 * all the validity dependences and minimizes
6833 * the dependence distances over the proximity dependences.
6835 * This function is kept for backward compatibility.
6837 __isl_give isl_schedule
*isl_union_set_compute_schedule(
6838 __isl_take isl_union_set
*domain
,
6839 __isl_take isl_union_map
*validity
,
6840 __isl_take isl_union_map
*proximity
)
6842 isl_schedule_constraints
*sc
;
6844 sc
= isl_schedule_constraints_on_domain(domain
);
6845 sc
= isl_schedule_constraints_set_validity(sc
, validity
);
6846 sc
= isl_schedule_constraints_set_proximity(sc
, proximity
);
6848 return isl_schedule_constraints_compute_schedule(sc
);