extract out shared isl_reordering_get_space
[isl.git] / isl_scheduler.c
blobb47dcc245cdc8899034d814fdc237a6d76d3d641
1 /*
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,
12 * 91893 Orsay, France
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>
22 #include <isl/hash.h>
23 #include <isl/id.h>
24 #include <isl/constraint.h>
25 #include <isl/schedule.h>
26 #include <isl_schedule_constraints.h>
27 #include <isl/schedule_node.h>
28 #include <isl_mat_private.h>
29 #include <isl_vec_private.h>
30 #include <isl/set.h>
31 #include <isl_union_set_private.h>
32 #include <isl_seq.h>
33 #include <isl_tab.h>
34 #include <isl_dim_map.h>
35 #include <isl/map_to_basic_set.h>
36 #include <isl_sort.h>
37 #include <isl_options_private.h>
38 #include <isl_tarjan.h>
39 #include <isl_morph.h>
40 #include <isl/ilp.h>
41 #include <isl_val_private.h>
44 * The scheduling algorithm implemented in this file was inspired by
45 * Bondhugula et al., "Automatic Transformations for Communication-Minimized
46 * Parallelization and Locality Optimization in the Polyhedral Model".
48 * For a detailed description of the variant implemented in isl,
49 * see Verdoolaege and Janssens, "Scheduling for PPCG" (2017).
53 /* Internal information about a node that is used during the construction
54 * of a schedule.
55 * space represents the original space in which the domain lives;
56 * that is, the space is not affected by compression
57 * sched is a matrix representation of the schedule being constructed
58 * for this node; if compressed is set, then this schedule is
59 * defined over the compressed domain space
60 * sched_map is an isl_map representation of the same (partial) schedule
61 * sched_map may be NULL; if compressed is set, then this map
62 * is defined over the uncompressed domain space
63 * rank is the number of linearly independent rows in the linear part
64 * of sched
65 * the rows of "vmap" represent a change of basis for the node
66 * variables; the first rank rows span the linear part of
67 * the schedule rows; the remaining rows are linearly independent
68 * the rows of "indep" represent linear combinations of the schedule
69 * coefficients that are non-zero when the schedule coefficients are
70 * linearly independent of previously computed schedule rows.
71 * start is the first variable in the LP problem in the sequences that
72 * represents the schedule coefficients of this node
73 * nvar is the dimension of the (compressed) domain
74 * nparam is the number of parameters or 0 if we are not constructing
75 * a parametric schedule
77 * If compressed is set, then hull represents the constraints
78 * that were used to derive the compression, while compress and
79 * decompress map the original space to the compressed space and
80 * vice versa.
82 * scc is the index of SCC (or WCC) this node belongs to
84 * "cluster" is only used inside extract_clusters and identifies
85 * the cluster of SCCs that the node belongs to.
87 * coincident contains a boolean for each of the rows of the schedule,
88 * indicating whether the corresponding scheduling dimension satisfies
89 * the coincidence constraints in the sense that the corresponding
90 * dependence distances are zero.
92 * If the schedule_treat_coalescing option is set, then
93 * "sizes" contains the sizes of the (compressed) instance set
94 * in each direction. If there is no fixed size in a given direction,
95 * then the corresponding size value is set to infinity.
96 * If the schedule_treat_coalescing option or the schedule_max_coefficient
97 * option is set, then "max" contains the maximal values for
98 * schedule coefficients of the (compressed) variables. If no bound
99 * needs to be imposed on a particular variable, then the corresponding
100 * value is negative.
101 * If not NULL, then "bounds" contains a non-parametric set
102 * in the compressed space that is bounded by the size in each direction.
104 struct isl_sched_node {
105 isl_space *space;
106 int compressed;
107 isl_set *hull;
108 isl_multi_aff *compress;
109 isl_multi_aff *decompress;
110 isl_mat *sched;
111 isl_map *sched_map;
112 int rank;
113 isl_mat *indep;
114 isl_mat *vmap;
115 int start;
116 int nvar;
117 int nparam;
119 int scc;
120 int cluster;
122 int *coincident;
124 isl_multi_val *sizes;
125 isl_basic_set *bounds;
126 isl_vec *max;
129 static int node_has_tuples(const void *entry, const void *val)
131 struct isl_sched_node *node = (struct isl_sched_node *)entry;
132 isl_space *space = (isl_space *) val;
134 return isl_space_has_equal_tuples(node->space, space);
137 static int node_scc_exactly(struct isl_sched_node *node, int scc)
139 return node->scc == scc;
142 static int node_scc_at_most(struct isl_sched_node *node, int scc)
144 return node->scc <= scc;
147 static int node_scc_at_least(struct isl_sched_node *node, int scc)
149 return node->scc >= scc;
152 /* An edge in the dependence graph. An edge may be used to
153 * ensure validity of the generated schedule, to minimize the dependence
154 * distance or both
156 * map is the dependence relation, with i -> j in the map if j depends on i
157 * tagged_condition and tagged_validity contain the union of all tagged
158 * condition or conditional validity dependence relations that
159 * specialize the dependence relation "map"; that is,
160 * if (i -> a) -> (j -> b) is an element of "tagged_condition"
161 * or "tagged_validity", then i -> j is an element of "map".
162 * If these fields are NULL, then they represent the empty relation.
163 * src is the source node
164 * dst is the sink node
166 * types is a bit vector containing the types of this edge.
167 * validity is set if the edge is used to ensure correctness
168 * coincidence is used to enforce zero dependence distances
169 * proximity is set if the edge is used to minimize dependence distances
170 * condition is set if the edge represents a condition
171 * for a conditional validity schedule constraint
172 * local can only be set for condition edges and indicates that
173 * the dependence distance over the edge should be zero
174 * conditional_validity is set if the edge is used to conditionally
175 * ensure correctness
177 * For validity edges, start and end mark the sequence of inequality
178 * constraints in the LP problem that encode the validity constraint
179 * corresponding to this edge.
181 * During clustering, an edge may be marked "no_merge" if it should
182 * not be used to merge clusters.
183 * The weight is also only used during clustering and it is
184 * an indication of how many schedule dimensions on either side
185 * of the schedule constraints can be aligned.
186 * If the weight is negative, then this means that this edge was postponed
187 * by has_bounded_distances or any_no_merge. The original weight can
188 * be retrieved by adding 1 + graph->max_weight, with "graph"
189 * the graph containing this edge.
191 struct isl_sched_edge {
192 isl_map *map;
193 isl_union_map *tagged_condition;
194 isl_union_map *tagged_validity;
196 struct isl_sched_node *src;
197 struct isl_sched_node *dst;
199 unsigned types;
201 int start;
202 int end;
204 int no_merge;
205 int weight;
208 /* Is "edge" marked as being of type "type"?
210 static int is_type(struct isl_sched_edge *edge, enum isl_edge_type type)
212 return ISL_FL_ISSET(edge->types, 1 << type);
215 /* Mark "edge" as being of type "type".
217 static void set_type(struct isl_sched_edge *edge, enum isl_edge_type type)
219 ISL_FL_SET(edge->types, 1 << type);
222 /* No longer mark "edge" as being of type "type"?
224 static void clear_type(struct isl_sched_edge *edge, enum isl_edge_type type)
226 ISL_FL_CLR(edge->types, 1 << type);
229 /* Is "edge" marked as a validity edge?
231 static int is_validity(struct isl_sched_edge *edge)
233 return is_type(edge, isl_edge_validity);
236 /* Mark "edge" as a validity edge.
238 static void set_validity(struct isl_sched_edge *edge)
240 set_type(edge, isl_edge_validity);
243 /* Is "edge" marked as a proximity edge?
245 static int is_proximity(struct isl_sched_edge *edge)
247 return is_type(edge, isl_edge_proximity);
250 /* Is "edge" marked as a local edge?
252 static int is_local(struct isl_sched_edge *edge)
254 return is_type(edge, isl_edge_local);
257 /* Mark "edge" as a local edge.
259 static void set_local(struct isl_sched_edge *edge)
261 set_type(edge, isl_edge_local);
264 /* No longer mark "edge" as a local edge.
266 static void clear_local(struct isl_sched_edge *edge)
268 clear_type(edge, isl_edge_local);
271 /* Is "edge" marked as a coincidence edge?
273 static int is_coincidence(struct isl_sched_edge *edge)
275 return is_type(edge, isl_edge_coincidence);
278 /* Is "edge" marked as a condition edge?
280 static int is_condition(struct isl_sched_edge *edge)
282 return is_type(edge, isl_edge_condition);
285 /* Is "edge" marked as a conditional validity edge?
287 static int is_conditional_validity(struct isl_sched_edge *edge)
289 return is_type(edge, isl_edge_conditional_validity);
292 /* Is "edge" of a type that can appear multiple times between
293 * the same pair of nodes?
295 * Condition edges and conditional validity edges may have tagged
296 * dependence relations, in which case an edge is added for each
297 * pair of tags.
299 static int is_multi_edge_type(struct isl_sched_edge *edge)
301 return is_condition(edge) || is_conditional_validity(edge);
304 /* Internal information about the dependence graph used during
305 * the construction of the schedule.
307 * intra_hmap is a cache, mapping dependence relations to their dual,
308 * for dependences from a node to itself, possibly without
309 * coefficients for the parameters
310 * intra_hmap_param is a cache, mapping dependence relations to their dual,
311 * for dependences from a node to itself, including coefficients
312 * for the parameters
313 * inter_hmap is a cache, mapping dependence relations to their dual,
314 * for dependences between distinct nodes
315 * if compression is involved then the key for these maps
316 * is the original, uncompressed dependence relation, while
317 * the value is the dual of the compressed dependence relation.
319 * n is the number of nodes
320 * node is the list of nodes
321 * maxvar is the maximal number of variables over all nodes
322 * max_row is the allocated number of rows in the schedule
323 * n_row is the current (maximal) number of linearly independent
324 * rows in the node schedules
325 * n_total_row is the current number of rows in the node schedules
326 * band_start is the starting row in the node schedules of the current band
327 * root is set to the original dependence graph from which this graph
328 * is derived through splitting. If this graph is not the result of
329 * splitting, then the root field points to the graph itself.
331 * sorted contains a list of node indices sorted according to the
332 * SCC to which a node belongs
334 * n_edge is the number of edges
335 * edge is the list of edges
336 * max_edge contains the maximal number of edges of each type;
337 * in particular, it contains the number of edges in the inital graph.
338 * edge_table contains pointers into the edge array, hashed on the source
339 * and sink spaces; there is one such table for each type;
340 * a given edge may be referenced from more than one table
341 * if the corresponding relation appears in more than one of the
342 * sets of dependences; however, for each type there is only
343 * a single edge between a given pair of source and sink space
344 * in the entire graph
346 * node_table contains pointers into the node array, hashed on the space tuples
348 * region contains a list of variable sequences that should be non-trivial
350 * lp contains the (I)LP problem used to obtain new schedule rows
352 * src_scc and dst_scc are the source and sink SCCs of an edge with
353 * conflicting constraints
355 * scc represents the number of components
356 * weak is set if the components are weakly connected
358 * max_weight is used during clustering and represents the maximal
359 * weight of the relevant proximity edges.
361 struct isl_sched_graph {
362 isl_map_to_basic_set *intra_hmap;
363 isl_map_to_basic_set *intra_hmap_param;
364 isl_map_to_basic_set *inter_hmap;
366 struct isl_sched_node *node;
367 int n;
368 int maxvar;
369 int max_row;
370 int n_row;
372 int *sorted;
374 int n_total_row;
375 int band_start;
377 struct isl_sched_graph *root;
379 struct isl_sched_edge *edge;
380 int n_edge;
381 int max_edge[isl_edge_last + 1];
382 struct isl_hash_table *edge_table[isl_edge_last + 1];
384 struct isl_hash_table *node_table;
385 struct isl_trivial_region *region;
387 isl_basic_set *lp;
389 int src_scc;
390 int dst_scc;
392 int scc;
393 int weak;
395 int max_weight;
398 /* Initialize node_table based on the list of nodes.
400 static int graph_init_table(isl_ctx *ctx, struct isl_sched_graph *graph)
402 int i;
404 graph->node_table = isl_hash_table_alloc(ctx, graph->n);
405 if (!graph->node_table)
406 return -1;
408 for (i = 0; i < graph->n; ++i) {
409 struct isl_hash_table_entry *entry;
410 uint32_t hash;
412 hash = isl_space_get_tuple_hash(graph->node[i].space);
413 entry = isl_hash_table_find(ctx, graph->node_table, hash,
414 &node_has_tuples,
415 graph->node[i].space, 1);
416 if (!entry)
417 return -1;
418 entry->data = &graph->node[i];
421 return 0;
424 /* Return a pointer to the node that lives within the given space,
425 * an invalid node if there is no such node, or NULL in case of error.
427 static struct isl_sched_node *graph_find_node(isl_ctx *ctx,
428 struct isl_sched_graph *graph, __isl_keep isl_space *space)
430 struct isl_hash_table_entry *entry;
431 uint32_t hash;
433 if (!space)
434 return NULL;
436 hash = isl_space_get_tuple_hash(space);
437 entry = isl_hash_table_find(ctx, graph->node_table, hash,
438 &node_has_tuples, space, 0);
440 return entry ? entry->data : graph->node + graph->n;
443 /* Is "node" a node in "graph"?
445 static int is_node(struct isl_sched_graph *graph,
446 struct isl_sched_node *node)
448 return node && node >= &graph->node[0] && node < &graph->node[graph->n];
451 static int edge_has_src_and_dst(const void *entry, const void *val)
453 const struct isl_sched_edge *edge = entry;
454 const struct isl_sched_edge *temp = val;
456 return edge->src == temp->src && edge->dst == temp->dst;
459 /* Add the given edge to graph->edge_table[type].
461 static isl_stat graph_edge_table_add(isl_ctx *ctx,
462 struct isl_sched_graph *graph, enum isl_edge_type type,
463 struct isl_sched_edge *edge)
465 struct isl_hash_table_entry *entry;
466 uint32_t hash;
468 hash = isl_hash_init();
469 hash = isl_hash_builtin(hash, edge->src);
470 hash = isl_hash_builtin(hash, edge->dst);
471 entry = isl_hash_table_find(ctx, graph->edge_table[type], hash,
472 &edge_has_src_and_dst, edge, 1);
473 if (!entry)
474 return isl_stat_error;
475 entry->data = edge;
477 return isl_stat_ok;
480 /* Add "edge" to all relevant edge tables.
481 * That is, for every type of the edge, add it to the corresponding table.
483 static isl_stat graph_edge_tables_add(isl_ctx *ctx,
484 struct isl_sched_graph *graph, struct isl_sched_edge *edge)
486 enum isl_edge_type t;
488 for (t = isl_edge_first; t <= isl_edge_last; ++t) {
489 if (!is_type(edge, t))
490 continue;
491 if (graph_edge_table_add(ctx, graph, t, edge) < 0)
492 return isl_stat_error;
495 return isl_stat_ok;
498 /* Allocate the edge_tables based on the maximal number of edges of
499 * each type.
501 static int graph_init_edge_tables(isl_ctx *ctx, struct isl_sched_graph *graph)
503 int i;
505 for (i = 0; i <= isl_edge_last; ++i) {
506 graph->edge_table[i] = isl_hash_table_alloc(ctx,
507 graph->max_edge[i]);
508 if (!graph->edge_table[i])
509 return -1;
512 return 0;
515 /* If graph->edge_table[type] contains an edge from the given source
516 * to the given destination, then return the hash table entry of this edge.
517 * Otherwise, return NULL.
519 static struct isl_hash_table_entry *graph_find_edge_entry(
520 struct isl_sched_graph *graph,
521 enum isl_edge_type type,
522 struct isl_sched_node *src, struct isl_sched_node *dst)
524 isl_ctx *ctx = isl_space_get_ctx(src->space);
525 uint32_t hash;
526 struct isl_sched_edge temp = { .src = src, .dst = dst };
528 hash = isl_hash_init();
529 hash = isl_hash_builtin(hash, temp.src);
530 hash = isl_hash_builtin(hash, temp.dst);
531 return isl_hash_table_find(ctx, graph->edge_table[type], hash,
532 &edge_has_src_and_dst, &temp, 0);
536 /* If graph->edge_table[type] contains an edge from the given source
537 * to the given destination, then return this edge.
538 * Otherwise, return NULL.
540 static struct isl_sched_edge *graph_find_edge(struct isl_sched_graph *graph,
541 enum isl_edge_type type,
542 struct isl_sched_node *src, struct isl_sched_node *dst)
544 struct isl_hash_table_entry *entry;
546 entry = graph_find_edge_entry(graph, type, src, dst);
547 if (!entry)
548 return NULL;
550 return entry->data;
553 /* Check whether the dependence graph has an edge of the given type
554 * between the given two nodes.
556 static isl_bool graph_has_edge(struct isl_sched_graph *graph,
557 enum isl_edge_type type,
558 struct isl_sched_node *src, struct isl_sched_node *dst)
560 struct isl_sched_edge *edge;
561 isl_bool empty;
563 edge = graph_find_edge(graph, type, src, dst);
564 if (!edge)
565 return 0;
567 empty = isl_map_plain_is_empty(edge->map);
568 if (empty < 0)
569 return isl_bool_error;
571 return !empty;
574 /* Look for any edge with the same src, dst and map fields as "model".
576 * Return the matching edge if one can be found.
577 * Return "model" if no matching edge is found.
578 * Return NULL on error.
580 static struct isl_sched_edge *graph_find_matching_edge(
581 struct isl_sched_graph *graph, struct isl_sched_edge *model)
583 enum isl_edge_type i;
584 struct isl_sched_edge *edge;
586 for (i = isl_edge_first; i <= isl_edge_last; ++i) {
587 int is_equal;
589 edge = graph_find_edge(graph, i, model->src, model->dst);
590 if (!edge)
591 continue;
592 is_equal = isl_map_plain_is_equal(model->map, edge->map);
593 if (is_equal < 0)
594 return NULL;
595 if (is_equal)
596 return edge;
599 return model;
602 /* Remove the given edge from all the edge_tables that refer to it.
604 static void graph_remove_edge(struct isl_sched_graph *graph,
605 struct isl_sched_edge *edge)
607 isl_ctx *ctx = isl_map_get_ctx(edge->map);
608 enum isl_edge_type i;
610 for (i = isl_edge_first; i <= isl_edge_last; ++i) {
611 struct isl_hash_table_entry *entry;
613 entry = graph_find_edge_entry(graph, i, edge->src, edge->dst);
614 if (!entry)
615 continue;
616 if (entry->data != edge)
617 continue;
618 isl_hash_table_remove(ctx, graph->edge_table[i], entry);
622 /* Check whether the dependence graph has any edge
623 * between the given two nodes.
625 static isl_bool graph_has_any_edge(struct isl_sched_graph *graph,
626 struct isl_sched_node *src, struct isl_sched_node *dst)
628 enum isl_edge_type i;
629 isl_bool r;
631 for (i = isl_edge_first; i <= isl_edge_last; ++i) {
632 r = graph_has_edge(graph, i, src, dst);
633 if (r < 0 || r)
634 return r;
637 return r;
640 /* Check whether the dependence graph has a validity edge
641 * between the given two nodes.
643 * Conditional validity edges are essentially validity edges that
644 * can be ignored if the corresponding condition edges are iteration private.
645 * Here, we are only checking for the presence of validity
646 * edges, so we need to consider the conditional validity edges too.
647 * In particular, this function is used during the detection
648 * of strongly connected components and we cannot ignore
649 * conditional validity edges during this detection.
651 static isl_bool graph_has_validity_edge(struct isl_sched_graph *graph,
652 struct isl_sched_node *src, struct isl_sched_node *dst)
654 isl_bool r;
656 r = graph_has_edge(graph, isl_edge_validity, src, dst);
657 if (r < 0 || r)
658 return r;
660 return graph_has_edge(graph, isl_edge_conditional_validity, src, dst);
663 /* Perform all the required memory allocations for a schedule graph "graph"
664 * with "n_node" nodes and "n_edge" edge and initialize the corresponding
665 * fields.
667 static isl_stat graph_alloc(isl_ctx *ctx, struct isl_sched_graph *graph,
668 int n_node, int n_edge)
670 int i;
672 graph->n = n_node;
673 graph->n_edge = n_edge;
674 graph->node = isl_calloc_array(ctx, struct isl_sched_node, graph->n);
675 graph->sorted = isl_calloc_array(ctx, int, graph->n);
676 graph->region = isl_alloc_array(ctx,
677 struct isl_trivial_region, graph->n);
678 graph->edge = isl_calloc_array(ctx,
679 struct isl_sched_edge, graph->n_edge);
681 graph->intra_hmap = isl_map_to_basic_set_alloc(ctx, 2 * n_edge);
682 graph->intra_hmap_param = isl_map_to_basic_set_alloc(ctx, 2 * n_edge);
683 graph->inter_hmap = isl_map_to_basic_set_alloc(ctx, 2 * n_edge);
685 if (!graph->node || !graph->region || (graph->n_edge && !graph->edge) ||
686 !graph->sorted)
687 return isl_stat_error;
689 for(i = 0; i < graph->n; ++i)
690 graph->sorted[i] = i;
692 return isl_stat_ok;
695 /* Free the memory associated to node "node" in "graph".
696 * The "coincident" field is shared by nodes in a graph and its subgraph.
697 * It therefore only needs to be freed for the original dependence graph,
698 * i.e., one that is not the result of splitting.
700 static void clear_node(struct isl_sched_graph *graph,
701 struct isl_sched_node *node)
703 isl_space_free(node->space);
704 isl_set_free(node->hull);
705 isl_multi_aff_free(node->compress);
706 isl_multi_aff_free(node->decompress);
707 isl_mat_free(node->sched);
708 isl_map_free(node->sched_map);
709 isl_mat_free(node->indep);
710 isl_mat_free(node->vmap);
711 if (graph->root == graph)
712 free(node->coincident);
713 isl_multi_val_free(node->sizes);
714 isl_basic_set_free(node->bounds);
715 isl_vec_free(node->max);
718 static void graph_free(isl_ctx *ctx, struct isl_sched_graph *graph)
720 int i;
722 isl_map_to_basic_set_free(graph->intra_hmap);
723 isl_map_to_basic_set_free(graph->intra_hmap_param);
724 isl_map_to_basic_set_free(graph->inter_hmap);
726 if (graph->node)
727 for (i = 0; i < graph->n; ++i)
728 clear_node(graph, &graph->node[i]);
729 free(graph->node);
730 free(graph->sorted);
731 if (graph->edge)
732 for (i = 0; i < graph->n_edge; ++i) {
733 isl_map_free(graph->edge[i].map);
734 isl_union_map_free(graph->edge[i].tagged_condition);
735 isl_union_map_free(graph->edge[i].tagged_validity);
737 free(graph->edge);
738 free(graph->region);
739 for (i = 0; i <= isl_edge_last; ++i)
740 isl_hash_table_free(ctx, graph->edge_table[i]);
741 isl_hash_table_free(ctx, graph->node_table);
742 isl_basic_set_free(graph->lp);
745 /* For each "set" on which this function is called, increment
746 * graph->n by one and update graph->maxvar.
748 static isl_stat init_n_maxvar(__isl_take isl_set *set, void *user)
750 struct isl_sched_graph *graph = user;
751 int nvar = isl_set_dim(set, isl_dim_set);
753 graph->n++;
754 if (nvar > graph->maxvar)
755 graph->maxvar = nvar;
757 isl_set_free(set);
759 return isl_stat_ok;
762 /* Compute the number of rows that should be allocated for the schedule.
763 * In particular, we need one row for each variable or one row
764 * for each basic map in the dependences.
765 * Note that it is practically impossible to exhaust both
766 * the number of dependences and the number of variables.
768 static isl_stat compute_max_row(struct isl_sched_graph *graph,
769 __isl_keep isl_schedule_constraints *sc)
771 int n_edge;
772 isl_stat r;
773 isl_union_set *domain;
775 graph->n = 0;
776 graph->maxvar = 0;
777 domain = isl_schedule_constraints_get_domain(sc);
778 r = isl_union_set_foreach_set(domain, &init_n_maxvar, graph);
779 isl_union_set_free(domain);
780 if (r < 0)
781 return isl_stat_error;
782 n_edge = isl_schedule_constraints_n_basic_map(sc);
783 if (n_edge < 0)
784 return isl_stat_error;
785 graph->max_row = n_edge + graph->maxvar;
787 return isl_stat_ok;
790 /* Does "bset" have any defining equalities for its set variables?
792 static isl_bool has_any_defining_equality(__isl_keep isl_basic_set *bset)
794 int i, n;
796 if (!bset)
797 return isl_bool_error;
799 n = isl_basic_set_dim(bset, isl_dim_set);
800 for (i = 0; i < n; ++i) {
801 isl_bool has;
803 has = isl_basic_set_has_defining_equality(bset, isl_dim_set, i,
804 NULL);
805 if (has < 0 || has)
806 return has;
809 return isl_bool_false;
812 /* Set the entries of node->max to the value of the schedule_max_coefficient
813 * option, if set.
815 static isl_stat set_max_coefficient(isl_ctx *ctx, struct isl_sched_node *node)
817 int max;
819 max = isl_options_get_schedule_max_coefficient(ctx);
820 if (max == -1)
821 return isl_stat_ok;
823 node->max = isl_vec_alloc(ctx, node->nvar);
824 node->max = isl_vec_set_si(node->max, max);
825 if (!node->max)
826 return isl_stat_error;
828 return isl_stat_ok;
831 /* Set the entries of node->max to the minimum of the schedule_max_coefficient
832 * option (if set) and half of the minimum of the sizes in the other
833 * dimensions. Round up when computing the half such that
834 * if the minimum of the sizes is one, half of the size is taken to be one
835 * rather than zero.
836 * If the global minimum is unbounded (i.e., if both
837 * the schedule_max_coefficient is not set and the sizes in the other
838 * dimensions are unbounded), then store a negative value.
839 * If the schedule coefficient is close to the size of the instance set
840 * in another dimension, then the schedule may represent a loop
841 * coalescing transformation (especially if the coefficient
842 * in that other dimension is one). Forcing the coefficient to be
843 * smaller than or equal to half the minimal size should avoid this
844 * situation.
846 static isl_stat compute_max_coefficient(isl_ctx *ctx,
847 struct isl_sched_node *node)
849 int max;
850 int i, j;
851 isl_vec *v;
853 max = isl_options_get_schedule_max_coefficient(ctx);
854 v = isl_vec_alloc(ctx, node->nvar);
855 if (!v)
856 return isl_stat_error;
858 for (i = 0; i < node->nvar; ++i) {
859 isl_int_set_si(v->el[i], max);
860 isl_int_mul_si(v->el[i], v->el[i], 2);
863 for (i = 0; i < node->nvar; ++i) {
864 isl_val *size;
866 size = isl_multi_val_get_val(node->sizes, i);
867 if (!size)
868 goto error;
869 if (!isl_val_is_int(size)) {
870 isl_val_free(size);
871 continue;
873 for (j = 0; j < node->nvar; ++j) {
874 if (j == i)
875 continue;
876 if (isl_int_is_neg(v->el[j]) ||
877 isl_int_gt(v->el[j], size->n))
878 isl_int_set(v->el[j], size->n);
880 isl_val_free(size);
883 for (i = 0; i < node->nvar; ++i)
884 isl_int_cdiv_q_ui(v->el[i], v->el[i], 2);
886 node->max = v;
887 return isl_stat_ok;
888 error:
889 isl_vec_free(v);
890 return isl_stat_error;
893 /* Compute and return the size of "set" in dimension "dim".
894 * The size is taken to be the difference in values for that variable
895 * for fixed values of the other variables.
896 * This assumes that "set" is convex.
897 * In particular, the variable is first isolated from the other variables
898 * in the range of a map
900 * [i_0, ..., i_dim-1, i_dim+1, ...] -> [i_dim]
902 * and then duplicated
904 * [i_0, ..., i_dim-1, i_dim+1, ...] -> [[i_dim] -> [i_dim']]
906 * The shared variables are then projected out and the maximal value
907 * of i_dim' - i_dim is computed.
909 static __isl_give isl_val *compute_size(__isl_take isl_set *set, int dim)
911 isl_map *map;
912 isl_local_space *ls;
913 isl_aff *obj;
914 isl_val *v;
916 map = isl_set_project_onto_map(set, isl_dim_set, dim, 1);
917 map = isl_map_project_out(map, isl_dim_in, dim, 1);
918 map = isl_map_range_product(map, isl_map_copy(map));
919 map = isl_set_unwrap(isl_map_range(map));
920 set = isl_map_deltas(map);
921 ls = isl_local_space_from_space(isl_set_get_space(set));
922 obj = isl_aff_var_on_domain(ls, isl_dim_set, 0);
923 v = isl_set_max_val(set, obj);
924 isl_aff_free(obj);
925 isl_set_free(set);
927 return v;
930 /* Compute the size of the instance set "set" of "node", after compression,
931 * as well as bounds on the corresponding coefficients, if needed.
933 * The sizes are needed when the schedule_treat_coalescing option is set.
934 * The bounds are needed when the schedule_treat_coalescing option or
935 * the schedule_max_coefficient option is set.
937 * If the schedule_treat_coalescing option is not set, then at most
938 * the bounds need to be set and this is done in set_max_coefficient.
939 * Otherwise, compress the domain if needed, compute the size
940 * in each direction and store the results in node->size.
941 * If the domain is not convex, then the sizes are computed
942 * on a convex superset in order to avoid picking up sizes
943 * that are valid for the individual disjuncts, but not for
944 * the domain as a whole.
945 * Finally, set the bounds on the coefficients based on the sizes
946 * and the schedule_max_coefficient option in compute_max_coefficient.
948 static isl_stat compute_sizes_and_max(isl_ctx *ctx, struct isl_sched_node *node,
949 __isl_take isl_set *set)
951 int j, n;
952 isl_multi_val *mv;
954 if (!isl_options_get_schedule_treat_coalescing(ctx)) {
955 isl_set_free(set);
956 return set_max_coefficient(ctx, node);
959 if (node->compressed)
960 set = isl_set_preimage_multi_aff(set,
961 isl_multi_aff_copy(node->decompress));
962 set = isl_set_from_basic_set(isl_set_simple_hull(set));
963 mv = isl_multi_val_zero(isl_set_get_space(set));
964 n = isl_set_dim(set, isl_dim_set);
965 for (j = 0; j < n; ++j) {
966 isl_val *v;
968 v = compute_size(isl_set_copy(set), j);
969 mv = isl_multi_val_set_val(mv, j, v);
971 node->sizes = mv;
972 isl_set_free(set);
973 if (!node->sizes)
974 return isl_stat_error;
975 return compute_max_coefficient(ctx, node);
978 /* Add a new node to the graph representing the given instance set.
979 * "nvar" is the (possibly compressed) number of variables and
980 * may be smaller than then number of set variables in "set"
981 * if "compressed" is set.
982 * If "compressed" is set, then "hull" represents the constraints
983 * that were used to derive the compression, while "compress" and
984 * "decompress" map the original space to the compressed space and
985 * vice versa.
986 * If "compressed" is not set, then "hull", "compress" and "decompress"
987 * should be NULL.
989 * Compute the size of the instance set and bounds on the coefficients,
990 * if needed.
992 static isl_stat add_node(struct isl_sched_graph *graph,
993 __isl_take isl_set *set, int nvar, int compressed,
994 __isl_take isl_set *hull, __isl_take isl_multi_aff *compress,
995 __isl_take isl_multi_aff *decompress)
997 int nparam;
998 isl_ctx *ctx;
999 isl_mat *sched;
1000 isl_space *space;
1001 int *coincident;
1002 struct isl_sched_node *node;
1004 if (!set)
1005 return isl_stat_error;
1007 ctx = isl_set_get_ctx(set);
1008 nparam = isl_set_dim(set, isl_dim_param);
1009 if (!ctx->opt->schedule_parametric)
1010 nparam = 0;
1011 sched = isl_mat_alloc(ctx, 0, 1 + nparam + nvar);
1012 node = &graph->node[graph->n];
1013 graph->n++;
1014 space = isl_set_get_space(set);
1015 node->space = space;
1016 node->nvar = nvar;
1017 node->nparam = nparam;
1018 node->sched = sched;
1019 node->sched_map = NULL;
1020 coincident = isl_calloc_array(ctx, int, graph->max_row);
1021 node->coincident = coincident;
1022 node->compressed = compressed;
1023 node->hull = hull;
1024 node->compress = compress;
1025 node->decompress = decompress;
1026 if (compute_sizes_and_max(ctx, node, set) < 0)
1027 return isl_stat_error;
1029 if (!space || !sched || (graph->max_row && !coincident))
1030 return isl_stat_error;
1031 if (compressed && (!hull || !compress || !decompress))
1032 return isl_stat_error;
1034 return isl_stat_ok;
1037 /* Construct an identifier for node "node", which will represent "set".
1038 * The name of the identifier is either "compressed" or
1039 * "compressed_<name>", with <name> the name of the space of "set".
1040 * The user pointer of the identifier points to "node".
1042 static __isl_give isl_id *construct_compressed_id(__isl_keep isl_set *set,
1043 struct isl_sched_node *node)
1045 isl_bool has_name;
1046 isl_ctx *ctx;
1047 isl_id *id;
1048 isl_printer *p;
1049 const char *name;
1050 char *id_name;
1052 has_name = isl_set_has_tuple_name(set);
1053 if (has_name < 0)
1054 return NULL;
1056 ctx = isl_set_get_ctx(set);
1057 if (!has_name)
1058 return isl_id_alloc(ctx, "compressed", node);
1060 p = isl_printer_to_str(ctx);
1061 name = isl_set_get_tuple_name(set);
1062 p = isl_printer_print_str(p, "compressed_");
1063 p = isl_printer_print_str(p, name);
1064 id_name = isl_printer_get_str(p);
1065 isl_printer_free(p);
1067 id = isl_id_alloc(ctx, id_name, node);
1068 free(id_name);
1070 return id;
1073 /* Add a new node to the graph representing the given set.
1075 * If any of the set variables is defined by an equality, then
1076 * we perform variable compression such that we can perform
1077 * the scheduling on the compressed domain.
1078 * In this case, an identifier is used that references the new node
1079 * such that each compressed space is unique and
1080 * such that the node can be recovered from the compressed space.
1082 static isl_stat extract_node(__isl_take isl_set *set, void *user)
1084 int nvar;
1085 isl_bool has_equality;
1086 isl_id *id;
1087 isl_basic_set *hull;
1088 isl_set *hull_set;
1089 isl_morph *morph;
1090 isl_multi_aff *compress, *decompress;
1091 struct isl_sched_graph *graph = user;
1093 hull = isl_set_affine_hull(isl_set_copy(set));
1094 hull = isl_basic_set_remove_divs(hull);
1095 nvar = isl_set_dim(set, isl_dim_set);
1096 has_equality = has_any_defining_equality(hull);
1098 if (has_equality < 0)
1099 goto error;
1100 if (!has_equality) {
1101 isl_basic_set_free(hull);
1102 return add_node(graph, set, nvar, 0, NULL, NULL, NULL);
1105 id = construct_compressed_id(set, &graph->node[graph->n]);
1106 morph = isl_basic_set_variable_compression_with_id(hull,
1107 isl_dim_set, id);
1108 isl_id_free(id);
1109 nvar = isl_morph_ran_dim(morph, isl_dim_set);
1110 compress = isl_morph_get_var_multi_aff(morph);
1111 morph = isl_morph_inverse(morph);
1112 decompress = isl_morph_get_var_multi_aff(morph);
1113 isl_morph_free(morph);
1115 hull_set = isl_set_from_basic_set(hull);
1116 return add_node(graph, set, nvar, 1, hull_set, compress, decompress);
1117 error:
1118 isl_basic_set_free(hull);
1119 isl_set_free(set);
1120 return isl_stat_error;
1123 struct isl_extract_edge_data {
1124 enum isl_edge_type type;
1125 struct isl_sched_graph *graph;
1128 /* Merge edge2 into edge1, freeing the contents of edge2.
1129 * Return 0 on success and -1 on failure.
1131 * edge1 and edge2 are assumed to have the same value for the map field.
1133 static int merge_edge(struct isl_sched_edge *edge1,
1134 struct isl_sched_edge *edge2)
1136 edge1->types |= edge2->types;
1137 isl_map_free(edge2->map);
1139 if (is_condition(edge2)) {
1140 if (!edge1->tagged_condition)
1141 edge1->tagged_condition = edge2->tagged_condition;
1142 else
1143 edge1->tagged_condition =
1144 isl_union_map_union(edge1->tagged_condition,
1145 edge2->tagged_condition);
1148 if (is_conditional_validity(edge2)) {
1149 if (!edge1->tagged_validity)
1150 edge1->tagged_validity = edge2->tagged_validity;
1151 else
1152 edge1->tagged_validity =
1153 isl_union_map_union(edge1->tagged_validity,
1154 edge2->tagged_validity);
1157 if (is_condition(edge2) && !edge1->tagged_condition)
1158 return -1;
1159 if (is_conditional_validity(edge2) && !edge1->tagged_validity)
1160 return -1;
1162 return 0;
1165 /* Insert dummy tags in domain and range of "map".
1167 * In particular, if "map" is of the form
1169 * A -> B
1171 * then return
1173 * [A -> dummy_tag] -> [B -> dummy_tag]
1175 * where the dummy_tags are identical and equal to any dummy tags
1176 * introduced by any other call to this function.
1178 static __isl_give isl_map *insert_dummy_tags(__isl_take isl_map *map)
1180 static char dummy;
1181 isl_ctx *ctx;
1182 isl_id *id;
1183 isl_space *space;
1184 isl_set *domain, *range;
1186 ctx = isl_map_get_ctx(map);
1188 id = isl_id_alloc(ctx, NULL, &dummy);
1189 space = isl_space_params(isl_map_get_space(map));
1190 space = isl_space_set_from_params(space);
1191 space = isl_space_set_tuple_id(space, isl_dim_set, id);
1192 space = isl_space_map_from_set(space);
1194 domain = isl_map_wrap(map);
1195 range = isl_map_wrap(isl_map_universe(space));
1196 map = isl_map_from_domain_and_range(domain, range);
1197 map = isl_map_zip(map);
1199 return map;
1202 /* Given that at least one of "src" or "dst" is compressed, return
1203 * a map between the spaces of these nodes restricted to the affine
1204 * hull that was used in the compression.
1206 static __isl_give isl_map *extract_hull(struct isl_sched_node *src,
1207 struct isl_sched_node *dst)
1209 isl_set *dom, *ran;
1211 if (src->compressed)
1212 dom = isl_set_copy(src->hull);
1213 else
1214 dom = isl_set_universe(isl_space_copy(src->space));
1215 if (dst->compressed)
1216 ran = isl_set_copy(dst->hull);
1217 else
1218 ran = isl_set_universe(isl_space_copy(dst->space));
1220 return isl_map_from_domain_and_range(dom, ran);
1223 /* Intersect the domains of the nested relations in domain and range
1224 * of "tagged" with "map".
1226 static __isl_give isl_map *map_intersect_domains(__isl_take isl_map *tagged,
1227 __isl_keep isl_map *map)
1229 isl_set *set;
1231 tagged = isl_map_zip(tagged);
1232 set = isl_map_wrap(isl_map_copy(map));
1233 tagged = isl_map_intersect_domain(tagged, set);
1234 tagged = isl_map_zip(tagged);
1235 return tagged;
1238 /* Return a pointer to the node that lives in the domain space of "map",
1239 * an invalid node if there is no such node, or NULL in case of error.
1241 static struct isl_sched_node *find_domain_node(isl_ctx *ctx,
1242 struct isl_sched_graph *graph, __isl_keep isl_map *map)
1244 struct isl_sched_node *node;
1245 isl_space *space;
1247 space = isl_space_domain(isl_map_get_space(map));
1248 node = graph_find_node(ctx, graph, space);
1249 isl_space_free(space);
1251 return node;
1254 /* Return a pointer to the node that lives in the range space of "map",
1255 * an invalid node if there is no such node, or NULL in case of error.
1257 static struct isl_sched_node *find_range_node(isl_ctx *ctx,
1258 struct isl_sched_graph *graph, __isl_keep isl_map *map)
1260 struct isl_sched_node *node;
1261 isl_space *space;
1263 space = isl_space_range(isl_map_get_space(map));
1264 node = graph_find_node(ctx, graph, space);
1265 isl_space_free(space);
1267 return node;
1270 /* Refrain from adding a new edge based on "map".
1271 * Instead, just free the map.
1272 * "tagged" is either a copy of "map" with additional tags or NULL.
1274 static isl_stat skip_edge(__isl_take isl_map *map, __isl_take isl_map *tagged)
1276 isl_map_free(map);
1277 isl_map_free(tagged);
1279 return isl_stat_ok;
1282 /* Add a new edge to the graph based on the given map
1283 * and add it to data->graph->edge_table[data->type].
1284 * If a dependence relation of a given type happens to be identical
1285 * to one of the dependence relations of a type that was added before,
1286 * then we don't create a new edge, but instead mark the original edge
1287 * as also representing a dependence of the current type.
1289 * Edges of type isl_edge_condition or isl_edge_conditional_validity
1290 * may be specified as "tagged" dependence relations. That is, "map"
1291 * may contain elements (i -> a) -> (j -> b), where i -> j denotes
1292 * the dependence on iterations and a and b are tags.
1293 * edge->map is set to the relation containing the elements i -> j,
1294 * while edge->tagged_condition and edge->tagged_validity contain
1295 * the union of all the "map" relations
1296 * for which extract_edge is called that result in the same edge->map.
1298 * If the source or the destination node is compressed, then
1299 * intersect both "map" and "tagged" with the constraints that
1300 * were used to construct the compression.
1301 * This ensures that there are no schedule constraints defined
1302 * outside of these domains, while the scheduler no longer has
1303 * any control over those outside parts.
1305 static isl_stat extract_edge(__isl_take isl_map *map, void *user)
1307 isl_bool empty;
1308 isl_ctx *ctx = isl_map_get_ctx(map);
1309 struct isl_extract_edge_data *data = user;
1310 struct isl_sched_graph *graph = data->graph;
1311 struct isl_sched_node *src, *dst;
1312 struct isl_sched_edge *edge;
1313 isl_map *tagged = NULL;
1315 if (data->type == isl_edge_condition ||
1316 data->type == isl_edge_conditional_validity) {
1317 if (isl_map_can_zip(map)) {
1318 tagged = isl_map_copy(map);
1319 map = isl_set_unwrap(isl_map_domain(isl_map_zip(map)));
1320 } else {
1321 tagged = insert_dummy_tags(isl_map_copy(map));
1325 src = find_domain_node(ctx, graph, map);
1326 dst = find_range_node(ctx, graph, map);
1328 if (!src || !dst)
1329 goto error;
1330 if (!is_node(graph, src) || !is_node(graph, dst))
1331 return skip_edge(map, tagged);
1333 if (src->compressed || dst->compressed) {
1334 isl_map *hull;
1335 hull = extract_hull(src, dst);
1336 if (tagged)
1337 tagged = map_intersect_domains(tagged, hull);
1338 map = isl_map_intersect(map, hull);
1341 empty = isl_map_plain_is_empty(map);
1342 if (empty < 0)
1343 goto error;
1344 if (empty)
1345 return skip_edge(map, tagged);
1347 graph->edge[graph->n_edge].src = src;
1348 graph->edge[graph->n_edge].dst = dst;
1349 graph->edge[graph->n_edge].map = map;
1350 graph->edge[graph->n_edge].types = 0;
1351 graph->edge[graph->n_edge].tagged_condition = NULL;
1352 graph->edge[graph->n_edge].tagged_validity = NULL;
1353 set_type(&graph->edge[graph->n_edge], data->type);
1354 if (data->type == isl_edge_condition)
1355 graph->edge[graph->n_edge].tagged_condition =
1356 isl_union_map_from_map(tagged);
1357 if (data->type == isl_edge_conditional_validity)
1358 graph->edge[graph->n_edge].tagged_validity =
1359 isl_union_map_from_map(tagged);
1361 edge = graph_find_matching_edge(graph, &graph->edge[graph->n_edge]);
1362 if (!edge) {
1363 graph->n_edge++;
1364 return isl_stat_error;
1366 if (edge == &graph->edge[graph->n_edge])
1367 return graph_edge_table_add(ctx, graph, data->type,
1368 &graph->edge[graph->n_edge++]);
1370 if (merge_edge(edge, &graph->edge[graph->n_edge]) < 0)
1371 return isl_stat_error;
1373 return graph_edge_table_add(ctx, graph, data->type, edge);
1374 error:
1375 isl_map_free(map);
1376 isl_map_free(tagged);
1377 return isl_stat_error;
1380 /* Initialize the schedule graph "graph" from the schedule constraints "sc".
1382 * The context is included in the domain before the nodes of
1383 * the graphs are extracted in order to be able to exploit
1384 * any possible additional equalities.
1385 * Note that this intersection is only performed locally here.
1387 static isl_stat graph_init(struct isl_sched_graph *graph,
1388 __isl_keep isl_schedule_constraints *sc)
1390 isl_ctx *ctx;
1391 isl_union_set *domain;
1392 isl_union_map *c;
1393 struct isl_extract_edge_data data;
1394 enum isl_edge_type i;
1395 isl_stat r;
1397 if (!sc)
1398 return isl_stat_error;
1400 ctx = isl_schedule_constraints_get_ctx(sc);
1402 domain = isl_schedule_constraints_get_domain(sc);
1403 graph->n = isl_union_set_n_set(domain);
1404 isl_union_set_free(domain);
1406 if (graph_alloc(ctx, graph, graph->n,
1407 isl_schedule_constraints_n_map(sc)) < 0)
1408 return isl_stat_error;
1410 if (compute_max_row(graph, sc) < 0)
1411 return isl_stat_error;
1412 graph->root = graph;
1413 graph->n = 0;
1414 domain = isl_schedule_constraints_get_domain(sc);
1415 domain = isl_union_set_intersect_params(domain,
1416 isl_schedule_constraints_get_context(sc));
1417 r = isl_union_set_foreach_set(domain, &extract_node, graph);
1418 isl_union_set_free(domain);
1419 if (r < 0)
1420 return isl_stat_error;
1421 if (graph_init_table(ctx, graph) < 0)
1422 return isl_stat_error;
1423 for (i = isl_edge_first; i <= isl_edge_last; ++i) {
1424 c = isl_schedule_constraints_get(sc, i);
1425 graph->max_edge[i] = isl_union_map_n_map(c);
1426 isl_union_map_free(c);
1427 if (!c)
1428 return isl_stat_error;
1430 if (graph_init_edge_tables(ctx, graph) < 0)
1431 return isl_stat_error;
1432 graph->n_edge = 0;
1433 data.graph = graph;
1434 for (i = isl_edge_first; i <= isl_edge_last; ++i) {
1435 isl_stat r;
1437 data.type = i;
1438 c = isl_schedule_constraints_get(sc, i);
1439 r = isl_union_map_foreach_map(c, &extract_edge, &data);
1440 isl_union_map_free(c);
1441 if (r < 0)
1442 return isl_stat_error;
1445 return isl_stat_ok;
1448 /* Check whether there is any dependence from node[j] to node[i]
1449 * or from node[i] to node[j].
1451 static isl_bool node_follows_weak(int i, int j, void *user)
1453 isl_bool f;
1454 struct isl_sched_graph *graph = user;
1456 f = graph_has_any_edge(graph, &graph->node[j], &graph->node[i]);
1457 if (f < 0 || f)
1458 return f;
1459 return graph_has_any_edge(graph, &graph->node[i], &graph->node[j]);
1462 /* Check whether there is a (conditional) validity dependence from node[j]
1463 * to node[i], forcing node[i] to follow node[j].
1465 static isl_bool node_follows_strong(int i, int j, void *user)
1467 struct isl_sched_graph *graph = user;
1469 return graph_has_validity_edge(graph, &graph->node[j], &graph->node[i]);
1472 /* Use Tarjan's algorithm for computing the strongly connected components
1473 * in the dependence graph only considering those edges defined by "follows".
1475 static isl_stat detect_ccs(isl_ctx *ctx, struct isl_sched_graph *graph,
1476 isl_bool (*follows)(int i, int j, void *user))
1478 int i, n;
1479 struct isl_tarjan_graph *g = NULL;
1481 g = isl_tarjan_graph_init(ctx, graph->n, follows, graph);
1482 if (!g)
1483 return isl_stat_error;
1485 graph->scc = 0;
1486 i = 0;
1487 n = graph->n;
1488 while (n) {
1489 while (g->order[i] != -1) {
1490 graph->node[g->order[i]].scc = graph->scc;
1491 --n;
1492 ++i;
1494 ++i;
1495 graph->scc++;
1498 isl_tarjan_graph_free(g);
1500 return isl_stat_ok;
1503 /* Apply Tarjan's algorithm to detect the strongly connected components
1504 * in the dependence graph.
1505 * Only consider the (conditional) validity dependences and clear "weak".
1507 static isl_stat detect_sccs(isl_ctx *ctx, struct isl_sched_graph *graph)
1509 graph->weak = 0;
1510 return detect_ccs(ctx, graph, &node_follows_strong);
1513 /* Apply Tarjan's algorithm to detect the (weakly) connected components
1514 * in the dependence graph.
1515 * Consider all dependences and set "weak".
1517 static isl_stat detect_wccs(isl_ctx *ctx, struct isl_sched_graph *graph)
1519 graph->weak = 1;
1520 return detect_ccs(ctx, graph, &node_follows_weak);
1523 static int cmp_scc(const void *a, const void *b, void *data)
1525 struct isl_sched_graph *graph = data;
1526 const int *i1 = a;
1527 const int *i2 = b;
1529 return graph->node[*i1].scc - graph->node[*i2].scc;
1532 /* Sort the elements of graph->sorted according to the corresponding SCCs.
1534 static int sort_sccs(struct isl_sched_graph *graph)
1536 return isl_sort(graph->sorted, graph->n, sizeof(int), &cmp_scc, graph);
1539 /* Return a non-parametric set in the compressed space of "node" that is
1540 * bounded by the size in each direction
1542 * { [x] : -S_i <= x_i <= S_i }
1544 * If S_i is infinity in direction i, then there are no constraints
1545 * in that direction.
1547 * Cache the result in node->bounds.
1549 static __isl_give isl_basic_set *get_size_bounds(struct isl_sched_node *node)
1551 isl_space *space;
1552 isl_basic_set *bounds;
1553 int i;
1554 unsigned nparam;
1556 if (node->bounds)
1557 return isl_basic_set_copy(node->bounds);
1559 if (node->compressed)
1560 space = isl_multi_aff_get_domain_space(node->decompress);
1561 else
1562 space = isl_space_copy(node->space);
1563 nparam = isl_space_dim(space, isl_dim_param);
1564 space = isl_space_drop_dims(space, isl_dim_param, 0, nparam);
1565 bounds = isl_basic_set_universe(space);
1567 for (i = 0; i < node->nvar; ++i) {
1568 isl_val *size;
1570 size = isl_multi_val_get_val(node->sizes, i);
1571 if (!size)
1572 return isl_basic_set_free(bounds);
1573 if (!isl_val_is_int(size)) {
1574 isl_val_free(size);
1575 continue;
1577 bounds = isl_basic_set_upper_bound_val(bounds, isl_dim_set, i,
1578 isl_val_copy(size));
1579 bounds = isl_basic_set_lower_bound_val(bounds, isl_dim_set, i,
1580 isl_val_neg(size));
1583 node->bounds = isl_basic_set_copy(bounds);
1584 return bounds;
1587 /* Drop some constraints from "delta" that could be exploited
1588 * to construct loop coalescing schedules.
1589 * In particular, drop those constraint that bound the difference
1590 * to the size of the domain.
1591 * First project out the parameters to improve the effectiveness.
1593 static __isl_give isl_set *drop_coalescing_constraints(
1594 __isl_take isl_set *delta, struct isl_sched_node *node)
1596 unsigned nparam;
1597 isl_basic_set *bounds;
1599 bounds = get_size_bounds(node);
1601 nparam = isl_set_dim(delta, isl_dim_param);
1602 delta = isl_set_project_out(delta, isl_dim_param, 0, nparam);
1603 delta = isl_set_remove_divs(delta);
1604 delta = isl_set_plain_gist_basic_set(delta, bounds);
1605 return delta;
1608 /* Given a dependence relation R from "node" to itself,
1609 * construct the set of coefficients of valid constraints for elements
1610 * in that dependence relation.
1611 * In particular, the result contains tuples of coefficients
1612 * c_0, c_n, c_x such that
1614 * c_0 + c_n n + c_x y - c_x x >= 0 for each (x,y) in R
1616 * or, equivalently,
1618 * c_0 + c_n n + c_x d >= 0 for each d in delta R = { y - x | (x,y) in R }
1620 * We choose here to compute the dual of delta R.
1621 * Alternatively, we could have computed the dual of R, resulting
1622 * in a set of tuples c_0, c_n, c_x, c_y, and then
1623 * plugged in (c_0, c_n, c_x, -c_x).
1625 * If "need_param" is set, then the resulting coefficients effectively
1626 * include coefficients for the parameters c_n. Otherwise, they may
1627 * have been projected out already.
1628 * Since the constraints may be different for these two cases,
1629 * they are stored in separate caches.
1630 * In particular, if no parameter coefficients are required and
1631 * the schedule_treat_coalescing option is set, then the parameters
1632 * are projected out and some constraints that could be exploited
1633 * to construct coalescing schedules are removed before the dual
1634 * is computed.
1636 * If "node" has been compressed, then the dependence relation
1637 * is also compressed before the set of coefficients is computed.
1639 static __isl_give isl_basic_set *intra_coefficients(
1640 struct isl_sched_graph *graph, struct isl_sched_node *node,
1641 __isl_take isl_map *map, int need_param)
1643 isl_ctx *ctx;
1644 isl_set *delta;
1645 isl_map *key;
1646 isl_basic_set *coef;
1647 isl_maybe_isl_basic_set m;
1648 isl_map_to_basic_set **hmap = &graph->intra_hmap;
1649 int treat;
1651 if (!map)
1652 return NULL;
1654 ctx = isl_map_get_ctx(map);
1655 treat = !need_param && isl_options_get_schedule_treat_coalescing(ctx);
1656 if (!treat)
1657 hmap = &graph->intra_hmap_param;
1658 m = isl_map_to_basic_set_try_get(*hmap, map);
1659 if (m.valid < 0 || m.valid) {
1660 isl_map_free(map);
1661 return m.value;
1664 key = isl_map_copy(map);
1665 if (node->compressed) {
1666 map = isl_map_preimage_domain_multi_aff(map,
1667 isl_multi_aff_copy(node->decompress));
1668 map = isl_map_preimage_range_multi_aff(map,
1669 isl_multi_aff_copy(node->decompress));
1671 delta = isl_map_deltas(map);
1672 if (treat)
1673 delta = drop_coalescing_constraints(delta, node);
1674 delta = isl_set_remove_divs(delta);
1675 coef = isl_set_coefficients(delta);
1676 *hmap = isl_map_to_basic_set_set(*hmap, key, isl_basic_set_copy(coef));
1678 return coef;
1681 /* Given a dependence relation R, construct the set of coefficients
1682 * of valid constraints for elements in that dependence relation.
1683 * In particular, the result contains tuples of coefficients
1684 * c_0, c_n, c_x, c_y such that
1686 * c_0 + c_n n + c_x x + c_y y >= 0 for each (x,y) in R
1688 * If the source or destination nodes of "edge" have been compressed,
1689 * then the dependence relation is also compressed before
1690 * the set of coefficients is computed.
1692 static __isl_give isl_basic_set *inter_coefficients(
1693 struct isl_sched_graph *graph, struct isl_sched_edge *edge,
1694 __isl_take isl_map *map)
1696 isl_set *set;
1697 isl_map *key;
1698 isl_basic_set *coef;
1699 isl_maybe_isl_basic_set m;
1701 m = isl_map_to_basic_set_try_get(graph->inter_hmap, map);
1702 if (m.valid < 0 || m.valid) {
1703 isl_map_free(map);
1704 return m.value;
1707 key = isl_map_copy(map);
1708 if (edge->src->compressed)
1709 map = isl_map_preimage_domain_multi_aff(map,
1710 isl_multi_aff_copy(edge->src->decompress));
1711 if (edge->dst->compressed)
1712 map = isl_map_preimage_range_multi_aff(map,
1713 isl_multi_aff_copy(edge->dst->decompress));
1714 set = isl_map_wrap(isl_map_remove_divs(map));
1715 coef = isl_set_coefficients(set);
1716 graph->inter_hmap = isl_map_to_basic_set_set(graph->inter_hmap, key,
1717 isl_basic_set_copy(coef));
1719 return coef;
1722 /* Return the position of the coefficients of the variables in
1723 * the coefficients constraints "coef".
1725 * The space of "coef" is of the form
1727 * { coefficients[[cst, params] -> S] }
1729 * Return the position of S.
1731 static int coef_var_offset(__isl_keep isl_basic_set *coef)
1733 int offset;
1734 isl_space *space;
1736 space = isl_space_unwrap(isl_basic_set_get_space(coef));
1737 offset = isl_space_dim(space, isl_dim_in);
1738 isl_space_free(space);
1740 return offset;
1743 /* Return the offset of the coefficient of the constant term of "node"
1744 * within the (I)LP.
1746 * Within each node, the coefficients have the following order:
1747 * - positive and negative parts of c_i_x
1748 * - c_i_n (if parametric)
1749 * - c_i_0
1751 static int node_cst_coef_offset(struct isl_sched_node *node)
1753 return node->start + 2 * node->nvar + node->nparam;
1756 /* Return the offset of the coefficients of the parameters of "node"
1757 * within the (I)LP.
1759 * Within each node, the coefficients have the following order:
1760 * - positive and negative parts of c_i_x
1761 * - c_i_n (if parametric)
1762 * - c_i_0
1764 static int node_par_coef_offset(struct isl_sched_node *node)
1766 return node->start + 2 * node->nvar;
1769 /* Return the offset of the coefficients of the variables of "node"
1770 * within the (I)LP.
1772 * Within each node, the coefficients have the following order:
1773 * - positive and negative parts of c_i_x
1774 * - c_i_n (if parametric)
1775 * - c_i_0
1777 static int node_var_coef_offset(struct isl_sched_node *node)
1779 return node->start;
1782 /* Return the position of the pair of variables encoding
1783 * coefficient "i" of "node".
1785 * The order of these variable pairs is the opposite of
1786 * that of the coefficients, with 2 variables per coefficient.
1788 static int node_var_coef_pos(struct isl_sched_node *node, int i)
1790 return node_var_coef_offset(node) + 2 * (node->nvar - 1 - i);
1793 /* Construct an isl_dim_map for mapping constraints on coefficients
1794 * for "node" to the corresponding positions in graph->lp.
1795 * "offset" is the offset of the coefficients for the variables
1796 * in the input constraints.
1797 * "s" is the sign of the mapping.
1799 * The input constraints are given in terms of the coefficients
1800 * (c_0, c_x) or (c_0, c_n, c_x).
1801 * The mapping produced by this function essentially plugs in
1802 * (0, c_i_x^+ - c_i_x^-) if s = 1 and
1803 * (0, -c_i_x^+ + c_i_x^-) if s = -1 or
1804 * (0, 0, c_i_x^+ - c_i_x^-) if s = 1 and
1805 * (0, 0, -c_i_x^+ + c_i_x^-) if s = -1.
1806 * In graph->lp, the c_i_x^- appear before their c_i_x^+ counterpart.
1807 * Furthermore, the order of these pairs is the opposite of that
1808 * of the corresponding coefficients.
1810 * The caller can extend the mapping to also map the other coefficients
1811 * (and therefore not plug in 0).
1813 static __isl_give isl_dim_map *intra_dim_map(isl_ctx *ctx,
1814 struct isl_sched_graph *graph, struct isl_sched_node *node,
1815 int offset, int s)
1817 int pos;
1818 unsigned total;
1819 isl_dim_map *dim_map;
1821 if (!node || !graph->lp)
1822 return NULL;
1824 total = isl_basic_set_total_dim(graph->lp);
1825 pos = node_var_coef_pos(node, 0);
1826 dim_map = isl_dim_map_alloc(ctx, total);
1827 isl_dim_map_range(dim_map, pos, -2, offset, 1, node->nvar, -s);
1828 isl_dim_map_range(dim_map, pos + 1, -2, offset, 1, node->nvar, s);
1830 return dim_map;
1833 /* Construct an isl_dim_map for mapping constraints on coefficients
1834 * for "src" (node i) and "dst" (node j) to the corresponding positions
1835 * in graph->lp.
1836 * "offset" is the offset of the coefficients for the variables of "src"
1837 * in the input constraints.
1838 * "s" is the sign of the mapping.
1840 * The input constraints are given in terms of the coefficients
1841 * (c_0, c_n, c_x, c_y).
1842 * The mapping produced by this function essentially plugs in
1843 * (c_j_0 - c_i_0, c_j_n - c_i_n,
1844 * -(c_i_x^+ - c_i_x^-), c_j_x^+ - c_j_x^-) if s = 1 and
1845 * (-c_j_0 + c_i_0, -c_j_n + c_i_n,
1846 * c_i_x^+ - c_i_x^-, -(c_j_x^+ - c_j_x^-)) if s = -1.
1847 * In graph->lp, the c_*^- appear before their c_*^+ counterpart.
1848 * Furthermore, the order of these pairs is the opposite of that
1849 * of the corresponding coefficients.
1851 * The caller can further extend the mapping.
1853 static __isl_give isl_dim_map *inter_dim_map(isl_ctx *ctx,
1854 struct isl_sched_graph *graph, struct isl_sched_node *src,
1855 struct isl_sched_node *dst, int offset, int s)
1857 int pos;
1858 unsigned total;
1859 isl_dim_map *dim_map;
1861 if (!src || !dst || !graph->lp)
1862 return NULL;
1864 total = isl_basic_set_total_dim(graph->lp);
1865 dim_map = isl_dim_map_alloc(ctx, total);
1867 pos = node_cst_coef_offset(dst);
1868 isl_dim_map_range(dim_map, pos, 0, 0, 0, 1, s);
1869 pos = node_par_coef_offset(dst);
1870 isl_dim_map_range(dim_map, pos, 1, 1, 1, dst->nparam, s);
1871 pos = node_var_coef_pos(dst, 0);
1872 isl_dim_map_range(dim_map, pos, -2, offset + src->nvar, 1,
1873 dst->nvar, -s);
1874 isl_dim_map_range(dim_map, pos + 1, -2, offset + src->nvar, 1,
1875 dst->nvar, s);
1877 pos = node_cst_coef_offset(src);
1878 isl_dim_map_range(dim_map, pos, 0, 0, 0, 1, -s);
1879 pos = node_par_coef_offset(src);
1880 isl_dim_map_range(dim_map, pos, 1, 1, 1, src->nparam, -s);
1881 pos = node_var_coef_pos(src, 0);
1882 isl_dim_map_range(dim_map, pos, -2, offset, 1, src->nvar, s);
1883 isl_dim_map_range(dim_map, pos + 1, -2, offset, 1, src->nvar, -s);
1885 return dim_map;
1888 /* Add the constraints from "src" to "dst" using "dim_map",
1889 * after making sure there is enough room in "dst" for the extra constraints.
1891 static __isl_give isl_basic_set *add_constraints_dim_map(
1892 __isl_take isl_basic_set *dst, __isl_take isl_basic_set *src,
1893 __isl_take isl_dim_map *dim_map)
1895 int n_eq, n_ineq;
1897 n_eq = isl_basic_set_n_equality(src);
1898 n_ineq = isl_basic_set_n_inequality(src);
1899 dst = isl_basic_set_extend_constraints(dst, n_eq, n_ineq);
1900 dst = isl_basic_set_add_constraints_dim_map(dst, src, dim_map);
1901 return dst;
1904 /* Add constraints to graph->lp that force validity for the given
1905 * dependence from a node i to itself.
1906 * That is, add constraints that enforce
1908 * (c_i_0 + c_i_n n + c_i_x y) - (c_i_0 + c_i_n n + c_i_x x)
1909 * = c_i_x (y - x) >= 0
1911 * for each (x,y) in R.
1912 * We obtain general constraints on coefficients (c_0, c_x)
1913 * of valid constraints for (y - x) and then plug in (0, c_i_x^+ - c_i_x^-),
1914 * where c_i_x = c_i_x^+ - c_i_x^-, with c_i_x^+ and c_i_x^- non-negative.
1915 * In graph->lp, the c_i_x^- appear before their c_i_x^+ counterpart.
1916 * Note that the result of intra_coefficients may also contain
1917 * parameter coefficients c_n, in which case 0 is plugged in for them as well.
1919 static isl_stat add_intra_validity_constraints(struct isl_sched_graph *graph,
1920 struct isl_sched_edge *edge)
1922 int offset;
1923 isl_map *map = isl_map_copy(edge->map);
1924 isl_ctx *ctx = isl_map_get_ctx(map);
1925 isl_dim_map *dim_map;
1926 isl_basic_set *coef;
1927 struct isl_sched_node *node = edge->src;
1929 coef = intra_coefficients(graph, node, map, 0);
1931 offset = coef_var_offset(coef);
1933 if (!coef)
1934 return isl_stat_error;
1936 dim_map = intra_dim_map(ctx, graph, node, offset, 1);
1937 graph->lp = add_constraints_dim_map(graph->lp, coef, dim_map);
1939 return isl_stat_ok;
1942 /* Add constraints to graph->lp that force validity for the given
1943 * dependence from node i to node j.
1944 * That is, add constraints that enforce
1946 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) >= 0
1948 * for each (x,y) in R.
1949 * We obtain general constraints on coefficients (c_0, c_n, c_x, c_y)
1950 * of valid constraints for R and then plug in
1951 * (c_j_0 - c_i_0, c_j_n - c_i_n, -(c_i_x^+ - c_i_x^-), c_j_x^+ - c_j_x^-),
1952 * where c_* = c_*^+ - c_*^-, with c_*^+ and c_*^- non-negative.
1953 * In graph->lp, the c_*^- appear before their c_*^+ counterpart.
1955 static isl_stat add_inter_validity_constraints(struct isl_sched_graph *graph,
1956 struct isl_sched_edge *edge)
1958 int offset;
1959 isl_map *map;
1960 isl_ctx *ctx;
1961 isl_dim_map *dim_map;
1962 isl_basic_set *coef;
1963 struct isl_sched_node *src = edge->src;
1964 struct isl_sched_node *dst = edge->dst;
1966 if (!graph->lp)
1967 return isl_stat_error;
1969 map = isl_map_copy(edge->map);
1970 ctx = isl_map_get_ctx(map);
1971 coef = inter_coefficients(graph, edge, map);
1973 offset = coef_var_offset(coef);
1975 if (!coef)
1976 return isl_stat_error;
1978 dim_map = inter_dim_map(ctx, graph, src, dst, offset, 1);
1980 edge->start = graph->lp->n_ineq;
1981 graph->lp = add_constraints_dim_map(graph->lp, coef, dim_map);
1982 if (!graph->lp)
1983 return isl_stat_error;
1984 edge->end = graph->lp->n_ineq;
1986 return isl_stat_ok;
1989 /* Add constraints to graph->lp that bound the dependence distance for the given
1990 * dependence from a node i to itself.
1991 * If s = 1, we add the constraint
1993 * c_i_x (y - x) <= m_0 + m_n n
1995 * or
1997 * -c_i_x (y - x) + m_0 + m_n n >= 0
1999 * for each (x,y) in R.
2000 * If s = -1, we add the constraint
2002 * -c_i_x (y - x) <= m_0 + m_n n
2004 * or
2006 * c_i_x (y - x) + m_0 + m_n n >= 0
2008 * for each (x,y) in R.
2009 * We obtain general constraints on coefficients (c_0, c_n, c_x)
2010 * of valid constraints for (y - x) and then plug in (m_0, m_n, -s * c_i_x),
2011 * with each coefficient (except m_0) represented as a pair of non-negative
2012 * coefficients.
2015 * If "local" is set, then we add constraints
2017 * c_i_x (y - x) <= 0
2019 * or
2021 * -c_i_x (y - x) <= 0
2023 * instead, forcing the dependence distance to be (less than or) equal to 0.
2024 * That is, we plug in (0, 0, -s * c_i_x),
2025 * intra_coefficients is not required to have c_n in its result when
2026 * "local" is set. If they are missing, then (0, -s * c_i_x) is plugged in.
2027 * Note that dependences marked local are treated as validity constraints
2028 * by add_all_validity_constraints and therefore also have
2029 * their distances bounded by 0 from below.
2031 static isl_stat add_intra_proximity_constraints(struct isl_sched_graph *graph,
2032 struct isl_sched_edge *edge, int s, int local)
2034 int offset;
2035 unsigned nparam;
2036 isl_map *map = isl_map_copy(edge->map);
2037 isl_ctx *ctx = isl_map_get_ctx(map);
2038 isl_dim_map *dim_map;
2039 isl_basic_set *coef;
2040 struct isl_sched_node *node = edge->src;
2042 coef = intra_coefficients(graph, node, map, !local);
2044 offset = coef_var_offset(coef);
2046 if (!coef)
2047 return isl_stat_error;
2049 nparam = isl_space_dim(node->space, isl_dim_param);
2050 dim_map = intra_dim_map(ctx, graph, node, offset, -s);
2052 if (!local) {
2053 isl_dim_map_range(dim_map, 1, 0, 0, 0, 1, 1);
2054 isl_dim_map_range(dim_map, 4, 2, 1, 1, nparam, -1);
2055 isl_dim_map_range(dim_map, 5, 2, 1, 1, nparam, 1);
2057 graph->lp = add_constraints_dim_map(graph->lp, coef, dim_map);
2059 return isl_stat_ok;
2062 /* Add constraints to graph->lp that bound the dependence distance for the given
2063 * dependence from node i to node j.
2064 * If s = 1, we add the constraint
2066 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x)
2067 * <= m_0 + m_n n
2069 * or
2071 * -(c_j_0 + c_j_n n + c_j_x y) + (c_i_0 + c_i_n n + c_i_x x) +
2072 * m_0 + m_n n >= 0
2074 * for each (x,y) in R.
2075 * If s = -1, we add the constraint
2077 * -((c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x))
2078 * <= m_0 + m_n n
2080 * or
2082 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) +
2083 * m_0 + m_n n >= 0
2085 * for each (x,y) in R.
2086 * We obtain general constraints on coefficients (c_0, c_n, c_x, c_y)
2087 * of valid constraints for R and then plug in
2088 * (m_0 - s*c_j_0 + s*c_i_0, m_n - s*c_j_n + s*c_i_n,
2089 * s*c_i_x, -s*c_j_x)
2090 * with each coefficient (except m_0, c_*_0 and c_*_n)
2091 * represented as a pair of non-negative coefficients.
2094 * If "local" is set (and s = 1), then we add constraints
2096 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) <= 0
2098 * or
2100 * -((c_j_0 + c_j_n n + c_j_x y) + (c_i_0 + c_i_n n + c_i_x x)) >= 0
2102 * instead, forcing the dependence distance to be (less than or) equal to 0.
2103 * That is, we plug in
2104 * (-s*c_j_0 + s*c_i_0, -s*c_j_n + s*c_i_n, s*c_i_x, -s*c_j_x).
2105 * Note that dependences marked local are treated as validity constraints
2106 * by add_all_validity_constraints and therefore also have
2107 * their distances bounded by 0 from below.
2109 static isl_stat add_inter_proximity_constraints(struct isl_sched_graph *graph,
2110 struct isl_sched_edge *edge, int s, int local)
2112 int offset;
2113 unsigned nparam;
2114 isl_map *map = isl_map_copy(edge->map);
2115 isl_ctx *ctx = isl_map_get_ctx(map);
2116 isl_dim_map *dim_map;
2117 isl_basic_set *coef;
2118 struct isl_sched_node *src = edge->src;
2119 struct isl_sched_node *dst = edge->dst;
2121 coef = inter_coefficients(graph, edge, map);
2123 offset = coef_var_offset(coef);
2125 if (!coef)
2126 return isl_stat_error;
2128 nparam = isl_space_dim(src->space, isl_dim_param);
2129 dim_map = inter_dim_map(ctx, graph, src, dst, offset, -s);
2131 if (!local) {
2132 isl_dim_map_range(dim_map, 1, 0, 0, 0, 1, 1);
2133 isl_dim_map_range(dim_map, 4, 2, 1, 1, nparam, -1);
2134 isl_dim_map_range(dim_map, 5, 2, 1, 1, nparam, 1);
2137 graph->lp = add_constraints_dim_map(graph->lp, coef, dim_map);
2139 return isl_stat_ok;
2142 /* Should the distance over "edge" be forced to zero?
2143 * That is, is it marked as a local edge?
2144 * If "use_coincidence" is set, then coincidence edges are treated
2145 * as local edges.
2147 static int force_zero(struct isl_sched_edge *edge, int use_coincidence)
2149 return is_local(edge) || (use_coincidence && is_coincidence(edge));
2152 /* Add all validity constraints to graph->lp.
2154 * An edge that is forced to be local needs to have its dependence
2155 * distances equal to zero. We take care of bounding them by 0 from below
2156 * here. add_all_proximity_constraints takes care of bounding them by 0
2157 * from above.
2159 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2160 * Otherwise, we ignore them.
2162 static int add_all_validity_constraints(struct isl_sched_graph *graph,
2163 int use_coincidence)
2165 int i;
2167 for (i = 0; i < graph->n_edge; ++i) {
2168 struct isl_sched_edge *edge = &graph->edge[i];
2169 int zero;
2171 zero = force_zero(edge, use_coincidence);
2172 if (!is_validity(edge) && !zero)
2173 continue;
2174 if (edge->src != edge->dst)
2175 continue;
2176 if (add_intra_validity_constraints(graph, edge) < 0)
2177 return -1;
2180 for (i = 0; i < graph->n_edge; ++i) {
2181 struct isl_sched_edge *edge = &graph->edge[i];
2182 int zero;
2184 zero = force_zero(edge, use_coincidence);
2185 if (!is_validity(edge) && !zero)
2186 continue;
2187 if (edge->src == edge->dst)
2188 continue;
2189 if (add_inter_validity_constraints(graph, edge) < 0)
2190 return -1;
2193 return 0;
2196 /* Add constraints to graph->lp that bound the dependence distance
2197 * for all dependence relations.
2198 * If a given proximity dependence is identical to a validity
2199 * dependence, then the dependence distance is already bounded
2200 * from below (by zero), so we only need to bound the distance
2201 * from above. (This includes the case of "local" dependences
2202 * which are treated as validity dependence by add_all_validity_constraints.)
2203 * Otherwise, we need to bound the distance both from above and from below.
2205 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2206 * Otherwise, we ignore them.
2208 static int add_all_proximity_constraints(struct isl_sched_graph *graph,
2209 int use_coincidence)
2211 int i;
2213 for (i = 0; i < graph->n_edge; ++i) {
2214 struct isl_sched_edge *edge = &graph->edge[i];
2215 int zero;
2217 zero = force_zero(edge, use_coincidence);
2218 if (!is_proximity(edge) && !zero)
2219 continue;
2220 if (edge->src == edge->dst &&
2221 add_intra_proximity_constraints(graph, edge, 1, zero) < 0)
2222 return -1;
2223 if (edge->src != edge->dst &&
2224 add_inter_proximity_constraints(graph, edge, 1, zero) < 0)
2225 return -1;
2226 if (is_validity(edge) || zero)
2227 continue;
2228 if (edge->src == edge->dst &&
2229 add_intra_proximity_constraints(graph, edge, -1, 0) < 0)
2230 return -1;
2231 if (edge->src != edge->dst &&
2232 add_inter_proximity_constraints(graph, edge, -1, 0) < 0)
2233 return -1;
2236 return 0;
2239 /* Normalize the rows of "indep" such that all rows are lexicographically
2240 * positive and such that each row contains as many final zeros as possible,
2241 * given the choice for the previous rows.
2242 * Do this by performing elementary row operations.
2244 static __isl_give isl_mat *normalize_independent(__isl_take isl_mat *indep)
2246 indep = isl_mat_reverse_gauss(indep);
2247 indep = isl_mat_lexnonneg_rows(indep);
2248 return indep;
2251 /* Compute a basis for the rows in the linear part of the schedule
2252 * and extend this basis to a full basis. The remaining rows
2253 * can then be used to force linear independence from the rows
2254 * in the schedule.
2256 * In particular, given the schedule rows S, we compute
2258 * S = H Q
2259 * S U = H
2261 * with H the Hermite normal form of S. That is, all but the
2262 * first rank columns of H are zero and so each row in S is
2263 * a linear combination of the first rank rows of Q.
2264 * The matrix Q can be used as a variable transformation
2265 * that isolates the directions of S in the first rank rows.
2266 * Transposing S U = H yields
2268 * U^T S^T = H^T
2270 * with all but the first rank rows of H^T zero.
2271 * The last rows of U^T are therefore linear combinations
2272 * of schedule coefficients that are all zero on schedule
2273 * coefficients that are linearly dependent on the rows of S.
2274 * At least one of these combinations is non-zero on
2275 * linearly independent schedule coefficients.
2276 * The rows are normalized to involve as few of the last
2277 * coefficients as possible and to have a positive initial value.
2279 static int node_update_vmap(struct isl_sched_node *node)
2281 isl_mat *H, *U, *Q;
2282 int n_row = isl_mat_rows(node->sched);
2284 H = isl_mat_sub_alloc(node->sched, 0, n_row,
2285 1 + node->nparam, node->nvar);
2287 H = isl_mat_left_hermite(H, 0, &U, &Q);
2288 isl_mat_free(node->indep);
2289 isl_mat_free(node->vmap);
2290 node->vmap = Q;
2291 node->indep = isl_mat_transpose(U);
2292 node->rank = isl_mat_initial_non_zero_cols(H);
2293 node->indep = isl_mat_drop_rows(node->indep, 0, node->rank);
2294 node->indep = normalize_independent(node->indep);
2295 isl_mat_free(H);
2297 if (!node->indep || !node->vmap || node->rank < 0)
2298 return -1;
2299 return 0;
2302 /* Is "edge" marked as a validity or a conditional validity edge?
2304 static int is_any_validity(struct isl_sched_edge *edge)
2306 return is_validity(edge) || is_conditional_validity(edge);
2309 /* How many times should we count the constraints in "edge"?
2311 * We count as follows
2312 * validity -> 1 (>= 0)
2313 * validity+proximity -> 2 (>= 0 and upper bound)
2314 * proximity -> 2 (lower and upper bound)
2315 * local(+any) -> 2 (>= 0 and <= 0)
2317 * If an edge is only marked conditional_validity then it counts
2318 * as zero since it is only checked afterwards.
2320 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2321 * Otherwise, we ignore them.
2323 static int edge_multiplicity(struct isl_sched_edge *edge, int use_coincidence)
2325 if (is_proximity(edge) || force_zero(edge, use_coincidence))
2326 return 2;
2327 if (is_validity(edge))
2328 return 1;
2329 return 0;
2332 /* How many times should the constraints in "edge" be counted
2333 * as a parametric intra-node constraint?
2335 * Only proximity edges that are not forced zero need
2336 * coefficient constraints that include coefficients for parameters.
2337 * If the edge is also a validity edge, then only
2338 * an upper bound is introduced. Otherwise, both lower and upper bounds
2339 * are introduced.
2341 static int parametric_intra_edge_multiplicity(struct isl_sched_edge *edge,
2342 int use_coincidence)
2344 if (edge->src != edge->dst)
2345 return 0;
2346 if (!is_proximity(edge))
2347 return 0;
2348 if (force_zero(edge, use_coincidence))
2349 return 0;
2350 if (is_validity(edge))
2351 return 1;
2352 else
2353 return 2;
2356 /* Add "f" times the number of equality and inequality constraints of "bset"
2357 * to "n_eq" and "n_ineq" and free "bset".
2359 static isl_stat update_count(__isl_take isl_basic_set *bset,
2360 int f, int *n_eq, int *n_ineq)
2362 if (!bset)
2363 return isl_stat_error;
2365 *n_eq += isl_basic_set_n_equality(bset);
2366 *n_ineq += isl_basic_set_n_inequality(bset);
2367 isl_basic_set_free(bset);
2369 return isl_stat_ok;
2372 /* Count the number of equality and inequality constraints
2373 * that will be added for the given map.
2375 * The edges that require parameter coefficients are counted separately.
2377 * "use_coincidence" is set if we should take into account coincidence edges.
2379 static isl_stat count_map_constraints(struct isl_sched_graph *graph,
2380 struct isl_sched_edge *edge, __isl_take isl_map *map,
2381 int *n_eq, int *n_ineq, int use_coincidence)
2383 isl_map *copy;
2384 isl_basic_set *coef;
2385 int f = edge_multiplicity(edge, use_coincidence);
2386 int fp = parametric_intra_edge_multiplicity(edge, use_coincidence);
2388 if (f == 0) {
2389 isl_map_free(map);
2390 return isl_stat_ok;
2393 if (edge->src != edge->dst) {
2394 coef = inter_coefficients(graph, edge, map);
2395 return update_count(coef, f, n_eq, n_ineq);
2398 if (fp > 0) {
2399 copy = isl_map_copy(map);
2400 coef = intra_coefficients(graph, edge->src, copy, 1);
2401 if (update_count(coef, fp, n_eq, n_ineq) < 0)
2402 goto error;
2405 if (f > fp) {
2406 copy = isl_map_copy(map);
2407 coef = intra_coefficients(graph, edge->src, copy, 0);
2408 if (update_count(coef, f - fp, n_eq, n_ineq) < 0)
2409 goto error;
2412 isl_map_free(map);
2413 return isl_stat_ok;
2414 error:
2415 isl_map_free(map);
2416 return isl_stat_error;
2419 /* Count the number of equality and inequality constraints
2420 * that will be added to the main lp problem.
2421 * We count as follows
2422 * validity -> 1 (>= 0)
2423 * validity+proximity -> 2 (>= 0 and upper bound)
2424 * proximity -> 2 (lower and upper bound)
2425 * local(+any) -> 2 (>= 0 and <= 0)
2427 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2428 * Otherwise, we ignore them.
2430 static int count_constraints(struct isl_sched_graph *graph,
2431 int *n_eq, int *n_ineq, int use_coincidence)
2433 int i;
2435 *n_eq = *n_ineq = 0;
2436 for (i = 0; i < graph->n_edge; ++i) {
2437 struct isl_sched_edge *edge = &graph->edge[i];
2438 isl_map *map = isl_map_copy(edge->map);
2440 if (count_map_constraints(graph, edge, map, n_eq, n_ineq,
2441 use_coincidence) < 0)
2442 return -1;
2445 return 0;
2448 /* Count the number of constraints that will be added by
2449 * add_bound_constant_constraints to bound the values of the constant terms
2450 * and increment *n_eq and *n_ineq accordingly.
2452 * In practice, add_bound_constant_constraints only adds inequalities.
2454 static isl_stat count_bound_constant_constraints(isl_ctx *ctx,
2455 struct isl_sched_graph *graph, int *n_eq, int *n_ineq)
2457 if (isl_options_get_schedule_max_constant_term(ctx) == -1)
2458 return isl_stat_ok;
2460 *n_ineq += graph->n;
2462 return isl_stat_ok;
2465 /* Add constraints to bound the values of the constant terms in the schedule,
2466 * if requested by the user.
2468 * The maximal value of the constant terms is defined by the option
2469 * "schedule_max_constant_term".
2471 static isl_stat add_bound_constant_constraints(isl_ctx *ctx,
2472 struct isl_sched_graph *graph)
2474 int i, k;
2475 int max;
2476 int total;
2478 max = isl_options_get_schedule_max_constant_term(ctx);
2479 if (max == -1)
2480 return isl_stat_ok;
2482 total = isl_basic_set_dim(graph->lp, isl_dim_set);
2484 for (i = 0; i < graph->n; ++i) {
2485 struct isl_sched_node *node = &graph->node[i];
2486 int pos;
2488 k = isl_basic_set_alloc_inequality(graph->lp);
2489 if (k < 0)
2490 return isl_stat_error;
2491 isl_seq_clr(graph->lp->ineq[k], 1 + total);
2492 pos = node_cst_coef_offset(node);
2493 isl_int_set_si(graph->lp->ineq[k][1 + pos], -1);
2494 isl_int_set_si(graph->lp->ineq[k][0], max);
2497 return isl_stat_ok;
2500 /* Count the number of constraints that will be added by
2501 * add_bound_coefficient_constraints and increment *n_eq and *n_ineq
2502 * accordingly.
2504 * In practice, add_bound_coefficient_constraints only adds inequalities.
2506 static int count_bound_coefficient_constraints(isl_ctx *ctx,
2507 struct isl_sched_graph *graph, int *n_eq, int *n_ineq)
2509 int i;
2511 if (isl_options_get_schedule_max_coefficient(ctx) == -1 &&
2512 !isl_options_get_schedule_treat_coalescing(ctx))
2513 return 0;
2515 for (i = 0; i < graph->n; ++i)
2516 *n_ineq += graph->node[i].nparam + 2 * graph->node[i].nvar;
2518 return 0;
2521 /* Add constraints to graph->lp that bound the values of
2522 * the parameter schedule coefficients of "node" to "max" and
2523 * the variable schedule coefficients to the corresponding entry
2524 * in node->max.
2525 * In either case, a negative value means that no bound needs to be imposed.
2527 * For parameter coefficients, this amounts to adding a constraint
2529 * c_n <= max
2531 * i.e.,
2533 * -c_n + max >= 0
2535 * The variables coefficients are, however, not represented directly.
2536 * Instead, the variable coefficients c_x are written as differences
2537 * c_x = c_x^+ - c_x^-.
2538 * That is,
2540 * -max_i <= c_x_i <= max_i
2542 * is encoded as
2544 * -max_i <= c_x_i^+ - c_x_i^- <= max_i
2546 * or
2548 * -(c_x_i^+ - c_x_i^-) + max_i >= 0
2549 * c_x_i^+ - c_x_i^- + max_i >= 0
2551 static isl_stat node_add_coefficient_constraints(isl_ctx *ctx,
2552 struct isl_sched_graph *graph, struct isl_sched_node *node, int max)
2554 int i, j, k;
2555 int total;
2556 isl_vec *ineq;
2558 total = isl_basic_set_dim(graph->lp, isl_dim_set);
2560 for (j = 0; j < node->nparam; ++j) {
2561 int dim;
2563 if (max < 0)
2564 continue;
2566 k = isl_basic_set_alloc_inequality(graph->lp);
2567 if (k < 0)
2568 return isl_stat_error;
2569 dim = 1 + node_par_coef_offset(node) + j;
2570 isl_seq_clr(graph->lp->ineq[k], 1 + total);
2571 isl_int_set_si(graph->lp->ineq[k][dim], -1);
2572 isl_int_set_si(graph->lp->ineq[k][0], max);
2575 ineq = isl_vec_alloc(ctx, 1 + total);
2576 ineq = isl_vec_clr(ineq);
2577 if (!ineq)
2578 return isl_stat_error;
2579 for (i = 0; i < node->nvar; ++i) {
2580 int pos = 1 + node_var_coef_pos(node, i);
2582 if (isl_int_is_neg(node->max->el[i]))
2583 continue;
2585 isl_int_set_si(ineq->el[pos], 1);
2586 isl_int_set_si(ineq->el[pos + 1], -1);
2587 isl_int_set(ineq->el[0], node->max->el[i]);
2589 k = isl_basic_set_alloc_inequality(graph->lp);
2590 if (k < 0)
2591 goto error;
2592 isl_seq_cpy(graph->lp->ineq[k], ineq->el, 1 + total);
2594 isl_seq_neg(ineq->el + pos, ineq->el + pos, 2);
2595 k = isl_basic_set_alloc_inequality(graph->lp);
2596 if (k < 0)
2597 goto error;
2598 isl_seq_cpy(graph->lp->ineq[k], ineq->el, 1 + total);
2600 isl_seq_clr(ineq->el + pos, 2);
2602 isl_vec_free(ineq);
2604 return isl_stat_ok;
2605 error:
2606 isl_vec_free(ineq);
2607 return isl_stat_error;
2610 /* Add constraints that bound the values of the variable and parameter
2611 * coefficients of the schedule.
2613 * The maximal value of the coefficients is defined by the option
2614 * 'schedule_max_coefficient' and the entries in node->max.
2615 * These latter entries are only set if either the schedule_max_coefficient
2616 * option or the schedule_treat_coalescing option is set.
2618 static isl_stat add_bound_coefficient_constraints(isl_ctx *ctx,
2619 struct isl_sched_graph *graph)
2621 int i;
2622 int max;
2624 max = isl_options_get_schedule_max_coefficient(ctx);
2626 if (max == -1 && !isl_options_get_schedule_treat_coalescing(ctx))
2627 return isl_stat_ok;
2629 for (i = 0; i < graph->n; ++i) {
2630 struct isl_sched_node *node = &graph->node[i];
2632 if (node_add_coefficient_constraints(ctx, graph, node, max) < 0)
2633 return isl_stat_error;
2636 return isl_stat_ok;
2639 /* Add a constraint to graph->lp that equates the value at position
2640 * "sum_pos" to the sum of the "n" values starting at "first".
2642 static isl_stat add_sum_constraint(struct isl_sched_graph *graph,
2643 int sum_pos, int first, int n)
2645 int i, k;
2646 int total;
2648 total = isl_basic_set_dim(graph->lp, isl_dim_set);
2650 k = isl_basic_set_alloc_equality(graph->lp);
2651 if (k < 0)
2652 return isl_stat_error;
2653 isl_seq_clr(graph->lp->eq[k], 1 + total);
2654 isl_int_set_si(graph->lp->eq[k][1 + sum_pos], -1);
2655 for (i = 0; i < n; ++i)
2656 isl_int_set_si(graph->lp->eq[k][1 + first + i], 1);
2658 return isl_stat_ok;
2661 /* Add a constraint to graph->lp that equates the value at position
2662 * "sum_pos" to the sum of the parameter coefficients of all nodes.
2664 static isl_stat add_param_sum_constraint(struct isl_sched_graph *graph,
2665 int sum_pos)
2667 int i, j, k;
2668 int total;
2670 total = isl_basic_set_dim(graph->lp, isl_dim_set);
2672 k = isl_basic_set_alloc_equality(graph->lp);
2673 if (k < 0)
2674 return isl_stat_error;
2675 isl_seq_clr(graph->lp->eq[k], 1 + total);
2676 isl_int_set_si(graph->lp->eq[k][1 + sum_pos], -1);
2677 for (i = 0; i < graph->n; ++i) {
2678 int pos = 1 + node_par_coef_offset(&graph->node[i]);
2680 for (j = 0; j < graph->node[i].nparam; ++j)
2681 isl_int_set_si(graph->lp->eq[k][pos + j], 1);
2684 return isl_stat_ok;
2687 /* Add a constraint to graph->lp that equates the value at position
2688 * "sum_pos" to the sum of the variable coefficients of all nodes.
2690 static isl_stat add_var_sum_constraint(struct isl_sched_graph *graph,
2691 int sum_pos)
2693 int i, j, k;
2694 int total;
2696 total = isl_basic_set_dim(graph->lp, isl_dim_set);
2698 k = isl_basic_set_alloc_equality(graph->lp);
2699 if (k < 0)
2700 return isl_stat_error;
2701 isl_seq_clr(graph->lp->eq[k], 1 + total);
2702 isl_int_set_si(graph->lp->eq[k][1 + sum_pos], -1);
2703 for (i = 0; i < graph->n; ++i) {
2704 struct isl_sched_node *node = &graph->node[i];
2705 int pos = 1 + node_var_coef_offset(node);
2707 for (j = 0; j < 2 * node->nvar; ++j)
2708 isl_int_set_si(graph->lp->eq[k][pos + j], 1);
2711 return isl_stat_ok;
2714 /* Construct an ILP problem for finding schedule coefficients
2715 * that result in non-negative, but small dependence distances
2716 * over all dependences.
2717 * In particular, the dependence distances over proximity edges
2718 * are bounded by m_0 + m_n n and we compute schedule coefficients
2719 * with small values (preferably zero) of m_n and m_0.
2721 * All variables of the ILP are non-negative. The actual coefficients
2722 * may be negative, so each coefficient is represented as the difference
2723 * of two non-negative variables. The negative part always appears
2724 * immediately before the positive part.
2725 * Other than that, the variables have the following order
2727 * - sum of positive and negative parts of m_n coefficients
2728 * - m_0
2729 * - sum of all c_n coefficients
2730 * (unconstrained when computing non-parametric schedules)
2731 * - sum of positive and negative parts of all c_x coefficients
2732 * - positive and negative parts of m_n coefficients
2733 * - for each node
2734 * - positive and negative parts of c_i_x, in opposite order
2735 * - c_i_n (if parametric)
2736 * - c_i_0
2738 * The constraints are those from the edges plus two or three equalities
2739 * to express the sums.
2741 * If "use_coincidence" is set, then we treat coincidence edges as local edges.
2742 * Otherwise, we ignore them.
2744 static isl_stat setup_lp(isl_ctx *ctx, struct isl_sched_graph *graph,
2745 int use_coincidence)
2747 int i;
2748 unsigned nparam;
2749 unsigned total;
2750 isl_space *space;
2751 int parametric;
2752 int param_pos;
2753 int n_eq, n_ineq;
2755 parametric = ctx->opt->schedule_parametric;
2756 nparam = isl_space_dim(graph->node[0].space, isl_dim_param);
2757 param_pos = 4;
2758 total = param_pos + 2 * nparam;
2759 for (i = 0; i < graph->n; ++i) {
2760 struct isl_sched_node *node = &graph->node[graph->sorted[i]];
2761 if (node_update_vmap(node) < 0)
2762 return isl_stat_error;
2763 node->start = total;
2764 total += 1 + node->nparam + 2 * node->nvar;
2767 if (count_constraints(graph, &n_eq, &n_ineq, use_coincidence) < 0)
2768 return isl_stat_error;
2769 if (count_bound_constant_constraints(ctx, graph, &n_eq, &n_ineq) < 0)
2770 return isl_stat_error;
2771 if (count_bound_coefficient_constraints(ctx, graph, &n_eq, &n_ineq) < 0)
2772 return isl_stat_error;
2774 space = isl_space_set_alloc(ctx, 0, total);
2775 isl_basic_set_free(graph->lp);
2776 n_eq += 2 + parametric;
2778 graph->lp = isl_basic_set_alloc_space(space, 0, n_eq, n_ineq);
2780 if (add_sum_constraint(graph, 0, param_pos, 2 * nparam) < 0)
2781 return isl_stat_error;
2782 if (parametric && add_param_sum_constraint(graph, 2) < 0)
2783 return isl_stat_error;
2784 if (add_var_sum_constraint(graph, 3) < 0)
2785 return isl_stat_error;
2786 if (add_bound_constant_constraints(ctx, graph) < 0)
2787 return isl_stat_error;
2788 if (add_bound_coefficient_constraints(ctx, graph) < 0)
2789 return isl_stat_error;
2790 if (add_all_validity_constraints(graph, use_coincidence) < 0)
2791 return isl_stat_error;
2792 if (add_all_proximity_constraints(graph, use_coincidence) < 0)
2793 return isl_stat_error;
2795 return isl_stat_ok;
2798 /* Analyze the conflicting constraint found by
2799 * isl_tab_basic_set_non_trivial_lexmin. If it corresponds to the validity
2800 * constraint of one of the edges between distinct nodes, living, moreover
2801 * in distinct SCCs, then record the source and sink SCC as this may
2802 * be a good place to cut between SCCs.
2804 static int check_conflict(int con, void *user)
2806 int i;
2807 struct isl_sched_graph *graph = user;
2809 if (graph->src_scc >= 0)
2810 return 0;
2812 con -= graph->lp->n_eq;
2814 if (con >= graph->lp->n_ineq)
2815 return 0;
2817 for (i = 0; i < graph->n_edge; ++i) {
2818 if (!is_validity(&graph->edge[i]))
2819 continue;
2820 if (graph->edge[i].src == graph->edge[i].dst)
2821 continue;
2822 if (graph->edge[i].src->scc == graph->edge[i].dst->scc)
2823 continue;
2824 if (graph->edge[i].start > con)
2825 continue;
2826 if (graph->edge[i].end <= con)
2827 continue;
2828 graph->src_scc = graph->edge[i].src->scc;
2829 graph->dst_scc = graph->edge[i].dst->scc;
2832 return 0;
2835 /* Check whether the next schedule row of the given node needs to be
2836 * non-trivial. Lower-dimensional domains may have some trivial rows,
2837 * but as soon as the number of remaining required non-trivial rows
2838 * is as large as the number or remaining rows to be computed,
2839 * all remaining rows need to be non-trivial.
2841 static int needs_row(struct isl_sched_graph *graph, struct isl_sched_node *node)
2843 return node->nvar - node->rank >= graph->maxvar - graph->n_row;
2846 /* Construct a non-triviality region with triviality directions
2847 * corresponding to the rows of "indep".
2848 * The rows of "indep" are expressed in terms of the schedule coefficients c_i,
2849 * while the triviality directions are expressed in terms of
2850 * pairs of non-negative variables c^+_i - c^-_i, with c^-_i appearing
2851 * before c^+_i. Furthermore,
2852 * the pairs of non-negative variables representing the coefficients
2853 * are stored in the opposite order.
2855 static __isl_give isl_mat *construct_trivial(__isl_keep isl_mat *indep)
2857 isl_ctx *ctx;
2858 isl_mat *mat;
2859 int i, j, n, n_var;
2861 if (!indep)
2862 return NULL;
2864 ctx = isl_mat_get_ctx(indep);
2865 n = isl_mat_rows(indep);
2866 n_var = isl_mat_cols(indep);
2867 mat = isl_mat_alloc(ctx, n, 2 * n_var);
2868 if (!mat)
2869 return NULL;
2870 for (i = 0; i < n; ++i) {
2871 for (j = 0; j < n_var; ++j) {
2872 int nj = n_var - 1 - j;
2873 isl_int_neg(mat->row[i][2 * nj], indep->row[i][j]);
2874 isl_int_set(mat->row[i][2 * nj + 1], indep->row[i][j]);
2878 return mat;
2881 /* Solve the ILP problem constructed in setup_lp.
2882 * For each node such that all the remaining rows of its schedule
2883 * need to be non-trivial, we construct a non-triviality region.
2884 * This region imposes that the next row is independent of previous rows.
2885 * In particular, the non-triviality region enforces that at least
2886 * one of the linear combinations in the rows of node->indep is non-zero.
2888 static __isl_give isl_vec *solve_lp(isl_ctx *ctx, struct isl_sched_graph *graph)
2890 int i;
2891 isl_vec *sol;
2892 isl_basic_set *lp;
2894 for (i = 0; i < graph->n; ++i) {
2895 struct isl_sched_node *node = &graph->node[i];
2896 isl_mat *trivial;
2898 graph->region[i].pos = node_var_coef_offset(node);
2899 if (needs_row(graph, node))
2900 trivial = construct_trivial(node->indep);
2901 else
2902 trivial = isl_mat_zero(ctx, 0, 0);
2903 graph->region[i].trivial = trivial;
2905 lp = isl_basic_set_copy(graph->lp);
2906 sol = isl_tab_basic_set_non_trivial_lexmin(lp, 2, graph->n,
2907 graph->region, &check_conflict, graph);
2908 for (i = 0; i < graph->n; ++i)
2909 isl_mat_free(graph->region[i].trivial);
2910 return sol;
2913 /* Extract the coefficients for the variables of "node" from "sol".
2915 * Each schedule coefficient c_i_x is represented as the difference
2916 * between two non-negative variables c_i_x^+ - c_i_x^-.
2917 * The c_i_x^- appear before their c_i_x^+ counterpart.
2918 * Furthermore, the order of these pairs is the opposite of that
2919 * of the corresponding coefficients.
2921 * Return c_i_x = c_i_x^+ - c_i_x^-
2923 static __isl_give isl_vec *extract_var_coef(struct isl_sched_node *node,
2924 __isl_keep isl_vec *sol)
2926 int i;
2927 int pos;
2928 isl_vec *csol;
2930 if (!sol)
2931 return NULL;
2932 csol = isl_vec_alloc(isl_vec_get_ctx(sol), node->nvar);
2933 if (!csol)
2934 return NULL;
2936 pos = 1 + node_var_coef_offset(node);
2937 for (i = 0; i < node->nvar; ++i)
2938 isl_int_sub(csol->el[node->nvar - 1 - i],
2939 sol->el[pos + 2 * i + 1], sol->el[pos + 2 * i]);
2941 return csol;
2944 /* Update the schedules of all nodes based on the given solution
2945 * of the LP problem.
2946 * The new row is added to the current band.
2947 * All possibly negative coefficients are encoded as a difference
2948 * of two non-negative variables, so we need to perform the subtraction
2949 * here.
2951 * If coincident is set, then the caller guarantees that the new
2952 * row satisfies the coincidence constraints.
2954 static int update_schedule(struct isl_sched_graph *graph,
2955 __isl_take isl_vec *sol, int coincident)
2957 int i, j;
2958 isl_vec *csol = NULL;
2960 if (!sol)
2961 goto error;
2962 if (sol->size == 0)
2963 isl_die(sol->ctx, isl_error_internal,
2964 "no solution found", goto error);
2965 if (graph->n_total_row >= graph->max_row)
2966 isl_die(sol->ctx, isl_error_internal,
2967 "too many schedule rows", goto error);
2969 for (i = 0; i < graph->n; ++i) {
2970 struct isl_sched_node *node = &graph->node[i];
2971 int pos;
2972 int row = isl_mat_rows(node->sched);
2974 isl_vec_free(csol);
2975 csol = extract_var_coef(node, sol);
2976 if (!csol)
2977 goto error;
2979 isl_map_free(node->sched_map);
2980 node->sched_map = NULL;
2981 node->sched = isl_mat_add_rows(node->sched, 1);
2982 if (!node->sched)
2983 goto error;
2984 pos = node_cst_coef_offset(node);
2985 node->sched = isl_mat_set_element(node->sched,
2986 row, 0, sol->el[1 + pos]);
2987 pos = node_par_coef_offset(node);
2988 for (j = 0; j < node->nparam; ++j)
2989 node->sched = isl_mat_set_element(node->sched,
2990 row, 1 + j, sol->el[1 + pos + j]);
2991 for (j = 0; j < node->nvar; ++j)
2992 node->sched = isl_mat_set_element(node->sched,
2993 row, 1 + node->nparam + j, csol->el[j]);
2994 node->coincident[graph->n_total_row] = coincident;
2996 isl_vec_free(sol);
2997 isl_vec_free(csol);
2999 graph->n_row++;
3000 graph->n_total_row++;
3002 return 0;
3003 error:
3004 isl_vec_free(sol);
3005 isl_vec_free(csol);
3006 return -1;
3009 /* Convert row "row" of node->sched into an isl_aff living in "ls"
3010 * and return this isl_aff.
3012 static __isl_give isl_aff *extract_schedule_row(__isl_take isl_local_space *ls,
3013 struct isl_sched_node *node, int row)
3015 int j;
3016 isl_int v;
3017 isl_aff *aff;
3019 isl_int_init(v);
3021 aff = isl_aff_zero_on_domain(ls);
3022 if (isl_mat_get_element(node->sched, row, 0, &v) < 0)
3023 goto error;
3024 aff = isl_aff_set_constant(aff, v);
3025 for (j = 0; j < node->nparam; ++j) {
3026 if (isl_mat_get_element(node->sched, row, 1 + j, &v) < 0)
3027 goto error;
3028 aff = isl_aff_set_coefficient(aff, isl_dim_param, j, v);
3030 for (j = 0; j < node->nvar; ++j) {
3031 if (isl_mat_get_element(node->sched, row,
3032 1 + node->nparam + j, &v) < 0)
3033 goto error;
3034 aff = isl_aff_set_coefficient(aff, isl_dim_in, j, v);
3037 isl_int_clear(v);
3039 return aff;
3040 error:
3041 isl_int_clear(v);
3042 isl_aff_free(aff);
3043 return NULL;
3046 /* Convert the "n" rows starting at "first" of node->sched into a multi_aff
3047 * and return this multi_aff.
3049 * The result is defined over the uncompressed node domain.
3051 static __isl_give isl_multi_aff *node_extract_partial_schedule_multi_aff(
3052 struct isl_sched_node *node, int first, int n)
3054 int i;
3055 isl_space *space;
3056 isl_local_space *ls;
3057 isl_aff *aff;
3058 isl_multi_aff *ma;
3059 int nrow;
3061 if (!node)
3062 return NULL;
3063 nrow = isl_mat_rows(node->sched);
3064 if (node->compressed)
3065 space = isl_multi_aff_get_domain_space(node->decompress);
3066 else
3067 space = isl_space_copy(node->space);
3068 ls = isl_local_space_from_space(isl_space_copy(space));
3069 space = isl_space_from_domain(space);
3070 space = isl_space_add_dims(space, isl_dim_out, n);
3071 ma = isl_multi_aff_zero(space);
3073 for (i = first; i < first + n; ++i) {
3074 aff = extract_schedule_row(isl_local_space_copy(ls), node, i);
3075 ma = isl_multi_aff_set_aff(ma, i - first, aff);
3078 isl_local_space_free(ls);
3080 if (node->compressed)
3081 ma = isl_multi_aff_pullback_multi_aff(ma,
3082 isl_multi_aff_copy(node->compress));
3084 return ma;
3087 /* Convert node->sched into a multi_aff and return this multi_aff.
3089 * The result is defined over the uncompressed node domain.
3091 static __isl_give isl_multi_aff *node_extract_schedule_multi_aff(
3092 struct isl_sched_node *node)
3094 int nrow;
3096 nrow = isl_mat_rows(node->sched);
3097 return node_extract_partial_schedule_multi_aff(node, 0, nrow);
3100 /* Convert node->sched into a map and return this map.
3102 * The result is cached in node->sched_map, which needs to be released
3103 * whenever node->sched is updated.
3104 * It is defined over the uncompressed node domain.
3106 static __isl_give isl_map *node_extract_schedule(struct isl_sched_node *node)
3108 if (!node->sched_map) {
3109 isl_multi_aff *ma;
3111 ma = node_extract_schedule_multi_aff(node);
3112 node->sched_map = isl_map_from_multi_aff(ma);
3115 return isl_map_copy(node->sched_map);
3118 /* Construct a map that can be used to update a dependence relation
3119 * based on the current schedule.
3120 * That is, construct a map expressing that source and sink
3121 * are executed within the same iteration of the current schedule.
3122 * This map can then be intersected with the dependence relation.
3123 * This is not the most efficient way, but this shouldn't be a critical
3124 * operation.
3126 static __isl_give isl_map *specializer(struct isl_sched_node *src,
3127 struct isl_sched_node *dst)
3129 isl_map *src_sched, *dst_sched;
3131 src_sched = node_extract_schedule(src);
3132 dst_sched = node_extract_schedule(dst);
3133 return isl_map_apply_range(src_sched, isl_map_reverse(dst_sched));
3136 /* Intersect the domains of the nested relations in domain and range
3137 * of "umap" with "map".
3139 static __isl_give isl_union_map *intersect_domains(
3140 __isl_take isl_union_map *umap, __isl_keep isl_map *map)
3142 isl_union_set *uset;
3144 umap = isl_union_map_zip(umap);
3145 uset = isl_union_set_from_set(isl_map_wrap(isl_map_copy(map)));
3146 umap = isl_union_map_intersect_domain(umap, uset);
3147 umap = isl_union_map_zip(umap);
3148 return umap;
3151 /* Update the dependence relation of the given edge based
3152 * on the current schedule.
3153 * If the dependence is carried completely by the current schedule, then
3154 * it is removed from the edge_tables. It is kept in the list of edges
3155 * as otherwise all edge_tables would have to be recomputed.
3157 * If the edge is of a type that can appear multiple times
3158 * between the same pair of nodes, then it is added to
3159 * the edge table (again). This prevents the situation
3160 * where none of these edges is referenced from the edge table
3161 * because the one that was referenced turned out to be empty and
3162 * was therefore removed from the table.
3164 static isl_stat update_edge(isl_ctx *ctx, struct isl_sched_graph *graph,
3165 struct isl_sched_edge *edge)
3167 int empty;
3168 isl_map *id;
3170 id = specializer(edge->src, edge->dst);
3171 edge->map = isl_map_intersect(edge->map, isl_map_copy(id));
3172 if (!edge->map)
3173 goto error;
3175 if (edge->tagged_condition) {
3176 edge->tagged_condition =
3177 intersect_domains(edge->tagged_condition, id);
3178 if (!edge->tagged_condition)
3179 goto error;
3181 if (edge->tagged_validity) {
3182 edge->tagged_validity =
3183 intersect_domains(edge->tagged_validity, id);
3184 if (!edge->tagged_validity)
3185 goto error;
3188 empty = isl_map_plain_is_empty(edge->map);
3189 if (empty < 0)
3190 goto error;
3191 if (empty) {
3192 graph_remove_edge(graph, edge);
3193 } else if (is_multi_edge_type(edge)) {
3194 if (graph_edge_tables_add(ctx, graph, edge) < 0)
3195 goto error;
3198 isl_map_free(id);
3199 return isl_stat_ok;
3200 error:
3201 isl_map_free(id);
3202 return isl_stat_error;
3205 /* Does the domain of "umap" intersect "uset"?
3207 static int domain_intersects(__isl_keep isl_union_map *umap,
3208 __isl_keep isl_union_set *uset)
3210 int empty;
3212 umap = isl_union_map_copy(umap);
3213 umap = isl_union_map_intersect_domain(umap, isl_union_set_copy(uset));
3214 empty = isl_union_map_is_empty(umap);
3215 isl_union_map_free(umap);
3217 return empty < 0 ? -1 : !empty;
3220 /* Does the range of "umap" intersect "uset"?
3222 static int range_intersects(__isl_keep isl_union_map *umap,
3223 __isl_keep isl_union_set *uset)
3225 int empty;
3227 umap = isl_union_map_copy(umap);
3228 umap = isl_union_map_intersect_range(umap, isl_union_set_copy(uset));
3229 empty = isl_union_map_is_empty(umap);
3230 isl_union_map_free(umap);
3232 return empty < 0 ? -1 : !empty;
3235 /* Are the condition dependences of "edge" local with respect to
3236 * the current schedule?
3238 * That is, are domain and range of the condition dependences mapped
3239 * to the same point?
3241 * In other words, is the condition false?
3243 static int is_condition_false(struct isl_sched_edge *edge)
3245 isl_union_map *umap;
3246 isl_map *map, *sched, *test;
3247 int empty, local;
3249 empty = isl_union_map_is_empty(edge->tagged_condition);
3250 if (empty < 0 || empty)
3251 return empty;
3253 umap = isl_union_map_copy(edge->tagged_condition);
3254 umap = isl_union_map_zip(umap);
3255 umap = isl_union_set_unwrap(isl_union_map_domain(umap));
3256 map = isl_map_from_union_map(umap);
3258 sched = node_extract_schedule(edge->src);
3259 map = isl_map_apply_domain(map, sched);
3260 sched = node_extract_schedule(edge->dst);
3261 map = isl_map_apply_range(map, sched);
3263 test = isl_map_identity(isl_map_get_space(map));
3264 local = isl_map_is_subset(map, test);
3265 isl_map_free(map);
3266 isl_map_free(test);
3268 return local;
3271 /* For each conditional validity constraint that is adjacent
3272 * to a condition with domain in condition_source or range in condition_sink,
3273 * turn it into an unconditional validity constraint.
3275 static int unconditionalize_adjacent_validity(struct isl_sched_graph *graph,
3276 __isl_take isl_union_set *condition_source,
3277 __isl_take isl_union_set *condition_sink)
3279 int i;
3281 condition_source = isl_union_set_coalesce(condition_source);
3282 condition_sink = isl_union_set_coalesce(condition_sink);
3284 for (i = 0; i < graph->n_edge; ++i) {
3285 int adjacent;
3286 isl_union_map *validity;
3288 if (!is_conditional_validity(&graph->edge[i]))
3289 continue;
3290 if (is_validity(&graph->edge[i]))
3291 continue;
3293 validity = graph->edge[i].tagged_validity;
3294 adjacent = domain_intersects(validity, condition_sink);
3295 if (adjacent >= 0 && !adjacent)
3296 adjacent = range_intersects(validity, condition_source);
3297 if (adjacent < 0)
3298 goto error;
3299 if (!adjacent)
3300 continue;
3302 set_validity(&graph->edge[i]);
3305 isl_union_set_free(condition_source);
3306 isl_union_set_free(condition_sink);
3307 return 0;
3308 error:
3309 isl_union_set_free(condition_source);
3310 isl_union_set_free(condition_sink);
3311 return -1;
3314 /* Update the dependence relations of all edges based on the current schedule
3315 * and enforce conditional validity constraints that are adjacent
3316 * to satisfied condition constraints.
3318 * First check if any of the condition constraints are satisfied
3319 * (i.e., not local to the outer schedule) and keep track of
3320 * their domain and range.
3321 * Then update all dependence relations (which removes the non-local
3322 * constraints).
3323 * Finally, if any condition constraints turned out to be satisfied,
3324 * then turn all adjacent conditional validity constraints into
3325 * unconditional validity constraints.
3327 static int update_edges(isl_ctx *ctx, struct isl_sched_graph *graph)
3329 int i;
3330 int any = 0;
3331 isl_union_set *source, *sink;
3333 source = isl_union_set_empty(isl_space_params_alloc(ctx, 0));
3334 sink = isl_union_set_empty(isl_space_params_alloc(ctx, 0));
3335 for (i = 0; i < graph->n_edge; ++i) {
3336 int local;
3337 isl_union_set *uset;
3338 isl_union_map *umap;
3340 if (!is_condition(&graph->edge[i]))
3341 continue;
3342 if (is_local(&graph->edge[i]))
3343 continue;
3344 local = is_condition_false(&graph->edge[i]);
3345 if (local < 0)
3346 goto error;
3347 if (local)
3348 continue;
3350 any = 1;
3352 umap = isl_union_map_copy(graph->edge[i].tagged_condition);
3353 uset = isl_union_map_domain(umap);
3354 source = isl_union_set_union(source, uset);
3356 umap = isl_union_map_copy(graph->edge[i].tagged_condition);
3357 uset = isl_union_map_range(umap);
3358 sink = isl_union_set_union(sink, uset);
3361 for (i = 0; i < graph->n_edge; ++i) {
3362 if (update_edge(ctx, graph, &graph->edge[i]) < 0)
3363 goto error;
3366 if (any)
3367 return unconditionalize_adjacent_validity(graph, source, sink);
3369 isl_union_set_free(source);
3370 isl_union_set_free(sink);
3371 return 0;
3372 error:
3373 isl_union_set_free(source);
3374 isl_union_set_free(sink);
3375 return -1;
3378 static void next_band(struct isl_sched_graph *graph)
3380 graph->band_start = graph->n_total_row;
3383 /* Return the union of the universe domains of the nodes in "graph"
3384 * that satisfy "pred".
3386 static __isl_give isl_union_set *isl_sched_graph_domain(isl_ctx *ctx,
3387 struct isl_sched_graph *graph,
3388 int (*pred)(struct isl_sched_node *node, int data), int data)
3390 int i;
3391 isl_set *set;
3392 isl_union_set *dom;
3394 for (i = 0; i < graph->n; ++i)
3395 if (pred(&graph->node[i], data))
3396 break;
3398 if (i >= graph->n)
3399 isl_die(ctx, isl_error_internal,
3400 "empty component", return NULL);
3402 set = isl_set_universe(isl_space_copy(graph->node[i].space));
3403 dom = isl_union_set_from_set(set);
3405 for (i = i + 1; i < graph->n; ++i) {
3406 if (!pred(&graph->node[i], data))
3407 continue;
3408 set = isl_set_universe(isl_space_copy(graph->node[i].space));
3409 dom = isl_union_set_union(dom, isl_union_set_from_set(set));
3412 return dom;
3415 /* Return a list of unions of universe domains, where each element
3416 * in the list corresponds to an SCC (or WCC) indexed by node->scc.
3418 static __isl_give isl_union_set_list *extract_sccs(isl_ctx *ctx,
3419 struct isl_sched_graph *graph)
3421 int i;
3422 isl_union_set_list *filters;
3424 filters = isl_union_set_list_alloc(ctx, graph->scc);
3425 for (i = 0; i < graph->scc; ++i) {
3426 isl_union_set *dom;
3428 dom = isl_sched_graph_domain(ctx, graph, &node_scc_exactly, i);
3429 filters = isl_union_set_list_add(filters, dom);
3432 return filters;
3435 /* Return a list of two unions of universe domains, one for the SCCs up
3436 * to and including graph->src_scc and another for the other SCCs.
3438 static __isl_give isl_union_set_list *extract_split(isl_ctx *ctx,
3439 struct isl_sched_graph *graph)
3441 isl_union_set *dom;
3442 isl_union_set_list *filters;
3444 filters = isl_union_set_list_alloc(ctx, 2);
3445 dom = isl_sched_graph_domain(ctx, graph,
3446 &node_scc_at_most, graph->src_scc);
3447 filters = isl_union_set_list_add(filters, dom);
3448 dom = isl_sched_graph_domain(ctx, graph,
3449 &node_scc_at_least, graph->src_scc + 1);
3450 filters = isl_union_set_list_add(filters, dom);
3452 return filters;
3455 /* Copy nodes that satisfy node_pred from the src dependence graph
3456 * to the dst dependence graph.
3458 static isl_stat copy_nodes(struct isl_sched_graph *dst,
3459 struct isl_sched_graph *src,
3460 int (*node_pred)(struct isl_sched_node *node, int data), int data)
3462 int i;
3464 dst->n = 0;
3465 for (i = 0; i < src->n; ++i) {
3466 int j;
3468 if (!node_pred(&src->node[i], data))
3469 continue;
3471 j = dst->n;
3472 dst->node[j].space = isl_space_copy(src->node[i].space);
3473 dst->node[j].compressed = src->node[i].compressed;
3474 dst->node[j].hull = isl_set_copy(src->node[i].hull);
3475 dst->node[j].compress =
3476 isl_multi_aff_copy(src->node[i].compress);
3477 dst->node[j].decompress =
3478 isl_multi_aff_copy(src->node[i].decompress);
3479 dst->node[j].nvar = src->node[i].nvar;
3480 dst->node[j].nparam = src->node[i].nparam;
3481 dst->node[j].sched = isl_mat_copy(src->node[i].sched);
3482 dst->node[j].sched_map = isl_map_copy(src->node[i].sched_map);
3483 dst->node[j].coincident = src->node[i].coincident;
3484 dst->node[j].sizes = isl_multi_val_copy(src->node[i].sizes);
3485 dst->node[j].bounds = isl_basic_set_copy(src->node[i].bounds);
3486 dst->node[j].max = isl_vec_copy(src->node[i].max);
3487 dst->n++;
3489 if (!dst->node[j].space || !dst->node[j].sched)
3490 return isl_stat_error;
3491 if (dst->node[j].compressed &&
3492 (!dst->node[j].hull || !dst->node[j].compress ||
3493 !dst->node[j].decompress))
3494 return isl_stat_error;
3497 return isl_stat_ok;
3500 /* Copy non-empty edges that satisfy edge_pred from the src dependence graph
3501 * to the dst dependence graph.
3502 * If the source or destination node of the edge is not in the destination
3503 * graph, then it must be a backward proximity edge and it should simply
3504 * be ignored.
3506 static isl_stat copy_edges(isl_ctx *ctx, struct isl_sched_graph *dst,
3507 struct isl_sched_graph *src,
3508 int (*edge_pred)(struct isl_sched_edge *edge, int data), int data)
3510 int i;
3512 dst->n_edge = 0;
3513 for (i = 0; i < src->n_edge; ++i) {
3514 struct isl_sched_edge *edge = &src->edge[i];
3515 isl_map *map;
3516 isl_union_map *tagged_condition;
3517 isl_union_map *tagged_validity;
3518 struct isl_sched_node *dst_src, *dst_dst;
3520 if (!edge_pred(edge, data))
3521 continue;
3523 if (isl_map_plain_is_empty(edge->map))
3524 continue;
3526 dst_src = graph_find_node(ctx, dst, edge->src->space);
3527 dst_dst = graph_find_node(ctx, dst, edge->dst->space);
3528 if (!dst_src || !dst_dst)
3529 return isl_stat_error;
3530 if (!is_node(dst, dst_src) || !is_node(dst, dst_dst)) {
3531 if (is_validity(edge) || is_conditional_validity(edge))
3532 isl_die(ctx, isl_error_internal,
3533 "backward (conditional) validity edge",
3534 return isl_stat_error);
3535 continue;
3538 map = isl_map_copy(edge->map);
3539 tagged_condition = isl_union_map_copy(edge->tagged_condition);
3540 tagged_validity = isl_union_map_copy(edge->tagged_validity);
3542 dst->edge[dst->n_edge].src = dst_src;
3543 dst->edge[dst->n_edge].dst = dst_dst;
3544 dst->edge[dst->n_edge].map = map;
3545 dst->edge[dst->n_edge].tagged_condition = tagged_condition;
3546 dst->edge[dst->n_edge].tagged_validity = tagged_validity;
3547 dst->edge[dst->n_edge].types = edge->types;
3548 dst->n_edge++;
3550 if (edge->tagged_condition && !tagged_condition)
3551 return isl_stat_error;
3552 if (edge->tagged_validity && !tagged_validity)
3553 return isl_stat_error;
3555 if (graph_edge_tables_add(ctx, dst,
3556 &dst->edge[dst->n_edge - 1]) < 0)
3557 return isl_stat_error;
3560 return isl_stat_ok;
3563 /* Compute the maximal number of variables over all nodes.
3564 * This is the maximal number of linearly independent schedule
3565 * rows that we need to compute.
3566 * Just in case we end up in a part of the dependence graph
3567 * with only lower-dimensional domains, we make sure we will
3568 * compute the required amount of extra linearly independent rows.
3570 static int compute_maxvar(struct isl_sched_graph *graph)
3572 int i;
3574 graph->maxvar = 0;
3575 for (i = 0; i < graph->n; ++i) {
3576 struct isl_sched_node *node = &graph->node[i];
3577 int nvar;
3579 if (node_update_vmap(node) < 0)
3580 return -1;
3581 nvar = node->nvar + graph->n_row - node->rank;
3582 if (nvar > graph->maxvar)
3583 graph->maxvar = nvar;
3586 return 0;
3589 /* Extract the subgraph of "graph" that consists of the nodes satisfying
3590 * "node_pred" and the edges satisfying "edge_pred" and store
3591 * the result in "sub".
3593 static isl_stat extract_sub_graph(isl_ctx *ctx, struct isl_sched_graph *graph,
3594 int (*node_pred)(struct isl_sched_node *node, int data),
3595 int (*edge_pred)(struct isl_sched_edge *edge, int data),
3596 int data, struct isl_sched_graph *sub)
3598 int i, n = 0, n_edge = 0;
3599 int t;
3601 for (i = 0; i < graph->n; ++i)
3602 if (node_pred(&graph->node[i], data))
3603 ++n;
3604 for (i = 0; i < graph->n_edge; ++i)
3605 if (edge_pred(&graph->edge[i], data))
3606 ++n_edge;
3607 if (graph_alloc(ctx, sub, n, n_edge) < 0)
3608 return isl_stat_error;
3609 sub->root = graph->root;
3610 if (copy_nodes(sub, graph, node_pred, data) < 0)
3611 return isl_stat_error;
3612 if (graph_init_table(ctx, sub) < 0)
3613 return isl_stat_error;
3614 for (t = 0; t <= isl_edge_last; ++t)
3615 sub->max_edge[t] = graph->max_edge[t];
3616 if (graph_init_edge_tables(ctx, sub) < 0)
3617 return isl_stat_error;
3618 if (copy_edges(ctx, sub, graph, edge_pred, data) < 0)
3619 return isl_stat_error;
3620 sub->n_row = graph->n_row;
3621 sub->max_row = graph->max_row;
3622 sub->n_total_row = graph->n_total_row;
3623 sub->band_start = graph->band_start;
3625 return isl_stat_ok;
3628 static __isl_give isl_schedule_node *compute_schedule(isl_schedule_node *node,
3629 struct isl_sched_graph *graph);
3630 static __isl_give isl_schedule_node *compute_schedule_wcc(
3631 isl_schedule_node *node, struct isl_sched_graph *graph);
3633 /* Compute a schedule for a subgraph of "graph". In particular, for
3634 * the graph composed of nodes that satisfy node_pred and edges that
3635 * that satisfy edge_pred.
3636 * If the subgraph is known to consist of a single component, then wcc should
3637 * be set and then we call compute_schedule_wcc on the constructed subgraph.
3638 * Otherwise, we call compute_schedule, which will check whether the subgraph
3639 * is connected.
3641 * The schedule is inserted at "node" and the updated schedule node
3642 * is returned.
3644 static __isl_give isl_schedule_node *compute_sub_schedule(
3645 __isl_take isl_schedule_node *node, isl_ctx *ctx,
3646 struct isl_sched_graph *graph,
3647 int (*node_pred)(struct isl_sched_node *node, int data),
3648 int (*edge_pred)(struct isl_sched_edge *edge, int data),
3649 int data, int wcc)
3651 struct isl_sched_graph split = { 0 };
3653 if (extract_sub_graph(ctx, graph, node_pred, edge_pred, data,
3654 &split) < 0)
3655 goto error;
3657 if (wcc)
3658 node = compute_schedule_wcc(node, &split);
3659 else
3660 node = compute_schedule(node, &split);
3662 graph_free(ctx, &split);
3663 return node;
3664 error:
3665 graph_free(ctx, &split);
3666 return isl_schedule_node_free(node);
3669 static int edge_scc_exactly(struct isl_sched_edge *edge, int scc)
3671 return edge->src->scc == scc && edge->dst->scc == scc;
3674 static int edge_dst_scc_at_most(struct isl_sched_edge *edge, int scc)
3676 return edge->dst->scc <= scc;
3679 static int edge_src_scc_at_least(struct isl_sched_edge *edge, int scc)
3681 return edge->src->scc >= scc;
3684 /* Reset the current band by dropping all its schedule rows.
3686 static isl_stat reset_band(struct isl_sched_graph *graph)
3688 int i;
3689 int drop;
3691 drop = graph->n_total_row - graph->band_start;
3692 graph->n_total_row -= drop;
3693 graph->n_row -= drop;
3695 for (i = 0; i < graph->n; ++i) {
3696 struct isl_sched_node *node = &graph->node[i];
3698 isl_map_free(node->sched_map);
3699 node->sched_map = NULL;
3701 node->sched = isl_mat_drop_rows(node->sched,
3702 graph->band_start, drop);
3704 if (!node->sched)
3705 return isl_stat_error;
3708 return isl_stat_ok;
3711 /* Split the current graph into two parts and compute a schedule for each
3712 * part individually. In particular, one part consists of all SCCs up
3713 * to and including graph->src_scc, while the other part contains the other
3714 * SCCs. The split is enforced by a sequence node inserted at position "node"
3715 * in the schedule tree. Return the updated schedule node.
3716 * If either of these two parts consists of a sequence, then it is spliced
3717 * into the sequence containing the two parts.
3719 * The current band is reset. It would be possible to reuse
3720 * the previously computed rows as the first rows in the next
3721 * band, but recomputing them may result in better rows as we are looking
3722 * at a smaller part of the dependence graph.
3724 static __isl_give isl_schedule_node *compute_split_schedule(
3725 __isl_take isl_schedule_node *node, struct isl_sched_graph *graph)
3727 int is_seq;
3728 isl_ctx *ctx;
3729 isl_union_set_list *filters;
3731 if (!node)
3732 return NULL;
3734 if (reset_band(graph) < 0)
3735 return isl_schedule_node_free(node);
3737 next_band(graph);
3739 ctx = isl_schedule_node_get_ctx(node);
3740 filters = extract_split(ctx, graph);
3741 node = isl_schedule_node_insert_sequence(node, filters);
3742 node = isl_schedule_node_child(node, 1);
3743 node = isl_schedule_node_child(node, 0);
3745 node = compute_sub_schedule(node, ctx, graph,
3746 &node_scc_at_least, &edge_src_scc_at_least,
3747 graph->src_scc + 1, 0);
3748 is_seq = isl_schedule_node_get_type(node) == isl_schedule_node_sequence;
3749 node = isl_schedule_node_parent(node);
3750 node = isl_schedule_node_parent(node);
3751 if (is_seq)
3752 node = isl_schedule_node_sequence_splice_child(node, 1);
3753 node = isl_schedule_node_child(node, 0);
3754 node = isl_schedule_node_child(node, 0);
3755 node = compute_sub_schedule(node, ctx, graph,
3756 &node_scc_at_most, &edge_dst_scc_at_most,
3757 graph->src_scc, 0);
3758 is_seq = isl_schedule_node_get_type(node) == isl_schedule_node_sequence;
3759 node = isl_schedule_node_parent(node);
3760 node = isl_schedule_node_parent(node);
3761 if (is_seq)
3762 node = isl_schedule_node_sequence_splice_child(node, 0);
3764 return node;
3767 /* Insert a band node at position "node" in the schedule tree corresponding
3768 * to the current band in "graph". Mark the band node permutable
3769 * if "permutable" is set.
3770 * The partial schedules and the coincidence property are extracted
3771 * from the graph nodes.
3772 * Return the updated schedule node.
3774 static __isl_give isl_schedule_node *insert_current_band(
3775 __isl_take isl_schedule_node *node, struct isl_sched_graph *graph,
3776 int permutable)
3778 int i;
3779 int start, end, n;
3780 isl_multi_aff *ma;
3781 isl_multi_pw_aff *mpa;
3782 isl_multi_union_pw_aff *mupa;
3784 if (!node)
3785 return NULL;
3787 if (graph->n < 1)
3788 isl_die(isl_schedule_node_get_ctx(node), isl_error_internal,
3789 "graph should have at least one node",
3790 return isl_schedule_node_free(node));
3792 start = graph->band_start;
3793 end = graph->n_total_row;
3794 n = end - start;
3796 ma = node_extract_partial_schedule_multi_aff(&graph->node[0], start, n);
3797 mpa = isl_multi_pw_aff_from_multi_aff(ma);
3798 mupa = isl_multi_union_pw_aff_from_multi_pw_aff(mpa);
3800 for (i = 1; i < graph->n; ++i) {
3801 isl_multi_union_pw_aff *mupa_i;
3803 ma = node_extract_partial_schedule_multi_aff(&graph->node[i],
3804 start, n);
3805 mpa = isl_multi_pw_aff_from_multi_aff(ma);
3806 mupa_i = isl_multi_union_pw_aff_from_multi_pw_aff(mpa);
3807 mupa = isl_multi_union_pw_aff_union_add(mupa, mupa_i);
3809 node = isl_schedule_node_insert_partial_schedule(node, mupa);
3811 for (i = 0; i < n; ++i)
3812 node = isl_schedule_node_band_member_set_coincident(node, i,
3813 graph->node[0].coincident[start + i]);
3814 node = isl_schedule_node_band_set_permutable(node, permutable);
3816 return node;
3819 /* Update the dependence relations based on the current schedule,
3820 * add the current band to "node" and then continue with the computation
3821 * of the next band.
3822 * Return the updated schedule node.
3824 static __isl_give isl_schedule_node *compute_next_band(
3825 __isl_take isl_schedule_node *node,
3826 struct isl_sched_graph *graph, int permutable)
3828 isl_ctx *ctx;
3830 if (!node)
3831 return NULL;
3833 ctx = isl_schedule_node_get_ctx(node);
3834 if (update_edges(ctx, graph) < 0)
3835 return isl_schedule_node_free(node);
3836 node = insert_current_band(node, graph, permutable);
3837 next_band(graph);
3839 node = isl_schedule_node_child(node, 0);
3840 node = compute_schedule(node, graph);
3841 node = isl_schedule_node_parent(node);
3843 return node;
3846 /* Add the constraints "coef" derived from an edge from "node" to itself
3847 * to graph->lp in order to respect the dependences and to try and carry them.
3848 * "pos" is the sequence number of the edge that needs to be carried.
3849 * "coef" represents general constraints on coefficients (c_0, c_x)
3850 * of valid constraints for (y - x) with x and y instances of the node.
3852 * The constraints added to graph->lp need to enforce
3854 * (c_j_0 + c_j_x y) - (c_j_0 + c_j_x x)
3855 * = c_j_x (y - x) >= e_i
3857 * for each (x,y) in the dependence relation of the edge.
3858 * That is, (-e_i, c_j_x) needs to be plugged in for (c_0, c_x),
3859 * taking into account that each coefficient in c_j_x is represented
3860 * as a pair of non-negative coefficients.
3862 static isl_stat add_intra_constraints(struct isl_sched_graph *graph,
3863 struct isl_sched_node *node, __isl_take isl_basic_set *coef, int pos)
3865 int offset;
3866 isl_ctx *ctx;
3867 isl_dim_map *dim_map;
3869 if (!coef)
3870 return isl_stat_error;
3872 ctx = isl_basic_set_get_ctx(coef);
3873 offset = coef_var_offset(coef);
3874 dim_map = intra_dim_map(ctx, graph, node, offset, 1);
3875 isl_dim_map_range(dim_map, 3 + pos, 0, 0, 0, 1, -1);
3876 graph->lp = add_constraints_dim_map(graph->lp, coef, dim_map);
3878 return isl_stat_ok;
3881 /* Add the constraints "coef" derived from an edge from "src" to "dst"
3882 * to graph->lp in order to respect the dependences and to try and carry them.
3883 * "pos" is the sequence number of the edge that needs to be carried or
3884 * -1 if no attempt should be made to carry the dependences.
3885 * "coef" represents general constraints on coefficients (c_0, c_n, c_x, c_y)
3886 * of valid constraints for (x, y) with x and y instances of "src" and "dst".
3888 * The constraints added to graph->lp need to enforce
3890 * (c_k_0 + c_k_n n + c_k_x y) - (c_j_0 + c_j_n n + c_j_x x) >= e_i
3892 * for each (x,y) in the dependence relation of the edge or
3894 * (c_k_0 + c_k_n n + c_k_x y) - (c_j_0 + c_j_n n + c_j_x x) >= 0
3896 * if pos is -1.
3897 * That is,
3898 * (-e_i + c_k_0 - c_j_0, c_k_n - c_j_n, -c_j_x, c_k_x)
3899 * or
3900 * (c_k_0 - c_j_0, c_k_n - c_j_n, -c_j_x, c_k_x)
3901 * needs to be plugged in for (c_0, c_n, c_x, c_y),
3902 * taking into account that each coefficient in c_j_x and c_k_x is represented
3903 * as a pair of non-negative coefficients.
3905 static isl_stat add_inter_constraints(struct isl_sched_graph *graph,
3906 struct isl_sched_node *src, struct isl_sched_node *dst,
3907 __isl_take isl_basic_set *coef, int pos)
3909 int offset;
3910 isl_ctx *ctx;
3911 isl_dim_map *dim_map;
3913 if (!coef)
3914 return isl_stat_error;
3916 ctx = isl_basic_set_get_ctx(coef);
3917 offset = coef_var_offset(coef);
3918 dim_map = inter_dim_map(ctx, graph, src, dst, offset, 1);
3919 if (pos >= 0)
3920 isl_dim_map_range(dim_map, 3 + pos, 0, 0, 0, 1, -1);
3921 graph->lp = add_constraints_dim_map(graph->lp, coef, dim_map);
3923 return isl_stat_ok;
3926 /* Data structure for keeping track of the data needed
3927 * to exploit non-trivial lineality spaces.
3929 * "any_non_trivial" is true if there are any non-trivial lineality spaces.
3930 * If "any_non_trivial" is not true, then "equivalent" and "mask" may be NULL.
3931 * "equivalent" connects instances to other instances on the same line(s).
3932 * "mask" contains the domain spaces of "equivalent".
3933 * Any instance set not in "mask" does not have a non-trivial lineality space.
3935 struct isl_exploit_lineality_data {
3936 isl_bool any_non_trivial;
3937 isl_union_map *equivalent;
3938 isl_union_set *mask;
3941 /* Data structure collecting information used during the construction
3942 * of an LP for carrying dependences.
3944 * "intra" is a sequence of coefficient constraints for intra-node edges.
3945 * "inter" is a sequence of coefficient constraints for inter-node edges.
3946 * "lineality" contains data used to exploit non-trivial lineality spaces.
3948 struct isl_carry {
3949 isl_basic_set_list *intra;
3950 isl_basic_set_list *inter;
3951 struct isl_exploit_lineality_data lineality;
3954 /* Free all the data stored in "carry".
3956 static void isl_carry_clear(struct isl_carry *carry)
3958 isl_basic_set_list_free(carry->intra);
3959 isl_basic_set_list_free(carry->inter);
3960 isl_union_map_free(carry->lineality.equivalent);
3961 isl_union_set_free(carry->lineality.mask);
3964 /* Return a pointer to the node in "graph" that lives in "space".
3965 * If the requested node has been compressed, then "space"
3966 * corresponds to the compressed space.
3967 * The graph is assumed to have such a node.
3968 * Return NULL in case of error.
3970 * First try and see if "space" is the space of an uncompressed node.
3971 * If so, return that node.
3972 * Otherwise, "space" was constructed by construct_compressed_id and
3973 * contains a user pointer pointing to the node in the tuple id.
3974 * However, this node belongs to the original dependence graph.
3975 * If "graph" is a subgraph of this original dependence graph,
3976 * then the node with the same space still needs to be looked up
3977 * in the current graph.
3979 static struct isl_sched_node *graph_find_compressed_node(isl_ctx *ctx,
3980 struct isl_sched_graph *graph, __isl_keep isl_space *space)
3982 isl_id *id;
3983 struct isl_sched_node *node;
3985 if (!space)
3986 return NULL;
3988 node = graph_find_node(ctx, graph, space);
3989 if (!node)
3990 return NULL;
3991 if (is_node(graph, node))
3992 return node;
3994 id = isl_space_get_tuple_id(space, isl_dim_set);
3995 node = isl_id_get_user(id);
3996 isl_id_free(id);
3998 if (!node)
3999 return NULL;
4001 if (!is_node(graph->root, node))
4002 isl_die(ctx, isl_error_internal,
4003 "space points to invalid node", return NULL);
4004 if (graph != graph->root)
4005 node = graph_find_node(ctx, graph, node->space);
4006 if (!is_node(graph, node))
4007 isl_die(ctx, isl_error_internal,
4008 "unable to find node", return NULL);
4010 return node;
4013 /* Internal data structure for add_all_constraints.
4015 * "graph" is the schedule constraint graph for which an LP problem
4016 * is being constructed.
4017 * "carry_inter" indicates whether inter-node edges should be carried.
4018 * "pos" is the position of the next edge that needs to be carried.
4020 struct isl_add_all_constraints_data {
4021 isl_ctx *ctx;
4022 struct isl_sched_graph *graph;
4023 int carry_inter;
4024 int pos;
4027 /* Add the constraints "coef" derived from an edge from a node to itself
4028 * to data->graph->lp in order to respect the dependences and
4029 * to try and carry them.
4031 * The space of "coef" is of the form
4033 * coefficients[[c_cst] -> S[c_x]]
4035 * with S[c_x] the (compressed) space of the node.
4036 * Extract the node from the space and call add_intra_constraints.
4038 static isl_stat lp_add_intra(__isl_take isl_basic_set *coef, void *user)
4040 struct isl_add_all_constraints_data *data = user;
4041 isl_space *space;
4042 struct isl_sched_node *node;
4044 space = isl_basic_set_get_space(coef);
4045 space = isl_space_range(isl_space_unwrap(space));
4046 node = graph_find_compressed_node(data->ctx, data->graph, space);
4047 isl_space_free(space);
4048 return add_intra_constraints(data->graph, node, coef, data->pos++);
4051 /* Add the constraints "coef" derived from an edge from a node j
4052 * to a node k to data->graph->lp in order to respect the dependences and
4053 * to try and carry them (provided data->carry_inter is set).
4055 * The space of "coef" is of the form
4057 * coefficients[[c_cst, c_n] -> [S_j[c_x] -> S_k[c_y]]]
4059 * with S_j[c_x] and S_k[c_y] the (compressed) spaces of the nodes.
4060 * Extract the nodes from the space and call add_inter_constraints.
4062 static isl_stat lp_add_inter(__isl_take isl_basic_set *coef, void *user)
4064 struct isl_add_all_constraints_data *data = user;
4065 isl_space *space, *dom;
4066 struct isl_sched_node *src, *dst;
4067 int pos;
4069 space = isl_basic_set_get_space(coef);
4070 space = isl_space_unwrap(isl_space_range(isl_space_unwrap(space)));
4071 dom = isl_space_domain(isl_space_copy(space));
4072 src = graph_find_compressed_node(data->ctx, data->graph, dom);
4073 isl_space_free(dom);
4074 space = isl_space_range(space);
4075 dst = graph_find_compressed_node(data->ctx, data->graph, space);
4076 isl_space_free(space);
4078 pos = data->carry_inter ? data->pos++ : -1;
4079 return add_inter_constraints(data->graph, src, dst, coef, pos);
4082 /* Add constraints to graph->lp that force all (conditional) validity
4083 * dependences to be respected and attempt to carry them.
4084 * "intra" is the sequence of coefficient constraints for intra-node edges.
4085 * "inter" is the sequence of coefficient constraints for inter-node edges.
4086 * "carry_inter" indicates whether inter-node edges should be carried or
4087 * only respected.
4089 static isl_stat add_all_constraints(isl_ctx *ctx, struct isl_sched_graph *graph,
4090 __isl_keep isl_basic_set_list *intra,
4091 __isl_keep isl_basic_set_list *inter, int carry_inter)
4093 struct isl_add_all_constraints_data data = { ctx, graph, carry_inter };
4095 data.pos = 0;
4096 if (isl_basic_set_list_foreach(intra, &lp_add_intra, &data) < 0)
4097 return isl_stat_error;
4098 if (isl_basic_set_list_foreach(inter, &lp_add_inter, &data) < 0)
4099 return isl_stat_error;
4100 return isl_stat_ok;
4103 /* Internal data structure for count_all_constraints
4104 * for keeping track of the number of equality and inequality constraints.
4106 struct isl_sched_count {
4107 int n_eq;
4108 int n_ineq;
4111 /* Add the number of equality and inequality constraints of "bset"
4112 * to data->n_eq and data->n_ineq.
4114 static isl_stat bset_update_count(__isl_take isl_basic_set *bset, void *user)
4116 struct isl_sched_count *data = user;
4118 return update_count(bset, 1, &data->n_eq, &data->n_ineq);
4121 /* Count the number of equality and inequality constraints
4122 * that will be added to the carry_lp problem.
4123 * We count each edge exactly once.
4124 * "intra" is the sequence of coefficient constraints for intra-node edges.
4125 * "inter" is the sequence of coefficient constraints for inter-node edges.
4127 static isl_stat count_all_constraints(__isl_keep isl_basic_set_list *intra,
4128 __isl_keep isl_basic_set_list *inter, int *n_eq, int *n_ineq)
4130 struct isl_sched_count data;
4132 data.n_eq = data.n_ineq = 0;
4133 if (isl_basic_set_list_foreach(inter, &bset_update_count, &data) < 0)
4134 return isl_stat_error;
4135 if (isl_basic_set_list_foreach(intra, &bset_update_count, &data) < 0)
4136 return isl_stat_error;
4138 *n_eq = data.n_eq;
4139 *n_ineq = data.n_ineq;
4141 return isl_stat_ok;
4144 /* Construct an LP problem for finding schedule coefficients
4145 * such that the schedule carries as many validity dependences as possible.
4146 * In particular, for each dependence i, we bound the dependence distance
4147 * from below by e_i, with 0 <= e_i <= 1 and then maximize the sum
4148 * of all e_i's. Dependences with e_i = 0 in the solution are simply
4149 * respected, while those with e_i > 0 (in practice e_i = 1) are carried.
4150 * "intra" is the sequence of coefficient constraints for intra-node edges.
4151 * "inter" is the sequence of coefficient constraints for inter-node edges.
4152 * "n_edge" is the total number of edges.
4153 * "carry_inter" indicates whether inter-node edges should be carried or
4154 * only respected. That is, if "carry_inter" is not set, then
4155 * no e_i variables are introduced for the inter-node edges.
4157 * All variables of the LP are non-negative. The actual coefficients
4158 * may be negative, so each coefficient is represented as the difference
4159 * of two non-negative variables. The negative part always appears
4160 * immediately before the positive part.
4161 * Other than that, the variables have the following order
4163 * - sum of (1 - e_i) over all edges
4164 * - sum of all c_n coefficients
4165 * (unconstrained when computing non-parametric schedules)
4166 * - sum of positive and negative parts of all c_x coefficients
4167 * - for each edge
4168 * - e_i
4169 * - for each node
4170 * - positive and negative parts of c_i_x, in opposite order
4171 * - c_i_n (if parametric)
4172 * - c_i_0
4174 * The constraints are those from the (validity) edges plus three equalities
4175 * to express the sums and n_edge inequalities to express e_i <= 1.
4177 static isl_stat setup_carry_lp(isl_ctx *ctx, struct isl_sched_graph *graph,
4178 int n_edge, __isl_keep isl_basic_set_list *intra,
4179 __isl_keep isl_basic_set_list *inter, int carry_inter)
4181 int i;
4182 int k;
4183 isl_space *dim;
4184 unsigned total;
4185 int n_eq, n_ineq;
4187 total = 3 + n_edge;
4188 for (i = 0; i < graph->n; ++i) {
4189 struct isl_sched_node *node = &graph->node[graph->sorted[i]];
4190 node->start = total;
4191 total += 1 + node->nparam + 2 * node->nvar;
4194 if (count_all_constraints(intra, inter, &n_eq, &n_ineq) < 0)
4195 return isl_stat_error;
4197 dim = isl_space_set_alloc(ctx, 0, total);
4198 isl_basic_set_free(graph->lp);
4199 n_eq += 3;
4200 n_ineq += n_edge;
4201 graph->lp = isl_basic_set_alloc_space(dim, 0, n_eq, n_ineq);
4202 graph->lp = isl_basic_set_set_rational(graph->lp);
4204 k = isl_basic_set_alloc_equality(graph->lp);
4205 if (k < 0)
4206 return isl_stat_error;
4207 isl_seq_clr(graph->lp->eq[k], 1 + total);
4208 isl_int_set_si(graph->lp->eq[k][0], -n_edge);
4209 isl_int_set_si(graph->lp->eq[k][1], 1);
4210 for (i = 0; i < n_edge; ++i)
4211 isl_int_set_si(graph->lp->eq[k][4 + i], 1);
4213 if (add_param_sum_constraint(graph, 1) < 0)
4214 return isl_stat_error;
4215 if (add_var_sum_constraint(graph, 2) < 0)
4216 return isl_stat_error;
4218 for (i = 0; i < n_edge; ++i) {
4219 k = isl_basic_set_alloc_inequality(graph->lp);
4220 if (k < 0)
4221 return isl_stat_error;
4222 isl_seq_clr(graph->lp->ineq[k], 1 + total);
4223 isl_int_set_si(graph->lp->ineq[k][4 + i], -1);
4224 isl_int_set_si(graph->lp->ineq[k][0], 1);
4227 if (add_all_constraints(ctx, graph, intra, inter, carry_inter) < 0)
4228 return isl_stat_error;
4230 return isl_stat_ok;
4233 static __isl_give isl_schedule_node *compute_component_schedule(
4234 __isl_take isl_schedule_node *node, struct isl_sched_graph *graph,
4235 int wcc);
4237 /* If the schedule_split_scaled option is set and if the linear
4238 * parts of the scheduling rows for all nodes in the graphs have
4239 * a non-trivial common divisor, then remove this
4240 * common divisor from the linear part.
4241 * Otherwise, insert a band node directly and continue with
4242 * the construction of the schedule.
4244 * If a non-trivial common divisor is found, then
4245 * the linear part is reduced and the remainder is ignored.
4246 * The pieces of the graph that are assigned different remainders
4247 * form (groups of) strongly connected components within
4248 * the scaled down band. If needed, they can therefore
4249 * be ordered along this remainder in a sequence node.
4250 * However, this ordering is not enforced here in order to allow
4251 * the scheduler to combine some of the strongly connected components.
4253 static __isl_give isl_schedule_node *split_scaled(
4254 __isl_take isl_schedule_node *node, struct isl_sched_graph *graph)
4256 int i;
4257 int row;
4258 isl_ctx *ctx;
4259 isl_int gcd, gcd_i;
4261 if (!node)
4262 return NULL;
4264 ctx = isl_schedule_node_get_ctx(node);
4265 if (!ctx->opt->schedule_split_scaled)
4266 return compute_next_band(node, graph, 0);
4267 if (graph->n <= 1)
4268 return compute_next_band(node, graph, 0);
4270 isl_int_init(gcd);
4271 isl_int_init(gcd_i);
4273 isl_int_set_si(gcd, 0);
4275 row = isl_mat_rows(graph->node[0].sched) - 1;
4277 for (i = 0; i < graph->n; ++i) {
4278 struct isl_sched_node *node = &graph->node[i];
4279 int cols = isl_mat_cols(node->sched);
4281 isl_seq_gcd(node->sched->row[row] + 1, cols - 1, &gcd_i);
4282 isl_int_gcd(gcd, gcd, gcd_i);
4285 isl_int_clear(gcd_i);
4287 if (isl_int_cmp_si(gcd, 1) <= 0) {
4288 isl_int_clear(gcd);
4289 return compute_next_band(node, graph, 0);
4292 for (i = 0; i < graph->n; ++i) {
4293 struct isl_sched_node *node = &graph->node[i];
4295 isl_int_fdiv_q(node->sched->row[row][0],
4296 node->sched->row[row][0], gcd);
4297 isl_int_mul(node->sched->row[row][0],
4298 node->sched->row[row][0], gcd);
4299 node->sched = isl_mat_scale_down_row(node->sched, row, gcd);
4300 if (!node->sched)
4301 goto error;
4304 isl_int_clear(gcd);
4306 return compute_next_band(node, graph, 0);
4307 error:
4308 isl_int_clear(gcd);
4309 return isl_schedule_node_free(node);
4312 /* Is the schedule row "sol" trivial on node "node"?
4313 * That is, is the solution zero on the dimensions linearly independent of
4314 * the previously found solutions?
4315 * Return 1 if the solution is trivial, 0 if it is not and -1 on error.
4317 * Each coefficient is represented as the difference between
4318 * two non-negative values in "sol".
4319 * We construct the schedule row s and check if it is linearly
4320 * independent of previously computed schedule rows
4321 * by computing T s, with T the linear combinations that are zero
4322 * on linearly dependent schedule rows.
4323 * If the result consists of all zeros, then the solution is trivial.
4325 static int is_trivial(struct isl_sched_node *node, __isl_keep isl_vec *sol)
4327 int trivial;
4328 isl_vec *node_sol;
4330 if (!sol)
4331 return -1;
4332 if (node->nvar == node->rank)
4333 return 0;
4335 node_sol = extract_var_coef(node, sol);
4336 node_sol = isl_mat_vec_product(isl_mat_copy(node->indep), node_sol);
4337 if (!node_sol)
4338 return -1;
4340 trivial = isl_seq_first_non_zero(node_sol->el,
4341 node->nvar - node->rank) == -1;
4343 isl_vec_free(node_sol);
4345 return trivial;
4348 /* Is the schedule row "sol" trivial on any node where it should
4349 * not be trivial?
4350 * Return 1 if any solution is trivial, 0 if they are not and -1 on error.
4352 static int is_any_trivial(struct isl_sched_graph *graph,
4353 __isl_keep isl_vec *sol)
4355 int i;
4357 for (i = 0; i < graph->n; ++i) {
4358 struct isl_sched_node *node = &graph->node[i];
4359 int trivial;
4361 if (!needs_row(graph, node))
4362 continue;
4363 trivial = is_trivial(node, sol);
4364 if (trivial < 0 || trivial)
4365 return trivial;
4368 return 0;
4371 /* Does the schedule represented by "sol" perform loop coalescing on "node"?
4372 * If so, return the position of the coalesced dimension.
4373 * Otherwise, return node->nvar or -1 on error.
4375 * In particular, look for pairs of coefficients c_i and c_j such that
4376 * |c_j/c_i| > ceil(size_i/2), i.e., |c_j| > |c_i * ceil(size_i/2)|.
4377 * If any such pair is found, then return i.
4378 * If size_i is infinity, then no check on c_i needs to be performed.
4380 static int find_node_coalescing(struct isl_sched_node *node,
4381 __isl_keep isl_vec *sol)
4383 int i, j;
4384 isl_int max;
4385 isl_vec *csol;
4387 if (node->nvar <= 1)
4388 return node->nvar;
4390 csol = extract_var_coef(node, sol);
4391 if (!csol)
4392 return -1;
4393 isl_int_init(max);
4394 for (i = 0; i < node->nvar; ++i) {
4395 isl_val *v;
4397 if (isl_int_is_zero(csol->el[i]))
4398 continue;
4399 v = isl_multi_val_get_val(node->sizes, i);
4400 if (!v)
4401 goto error;
4402 if (!isl_val_is_int(v)) {
4403 isl_val_free(v);
4404 continue;
4406 v = isl_val_div_ui(v, 2);
4407 v = isl_val_ceil(v);
4408 if (!v)
4409 goto error;
4410 isl_int_mul(max, v->n, csol->el[i]);
4411 isl_val_free(v);
4413 for (j = 0; j < node->nvar; ++j) {
4414 if (j == i)
4415 continue;
4416 if (isl_int_abs_gt(csol->el[j], max))
4417 break;
4419 if (j < node->nvar)
4420 break;
4423 isl_int_clear(max);
4424 isl_vec_free(csol);
4425 return i;
4426 error:
4427 isl_int_clear(max);
4428 isl_vec_free(csol);
4429 return -1;
4432 /* Force the schedule coefficient at position "pos" of "node" to be zero
4433 * in "tl".
4434 * The coefficient is encoded as the difference between two non-negative
4435 * variables. Force these two variables to have the same value.
4437 static __isl_give isl_tab_lexmin *zero_out_node_coef(
4438 __isl_take isl_tab_lexmin *tl, struct isl_sched_node *node, int pos)
4440 int dim;
4441 isl_ctx *ctx;
4442 isl_vec *eq;
4444 ctx = isl_space_get_ctx(node->space);
4445 dim = isl_tab_lexmin_dim(tl);
4446 if (dim < 0)
4447 return isl_tab_lexmin_free(tl);
4448 eq = isl_vec_alloc(ctx, 1 + dim);
4449 eq = isl_vec_clr(eq);
4450 if (!eq)
4451 return isl_tab_lexmin_free(tl);
4453 pos = 1 + node_var_coef_pos(node, pos);
4454 isl_int_set_si(eq->el[pos], 1);
4455 isl_int_set_si(eq->el[pos + 1], -1);
4456 tl = isl_tab_lexmin_add_eq(tl, eq->el);
4457 isl_vec_free(eq);
4459 return tl;
4462 /* Return the lexicographically smallest rational point in the basic set
4463 * from which "tl" was constructed, double checking that this input set
4464 * was not empty.
4466 static __isl_give isl_vec *non_empty_solution(__isl_keep isl_tab_lexmin *tl)
4468 isl_vec *sol;
4470 sol = isl_tab_lexmin_get_solution(tl);
4471 if (!sol)
4472 return NULL;
4473 if (sol->size == 0)
4474 isl_die(isl_vec_get_ctx(sol), isl_error_internal,
4475 "error in schedule construction",
4476 return isl_vec_free(sol));
4477 return sol;
4480 /* Does the solution "sol" of the LP problem constructed by setup_carry_lp
4481 * carry any of the "n_edge" groups of dependences?
4482 * The value in the first position is the sum of (1 - e_i) over all "n_edge"
4483 * edges, with 0 <= e_i <= 1 equal to 1 when the dependences represented
4484 * by the edge are carried by the solution.
4485 * If the sum of the (1 - e_i) is smaller than "n_edge" then at least
4486 * one of those is carried.
4488 * Note that despite the fact that the problem is solved using a rational
4489 * solver, the solution is guaranteed to be integral.
4490 * Specifically, the dependence distance lower bounds e_i (and therefore
4491 * also their sum) are integers. See Lemma 5 of [1].
4493 * Any potential denominator of the sum is cleared by this function.
4494 * The denominator is not relevant for any of the other elements
4495 * in the solution.
4497 * [1] P. Feautrier, Some Efficient Solutions to the Affine Scheduling
4498 * Problem, Part II: Multi-Dimensional Time.
4499 * In Intl. Journal of Parallel Programming, 1992.
4501 static int carries_dependences(__isl_keep isl_vec *sol, int n_edge)
4503 isl_int_divexact(sol->el[1], sol->el[1], sol->el[0]);
4504 isl_int_set_si(sol->el[0], 1);
4505 return isl_int_cmp_si(sol->el[1], n_edge) < 0;
4508 /* Return the lexicographically smallest rational point in "lp",
4509 * assuming that all variables are non-negative and performing some
4510 * additional sanity checks.
4511 * If "want_integral" is set, then compute the lexicographically smallest
4512 * integer point instead.
4513 * In particular, "lp" should not be empty by construction.
4514 * Double check that this is the case.
4515 * If dependences are not carried for any of the "n_edge" edges,
4516 * then return an empty vector.
4518 * If the schedule_treat_coalescing option is set and
4519 * if the computed schedule performs loop coalescing on a given node,
4520 * i.e., if it is of the form
4522 * c_i i + c_j j + ...
4524 * with |c_j/c_i| >= size_i, then force the coefficient c_i to be zero
4525 * to cut out this solution. Repeat this process until no more loop
4526 * coalescing occurs or until no more dependences can be carried.
4527 * In the latter case, revert to the previously computed solution.
4529 * If the caller requests an integral solution and if coalescing should
4530 * be treated, then perform the coalescing treatment first as
4531 * an integral solution computed before coalescing treatment
4532 * would carry the same number of edges and would therefore probably
4533 * also be coalescing.
4535 * To allow the coalescing treatment to be performed first,
4536 * the initial solution is allowed to be rational and it is only
4537 * cut out (if needed) in the next iteration, if no coalescing measures
4538 * were taken.
4540 static __isl_give isl_vec *non_neg_lexmin(struct isl_sched_graph *graph,
4541 __isl_take isl_basic_set *lp, int n_edge, int want_integral)
4543 int i, pos, cut;
4544 isl_ctx *ctx;
4545 isl_tab_lexmin *tl;
4546 isl_vec *sol = NULL, *prev;
4547 int treat_coalescing;
4548 int try_again;
4550 if (!lp)
4551 return NULL;
4552 ctx = isl_basic_set_get_ctx(lp);
4553 treat_coalescing = isl_options_get_schedule_treat_coalescing(ctx);
4554 tl = isl_tab_lexmin_from_basic_set(lp);
4556 cut = 0;
4557 do {
4558 int integral;
4560 try_again = 0;
4561 if (cut)
4562 tl = isl_tab_lexmin_cut_to_integer(tl);
4563 prev = sol;
4564 sol = non_empty_solution(tl);
4565 if (!sol)
4566 goto error;
4568 integral = isl_int_is_one(sol->el[0]);
4569 if (!carries_dependences(sol, n_edge)) {
4570 if (!prev)
4571 prev = isl_vec_alloc(ctx, 0);
4572 isl_vec_free(sol);
4573 sol = prev;
4574 break;
4576 prev = isl_vec_free(prev);
4577 cut = want_integral && !integral;
4578 if (cut)
4579 try_again = 1;
4580 if (!treat_coalescing)
4581 continue;
4582 for (i = 0; i < graph->n; ++i) {
4583 struct isl_sched_node *node = &graph->node[i];
4585 pos = find_node_coalescing(node, sol);
4586 if (pos < 0)
4587 goto error;
4588 if (pos < node->nvar)
4589 break;
4591 if (i < graph->n) {
4592 try_again = 1;
4593 tl = zero_out_node_coef(tl, &graph->node[i], pos);
4594 cut = 0;
4596 } while (try_again);
4598 isl_tab_lexmin_free(tl);
4600 return sol;
4601 error:
4602 isl_tab_lexmin_free(tl);
4603 isl_vec_free(prev);
4604 isl_vec_free(sol);
4605 return NULL;
4608 /* If "edge" is an edge from a node to itself, then add the corresponding
4609 * dependence relation to "umap".
4610 * If "node" has been compressed, then the dependence relation
4611 * is also compressed first.
4613 static __isl_give isl_union_map *add_intra(__isl_take isl_union_map *umap,
4614 struct isl_sched_edge *edge)
4616 isl_map *map;
4617 struct isl_sched_node *node = edge->src;
4619 if (edge->src != edge->dst)
4620 return umap;
4622 map = isl_map_copy(edge->map);
4623 if (node->compressed) {
4624 map = isl_map_preimage_domain_multi_aff(map,
4625 isl_multi_aff_copy(node->decompress));
4626 map = isl_map_preimage_range_multi_aff(map,
4627 isl_multi_aff_copy(node->decompress));
4629 umap = isl_union_map_add_map(umap, map);
4630 return umap;
4633 /* If "edge" is an edge from a node to another node, then add the corresponding
4634 * dependence relation to "umap".
4635 * If the source or destination nodes of "edge" have been compressed,
4636 * then the dependence relation is also compressed first.
4638 static __isl_give isl_union_map *add_inter(__isl_take isl_union_map *umap,
4639 struct isl_sched_edge *edge)
4641 isl_map *map;
4643 if (edge->src == edge->dst)
4644 return umap;
4646 map = isl_map_copy(edge->map);
4647 if (edge->src->compressed)
4648 map = isl_map_preimage_domain_multi_aff(map,
4649 isl_multi_aff_copy(edge->src->decompress));
4650 if (edge->dst->compressed)
4651 map = isl_map_preimage_range_multi_aff(map,
4652 isl_multi_aff_copy(edge->dst->decompress));
4653 umap = isl_union_map_add_map(umap, map);
4654 return umap;
4657 /* Internal data structure used by union_drop_coalescing_constraints
4658 * to collect bounds on all relevant statements.
4660 * "graph" is the schedule constraint graph for which an LP problem
4661 * is being constructed.
4662 * "bounds" collects the bounds.
4664 struct isl_collect_bounds_data {
4665 isl_ctx *ctx;
4666 struct isl_sched_graph *graph;
4667 isl_union_set *bounds;
4670 /* Add the size bounds for the node with instance deltas in "set"
4671 * to data->bounds.
4673 static isl_stat collect_bounds(__isl_take isl_set *set, void *user)
4675 struct isl_collect_bounds_data *data = user;
4676 struct isl_sched_node *node;
4677 isl_space *space;
4678 isl_set *bounds;
4680 space = isl_set_get_space(set);
4681 isl_set_free(set);
4683 node = graph_find_compressed_node(data->ctx, data->graph, space);
4684 isl_space_free(space);
4686 bounds = isl_set_from_basic_set(get_size_bounds(node));
4687 data->bounds = isl_union_set_add_set(data->bounds, bounds);
4689 return isl_stat_ok;
4692 /* Drop some constraints from "delta" that could be exploited
4693 * to construct loop coalescing schedules.
4694 * In particular, drop those constraint that bound the difference
4695 * to the size of the domain.
4696 * Do this for each set/node in "delta" separately.
4697 * The parameters are assumed to have been projected out by the caller.
4699 static __isl_give isl_union_set *union_drop_coalescing_constraints(isl_ctx *ctx,
4700 struct isl_sched_graph *graph, __isl_take isl_union_set *delta)
4702 struct isl_collect_bounds_data data = { ctx, graph };
4704 data.bounds = isl_union_set_empty(isl_space_params_alloc(ctx, 0));
4705 if (isl_union_set_foreach_set(delta, &collect_bounds, &data) < 0)
4706 data.bounds = isl_union_set_free(data.bounds);
4707 delta = isl_union_set_plain_gist(delta, data.bounds);
4709 return delta;
4712 /* Given a non-trivial lineality space "lineality", add the corresponding
4713 * universe set to data->mask and add a map from elements to
4714 * other elements along the lines in "lineality" to data->equivalent.
4715 * If this is the first time this function gets called
4716 * (data->any_non_trivial is still false), then set data->any_non_trivial and
4717 * initialize data->mask and data->equivalent.
4719 * In particular, if the lineality space is defined by equality constraints
4721 * E x = 0
4723 * then construct an affine mapping
4725 * f : x -> E x
4727 * and compute the equivalence relation of having the same image under f:
4729 * { x -> x' : E x = E x' }
4731 static isl_stat add_non_trivial_lineality(__isl_take isl_basic_set *lineality,
4732 struct isl_exploit_lineality_data *data)
4734 isl_mat *eq;
4735 isl_space *space;
4736 isl_set *univ;
4737 isl_multi_aff *ma;
4738 isl_multi_pw_aff *mpa;
4739 isl_map *map;
4740 int n;
4742 if (!lineality)
4743 return isl_stat_error;
4744 if (isl_basic_set_dim(lineality, isl_dim_div) != 0)
4745 isl_die(isl_basic_set_get_ctx(lineality), isl_error_internal,
4746 "local variables not allowed", goto error);
4748 space = isl_basic_set_get_space(lineality);
4749 if (!data->any_non_trivial) {
4750 data->equivalent = isl_union_map_empty(isl_space_copy(space));
4751 data->mask = isl_union_set_empty(isl_space_copy(space));
4753 data->any_non_trivial = isl_bool_true;
4755 univ = isl_set_universe(isl_space_copy(space));
4756 data->mask = isl_union_set_add_set(data->mask, univ);
4758 eq = isl_basic_set_extract_equalities(lineality);
4759 n = isl_mat_rows(eq);
4760 eq = isl_mat_insert_zero_rows(eq, 0, 1);
4761 eq = isl_mat_set_element_si(eq, 0, 0, 1);
4762 space = isl_space_from_domain(space);
4763 space = isl_space_add_dims(space, isl_dim_out, n);
4764 ma = isl_multi_aff_from_aff_mat(space, eq);
4765 mpa = isl_multi_pw_aff_from_multi_aff(ma);
4766 map = isl_multi_pw_aff_eq_map(mpa, isl_multi_pw_aff_copy(mpa));
4767 data->equivalent = isl_union_map_add_map(data->equivalent, map);
4769 isl_basic_set_free(lineality);
4770 return isl_stat_ok;
4771 error:
4772 isl_basic_set_free(lineality);
4773 return isl_stat_error;
4776 /* Check if the lineality space "set" is non-trivial (i.e., is not just
4777 * the origin or, in other words, satisfies a number of equality constraints
4778 * that is smaller than the dimension of the set).
4779 * If so, extend data->mask and data->equivalent accordingly.
4781 * The input should not have any local variables already, but
4782 * isl_set_remove_divs is called to make sure it does not.
4784 static isl_stat add_lineality(__isl_take isl_set *set, void *user)
4786 struct isl_exploit_lineality_data *data = user;
4787 isl_basic_set *hull;
4788 int dim, n_eq;
4790 set = isl_set_remove_divs(set);
4791 hull = isl_set_unshifted_simple_hull(set);
4792 dim = isl_basic_set_dim(hull, isl_dim_set);
4793 n_eq = isl_basic_set_n_equality(hull);
4794 if (!hull)
4795 return isl_stat_error;
4796 if (dim != n_eq)
4797 return add_non_trivial_lineality(hull, data);
4798 isl_basic_set_free(hull);
4799 return isl_stat_ok;
4802 /* Check if the difference set on intra-node schedule constraints "intra"
4803 * has any non-trivial lineality space.
4804 * If so, then extend the difference set to a difference set
4805 * on equivalent elements. That is, if "intra" is
4807 * { y - x : (x,y) \in V }
4809 * and elements are equivalent if they have the same image under f,
4810 * then return
4812 * { y' - x' : (x,y) \in V and f(x) = f(x') and f(y) = f(y') }
4814 * or, since f is linear,
4816 * { y' - x' : (x,y) \in V and f(y - x) = f(y' - x') }
4818 * The results of the search for non-trivial lineality spaces is stored
4819 * in "data".
4821 static __isl_give isl_union_set *exploit_intra_lineality(
4822 __isl_take isl_union_set *intra,
4823 struct isl_exploit_lineality_data *data)
4825 isl_union_set *lineality;
4826 isl_union_set *uset;
4828 data->any_non_trivial = isl_bool_false;
4829 lineality = isl_union_set_copy(intra);
4830 lineality = isl_union_set_combined_lineality_space(lineality);
4831 if (isl_union_set_foreach_set(lineality, &add_lineality, data) < 0)
4832 data->any_non_trivial = isl_bool_error;
4833 isl_union_set_free(lineality);
4835 if (data->any_non_trivial < 0)
4836 return isl_union_set_free(intra);
4837 if (!data->any_non_trivial)
4838 return intra;
4840 uset = isl_union_set_copy(intra);
4841 intra = isl_union_set_subtract(intra, isl_union_set_copy(data->mask));
4842 uset = isl_union_set_apply(uset, isl_union_map_copy(data->equivalent));
4843 intra = isl_union_set_union(intra, uset);
4845 intra = isl_union_set_remove_divs(intra);
4847 return intra;
4850 /* If the difference set on intra-node schedule constraints was found to have
4851 * any non-trivial lineality space by exploit_intra_lineality,
4852 * as recorded in "data", then extend the inter-node
4853 * schedule constraints "inter" to schedule constraints on equivalent elements.
4854 * That is, if "inter" is V and
4855 * elements are equivalent if they have the same image under f, then return
4857 * { (x', y') : (x,y) \in V and f(x) = f(x') and f(y) = f(y') }
4859 static __isl_give isl_union_map *exploit_inter_lineality(
4860 __isl_take isl_union_map *inter,
4861 struct isl_exploit_lineality_data *data)
4863 isl_union_map *umap;
4865 if (data->any_non_trivial < 0)
4866 return isl_union_map_free(inter);
4867 if (!data->any_non_trivial)
4868 return inter;
4870 umap = isl_union_map_copy(inter);
4871 inter = isl_union_map_subtract_range(inter,
4872 isl_union_set_copy(data->mask));
4873 umap = isl_union_map_apply_range(umap,
4874 isl_union_map_copy(data->equivalent));
4875 inter = isl_union_map_union(inter, umap);
4876 umap = isl_union_map_copy(inter);
4877 inter = isl_union_map_subtract_domain(inter,
4878 isl_union_set_copy(data->mask));
4879 umap = isl_union_map_apply_range(isl_union_map_copy(data->equivalent),
4880 umap);
4881 inter = isl_union_map_union(inter, umap);
4883 inter = isl_union_map_remove_divs(inter);
4885 return inter;
4888 /* For each (conditional) validity edge in "graph",
4889 * add the corresponding dependence relation using "add"
4890 * to a collection of dependence relations and return the result.
4891 * If "coincidence" is set, then coincidence edges are considered as well.
4893 static __isl_give isl_union_map *collect_validity(struct isl_sched_graph *graph,
4894 __isl_give isl_union_map *(*add)(__isl_take isl_union_map *umap,
4895 struct isl_sched_edge *edge), int coincidence)
4897 int i;
4898 isl_space *space;
4899 isl_union_map *umap;
4901 space = isl_space_copy(graph->node[0].space);
4902 umap = isl_union_map_empty(space);
4904 for (i = 0; i < graph->n_edge; ++i) {
4905 struct isl_sched_edge *edge = &graph->edge[i];
4907 if (!is_any_validity(edge) &&
4908 (!coincidence || !is_coincidence(edge)))
4909 continue;
4911 umap = add(umap, edge);
4914 return umap;
4917 /* Project out all parameters from "uset" and return the result.
4919 static __isl_give isl_union_set *union_set_drop_parameters(
4920 __isl_take isl_union_set *uset)
4922 unsigned nparam;
4924 nparam = isl_union_set_dim(uset, isl_dim_param);
4925 return isl_union_set_project_out(uset, isl_dim_param, 0, nparam);
4928 /* For each dependence relation on a (conditional) validity edge
4929 * from a node to itself,
4930 * construct the set of coefficients of valid constraints for elements
4931 * in that dependence relation and collect the results.
4932 * If "coincidence" is set, then coincidence edges are considered as well.
4934 * In particular, for each dependence relation R, constraints
4935 * on coefficients (c_0, c_x) are constructed such that
4937 * c_0 + c_x d >= 0 for each d in delta R = { y - x | (x,y) in R }
4939 * If the schedule_treat_coalescing option is set, then some constraints
4940 * that could be exploited to construct coalescing schedules
4941 * are removed before the dual is computed, but after the parameters
4942 * have been projected out.
4943 * The entire computation is essentially the same as that performed
4944 * by intra_coefficients, except that it operates on multiple
4945 * edges together and that the parameters are always projected out.
4947 * Additionally, exploit any non-trivial lineality space
4948 * in the difference set after removing coalescing constraints and
4949 * store the results of the non-trivial lineality space detection in "data".
4950 * The procedure is currently run unconditionally, but it is unlikely
4951 * to find any non-trivial lineality spaces if no coalescing constraints
4952 * have been removed.
4954 * Note that if a dependence relation is a union of basic maps,
4955 * then each basic map needs to be treated individually as it may only
4956 * be possible to carry the dependences expressed by some of those
4957 * basic maps and not all of them.
4958 * The collected validity constraints are therefore not coalesced and
4959 * it is assumed that they are not coalesced automatically.
4960 * Duplicate basic maps can be removed, however.
4961 * In particular, if the same basic map appears as a disjunct
4962 * in multiple edges, then it only needs to be carried once.
4964 static __isl_give isl_basic_set_list *collect_intra_validity(isl_ctx *ctx,
4965 struct isl_sched_graph *graph, int coincidence,
4966 struct isl_exploit_lineality_data *data)
4968 isl_union_map *intra;
4969 isl_union_set *delta;
4970 isl_basic_set_list *list;
4972 intra = collect_validity(graph, &add_intra, coincidence);
4973 delta = isl_union_map_deltas(intra);
4974 delta = union_set_drop_parameters(delta);
4975 delta = isl_union_set_remove_divs(delta);
4976 if (isl_options_get_schedule_treat_coalescing(ctx))
4977 delta = union_drop_coalescing_constraints(ctx, graph, delta);
4978 delta = exploit_intra_lineality(delta, data);
4979 list = isl_union_set_get_basic_set_list(delta);
4980 isl_union_set_free(delta);
4982 return isl_basic_set_list_coefficients(list);
4985 /* For each dependence relation on a (conditional) validity edge
4986 * from a node to some other node,
4987 * construct the set of coefficients of valid constraints for elements
4988 * in that dependence relation and collect the results.
4989 * If "coincidence" is set, then coincidence edges are considered as well.
4991 * In particular, for each dependence relation R, constraints
4992 * on coefficients (c_0, c_n, c_x, c_y) are constructed such that
4994 * c_0 + c_n n + c_x x + c_y y >= 0 for each (x,y) in R
4996 * This computation is essentially the same as that performed
4997 * by inter_coefficients, except that it operates on multiple
4998 * edges together.
5000 * Additionally, exploit any non-trivial lineality space
5001 * that may have been discovered by collect_intra_validity
5002 * (as stored in "data").
5004 * Note that if a dependence relation is a union of basic maps,
5005 * then each basic map needs to be treated individually as it may only
5006 * be possible to carry the dependences expressed by some of those
5007 * basic maps and not all of them.
5008 * The collected validity constraints are therefore not coalesced and
5009 * it is assumed that they are not coalesced automatically.
5010 * Duplicate basic maps can be removed, however.
5011 * In particular, if the same basic map appears as a disjunct
5012 * in multiple edges, then it only needs to be carried once.
5014 static __isl_give isl_basic_set_list *collect_inter_validity(
5015 struct isl_sched_graph *graph, int coincidence,
5016 struct isl_exploit_lineality_data *data)
5018 isl_union_map *inter;
5019 isl_union_set *wrap;
5020 isl_basic_set_list *list;
5022 inter = collect_validity(graph, &add_inter, coincidence);
5023 inter = exploit_inter_lineality(inter, data);
5024 inter = isl_union_map_remove_divs(inter);
5025 wrap = isl_union_map_wrap(inter);
5026 list = isl_union_set_get_basic_set_list(wrap);
5027 isl_union_set_free(wrap);
5028 return isl_basic_set_list_coefficients(list);
5031 /* Construct an LP problem for finding schedule coefficients
5032 * such that the schedule carries as many of the "n_edge" groups of
5033 * dependences as possible based on the corresponding coefficient
5034 * constraints and return the lexicographically smallest non-trivial solution.
5035 * "intra" is the sequence of coefficient constraints for intra-node edges.
5036 * "inter" is the sequence of coefficient constraints for inter-node edges.
5037 * If "want_integral" is set, then compute an integral solution
5038 * for the coefficients rather than using the numerators
5039 * of a rational solution.
5040 * "carry_inter" indicates whether inter-node edges should be carried or
5041 * only respected.
5043 * If none of the "n_edge" groups can be carried
5044 * then return an empty vector.
5046 static __isl_give isl_vec *compute_carrying_sol_coef(isl_ctx *ctx,
5047 struct isl_sched_graph *graph, int n_edge,
5048 __isl_keep isl_basic_set_list *intra,
5049 __isl_keep isl_basic_set_list *inter, int want_integral,
5050 int carry_inter)
5052 isl_basic_set *lp;
5054 if (setup_carry_lp(ctx, graph, n_edge, intra, inter, carry_inter) < 0)
5055 return NULL;
5057 lp = isl_basic_set_copy(graph->lp);
5058 return non_neg_lexmin(graph, lp, n_edge, want_integral);
5061 /* Construct an LP problem for finding schedule coefficients
5062 * such that the schedule carries as many of the validity dependences
5063 * as possible and
5064 * return the lexicographically smallest non-trivial solution.
5065 * If "fallback" is set, then the carrying is performed as a fallback
5066 * for the Pluto-like scheduler.
5067 * If "coincidence" is set, then try and carry coincidence edges as well.
5069 * The variable "n_edge" stores the number of groups that should be carried.
5070 * If none of the "n_edge" groups can be carried
5071 * then return an empty vector.
5072 * If, moreover, "n_edge" is zero, then the LP problem does not even
5073 * need to be constructed.
5075 * If a fallback solution is being computed, then compute an integral solution
5076 * for the coefficients rather than using the numerators
5077 * of a rational solution.
5079 * If a fallback solution is being computed, if there are any intra-node
5080 * dependences, and if requested by the user, then first try
5081 * to only carry those intra-node dependences.
5082 * If this fails to carry any dependences, then try again
5083 * with the inter-node dependences included.
5085 static __isl_give isl_vec *compute_carrying_sol(isl_ctx *ctx,
5086 struct isl_sched_graph *graph, int fallback, int coincidence)
5088 int n_intra, n_inter;
5089 int n_edge;
5090 struct isl_carry carry = { 0 };
5091 isl_vec *sol;
5093 carry.intra = collect_intra_validity(ctx, graph, coincidence,
5094 &carry.lineality);
5095 carry.inter = collect_inter_validity(graph, coincidence,
5096 &carry.lineality);
5097 if (!carry.intra || !carry.inter)
5098 goto error;
5099 n_intra = isl_basic_set_list_n_basic_set(carry.intra);
5100 n_inter = isl_basic_set_list_n_basic_set(carry.inter);
5102 if (fallback && n_intra > 0 &&
5103 isl_options_get_schedule_carry_self_first(ctx)) {
5104 sol = compute_carrying_sol_coef(ctx, graph, n_intra,
5105 carry.intra, carry.inter, fallback, 0);
5106 if (!sol || sol->size != 0 || n_inter == 0) {
5107 isl_carry_clear(&carry);
5108 return sol;
5110 isl_vec_free(sol);
5113 n_edge = n_intra + n_inter;
5114 if (n_edge == 0) {
5115 isl_carry_clear(&carry);
5116 return isl_vec_alloc(ctx, 0);
5119 sol = compute_carrying_sol_coef(ctx, graph, n_edge,
5120 carry.intra, carry.inter, fallback, 1);
5121 isl_carry_clear(&carry);
5122 return sol;
5123 error:
5124 isl_carry_clear(&carry);
5125 return NULL;
5128 /* Construct a schedule row for each node such that as many validity dependences
5129 * as possible are carried and then continue with the next band.
5130 * If "fallback" is set, then the carrying is performed as a fallback
5131 * for the Pluto-like scheduler.
5132 * If "coincidence" is set, then try and carry coincidence edges as well.
5134 * If there are no validity dependences, then no dependence can be carried and
5135 * the procedure is guaranteed to fail. If there is more than one component,
5136 * then try computing a schedule on each component separately
5137 * to prevent or at least postpone this failure.
5139 * If a schedule row is computed, then check that dependences are carried
5140 * for at least one of the edges.
5142 * If the computed schedule row turns out to be trivial on one or
5143 * more nodes where it should not be trivial, then we throw it away
5144 * and try again on each component separately.
5146 * If there is only one component, then we accept the schedule row anyway,
5147 * but we do not consider it as a complete row and therefore do not
5148 * increment graph->n_row. Note that the ranks of the nodes that
5149 * do get a non-trivial schedule part will get updated regardless and
5150 * graph->maxvar is computed based on these ranks. The test for
5151 * whether more schedule rows are required in compute_schedule_wcc
5152 * is therefore not affected.
5154 * Insert a band corresponding to the schedule row at position "node"
5155 * of the schedule tree and continue with the construction of the schedule.
5156 * This insertion and the continued construction is performed by split_scaled
5157 * after optionally checking for non-trivial common divisors.
5159 static __isl_give isl_schedule_node *carry(__isl_take isl_schedule_node *node,
5160 struct isl_sched_graph *graph, int fallback, int coincidence)
5162 int trivial;
5163 isl_ctx *ctx;
5164 isl_vec *sol;
5166 if (!node)
5167 return NULL;
5169 ctx = isl_schedule_node_get_ctx(node);
5170 sol = compute_carrying_sol(ctx, graph, fallback, coincidence);
5171 if (!sol)
5172 return isl_schedule_node_free(node);
5173 if (sol->size == 0) {
5174 isl_vec_free(sol);
5175 if (graph->scc > 1)
5176 return compute_component_schedule(node, graph, 1);
5177 isl_die(ctx, isl_error_unknown, "unable to carry dependences",
5178 return isl_schedule_node_free(node));
5181 trivial = is_any_trivial(graph, sol);
5182 if (trivial < 0) {
5183 sol = isl_vec_free(sol);
5184 } else if (trivial && graph->scc > 1) {
5185 isl_vec_free(sol);
5186 return compute_component_schedule(node, graph, 1);
5189 if (update_schedule(graph, sol, 0) < 0)
5190 return isl_schedule_node_free(node);
5191 if (trivial)
5192 graph->n_row--;
5194 return split_scaled(node, graph);
5197 /* Construct a schedule row for each node such that as many validity dependences
5198 * as possible are carried and then continue with the next band.
5199 * Do so as a fallback for the Pluto-like scheduler.
5200 * If "coincidence" is set, then try and carry coincidence edges as well.
5202 static __isl_give isl_schedule_node *carry_fallback(
5203 __isl_take isl_schedule_node *node, struct isl_sched_graph *graph,
5204 int coincidence)
5206 return carry(node, graph, 1, coincidence);
5209 /* Construct a schedule row for each node such that as many validity dependences
5210 * as possible are carried and then continue with the next band.
5211 * Do so for the case where the Feautrier scheduler was selected
5212 * by the user.
5214 static __isl_give isl_schedule_node *carry_feautrier(
5215 __isl_take isl_schedule_node *node, struct isl_sched_graph *graph)
5217 return carry(node, graph, 0, 0);
5220 /* Construct a schedule row for each node such that as many validity dependences
5221 * as possible are carried and then continue with the next band.
5222 * Do so as a fallback for the Pluto-like scheduler.
5224 static __isl_give isl_schedule_node *carry_dependences(
5225 __isl_take isl_schedule_node *node, struct isl_sched_graph *graph)
5227 return carry_fallback(node, graph, 0);
5230 /* Construct a schedule row for each node such that as many validity or
5231 * coincidence dependences as possible are carried and
5232 * then continue with the next band.
5233 * Do so as a fallback for the Pluto-like scheduler.
5235 static __isl_give isl_schedule_node *carry_coincidence(
5236 __isl_take isl_schedule_node *node, struct isl_sched_graph *graph)
5238 return carry_fallback(node, graph, 1);
5241 /* Topologically sort statements mapped to the same schedule iteration
5242 * and add insert a sequence node in front of "node"
5243 * corresponding to this order.
5244 * If "initialized" is set, then it may be assumed that compute_maxvar
5245 * has been called on the current band. Otherwise, call
5246 * compute_maxvar if and before carry_dependences gets called.
5248 * If it turns out to be impossible to sort the statements apart,
5249 * because different dependences impose different orderings
5250 * on the statements, then we extend the schedule such that
5251 * it carries at least one more dependence.
5253 static __isl_give isl_schedule_node *sort_statements(
5254 __isl_take isl_schedule_node *node, struct isl_sched_graph *graph,
5255 int initialized)
5257 isl_ctx *ctx;
5258 isl_union_set_list *filters;
5260 if (!node)
5261 return NULL;
5263 ctx = isl_schedule_node_get_ctx(node);
5264 if (graph->n < 1)
5265 isl_die(ctx, isl_error_internal,
5266 "graph should have at least one node",
5267 return isl_schedule_node_free(node));
5269 if (graph->n == 1)
5270 return node;
5272 if (update_edges(ctx, graph) < 0)
5273 return isl_schedule_node_free(node);
5275 if (graph->n_edge == 0)
5276 return node;
5278 if (detect_sccs(ctx, graph) < 0)
5279 return isl_schedule_node_free(node);
5281 next_band(graph);
5282 if (graph->scc < graph->n) {
5283 if (!initialized && compute_maxvar(graph) < 0)
5284 return isl_schedule_node_free(node);
5285 return carry_dependences(node, graph);
5288 filters = extract_sccs(ctx, graph);
5289 node = isl_schedule_node_insert_sequence(node, filters);
5291 return node;
5294 /* Are there any (non-empty) (conditional) validity edges in the graph?
5296 static int has_validity_edges(struct isl_sched_graph *graph)
5298 int i;
5300 for (i = 0; i < graph->n_edge; ++i) {
5301 int empty;
5303 empty = isl_map_plain_is_empty(graph->edge[i].map);
5304 if (empty < 0)
5305 return -1;
5306 if (empty)
5307 continue;
5308 if (is_any_validity(&graph->edge[i]))
5309 return 1;
5312 return 0;
5315 /* Should we apply a Feautrier step?
5316 * That is, did the user request the Feautrier algorithm and are
5317 * there any validity dependences (left)?
5319 static int need_feautrier_step(isl_ctx *ctx, struct isl_sched_graph *graph)
5321 if (ctx->opt->schedule_algorithm != ISL_SCHEDULE_ALGORITHM_FEAUTRIER)
5322 return 0;
5324 return has_validity_edges(graph);
5327 /* Compute a schedule for a connected dependence graph using Feautrier's
5328 * multi-dimensional scheduling algorithm and return the updated schedule node.
5330 * The original algorithm is described in [1].
5331 * The main idea is to minimize the number of scheduling dimensions, by
5332 * trying to satisfy as many dependences as possible per scheduling dimension.
5334 * [1] P. Feautrier, Some Efficient Solutions to the Affine Scheduling
5335 * Problem, Part II: Multi-Dimensional Time.
5336 * In Intl. Journal of Parallel Programming, 1992.
5338 static __isl_give isl_schedule_node *compute_schedule_wcc_feautrier(
5339 isl_schedule_node *node, struct isl_sched_graph *graph)
5341 return carry_feautrier(node, graph);
5344 /* Turn off the "local" bit on all (condition) edges.
5346 static void clear_local_edges(struct isl_sched_graph *graph)
5348 int i;
5350 for (i = 0; i < graph->n_edge; ++i)
5351 if (is_condition(&graph->edge[i]))
5352 clear_local(&graph->edge[i]);
5355 /* Does "graph" have both condition and conditional validity edges?
5357 static int need_condition_check(struct isl_sched_graph *graph)
5359 int i;
5360 int any_condition = 0;
5361 int any_conditional_validity = 0;
5363 for (i = 0; i < graph->n_edge; ++i) {
5364 if (is_condition(&graph->edge[i]))
5365 any_condition = 1;
5366 if (is_conditional_validity(&graph->edge[i]))
5367 any_conditional_validity = 1;
5370 return any_condition && any_conditional_validity;
5373 /* Does "graph" contain any coincidence edge?
5375 static int has_any_coincidence(struct isl_sched_graph *graph)
5377 int i;
5379 for (i = 0; i < graph->n_edge; ++i)
5380 if (is_coincidence(&graph->edge[i]))
5381 return 1;
5383 return 0;
5386 /* Extract the final schedule row as a map with the iteration domain
5387 * of "node" as domain.
5389 static __isl_give isl_map *final_row(struct isl_sched_node *node)
5391 isl_multi_aff *ma;
5392 int row;
5394 row = isl_mat_rows(node->sched) - 1;
5395 ma = node_extract_partial_schedule_multi_aff(node, row, 1);
5396 return isl_map_from_multi_aff(ma);
5399 /* Is the conditional validity dependence in the edge with index "edge_index"
5400 * violated by the latest (i.e., final) row of the schedule?
5401 * That is, is i scheduled after j
5402 * for any conditional validity dependence i -> j?
5404 static int is_violated(struct isl_sched_graph *graph, int edge_index)
5406 isl_map *src_sched, *dst_sched, *map;
5407 struct isl_sched_edge *edge = &graph->edge[edge_index];
5408 int empty;
5410 src_sched = final_row(edge->src);
5411 dst_sched = final_row(edge->dst);
5412 map = isl_map_copy(edge->map);
5413 map = isl_map_apply_domain(map, src_sched);
5414 map = isl_map_apply_range(map, dst_sched);
5415 map = isl_map_order_gt(map, isl_dim_in, 0, isl_dim_out, 0);
5416 empty = isl_map_is_empty(map);
5417 isl_map_free(map);
5419 if (empty < 0)
5420 return -1;
5422 return !empty;
5425 /* Does "graph" have any satisfied condition edges that
5426 * are adjacent to the conditional validity constraint with
5427 * domain "conditional_source" and range "conditional_sink"?
5429 * A satisfied condition is one that is not local.
5430 * If a condition was forced to be local already (i.e., marked as local)
5431 * then there is no need to check if it is in fact local.
5433 * Additionally, mark all adjacent condition edges found as local.
5435 static int has_adjacent_true_conditions(struct isl_sched_graph *graph,
5436 __isl_keep isl_union_set *conditional_source,
5437 __isl_keep isl_union_set *conditional_sink)
5439 int i;
5440 int any = 0;
5442 for (i = 0; i < graph->n_edge; ++i) {
5443 int adjacent, local;
5444 isl_union_map *condition;
5446 if (!is_condition(&graph->edge[i]))
5447 continue;
5448 if (is_local(&graph->edge[i]))
5449 continue;
5451 condition = graph->edge[i].tagged_condition;
5452 adjacent = domain_intersects(condition, conditional_sink);
5453 if (adjacent >= 0 && !adjacent)
5454 adjacent = range_intersects(condition,
5455 conditional_source);
5456 if (adjacent < 0)
5457 return -1;
5458 if (!adjacent)
5459 continue;
5461 set_local(&graph->edge[i]);
5463 local = is_condition_false(&graph->edge[i]);
5464 if (local < 0)
5465 return -1;
5466 if (!local)
5467 any = 1;
5470 return any;
5473 /* Are there any violated conditional validity dependences with
5474 * adjacent condition dependences that are not local with respect
5475 * to the current schedule?
5476 * That is, is the conditional validity constraint violated?
5478 * Additionally, mark all those adjacent condition dependences as local.
5479 * We also mark those adjacent condition dependences that were not marked
5480 * as local before, but just happened to be local already. This ensures
5481 * that they remain local if the schedule is recomputed.
5483 * We first collect domain and range of all violated conditional validity
5484 * dependences and then check if there are any adjacent non-local
5485 * condition dependences.
5487 static int has_violated_conditional_constraint(isl_ctx *ctx,
5488 struct isl_sched_graph *graph)
5490 int i;
5491 int any = 0;
5492 isl_union_set *source, *sink;
5494 source = isl_union_set_empty(isl_space_params_alloc(ctx, 0));
5495 sink = isl_union_set_empty(isl_space_params_alloc(ctx, 0));
5496 for (i = 0; i < graph->n_edge; ++i) {
5497 isl_union_set *uset;
5498 isl_union_map *umap;
5499 int violated;
5501 if (!is_conditional_validity(&graph->edge[i]))
5502 continue;
5504 violated = is_violated(graph, i);
5505 if (violated < 0)
5506 goto error;
5507 if (!violated)
5508 continue;
5510 any = 1;
5512 umap = isl_union_map_copy(graph->edge[i].tagged_validity);
5513 uset = isl_union_map_domain(umap);
5514 source = isl_union_set_union(source, uset);
5515 source = isl_union_set_coalesce(source);
5517 umap = isl_union_map_copy(graph->edge[i].tagged_validity);
5518 uset = isl_union_map_range(umap);
5519 sink = isl_union_set_union(sink, uset);
5520 sink = isl_union_set_coalesce(sink);
5523 if (any)
5524 any = has_adjacent_true_conditions(graph, source, sink);
5526 isl_union_set_free(source);
5527 isl_union_set_free(sink);
5528 return any;
5529 error:
5530 isl_union_set_free(source);
5531 isl_union_set_free(sink);
5532 return -1;
5535 /* Examine the current band (the rows between graph->band_start and
5536 * graph->n_total_row), deciding whether to drop it or add it to "node"
5537 * and then continue with the computation of the next band, if any.
5538 * If "initialized" is set, then it may be assumed that compute_maxvar
5539 * has been called on the current band. Otherwise, call
5540 * compute_maxvar if and before carry_dependences gets called.
5542 * The caller keeps looking for a new row as long as
5543 * graph->n_row < graph->maxvar. If the latest attempt to find
5544 * such a row failed (i.e., we still have graph->n_row < graph->maxvar),
5545 * then we either
5546 * - split between SCCs and start over (assuming we found an interesting
5547 * pair of SCCs between which to split)
5548 * - continue with the next band (assuming the current band has at least
5549 * one row)
5550 * - if there is more than one SCC left, then split along all SCCs
5551 * - if outer coincidence needs to be enforced, then try to carry as many
5552 * validity or coincidence dependences as possible and
5553 * continue with the next band
5554 * - try to carry as many validity dependences as possible and
5555 * continue with the next band
5556 * In each case, we first insert a band node in the schedule tree
5557 * if any rows have been computed.
5559 * If the caller managed to complete the schedule and the current band
5560 * is empty, then finish off by topologically
5561 * sorting the statements based on the remaining dependences.
5562 * If, on the other hand, the current band has at least one row,
5563 * then continue with the next band. Note that this next band
5564 * will necessarily be empty, but the graph may still be split up
5565 * into weakly connected components before arriving back here.
5567 static __isl_give isl_schedule_node *compute_schedule_finish_band(
5568 __isl_take isl_schedule_node *node, struct isl_sched_graph *graph,
5569 int initialized)
5571 int empty;
5573 if (!node)
5574 return NULL;
5576 empty = graph->n_total_row == graph->band_start;
5577 if (graph->n_row < graph->maxvar) {
5578 isl_ctx *ctx;
5580 ctx = isl_schedule_node_get_ctx(node);
5581 if (!ctx->opt->schedule_maximize_band_depth && !empty)
5582 return compute_next_band(node, graph, 1);
5583 if (graph->src_scc >= 0)
5584 return compute_split_schedule(node, graph);
5585 if (!empty)
5586 return compute_next_band(node, graph, 1);
5587 if (graph->scc > 1)
5588 return compute_component_schedule(node, graph, 1);
5589 if (!initialized && compute_maxvar(graph) < 0)
5590 return isl_schedule_node_free(node);
5591 if (isl_options_get_schedule_outer_coincidence(ctx))
5592 return carry_coincidence(node, graph);
5593 return carry_dependences(node, graph);
5596 if (!empty)
5597 return compute_next_band(node, graph, 1);
5598 return sort_statements(node, graph, initialized);
5601 /* Construct a band of schedule rows for a connected dependence graph.
5602 * The caller is responsible for determining the strongly connected
5603 * components and calling compute_maxvar first.
5605 * We try to find a sequence of as many schedule rows as possible that result
5606 * in non-negative dependence distances (independent of the previous rows
5607 * in the sequence, i.e., such that the sequence is tilable), with as
5608 * many of the initial rows as possible satisfying the coincidence constraints.
5609 * The computation stops if we can't find any more rows or if we have found
5610 * all the rows we wanted to find.
5612 * If ctx->opt->schedule_outer_coincidence is set, then we force the
5613 * outermost dimension to satisfy the coincidence constraints. If this
5614 * turns out to be impossible, we fall back on the general scheme above
5615 * and try to carry as many dependences as possible.
5617 * If "graph" contains both condition and conditional validity dependences,
5618 * then we need to check that that the conditional schedule constraint
5619 * is satisfied, i.e., there are no violated conditional validity dependences
5620 * that are adjacent to any non-local condition dependences.
5621 * If there are, then we mark all those adjacent condition dependences
5622 * as local and recompute the current band. Those dependences that
5623 * are marked local will then be forced to be local.
5624 * The initial computation is performed with no dependences marked as local.
5625 * If we are lucky, then there will be no violated conditional validity
5626 * dependences adjacent to any non-local condition dependences.
5627 * Otherwise, we mark some additional condition dependences as local and
5628 * recompute. We continue this process until there are no violations left or
5629 * until we are no longer able to compute a schedule.
5630 * Since there are only a finite number of dependences,
5631 * there will only be a finite number of iterations.
5633 static isl_stat compute_schedule_wcc_band(isl_ctx *ctx,
5634 struct isl_sched_graph *graph)
5636 int has_coincidence;
5637 int use_coincidence;
5638 int force_coincidence = 0;
5639 int check_conditional;
5641 if (sort_sccs(graph) < 0)
5642 return isl_stat_error;
5644 clear_local_edges(graph);
5645 check_conditional = need_condition_check(graph);
5646 has_coincidence = has_any_coincidence(graph);
5648 if (ctx->opt->schedule_outer_coincidence)
5649 force_coincidence = 1;
5651 use_coincidence = has_coincidence;
5652 while (graph->n_row < graph->maxvar) {
5653 isl_vec *sol;
5654 int violated;
5655 int coincident;
5657 graph->src_scc = -1;
5658 graph->dst_scc = -1;
5660 if (setup_lp(ctx, graph, use_coincidence) < 0)
5661 return isl_stat_error;
5662 sol = solve_lp(ctx, graph);
5663 if (!sol)
5664 return isl_stat_error;
5665 if (sol->size == 0) {
5666 int empty = graph->n_total_row == graph->band_start;
5668 isl_vec_free(sol);
5669 if (use_coincidence && (!force_coincidence || !empty)) {
5670 use_coincidence = 0;
5671 continue;
5673 return isl_stat_ok;
5675 coincident = !has_coincidence || use_coincidence;
5676 if (update_schedule(graph, sol, coincident) < 0)
5677 return isl_stat_error;
5679 if (!check_conditional)
5680 continue;
5681 violated = has_violated_conditional_constraint(ctx, graph);
5682 if (violated < 0)
5683 return isl_stat_error;
5684 if (!violated)
5685 continue;
5686 if (reset_band(graph) < 0)
5687 return isl_stat_error;
5688 use_coincidence = has_coincidence;
5691 return isl_stat_ok;
5694 /* Compute a schedule for a connected dependence graph by considering
5695 * the graph as a whole and return the updated schedule node.
5697 * The actual schedule rows of the current band are computed by
5698 * compute_schedule_wcc_band. compute_schedule_finish_band takes
5699 * care of integrating the band into "node" and continuing
5700 * the computation.
5702 static __isl_give isl_schedule_node *compute_schedule_wcc_whole(
5703 __isl_take isl_schedule_node *node, struct isl_sched_graph *graph)
5705 isl_ctx *ctx;
5707 if (!node)
5708 return NULL;
5710 ctx = isl_schedule_node_get_ctx(node);
5711 if (compute_schedule_wcc_band(ctx, graph) < 0)
5712 return isl_schedule_node_free(node);
5714 return compute_schedule_finish_band(node, graph, 1);
5717 /* Clustering information used by compute_schedule_wcc_clustering.
5719 * "n" is the number of SCCs in the original dependence graph
5720 * "scc" is an array of "n" elements, each representing an SCC
5721 * of the original dependence graph. All entries in the same cluster
5722 * have the same number of schedule rows.
5723 * "scc_cluster" maps each SCC index to the cluster to which it belongs,
5724 * where each cluster is represented by the index of the first SCC
5725 * in the cluster. Initially, each SCC belongs to a cluster containing
5726 * only that SCC.
5728 * "scc_in_merge" is used by merge_clusters_along_edge to keep
5729 * track of which SCCs need to be merged.
5731 * "cluster" contains the merged clusters of SCCs after the clustering
5732 * has completed.
5734 * "scc_node" is a temporary data structure used inside copy_partial.
5735 * For each SCC, it keeps track of the number of nodes in the SCC
5736 * that have already been copied.
5738 struct isl_clustering {
5739 int n;
5740 struct isl_sched_graph *scc;
5741 struct isl_sched_graph *cluster;
5742 int *scc_cluster;
5743 int *scc_node;
5744 int *scc_in_merge;
5747 /* Initialize the clustering data structure "c" from "graph".
5749 * In particular, allocate memory, extract the SCCs from "graph"
5750 * into c->scc, initialize scc_cluster and construct
5751 * a band of schedule rows for each SCC.
5752 * Within each SCC, there is only one SCC by definition.
5753 * Each SCC initially belongs to a cluster containing only that SCC.
5755 static isl_stat clustering_init(isl_ctx *ctx, struct isl_clustering *c,
5756 struct isl_sched_graph *graph)
5758 int i;
5760 c->n = graph->scc;
5761 c->scc = isl_calloc_array(ctx, struct isl_sched_graph, c->n);
5762 c->cluster = isl_calloc_array(ctx, struct isl_sched_graph, c->n);
5763 c->scc_cluster = isl_calloc_array(ctx, int, c->n);
5764 c->scc_node = isl_calloc_array(ctx, int, c->n);
5765 c->scc_in_merge = isl_calloc_array(ctx, int, c->n);
5766 if (!c->scc || !c->cluster ||
5767 !c->scc_cluster || !c->scc_node || !c->scc_in_merge)
5768 return isl_stat_error;
5770 for (i = 0; i < c->n; ++i) {
5771 if (extract_sub_graph(ctx, graph, &node_scc_exactly,
5772 &edge_scc_exactly, i, &c->scc[i]) < 0)
5773 return isl_stat_error;
5774 c->scc[i].scc = 1;
5775 if (compute_maxvar(&c->scc[i]) < 0)
5776 return isl_stat_error;
5777 if (compute_schedule_wcc_band(ctx, &c->scc[i]) < 0)
5778 return isl_stat_error;
5779 c->scc_cluster[i] = i;
5782 return isl_stat_ok;
5785 /* Free all memory allocated for "c".
5787 static void clustering_free(isl_ctx *ctx, struct isl_clustering *c)
5789 int i;
5791 if (c->scc)
5792 for (i = 0; i < c->n; ++i)
5793 graph_free(ctx, &c->scc[i]);
5794 free(c->scc);
5795 if (c->cluster)
5796 for (i = 0; i < c->n; ++i)
5797 graph_free(ctx, &c->cluster[i]);
5798 free(c->cluster);
5799 free(c->scc_cluster);
5800 free(c->scc_node);
5801 free(c->scc_in_merge);
5804 /* Should we refrain from merging the cluster in "graph" with
5805 * any other cluster?
5806 * In particular, is its current schedule band empty and incomplete.
5808 static int bad_cluster(struct isl_sched_graph *graph)
5810 return graph->n_row < graph->maxvar &&
5811 graph->n_total_row == graph->band_start;
5814 /* Is "edge" a proximity edge with a non-empty dependence relation?
5816 static isl_bool is_non_empty_proximity(struct isl_sched_edge *edge)
5818 if (!is_proximity(edge))
5819 return isl_bool_false;
5820 return isl_bool_not(isl_map_plain_is_empty(edge->map));
5823 /* Return the index of an edge in "graph" that can be used to merge
5824 * two clusters in "c".
5825 * Return graph->n_edge if no such edge can be found.
5826 * Return -1 on error.
5828 * In particular, return a proximity edge between two clusters
5829 * that is not marked "no_merge" and such that neither of the
5830 * two clusters has an incomplete, empty band.
5832 * If there are multiple such edges, then try and find the most
5833 * appropriate edge to use for merging. In particular, pick the edge
5834 * with the greatest weight. If there are multiple of those,
5835 * then pick one with the shortest distance between
5836 * the two cluster representatives.
5838 static int find_proximity(struct isl_sched_graph *graph,
5839 struct isl_clustering *c)
5841 int i, best = graph->n_edge, best_dist, best_weight;
5843 for (i = 0; i < graph->n_edge; ++i) {
5844 struct isl_sched_edge *edge = &graph->edge[i];
5845 int dist, weight;
5846 isl_bool prox;
5848 prox = is_non_empty_proximity(edge);
5849 if (prox < 0)
5850 return -1;
5851 if (!prox)
5852 continue;
5853 if (edge->no_merge)
5854 continue;
5855 if (bad_cluster(&c->scc[edge->src->scc]) ||
5856 bad_cluster(&c->scc[edge->dst->scc]))
5857 continue;
5858 dist = c->scc_cluster[edge->dst->scc] -
5859 c->scc_cluster[edge->src->scc];
5860 if (dist == 0)
5861 continue;
5862 weight = edge->weight;
5863 if (best < graph->n_edge) {
5864 if (best_weight > weight)
5865 continue;
5866 if (best_weight == weight && best_dist <= dist)
5867 continue;
5869 best = i;
5870 best_dist = dist;
5871 best_weight = weight;
5874 return best;
5877 /* Internal data structure used in mark_merge_sccs.
5879 * "graph" is the dependence graph in which a strongly connected
5880 * component is constructed.
5881 * "scc_cluster" maps each SCC index to the cluster to which it belongs.
5882 * "src" and "dst" are the indices of the nodes that are being merged.
5884 struct isl_mark_merge_sccs_data {
5885 struct isl_sched_graph *graph;
5886 int *scc_cluster;
5887 int src;
5888 int dst;
5891 /* Check whether the cluster containing node "i" depends on the cluster
5892 * containing node "j". If "i" and "j" belong to the same cluster,
5893 * then they are taken to depend on each other to ensure that
5894 * the resulting strongly connected component consists of complete
5895 * clusters. Furthermore, if "i" and "j" are the two nodes that
5896 * are being merged, then they are taken to depend on each other as well.
5897 * Otherwise, check if there is a (conditional) validity dependence
5898 * from node[j] to node[i], forcing node[i] to follow node[j].
5900 static isl_bool cluster_follows(int i, int j, void *user)
5902 struct isl_mark_merge_sccs_data *data = user;
5903 struct isl_sched_graph *graph = data->graph;
5904 int *scc_cluster = data->scc_cluster;
5906 if (data->src == i && data->dst == j)
5907 return isl_bool_true;
5908 if (data->src == j && data->dst == i)
5909 return isl_bool_true;
5910 if (scc_cluster[graph->node[i].scc] == scc_cluster[graph->node[j].scc])
5911 return isl_bool_true;
5913 return graph_has_validity_edge(graph, &graph->node[j], &graph->node[i]);
5916 /* Mark all SCCs that belong to either of the two clusters in "c"
5917 * connected by the edge in "graph" with index "edge", or to any
5918 * of the intermediate clusters.
5919 * The marking is recorded in c->scc_in_merge.
5921 * The given edge has been selected for merging two clusters,
5922 * meaning that there is at least a proximity edge between the two nodes.
5923 * However, there may also be (indirect) validity dependences
5924 * between the two nodes. When merging the two clusters, all clusters
5925 * containing one or more of the intermediate nodes along the
5926 * indirect validity dependences need to be merged in as well.
5928 * First collect all such nodes by computing the strongly connected
5929 * component (SCC) containing the two nodes connected by the edge, where
5930 * the two nodes are considered to depend on each other to make
5931 * sure they end up in the same SCC. Similarly, each node is considered
5932 * to depend on every other node in the same cluster to ensure
5933 * that the SCC consists of complete clusters.
5935 * Then the original SCCs that contain any of these nodes are marked
5936 * in c->scc_in_merge.
5938 static isl_stat mark_merge_sccs(isl_ctx *ctx, struct isl_sched_graph *graph,
5939 int edge, struct isl_clustering *c)
5941 struct isl_mark_merge_sccs_data data;
5942 struct isl_tarjan_graph *g;
5943 int i;
5945 for (i = 0; i < c->n; ++i)
5946 c->scc_in_merge[i] = 0;
5948 data.graph = graph;
5949 data.scc_cluster = c->scc_cluster;
5950 data.src = graph->edge[edge].src - graph->node;
5951 data.dst = graph->edge[edge].dst - graph->node;
5953 g = isl_tarjan_graph_component(ctx, graph->n, data.dst,
5954 &cluster_follows, &data);
5955 if (!g)
5956 goto error;
5958 i = g->op;
5959 if (i < 3)
5960 isl_die(ctx, isl_error_internal,
5961 "expecting at least two nodes in component",
5962 goto error);
5963 if (g->order[--i] != -1)
5964 isl_die(ctx, isl_error_internal,
5965 "expecting end of component marker", goto error);
5967 for (--i; i >= 0 && g->order[i] != -1; --i) {
5968 int scc = graph->node[g->order[i]].scc;
5969 c->scc_in_merge[scc] = 1;
5972 isl_tarjan_graph_free(g);
5973 return isl_stat_ok;
5974 error:
5975 isl_tarjan_graph_free(g);
5976 return isl_stat_error;
5979 /* Construct the identifier "cluster_i".
5981 static __isl_give isl_id *cluster_id(isl_ctx *ctx, int i)
5983 char name[40];
5985 snprintf(name, sizeof(name), "cluster_%d", i);
5986 return isl_id_alloc(ctx, name, NULL);
5989 /* Construct the space of the cluster with index "i" containing
5990 * the strongly connected component "scc".
5992 * In particular, construct a space called cluster_i with dimension equal
5993 * to the number of schedule rows in the current band of "scc".
5995 static __isl_give isl_space *cluster_space(struct isl_sched_graph *scc, int i)
5997 int nvar;
5998 isl_space *space;
5999 isl_id *id;
6001 nvar = scc->n_total_row - scc->band_start;
6002 space = isl_space_copy(scc->node[0].space);
6003 space = isl_space_params(space);
6004 space = isl_space_set_from_params(space);
6005 space = isl_space_add_dims(space, isl_dim_set, nvar);
6006 id = cluster_id(isl_space_get_ctx(space), i);
6007 space = isl_space_set_tuple_id(space, isl_dim_set, id);
6009 return space;
6012 /* Collect the domain of the graph for merging clusters.
6014 * In particular, for each cluster with first SCC "i", construct
6015 * a set in the space called cluster_i with dimension equal
6016 * to the number of schedule rows in the current band of the cluster.
6018 static __isl_give isl_union_set *collect_domain(isl_ctx *ctx,
6019 struct isl_sched_graph *graph, struct isl_clustering *c)
6021 int i;
6022 isl_space *space;
6023 isl_union_set *domain;
6025 space = isl_space_params_alloc(ctx, 0);
6026 domain = isl_union_set_empty(space);
6028 for (i = 0; i < graph->scc; ++i) {
6029 isl_space *space;
6031 if (!c->scc_in_merge[i])
6032 continue;
6033 if (c->scc_cluster[i] != i)
6034 continue;
6035 space = cluster_space(&c->scc[i], i);
6036 domain = isl_union_set_add_set(domain, isl_set_universe(space));
6039 return domain;
6042 /* Construct a map from the original instances to the corresponding
6043 * cluster instance in the current bands of the clusters in "c".
6045 static __isl_give isl_union_map *collect_cluster_map(isl_ctx *ctx,
6046 struct isl_sched_graph *graph, struct isl_clustering *c)
6048 int i, j;
6049 isl_space *space;
6050 isl_union_map *cluster_map;
6052 space = isl_space_params_alloc(ctx, 0);
6053 cluster_map = isl_union_map_empty(space);
6054 for (i = 0; i < graph->scc; ++i) {
6055 int start, n;
6056 isl_id *id;
6058 if (!c->scc_in_merge[i])
6059 continue;
6061 id = cluster_id(ctx, c->scc_cluster[i]);
6062 start = c->scc[i].band_start;
6063 n = c->scc[i].n_total_row - start;
6064 for (j = 0; j < c->scc[i].n; ++j) {
6065 isl_multi_aff *ma;
6066 isl_map *map;
6067 struct isl_sched_node *node = &c->scc[i].node[j];
6069 ma = node_extract_partial_schedule_multi_aff(node,
6070 start, n);
6071 ma = isl_multi_aff_set_tuple_id(ma, isl_dim_out,
6072 isl_id_copy(id));
6073 map = isl_map_from_multi_aff(ma);
6074 cluster_map = isl_union_map_add_map(cluster_map, map);
6076 isl_id_free(id);
6079 return cluster_map;
6082 /* Add "umap" to the schedule constraints "sc" of all types of "edge"
6083 * that are not isl_edge_condition or isl_edge_conditional_validity.
6085 static __isl_give isl_schedule_constraints *add_non_conditional_constraints(
6086 struct isl_sched_edge *edge, __isl_keep isl_union_map *umap,
6087 __isl_take isl_schedule_constraints *sc)
6089 enum isl_edge_type t;
6091 if (!sc)
6092 return NULL;
6094 for (t = isl_edge_first; t <= isl_edge_last; ++t) {
6095 if (t == isl_edge_condition ||
6096 t == isl_edge_conditional_validity)
6097 continue;
6098 if (!is_type(edge, t))
6099 continue;
6100 sc = isl_schedule_constraints_add(sc, t,
6101 isl_union_map_copy(umap));
6104 return sc;
6107 /* Add schedule constraints of types isl_edge_condition and
6108 * isl_edge_conditional_validity to "sc" by applying "umap" to
6109 * the domains of the wrapped relations in domain and range
6110 * of the corresponding tagged constraints of "edge".
6112 static __isl_give isl_schedule_constraints *add_conditional_constraints(
6113 struct isl_sched_edge *edge, __isl_keep isl_union_map *umap,
6114 __isl_take isl_schedule_constraints *sc)
6116 enum isl_edge_type t;
6117 isl_union_map *tagged;
6119 for (t = isl_edge_condition; t <= isl_edge_conditional_validity; ++t) {
6120 if (!is_type(edge, t))
6121 continue;
6122 if (t == isl_edge_condition)
6123 tagged = isl_union_map_copy(edge->tagged_condition);
6124 else
6125 tagged = isl_union_map_copy(edge->tagged_validity);
6126 tagged = isl_union_map_zip(tagged);
6127 tagged = isl_union_map_apply_domain(tagged,
6128 isl_union_map_copy(umap));
6129 tagged = isl_union_map_zip(tagged);
6130 sc = isl_schedule_constraints_add(sc, t, tagged);
6131 if (!sc)
6132 return NULL;
6135 return sc;
6138 /* Given a mapping "cluster_map" from the original instances to
6139 * the cluster instances, add schedule constraints on the clusters
6140 * to "sc" corresponding to the original constraints represented by "edge".
6142 * For non-tagged dependence constraints, the cluster constraints
6143 * are obtained by applying "cluster_map" to the edge->map.
6145 * For tagged dependence constraints, "cluster_map" needs to be applied
6146 * to the domains of the wrapped relations in domain and range
6147 * of the tagged dependence constraints. Pick out the mappings
6148 * from these domains from "cluster_map" and construct their product.
6149 * This mapping can then be applied to the pair of domains.
6151 static __isl_give isl_schedule_constraints *collect_edge_constraints(
6152 struct isl_sched_edge *edge, __isl_keep isl_union_map *cluster_map,
6153 __isl_take isl_schedule_constraints *sc)
6155 isl_union_map *umap;
6156 isl_space *space;
6157 isl_union_set *uset;
6158 isl_union_map *umap1, *umap2;
6160 if (!sc)
6161 return NULL;
6163 umap = isl_union_map_from_map(isl_map_copy(edge->map));
6164 umap = isl_union_map_apply_domain(umap,
6165 isl_union_map_copy(cluster_map));
6166 umap = isl_union_map_apply_range(umap,
6167 isl_union_map_copy(cluster_map));
6168 sc = add_non_conditional_constraints(edge, umap, sc);
6169 isl_union_map_free(umap);
6171 if (!sc || (!is_condition(edge) && !is_conditional_validity(edge)))
6172 return sc;
6174 space = isl_space_domain(isl_map_get_space(edge->map));
6175 uset = isl_union_set_from_set(isl_set_universe(space));
6176 umap1 = isl_union_map_copy(cluster_map);
6177 umap1 = isl_union_map_intersect_domain(umap1, uset);
6178 space = isl_space_range(isl_map_get_space(edge->map));
6179 uset = isl_union_set_from_set(isl_set_universe(space));
6180 umap2 = isl_union_map_copy(cluster_map);
6181 umap2 = isl_union_map_intersect_domain(umap2, uset);
6182 umap = isl_union_map_product(umap1, umap2);
6184 sc = add_conditional_constraints(edge, umap, sc);
6186 isl_union_map_free(umap);
6187 return sc;
6190 /* Given a mapping "cluster_map" from the original instances to
6191 * the cluster instances, add schedule constraints on the clusters
6192 * to "sc" corresponding to all edges in "graph" between nodes that
6193 * belong to SCCs that are marked for merging in "scc_in_merge".
6195 static __isl_give isl_schedule_constraints *collect_constraints(
6196 struct isl_sched_graph *graph, int *scc_in_merge,
6197 __isl_keep isl_union_map *cluster_map,
6198 __isl_take isl_schedule_constraints *sc)
6200 int i;
6202 for (i = 0; i < graph->n_edge; ++i) {
6203 struct isl_sched_edge *edge = &graph->edge[i];
6205 if (!scc_in_merge[edge->src->scc])
6206 continue;
6207 if (!scc_in_merge[edge->dst->scc])
6208 continue;
6209 sc = collect_edge_constraints(edge, cluster_map, sc);
6212 return sc;
6215 /* Construct a dependence graph for scheduling clusters with respect
6216 * to each other and store the result in "merge_graph".
6217 * In particular, the nodes of the graph correspond to the schedule
6218 * dimensions of the current bands of those clusters that have been
6219 * marked for merging in "c".
6221 * First construct an isl_schedule_constraints object for this domain
6222 * by transforming the edges in "graph" to the domain.
6223 * Then initialize a dependence graph for scheduling from these
6224 * constraints.
6226 static isl_stat init_merge_graph(isl_ctx *ctx, struct isl_sched_graph *graph,
6227 struct isl_clustering *c, struct isl_sched_graph *merge_graph)
6229 isl_union_set *domain;
6230 isl_union_map *cluster_map;
6231 isl_schedule_constraints *sc;
6232 isl_stat r;
6234 domain = collect_domain(ctx, graph, c);
6235 sc = isl_schedule_constraints_on_domain(domain);
6236 if (!sc)
6237 return isl_stat_error;
6238 cluster_map = collect_cluster_map(ctx, graph, c);
6239 sc = collect_constraints(graph, c->scc_in_merge, cluster_map, sc);
6240 isl_union_map_free(cluster_map);
6242 r = graph_init(merge_graph, sc);
6244 isl_schedule_constraints_free(sc);
6246 return r;
6249 /* Compute the maximal number of remaining schedule rows that still need
6250 * to be computed for the nodes that belong to clusters with the maximal
6251 * dimension for the current band (i.e., the band that is to be merged).
6252 * Only clusters that are about to be merged are considered.
6253 * "maxvar" is the maximal dimension for the current band.
6254 * "c" contains information about the clusters.
6256 * Return the maximal number of remaining schedule rows or -1 on error.
6258 static int compute_maxvar_max_slack(int maxvar, struct isl_clustering *c)
6260 int i, j;
6261 int max_slack;
6263 max_slack = 0;
6264 for (i = 0; i < c->n; ++i) {
6265 int nvar;
6266 struct isl_sched_graph *scc;
6268 if (!c->scc_in_merge[i])
6269 continue;
6270 scc = &c->scc[i];
6271 nvar = scc->n_total_row - scc->band_start;
6272 if (nvar != maxvar)
6273 continue;
6274 for (j = 0; j < scc->n; ++j) {
6275 struct isl_sched_node *node = &scc->node[j];
6276 int slack;
6278 if (node_update_vmap(node) < 0)
6279 return -1;
6280 slack = node->nvar - node->rank;
6281 if (slack > max_slack)
6282 max_slack = slack;
6286 return max_slack;
6289 /* If there are any clusters where the dimension of the current band
6290 * (i.e., the band that is to be merged) is smaller than "maxvar" and
6291 * if there are any nodes in such a cluster where the number
6292 * of remaining schedule rows that still need to be computed
6293 * is greater than "max_slack", then return the smallest current band
6294 * dimension of all these clusters. Otherwise return the original value
6295 * of "maxvar". Return -1 in case of any error.
6296 * Only clusters that are about to be merged are considered.
6297 * "c" contains information about the clusters.
6299 static int limit_maxvar_to_slack(int maxvar, int max_slack,
6300 struct isl_clustering *c)
6302 int i, j;
6304 for (i = 0; i < c->n; ++i) {
6305 int nvar;
6306 struct isl_sched_graph *scc;
6308 if (!c->scc_in_merge[i])
6309 continue;
6310 scc = &c->scc[i];
6311 nvar = scc->n_total_row - scc->band_start;
6312 if (nvar >= maxvar)
6313 continue;
6314 for (j = 0; j < scc->n; ++j) {
6315 struct isl_sched_node *node = &scc->node[j];
6316 int slack;
6318 if (node_update_vmap(node) < 0)
6319 return -1;
6320 slack = node->nvar - node->rank;
6321 if (slack > max_slack) {
6322 maxvar = nvar;
6323 break;
6328 return maxvar;
6331 /* Adjust merge_graph->maxvar based on the number of remaining schedule rows
6332 * that still need to be computed. In particular, if there is a node
6333 * in a cluster where the dimension of the current band is smaller
6334 * than merge_graph->maxvar, but the number of remaining schedule rows
6335 * is greater than that of any node in a cluster with the maximal
6336 * dimension for the current band (i.e., merge_graph->maxvar),
6337 * then adjust merge_graph->maxvar to the (smallest) current band dimension
6338 * of those clusters. Without this adjustment, the total number of
6339 * schedule dimensions would be increased, resulting in a skewed view
6340 * of the number of coincident dimensions.
6341 * "c" contains information about the clusters.
6343 * If the maximize_band_depth option is set and merge_graph->maxvar is reduced,
6344 * then there is no point in attempting any merge since it will be rejected
6345 * anyway. Set merge_graph->maxvar to zero in such cases.
6347 static isl_stat adjust_maxvar_to_slack(isl_ctx *ctx,
6348 struct isl_sched_graph *merge_graph, struct isl_clustering *c)
6350 int max_slack, maxvar;
6352 max_slack = compute_maxvar_max_slack(merge_graph->maxvar, c);
6353 if (max_slack < 0)
6354 return isl_stat_error;
6355 maxvar = limit_maxvar_to_slack(merge_graph->maxvar, max_slack, c);
6356 if (maxvar < 0)
6357 return isl_stat_error;
6359 if (maxvar < merge_graph->maxvar) {
6360 if (isl_options_get_schedule_maximize_band_depth(ctx))
6361 merge_graph->maxvar = 0;
6362 else
6363 merge_graph->maxvar = maxvar;
6366 return isl_stat_ok;
6369 /* Return the number of coincident dimensions in the current band of "graph",
6370 * where the nodes of "graph" are assumed to be scheduled by a single band.
6372 static int get_n_coincident(struct isl_sched_graph *graph)
6374 int i;
6376 for (i = graph->band_start; i < graph->n_total_row; ++i)
6377 if (!graph->node[0].coincident[i])
6378 break;
6380 return i - graph->band_start;
6383 /* Should the clusters be merged based on the cluster schedule
6384 * in the current (and only) band of "merge_graph", given that
6385 * coincidence should be maximized?
6387 * If the number of coincident schedule dimensions in the merged band
6388 * would be less than the maximal number of coincident schedule dimensions
6389 * in any of the merged clusters, then the clusters should not be merged.
6391 static isl_bool ok_to_merge_coincident(struct isl_clustering *c,
6392 struct isl_sched_graph *merge_graph)
6394 int i;
6395 int n_coincident;
6396 int max_coincident;
6398 max_coincident = 0;
6399 for (i = 0; i < c->n; ++i) {
6400 if (!c->scc_in_merge[i])
6401 continue;
6402 n_coincident = get_n_coincident(&c->scc[i]);
6403 if (n_coincident > max_coincident)
6404 max_coincident = n_coincident;
6407 n_coincident = get_n_coincident(merge_graph);
6409 return n_coincident >= max_coincident;
6412 /* Return the transformation on "node" expressed by the current (and only)
6413 * band of "merge_graph" applied to the clusters in "c".
6415 * First find the representation of "node" in its SCC in "c" and
6416 * extract the transformation expressed by the current band.
6417 * Then extract the transformation applied by "merge_graph"
6418 * to the cluster to which this SCC belongs.
6419 * Combine the two to obtain the complete transformation on the node.
6421 * Note that the range of the first transformation is an anonymous space,
6422 * while the domain of the second is named "cluster_X". The range
6423 * of the former therefore needs to be adjusted before the two
6424 * can be combined.
6426 static __isl_give isl_map *extract_node_transformation(isl_ctx *ctx,
6427 struct isl_sched_node *node, struct isl_clustering *c,
6428 struct isl_sched_graph *merge_graph)
6430 struct isl_sched_node *scc_node, *cluster_node;
6431 int start, n;
6432 isl_id *id;
6433 isl_space *space;
6434 isl_multi_aff *ma, *ma2;
6436 scc_node = graph_find_node(ctx, &c->scc[node->scc], node->space);
6437 if (scc_node && !is_node(&c->scc[node->scc], scc_node))
6438 isl_die(ctx, isl_error_internal, "unable to find node",
6439 return NULL);
6440 start = c->scc[node->scc].band_start;
6441 n = c->scc[node->scc].n_total_row - start;
6442 ma = node_extract_partial_schedule_multi_aff(scc_node, start, n);
6443 space = cluster_space(&c->scc[node->scc], c->scc_cluster[node->scc]);
6444 cluster_node = graph_find_node(ctx, merge_graph, space);
6445 if (cluster_node && !is_node(merge_graph, cluster_node))
6446 isl_die(ctx, isl_error_internal, "unable to find cluster",
6447 space = isl_space_free(space));
6448 id = isl_space_get_tuple_id(space, isl_dim_set);
6449 ma = isl_multi_aff_set_tuple_id(ma, isl_dim_out, id);
6450 isl_space_free(space);
6451 n = merge_graph->n_total_row;
6452 ma2 = node_extract_partial_schedule_multi_aff(cluster_node, 0, n);
6453 ma = isl_multi_aff_pullback_multi_aff(ma2, ma);
6455 return isl_map_from_multi_aff(ma);
6458 /* Give a set of distances "set", are they bounded by a small constant
6459 * in direction "pos"?
6460 * In practice, check if they are bounded by 2 by checking that there
6461 * are no elements with a value greater than or equal to 3 or
6462 * smaller than or equal to -3.
6464 static isl_bool distance_is_bounded(__isl_keep isl_set *set, int pos)
6466 isl_bool bounded;
6467 isl_set *test;
6469 if (!set)
6470 return isl_bool_error;
6472 test = isl_set_copy(set);
6473 test = isl_set_lower_bound_si(test, isl_dim_set, pos, 3);
6474 bounded = isl_set_is_empty(test);
6475 isl_set_free(test);
6477 if (bounded < 0 || !bounded)
6478 return bounded;
6480 test = isl_set_copy(set);
6481 test = isl_set_upper_bound_si(test, isl_dim_set, pos, -3);
6482 bounded = isl_set_is_empty(test);
6483 isl_set_free(test);
6485 return bounded;
6488 /* Does the set "set" have a fixed (but possible parametric) value
6489 * at dimension "pos"?
6491 static isl_bool has_single_value(__isl_keep isl_set *set, int pos)
6493 int n;
6494 isl_bool single;
6496 if (!set)
6497 return isl_bool_error;
6498 set = isl_set_copy(set);
6499 n = isl_set_dim(set, isl_dim_set);
6500 set = isl_set_project_out(set, isl_dim_set, pos + 1, n - (pos + 1));
6501 set = isl_set_project_out(set, isl_dim_set, 0, pos);
6502 single = isl_set_is_singleton(set);
6503 isl_set_free(set);
6505 return single;
6508 /* Does "map" have a fixed (but possible parametric) value
6509 * at dimension "pos" of either its domain or its range?
6511 static isl_bool has_singular_src_or_dst(__isl_keep isl_map *map, int pos)
6513 isl_set *set;
6514 isl_bool single;
6516 set = isl_map_domain(isl_map_copy(map));
6517 single = has_single_value(set, pos);
6518 isl_set_free(set);
6520 if (single < 0 || single)
6521 return single;
6523 set = isl_map_range(isl_map_copy(map));
6524 single = has_single_value(set, pos);
6525 isl_set_free(set);
6527 return single;
6530 /* Does the edge "edge" from "graph" have bounded dependence distances
6531 * in the merged graph "merge_graph" of a selection of clusters in "c"?
6533 * Extract the complete transformations of the source and destination
6534 * nodes of the edge, apply them to the edge constraints and
6535 * compute the differences. Finally, check if these differences are bounded
6536 * in each direction.
6538 * If the dimension of the band is greater than the number of
6539 * dimensions that can be expected to be optimized by the edge
6540 * (based on its weight), then also allow the differences to be unbounded
6541 * in the remaining dimensions, but only if either the source or
6542 * the destination has a fixed value in that direction.
6543 * This allows a statement that produces values that are used by
6544 * several instances of another statement to be merged with that
6545 * other statement.
6546 * However, merging such clusters will introduce an inherently
6547 * large proximity distance inside the merged cluster, meaning
6548 * that proximity distances will no longer be optimized in
6549 * subsequent merges. These merges are therefore only allowed
6550 * after all other possible merges have been tried.
6551 * The first time such a merge is encountered, the weight of the edge
6552 * is replaced by a negative weight. The second time (i.e., after
6553 * all merges over edges with a non-negative weight have been tried),
6554 * the merge is allowed.
6556 static isl_bool has_bounded_distances(isl_ctx *ctx, struct isl_sched_edge *edge,
6557 struct isl_sched_graph *graph, struct isl_clustering *c,
6558 struct isl_sched_graph *merge_graph)
6560 int i, n, n_slack;
6561 isl_bool bounded;
6562 isl_map *map, *t;
6563 isl_set *dist;
6565 map = isl_map_copy(edge->map);
6566 t = extract_node_transformation(ctx, edge->src, c, merge_graph);
6567 map = isl_map_apply_domain(map, t);
6568 t = extract_node_transformation(ctx, edge->dst, c, merge_graph);
6569 map = isl_map_apply_range(map, t);
6570 dist = isl_map_deltas(isl_map_copy(map));
6572 bounded = isl_bool_true;
6573 n = isl_set_dim(dist, isl_dim_set);
6574 n_slack = n - edge->weight;
6575 if (edge->weight < 0)
6576 n_slack -= graph->max_weight + 1;
6577 for (i = 0; i < n; ++i) {
6578 isl_bool bounded_i, singular_i;
6580 bounded_i = distance_is_bounded(dist, i);
6581 if (bounded_i < 0)
6582 goto error;
6583 if (bounded_i)
6584 continue;
6585 if (edge->weight >= 0)
6586 bounded = isl_bool_false;
6587 n_slack--;
6588 if (n_slack < 0)
6589 break;
6590 singular_i = has_singular_src_or_dst(map, i);
6591 if (singular_i < 0)
6592 goto error;
6593 if (singular_i)
6594 continue;
6595 bounded = isl_bool_false;
6596 break;
6598 if (!bounded && i >= n && edge->weight >= 0)
6599 edge->weight -= graph->max_weight + 1;
6600 isl_map_free(map);
6601 isl_set_free(dist);
6603 return bounded;
6604 error:
6605 isl_map_free(map);
6606 isl_set_free(dist);
6607 return isl_bool_error;
6610 /* Should the clusters be merged based on the cluster schedule
6611 * in the current (and only) band of "merge_graph"?
6612 * "graph" is the original dependence graph, while "c" records
6613 * which SCCs are involved in the latest merge.
6615 * In particular, is there at least one proximity constraint
6616 * that is optimized by the merge?
6618 * A proximity constraint is considered to be optimized
6619 * if the dependence distances are small.
6621 static isl_bool ok_to_merge_proximity(isl_ctx *ctx,
6622 struct isl_sched_graph *graph, struct isl_clustering *c,
6623 struct isl_sched_graph *merge_graph)
6625 int i;
6627 for (i = 0; i < graph->n_edge; ++i) {
6628 struct isl_sched_edge *edge = &graph->edge[i];
6629 isl_bool bounded;
6631 if (!is_proximity(edge))
6632 continue;
6633 if (!c->scc_in_merge[edge->src->scc])
6634 continue;
6635 if (!c->scc_in_merge[edge->dst->scc])
6636 continue;
6637 if (c->scc_cluster[edge->dst->scc] ==
6638 c->scc_cluster[edge->src->scc])
6639 continue;
6640 bounded = has_bounded_distances(ctx, edge, graph, c,
6641 merge_graph);
6642 if (bounded < 0 || bounded)
6643 return bounded;
6646 return isl_bool_false;
6649 /* Should the clusters be merged based on the cluster schedule
6650 * in the current (and only) band of "merge_graph"?
6651 * "graph" is the original dependence graph, while "c" records
6652 * which SCCs are involved in the latest merge.
6654 * If the current band is empty, then the clusters should not be merged.
6656 * If the band depth should be maximized and the merge schedule
6657 * is incomplete (meaning that the dimension of some of the schedule
6658 * bands in the original schedule will be reduced), then the clusters
6659 * should not be merged.
6661 * If the schedule_maximize_coincidence option is set, then check that
6662 * the number of coincident schedule dimensions is not reduced.
6664 * Finally, only allow the merge if at least one proximity
6665 * constraint is optimized.
6667 static isl_bool ok_to_merge(isl_ctx *ctx, struct isl_sched_graph *graph,
6668 struct isl_clustering *c, struct isl_sched_graph *merge_graph)
6670 if (merge_graph->n_total_row == merge_graph->band_start)
6671 return isl_bool_false;
6673 if (isl_options_get_schedule_maximize_band_depth(ctx) &&
6674 merge_graph->n_total_row < merge_graph->maxvar)
6675 return isl_bool_false;
6677 if (isl_options_get_schedule_maximize_coincidence(ctx)) {
6678 isl_bool ok;
6680 ok = ok_to_merge_coincident(c, merge_graph);
6681 if (ok < 0 || !ok)
6682 return ok;
6685 return ok_to_merge_proximity(ctx, graph, c, merge_graph);
6688 /* Apply the schedule in "t_node" to the "n" rows starting at "first"
6689 * of the schedule in "node" and return the result.
6691 * That is, essentially compute
6693 * T * N(first:first+n-1)
6695 * taking into account the constant term and the parameter coefficients
6696 * in "t_node".
6698 static __isl_give isl_mat *node_transformation(isl_ctx *ctx,
6699 struct isl_sched_node *t_node, struct isl_sched_node *node,
6700 int first, int n)
6702 int i, j;
6703 isl_mat *t;
6704 int n_row, n_col, n_param, n_var;
6706 n_param = node->nparam;
6707 n_var = node->nvar;
6708 n_row = isl_mat_rows(t_node->sched);
6709 n_col = isl_mat_cols(node->sched);
6710 t = isl_mat_alloc(ctx, n_row, n_col);
6711 if (!t)
6712 return NULL;
6713 for (i = 0; i < n_row; ++i) {
6714 isl_seq_cpy(t->row[i], t_node->sched->row[i], 1 + n_param);
6715 isl_seq_clr(t->row[i] + 1 + n_param, n_var);
6716 for (j = 0; j < n; ++j)
6717 isl_seq_addmul(t->row[i],
6718 t_node->sched->row[i][1 + n_param + j],
6719 node->sched->row[first + j],
6720 1 + n_param + n_var);
6722 return t;
6725 /* Apply the cluster schedule in "t_node" to the current band
6726 * schedule of the nodes in "graph".
6728 * In particular, replace the rows starting at band_start
6729 * by the result of applying the cluster schedule in "t_node"
6730 * to the original rows.
6732 * The coincidence of the schedule is determined by the coincidence
6733 * of the cluster schedule.
6735 static isl_stat transform(isl_ctx *ctx, struct isl_sched_graph *graph,
6736 struct isl_sched_node *t_node)
6738 int i, j;
6739 int n_new;
6740 int start, n;
6742 start = graph->band_start;
6743 n = graph->n_total_row - start;
6745 n_new = isl_mat_rows(t_node->sched);
6746 for (i = 0; i < graph->n; ++i) {
6747 struct isl_sched_node *node = &graph->node[i];
6748 isl_mat *t;
6750 t = node_transformation(ctx, t_node, node, start, n);
6751 node->sched = isl_mat_drop_rows(node->sched, start, n);
6752 node->sched = isl_mat_concat(node->sched, t);
6753 node->sched_map = isl_map_free(node->sched_map);
6754 if (!node->sched)
6755 return isl_stat_error;
6756 for (j = 0; j < n_new; ++j)
6757 node->coincident[start + j] = t_node->coincident[j];
6759 graph->n_total_row -= n;
6760 graph->n_row -= n;
6761 graph->n_total_row += n_new;
6762 graph->n_row += n_new;
6764 return isl_stat_ok;
6767 /* Merge the clusters marked for merging in "c" into a single
6768 * cluster using the cluster schedule in the current band of "merge_graph".
6769 * The representative SCC for the new cluster is the SCC with
6770 * the smallest index.
6772 * The current band schedule of each SCC in the new cluster is obtained
6773 * by applying the schedule of the corresponding original cluster
6774 * to the original band schedule.
6775 * All SCCs in the new cluster have the same number of schedule rows.
6777 static isl_stat merge(isl_ctx *ctx, struct isl_clustering *c,
6778 struct isl_sched_graph *merge_graph)
6780 int i;
6781 int cluster = -1;
6782 isl_space *space;
6784 for (i = 0; i < c->n; ++i) {
6785 struct isl_sched_node *node;
6787 if (!c->scc_in_merge[i])
6788 continue;
6789 if (cluster < 0)
6790 cluster = i;
6791 space = cluster_space(&c->scc[i], c->scc_cluster[i]);
6792 node = graph_find_node(ctx, merge_graph, space);
6793 isl_space_free(space);
6794 if (!node)
6795 return isl_stat_error;
6796 if (!is_node(merge_graph, node))
6797 isl_die(ctx, isl_error_internal,
6798 "unable to find cluster",
6799 return isl_stat_error);
6800 if (transform(ctx, &c->scc[i], node) < 0)
6801 return isl_stat_error;
6802 c->scc_cluster[i] = cluster;
6805 return isl_stat_ok;
6808 /* Try and merge the clusters of SCCs marked in c->scc_in_merge
6809 * by scheduling the current cluster bands with respect to each other.
6811 * Construct a dependence graph with a space for each cluster and
6812 * with the coordinates of each space corresponding to the schedule
6813 * dimensions of the current band of that cluster.
6814 * Construct a cluster schedule in this cluster dependence graph and
6815 * apply it to the current cluster bands if it is applicable
6816 * according to ok_to_merge.
6818 * If the number of remaining schedule dimensions in a cluster
6819 * with a non-maximal current schedule dimension is greater than
6820 * the number of remaining schedule dimensions in clusters
6821 * with a maximal current schedule dimension, then restrict
6822 * the number of rows to be computed in the cluster schedule
6823 * to the minimal such non-maximal current schedule dimension.
6824 * Do this by adjusting merge_graph.maxvar.
6826 * Return isl_bool_true if the clusters have effectively been merged
6827 * into a single cluster.
6829 * Note that since the standard scheduling algorithm minimizes the maximal
6830 * distance over proximity constraints, the proximity constraints between
6831 * the merged clusters may not be optimized any further than what is
6832 * sufficient to bring the distances within the limits of the internal
6833 * proximity constraints inside the individual clusters.
6834 * It may therefore make sense to perform an additional translation step
6835 * to bring the clusters closer to each other, while maintaining
6836 * the linear part of the merging schedule found using the standard
6837 * scheduling algorithm.
6839 static isl_bool try_merge(isl_ctx *ctx, struct isl_sched_graph *graph,
6840 struct isl_clustering *c)
6842 struct isl_sched_graph merge_graph = { 0 };
6843 isl_bool merged;
6845 if (init_merge_graph(ctx, graph, c, &merge_graph) < 0)
6846 goto error;
6848 if (compute_maxvar(&merge_graph) < 0)
6849 goto error;
6850 if (adjust_maxvar_to_slack(ctx, &merge_graph,c) < 0)
6851 goto error;
6852 if (compute_schedule_wcc_band(ctx, &merge_graph) < 0)
6853 goto error;
6854 merged = ok_to_merge(ctx, graph, c, &merge_graph);
6855 if (merged && merge(ctx, c, &merge_graph) < 0)
6856 goto error;
6858 graph_free(ctx, &merge_graph);
6859 return merged;
6860 error:
6861 graph_free(ctx, &merge_graph);
6862 return isl_bool_error;
6865 /* Is there any edge marked "no_merge" between two SCCs that are
6866 * about to be merged (i.e., that are set in "scc_in_merge")?
6867 * "merge_edge" is the proximity edge along which the clusters of SCCs
6868 * are going to be merged.
6870 * If there is any edge between two SCCs with a negative weight,
6871 * while the weight of "merge_edge" is non-negative, then this
6872 * means that the edge was postponed. "merge_edge" should then
6873 * also be postponed since merging along the edge with negative weight should
6874 * be postponed until all edges with non-negative weight have been tried.
6875 * Replace the weight of "merge_edge" by a negative weight as well and
6876 * tell the caller not to attempt a merge.
6878 static int any_no_merge(struct isl_sched_graph *graph, int *scc_in_merge,
6879 struct isl_sched_edge *merge_edge)
6881 int i;
6883 for (i = 0; i < graph->n_edge; ++i) {
6884 struct isl_sched_edge *edge = &graph->edge[i];
6886 if (!scc_in_merge[edge->src->scc])
6887 continue;
6888 if (!scc_in_merge[edge->dst->scc])
6889 continue;
6890 if (edge->no_merge)
6891 return 1;
6892 if (merge_edge->weight >= 0 && edge->weight < 0) {
6893 merge_edge->weight -= graph->max_weight + 1;
6894 return 1;
6898 return 0;
6901 /* Merge the two clusters in "c" connected by the edge in "graph"
6902 * with index "edge" into a single cluster.
6903 * If it turns out to be impossible to merge these two clusters,
6904 * then mark the edge as "no_merge" such that it will not be
6905 * considered again.
6907 * First mark all SCCs that need to be merged. This includes the SCCs
6908 * in the two clusters, but it may also include the SCCs
6909 * of intermediate clusters.
6910 * If there is already a no_merge edge between any pair of such SCCs,
6911 * then simply mark the current edge as no_merge as well.
6912 * Likewise, if any of those edges was postponed by has_bounded_distances,
6913 * then postpone the current edge as well.
6914 * Otherwise, try and merge the clusters and mark "edge" as "no_merge"
6915 * if the clusters did not end up getting merged, unless the non-merge
6916 * is due to the fact that the edge was postponed. This postponement
6917 * can be recognized by a change in weight (from non-negative to negative).
6919 static isl_stat merge_clusters_along_edge(isl_ctx *ctx,
6920 struct isl_sched_graph *graph, int edge, struct isl_clustering *c)
6922 isl_bool merged;
6923 int edge_weight = graph->edge[edge].weight;
6925 if (mark_merge_sccs(ctx, graph, edge, c) < 0)
6926 return isl_stat_error;
6928 if (any_no_merge(graph, c->scc_in_merge, &graph->edge[edge]))
6929 merged = isl_bool_false;
6930 else
6931 merged = try_merge(ctx, graph, c);
6932 if (merged < 0)
6933 return isl_stat_error;
6934 if (!merged && edge_weight == graph->edge[edge].weight)
6935 graph->edge[edge].no_merge = 1;
6937 return isl_stat_ok;
6940 /* Does "node" belong to the cluster identified by "cluster"?
6942 static int node_cluster_exactly(struct isl_sched_node *node, int cluster)
6944 return node->cluster == cluster;
6947 /* Does "edge" connect two nodes belonging to the cluster
6948 * identified by "cluster"?
6950 static int edge_cluster_exactly(struct isl_sched_edge *edge, int cluster)
6952 return edge->src->cluster == cluster && edge->dst->cluster == cluster;
6955 /* Swap the schedule of "node1" and "node2".
6956 * Both nodes have been derived from the same node in a common parent graph.
6957 * Since the "coincident" field is shared with that node
6958 * in the parent graph, there is no need to also swap this field.
6960 static void swap_sched(struct isl_sched_node *node1,
6961 struct isl_sched_node *node2)
6963 isl_mat *sched;
6964 isl_map *sched_map;
6966 sched = node1->sched;
6967 node1->sched = node2->sched;
6968 node2->sched = sched;
6970 sched_map = node1->sched_map;
6971 node1->sched_map = node2->sched_map;
6972 node2->sched_map = sched_map;
6975 /* Copy the current band schedule from the SCCs that form the cluster
6976 * with index "pos" to the actual cluster at position "pos".
6977 * By construction, the index of the first SCC that belongs to the cluster
6978 * is also "pos".
6980 * The order of the nodes inside both the SCCs and the cluster
6981 * is assumed to be same as the order in the original "graph".
6983 * Since the SCC graphs will no longer be used after this function,
6984 * the schedules are actually swapped rather than copied.
6986 static isl_stat copy_partial(struct isl_sched_graph *graph,
6987 struct isl_clustering *c, int pos)
6989 int i, j;
6991 c->cluster[pos].n_total_row = c->scc[pos].n_total_row;
6992 c->cluster[pos].n_row = c->scc[pos].n_row;
6993 c->cluster[pos].maxvar = c->scc[pos].maxvar;
6994 j = 0;
6995 for (i = 0; i < graph->n; ++i) {
6996 int k;
6997 int s;
6999 if (graph->node[i].cluster != pos)
7000 continue;
7001 s = graph->node[i].scc;
7002 k = c->scc_node[s]++;
7003 swap_sched(&c->cluster[pos].node[j], &c->scc[s].node[k]);
7004 if (c->scc[s].maxvar > c->cluster[pos].maxvar)
7005 c->cluster[pos].maxvar = c->scc[s].maxvar;
7006 ++j;
7009 return isl_stat_ok;
7012 /* Is there a (conditional) validity dependence from node[j] to node[i],
7013 * forcing node[i] to follow node[j] or do the nodes belong to the same
7014 * cluster?
7016 static isl_bool node_follows_strong_or_same_cluster(int i, int j, void *user)
7018 struct isl_sched_graph *graph = user;
7020 if (graph->node[i].cluster == graph->node[j].cluster)
7021 return isl_bool_true;
7022 return graph_has_validity_edge(graph, &graph->node[j], &graph->node[i]);
7025 /* Extract the merged clusters of SCCs in "graph", sort them, and
7026 * store them in c->clusters. Update c->scc_cluster accordingly.
7028 * First keep track of the cluster containing the SCC to which a node
7029 * belongs in the node itself.
7030 * Then extract the clusters into c->clusters, copying the current
7031 * band schedule from the SCCs that belong to the cluster.
7032 * Do this only once per cluster.
7034 * Finally, topologically sort the clusters and update c->scc_cluster
7035 * to match the new scc numbering. While the SCCs were originally
7036 * sorted already, some SCCs that depend on some other SCCs may
7037 * have been merged with SCCs that appear before these other SCCs.
7038 * A reordering may therefore be required.
7040 static isl_stat extract_clusters(isl_ctx *ctx, struct isl_sched_graph *graph,
7041 struct isl_clustering *c)
7043 int i;
7045 for (i = 0; i < graph->n; ++i)
7046 graph->node[i].cluster = c->scc_cluster[graph->node[i].scc];
7048 for (i = 0; i < graph->scc; ++i) {
7049 if (c->scc_cluster[i] != i)
7050 continue;
7051 if (extract_sub_graph(ctx, graph, &node_cluster_exactly,
7052 &edge_cluster_exactly, i, &c->cluster[i]) < 0)
7053 return isl_stat_error;
7054 c->cluster[i].src_scc = -1;
7055 c->cluster[i].dst_scc = -1;
7056 if (copy_partial(graph, c, i) < 0)
7057 return isl_stat_error;
7060 if (detect_ccs(ctx, graph, &node_follows_strong_or_same_cluster) < 0)
7061 return isl_stat_error;
7062 for (i = 0; i < graph->n; ++i)
7063 c->scc_cluster[graph->node[i].scc] = graph->node[i].cluster;
7065 return isl_stat_ok;
7068 /* Compute weights on the proximity edges of "graph" that can
7069 * be used by find_proximity to find the most appropriate
7070 * proximity edge to use to merge two clusters in "c".
7071 * The weights are also used by has_bounded_distances to determine
7072 * whether the merge should be allowed.
7073 * Store the maximum of the computed weights in graph->max_weight.
7075 * The computed weight is a measure for the number of remaining schedule
7076 * dimensions that can still be completely aligned.
7077 * In particular, compute the number of equalities between
7078 * input dimensions and output dimensions in the proximity constraints.
7079 * The directions that are already handled by outer schedule bands
7080 * are projected out prior to determining this number.
7082 * Edges that will never be considered by find_proximity are ignored.
7084 static isl_stat compute_weights(struct isl_sched_graph *graph,
7085 struct isl_clustering *c)
7087 int i;
7089 graph->max_weight = 0;
7091 for (i = 0; i < graph->n_edge; ++i) {
7092 struct isl_sched_edge *edge = &graph->edge[i];
7093 struct isl_sched_node *src = edge->src;
7094 struct isl_sched_node *dst = edge->dst;
7095 isl_basic_map *hull;
7096 isl_bool prox;
7097 int n_in, n_out;
7099 prox = is_non_empty_proximity(edge);
7100 if (prox < 0)
7101 return isl_stat_error;
7102 if (!prox)
7103 continue;
7104 if (bad_cluster(&c->scc[edge->src->scc]) ||
7105 bad_cluster(&c->scc[edge->dst->scc]))
7106 continue;
7107 if (c->scc_cluster[edge->dst->scc] ==
7108 c->scc_cluster[edge->src->scc])
7109 continue;
7111 hull = isl_map_affine_hull(isl_map_copy(edge->map));
7112 hull = isl_basic_map_transform_dims(hull, isl_dim_in, 0,
7113 isl_mat_copy(src->vmap));
7114 hull = isl_basic_map_transform_dims(hull, isl_dim_out, 0,
7115 isl_mat_copy(dst->vmap));
7116 hull = isl_basic_map_project_out(hull,
7117 isl_dim_in, 0, src->rank);
7118 hull = isl_basic_map_project_out(hull,
7119 isl_dim_out, 0, dst->rank);
7120 hull = isl_basic_map_remove_divs(hull);
7121 n_in = isl_basic_map_dim(hull, isl_dim_in);
7122 n_out = isl_basic_map_dim(hull, isl_dim_out);
7123 hull = isl_basic_map_drop_constraints_not_involving_dims(hull,
7124 isl_dim_in, 0, n_in);
7125 hull = isl_basic_map_drop_constraints_not_involving_dims(hull,
7126 isl_dim_out, 0, n_out);
7127 if (!hull)
7128 return isl_stat_error;
7129 edge->weight = isl_basic_map_n_equality(hull);
7130 isl_basic_map_free(hull);
7132 if (edge->weight > graph->max_weight)
7133 graph->max_weight = edge->weight;
7136 return isl_stat_ok;
7139 /* Call compute_schedule_finish_band on each of the clusters in "c"
7140 * in their topological order. This order is determined by the scc
7141 * fields of the nodes in "graph".
7142 * Combine the results in a sequence expressing the topological order.
7144 * If there is only one cluster left, then there is no need to introduce
7145 * a sequence node. Also, in this case, the cluster necessarily contains
7146 * the SCC at position 0 in the original graph and is therefore also
7147 * stored in the first cluster of "c".
7149 static __isl_give isl_schedule_node *finish_bands_clustering(
7150 __isl_take isl_schedule_node *node, struct isl_sched_graph *graph,
7151 struct isl_clustering *c)
7153 int i;
7154 isl_ctx *ctx;
7155 isl_union_set_list *filters;
7157 if (graph->scc == 1)
7158 return compute_schedule_finish_band(node, &c->cluster[0], 0);
7160 ctx = isl_schedule_node_get_ctx(node);
7162 filters = extract_sccs(ctx, graph);
7163 node = isl_schedule_node_insert_sequence(node, filters);
7165 for (i = 0; i < graph->scc; ++i) {
7166 int j = c->scc_cluster[i];
7167 node = isl_schedule_node_child(node, i);
7168 node = isl_schedule_node_child(node, 0);
7169 node = compute_schedule_finish_band(node, &c->cluster[j], 0);
7170 node = isl_schedule_node_parent(node);
7171 node = isl_schedule_node_parent(node);
7174 return node;
7177 /* Compute a schedule for a connected dependence graph by first considering
7178 * each strongly connected component (SCC) in the graph separately and then
7179 * incrementally combining them into clusters.
7180 * Return the updated schedule node.
7182 * Initially, each cluster consists of a single SCC, each with its
7183 * own band schedule. The algorithm then tries to merge pairs
7184 * of clusters along a proximity edge until no more suitable
7185 * proximity edges can be found. During this merging, the schedule
7186 * is maintained in the individual SCCs.
7187 * After the merging is completed, the full resulting clusters
7188 * are extracted and in finish_bands_clustering,
7189 * compute_schedule_finish_band is called on each of them to integrate
7190 * the band into "node" and to continue the computation.
7192 * compute_weights initializes the weights that are used by find_proximity.
7194 static __isl_give isl_schedule_node *compute_schedule_wcc_clustering(
7195 __isl_take isl_schedule_node *node, struct isl_sched_graph *graph)
7197 isl_ctx *ctx;
7198 struct isl_clustering c;
7199 int i;
7201 ctx = isl_schedule_node_get_ctx(node);
7203 if (clustering_init(ctx, &c, graph) < 0)
7204 goto error;
7206 if (compute_weights(graph, &c) < 0)
7207 goto error;
7209 for (;;) {
7210 i = find_proximity(graph, &c);
7211 if (i < 0)
7212 goto error;
7213 if (i >= graph->n_edge)
7214 break;
7215 if (merge_clusters_along_edge(ctx, graph, i, &c) < 0)
7216 goto error;
7219 if (extract_clusters(ctx, graph, &c) < 0)
7220 goto error;
7222 node = finish_bands_clustering(node, graph, &c);
7224 clustering_free(ctx, &c);
7225 return node;
7226 error:
7227 clustering_free(ctx, &c);
7228 return isl_schedule_node_free(node);
7231 /* Compute a schedule for a connected dependence graph and return
7232 * the updated schedule node.
7234 * If Feautrier's algorithm is selected, we first recursively try to satisfy
7235 * as many validity dependences as possible. When all validity dependences
7236 * are satisfied we extend the schedule to a full-dimensional schedule.
7238 * Call compute_schedule_wcc_whole or compute_schedule_wcc_clustering
7239 * depending on whether the user has selected the option to try and
7240 * compute a schedule for the entire (weakly connected) component first.
7241 * If there is only a single strongly connected component (SCC), then
7242 * there is no point in trying to combine SCCs
7243 * in compute_schedule_wcc_clustering, so compute_schedule_wcc_whole
7244 * is called instead.
7246 static __isl_give isl_schedule_node *compute_schedule_wcc(
7247 __isl_take isl_schedule_node *node, struct isl_sched_graph *graph)
7249 isl_ctx *ctx;
7251 if (!node)
7252 return NULL;
7254 ctx = isl_schedule_node_get_ctx(node);
7255 if (detect_sccs(ctx, graph) < 0)
7256 return isl_schedule_node_free(node);
7258 if (compute_maxvar(graph) < 0)
7259 return isl_schedule_node_free(node);
7261 if (need_feautrier_step(ctx, graph))
7262 return compute_schedule_wcc_feautrier(node, graph);
7264 if (graph->scc <= 1 || isl_options_get_schedule_whole_component(ctx))
7265 return compute_schedule_wcc_whole(node, graph);
7266 else
7267 return compute_schedule_wcc_clustering(node, graph);
7270 /* Compute a schedule for each group of nodes identified by node->scc
7271 * separately and then combine them in a sequence node (or as set node
7272 * if graph->weak is set) inserted at position "node" of the schedule tree.
7273 * Return the updated schedule node.
7275 * If "wcc" is set then each of the groups belongs to a single
7276 * weakly connected component in the dependence graph so that
7277 * there is no need for compute_sub_schedule to look for weakly
7278 * connected components.
7280 * If a set node would be introduced and if the number of components
7281 * is equal to the number of nodes, then check if the schedule
7282 * is already complete. If so, a redundant set node would be introduced
7283 * (without any further descendants) stating that the statements
7284 * can be executed in arbitrary order, which is also expressed
7285 * by the absence of any node. Refrain from inserting any nodes
7286 * in this case and simply return.
7288 static __isl_give isl_schedule_node *compute_component_schedule(
7289 __isl_take isl_schedule_node *node, struct isl_sched_graph *graph,
7290 int wcc)
7292 int component;
7293 isl_ctx *ctx;
7294 isl_union_set_list *filters;
7296 if (!node)
7297 return NULL;
7299 if (graph->weak && graph->scc == graph->n) {
7300 if (compute_maxvar(graph) < 0)
7301 return isl_schedule_node_free(node);
7302 if (graph->n_row >= graph->maxvar)
7303 return node;
7306 ctx = isl_schedule_node_get_ctx(node);
7307 filters = extract_sccs(ctx, graph);
7308 if (graph->weak)
7309 node = isl_schedule_node_insert_set(node, filters);
7310 else
7311 node = isl_schedule_node_insert_sequence(node, filters);
7313 for (component = 0; component < graph->scc; ++component) {
7314 node = isl_schedule_node_child(node, component);
7315 node = isl_schedule_node_child(node, 0);
7316 node = compute_sub_schedule(node, ctx, graph,
7317 &node_scc_exactly,
7318 &edge_scc_exactly, component, wcc);
7319 node = isl_schedule_node_parent(node);
7320 node = isl_schedule_node_parent(node);
7323 return node;
7326 /* Compute a schedule for the given dependence graph and insert it at "node".
7327 * Return the updated schedule node.
7329 * We first check if the graph is connected (through validity and conditional
7330 * validity dependences) and, if not, compute a schedule
7331 * for each component separately.
7332 * If the schedule_serialize_sccs option is set, then we check for strongly
7333 * connected components instead and compute a separate schedule for
7334 * each such strongly connected component.
7336 static __isl_give isl_schedule_node *compute_schedule(isl_schedule_node *node,
7337 struct isl_sched_graph *graph)
7339 isl_ctx *ctx;
7341 if (!node)
7342 return NULL;
7344 ctx = isl_schedule_node_get_ctx(node);
7345 if (isl_options_get_schedule_serialize_sccs(ctx)) {
7346 if (detect_sccs(ctx, graph) < 0)
7347 return isl_schedule_node_free(node);
7348 } else {
7349 if (detect_wccs(ctx, graph) < 0)
7350 return isl_schedule_node_free(node);
7353 if (graph->scc > 1)
7354 return compute_component_schedule(node, graph, 1);
7356 return compute_schedule_wcc(node, graph);
7359 /* Compute a schedule on sc->domain that respects the given schedule
7360 * constraints.
7362 * In particular, the schedule respects all the validity dependences.
7363 * If the default isl scheduling algorithm is used, it tries to minimize
7364 * the dependence distances over the proximity dependences.
7365 * If Feautrier's scheduling algorithm is used, the proximity dependence
7366 * distances are only minimized during the extension to a full-dimensional
7367 * schedule.
7369 * If there are any condition and conditional validity dependences,
7370 * then the conditional validity dependences may be violated inside
7371 * a tilable band, provided they have no adjacent non-local
7372 * condition dependences.
7374 __isl_give isl_schedule *isl_schedule_constraints_compute_schedule(
7375 __isl_take isl_schedule_constraints *sc)
7377 isl_ctx *ctx = isl_schedule_constraints_get_ctx(sc);
7378 struct isl_sched_graph graph = { 0 };
7379 isl_schedule *sched;
7380 isl_schedule_node *node;
7381 isl_union_set *domain;
7383 sc = isl_schedule_constraints_align_params(sc);
7385 domain = isl_schedule_constraints_get_domain(sc);
7386 if (isl_union_set_n_set(domain) == 0) {
7387 isl_schedule_constraints_free(sc);
7388 return isl_schedule_from_domain(domain);
7391 if (graph_init(&graph, sc) < 0)
7392 domain = isl_union_set_free(domain);
7394 node = isl_schedule_node_from_domain(domain);
7395 node = isl_schedule_node_child(node, 0);
7396 if (graph.n > 0)
7397 node = compute_schedule(node, &graph);
7398 sched = isl_schedule_node_get_schedule(node);
7399 isl_schedule_node_free(node);
7401 graph_free(ctx, &graph);
7402 isl_schedule_constraints_free(sc);
7404 return sched;
7407 /* Compute a schedule for the given union of domains that respects
7408 * all the validity dependences and minimizes
7409 * the dependence distances over the proximity dependences.
7411 * This function is kept for backward compatibility.
7413 __isl_give isl_schedule *isl_union_set_compute_schedule(
7414 __isl_take isl_union_set *domain,
7415 __isl_take isl_union_map *validity,
7416 __isl_take isl_union_map *proximity)
7418 isl_schedule_constraints *sc;
7420 sc = isl_schedule_constraints_on_domain(domain);
7421 sc = isl_schedule_constraints_set_validity(sc, validity);
7422 sc = isl_schedule_constraints_set_proximity(sc, proximity);
7424 return isl_schedule_constraints_compute_schedule(sc);