2 * Copyright 2011 INRIA Saclay
4 * Use of this software is governed by the GNU LGPLv2.1 license
6 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
7 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
11 #include <isl_ctx_private.h>
12 #include <isl_map_private.h>
13 #include <isl_space_private.h>
15 #include <isl/constraint.h>
16 #include <isl/schedule.h>
17 #include <isl_mat_private.h>
21 #include <isl_dim_map.h>
22 #include <isl_hmap_map_basic_set.h>
23 #include <isl_qsort.h>
24 #include <isl_schedule_private.h>
25 #include <isl_band_private.h>
26 #include <isl_list_private.h>
27 #include <isl_options_private.h>
30 * The scheduling algorithm implemented in this file was inspired by
31 * Bondhugula et al., "Automatic Transformations for Communication-Minimized
32 * Parallelization and Locality Optimization in the Polyhedral Model".
36 /* Internal information about a node that is used during the construction
38 * dim represents the space in which the domain lives
39 * sched is a matrix representation of the schedule being constructed
41 * sched_map is an isl_map representation of the same (partial) schedule
42 * sched_map may be NULL
43 * rank is the number of linearly independent rows in the linear part
45 * the columns of cmap represent a change of basis for the schedule
46 * coefficients; the first rank columns span the linear part of
48 * start is the first variable in the LP problem in the sequences that
49 * represents the schedule coefficients of this node
50 * nvar is the dimension of the domain
51 * nparam is the number of parameters or 0 if we are not constructing
52 * a parametric schedule
54 * scc is the index of SCC (or WCC) this node belongs to
56 * band contains the band index for each of the rows of the schedule.
57 * band_id is used to differentiate between separate bands at the same
58 * level within the same parent band, i.e., bands that are separated
59 * by the parent band or bands that are independent of each other.
60 * zero contains a boolean for each of the rows of the schedule,
61 * indicating whether the corresponding scheduling dimension results
62 * in zero dependence distances within its band and with respect
63 * to the proximity edges.
65 * index, min_index and on_stack are used during the SCC detection
66 * index represents the order in which nodes are visited.
67 * min_index is the index of the root of a (sub)component.
68 * on_stack indicates whether the node is currently on the stack.
70 struct isl_sched_node
{
92 static int node_has_dim(const void *entry
, const void *val
)
94 struct isl_sched_node
*node
= (struct isl_sched_node
*)entry
;
95 isl_space
*dim
= (isl_space
*)val
;
97 return isl_space_is_equal(node
->dim
, dim
);
100 /* An edge in the dependence graph. An edge may be used to
101 * ensure validity of the generated schedule, to minimize the dependence
104 * map is the dependence relation
105 * src is the source node
106 * dst is the sink node
107 * validity is set if the edge is used to ensure correctness
108 * proximity is set if the edge is used to minimize dependence distances
110 * For validity edges, start and end mark the sequence of inequality
111 * constraints in the LP problem that encode the validity constraint
112 * corresponding to this edge.
114 struct isl_sched_edge
{
117 struct isl_sched_node
*src
;
118 struct isl_sched_node
*dst
;
127 /* Internal information about the dependence graph used during
128 * the construction of the schedule.
130 * intra_hmap is a cache, mapping dependence relations to their dual,
131 * for dependences from a node to itself
132 * inter_hmap is a cache, mapping dependence relations to their dual,
133 * for dependences between distinct nodes
135 * n is the number of nodes
136 * node is the list of nodes
137 * maxvar is the maximal number of variables over all nodes
138 * n_row is the current (maximal) number of linearly independent
139 * rows in the node schedules
140 * n_total_row is the current number of rows in the node schedules
141 * n_band is the current number of completed bands
142 * band_start is the starting row in the node schedules of the current band
143 * root is set if this graph is the original dependence graph,
144 * without any splitting
146 * sorted contains a list of node indices sorted according to the
147 * SCC to which a node belongs
149 * n_edge is the number of edges
150 * edge is the list of edges
151 * edge_table contains pointers into the edge array, hashed on the source
152 * and sink spaces; the table only contains edges that represent
153 * validity constraints (and that may or may not also represent proximity
156 * node_table contains pointers into the node array, hashed on the space
158 * region contains a list of variable sequences that should be non-trivial
160 * lp contains the (I)LP problem used to obtain new schedule rows
162 * src_scc and dst_scc are the source and sink SCCs of an edge with
163 * conflicting constraints
165 * scc, sp, index and stack are used during the detection of SCCs
166 * scc is the number of the next SCC
167 * stack contains the nodes on the path from the root to the current node
168 * sp is the stack pointer
169 * index is the index of the last node visited
171 struct isl_sched_graph
{
172 isl_hmap_map_basic_set
*intra_hmap
;
173 isl_hmap_map_basic_set
*inter_hmap
;
175 struct isl_sched_node
*node
;
188 struct isl_sched_edge
*edge
;
190 struct isl_hash_table
*edge_table
;
192 struct isl_hash_table
*node_table
;
193 struct isl_region
*region
;
207 /* Initialize node_table based on the list of nodes.
209 static int graph_init_table(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
213 graph
->node_table
= isl_hash_table_alloc(ctx
, graph
->n
);
214 if (!graph
->node_table
)
217 for (i
= 0; i
< graph
->n
; ++i
) {
218 struct isl_hash_table_entry
*entry
;
221 hash
= isl_space_get_hash(graph
->node
[i
].dim
);
222 entry
= isl_hash_table_find(ctx
, graph
->node_table
, hash
,
224 graph
->node
[i
].dim
, 1);
227 entry
->data
= &graph
->node
[i
];
233 /* Return a pointer to the node that lives within the given space,
234 * or NULL if there is no such node.
236 static struct isl_sched_node
*graph_find_node(isl_ctx
*ctx
,
237 struct isl_sched_graph
*graph
, __isl_keep isl_space
*dim
)
239 struct isl_hash_table_entry
*entry
;
242 hash
= isl_space_get_hash(dim
);
243 entry
= isl_hash_table_find(ctx
, graph
->node_table
, hash
,
244 &node_has_dim
, dim
, 0);
246 return entry
? entry
->data
: NULL
;
249 static int edge_has_src_and_dst(const void *entry
, const void *val
)
251 const struct isl_sched_edge
*edge
= entry
;
252 const struct isl_sched_edge
*temp
= val
;
254 return edge
->src
== temp
->src
&& edge
->dst
== temp
->dst
;
257 /* Initialize edge_table based on the list of edges.
258 * Only edges with validity set are added to the table.
260 static int graph_init_edge_table(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
264 graph
->edge_table
= isl_hash_table_alloc(ctx
, graph
->n_edge
);
265 if (!graph
->edge_table
)
268 for (i
= 0; i
< graph
->n_edge
; ++i
) {
269 struct isl_hash_table_entry
*entry
;
272 if (!graph
->edge
[i
].validity
)
275 hash
= isl_hash_init();
276 hash
= isl_hash_builtin(hash
, graph
->edge
[i
].src
);
277 hash
= isl_hash_builtin(hash
, graph
->edge
[i
].dst
);
278 entry
= isl_hash_table_find(ctx
, graph
->edge_table
, hash
,
279 &edge_has_src_and_dst
,
283 entry
->data
= &graph
->edge
[i
];
289 /* Check whether the dependence graph has a (validity) edge
290 * between the given two nodes.
292 static int graph_has_edge(struct isl_sched_graph
*graph
,
293 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
295 isl_ctx
*ctx
= isl_space_get_ctx(src
->dim
);
296 struct isl_hash_table_entry
*entry
;
298 struct isl_sched_edge temp
= { .src
= src
, .dst
= dst
};
299 struct isl_sched_edge
*edge
;
302 hash
= isl_hash_init();
303 hash
= isl_hash_builtin(hash
, temp
.src
);
304 hash
= isl_hash_builtin(hash
, temp
.dst
);
305 entry
= isl_hash_table_find(ctx
, graph
->edge_table
, hash
,
306 &edge_has_src_and_dst
, &temp
, 0);
311 empty
= isl_map_plain_is_empty(edge
->map
);
318 static int graph_alloc(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
319 int n_node
, int n_edge
)
324 graph
->n_edge
= n_edge
;
325 graph
->node
= isl_calloc_array(ctx
, struct isl_sched_node
, graph
->n
);
326 graph
->sorted
= isl_calloc_array(ctx
, int, graph
->n
);
327 graph
->region
= isl_alloc_array(ctx
, struct isl_region
, graph
->n
);
328 graph
->stack
= isl_alloc_array(ctx
, int, graph
->n
);
329 graph
->edge
= isl_calloc_array(ctx
,
330 struct isl_sched_edge
, graph
->n_edge
);
332 graph
->intra_hmap
= isl_hmap_map_basic_set_alloc(ctx
, 2 * n_edge
);
333 graph
->inter_hmap
= isl_hmap_map_basic_set_alloc(ctx
, 2 * n_edge
);
335 if (!graph
->node
|| !graph
->region
|| !graph
->stack
|| !graph
->edge
||
339 for(i
= 0; i
< graph
->n
; ++i
)
340 graph
->sorted
[i
] = i
;
345 static void graph_free(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
349 isl_hmap_map_basic_set_free(ctx
, graph
->intra_hmap
);
350 isl_hmap_map_basic_set_free(ctx
, graph
->inter_hmap
);
352 for (i
= 0; i
< graph
->n
; ++i
) {
353 isl_space_free(graph
->node
[i
].dim
);
354 isl_mat_free(graph
->node
[i
].sched
);
355 isl_map_free(graph
->node
[i
].sched_map
);
356 isl_mat_free(graph
->node
[i
].cmap
);
358 free(graph
->node
[i
].band
);
359 free(graph
->node
[i
].band_id
);
360 free(graph
->node
[i
].zero
);
365 for (i
= 0; i
< graph
->n_edge
; ++i
)
366 isl_map_free(graph
->edge
[i
].map
);
370 isl_hash_table_free(ctx
, graph
->edge_table
);
371 isl_hash_table_free(ctx
, graph
->node_table
);
372 isl_basic_set_free(graph
->lp
);
375 /* Add a new node to the graph representing the given set.
377 static int extract_node(__isl_take isl_set
*set
, void *user
)
383 struct isl_sched_graph
*graph
= user
;
384 int *band
, *band_id
, *zero
;
386 ctx
= isl_set_get_ctx(set
);
387 dim
= isl_set_get_space(set
);
389 nvar
= isl_space_dim(dim
, isl_dim_set
);
390 nparam
= isl_space_dim(dim
, isl_dim_param
);
391 if (!ctx
->opt
->schedule_parametric
)
393 sched
= isl_mat_alloc(ctx
, 0, 1 + nparam
+ nvar
);
394 graph
->node
[graph
->n
].dim
= dim
;
395 graph
->node
[graph
->n
].nvar
= nvar
;
396 graph
->node
[graph
->n
].nparam
= nparam
;
397 graph
->node
[graph
->n
].sched
= sched
;
398 graph
->node
[graph
->n
].sched_map
= NULL
;
399 band
= isl_alloc_array(ctx
, int, graph
->n_edge
+ nvar
);
400 graph
->node
[graph
->n
].band
= band
;
401 band_id
= isl_calloc_array(ctx
, int, graph
->n_edge
+ nvar
);
402 graph
->node
[graph
->n
].band_id
= band_id
;
403 zero
= isl_calloc_array(ctx
, int, graph
->n_edge
+ nvar
);
404 graph
->node
[graph
->n
].zero
= zero
;
407 if (!sched
|| !band
|| !band_id
|| !zero
)
413 /* Add a new edge to the graph based on the given map.
414 * Edges are first extracted from the validity dependences,
415 * from which the edge_table is constructed.
416 * Afterwards, the proximity dependences are added. If a proximity
417 * dependence relation happens to be identical to one of the
418 * validity dependence relations added before, then we don't create
419 * a new edge, but instead mark the original edge as also representing
420 * a proximity dependence.
422 static int extract_edge(__isl_take isl_map
*map
, void *user
)
424 isl_ctx
*ctx
= isl_map_get_ctx(map
);
425 struct isl_sched_graph
*graph
= user
;
426 struct isl_sched_node
*src
, *dst
;
429 dim
= isl_space_domain(isl_map_get_space(map
));
430 src
= graph_find_node(ctx
, graph
, dim
);
432 dim
= isl_space_range(isl_map_get_space(map
));
433 dst
= graph_find_node(ctx
, graph
, dim
);
441 graph
->edge
[graph
->n_edge
].src
= src
;
442 graph
->edge
[graph
->n_edge
].dst
= dst
;
443 graph
->edge
[graph
->n_edge
].map
= map
;
444 graph
->edge
[graph
->n_edge
].validity
= !graph
->edge_table
;
445 graph
->edge
[graph
->n_edge
].proximity
= !!graph
->edge_table
;
448 if (graph
->edge_table
) {
450 struct isl_hash_table_entry
*entry
;
451 struct isl_sched_edge
*edge
;
454 hash
= isl_hash_init();
455 hash
= isl_hash_builtin(hash
, src
);
456 hash
= isl_hash_builtin(hash
, dst
);
457 entry
= isl_hash_table_find(ctx
, graph
->edge_table
, hash
,
458 &edge_has_src_and_dst
,
459 &graph
->edge
[graph
->n_edge
- 1], 0);
463 is_equal
= isl_map_plain_is_equal(map
, edge
->map
);
477 /* Check whether there is a validity dependence from src to dst,
478 * forcing dst to follow src.
480 static int node_follows(struct isl_sched_graph
*graph
,
481 struct isl_sched_node
*dst
, struct isl_sched_node
*src
)
483 return graph_has_edge(graph
, src
, dst
);
486 /* Perform Tarjan's algorithm for computing the strongly connected components
487 * in the dependence graph (only validity edges).
488 * If directed is not set, we consider the graph to be undirected and
489 * we effectively compute the (weakly) connected components.
491 static int detect_sccs_tarjan(struct isl_sched_graph
*g
, int i
, int directed
)
495 g
->node
[i
].index
= g
->index
;
496 g
->node
[i
].min_index
= g
->index
;
497 g
->node
[i
].on_stack
= 1;
499 g
->stack
[g
->sp
++] = i
;
501 for (j
= g
->n
- 1; j
>= 0; --j
) {
506 if (g
->node
[j
].index
>= 0 &&
507 (!g
->node
[j
].on_stack
||
508 g
->node
[j
].index
> g
->node
[i
].min_index
))
511 f
= node_follows(g
, &g
->node
[i
], &g
->node
[j
]);
514 if (!f
&& !directed
) {
515 f
= node_follows(g
, &g
->node
[j
], &g
->node
[i
]);
521 if (g
->node
[j
].index
< 0) {
522 detect_sccs_tarjan(g
, j
, directed
);
523 if (g
->node
[j
].min_index
< g
->node
[i
].min_index
)
524 g
->node
[i
].min_index
= g
->node
[j
].min_index
;
525 } else if (g
->node
[j
].index
< g
->node
[i
].min_index
)
526 g
->node
[i
].min_index
= g
->node
[j
].index
;
529 if (g
->node
[i
].index
!= g
->node
[i
].min_index
)
533 j
= g
->stack
[--g
->sp
];
534 g
->node
[j
].on_stack
= 0;
535 g
->node
[j
].scc
= g
->scc
;
542 static int detect_ccs(struct isl_sched_graph
*graph
, int directed
)
549 for (i
= graph
->n
- 1; i
>= 0; --i
)
550 graph
->node
[i
].index
= -1;
552 for (i
= graph
->n
- 1; i
>= 0; --i
) {
553 if (graph
->node
[i
].index
>= 0)
555 if (detect_sccs_tarjan(graph
, i
, directed
) < 0)
562 /* Apply Tarjan's algorithm to detect the strongly connected components
563 * in the dependence graph.
565 static int detect_sccs(struct isl_sched_graph
*graph
)
567 return detect_ccs(graph
, 1);
570 /* Apply Tarjan's algorithm to detect the (weakly) connected components
571 * in the dependence graph.
573 static int detect_wccs(struct isl_sched_graph
*graph
)
575 return detect_ccs(graph
, 0);
578 static int cmp_scc(const void *a
, const void *b
, void *data
)
580 struct isl_sched_graph
*graph
= data
;
584 return graph
->node
[*i1
].scc
- graph
->node
[*i2
].scc
;
587 /* Sort the elements of graph->sorted according to the corresponding SCCs.
589 static void sort_sccs(struct isl_sched_graph
*graph
)
591 isl_quicksort(graph
->sorted
, graph
->n
, sizeof(int), &cmp_scc
, graph
);
594 /* Given a dependence relation R from a node to itself,
595 * construct the set of coefficients of valid constraints for elements
596 * in that dependence relation.
597 * In particular, the result contains tuples of coefficients
598 * c_0, c_n, c_x such that
600 * c_0 + c_n n + c_x y - c_x x >= 0 for each (x,y) in R
604 * c_0 + c_n n + c_x d >= 0 for each d in delta R = { y - x | (x,y) in R }
606 * We choose here to compute the dual of delta R.
607 * Alternatively, we could have computed the dual of R, resulting
608 * in a set of tuples c_0, c_n, c_x, c_y, and then
609 * plugged in (c_0, c_n, c_x, -c_x).
611 static __isl_give isl_basic_set
*intra_coefficients(
612 struct isl_sched_graph
*graph
, __isl_take isl_map
*map
)
614 isl_ctx
*ctx
= isl_map_get_ctx(map
);
618 if (isl_hmap_map_basic_set_has(ctx
, graph
->intra_hmap
, map
))
619 return isl_hmap_map_basic_set_get(ctx
, graph
->intra_hmap
, map
);
621 delta
= isl_set_remove_divs(isl_map_deltas(isl_map_copy(map
)));
622 coef
= isl_set_coefficients(delta
);
623 isl_hmap_map_basic_set_set(ctx
, graph
->intra_hmap
, map
,
624 isl_basic_set_copy(coef
));
629 /* Given a dependence relation R, * construct the set of coefficients
630 * of valid constraints for elements in that dependence relation.
631 * In particular, the result contains tuples of coefficients
632 * c_0, c_n, c_x, c_y such that
634 * c_0 + c_n n + c_x x + c_y y >= 0 for each (x,y) in R
637 static __isl_give isl_basic_set
*inter_coefficients(
638 struct isl_sched_graph
*graph
, __isl_take isl_map
*map
)
640 isl_ctx
*ctx
= isl_map_get_ctx(map
);
644 if (isl_hmap_map_basic_set_has(ctx
, graph
->inter_hmap
, map
))
645 return isl_hmap_map_basic_set_get(ctx
, graph
->inter_hmap
, map
);
647 set
= isl_map_wrap(isl_map_remove_divs(isl_map_copy(map
)));
648 coef
= isl_set_coefficients(set
);
649 isl_hmap_map_basic_set_set(ctx
, graph
->inter_hmap
, map
,
650 isl_basic_set_copy(coef
));
655 /* Add constraints to graph->lp that force validity for the given
656 * dependence from a node i to itself.
657 * That is, add constraints that enforce
659 * (c_i_0 + c_i_n n + c_i_x y) - (c_i_0 + c_i_n n + c_i_x x)
660 * = c_i_x (y - x) >= 0
662 * for each (x,y) in R.
663 * We obtain general constraints on coefficients (c_0, c_n, c_x)
664 * of valid constraints for (y - x) and then plug in (0, 0, c_i_x^+ - c_i_x^-),
665 * where c_i_x = c_i_x^+ - c_i_x^-, with c_i_x^+ and c_i_x^- non-negative.
666 * In graph->lp, the c_i_x^- appear before their c_i_x^+ counterpart.
668 * Actually, we do not construct constraints for the c_i_x themselves,
669 * but for the coefficients of c_i_x written as a linear combination
670 * of the columns in node->cmap.
672 static int add_intra_validity_constraints(struct isl_sched_graph
*graph
,
673 struct isl_sched_edge
*edge
)
676 isl_map
*map
= isl_map_copy(edge
->map
);
677 isl_ctx
*ctx
= isl_map_get_ctx(map
);
679 isl_dim_map
*dim_map
;
681 struct isl_sched_node
*node
= edge
->src
;
683 coef
= intra_coefficients(graph
, map
);
685 dim
= isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef
)));
687 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
688 isl_space_dim(dim
, isl_dim_set
), isl_mat_copy(node
->cmap
));
690 total
= isl_basic_set_total_dim(graph
->lp
);
691 dim_map
= isl_dim_map_alloc(ctx
, total
);
692 isl_dim_map_range(dim_map
, node
->start
+ 2 * node
->nparam
+ 1, 2,
693 isl_space_dim(dim
, isl_dim_set
), 1,
695 isl_dim_map_range(dim_map
, node
->start
+ 2 * node
->nparam
+ 2, 2,
696 isl_space_dim(dim
, isl_dim_set
), 1,
698 graph
->lp
= isl_basic_set_extend_constraints(graph
->lp
,
699 coef
->n_eq
, coef
->n_ineq
);
700 graph
->lp
= isl_basic_set_add_constraints_dim_map(graph
->lp
,
707 /* Add constraints to graph->lp that force validity for the given
708 * dependence from node i to node j.
709 * That is, add constraints that enforce
711 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) >= 0
713 * for each (x,y) in R.
714 * We obtain general constraints on coefficients (c_0, c_n, c_x, c_y)
715 * of valid constraints for R and then plug in
716 * (c_j_0 - c_i_0, c_j_n^+ - c_j_n^- - (c_i_n^+ - c_i_n^-),
717 * c_j_x^+ - c_j_x^- - (c_i_x^+ - c_i_x^-)),
718 * where c_* = c_*^+ - c_*^-, with c_*^+ and c_*^- non-negative.
719 * In graph->lp, the c_*^- appear before their c_*^+ counterpart.
721 * Actually, we do not construct constraints for the c_*_x themselves,
722 * but for the coefficients of c_*_x written as a linear combination
723 * of the columns in node->cmap.
725 static int add_inter_validity_constraints(struct isl_sched_graph
*graph
,
726 struct isl_sched_edge
*edge
)
729 isl_map
*map
= isl_map_copy(edge
->map
);
730 isl_ctx
*ctx
= isl_map_get_ctx(map
);
732 isl_dim_map
*dim_map
;
734 struct isl_sched_node
*src
= edge
->src
;
735 struct isl_sched_node
*dst
= edge
->dst
;
737 coef
= inter_coefficients(graph
, map
);
739 dim
= isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef
)));
741 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
742 isl_space_dim(dim
, isl_dim_set
), isl_mat_copy(src
->cmap
));
743 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
744 isl_space_dim(dim
, isl_dim_set
) + src
->nvar
,
745 isl_mat_copy(dst
->cmap
));
747 total
= isl_basic_set_total_dim(graph
->lp
);
748 dim_map
= isl_dim_map_alloc(ctx
, total
);
750 isl_dim_map_range(dim_map
, dst
->start
, 0, 0, 0, 1, 1);
751 isl_dim_map_range(dim_map
, dst
->start
+ 1, 2, 1, 1, dst
->nparam
, -1);
752 isl_dim_map_range(dim_map
, dst
->start
+ 2, 2, 1, 1, dst
->nparam
, 1);
753 isl_dim_map_range(dim_map
, dst
->start
+ 2 * dst
->nparam
+ 1, 2,
754 isl_space_dim(dim
, isl_dim_set
) + src
->nvar
, 1,
756 isl_dim_map_range(dim_map
, dst
->start
+ 2 * dst
->nparam
+ 2, 2,
757 isl_space_dim(dim
, isl_dim_set
) + src
->nvar
, 1,
760 isl_dim_map_range(dim_map
, src
->start
, 0, 0, 0, 1, -1);
761 isl_dim_map_range(dim_map
, src
->start
+ 1, 2, 1, 1, src
->nparam
, 1);
762 isl_dim_map_range(dim_map
, src
->start
+ 2, 2, 1, 1, src
->nparam
, -1);
763 isl_dim_map_range(dim_map
, src
->start
+ 2 * src
->nparam
+ 1, 2,
764 isl_space_dim(dim
, isl_dim_set
), 1,
766 isl_dim_map_range(dim_map
, src
->start
+ 2 * src
->nparam
+ 2, 2,
767 isl_space_dim(dim
, isl_dim_set
), 1,
770 edge
->start
= graph
->lp
->n_ineq
;
771 graph
->lp
= isl_basic_set_extend_constraints(graph
->lp
,
772 coef
->n_eq
, coef
->n_ineq
);
773 graph
->lp
= isl_basic_set_add_constraints_dim_map(graph
->lp
,
776 edge
->end
= graph
->lp
->n_ineq
;
781 /* Add constraints to graph->lp that bound the dependence distance for the given
782 * dependence from a node i to itself.
783 * If s = 1, we add the constraint
785 * c_i_x (y - x) <= m_0 + m_n n
789 * -c_i_x (y - x) + m_0 + m_n n >= 0
791 * for each (x,y) in R.
792 * If s = -1, we add the constraint
794 * -c_i_x (y - x) <= m_0 + m_n n
798 * c_i_x (y - x) + m_0 + m_n n >= 0
800 * for each (x,y) in R.
801 * We obtain general constraints on coefficients (c_0, c_n, c_x)
802 * of valid constraints for (y - x) and then plug in (m_0, m_n, -s * c_i_x),
803 * with each coefficient (except m_0) represented as a pair of non-negative
806 * Actually, we do not construct constraints for the c_i_x themselves,
807 * but for the coefficients of c_i_x written as a linear combination
808 * of the columns in node->cmap.
810 static int add_intra_proximity_constraints(struct isl_sched_graph
*graph
,
811 struct isl_sched_edge
*edge
, int s
)
815 isl_map
*map
= isl_map_copy(edge
->map
);
816 isl_ctx
*ctx
= isl_map_get_ctx(map
);
818 isl_dim_map
*dim_map
;
820 struct isl_sched_node
*node
= edge
->src
;
822 coef
= intra_coefficients(graph
, map
);
824 dim
= isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef
)));
826 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
827 isl_space_dim(dim
, isl_dim_set
), isl_mat_copy(node
->cmap
));
829 nparam
= isl_space_dim(node
->dim
, isl_dim_param
);
830 total
= isl_basic_set_total_dim(graph
->lp
);
831 dim_map
= isl_dim_map_alloc(ctx
, total
);
832 isl_dim_map_range(dim_map
, 1, 0, 0, 0, 1, 1);
833 isl_dim_map_range(dim_map
, 4, 2, 1, 1, nparam
, -1);
834 isl_dim_map_range(dim_map
, 5, 2, 1, 1, nparam
, 1);
835 isl_dim_map_range(dim_map
, node
->start
+ 2 * node
->nparam
+ 1, 2,
836 isl_space_dim(dim
, isl_dim_set
), 1,
838 isl_dim_map_range(dim_map
, node
->start
+ 2 * node
->nparam
+ 2, 2,
839 isl_space_dim(dim
, isl_dim_set
), 1,
841 graph
->lp
= isl_basic_set_extend_constraints(graph
->lp
,
842 coef
->n_eq
, coef
->n_ineq
);
843 graph
->lp
= isl_basic_set_add_constraints_dim_map(graph
->lp
,
850 /* Add constraints to graph->lp that bound the dependence distance for the given
851 * dependence from node i to node j.
852 * If s = 1, we add the constraint
854 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x)
859 * -(c_j_0 + c_j_n n + c_j_x y) + (c_i_0 + c_i_n n + c_i_x x) +
862 * for each (x,y) in R.
863 * If s = -1, we add the constraint
865 * -((c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x))
870 * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) +
873 * for each (x,y) in R.
874 * We obtain general constraints on coefficients (c_0, c_n, c_x, c_y)
875 * of valid constraints for R and then plug in
876 * (m_0 - s*c_j_0 + s*c_i_0, m_n - s*c_j_n + s*c_i_n,
878 * with each coefficient (except m_0, c_j_0 and c_i_0)
879 * represented as a pair of non-negative coefficients.
881 * Actually, we do not construct constraints for the c_*_x themselves,
882 * but for the coefficients of c_*_x written as a linear combination
883 * of the columns in node->cmap.
885 static int add_inter_proximity_constraints(struct isl_sched_graph
*graph
,
886 struct isl_sched_edge
*edge
, int s
)
890 isl_map
*map
= isl_map_copy(edge
->map
);
891 isl_ctx
*ctx
= isl_map_get_ctx(map
);
893 isl_dim_map
*dim_map
;
895 struct isl_sched_node
*src
= edge
->src
;
896 struct isl_sched_node
*dst
= edge
->dst
;
898 coef
= inter_coefficients(graph
, map
);
900 dim
= isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef
)));
902 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
903 isl_space_dim(dim
, isl_dim_set
), isl_mat_copy(src
->cmap
));
904 coef
= isl_basic_set_transform_dims(coef
, isl_dim_set
,
905 isl_space_dim(dim
, isl_dim_set
) + src
->nvar
,
906 isl_mat_copy(dst
->cmap
));
908 nparam
= isl_space_dim(src
->dim
, isl_dim_param
);
909 total
= isl_basic_set_total_dim(graph
->lp
);
910 dim_map
= isl_dim_map_alloc(ctx
, total
);
912 isl_dim_map_range(dim_map
, 1, 0, 0, 0, 1, 1);
913 isl_dim_map_range(dim_map
, 4, 2, 1, 1, nparam
, -1);
914 isl_dim_map_range(dim_map
, 5, 2, 1, 1, nparam
, 1);
916 isl_dim_map_range(dim_map
, dst
->start
, 0, 0, 0, 1, -s
);
917 isl_dim_map_range(dim_map
, dst
->start
+ 1, 2, 1, 1, dst
->nparam
, s
);
918 isl_dim_map_range(dim_map
, dst
->start
+ 2, 2, 1, 1, dst
->nparam
, -s
);
919 isl_dim_map_range(dim_map
, dst
->start
+ 2 * dst
->nparam
+ 1, 2,
920 isl_space_dim(dim
, isl_dim_set
) + src
->nvar
, 1,
922 isl_dim_map_range(dim_map
, dst
->start
+ 2 * dst
->nparam
+ 2, 2,
923 isl_space_dim(dim
, isl_dim_set
) + src
->nvar
, 1,
926 isl_dim_map_range(dim_map
, src
->start
, 0, 0, 0, 1, s
);
927 isl_dim_map_range(dim_map
, src
->start
+ 1, 2, 1, 1, src
->nparam
, -s
);
928 isl_dim_map_range(dim_map
, src
->start
+ 2, 2, 1, 1, src
->nparam
, s
);
929 isl_dim_map_range(dim_map
, src
->start
+ 2 * src
->nparam
+ 1, 2,
930 isl_space_dim(dim
, isl_dim_set
), 1,
932 isl_dim_map_range(dim_map
, src
->start
+ 2 * src
->nparam
+ 2, 2,
933 isl_space_dim(dim
, isl_dim_set
), 1,
936 graph
->lp
= isl_basic_set_extend_constraints(graph
->lp
,
937 coef
->n_eq
, coef
->n_ineq
);
938 graph
->lp
= isl_basic_set_add_constraints_dim_map(graph
->lp
,
945 static int add_all_validity_constraints(struct isl_sched_graph
*graph
)
949 for (i
= 0; i
< graph
->n_edge
; ++i
) {
950 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
953 if (edge
->src
!= edge
->dst
)
955 if (add_intra_validity_constraints(graph
, edge
) < 0)
959 for (i
= 0; i
< graph
->n_edge
; ++i
) {
960 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
963 if (edge
->src
== edge
->dst
)
965 if (add_inter_validity_constraints(graph
, edge
) < 0)
972 /* Add constraints to graph->lp that bound the dependence distance
973 * for all dependence relations.
974 * If a given proximity dependence is identical to a validity
975 * dependence, then the dependence distance is already bounded
976 * from below (by zero), so we only need to bound the distance
978 * Otherwise, we need to bound the distance both from above and from below.
980 static int add_all_proximity_constraints(struct isl_sched_graph
*graph
)
984 for (i
= 0; i
< graph
->n_edge
; ++i
) {
985 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
986 if (!edge
->proximity
)
988 if (edge
->src
== edge
->dst
&&
989 add_intra_proximity_constraints(graph
, edge
, 1) < 0)
991 if (edge
->src
!= edge
->dst
&&
992 add_inter_proximity_constraints(graph
, edge
, 1) < 0)
996 if (edge
->src
== edge
->dst
&&
997 add_intra_proximity_constraints(graph
, edge
, -1) < 0)
999 if (edge
->src
!= edge
->dst
&&
1000 add_inter_proximity_constraints(graph
, edge
, -1) < 0)
1007 /* Compute a basis for the rows in the linear part of the schedule
1008 * and extend this basis to a full basis. The remaining rows
1009 * can then be used to force linear independence from the rows
1012 * In particular, given the schedule rows S, we compute
1016 * with H the Hermite normal form of S. That is, all but the
1017 * first rank columns of Q are zero and so each row in S is
1018 * a linear combination of the first rank rows of Q.
1019 * The matrix Q is then transposed because we will write the
1020 * coefficients of the next schedule row as a column vector s
1021 * and express this s as a linear combination s = Q c of the
1024 static int node_update_cmap(struct isl_sched_node
*node
)
1027 int n_row
= isl_mat_rows(node
->sched
);
1029 H
= isl_mat_sub_alloc(node
->sched
, 0, n_row
,
1030 1 + node
->nparam
, node
->nvar
);
1032 H
= isl_mat_left_hermite(H
, 0, NULL
, &Q
);
1033 isl_mat_free(node
->cmap
);
1034 node
->cmap
= isl_mat_transpose(Q
);
1035 node
->rank
= isl_mat_initial_non_zero_cols(H
);
1038 if (!node
->cmap
|| node
->rank
< 0)
1043 /* Count the number of equality and inequality constraints
1044 * that will be added for the given map.
1045 * If once is set, then we count
1046 * each edge exactly once. Otherwise, we count as follows
1047 * validity -> 1 (>= 0)
1048 * validity+proximity -> 2 (>= 0 and upper bound)
1049 * proximity -> 2 (lower and upper bound)
1051 static int count_map_constraints(struct isl_sched_graph
*graph
,
1052 struct isl_sched_edge
*edge
, __isl_take isl_map
*map
,
1053 int *n_eq
, int *n_ineq
, int once
)
1055 isl_basic_set
*coef
;
1056 int f
= once
? 1 : edge
->proximity
? 2 : 1;
1058 if (edge
->src
== edge
->dst
)
1059 coef
= intra_coefficients(graph
, map
);
1061 coef
= inter_coefficients(graph
, map
);
1064 *n_eq
+= f
* coef
->n_eq
;
1065 *n_ineq
+= f
* coef
->n_ineq
;
1066 isl_basic_set_free(coef
);
1071 /* Count the number of equality and inequality constraints
1072 * that will be added to the main lp problem.
1073 * If once is set, then we count
1074 * each edge exactly once. Otherwise, we count as follows
1075 * validity -> 1 (>= 0)
1076 * validity+proximity -> 2 (>= 0 and upper bound)
1077 * proximity -> 2 (lower and upper bound)
1079 static int count_constraints(struct isl_sched_graph
*graph
,
1080 int *n_eq
, int *n_ineq
, int once
)
1084 *n_eq
= *n_ineq
= 0;
1085 for (i
= 0; i
< graph
->n_edge
; ++i
) {
1086 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
1087 isl_map
*map
= isl_map_copy(edge
->map
);
1089 if (count_map_constraints(graph
, edge
, map
,
1090 n_eq
, n_ineq
, once
) < 0)
1097 /* Construct an ILP problem for finding schedule coefficients
1098 * that result in non-negative, but small dependence distances
1099 * over all dependences.
1100 * In particular, the dependence distances over proximity edges
1101 * are bounded by m_0 + m_n n and we compute schedule coefficients
1102 * with small values (preferably zero) of m_n and m_0.
1104 * All variables of the ILP are non-negative. The actual coefficients
1105 * may be negative, so each coefficient is represented as the difference
1106 * of two non-negative variables. The negative part always appears
1107 * immediately before the positive part.
1108 * Other than that, the variables have the following order
1110 * - sum of positive and negative parts of m_n coefficients
1112 * - sum of positive and negative parts of all c_n coefficients
1113 * (unconstrained when computing non-parametric schedules)
1114 * - sum of positive and negative parts of all c_x coefficients
1115 * - positive and negative parts of m_n coefficients
1118 * - positive and negative parts of c_i_n (if parametric)
1119 * - positive and negative parts of c_i_x
1121 * The c_i_x are not represented directly, but through the columns of
1122 * node->cmap. That is, the computed values are for variable t_i_x
1123 * such that c_i_x = Q t_i_x with Q equal to node->cmap.
1125 * The constraints are those from the edges plus two or three equalities
1126 * to express the sums.
1128 * If force_zero is set, then we add equalities to ensure that
1129 * the sum of the m_n coefficients and m_0 are both zero.
1131 static int setup_lp(isl_ctx
*ctx
, struct isl_sched_graph
*graph
,
1142 int max_constant_term
;
1144 max_constant_term
= ctx
->opt
->schedule_max_constant_term
;
1146 parametric
= ctx
->opt
->schedule_parametric
;
1147 nparam
= isl_space_dim(graph
->node
[0].dim
, isl_dim_param
);
1149 total
= param_pos
+ 2 * nparam
;
1150 for (i
= 0; i
< graph
->n
; ++i
) {
1151 struct isl_sched_node
*node
= &graph
->node
[graph
->sorted
[i
]];
1152 if (node_update_cmap(node
) < 0)
1154 node
->start
= total
;
1155 total
+= 1 + 2 * (node
->nparam
+ node
->nvar
);
1158 if (count_constraints(graph
, &n_eq
, &n_ineq
, 0) < 0)
1161 dim
= isl_space_set_alloc(ctx
, 0, total
);
1162 isl_basic_set_free(graph
->lp
);
1163 n_eq
+= 2 + parametric
+ force_zero
;
1164 if (max_constant_term
!= -1)
1167 graph
->lp
= isl_basic_set_alloc_space(dim
, 0, n_eq
, n_ineq
);
1169 k
= isl_basic_set_alloc_equality(graph
->lp
);
1172 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
1174 isl_int_set_si(graph
->lp
->eq
[k
][1], -1);
1175 for (i
= 0; i
< 2 * nparam
; ++i
)
1176 isl_int_set_si(graph
->lp
->eq
[k
][1 + param_pos
+ i
], 1);
1179 k
= isl_basic_set_alloc_equality(graph
->lp
);
1182 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
1183 isl_int_set_si(graph
->lp
->eq
[k
][2], -1);
1187 k
= isl_basic_set_alloc_equality(graph
->lp
);
1190 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
1191 isl_int_set_si(graph
->lp
->eq
[k
][3], -1);
1192 for (i
= 0; i
< graph
->n
; ++i
) {
1193 int pos
= 1 + graph
->node
[i
].start
+ 1;
1195 for (j
= 0; j
< 2 * graph
->node
[i
].nparam
; ++j
)
1196 isl_int_set_si(graph
->lp
->eq
[k
][pos
+ j
], 1);
1200 k
= isl_basic_set_alloc_equality(graph
->lp
);
1203 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
1204 isl_int_set_si(graph
->lp
->eq
[k
][4], -1);
1205 for (i
= 0; i
< graph
->n
; ++i
) {
1206 struct isl_sched_node
*node
= &graph
->node
[i
];
1207 int pos
= 1 + node
->start
+ 1 + 2 * node
->nparam
;
1209 for (j
= 0; j
< 2 * node
->nvar
; ++j
)
1210 isl_int_set_si(graph
->lp
->eq
[k
][pos
+ j
], 1);
1213 if (max_constant_term
!= -1)
1214 for (i
= 0; i
< graph
->n
; ++i
) {
1215 struct isl_sched_node
*node
= &graph
->node
[i
];
1216 k
= isl_basic_set_alloc_inequality(graph
->lp
);
1219 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
1220 isl_int_set_si(graph
->lp
->ineq
[k
][1 + node
->start
], -1);
1221 isl_int_set_si(graph
->lp
->ineq
[k
][0], max_constant_term
);
1224 if (add_all_validity_constraints(graph
) < 0)
1226 if (add_all_proximity_constraints(graph
) < 0)
1232 /* Analyze the conflicting constraint found by
1233 * isl_tab_basic_set_non_trivial_lexmin. If it corresponds to the validity
1234 * constraint of one of the edges between distinct nodes, living, moreover
1235 * in distinct SCCs, then record the source and sink SCC as this may
1236 * be a good place to cut between SCCs.
1238 static int check_conflict(int con
, void *user
)
1241 struct isl_sched_graph
*graph
= user
;
1243 if (graph
->src_scc
>= 0)
1246 con
-= graph
->lp
->n_eq
;
1248 if (con
>= graph
->lp
->n_ineq
)
1251 for (i
= 0; i
< graph
->n_edge
; ++i
) {
1252 if (!graph
->edge
[i
].validity
)
1254 if (graph
->edge
[i
].src
== graph
->edge
[i
].dst
)
1256 if (graph
->edge
[i
].src
->scc
== graph
->edge
[i
].dst
->scc
)
1258 if (graph
->edge
[i
].start
> con
)
1260 if (graph
->edge
[i
].end
<= con
)
1262 graph
->src_scc
= graph
->edge
[i
].src
->scc
;
1263 graph
->dst_scc
= graph
->edge
[i
].dst
->scc
;
1269 /* Check whether the next schedule row of the given node needs to be
1270 * non-trivial. Lower-dimensional domains may have some trivial rows,
1271 * but as soon as the number of remaining required non-trivial rows
1272 * is as large as the number or remaining rows to be computed,
1273 * all remaining rows need to be non-trivial.
1275 static int needs_row(struct isl_sched_graph
*graph
, struct isl_sched_node
*node
)
1277 return node
->nvar
- node
->rank
>= graph
->maxvar
- graph
->n_row
;
1280 /* Solve the ILP problem constructed in setup_lp.
1281 * For each node such that all the remaining rows of its schedule
1282 * need to be non-trivial, we construct a non-triviality region.
1283 * This region imposes that the next row is independent of previous rows.
1284 * In particular the coefficients c_i_x are represented by t_i_x
1285 * variables with c_i_x = Q t_i_x and Q a unimodular matrix such that
1286 * its first columns span the rows of the previously computed part
1287 * of the schedule. The non-triviality region enforces that at least
1288 * one of the remaining components of t_i_x is non-zero, i.e.,
1289 * that the new schedule row depends on at least one of the remaining
1292 static __isl_give isl_vec
*solve_lp(struct isl_sched_graph
*graph
)
1298 for (i
= 0; i
< graph
->n
; ++i
) {
1299 struct isl_sched_node
*node
= &graph
->node
[i
];
1300 int skip
= node
->rank
;
1301 graph
->region
[i
].pos
= node
->start
+ 1 + 2*(node
->nparam
+skip
);
1302 if (needs_row(graph
, node
))
1303 graph
->region
[i
].len
= 2 * (node
->nvar
- skip
);
1305 graph
->region
[i
].len
= 0;
1307 lp
= isl_basic_set_copy(graph
->lp
);
1308 sol
= isl_tab_basic_set_non_trivial_lexmin(lp
, 2, graph
->n
,
1309 graph
->region
, &check_conflict
, graph
);
1313 /* Update the schedules of all nodes based on the given solution
1314 * of the LP problem.
1315 * The new row is added to the current band.
1316 * All possibly negative coefficients are encoded as a difference
1317 * of two non-negative variables, so we need to perform the subtraction
1318 * here. Moreover, if use_cmap is set, then the solution does
1319 * not refer to the actual coefficients c_i_x, but instead to variables
1320 * t_i_x such that c_i_x = Q t_i_x and Q is equal to node->cmap.
1321 * In this case, we then also need to perform this multiplication
1322 * to obtain the values of c_i_x.
1324 * If check_zero is set, then the first two coordinates of sol are
1325 * assumed to correspond to the dependence distance. If these two
1326 * coordinates are zero, then the corresponding scheduling dimension
1327 * is marked as being zero distance.
1329 static int update_schedule(struct isl_sched_graph
*graph
,
1330 __isl_take isl_vec
*sol
, int use_cmap
, int check_zero
)
1334 isl_vec
*csol
= NULL
;
1339 isl_die(sol
->ctx
, isl_error_internal
,
1340 "no solution found", goto error
);
1343 zero
= isl_int_is_zero(sol
->el
[1]) &&
1344 isl_int_is_zero(sol
->el
[2]);
1346 for (i
= 0; i
< graph
->n
; ++i
) {
1347 struct isl_sched_node
*node
= &graph
->node
[i
];
1348 int pos
= node
->start
;
1349 int row
= isl_mat_rows(node
->sched
);
1352 csol
= isl_vec_alloc(sol
->ctx
, node
->nvar
);
1356 isl_map_free(node
->sched_map
);
1357 node
->sched_map
= NULL
;
1358 node
->sched
= isl_mat_add_rows(node
->sched
, 1);
1361 node
->sched
= isl_mat_set_element(node
->sched
, row
, 0,
1363 for (j
= 0; j
< node
->nparam
+ node
->nvar
; ++j
)
1364 isl_int_sub(sol
->el
[1 + pos
+ 1 + 2 * j
+ 1],
1365 sol
->el
[1 + pos
+ 1 + 2 * j
+ 1],
1366 sol
->el
[1 + pos
+ 1 + 2 * j
]);
1367 for (j
= 0; j
< node
->nparam
; ++j
)
1368 node
->sched
= isl_mat_set_element(node
->sched
,
1369 row
, 1 + j
, sol
->el
[1+pos
+1+2*j
+1]);
1370 for (j
= 0; j
< node
->nvar
; ++j
)
1371 isl_int_set(csol
->el
[j
],
1372 sol
->el
[1+pos
+1+2*(node
->nparam
+j
)+1]);
1374 csol
= isl_mat_vec_product(isl_mat_copy(node
->cmap
),
1378 for (j
= 0; j
< node
->nvar
; ++j
)
1379 node
->sched
= isl_mat_set_element(node
->sched
,
1380 row
, 1 + node
->nparam
+ j
, csol
->el
[j
]);
1381 node
->band
[graph
->n_total_row
] = graph
->n_band
;
1382 node
->zero
[graph
->n_total_row
] = zero
;
1388 graph
->n_total_row
++;
1397 /* Convert node->sched into a map and return this map.
1398 * We simply add equality constraints that express each output variable
1399 * as the affine combination of parameters and input variables specified
1400 * by the schedule matrix.
1402 * The result is cached in node->sched_map, which needs to be released
1403 * whenever node->sched is updated.
1405 static __isl_give isl_map
*node_extract_schedule(struct isl_sched_node
*node
)
1409 isl_local_space
*ls
;
1410 isl_basic_map
*bmap
;
1415 if (node
->sched_map
)
1416 return isl_map_copy(node
->sched_map
);
1418 nrow
= isl_mat_rows(node
->sched
);
1419 ncol
= isl_mat_cols(node
->sched
) - 1;
1420 dim
= isl_space_from_domain(isl_space_copy(node
->dim
));
1421 dim
= isl_space_add_dims(dim
, isl_dim_out
, nrow
);
1422 bmap
= isl_basic_map_universe(isl_space_copy(dim
));
1423 ls
= isl_local_space_from_space(dim
);
1427 for (i
= 0; i
< nrow
; ++i
) {
1428 c
= isl_equality_alloc(isl_local_space_copy(ls
));
1429 isl_constraint_set_coefficient_si(c
, isl_dim_out
, i
, -1);
1430 isl_mat_get_element(node
->sched
, i
, 0, &v
);
1431 isl_constraint_set_constant(c
, v
);
1432 for (j
= 0; j
< node
->nparam
; ++j
) {
1433 isl_mat_get_element(node
->sched
, i
, 1 + j
, &v
);
1434 isl_constraint_set_coefficient(c
, isl_dim_param
, j
, v
);
1436 for (j
= 0; j
< node
->nvar
; ++j
) {
1437 isl_mat_get_element(node
->sched
,
1438 i
, 1 + node
->nparam
+ j
, &v
);
1439 isl_constraint_set_coefficient(c
, isl_dim_in
, j
, v
);
1441 bmap
= isl_basic_map_add_constraint(bmap
, c
);
1446 isl_local_space_free(ls
);
1448 node
->sched_map
= isl_map_from_basic_map(bmap
);
1449 return isl_map_copy(node
->sched_map
);
1452 /* Update the given dependence relation based on the current schedule.
1453 * That is, intersect the dependence relation with a map expressing
1454 * that source and sink are executed within the same iteration of
1455 * the current schedule.
1456 * This is not the most efficient way, but this shouldn't be a critical
1459 static __isl_give isl_map
*specialize(__isl_take isl_map
*map
,
1460 struct isl_sched_node
*src
, struct isl_sched_node
*dst
)
1462 isl_map
*src_sched
, *dst_sched
, *id
;
1464 src_sched
= node_extract_schedule(src
);
1465 dst_sched
= node_extract_schedule(dst
);
1466 id
= isl_map_apply_range(src_sched
, isl_map_reverse(dst_sched
));
1467 return isl_map_intersect(map
, id
);
1470 /* Update the dependence relations of all edges based on the current schedule.
1471 * If a dependence is carried completely by the current schedule, then
1472 * it is removed and edge_table is updated accordingly.
1474 static int update_edges(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
1477 int reset_table
= 0;
1479 for (i
= graph
->n_edge
- 1; i
>= 0; --i
) {
1480 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
1481 edge
->map
= specialize(edge
->map
, edge
->src
, edge
->dst
);
1485 if (isl_map_plain_is_empty(edge
->map
)) {
1487 isl_map_free(edge
->map
);
1488 if (i
!= graph
->n_edge
- 1)
1489 graph
->edge
[i
] = graph
->edge
[graph
->n_edge
- 1];
1495 isl_hash_table_free(ctx
, graph
->edge_table
);
1496 graph
->edge_table
= NULL
;
1497 return graph_init_edge_table(ctx
, graph
);
1503 static void next_band(struct isl_sched_graph
*graph
)
1505 graph
->band_start
= graph
->n_total_row
;
1509 /* Topologically sort statements mapped to same schedule iteration
1510 * and add a row to the schedule corresponding to this order.
1512 static int sort_statements(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
1519 if (update_edges(ctx
, graph
) < 0)
1522 if (graph
->n_edge
== 0)
1525 if (detect_sccs(graph
) < 0)
1528 for (i
= 0; i
< graph
->n
; ++i
) {
1529 struct isl_sched_node
*node
= &graph
->node
[i
];
1530 int row
= isl_mat_rows(node
->sched
);
1531 int cols
= isl_mat_cols(node
->sched
);
1533 isl_map_free(node
->sched_map
);
1534 node
->sched_map
= NULL
;
1535 node
->sched
= isl_mat_add_rows(node
->sched
, 1);
1538 node
->sched
= isl_mat_set_element_si(node
->sched
, row
, 0,
1540 for (j
= 1; j
< cols
; ++j
)
1541 node
->sched
= isl_mat_set_element_si(node
->sched
,
1543 node
->band
[graph
->n_total_row
] = graph
->n_band
;
1546 graph
->n_total_row
++;
1552 /* Construct an isl_schedule based on the computed schedule stored
1553 * in graph and with parameters specified by dim.
1555 static __isl_give isl_schedule
*extract_schedule(struct isl_sched_graph
*graph
,
1556 __isl_take isl_space
*dim
)
1560 isl_schedule
*sched
= NULL
;
1565 ctx
= isl_space_get_ctx(dim
);
1566 sched
= isl_calloc(ctx
, struct isl_schedule
,
1567 sizeof(struct isl_schedule
) +
1568 (graph
->n
- 1) * sizeof(struct isl_schedule_node
));
1573 sched
->n
= graph
->n
;
1574 sched
->n_band
= graph
->n_band
;
1575 sched
->n_total_row
= graph
->n_total_row
;
1577 for (i
= 0; i
< sched
->n
; ++i
) {
1579 int *band_end
, *band_id
, *zero
;
1581 band_end
= isl_alloc_array(ctx
, int, graph
->n_band
);
1582 band_id
= isl_alloc_array(ctx
, int, graph
->n_band
);
1583 zero
= isl_alloc_array(ctx
, int, graph
->n_total_row
);
1584 sched
->node
[i
].sched
= node_extract_schedule(&graph
->node
[i
]);
1585 sched
->node
[i
].band_end
= band_end
;
1586 sched
->node
[i
].band_id
= band_id
;
1587 sched
->node
[i
].zero
= zero
;
1588 if (!band_end
|| !band_id
|| !zero
)
1591 for (r
= 0; r
< graph
->n_total_row
; ++r
)
1592 zero
[r
] = graph
->node
[i
].zero
[r
];
1593 for (r
= b
= 0; r
< graph
->n_total_row
; ++r
) {
1594 if (graph
->node
[i
].band
[r
] == b
)
1597 if (graph
->node
[i
].band
[r
] == -1)
1600 if (r
== graph
->n_total_row
)
1602 sched
->node
[i
].n_band
= b
;
1603 for (--b
; b
>= 0; --b
)
1604 band_id
[b
] = graph
->node
[i
].band_id
[b
];
1611 isl_space_free(dim
);
1612 isl_schedule_free(sched
);
1616 /* Copy nodes that satisfy node_pred from the src dependence graph
1617 * to the dst dependence graph.
1619 static int copy_nodes(struct isl_sched_graph
*dst
, struct isl_sched_graph
*src
,
1620 int (*node_pred
)(struct isl_sched_node
*node
, int data
), int data
)
1625 for (i
= 0; i
< src
->n
; ++i
) {
1626 if (!node_pred(&src
->node
[i
], data
))
1628 dst
->node
[dst
->n
].dim
= isl_space_copy(src
->node
[i
].dim
);
1629 dst
->node
[dst
->n
].nvar
= src
->node
[i
].nvar
;
1630 dst
->node
[dst
->n
].nparam
= src
->node
[i
].nparam
;
1631 dst
->node
[dst
->n
].sched
= isl_mat_copy(src
->node
[i
].sched
);
1632 dst
->node
[dst
->n
].sched_map
=
1633 isl_map_copy(src
->node
[i
].sched_map
);
1634 dst
->node
[dst
->n
].band
= src
->node
[i
].band
;
1635 dst
->node
[dst
->n
].band_id
= src
->node
[i
].band_id
;
1636 dst
->node
[dst
->n
].zero
= src
->node
[i
].zero
;
1643 /* Copy non-empty edges that satisfy edge_pred from the src dependence graph
1644 * to the dst dependence graph.
1645 * If the source or destination node of the edge is not in the destination
1646 * graph, then it must be a backward proximity edge and it should simply
1649 static int copy_edges(isl_ctx
*ctx
, struct isl_sched_graph
*dst
,
1650 struct isl_sched_graph
*src
,
1651 int (*edge_pred
)(struct isl_sched_edge
*edge
, int data
), int data
)
1656 for (i
= 0; i
< src
->n_edge
; ++i
) {
1657 struct isl_sched_edge
*edge
= &src
->edge
[i
];
1659 struct isl_sched_node
*dst_src
, *dst_dst
;
1661 if (!edge_pred(edge
, data
))
1664 if (isl_map_plain_is_empty(edge
->map
))
1667 dst_src
= graph_find_node(ctx
, dst
, edge
->src
->dim
);
1668 dst_dst
= graph_find_node(ctx
, dst
, edge
->dst
->dim
);
1669 if (!dst_src
|| !dst_dst
) {
1671 isl_die(ctx
, isl_error_internal
,
1672 "backward validity edge", return -1);
1676 map
= isl_map_copy(edge
->map
);
1678 dst
->edge
[dst
->n_edge
].src
= dst_src
;
1679 dst
->edge
[dst
->n_edge
].dst
= dst_dst
;
1680 dst
->edge
[dst
->n_edge
].map
= map
;
1681 dst
->edge
[dst
->n_edge
].validity
= edge
->validity
;
1682 dst
->edge
[dst
->n_edge
].proximity
= edge
->proximity
;
1689 /* Given a "src" dependence graph that contains the nodes from "dst"
1690 * that satisfy node_pred, copy the schedule computed in "src"
1691 * for those nodes back to "dst".
1693 static int copy_schedule(struct isl_sched_graph
*dst
,
1694 struct isl_sched_graph
*src
,
1695 int (*node_pred
)(struct isl_sched_node
*node
, int data
), int data
)
1700 for (i
= 0; i
< dst
->n
; ++i
) {
1701 if (!node_pred(&dst
->node
[i
], data
))
1703 isl_mat_free(dst
->node
[i
].sched
);
1704 isl_map_free(dst
->node
[i
].sched_map
);
1705 dst
->node
[i
].sched
= isl_mat_copy(src
->node
[src
->n
].sched
);
1706 dst
->node
[i
].sched_map
=
1707 isl_map_copy(src
->node
[src
->n
].sched_map
);
1711 dst
->n_total_row
= src
->n_total_row
;
1712 dst
->n_band
= src
->n_band
;
1717 /* Compute the maximal number of variables over all nodes.
1718 * This is the maximal number of linearly independent schedule
1719 * rows that we need to compute.
1720 * Just in case we end up in a part of the dependence graph
1721 * with only lower-dimensional domains, we make sure we will
1722 * compute the required amount of extra linearly independent rows.
1724 static int compute_maxvar(struct isl_sched_graph
*graph
)
1729 for (i
= 0; i
< graph
->n
; ++i
) {
1730 struct isl_sched_node
*node
= &graph
->node
[i
];
1733 if (node_update_cmap(node
) < 0)
1735 nvar
= node
->nvar
+ graph
->n_row
- node
->rank
;
1736 if (nvar
> graph
->maxvar
)
1737 graph
->maxvar
= nvar
;
1743 static int compute_schedule(isl_ctx
*ctx
, struct isl_sched_graph
*graph
);
1744 static int compute_schedule_wcc(isl_ctx
*ctx
, struct isl_sched_graph
*graph
);
1746 /* Compute a schedule for a subgraph of "graph". In particular, for
1747 * the graph composed of nodes that satisfy node_pred and edges that
1748 * that satisfy edge_pred. The caller should precompute the number
1749 * of nodes and edges that satisfy these predicates and pass them along
1750 * as "n" and "n_edge".
1751 * If the subgraph is known to consist of a single component, then wcc should
1752 * be set and then we call compute_schedule_wcc on the constructed subgraph.
1753 * Otherwise, we call compute_schedule, which will check whether the subgraph
1756 static int compute_sub_schedule(isl_ctx
*ctx
,
1757 struct isl_sched_graph
*graph
, int n
, int n_edge
,
1758 int (*node_pred
)(struct isl_sched_node
*node
, int data
),
1759 int (*edge_pred
)(struct isl_sched_edge
*edge
, int data
),
1762 struct isl_sched_graph split
= { 0 };
1764 if (graph_alloc(ctx
, &split
, n
, n_edge
) < 0)
1766 if (copy_nodes(&split
, graph
, node_pred
, data
) < 0)
1768 if (graph_init_table(ctx
, &split
) < 0)
1770 if (copy_edges(ctx
, &split
, graph
, edge_pred
, data
) < 0)
1772 if (graph_init_edge_table(ctx
, &split
) < 0)
1774 split
.n_row
= graph
->n_row
;
1775 split
.n_total_row
= graph
->n_total_row
;
1776 split
.n_band
= graph
->n_band
;
1777 split
.band_start
= graph
->band_start
;
1779 if (wcc
&& compute_schedule_wcc(ctx
, &split
) < 0)
1781 if (!wcc
&& compute_schedule(ctx
, &split
) < 0)
1784 copy_schedule(graph
, &split
, node_pred
, data
);
1786 graph_free(ctx
, &split
);
1789 graph_free(ctx
, &split
);
1793 static int node_scc_exactly(struct isl_sched_node
*node
, int scc
)
1795 return node
->scc
== scc
;
1798 static int node_scc_at_most(struct isl_sched_node
*node
, int scc
)
1800 return node
->scc
<= scc
;
1803 static int node_scc_at_least(struct isl_sched_node
*node
, int scc
)
1805 return node
->scc
>= scc
;
1808 static int edge_src_scc_exactly(struct isl_sched_edge
*edge
, int scc
)
1810 return edge
->src
->scc
== scc
;
1813 static int edge_dst_scc_at_most(struct isl_sched_edge
*edge
, int scc
)
1815 return edge
->dst
->scc
<= scc
;
1818 static int edge_src_scc_at_least(struct isl_sched_edge
*edge
, int scc
)
1820 return edge
->src
->scc
>= scc
;
1823 /* Pad the schedules of all nodes with zero rows such that in the end
1824 * they all have graph->n_total_row rows.
1825 * The extra rows don't belong to any band, so they get assigned band number -1.
1827 static int pad_schedule(struct isl_sched_graph
*graph
)
1831 for (i
= 0; i
< graph
->n
; ++i
) {
1832 struct isl_sched_node
*node
= &graph
->node
[i
];
1833 int row
= isl_mat_rows(node
->sched
);
1834 if (graph
->n_total_row
> row
) {
1835 isl_map_free(node
->sched_map
);
1836 node
->sched_map
= NULL
;
1838 node
->sched
= isl_mat_add_zero_rows(node
->sched
,
1839 graph
->n_total_row
- row
);
1842 for (j
= row
; j
< graph
->n_total_row
; ++j
)
1849 /* Split the current graph into two parts and compute a schedule for each
1850 * part individually. In particular, one part consists of all SCCs up
1851 * to and including graph->src_scc, while the other part contains the other
1854 * The split is enforced in the schedule by constant rows with two different
1855 * values (0 and 1). These constant rows replace the previously computed rows
1856 * in the current band.
1857 * It would be possible to reuse them as the first rows in the next
1858 * band, but recomputing them may result in better rows as we are looking
1859 * at a smaller part of the dependence graph.
1860 * compute_split_schedule is only called when no zero-distance schedule row
1861 * could be found on the entire graph, so we wark the splitting row as
1862 * non zero-distance.
1864 * The band_id of the second group is set to n, where n is the number
1865 * of nodes in the first group. This ensures that the band_ids over
1866 * the two groups remain disjoint, even if either or both of the two
1867 * groups contain independent components.
1869 static int compute_split_schedule(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
1871 int i
, j
, n
, e1
, e2
;
1872 int n_total_row
, orig_total_row
;
1873 int n_band
, orig_band
;
1876 drop
= graph
->n_total_row
- graph
->band_start
;
1877 graph
->n_total_row
-= drop
;
1878 graph
->n_row
-= drop
;
1881 for (i
= 0; i
< graph
->n
; ++i
) {
1882 struct isl_sched_node
*node
= &graph
->node
[i
];
1883 int row
= isl_mat_rows(node
->sched
) - drop
;
1884 int cols
= isl_mat_cols(node
->sched
);
1885 int before
= node
->scc
<= graph
->src_scc
;
1890 isl_map_free(node
->sched_map
);
1891 node
->sched_map
= NULL
;
1892 node
->sched
= isl_mat_drop_rows(node
->sched
,
1893 graph
->band_start
, drop
);
1894 node
->sched
= isl_mat_add_rows(node
->sched
, 1);
1897 node
->sched
= isl_mat_set_element_si(node
->sched
, row
, 0,
1899 for (j
= 1; j
< cols
; ++j
)
1900 node
->sched
= isl_mat_set_element_si(node
->sched
,
1902 node
->band
[graph
->n_total_row
] = graph
->n_band
;
1903 node
->zero
[graph
->n_total_row
] = 0;
1907 for (i
= 0; i
< graph
->n_edge
; ++i
) {
1908 if (graph
->edge
[i
].dst
->scc
<= graph
->src_scc
)
1910 if (graph
->edge
[i
].src
->scc
> graph
->src_scc
)
1914 graph
->n_total_row
++;
1917 for (i
= 0; i
< graph
->n
; ++i
) {
1918 struct isl_sched_node
*node
= &graph
->node
[i
];
1919 if (node
->scc
> graph
->src_scc
)
1920 node
->band_id
[graph
->n_band
] = n
;
1923 orig_total_row
= graph
->n_total_row
;
1924 orig_band
= graph
->n_band
;
1925 if (compute_sub_schedule(ctx
, graph
, n
, e1
,
1926 &node_scc_at_most
, &edge_dst_scc_at_most
,
1927 graph
->src_scc
, 0) < 0)
1929 n_total_row
= graph
->n_total_row
;
1930 graph
->n_total_row
= orig_total_row
;
1931 n_band
= graph
->n_band
;
1932 graph
->n_band
= orig_band
;
1933 if (compute_sub_schedule(ctx
, graph
, graph
->n
- n
, e2
,
1934 &node_scc_at_least
, &edge_src_scc_at_least
,
1935 graph
->src_scc
+ 1, 0) < 0)
1937 if (n_total_row
> graph
->n_total_row
)
1938 graph
->n_total_row
= n_total_row
;
1939 if (n_band
> graph
->n_band
)
1940 graph
->n_band
= n_band
;
1942 return pad_schedule(graph
);
1945 /* Compute the next band of the schedule after updating the dependence
1946 * relations based on the the current schedule.
1948 static int compute_next_band(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
1950 if (update_edges(ctx
, graph
) < 0)
1954 return compute_schedule(ctx
, graph
);
1957 /* Add constraints to graph->lp that force the dependence "map" (which
1958 * is part of the dependence relation of "edge")
1959 * to be respected and attempt to carry it, where the edge is one from
1960 * a node j to itself. "pos" is the sequence number of the given map.
1961 * That is, add constraints that enforce
1963 * (c_j_0 + c_j_n n + c_j_x y) - (c_j_0 + c_j_n n + c_j_x x)
1964 * = c_j_x (y - x) >= e_i
1966 * for each (x,y) in R.
1967 * We obtain general constraints on coefficients (c_0, c_n, c_x)
1968 * of valid constraints for (y - x) and then plug in (-e_i, 0, c_j_x),
1969 * with each coefficient in c_j_x represented as a pair of non-negative
1972 static int add_intra_constraints(struct isl_sched_graph
*graph
,
1973 struct isl_sched_edge
*edge
, __isl_take isl_map
*map
, int pos
)
1976 isl_ctx
*ctx
= isl_map_get_ctx(map
);
1978 isl_dim_map
*dim_map
;
1979 isl_basic_set
*coef
;
1980 struct isl_sched_node
*node
= edge
->src
;
1982 coef
= intra_coefficients(graph
, map
);
1984 dim
= isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef
)));
1986 total
= isl_basic_set_total_dim(graph
->lp
);
1987 dim_map
= isl_dim_map_alloc(ctx
, total
);
1988 isl_dim_map_range(dim_map
, 3 + pos
, 0, 0, 0, 1, -1);
1989 isl_dim_map_range(dim_map
, node
->start
+ 2 * node
->nparam
+ 1, 2,
1990 isl_space_dim(dim
, isl_dim_set
), 1,
1992 isl_dim_map_range(dim_map
, node
->start
+ 2 * node
->nparam
+ 2, 2,
1993 isl_space_dim(dim
, isl_dim_set
), 1,
1995 graph
->lp
= isl_basic_set_extend_constraints(graph
->lp
,
1996 coef
->n_eq
, coef
->n_ineq
);
1997 graph
->lp
= isl_basic_set_add_constraints_dim_map(graph
->lp
,
1999 isl_space_free(dim
);
2004 /* Add constraints to graph->lp that force the dependence "map" (which
2005 * is part of the dependence relation of "edge")
2006 * to be respected and attempt to carry it, where the edge is one from
2007 * node j to node k. "pos" is the sequence number of the given map.
2008 * That is, add constraints that enforce
2010 * (c_k_0 + c_k_n n + c_k_x y) - (c_j_0 + c_j_n n + c_j_x x) >= e_i
2012 * for each (x,y) in R.
2013 * We obtain general constraints on coefficients (c_0, c_n, c_x)
2014 * of valid constraints for R and then plug in
2015 * (-e_i + c_k_0 - c_j_0, c_k_n - c_j_n, c_k_x - c_j_x)
2016 * with each coefficient (except e_i, c_k_0 and c_j_0)
2017 * represented as a pair of non-negative coefficients.
2019 static int add_inter_constraints(struct isl_sched_graph
*graph
,
2020 struct isl_sched_edge
*edge
, __isl_take isl_map
*map
, int pos
)
2023 isl_ctx
*ctx
= isl_map_get_ctx(map
);
2025 isl_dim_map
*dim_map
;
2026 isl_basic_set
*coef
;
2027 struct isl_sched_node
*src
= edge
->src
;
2028 struct isl_sched_node
*dst
= edge
->dst
;
2030 coef
= inter_coefficients(graph
, map
);
2032 dim
= isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef
)));
2034 total
= isl_basic_set_total_dim(graph
->lp
);
2035 dim_map
= isl_dim_map_alloc(ctx
, total
);
2037 isl_dim_map_range(dim_map
, 3 + pos
, 0, 0, 0, 1, -1);
2039 isl_dim_map_range(dim_map
, dst
->start
, 0, 0, 0, 1, 1);
2040 isl_dim_map_range(dim_map
, dst
->start
+ 1, 2, 1, 1, dst
->nparam
, -1);
2041 isl_dim_map_range(dim_map
, dst
->start
+ 2, 2, 1, 1, dst
->nparam
, 1);
2042 isl_dim_map_range(dim_map
, dst
->start
+ 2 * dst
->nparam
+ 1, 2,
2043 isl_space_dim(dim
, isl_dim_set
) + src
->nvar
, 1,
2045 isl_dim_map_range(dim_map
, dst
->start
+ 2 * dst
->nparam
+ 2, 2,
2046 isl_space_dim(dim
, isl_dim_set
) + src
->nvar
, 1,
2049 isl_dim_map_range(dim_map
, src
->start
, 0, 0, 0, 1, -1);
2050 isl_dim_map_range(dim_map
, src
->start
+ 1, 2, 1, 1, src
->nparam
, 1);
2051 isl_dim_map_range(dim_map
, src
->start
+ 2, 2, 1, 1, src
->nparam
, -1);
2052 isl_dim_map_range(dim_map
, src
->start
+ 2 * src
->nparam
+ 1, 2,
2053 isl_space_dim(dim
, isl_dim_set
), 1,
2055 isl_dim_map_range(dim_map
, src
->start
+ 2 * src
->nparam
+ 2, 2,
2056 isl_space_dim(dim
, isl_dim_set
), 1,
2059 graph
->lp
= isl_basic_set_extend_constraints(graph
->lp
,
2060 coef
->n_eq
, coef
->n_ineq
);
2061 graph
->lp
= isl_basic_set_add_constraints_dim_map(graph
->lp
,
2063 isl_space_free(dim
);
2068 /* Add constraints to graph->lp that force all dependence
2069 * to be respected and attempt to carry it.
2071 static int add_all_constraints(struct isl_sched_graph
*graph
)
2077 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2078 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
2079 for (j
= 0; j
< edge
->map
->n
; ++j
) {
2080 isl_basic_map
*bmap
;
2083 bmap
= isl_basic_map_copy(edge
->map
->p
[j
]);
2084 map
= isl_map_from_basic_map(bmap
);
2086 if (edge
->src
== edge
->dst
&&
2087 add_intra_constraints(graph
, edge
, map
, pos
) < 0)
2089 if (edge
->src
!= edge
->dst
&&
2090 add_inter_constraints(graph
, edge
, map
, pos
) < 0)
2099 /* Count the number of equality and inequality constraints
2100 * that will be added to the carry_lp problem.
2101 * If once is set, then we count
2102 * each edge exactly once. Otherwise, we count as follows
2103 * validity -> 1 (>= 0)
2104 * validity+proximity -> 2 (>= 0 and upper bound)
2105 * proximity -> 2 (lower and upper bound)
2107 static int count_all_constraints(struct isl_sched_graph
*graph
,
2108 int *n_eq
, int *n_ineq
, int once
)
2112 *n_eq
= *n_ineq
= 0;
2113 for (i
= 0; i
< graph
->n_edge
; ++i
) {
2114 struct isl_sched_edge
*edge
= &graph
->edge
[i
];
2115 for (j
= 0; j
< edge
->map
->n
; ++j
) {
2116 isl_basic_map
*bmap
;
2119 bmap
= isl_basic_map_copy(edge
->map
->p
[j
]);
2120 map
= isl_map_from_basic_map(bmap
);
2122 if (count_map_constraints(graph
, edge
, map
,
2123 n_eq
, n_ineq
, once
) < 0)
2131 /* Construct an LP problem for finding schedule coefficients
2132 * such that the schedule carries as many dependences as possible.
2133 * In particular, for each dependence i, we bound the dependence distance
2134 * from below by e_i, with 0 <= e_i <= 1 and then maximize the sum
2135 * of all e_i's. Dependence with e_i = 0 in the solution are simply
2136 * respected, while those with e_i > 0 (in practice e_i = 1) are carried.
2137 * Note that if the dependence relation is a union of basic maps,
2138 * then we have to consider each basic map individually as it may only
2139 * be possible to carry the dependences expressed by some of those
2140 * basic maps and not all off them.
2141 * Below, we consider each of those basic maps as a separate "edge".
2143 * All variables of the LP are non-negative. The actual coefficients
2144 * may be negative, so each coefficient is represented as the difference
2145 * of two non-negative variables. The negative part always appears
2146 * immediately before the positive part.
2147 * Other than that, the variables have the following order
2149 * - sum of (1 - e_i) over all edges
2150 * - sum of positive and negative parts of all c_n coefficients
2151 * (unconstrained when computing non-parametric schedules)
2152 * - sum of positive and negative parts of all c_x coefficients
2157 * - positive and negative parts of c_i_n (if parametric)
2158 * - positive and negative parts of c_i_x
2160 * The constraints are those from the edges plus three equalities
2161 * to express the sums and n_edge inequalities to express e_i <= 1.
2163 static int setup_carry_lp(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2173 for (i
= 0; i
< graph
->n_edge
; ++i
)
2174 n_edge
+= graph
->edge
[i
].map
->n
;
2177 for (i
= 0; i
< graph
->n
; ++i
) {
2178 struct isl_sched_node
*node
= &graph
->node
[graph
->sorted
[i
]];
2179 node
->start
= total
;
2180 total
+= 1 + 2 * (node
->nparam
+ node
->nvar
);
2183 if (count_all_constraints(graph
, &n_eq
, &n_ineq
, 1) < 0)
2186 dim
= isl_space_set_alloc(ctx
, 0, total
);
2187 isl_basic_set_free(graph
->lp
);
2190 graph
->lp
= isl_basic_set_alloc_space(dim
, 0, n_eq
, n_ineq
);
2191 graph
->lp
= isl_basic_set_set_rational(graph
->lp
);
2193 k
= isl_basic_set_alloc_equality(graph
->lp
);
2196 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2197 isl_int_set_si(graph
->lp
->eq
[k
][0], -n_edge
);
2198 isl_int_set_si(graph
->lp
->eq
[k
][1], 1);
2199 for (i
= 0; i
< n_edge
; ++i
)
2200 isl_int_set_si(graph
->lp
->eq
[k
][4 + i
], 1);
2202 k
= isl_basic_set_alloc_equality(graph
->lp
);
2205 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2206 isl_int_set_si(graph
->lp
->eq
[k
][2], -1);
2207 for (i
= 0; i
< graph
->n
; ++i
) {
2208 int pos
= 1 + graph
->node
[i
].start
+ 1;
2210 for (j
= 0; j
< 2 * graph
->node
[i
].nparam
; ++j
)
2211 isl_int_set_si(graph
->lp
->eq
[k
][pos
+ j
], 1);
2214 k
= isl_basic_set_alloc_equality(graph
->lp
);
2217 isl_seq_clr(graph
->lp
->eq
[k
], 1 + total
);
2218 isl_int_set_si(graph
->lp
->eq
[k
][3], -1);
2219 for (i
= 0; i
< graph
->n
; ++i
) {
2220 struct isl_sched_node
*node
= &graph
->node
[i
];
2221 int pos
= 1 + node
->start
+ 1 + 2 * node
->nparam
;
2223 for (j
= 0; j
< 2 * node
->nvar
; ++j
)
2224 isl_int_set_si(graph
->lp
->eq
[k
][pos
+ j
], 1);
2227 for (i
= 0; i
< n_edge
; ++i
) {
2228 k
= isl_basic_set_alloc_inequality(graph
->lp
);
2231 isl_seq_clr(graph
->lp
->ineq
[k
], 1 + total
);
2232 isl_int_set_si(graph
->lp
->ineq
[k
][4 + i
], -1);
2233 isl_int_set_si(graph
->lp
->ineq
[k
][0], 1);
2236 if (add_all_constraints(graph
) < 0)
2242 /* If the schedule_split_parallel option is set and if the linear
2243 * parts of the scheduling rows for all nodes in the graphs are the same,
2244 * then split off the constant term from the linear part.
2245 * The constant term is then placed in a separate band and
2246 * the linear part is simplified.
2248 static int split_parallel(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2253 struct isl_sched_node
*node0
;
2255 if (!ctx
->opt
->schedule_split_parallel
)
2260 node0
= &graph
->node
[0];
2261 row
= isl_mat_rows(node0
->sched
) - 1;
2262 cols
= isl_mat_cols(node0
->sched
);
2263 for (i
= 1; i
< graph
->n
; ++i
) {
2264 struct isl_sched_node
*node
= &graph
->node
[i
];
2266 if (isl_mat_cols(node
->sched
) != cols
)
2268 if (!isl_seq_eq(node0
->sched
->row
[row
] + 1,
2269 node
->sched
->row
[row
] + 1, cols
- 1))
2272 isl_int_ne(node0
->sched
->row
[row
][0],
2273 node
->sched
->row
[row
][0]))
2281 for (i
= 0; i
< graph
->n
; ++i
) {
2282 struct isl_sched_node
*node
= &graph
->node
[i
];
2284 isl_map_free(node
->sched_map
);
2285 node
->sched_map
= NULL
;
2286 node
->sched
= isl_mat_add_zero_rows(node
->sched
, 1);
2289 isl_int_set(node
->sched
->row
[row
+ 1][0],
2290 node
->sched
->row
[row
][0]);
2291 isl_int_set_si(node
->sched
->row
[row
][0], 0);
2292 node
->sched
= isl_mat_normalize_row(node
->sched
, row
);
2295 node
->band
[graph
->n_total_row
] = graph
->n_band
;
2298 graph
->n_total_row
++;
2303 /* Construct a schedule row for each node such that as many dependences
2304 * as possible are carried and then continue with the next band.
2306 static int carry_dependences(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2314 for (i
= 0; i
< graph
->n_edge
; ++i
)
2315 n_edge
+= graph
->edge
[i
].map
->n
;
2317 if (setup_carry_lp(ctx
, graph
) < 0)
2320 lp
= isl_basic_set_copy(graph
->lp
);
2321 sol
= isl_tab_basic_set_non_neg_lexmin(lp
);
2325 if (sol
->size
== 0) {
2327 isl_die(ctx
, isl_error_internal
,
2328 "error in schedule construction", return -1);
2331 if (isl_int_cmp_si(sol
->el
[1], n_edge
) >= 0) {
2333 isl_die(ctx
, isl_error_unknown
,
2334 "unable to carry dependences", return -1);
2337 if (update_schedule(graph
, sol
, 0, 0) < 0)
2340 if (split_parallel(ctx
, graph
) < 0)
2343 return compute_next_band(ctx
, graph
);
2346 /* Are there any validity edges in the graph?
2348 static int has_validity_edges(struct isl_sched_graph
*graph
)
2352 for (i
= 0; i
< graph
->n_edge
; ++i
)
2353 if (graph
->edge
[i
].validity
)
2359 /* Should we apply a Feautrier step?
2360 * That is, did the user request the Feautrier algorithm and are
2361 * there any validity dependences (left)?
2363 static int need_feautrier_step(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2365 if (ctx
->opt
->schedule_algorithm
!= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
)
2368 return has_validity_edges(graph
);
2371 /* Compute a schedule for a connected dependence graph using Feautrier's
2372 * multi-dimensional scheduling algorithm.
2373 * The original algorithm is described in [1].
2374 * The main idea is to minimize the number of scheduling dimensions, by
2375 * trying to satisfy as many dependences as possible per scheduling dimension.
2377 * [1] P. Feautrier, Some Efficient Solutions to the Affine Scheduling
2378 * Problem, Part II: Multi-Dimensional Time.
2379 * In Intl. Journal of Parallel Programming, 1992.
2381 static int compute_schedule_wcc_feautrier(isl_ctx
*ctx
,
2382 struct isl_sched_graph
*graph
)
2384 return carry_dependences(ctx
, graph
);
2387 /* Compute a schedule for a connected dependence graph.
2388 * We try to find a sequence of as many schedule rows as possible that result
2389 * in non-negative dependence distances (independent of the previous rows
2390 * in the sequence, i.e., such that the sequence is tilable).
2391 * If we can't find any more rows we either
2392 * - split between SCCs and start over (assuming we found an interesting
2393 * pair of SCCs between which to split)
2394 * - continue with the next band (assuming the current band has at least
2396 * - try to carry as many dependences as possible and continue with the next
2399 * If Feautrier's algorithm is selected, we first recursively try to satisfy
2400 * as many validity dependences as possible. When all validity dependences
2401 * are satisfied we extend the schedule to a full-dimensional schedule.
2403 * If we manage to complete the schedule, we finish off by topologically
2404 * sorting the statements based on the remaining dependences.
2406 * If ctx->opt->schedule_outer_zero_distance is set, then we force the
2407 * outermost dimension in the current band to be zero distance. If this
2408 * turns out to be impossible, we fall back on the general scheme above
2409 * and try to carry as many dependences as possible.
2411 static int compute_schedule_wcc(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2415 if (detect_sccs(graph
) < 0)
2419 if (compute_maxvar(graph
) < 0)
2422 if (need_feautrier_step(ctx
, graph
))
2423 return compute_schedule_wcc_feautrier(ctx
, graph
);
2425 if (ctx
->opt
->schedule_outer_zero_distance
)
2428 while (graph
->n_row
< graph
->maxvar
) {
2431 graph
->src_scc
= -1;
2432 graph
->dst_scc
= -1;
2434 if (setup_lp(ctx
, graph
, force_zero
) < 0)
2436 sol
= solve_lp(graph
);
2439 if (sol
->size
== 0) {
2441 if (!ctx
->opt
->schedule_maximize_band_depth
&&
2442 graph
->n_total_row
> graph
->band_start
)
2443 return compute_next_band(ctx
, graph
);
2444 if (graph
->src_scc
>= 0)
2445 return compute_split_schedule(ctx
, graph
);
2446 if (graph
->n_total_row
> graph
->band_start
)
2447 return compute_next_band(ctx
, graph
);
2448 return carry_dependences(ctx
, graph
);
2450 if (update_schedule(graph
, sol
, 1, 1) < 0)
2455 if (graph
->n_total_row
> graph
->band_start
)
2457 return sort_statements(ctx
, graph
);
2460 /* Compute a schedule for each component (identified by node->scc)
2461 * of the dependence graph separately and then combine the results.
2463 * The band_id is adjusted such that each component has a separate id.
2464 * Note that the band_id may have already been set to a value different
2465 * from zero by compute_split_schedule.
2467 static int compute_component_schedule(isl_ctx
*ctx
,
2468 struct isl_sched_graph
*graph
)
2472 int n_total_row
, orig_total_row
;
2473 int n_band
, orig_band
;
2476 orig_total_row
= graph
->n_total_row
;
2478 orig_band
= graph
->n_band
;
2479 for (i
= 0; i
< graph
->n
; ++i
)
2480 graph
->node
[i
].band_id
[graph
->n_band
] += graph
->node
[i
].scc
;
2481 for (wcc
= 0; wcc
< graph
->scc
; ++wcc
) {
2483 for (i
= 0; i
< graph
->n
; ++i
)
2484 if (graph
->node
[i
].scc
== wcc
)
2487 for (i
= 0; i
< graph
->n_edge
; ++i
)
2488 if (graph
->edge
[i
].src
->scc
== wcc
)
2491 if (compute_sub_schedule(ctx
, graph
, n
, n_edge
,
2493 &edge_src_scc_exactly
, wcc
, 1) < 0)
2495 if (graph
->n_total_row
> n_total_row
)
2496 n_total_row
= graph
->n_total_row
;
2497 graph
->n_total_row
= orig_total_row
;
2498 if (graph
->n_band
> n_band
)
2499 n_band
= graph
->n_band
;
2500 graph
->n_band
= orig_band
;
2503 graph
->n_total_row
= n_total_row
;
2504 graph
->n_band
= n_band
;
2506 return pad_schedule(graph
);
2509 /* Compute a schedule for the given dependence graph.
2510 * We first check if the graph is connected (through validity dependences)
2511 * and, if not, compute a schedule for each component separately.
2513 static int compute_schedule(isl_ctx
*ctx
, struct isl_sched_graph
*graph
)
2515 if (detect_wccs(graph
) < 0)
2519 return compute_component_schedule(ctx
, graph
);
2521 return compute_schedule_wcc(ctx
, graph
);
2524 /* Compute a schedule for the given union of domains that respects
2525 * all the validity dependences.
2526 * If the default isl scheduling algorithm is used, it tries to minimize
2527 * the dependence distances over the proximity dependences.
2528 * If Feautrier's scheduling algorithm is used, the proximity dependence
2529 * distances are only minimized during the extension to a full-dimensional
2532 __isl_give isl_schedule
*isl_union_set_compute_schedule(
2533 __isl_take isl_union_set
*domain
,
2534 __isl_take isl_union_map
*validity
,
2535 __isl_take isl_union_map
*proximity
)
2537 isl_ctx
*ctx
= isl_union_set_get_ctx(domain
);
2539 struct isl_sched_graph graph
= { 0 };
2540 isl_schedule
*sched
;
2542 domain
= isl_union_set_align_params(domain
,
2543 isl_union_map_get_space(validity
));
2544 domain
= isl_union_set_align_params(domain
,
2545 isl_union_map_get_space(proximity
));
2546 dim
= isl_union_set_get_space(domain
);
2547 validity
= isl_union_map_align_params(validity
, isl_space_copy(dim
));
2548 proximity
= isl_union_map_align_params(proximity
, dim
);
2553 graph
.n
= isl_union_set_n_set(domain
);
2556 if (graph_alloc(ctx
, &graph
, graph
.n
,
2557 isl_union_map_n_map(validity
) + isl_union_map_n_map(proximity
)) < 0)
2561 if (isl_union_set_foreach_set(domain
, &extract_node
, &graph
) < 0)
2563 if (graph_init_table(ctx
, &graph
) < 0)
2566 if (isl_union_map_foreach_map(validity
, &extract_edge
, &graph
) < 0)
2568 if (graph_init_edge_table(ctx
, &graph
) < 0)
2570 if (isl_union_map_foreach_map(proximity
, &extract_edge
, &graph
) < 0)
2573 if (compute_schedule(ctx
, &graph
) < 0)
2577 sched
= extract_schedule(&graph
, isl_union_set_get_space(domain
));
2579 graph_free(ctx
, &graph
);
2580 isl_union_set_free(domain
);
2581 isl_union_map_free(validity
);
2582 isl_union_map_free(proximity
);
2586 graph_free(ctx
, &graph
);
2587 isl_union_set_free(domain
);
2588 isl_union_map_free(validity
);
2589 isl_union_map_free(proximity
);
2593 void *isl_schedule_free(__isl_take isl_schedule
*sched
)
2599 if (--sched
->ref
> 0)
2602 for (i
= 0; i
< sched
->n
; ++i
) {
2603 isl_map_free(sched
->node
[i
].sched
);
2604 free(sched
->node
[i
].band_end
);
2605 free(sched
->node
[i
].band_id
);
2606 free(sched
->node
[i
].zero
);
2608 isl_space_free(sched
->dim
);
2609 isl_band_list_free(sched
->band_forest
);
2614 isl_ctx
*isl_schedule_get_ctx(__isl_keep isl_schedule
*schedule
)
2616 return schedule
? isl_space_get_ctx(schedule
->dim
) : NULL
;
2619 __isl_give isl_union_map
*isl_schedule_get_map(__isl_keep isl_schedule
*sched
)
2622 isl_union_map
*umap
;
2627 umap
= isl_union_map_empty(isl_space_copy(sched
->dim
));
2628 for (i
= 0; i
< sched
->n
; ++i
)
2629 umap
= isl_union_map_add_map(umap
,
2630 isl_map_copy(sched
->node
[i
].sched
));
2635 static __isl_give isl_band_list
*construct_band_list(
2636 __isl_keep isl_schedule
*schedule
, __isl_keep isl_band
*parent
,
2637 int band_nr
, int *parent_active
, int n_active
);
2639 /* Construct an isl_band structure for the band in the given schedule
2640 * with sequence number band_nr for the n_active nodes marked by active.
2641 * If the nodes don't have a band with the given sequence number,
2642 * then a band without members is created.
2644 * Because of the way the schedule is constructed, we know that
2645 * the position of the band inside the schedule of a node is the same
2646 * for all active nodes.
2648 static __isl_give isl_band
*construct_band(__isl_keep isl_schedule
*schedule
,
2649 __isl_keep isl_band
*parent
,
2650 int band_nr
, int *active
, int n_active
)
2653 isl_ctx
*ctx
= isl_schedule_get_ctx(schedule
);
2655 unsigned start
, end
;
2657 band
= isl_calloc_type(ctx
, isl_band
);
2662 band
->schedule
= schedule
;
2663 band
->parent
= parent
;
2665 for (i
= 0; i
< schedule
->n
; ++i
)
2666 if (active
[i
] && schedule
->node
[i
].n_band
> band_nr
+ 1)
2669 if (i
< schedule
->n
) {
2670 band
->children
= construct_band_list(schedule
, band
,
2671 band_nr
+ 1, active
, n_active
);
2672 if (!band
->children
)
2676 for (i
= 0; i
< schedule
->n
; ++i
)
2680 if (i
>= schedule
->n
)
2681 isl_die(ctx
, isl_error_internal
,
2682 "band without active statements", goto error
);
2684 start
= band_nr
? schedule
->node
[i
].band_end
[band_nr
- 1] : 0;
2685 end
= band_nr
< schedule
->node
[i
].n_band
?
2686 schedule
->node
[i
].band_end
[band_nr
] : start
;
2687 band
->n
= end
- start
;
2689 band
->zero
= isl_alloc_array(ctx
, int, band
->n
);
2693 for (j
= 0; j
< band
->n
; ++j
)
2694 band
->zero
[j
] = schedule
->node
[i
].zero
[start
+ j
];
2696 band
->map
= isl_union_map_empty(isl_space_copy(schedule
->dim
));
2697 for (i
= 0; i
< schedule
->n
; ++i
) {
2704 map
= isl_map_copy(schedule
->node
[i
].sched
);
2705 n_out
= isl_map_dim(map
, isl_dim_out
);
2706 map
= isl_map_project_out(map
, isl_dim_out
, end
, n_out
- end
);
2707 map
= isl_map_project_out(map
, isl_dim_out
, 0, start
);
2708 band
->map
= isl_union_map_union(band
->map
,
2709 isl_union_map_from_map(map
));
2716 isl_band_free(band
);
2720 /* Construct a list of bands that start at the same position (with
2721 * sequence number band_nr) in the schedules of the nodes that
2722 * were active in the parent band.
2724 * A separate isl_band structure is created for each band_id
2725 * and for each node that does not have a band with sequence
2726 * number band_nr. In the latter case, a band without members
2728 * This ensures that if a band has any children, then each node
2729 * that was active in the band is active in exactly one of the children.
2731 static __isl_give isl_band_list
*construct_band_list(
2732 __isl_keep isl_schedule
*schedule
, __isl_keep isl_band
*parent
,
2733 int band_nr
, int *parent_active
, int n_active
)
2736 isl_ctx
*ctx
= isl_schedule_get_ctx(schedule
);
2739 isl_band_list
*list
;
2742 for (i
= 0; i
< n_active
; ++i
) {
2743 for (j
= 0; j
< schedule
->n
; ++j
) {
2744 if (!parent_active
[j
])
2746 if (schedule
->node
[j
].n_band
<= band_nr
)
2748 if (schedule
->node
[j
].band_id
[band_nr
] == i
) {
2754 for (j
= 0; j
< schedule
->n
; ++j
)
2755 if (schedule
->node
[j
].n_band
<= band_nr
)
2760 list
= isl_band_list_alloc(ctx
, n_band
);
2761 band
= construct_band(schedule
, parent
, band_nr
,
2762 parent_active
, n_active
);
2763 return isl_band_list_add(list
, band
);
2766 active
= isl_alloc_array(ctx
, int, schedule
->n
);
2770 list
= isl_band_list_alloc(ctx
, n_band
);
2772 for (i
= 0; i
< n_active
; ++i
) {
2776 for (j
= 0; j
< schedule
->n
; ++j
) {
2777 active
[j
] = parent_active
[j
] &&
2778 schedule
->node
[j
].n_band
> band_nr
&&
2779 schedule
->node
[j
].band_id
[band_nr
] == i
;
2786 band
= construct_band(schedule
, parent
, band_nr
, active
, n
);
2788 list
= isl_band_list_add(list
, band
);
2790 for (i
= 0; i
< schedule
->n
; ++i
) {
2792 if (!parent_active
[i
])
2794 if (schedule
->node
[i
].n_band
> band_nr
)
2796 for (j
= 0; j
< schedule
->n
; ++j
)
2798 band
= construct_band(schedule
, parent
, band_nr
, active
, 1);
2799 list
= isl_band_list_add(list
, band
);
2807 /* Construct a band forest representation of the schedule and
2808 * return the list of roots.
2810 static __isl_give isl_band_list
*construct_forest(
2811 __isl_keep isl_schedule
*schedule
)
2814 isl_ctx
*ctx
= isl_schedule_get_ctx(schedule
);
2815 isl_band_list
*forest
;
2818 active
= isl_alloc_array(ctx
, int, schedule
->n
);
2822 for (i
= 0; i
< schedule
->n
; ++i
)
2825 forest
= construct_band_list(schedule
, NULL
, 0, active
, schedule
->n
);
2832 /* Return the roots of a band forest representation of the schedule.
2834 __isl_give isl_band_list
*isl_schedule_get_band_forest(
2835 __isl_keep isl_schedule
*schedule
)
2839 if (!schedule
->band_forest
)
2840 schedule
->band_forest
= construct_forest(schedule
);
2841 return isl_band_list_dup(schedule
->band_forest
);
2844 static __isl_give isl_printer
*print_band_list(__isl_take isl_printer
*p
,
2845 __isl_keep isl_band_list
*list
);
2847 static __isl_give isl_printer
*print_band(__isl_take isl_printer
*p
,
2848 __isl_keep isl_band
*band
)
2850 isl_band_list
*children
;
2852 p
= isl_printer_start_line(p
);
2853 p
= isl_printer_print_union_map(p
, band
->map
);
2854 p
= isl_printer_end_line(p
);
2856 if (!isl_band_has_children(band
))
2859 children
= isl_band_get_children(band
);
2861 p
= isl_printer_indent(p
, 4);
2862 p
= print_band_list(p
, children
);
2863 p
= isl_printer_indent(p
, -4);
2865 isl_band_list_free(children
);
2870 static __isl_give isl_printer
*print_band_list(__isl_take isl_printer
*p
,
2871 __isl_keep isl_band_list
*list
)
2875 n
= isl_band_list_n_band(list
);
2876 for (i
= 0; i
< n
; ++i
) {
2878 band
= isl_band_list_get_band(list
, i
);
2879 p
= print_band(p
, band
);
2880 isl_band_free(band
);
2886 __isl_give isl_printer
*isl_printer_print_schedule(__isl_take isl_printer
*p
,
2887 __isl_keep isl_schedule
*schedule
)
2889 isl_band_list
*forest
;
2891 forest
= isl_schedule_get_band_forest(schedule
);
2893 p
= print_band_list(p
, forest
);
2895 isl_band_list_free(forest
);
2900 void isl_schedule_dump(__isl_keep isl_schedule
*schedule
)
2902 isl_printer
*printer
;
2907 printer
= isl_printer_to_file(isl_schedule_get_ctx(schedule
), stderr
);
2908 printer
= isl_printer_print_schedule(printer
, schedule
);
2910 isl_printer_free(printer
);