1 /* Routines to implement minimum-cost maximal flow algorithm used to smooth
2 basic block and edge frequency counts.
3 Copyright (C) 2008-2016 Free Software Foundation, Inc.
4 Contributed by Paul Yuan (yingbo.com@gmail.com) and
5 Vinodha Ramasamy (vinodha@google.com).
7 This file is part of GCC.
8 GCC is free software; you can redistribute it and/or modify it under
9 the terms of the GNU General Public License as published by the Free
10 Software Foundation; either version 3, or (at your option) any later
13 GCC is distributed in the hope that it will be useful, but WITHOUT ANY
14 WARRANTY; without even the implied warranty of MERCHANTABILITY or
15 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
18 You should have received a copy of the GNU General Public License
19 along with GCC; see the file COPYING3. If not see
20 <http://www.gnu.org/licenses/>. */
23 [1] "Feedback-directed Optimizations in GCC with Estimated Edge Profiles
24 from Hardware Event Sampling", Vinodha Ramasamy, Paul Yuan, Dehao Chen,
25 and Robert Hundt; GCC Summit 2008.
26 [2] "Complementing Missing and Inaccurate Profiling Using a Minimum Cost
27 Circulation Algorithm", Roy Levin, Ilan Newman and Gadi Haber;
30 Algorithm to smooth basic block and edge counts:
31 1. create_fixup_graph: Create fixup graph by translating function CFG into
32 a graph that satisfies MCF algorithm requirements.
33 2. find_max_flow: Find maximal flow.
34 3. compute_residual_flow: Form residual network.
36 cancel_negative_cycle: While G contains a negative cost cycle C, reverse
37 the flow on the found cycle by the minimum residual capacity in that
39 5. Form the minimal cost flow
41 6. adjust_cfg_counts: Update initial edge weights with corrected weights.
42 delta(u.v) = f(u,v) -f(v,u).
43 w*(u,v) = w(u,v) + delta(u,v). */
47 #include "coretypes.h"
52 /* CAP_INFINITY: Constant to represent infinite capacity. */
53 #define CAP_INFINITY INTTYPE_MAXIMUM (int64_t)
56 #define K_POS(b) ((b))
57 #define K_NEG(b) (50 * (b))
58 #define COST(k, w) ((k) / mcf_ln ((w) + 2))
59 /* Limit the number of iterations for cancel_negative_cycles() to ensure
60 reasonable compile time. */
61 #define MAX_ITER(n, e) 10 + (1000000 / ((n) * (e)))
65 VERTEX_SPLIT_EDGE, /* Edge to represent vertex with w(e) = w(v). */
66 REDIRECT_EDGE, /* Edge after vertex transformation. */
68 SOURCE_CONNECT_EDGE, /* Single edge connecting to single source. */
69 SINK_CONNECT_EDGE, /* Single edge connecting to single sink. */
70 BALANCE_EDGE, /* Edge connecting with source/sink: cp(e) = 0. */
71 REDIRECT_NORMALIZED_EDGE, /* Normalized edge for a redirect edge. */
72 REVERSE_NORMALIZED_EDGE /* Normalized edge for a reverse edge. */
75 /* Structure to represent an edge in the fixup graph. */
76 struct fixup_edge_type
80 /* Flag denoting type of edge and attributes for the flow field. */
83 /* Index to the normalization vertex added for this edge. */
84 int norm_vertex_index;
85 /* Flow for this edge. */
87 /* Residual flow for this edge - used during negative cycle canceling. */
91 gcov_type max_capacity;
94 typedef fixup_edge_type *fixup_edge_p;
97 /* Structure to represent a vertex in the fixup graph. */
98 struct fixup_vertex_type
100 vec<fixup_edge_p> succ_edges;
103 typedef fixup_vertex_type *fixup_vertex_p;
105 /* Fixup graph used in the MCF algorithm. */
106 struct fixup_graph_type
108 /* Current number of vertices for the graph. */
110 /* Current number of edges for the graph. */
112 /* Index of new entry vertex. */
114 /* Index of new exit vertex. */
116 /* Fixup vertex list. Adjacency list for fixup graph. */
117 fixup_vertex_p vertex_list;
118 /* Fixup edge list. */
119 fixup_edge_p edge_list;
130 /* Structure used in the maximal flow routines to find augmenting path. */
131 struct augmenting_path_type
133 /* Queue used to hold vertex indices. */
134 queue_type queue_list;
135 /* Vector to hold chain of pred vertex indices in augmenting path. */
137 /* Vector that indicates if basic block i has been visited. */
142 /* Function definitions. */
144 /* Dump routines to aid debugging. */
146 /* Print basic block with index N for FIXUP_GRAPH in n' and n'' format. */
149 print_basic_block (FILE *file, fixup_graph_type *fixup_graph, int n)
151 if (n == ENTRY_BLOCK)
152 fputs ("ENTRY", file);
153 else if (n == ENTRY_BLOCK + 1)
154 fputs ("ENTRY''", file);
155 else if (n == 2 * EXIT_BLOCK)
156 fputs ("EXIT", file);
157 else if (n == 2 * EXIT_BLOCK + 1)
158 fputs ("EXIT''", file);
159 else if (n == fixup_graph->new_exit_index)
160 fputs ("NEW_EXIT", file);
161 else if (n == fixup_graph->new_entry_index)
162 fputs ("NEW_ENTRY", file);
165 fprintf (file, "%d", n / 2);
174 /* Print edge S->D for given fixup_graph with n' and n'' format.
176 S is the index of the source vertex of the edge (input) and
177 D is the index of the destination vertex of the edge (input) for the given
178 fixup_graph (input). */
181 print_edge (FILE *file, fixup_graph_type *fixup_graph, int s, int d)
183 print_basic_block (file, fixup_graph, s);
185 print_basic_block (file, fixup_graph, d);
189 /* Dump out the attributes of a given edge FEDGE in the fixup_graph to a
192 dump_fixup_edge (FILE *file, fixup_graph_type *fixup_graph, fixup_edge_p fedge)
196 fputs ("NULL fixup graph edge.\n", file);
200 print_edge (file, fixup_graph, fedge->src, fedge->dest);
205 fprintf (file, "flow/capacity=%" PRId64 "/",
207 if (fedge->max_capacity == CAP_INFINITY)
208 fputs ("+oo,", file);
210 fprintf (file, "%" PRId64 ",", fedge->max_capacity);
213 if (fedge->is_rflow_valid)
215 if (fedge->rflow == CAP_INFINITY)
216 fputs (" rflow=+oo.", file);
218 fprintf (file, " rflow=%" PRId64 ",", fedge->rflow);
221 fprintf (file, " cost=%" PRId64 ".", fedge->cost);
223 fprintf (file, "\t(%d->%d)", fedge->src, fedge->dest);
229 case VERTEX_SPLIT_EDGE:
230 fputs (" @VERTEX_SPLIT_EDGE", file);
234 fputs (" @REDIRECT_EDGE", file);
237 case SOURCE_CONNECT_EDGE:
238 fputs (" @SOURCE_CONNECT_EDGE", file);
241 case SINK_CONNECT_EDGE:
242 fputs (" @SINK_CONNECT_EDGE", file);
246 fputs (" @REVERSE_EDGE", file);
250 fputs (" @BALANCE_EDGE", file);
253 case REDIRECT_NORMALIZED_EDGE:
254 case REVERSE_NORMALIZED_EDGE:
255 fputs (" @NORMALIZED_EDGE", file);
259 fputs (" @INVALID_EDGE", file);
267 /* Print out the edges and vertices of the given FIXUP_GRAPH, into the dump
268 file. The input string MSG is printed out as a heading. */
271 dump_fixup_graph (FILE *file, fixup_graph_type *fixup_graph, const char *msg)
274 int fnum_vertices, fnum_edges;
276 fixup_vertex_p fvertex_list, pfvertex;
279 gcc_assert (fixup_graph);
280 fvertex_list = fixup_graph->vertex_list;
281 fnum_vertices = fixup_graph->num_vertices;
282 fnum_edges = fixup_graph->num_edges;
284 fprintf (file, "\nDump fixup graph for %s(): %s.\n",
285 current_function_name (), msg);
287 "There are %d vertices and %d edges. new_exit_index is %d.\n\n",
288 fnum_vertices, fnum_edges, fixup_graph->new_exit_index);
290 for (i = 0; i < fnum_vertices; i++)
292 pfvertex = fvertex_list + i;
293 fprintf (file, "vertex_list[%d]: %d succ fixup edges.\n",
294 i, pfvertex->succ_edges.length ());
296 for (j = 0; pfvertex->succ_edges.iterate (j, &pfedge);
299 /* Distinguish forward edges and backward edges in the residual flow
302 fputs ("(f) ", file);
303 else if (pfedge->is_rflow_valid)
304 fputs ("(b) ", file);
305 dump_fixup_edge (file, fixup_graph, pfedge);
313 /* Utility routines. */
314 /* ln() implementation: approximate calculation. Returns ln of X. */
335 /* sqrt() implementation: based on open source QUAKE3 code (magic sqrt
336 implementation) by John Carmack. Returns sqrt of X. */
341 #define MAGIC_CONST1 0x1fbcf800
342 #define MAGIC_CONST2 0x5f3759df
346 } convertor, convertor2;
350 convertor.floatPart = x;
351 convertor2.floatPart = x;
352 convertor.intPart = MAGIC_CONST1 + (convertor.intPart >> 1);
353 convertor2.intPart = MAGIC_CONST2 - (convertor2.intPart >> 1);
355 return 0.5f * (convertor.floatPart + (x * convertor2.floatPart));
359 /* Common code shared between add_fixup_edge and add_rfixup_edge. Adds an edge
360 (SRC->DEST) to the edge_list maintained in FIXUP_GRAPH with cost of the edge
361 added set to COST. */
364 add_edge (fixup_graph_type *fixup_graph, int src, int dest, gcov_type cost)
366 fixup_vertex_p curr_vertex = fixup_graph->vertex_list + src;
367 fixup_edge_p curr_edge = fixup_graph->edge_list + fixup_graph->num_edges;
368 curr_edge->src = src;
369 curr_edge->dest = dest;
370 curr_edge->cost = cost;
371 fixup_graph->num_edges++;
373 dump_fixup_edge (dump_file, fixup_graph, curr_edge);
374 curr_vertex->succ_edges.safe_push (curr_edge);
379 /* Add a fixup edge (src->dest) with attributes TYPE, WEIGHT, COST and
380 MAX_CAPACITY to the edge_list in the fixup graph. */
383 add_fixup_edge (fixup_graph_type *fixup_graph, int src, int dest,
384 edge_type type, gcov_type weight, gcov_type cost,
385 gcov_type max_capacity)
387 fixup_edge_p curr_edge = add_edge (fixup_graph, src, dest, cost);
388 curr_edge->type = type;
389 curr_edge->weight = weight;
390 curr_edge->max_capacity = max_capacity;
394 /* Add a residual edge (SRC->DEST) with attributes RFLOW and COST
395 to the fixup graph. */
398 add_rfixup_edge (fixup_graph_type *fixup_graph, int src, int dest,
399 gcov_type rflow, gcov_type cost)
401 fixup_edge_p curr_edge = add_edge (fixup_graph, src, dest, cost);
402 curr_edge->rflow = rflow;
403 curr_edge->is_rflow_valid = true;
404 /* This edge is not a valid edge - merely used to hold residual flow. */
405 curr_edge->type = INVALID_EDGE;
409 /* Return the pointer to fixup edge SRC->DEST or NULL if edge does not
410 exist in the FIXUP_GRAPH. */
413 find_fixup_edge (fixup_graph_type *fixup_graph, int src, int dest)
417 fixup_vertex_p pfvertex;
419 gcc_assert (src < fixup_graph->num_vertices);
421 pfvertex = fixup_graph->vertex_list + src;
423 for (j = 0; pfvertex->succ_edges.iterate (j, &pfedge);
425 if (pfedge->dest == dest)
432 /* Cleanup routine to free structures in FIXUP_GRAPH. */
435 delete_fixup_graph (fixup_graph_type *fixup_graph)
438 int fnum_vertices = fixup_graph->num_vertices;
439 fixup_vertex_p pfvertex = fixup_graph->vertex_list;
441 for (i = 0; i < fnum_vertices; i++, pfvertex++)
442 pfvertex->succ_edges.release ();
444 free (fixup_graph->vertex_list);
445 free (fixup_graph->edge_list);
449 /* Creates a fixup graph FIXUP_GRAPH from the function CFG. */
452 create_fixup_graph (fixup_graph_type *fixup_graph)
454 double sqrt_avg_vertex_weight = 0;
455 double total_vertex_weight = 0;
458 /* Vector to hold D(v) = sum_out_edges(v) - sum_in_edges(v). */
459 gcov_type *diff_out_in = NULL;
460 gcov_type supply_value = 1, demand_value = 0;
462 int new_entry_index = 0, new_exit_index = 0;
468 fixup_edge_p pfedge, r_pfedge;
469 fixup_edge_p fedge_list;
472 /* Each basic_block will be split into 2 during vertex transformation. */
473 int fnum_vertices_after_transform = 2 * n_basic_blocks_for_fn (cfun);
474 int fnum_edges_after_transform =
475 n_edges_for_fn (cfun) + n_basic_blocks_for_fn (cfun);
477 /* Count the new SOURCE and EXIT vertices to be added. */
478 int fmax_num_vertices =
479 (fnum_vertices_after_transform + n_edges_for_fn (cfun)
480 + n_basic_blocks_for_fn (cfun) + 2);
482 /* In create_fixup_graph: Each basic block and edge can be split into 3
483 edges. Number of balance edges = n_basic_blocks. So after
485 max_edges = 4 * n_basic_blocks + 3 * n_edges
486 Accounting for residual flow edges
487 max_edges = 2 * (4 * n_basic_blocks + 3 * n_edges)
488 = 8 * n_basic_blocks + 6 * n_edges
489 < 8 * n_basic_blocks + 8 * n_edges. */
490 int fmax_num_edges = 8 * (n_basic_blocks_for_fn (cfun) +
491 n_edges_for_fn (cfun));
493 /* Initial num of vertices in the fixup graph. */
494 fixup_graph->num_vertices = n_basic_blocks_for_fn (cfun);
496 /* Fixup graph vertex list. */
497 fixup_graph->vertex_list =
498 (fixup_vertex_p) xcalloc (fmax_num_vertices, sizeof (fixup_vertex_type));
500 /* Fixup graph edge list. */
501 fixup_graph->edge_list =
502 (fixup_edge_p) xcalloc (fmax_num_edges, sizeof (fixup_edge_type));
505 (gcov_type *) xcalloc (1 + fnum_vertices_after_transform,
508 /* Compute constants b, k_pos, k_neg used in the cost function calculation.
509 b = sqrt(avg_vertex_weight(cfg)); k_pos = b; k_neg = 50b. */
510 FOR_BB_BETWEEN (bb, ENTRY_BLOCK_PTR_FOR_FN (cfun), NULL, next_bb)
511 total_vertex_weight += bb->count;
513 sqrt_avg_vertex_weight = mcf_sqrt (total_vertex_weight /
514 n_basic_blocks_for_fn (cfun));
516 k_pos = K_POS (sqrt_avg_vertex_weight);
517 k_neg = K_NEG (sqrt_avg_vertex_weight);
519 /* 1. Vertex Transformation: Split each vertex v into two vertices v' and v'',
520 connected by an edge e from v' to v''. w(e) = w(v). */
523 fprintf (dump_file, "\nVertex transformation:\n");
525 FOR_BB_BETWEEN (bb, ENTRY_BLOCK_PTR_FOR_FN (cfun), NULL, next_bb)
527 /* v'->v'': index1->(index1+1). */
529 fcost = (gcov_type) COST (k_pos, bb->count);
530 add_fixup_edge (fixup_graph, i, i + 1, VERTEX_SPLIT_EDGE, bb->count,
531 fcost, CAP_INFINITY);
532 fixup_graph->num_vertices++;
534 FOR_EACH_EDGE (e, ei, bb->succs)
536 /* Edges with ignore attribute set should be treated like they don't
538 if (EDGE_INFO (e) && EDGE_INFO (e)->ignore)
540 j = 2 * e->dest->index;
541 fcost = (gcov_type) COST (k_pos, e->count);
542 add_fixup_edge (fixup_graph, i + 1, j, REDIRECT_EDGE, e->count, fcost,
547 /* After vertex transformation. */
548 gcc_assert (fixup_graph->num_vertices == fnum_vertices_after_transform);
549 /* Redirect edges are not added for edges with ignore attribute. */
550 gcc_assert (fixup_graph->num_edges <= fnum_edges_after_transform);
552 fnum_edges_after_transform = fixup_graph->num_edges;
554 /* 2. Initialize D(v). */
555 for (i = 0; i < fnum_edges_after_transform; i++)
557 pfedge = fixup_graph->edge_list + i;
558 diff_out_in[pfedge->src] += pfedge->weight;
559 diff_out_in[pfedge->dest] -= pfedge->weight;
562 /* Entry block - vertex indices 0, 1; EXIT block - vertex indices 2, 3. */
563 for (i = 0; i <= 3; i++)
566 /* 3. Add reverse edges: needed to decrease counts during smoothing. */
568 fprintf (dump_file, "\nReverse edges:\n");
569 for (i = 0; i < fnum_edges_after_transform; i++)
571 pfedge = fixup_graph->edge_list + i;
572 if ((pfedge->src == 0) || (pfedge->src == 2))
574 r_pfedge = find_fixup_edge (fixup_graph, pfedge->dest, pfedge->src);
575 if (!r_pfedge && pfedge->weight)
577 /* Skip adding reverse edges for edges with w(e) = 0, as its maximum
579 fcost = (gcov_type) COST (k_neg, pfedge->weight);
580 add_fixup_edge (fixup_graph, pfedge->dest, pfedge->src,
581 REVERSE_EDGE, 0, fcost, pfedge->weight);
585 /* 4. Create single source and sink. Connect new source vertex s' to function
586 entry block. Connect sink vertex t' to function exit. */
588 fprintf (dump_file, "\ns'->S, T->t':\n");
590 new_entry_index = fixup_graph->new_entry_index = fixup_graph->num_vertices;
591 fixup_graph->num_vertices++;
592 /* Set supply_value to 1 to avoid zero count function ENTRY. */
593 add_fixup_edge (fixup_graph, new_entry_index, ENTRY_BLOCK, SOURCE_CONNECT_EDGE,
594 1 /* supply_value */, 0, 1 /* supply_value */);
596 /* Create new exit with EXIT_BLOCK as single pred. */
597 new_exit_index = fixup_graph->new_exit_index = fixup_graph->num_vertices;
598 fixup_graph->num_vertices++;
599 add_fixup_edge (fixup_graph, 2 * EXIT_BLOCK + 1, new_exit_index,
601 0 /* demand_value */, 0, 0 /* demand_value */);
603 /* Connect vertices with unbalanced D(v) to source/sink. */
605 fprintf (dump_file, "\nD(v) balance:\n");
606 /* Skip vertices for ENTRY (0, 1) and EXIT (2,3) blocks, so start with i = 4.
607 diff_out_in[v''] will be 0, so skip v'' vertices, hence i += 2. */
608 for (i = 4; i < new_entry_index; i += 2)
610 if (diff_out_in[i] > 0)
612 add_fixup_edge (fixup_graph, i, new_exit_index, BALANCE_EDGE, 0, 0,
614 demand_value += diff_out_in[i];
616 else if (diff_out_in[i] < 0)
618 add_fixup_edge (fixup_graph, new_entry_index, i, BALANCE_EDGE, 0, 0,
620 supply_value -= diff_out_in[i];
624 /* Set supply = demand. */
627 fprintf (dump_file, "\nAdjust supply and demand:\n");
628 fprintf (dump_file, "supply_value=%" PRId64 "\n",
630 fprintf (dump_file, "demand_value=%" PRId64 "\n",
634 if (demand_value > supply_value)
636 pfedge = find_fixup_edge (fixup_graph, new_entry_index, ENTRY_BLOCK);
637 pfedge->max_capacity += (demand_value - supply_value);
641 pfedge = find_fixup_edge (fixup_graph, 2 * EXIT_BLOCK + 1, new_exit_index);
642 pfedge->max_capacity += (supply_value - demand_value);
645 /* 6. Normalize edges: remove anti-parallel edges. Anti-parallel edges are
646 created by the vertex transformation step from self-edges in the original
647 CFG and by the reverse edges added earlier. */
649 fprintf (dump_file, "\nNormalize edges:\n");
651 fnum_edges = fixup_graph->num_edges;
652 fedge_list = fixup_graph->edge_list;
654 for (i = 0; i < fnum_edges; i++)
656 pfedge = fedge_list + i;
657 r_pfedge = find_fixup_edge (fixup_graph, pfedge->dest, pfedge->src);
658 if (((pfedge->type == VERTEX_SPLIT_EDGE)
659 || (pfedge->type == REDIRECT_EDGE)) && r_pfedge)
661 new_index = fixup_graph->num_vertices;
662 fixup_graph->num_vertices++;
666 fprintf (dump_file, "\nAnti-parallel edge:\n");
667 dump_fixup_edge (dump_file, fixup_graph, pfedge);
668 dump_fixup_edge (dump_file, fixup_graph, r_pfedge);
669 fprintf (dump_file, "New vertex is %d.\n", new_index);
670 fprintf (dump_file, "------------------\n");
674 pfedge->norm_vertex_index = new_index;
677 fprintf (dump_file, "After normalization:\n");
678 dump_fixup_edge (dump_file, fixup_graph, pfedge);
681 /* Add a new fixup edge: new_index->src. */
682 add_fixup_edge (fixup_graph, new_index, pfedge->src,
683 REVERSE_NORMALIZED_EDGE, 0, r_pfedge->cost,
684 r_pfedge->max_capacity);
685 gcc_assert (fixup_graph->num_vertices <= fmax_num_vertices);
687 /* Edge: r_pfedge->src -> r_pfedge->dest
688 ==> r_pfedge->src -> new_index. */
689 r_pfedge->dest = new_index;
690 r_pfedge->type = REVERSE_NORMALIZED_EDGE;
691 r_pfedge->cost = pfedge->cost;
692 r_pfedge->max_capacity = pfedge->max_capacity;
694 dump_fixup_edge (dump_file, fixup_graph, r_pfedge);
699 dump_fixup_graph (dump_file, fixup_graph, "After create_fixup_graph()");
706 /* Allocates space for the structures in AUGMENTING_PATH. The space needed is
707 proportional to the number of nodes in the graph, which is given by
711 init_augmenting_path (augmenting_path_type *augmenting_path, int graph_size)
713 augmenting_path->queue_list.queue = (int *)
714 xcalloc (graph_size + 2, sizeof (int));
715 augmenting_path->queue_list.size = graph_size + 2;
716 augmenting_path->bb_pred = (int *) xcalloc (graph_size, sizeof (int));
717 augmenting_path->is_visited = (int *) xcalloc (graph_size, sizeof (int));
720 /* Free the structures in AUGMENTING_PATH. */
722 free_augmenting_path (augmenting_path_type *augmenting_path)
724 free (augmenting_path->queue_list.queue);
725 free (augmenting_path->bb_pred);
726 free (augmenting_path->is_visited);
730 /* Queue routines. Assumes queue will never overflow. */
733 init_queue (queue_type *queue_list)
735 gcc_assert (queue_list);
736 queue_list->head = 0;
737 queue_list->tail = 0;
740 /* Return true if QUEUE_LIST is empty. */
742 is_empty (queue_type *queue_list)
744 return (queue_list->head == queue_list->tail);
747 /* Insert element X into QUEUE_LIST. */
749 enqueue (queue_type *queue_list, int x)
751 gcc_assert (queue_list->tail < queue_list->size);
752 queue_list->queue[queue_list->tail] = x;
753 (queue_list->tail)++;
756 /* Return the first element in QUEUE_LIST. */
758 dequeue (queue_type *queue_list)
761 gcc_assert (queue_list->head >= 0);
762 x = queue_list->queue[queue_list->head];
763 (queue_list->head)++;
768 /* Finds a negative cycle in the residual network using
769 the Bellman-Ford algorithm. The flow on the found cycle is reversed by the
770 minimum residual capacity of that cycle. ENTRY and EXIT vertices are not
774 FIXUP_GRAPH - Residual graph (input/output)
775 The following are allocated/freed by the caller:
776 PI - Vector to hold predecessors in path (pi = pred index)
777 D - D[I] holds minimum cost of path from i to sink
778 CYCLE - Vector to hold the minimum cost cycle
781 true if a negative cycle was found, false otherwise. */
784 cancel_negative_cycle (fixup_graph_type *fixup_graph,
785 int *pi, gcov_type *d, int *cycle)
788 int fnum_vertices, fnum_edges;
789 fixup_edge_p fedge_list, pfedge, r_pfedge;
790 bool found_cycle = false;
791 int cycle_start = 0, cycle_end = 0;
792 gcov_type sum_cost = 0, cycle_flow = 0;
794 bool propagated = false;
796 gcc_assert (fixup_graph);
797 fnum_vertices = fixup_graph->num_vertices;
798 fnum_edges = fixup_graph->num_edges;
799 fedge_list = fixup_graph->edge_list;
800 new_entry_index = fixup_graph->new_entry_index;
804 for (i = 1; i < fnum_vertices; i++)
813 for (k = 1; k < fnum_vertices; k++)
816 for (i = 0; i < fnum_edges; i++)
818 pfedge = fedge_list + i;
819 if (pfedge->src == new_entry_index)
821 if (pfedge->is_rflow_valid && pfedge->rflow
822 && d[pfedge->src] != CAP_INFINITY
823 && (d[pfedge->dest] > d[pfedge->src] + pfedge->cost))
825 d[pfedge->dest] = d[pfedge->src] + pfedge->cost;
826 pi[pfedge->dest] = pfedge->src;
835 /* No negative cycles exist. */
839 for (i = 0; i < fnum_edges; i++)
841 pfedge = fedge_list + i;
842 if (pfedge->src == new_entry_index)
844 if (pfedge->is_rflow_valid && pfedge->rflow
845 && d[pfedge->src] != CAP_INFINITY
846 && (d[pfedge->dest] > d[pfedge->src] + pfedge->cost))
856 /* Augment the cycle with the cycle's minimum residual capacity. */
858 cycle[0] = pfedge->dest;
861 for (i = 1; i < fnum_vertices; i++)
865 for (k = 0; k < i; k++)
869 /* cycle[k] -> ... -> cycle[i]. */
880 gcc_assert (cycle[cycle_start] == cycle[cycle_end]);
882 fprintf (dump_file, "\nNegative cycle length is %d:\n",
883 cycle_end - cycle_start);
886 cycle_flow = CAP_INFINITY;
887 for (k = cycle_start; k < cycle_end; k++)
889 pfedge = find_fixup_edge (fixup_graph, cycle[k + 1], cycle[k]);
890 cycle_flow = MIN (cycle_flow, pfedge->rflow);
891 sum_cost += pfedge->cost;
893 fprintf (dump_file, "%d ", cycle[k]);
898 fprintf (dump_file, "%d", cycle[k]);
900 ": (%" PRId64 ", %" PRId64
901 ")\n", sum_cost, cycle_flow);
903 "Augment cycle with %" PRId64 "\n",
907 for (k = cycle_start; k < cycle_end; k++)
909 pfedge = find_fixup_edge (fixup_graph, cycle[k + 1], cycle[k]);
910 r_pfedge = find_fixup_edge (fixup_graph, cycle[k], cycle[k + 1]);
911 pfedge->rflow -= cycle_flow;
913 pfedge->flow += cycle_flow;
914 r_pfedge->rflow += cycle_flow;
916 r_pfedge->flow -= cycle_flow;
923 /* Computes the residual flow for FIXUP_GRAPH by setting the rflow field of
924 the edges. ENTRY and EXIT vertices should not be considered. */
927 compute_residual_flow (fixup_graph_type *fixup_graph)
931 fixup_edge_p fedge_list, pfedge;
933 gcc_assert (fixup_graph);
936 fputs ("\ncompute_residual_flow():\n", dump_file);
938 fnum_edges = fixup_graph->num_edges;
939 fedge_list = fixup_graph->edge_list;
941 for (i = 0; i < fnum_edges; i++)
943 pfedge = fedge_list + i;
944 pfedge->rflow = pfedge->max_capacity - pfedge->flow;
945 pfedge->is_rflow_valid = true;
946 add_rfixup_edge (fixup_graph, pfedge->dest, pfedge->src, pfedge->flow,
952 /* Uses Edmonds-Karp algorithm - BFS to find augmenting path from SOURCE to
953 SINK. The fields in the edge vector in the FIXUP_GRAPH are not modified by
954 this routine. The vector bb_pred in the AUGMENTING_PATH structure is updated
955 to reflect the path found.
956 Returns: 0 if no augmenting path is found, 1 otherwise. */
959 find_augmenting_path (fixup_graph_type *fixup_graph,
960 augmenting_path_type *augmenting_path, int source,
965 fixup_vertex_p fvertex_list, pfvertex;
967 int *bb_pred, *is_visited;
968 queue_type *queue_list;
970 gcc_assert (augmenting_path);
971 bb_pred = augmenting_path->bb_pred;
972 gcc_assert (bb_pred);
973 is_visited = augmenting_path->is_visited;
974 gcc_assert (is_visited);
975 queue_list = &(augmenting_path->queue_list);
977 gcc_assert (fixup_graph);
979 fvertex_list = fixup_graph->vertex_list;
981 for (u = 0; u < fixup_graph->num_vertices; u++)
984 init_queue (queue_list);
985 enqueue (queue_list, source);
986 bb_pred[source] = -1;
988 while (!is_empty (queue_list))
990 u = dequeue (queue_list);
992 pfvertex = fvertex_list + u;
993 for (i = 0; pfvertex->succ_edges.iterate (i, &pfedge);
996 int dest = pfedge->dest;
997 if ((pfedge->rflow > 0) && (is_visited[dest] == 0))
999 enqueue (queue_list, dest);
1001 is_visited[dest] = 1;
1012 /* Routine to find the maximal flow:
1014 1. Initialize flow to 0
1015 2. Find an augmenting path form source to sink.
1016 3. Send flow equal to the path's residual capacity along the edges of this path.
1017 4. Repeat steps 2 and 3 until no new augmenting path is found.
1020 SOURCE: index of source vertex (input)
1021 SINK: index of sink vertex (input)
1022 FIXUP_GRAPH: adjacency matrix representing the graph. The flow of the edges will be
1023 set to have a valid maximal flow by this routine. (input)
1024 Return: Maximum flow possible. */
1027 find_max_flow (fixup_graph_type *fixup_graph, int source, int sink)
1030 augmenting_path_type augmenting_path;
1032 gcov_type max_flow = 0;
1034 fixup_edge_p fedge_list, pfedge, r_pfedge;
1036 gcc_assert (fixup_graph);
1038 fnum_edges = fixup_graph->num_edges;
1039 fedge_list = fixup_graph->edge_list;
1041 /* Initialize flow to 0. */
1042 for (i = 0; i < fnum_edges; i++)
1044 pfedge = fedge_list + i;
1048 compute_residual_flow (fixup_graph);
1050 init_augmenting_path (&augmenting_path, fixup_graph->num_vertices);
1052 bb_pred = augmenting_path.bb_pred;
1053 while (find_augmenting_path (fixup_graph, &augmenting_path, source, sink))
1055 /* Determine the amount by which we can increment the flow. */
1056 gcov_type increment = CAP_INFINITY;
1057 for (u = sink; u != source; u = bb_pred[u])
1059 pfedge = find_fixup_edge (fixup_graph, bb_pred[u], u);
1060 increment = MIN (increment, pfedge->rflow);
1062 max_flow += increment;
1064 /* Now increment the flow. EXIT vertex index is 1. */
1065 for (u = sink; u != source; u = bb_pred[u])
1067 pfedge = find_fixup_edge (fixup_graph, bb_pred[u], u);
1068 r_pfedge = find_fixup_edge (fixup_graph, u, bb_pred[u]);
1072 pfedge->flow += increment;
1073 pfedge->rflow -= increment;
1074 r_pfedge->rflow += increment;
1078 /* backward edge. */
1079 gcc_assert (r_pfedge->type);
1080 r_pfedge->rflow += increment;
1081 r_pfedge->flow -= increment;
1082 pfedge->rflow -= increment;
1088 fprintf (dump_file, "\nDump augmenting path:\n");
1089 for (u = sink; u != source; u = bb_pred[u])
1091 print_basic_block (dump_file, fixup_graph, u);
1092 fprintf (dump_file, "<-");
1095 "ENTRY (path_capacity=%" PRId64 ")\n",
1098 "Network flow is %" PRId64 ".\n",
1103 free_augmenting_path (&augmenting_path);
1105 dump_fixup_graph (dump_file, fixup_graph, "After find_max_flow()");
1110 /* Computes the corrected edge and basic block weights using FIXUP_GRAPH
1111 after applying the find_minimum_cost_flow() routine. */
1114 adjust_cfg_counts (fixup_graph_type *fixup_graph)
1120 fixup_edge_p pfedge, pfedge_n;
1122 gcc_assert (fixup_graph);
1125 fprintf (dump_file, "\nadjust_cfg_counts():\n");
1127 FOR_BB_BETWEEN (bb, ENTRY_BLOCK_PTR_FOR_FN (cfun),
1128 EXIT_BLOCK_PTR_FOR_FN (cfun), next_bb)
1135 "BB%d: %" PRId64 "", bb->index, bb->count);
1137 pfedge = find_fixup_edge (fixup_graph, i, i + 1);
1140 bb->count += pfedge->flow;
1143 fprintf (dump_file, " + %" PRId64 "(",
1145 print_edge (dump_file, fixup_graph, i, i + 1);
1146 fprintf (dump_file, ")");
1151 find_fixup_edge (fixup_graph, i + 1, pfedge->norm_vertex_index);
1152 /* Deduct flow from normalized reverse edge. */
1153 if (pfedge->norm_vertex_index && pfedge_n->flow)
1155 bb->count -= pfedge_n->flow;
1158 fprintf (dump_file, " - %" PRId64 "(",
1160 print_edge (dump_file, fixup_graph, i + 1,
1161 pfedge->norm_vertex_index);
1162 fprintf (dump_file, ")");
1166 fprintf (dump_file, " = %" PRId64 "\n", bb->count);
1169 FOR_EACH_EDGE (e, ei, bb->succs)
1171 /* Treat edges with ignore attribute set as if they don't exist. */
1172 if (EDGE_INFO (e) && EDGE_INFO (e)->ignore)
1175 j = 2 * e->dest->index;
1177 fprintf (dump_file, "%d->%d: %" PRId64 "",
1178 bb->index, e->dest->index, e->count);
1180 pfedge = find_fixup_edge (fixup_graph, i + 1, j);
1182 if (bb->index != e->dest->index)
1184 /* Non-self edge. */
1187 e->count += pfedge->flow;
1190 fprintf (dump_file, " + %" PRId64 "(",
1192 print_edge (dump_file, fixup_graph, i + 1, j);
1193 fprintf (dump_file, ")");
1198 find_fixup_edge (fixup_graph, j, pfedge->norm_vertex_index);
1199 /* Deduct flow from normalized reverse edge. */
1200 if (pfedge->norm_vertex_index && pfedge_n->flow)
1202 e->count -= pfedge_n->flow;
1205 fprintf (dump_file, " - %" PRId64 "(",
1207 print_edge (dump_file, fixup_graph, j,
1208 pfedge->norm_vertex_index);
1209 fprintf (dump_file, ")");
1215 /* Handle self edges. Self edge is split with a normalization
1216 vertex. Here i=j. */
1217 pfedge = find_fixup_edge (fixup_graph, j, i + 1);
1219 find_fixup_edge (fixup_graph, i + 1, pfedge->norm_vertex_index);
1220 e->count += pfedge_n->flow;
1221 bb->count += pfedge_n->flow;
1224 fprintf (dump_file, "(self edge)");
1225 fprintf (dump_file, " + %" PRId64 "(",
1227 print_edge (dump_file, fixup_graph, i + 1,
1228 pfedge->norm_vertex_index);
1229 fprintf (dump_file, ")");
1234 e->probability = REG_BR_PROB_BASE * e->count / bb->count;
1236 fprintf (dump_file, " = %" PRId64 "\t(%.1f%%)\n",
1237 e->count, e->probability * 100.0 / REG_BR_PROB_BASE);
1241 ENTRY_BLOCK_PTR_FOR_FN (cfun)->count =
1242 sum_edge_counts (ENTRY_BLOCK_PTR_FOR_FN (cfun)->succs);
1243 EXIT_BLOCK_PTR_FOR_FN (cfun)->count =
1244 sum_edge_counts (EXIT_BLOCK_PTR_FOR_FN (cfun)->preds);
1246 /* Compute edge probabilities. */
1247 FOR_ALL_BB_FN (bb, cfun)
1251 FOR_EACH_EDGE (e, ei, bb->succs)
1252 e->probability = REG_BR_PROB_BASE * e->count / bb->count;
1257 FOR_EACH_EDGE (e, ei, bb->succs)
1258 if (!(e->flags & (EDGE_COMPLEX | EDGE_FAKE)))
1262 FOR_EACH_EDGE (e, ei, bb->succs)
1264 if (!(e->flags & (EDGE_COMPLEX | EDGE_FAKE)))
1265 e->probability = REG_BR_PROB_BASE / total;
1272 total += EDGE_COUNT (bb->succs);
1273 FOR_EACH_EDGE (e, ei, bb->succs)
1274 e->probability = REG_BR_PROB_BASE / total;
1281 fprintf (dump_file, "\nCheck %s() CFG flow conservation:\n",
1282 current_function_name ());
1283 FOR_EACH_BB_FN (bb, cfun)
1285 if ((bb->count != sum_edge_counts (bb->preds))
1286 || (bb->count != sum_edge_counts (bb->succs)))
1289 "BB%d(%" PRId64 ") **INVALID**: ",
1290 bb->index, bb->count);
1292 "******** BB%d(%" PRId64
1293 ") **INVALID**: \n", bb->index, bb->count);
1294 fprintf (dump_file, "in_edges=%" PRId64 " ",
1295 sum_edge_counts (bb->preds));
1296 fprintf (dump_file, "out_edges=%" PRId64 "\n",
1297 sum_edge_counts (bb->succs));
1304 /* Implements the negative cycle canceling algorithm to compute a minimum cost
1307 1. Find maximal flow.
1308 2. Form residual network
1310 While G contains a negative cost cycle C, reverse the flow on the found cycle
1311 by the minimum residual capacity in that cycle.
1312 4. Form the minimal cost flow
1315 FIXUP_GRAPH - Initial fixup graph.
1316 The flow field is modified to represent the minimum cost flow. */
1319 find_minimum_cost_flow (fixup_graph_type *fixup_graph)
1321 /* Holds the index of predecessor in path. */
1323 /* Used to hold the minimum cost cycle. */
1325 /* Used to record the number of iterations of cancel_negative_cycle. */
1327 /* Vector d[i] holds the minimum cost of path from i to sink. */
1331 int new_entry_index;
1333 gcc_assert (fixup_graph);
1334 fnum_vertices = fixup_graph->num_vertices;
1335 new_exit_index = fixup_graph->new_exit_index;
1336 new_entry_index = fixup_graph->new_entry_index;
1338 find_max_flow (fixup_graph, new_entry_index, new_exit_index);
1340 /* Initialize the structures for find_negative_cycle(). */
1341 pred = (int *) xcalloc (fnum_vertices, sizeof (int));
1342 d = (gcov_type *) xcalloc (fnum_vertices, sizeof (gcov_type));
1343 cycle = (int *) xcalloc (fnum_vertices, sizeof (int));
1345 /* Repeatedly find and cancel negative cost cycles, until
1346 no more negative cycles exist. This also updates the flow field
1347 to represent the minimum cost flow so far. */
1349 while (cancel_negative_cycle (fixup_graph, pred, d, cycle))
1352 if (iteration > MAX_ITER (fixup_graph->num_vertices,
1353 fixup_graph->num_edges))
1358 dump_fixup_graph (dump_file, fixup_graph,
1359 "After find_minimum_cost_flow()");
1361 /* Cleanup structures. */
1368 /* Compute the sum of the edge counts in TO_EDGES. */
1371 sum_edge_counts (vec<edge, va_gc> *to_edges)
1377 FOR_EACH_EDGE (e, ei, to_edges)
1379 if (EDGE_INFO (e) && EDGE_INFO (e)->ignore)
1387 /* Main routine. Smoothes the initial assigned basic block and edge counts using
1388 a minimum cost flow algorithm, to ensure that the flow consistency rule is
1389 obeyed: sum of outgoing edges = sum of incoming edges for each basic
1393 mcf_smooth_cfg (void)
1395 fixup_graph_type fixup_graph;
1396 memset (&fixup_graph, 0, sizeof (fixup_graph));
1397 create_fixup_graph (&fixup_graph);
1398 find_minimum_cost_flow (&fixup_graph);
1399 adjust_cfg_counts (&fixup_graph);
1400 delete_fixup_graph (&fixup_graph);