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author kent <kent@cr.ie.u-ryukyu.ac.jp>
date Fri, 17 Jul 2009 14:47:48 +0900
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1 /* Routines to implement minimum-cost maximal flow algorithm used to smooth
2 basic block and edge frequency counts.
3 Copyright (C) 2008
4 Free Software Foundation, Inc.
5 Contributed by Paul Yuan (yingbo.com@gmail.com) and
6 Vinodha Ramasamy (vinodha@google.com).
7
8 This file is part of GCC.
9 GCC is free software; you can redistribute it and/or modify it under
10 the terms of the GNU General Public License as published by the Free
11 Software Foundation; either version 3, or (at your option) any later
12 version.
13
14 GCC is distributed in the hope that it will be useful, but WITHOUT ANY
15 WARRANTY; without even the implied warranty of MERCHANTABILITY or
16 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
17 for more details.
18
19 You should have received a copy of the GNU General Public License
20 along with GCC; see the file COPYING3. If not see
21 <http://www.gnu.org/licenses/>. */
22
23 /* References:
24 [1] "Feedback-directed Optimizations in GCC with Estimated Edge Profiles
25 from Hardware Event Sampling", Vinodha Ramasamy, Paul Yuan, Dehao Chen,
26 and Robert Hundt; GCC Summit 2008.
27 [2] "Complementing Missing and Inaccurate Profiling Using a Minimum Cost
28 Circulation Algorithm", Roy Levin, Ilan Newman and Gadi Haber;
29 HiPEAC '08.
30
31 Algorithm to smooth basic block and edge counts:
32 1. create_fixup_graph: Create fixup graph by translating function CFG into
33 a graph that satisfies MCF algorithm requirements.
34 2. find_max_flow: Find maximal flow.
35 3. compute_residual_flow: Form residual network.
36 4. Repeat:
37 cancel_negative_cycle: While G contains a negative cost cycle C, reverse
38 the flow on the found cycle by the minimum residual capacity in that
39 cycle.
40 5. Form the minimal cost flow
41 f(u,v) = rf(v, u).
42 6. adjust_cfg_counts: Update initial edge weights with corrected weights.
43 delta(u.v) = f(u,v) -f(v,u).
44 w*(u,v) = w(u,v) + delta(u,v). */
45
46 #include "config.h"
47 #include "system.h"
48 #include "coretypes.h"
49 #include "tm.h"
50 #include "basic-block.h"
51 #include "output.h"
52 #include "langhooks.h"
53 #include "tree.h"
54 #include "gcov-io.h"
55
56 #include "profile.h"
57
58 /* CAP_INFINITY: Constant to represent infinite capacity. */
59 #define CAP_INFINITY INTTYPE_MAXIMUM (HOST_WIDEST_INT)
60
61 /* COST FUNCTION. */
62 #define K_POS(b) ((b))
63 #define K_NEG(b) (50 * (b))
64 #define COST(k, w) ((k) / mcf_ln ((w) + 2))
65 /* Limit the number of iterations for cancel_negative_cycles() to ensure
66 reasonable compile time. */
67 #define MAX_ITER(n, e) 10 + (1000000 / ((n) * (e)))
68 typedef enum
69 {
70 INVALID_EDGE,
71 VERTEX_SPLIT_EDGE, /* Edge to represent vertex with w(e) = w(v). */
72 REDIRECT_EDGE, /* Edge after vertex transformation. */
73 REVERSE_EDGE,
74 SOURCE_CONNECT_EDGE, /* Single edge connecting to single source. */
75 SINK_CONNECT_EDGE, /* Single edge connecting to single sink. */
76 BALANCE_EDGE, /* Edge connecting with source/sink: cp(e) = 0. */
77 REDIRECT_NORMALIZED_EDGE, /* Normalized edge for a redirect edge. */
78 REVERSE_NORMALIZED_EDGE /* Normalized edge for a reverse edge. */
79 } edge_type;
80
81 /* Structure to represent an edge in the fixup graph. */
82 typedef struct fixup_edge_d
83 {
84 int src;
85 int dest;
86 /* Flag denoting type of edge and attributes for the flow field. */
87 edge_type type;
88 bool is_rflow_valid;
89 /* Index to the normalization vertex added for this edge. */
90 int norm_vertex_index;
91 /* Flow for this edge. */
92 gcov_type flow;
93 /* Residual flow for this edge - used during negative cycle canceling. */
94 gcov_type rflow;
95 gcov_type weight;
96 gcov_type cost;
97 gcov_type max_capacity;
98 } fixup_edge_type;
99
100 typedef fixup_edge_type *fixup_edge_p;
101
102 DEF_VEC_P (fixup_edge_p);
103 DEF_VEC_ALLOC_P (fixup_edge_p, heap);
104
105 /* Structure to represent a vertex in the fixup graph. */
106 typedef struct fixup_vertex_d
107 {
108 VEC (fixup_edge_p, heap) *succ_edges;
109 } fixup_vertex_type;
110
111 typedef fixup_vertex_type *fixup_vertex_p;
112
113 /* Fixup graph used in the MCF algorithm. */
114 typedef struct fixup_graph_d
115 {
116 /* Current number of vertices for the graph. */
117 int num_vertices;
118 /* Current number of edges for the graph. */
119 int num_edges;
120 /* Index of new entry vertex. */
121 int new_entry_index;
122 /* Index of new exit vertex. */
123 int new_exit_index;
124 /* Fixup vertex list. Adjacency list for fixup graph. */
125 fixup_vertex_p vertex_list;
126 /* Fixup edge list. */
127 fixup_edge_p edge_list;
128 } fixup_graph_type;
129
130 typedef struct queue_d
131 {
132 int *queue;
133 int head;
134 int tail;
135 int size;
136 } queue_type;
137
138 /* Structure used in the maximal flow routines to find augmenting path. */
139 typedef struct augmenting_path_d
140 {
141 /* Queue used to hold vertex indices. */
142 queue_type queue_list;
143 /* Vector to hold chain of pred vertex indices in augmenting path. */
144 int *bb_pred;
145 /* Vector that indicates if basic block i has been visited. */
146 int *is_visited;
147 } augmenting_path_type;
148
149
150 /* Function definitions. */
151
152 /* Dump routines to aid debugging. */
153
154 /* Print basic block with index N for FIXUP_GRAPH in n' and n'' format. */
155
156 static void
157 print_basic_block (FILE *file, fixup_graph_type *fixup_graph, int n)
158 {
159 if (n == ENTRY_BLOCK)
160 fputs ("ENTRY", file);
161 else if (n == ENTRY_BLOCK + 1)
162 fputs ("ENTRY''", file);
163 else if (n == 2 * EXIT_BLOCK)
164 fputs ("EXIT", file);
165 else if (n == 2 * EXIT_BLOCK + 1)
166 fputs ("EXIT''", file);
167 else if (n == fixup_graph->new_exit_index)
168 fputs ("NEW_EXIT", file);
169 else if (n == fixup_graph->new_entry_index)
170 fputs ("NEW_ENTRY", file);
171 else
172 {
173 fprintf (file, "%d", n / 2);
174 if (n % 2)
175 fputs ("''", file);
176 else
177 fputs ("'", file);
178 }
179 }
180
181
182 /* Print edge S->D for given fixup_graph with n' and n'' format.
183 PARAMETERS:
184 S is the index of the source vertex of the edge (input) and
185 D is the index of the destination vertex of the edge (input) for the given
186 fixup_graph (input). */
187
188 static void
189 print_edge (FILE *file, fixup_graph_type *fixup_graph, int s, int d)
190 {
191 print_basic_block (file, fixup_graph, s);
192 fputs ("->", file);
193 print_basic_block (file, fixup_graph, d);
194 }
195
196
197 /* Dump out the attributes of a given edge FEDGE in the fixup_graph to a
198 file. */
199 static void
200 dump_fixup_edge (FILE *file, fixup_graph_type *fixup_graph, fixup_edge_p fedge)
201 {
202 if (!fedge)
203 {
204 fputs ("NULL fixup graph edge.\n", file);
205 return;
206 }
207
208 print_edge (file, fixup_graph, fedge->src, fedge->dest);
209 fputs (": ", file);
210
211 if (fedge->type)
212 {
213 fprintf (file, "flow/capacity=" HOST_WIDEST_INT_PRINT_DEC "/",
214 fedge->flow);
215 if (fedge->max_capacity == CAP_INFINITY)
216 fputs ("+oo,", file);
217 else
218 fprintf (file, "" HOST_WIDEST_INT_PRINT_DEC ",", fedge->max_capacity);
219 }
220
221 if (fedge->is_rflow_valid)
222 {
223 if (fedge->rflow == CAP_INFINITY)
224 fputs (" rflow=+oo.", file);
225 else
226 fprintf (file, " rflow=" HOST_WIDEST_INT_PRINT_DEC ",", fedge->rflow);
227 }
228
229 fprintf (file, " cost=" HOST_WIDEST_INT_PRINT_DEC ".", fedge->cost);
230
231 fprintf (file, "\t(%d->%d)", fedge->src, fedge->dest);
232
233 if (fedge->type)
234 {
235 switch (fedge->type)
236 {
237 case VERTEX_SPLIT_EDGE:
238 fputs (" @VERTEX_SPLIT_EDGE", file);
239 break;
240
241 case REDIRECT_EDGE:
242 fputs (" @REDIRECT_EDGE", file);
243 break;
244
245 case SOURCE_CONNECT_EDGE:
246 fputs (" @SOURCE_CONNECT_EDGE", file);
247 break;
248
249 case SINK_CONNECT_EDGE:
250 fputs (" @SINK_CONNECT_EDGE", file);
251 break;
252
253 case REVERSE_EDGE:
254 fputs (" @REVERSE_EDGE", file);
255 break;
256
257 case BALANCE_EDGE:
258 fputs (" @BALANCE_EDGE", file);
259 break;
260
261 case REDIRECT_NORMALIZED_EDGE:
262 case REVERSE_NORMALIZED_EDGE:
263 fputs (" @NORMALIZED_EDGE", file);
264 break;
265
266 default:
267 fputs (" @INVALID_EDGE", file);
268 break;
269 }
270 }
271 fputs ("\n", file);
272 }
273
274
275 /* Print out the edges and vertices of the given FIXUP_GRAPH, into the dump
276 file. The input string MSG is printed out as a heading. */
277
278 static void
279 dump_fixup_graph (FILE *file, fixup_graph_type *fixup_graph, const char *msg)
280 {
281 int i, j;
282 int fnum_vertices, fnum_edges;
283
284 fixup_vertex_p fvertex_list, pfvertex;
285 fixup_edge_p pfedge;
286
287 gcc_assert (fixup_graph);
288 fvertex_list = fixup_graph->vertex_list;
289 fnum_vertices = fixup_graph->num_vertices;
290 fnum_edges = fixup_graph->num_edges;
291
292 fprintf (file, "\nDump fixup graph for %s(): %s.\n",
293 lang_hooks.decl_printable_name (current_function_decl, 2), msg);
294 fprintf (file,
295 "There are %d vertices and %d edges. new_exit_index is %d.\n\n",
296 fnum_vertices, fnum_edges, fixup_graph->new_exit_index);
297
298 for (i = 0; i < fnum_vertices; i++)
299 {
300 pfvertex = fvertex_list + i;
301 fprintf (file, "vertex_list[%d]: %d succ fixup edges.\n",
302 i, VEC_length (fixup_edge_p, pfvertex->succ_edges));
303
304 for (j = 0; VEC_iterate (fixup_edge_p, pfvertex->succ_edges, j, pfedge);
305 j++)
306 {
307 /* Distinguish forward edges and backward edges in the residual flow
308 network. */
309 if (pfedge->type)
310 fputs ("(f) ", file);
311 else if (pfedge->is_rflow_valid)
312 fputs ("(b) ", file);
313 dump_fixup_edge (file, fixup_graph, pfedge);
314 }
315 }
316
317 fputs ("\n", file);
318 }
319
320
321 /* Utility routines. */
322 /* ln() implementation: approximate calculation. Returns ln of X. */
323
324 static double
325 mcf_ln (double x)
326 {
327 #define E 2.71828
328 int l = 1;
329 double m = E;
330
331 gcc_assert (x >= 0);
332
333 while (m < x)
334 {
335 m *= E;
336 l++;
337 }
338
339 return l;
340 }
341
342
343 /* sqrt() implementation: based on open source QUAKE3 code (magic sqrt
344 implementation) by John Carmack. Returns sqrt of X. */
345
346 static double
347 mcf_sqrt (double x)
348 {
349 #define MAGIC_CONST1 0x1fbcf800
350 #define MAGIC_CONST2 0x5f3759df
351 union {
352 int intPart;
353 float floatPart;
354 } convertor, convertor2;
355
356 gcc_assert (x >= 0);
357
358 convertor.floatPart = x;
359 convertor2.floatPart = x;
360 convertor.intPart = MAGIC_CONST1 + (convertor.intPart >> 1);
361 convertor2.intPart = MAGIC_CONST2 - (convertor2.intPart >> 1);
362
363 return 0.5f * (convertor.floatPart + (x * convertor2.floatPart));
364 }
365
366
367 /* Common code shared between add_fixup_edge and add_rfixup_edge. Adds an edge
368 (SRC->DEST) to the edge_list maintained in FIXUP_GRAPH with cost of the edge
369 added set to COST. */
370
371 static fixup_edge_p
372 add_edge (fixup_graph_type *fixup_graph, int src, int dest, gcov_type cost)
373 {
374 fixup_vertex_p curr_vertex = fixup_graph->vertex_list + src;
375 fixup_edge_p curr_edge = fixup_graph->edge_list + fixup_graph->num_edges;
376 curr_edge->src = src;
377 curr_edge->dest = dest;
378 curr_edge->cost = cost;
379 fixup_graph->num_edges++;
380 if (dump_file)
381 dump_fixup_edge (dump_file, fixup_graph, curr_edge);
382 VEC_safe_push (fixup_edge_p, heap, curr_vertex->succ_edges, curr_edge);
383 return curr_edge;
384 }
385
386
387 /* Add a fixup edge (src->dest) with attributes TYPE, WEIGHT, COST and
388 MAX_CAPACITY to the edge_list in the fixup graph. */
389
390 static void
391 add_fixup_edge (fixup_graph_type *fixup_graph, int src, int dest, int type,
392 gcov_type weight, gcov_type cost, gcov_type max_capacity)
393 {
394 fixup_edge_p curr_edge = add_edge(fixup_graph, src, dest, cost);
395 curr_edge->type = type;
396 curr_edge->weight = weight;
397 curr_edge->max_capacity = max_capacity;
398 }
399
400
401 /* Add a residual edge (SRC->DEST) with attributes RFLOW and COST
402 to the fixup graph. */
403
404 static void
405 add_rfixup_edge (fixup_graph_type *fixup_graph, int src, int dest,
406 gcov_type rflow, gcov_type cost)
407 {
408 fixup_edge_p curr_edge = add_edge (fixup_graph, src, dest, cost);
409 curr_edge->rflow = rflow;
410 curr_edge->is_rflow_valid = true;
411 /* This edge is not a valid edge - merely used to hold residual flow. */
412 curr_edge->type = INVALID_EDGE;
413 }
414
415
416 /* Return the pointer to fixup edge SRC->DEST or NULL if edge does not
417 exist in the FIXUP_GRAPH. */
418
419 static fixup_edge_p
420 find_fixup_edge (fixup_graph_type *fixup_graph, int src, int dest)
421 {
422 int j;
423 fixup_edge_p pfedge;
424 fixup_vertex_p pfvertex;
425
426 gcc_assert (src < fixup_graph->num_vertices);
427
428 pfvertex = fixup_graph->vertex_list + src;
429
430 for (j = 0; VEC_iterate (fixup_edge_p, pfvertex->succ_edges, j, pfedge);
431 j++)
432 if (pfedge->dest == dest)
433 return pfedge;
434
435 return NULL;
436 }
437
438
439 /* Cleanup routine to free structures in FIXUP_GRAPH. */
440
441 static void
442 delete_fixup_graph (fixup_graph_type *fixup_graph)
443 {
444 int i;
445 int fnum_vertices = fixup_graph->num_vertices;
446 fixup_vertex_p pfvertex = fixup_graph->vertex_list;
447
448 for (i = 0; i < fnum_vertices; i++, pfvertex++)
449 VEC_free (fixup_edge_p, heap, pfvertex->succ_edges);
450
451 free (fixup_graph->vertex_list);
452 free (fixup_graph->edge_list);
453 }
454
455
456 /* Creates a fixup graph FIXUP_GRAPH from the function CFG. */
457
458 static void
459 create_fixup_graph (fixup_graph_type *fixup_graph)
460 {
461 double sqrt_avg_vertex_weight = 0;
462 double total_vertex_weight = 0;
463 double k_pos = 0;
464 double k_neg = 0;
465 /* Vector to hold D(v) = sum_out_edges(v) - sum_in_edges(v). */
466 gcov_type *diff_out_in = NULL;
467 gcov_type supply_value = 1, demand_value = 0;
468 gcov_type fcost = 0;
469 int new_entry_index = 0, new_exit_index = 0;
470 int i = 0, j = 0;
471 int new_index = 0;
472 basic_block bb;
473 edge e;
474 edge_iterator ei;
475 fixup_edge_p pfedge, r_pfedge;
476 fixup_edge_p fedge_list;
477 int fnum_edges;
478
479 /* Each basic_block will be split into 2 during vertex transformation. */
480 int fnum_vertices_after_transform = 2 * n_basic_blocks;
481 int fnum_edges_after_transform = n_edges + n_basic_blocks;
482
483 /* Count the new SOURCE and EXIT vertices to be added. */
484 int fmax_num_vertices =
485 fnum_vertices_after_transform + n_edges + n_basic_blocks + 2;
486
487 /* In create_fixup_graph: Each basic block and edge can be split into 3
488 edges. Number of balance edges = n_basic_blocks. So after
489 create_fixup_graph:
490 max_edges = 4 * n_basic_blocks + 3 * n_edges
491 Accounting for residual flow edges
492 max_edges = 2 * (4 * n_basic_blocks + 3 * n_edges)
493 = 8 * n_basic_blocks + 6 * n_edges
494 < 8 * n_basic_blocks + 8 * n_edges. */
495 int fmax_num_edges = 8 * (n_basic_blocks + n_edges);
496
497 /* Initial num of vertices in the fixup graph. */
498 fixup_graph->num_vertices = n_basic_blocks;
499
500 /* Fixup graph vertex list. */
501 fixup_graph->vertex_list =
502 (fixup_vertex_p) xcalloc (fmax_num_vertices, sizeof (fixup_vertex_type));
503
504 /* Fixup graph edge list. */
505 fixup_graph->edge_list =
506 (fixup_edge_p) xcalloc (fmax_num_edges, sizeof (fixup_edge_type));
507
508 diff_out_in =
509 (gcov_type *) xcalloc (1 + fnum_vertices_after_transform,
510 sizeof (gcov_type));
511
512 /* Compute constants b, k_pos, k_neg used in the cost function calculation.
513 b = sqrt(avg_vertex_weight(cfg)); k_pos = b; k_neg = 50b. */
514 FOR_BB_BETWEEN (bb, ENTRY_BLOCK_PTR, NULL, next_bb)
515 total_vertex_weight += bb->count;
516
517 sqrt_avg_vertex_weight = mcf_sqrt (total_vertex_weight / n_basic_blocks);
518
519 k_pos = K_POS (sqrt_avg_vertex_weight);
520 k_neg = K_NEG (sqrt_avg_vertex_weight);
521
522 /* 1. Vertex Transformation: Split each vertex v into two vertices v' and v'',
523 connected by an edge e from v' to v''. w(e) = w(v). */
524
525 if (dump_file)
526 fprintf (dump_file, "\nVertex transformation:\n");
527
528 FOR_BB_BETWEEN (bb, ENTRY_BLOCK_PTR, NULL, next_bb)
529 {
530 /* v'->v'': index1->(index1+1). */
531 i = 2 * bb->index;
532 fcost = (gcov_type) COST (k_pos, bb->count);
533 add_fixup_edge (fixup_graph, i, i + 1, VERTEX_SPLIT_EDGE, bb->count,
534 fcost, CAP_INFINITY);
535 fixup_graph->num_vertices++;
536
537 FOR_EACH_EDGE (e, ei, bb->succs)
538 {
539 /* Edges with ignore attribute set should be treated like they don't
540 exist. */
541 if (EDGE_INFO (e) && EDGE_INFO (e)->ignore)
542 continue;
543 j = 2 * e->dest->index;
544 fcost = (gcov_type) COST (k_pos, e->count);
545 add_fixup_edge (fixup_graph, i + 1, j, REDIRECT_EDGE, e->count, fcost,
546 CAP_INFINITY);
547 }
548 }
549
550 /* After vertex transformation. */
551 gcc_assert (fixup_graph->num_vertices == fnum_vertices_after_transform);
552 /* Redirect edges are not added for edges with ignore attribute. */
553 gcc_assert (fixup_graph->num_edges <= fnum_edges_after_transform);
554
555 fnum_edges_after_transform = fixup_graph->num_edges;
556
557 /* 2. Initialize D(v). */
558 for (i = 0; i < fnum_edges_after_transform; i++)
559 {
560 pfedge = fixup_graph->edge_list + i;
561 diff_out_in[pfedge->src] += pfedge->weight;
562 diff_out_in[pfedge->dest] -= pfedge->weight;
563 }
564
565 /* Entry block - vertex indices 0, 1; EXIT block - vertex indices 2, 3. */
566 for (i = 0; i <= 3; i++)
567 diff_out_in[i] = 0;
568
569 /* 3. Add reverse edges: needed to decrease counts during smoothing. */
570 if (dump_file)
571 fprintf (dump_file, "\nReverse edges:\n");
572 for (i = 0; i < fnum_edges_after_transform; i++)
573 {
574 pfedge = fixup_graph->edge_list + i;
575 if ((pfedge->src == 0) || (pfedge->src == 2))
576 continue;
577 r_pfedge = find_fixup_edge (fixup_graph, pfedge->dest, pfedge->src);
578 if (!r_pfedge && pfedge->weight)
579 {
580 /* Skip adding reverse edges for edges with w(e) = 0, as its maximum
581 capacity is 0. */
582 fcost = (gcov_type) COST (k_neg, pfedge->weight);
583 add_fixup_edge (fixup_graph, pfedge->dest, pfedge->src,
584 REVERSE_EDGE, 0, fcost, pfedge->weight);
585 }
586 }
587
588 /* 4. Create single source and sink. Connect new source vertex s' to function
589 entry block. Connect sink vertex t' to function exit. */
590 if (dump_file)
591 fprintf (dump_file, "\ns'->S, T->t':\n");
592
593 new_entry_index = fixup_graph->new_entry_index = fixup_graph->num_vertices;
594 fixup_graph->num_vertices++;
595 /* Set supply_value to 1 to avoid zero count function ENTRY. */
596 add_fixup_edge (fixup_graph, new_entry_index, ENTRY_BLOCK, SOURCE_CONNECT_EDGE,
597 1 /* supply_value */, 0, 1 /* supply_value */);
598
599 /* Create new exit with EXIT_BLOCK as single pred. */
600 new_exit_index = fixup_graph->new_exit_index = fixup_graph->num_vertices;
601 fixup_graph->num_vertices++;
602 add_fixup_edge (fixup_graph, 2 * EXIT_BLOCK + 1, new_exit_index,
603 SINK_CONNECT_EDGE,
604 0 /* demand_value */, 0, 0 /* demand_value */);
605
606 /* Connect vertices with unbalanced D(v) to source/sink. */
607 if (dump_file)
608 fprintf (dump_file, "\nD(v) balance:\n");
609 /* Skip vertices for ENTRY (0, 1) and EXIT (2,3) blocks, so start with i = 4.
610 diff_out_in[v''] will be 0, so skip v'' vertices, hence i += 2. */
611 for (i = 4; i < new_entry_index; i += 2)
612 {
613 if (diff_out_in[i] > 0)
614 {
615 add_fixup_edge (fixup_graph, i, new_exit_index, BALANCE_EDGE, 0, 0,
616 diff_out_in[i]);
617 demand_value += diff_out_in[i];
618 }
619 else if (diff_out_in[i] < 0)
620 {
621 add_fixup_edge (fixup_graph, new_entry_index, i, BALANCE_EDGE, 0, 0,
622 -diff_out_in[i]);
623 supply_value -= diff_out_in[i];
624 }
625 }
626
627 /* Set supply = demand. */
628 if (dump_file)
629 {
630 fprintf (dump_file, "\nAdjust supply and demand:\n");
631 fprintf (dump_file, "supply_value=" HOST_WIDEST_INT_PRINT_DEC "\n",
632 supply_value);
633 fprintf (dump_file, "demand_value=" HOST_WIDEST_INT_PRINT_DEC "\n",
634 demand_value);
635 }
636
637 if (demand_value > supply_value)
638 {
639 pfedge = find_fixup_edge (fixup_graph, new_entry_index, ENTRY_BLOCK);
640 pfedge->max_capacity += (demand_value - supply_value);
641 }
642 else
643 {
644 pfedge = find_fixup_edge (fixup_graph, 2 * EXIT_BLOCK + 1, new_exit_index);
645 pfedge->max_capacity += (supply_value - demand_value);
646 }
647
648 /* 6. Normalize edges: remove anti-parallel edges. Anti-parallel edges are
649 created by the vertex transformation step from self-edges in the original
650 CFG and by the reverse edges added earlier. */
651 if (dump_file)
652 fprintf (dump_file, "\nNormalize edges:\n");
653
654 fnum_edges = fixup_graph->num_edges;
655 fedge_list = fixup_graph->edge_list;
656
657 for (i = 0; i < fnum_edges; i++)
658 {
659 pfedge = fedge_list + i;
660 r_pfedge = find_fixup_edge (fixup_graph, pfedge->dest, pfedge->src);
661 if (((pfedge->type == VERTEX_SPLIT_EDGE)
662 || (pfedge->type == REDIRECT_EDGE)) && r_pfedge)
663 {
664 new_index = fixup_graph->num_vertices;
665 fixup_graph->num_vertices++;
666
667 if (dump_file)
668 {
669 fprintf (dump_file, "\nAnti-parallel edge:\n");
670 dump_fixup_edge (dump_file, fixup_graph, pfedge);
671 dump_fixup_edge (dump_file, fixup_graph, r_pfedge);
672 fprintf (dump_file, "New vertex is %d.\n", new_index);
673 fprintf (dump_file, "------------------\n");
674 }
675
676 pfedge->cost /= 2;
677 pfedge->norm_vertex_index = new_index;
678 if (dump_file)
679 {
680 fprintf (dump_file, "After normalization:\n");
681 dump_fixup_edge (dump_file, fixup_graph, pfedge);
682 }
683
684 /* Add a new fixup edge: new_index->src. */
685 add_fixup_edge (fixup_graph, new_index, pfedge->src,
686 REVERSE_NORMALIZED_EDGE, 0, r_pfedge->cost,
687 r_pfedge->max_capacity);
688 gcc_assert (fixup_graph->num_vertices <= fmax_num_vertices);
689
690 /* Edge: r_pfedge->src -> r_pfedge->dest
691 ==> r_pfedge->src -> new_index. */
692 r_pfedge->dest = new_index;
693 r_pfedge->type = REVERSE_NORMALIZED_EDGE;
694 r_pfedge->cost = pfedge->cost;
695 r_pfedge->max_capacity = pfedge->max_capacity;
696 if (dump_file)
697 dump_fixup_edge (dump_file, fixup_graph, r_pfedge);
698 }
699 }
700
701 if (dump_file)
702 dump_fixup_graph (dump_file, fixup_graph, "After create_fixup_graph()");
703
704 /* Cleanup. */
705 free (diff_out_in);
706 }
707
708
709 /* Allocates space for the structures in AUGMENTING_PATH. The space needed is
710 proportional to the number of nodes in the graph, which is given by
711 GRAPH_SIZE. */
712
713 static void
714 init_augmenting_path (augmenting_path_type *augmenting_path, int graph_size)
715 {
716 augmenting_path->queue_list.queue = (int *)
717 xcalloc (graph_size + 2, sizeof (int));
718 augmenting_path->queue_list.size = graph_size + 2;
719 augmenting_path->bb_pred = (int *) xcalloc (graph_size, sizeof (int));
720 augmenting_path->is_visited = (int *) xcalloc (graph_size, sizeof (int));
721 }
722
723 /* Free the structures in AUGMENTING_PATH. */
724 static void
725 free_augmenting_path (augmenting_path_type *augmenting_path)
726 {
727 free (augmenting_path->queue_list.queue);
728 free (augmenting_path->bb_pred);
729 free (augmenting_path->is_visited);
730 }
731
732
733 /* Queue routines. Assumes queue will never overflow. */
734
735 static void
736 init_queue (queue_type *queue_list)
737 {
738 gcc_assert (queue_list);
739 queue_list->head = 0;
740 queue_list->tail = 0;
741 }
742
743 /* Return true if QUEUE_LIST is empty. */
744 static bool
745 is_empty (queue_type *queue_list)
746 {
747 return (queue_list->head == queue_list->tail);
748 }
749
750 /* Insert element X into QUEUE_LIST. */
751 static void
752 enqueue (queue_type *queue_list, int x)
753 {
754 gcc_assert (queue_list->tail < queue_list->size);
755 queue_list->queue[queue_list->tail] = x;
756 (queue_list->tail)++;
757 }
758
759 /* Return the first element in QUEUE_LIST. */
760 static int
761 dequeue (queue_type *queue_list)
762 {
763 int x;
764 gcc_assert (queue_list->head >= 0);
765 x = queue_list->queue[queue_list->head];
766 (queue_list->head)++;
767 return x;
768 }
769
770
771 /* Finds a negative cycle in the residual network using
772 the Bellman-Ford algorithm. The flow on the found cycle is reversed by the
773 minimum residual capacity of that cycle. ENTRY and EXIT vertices are not
774 considered.
775
776 Parameters:
777 FIXUP_GRAPH - Residual graph (input/output)
778 The following are allocated/freed by the caller:
779 PI - Vector to hold predecessors in path (pi = pred index)
780 D - D[I] holds minimum cost of path from i to sink
781 CYCLE - Vector to hold the minimum cost cycle
782
783 Return:
784 true if a negative cycle was found, false otherwise. */
785
786 static bool
787 cancel_negative_cycle (fixup_graph_type *fixup_graph,
788 int *pi, gcov_type *d, int *cycle)
789 {
790 int i, j, k;
791 int fnum_vertices, fnum_edges;
792 fixup_edge_p fedge_list, pfedge, r_pfedge;
793 bool found_cycle = false;
794 int cycle_start = 0, cycle_end = 0;
795 gcov_type sum_cost = 0, cycle_flow = 0;
796 int new_entry_index;
797 bool propagated = false;
798
799 gcc_assert (fixup_graph);
800 fnum_vertices = fixup_graph->num_vertices;
801 fnum_edges = fixup_graph->num_edges;
802 fedge_list = fixup_graph->edge_list;
803 new_entry_index = fixup_graph->new_entry_index;
804
805 /* Initialize. */
806 /* Skip ENTRY. */
807 for (i = 1; i < fnum_vertices; i++)
808 {
809 d[i] = CAP_INFINITY;
810 pi[i] = -1;
811 cycle[i] = -1;
812 }
813 d[ENTRY_BLOCK] = 0;
814
815 /* Relax. */
816 for (k = 1; k < fnum_vertices; k++)
817 {
818 propagated = false;
819 for (i = 0; i < fnum_edges; i++)
820 {
821 pfedge = fedge_list + i;
822 if (pfedge->src == new_entry_index)
823 continue;
824 if (pfedge->is_rflow_valid && pfedge->rflow
825 && d[pfedge->src] != CAP_INFINITY
826 && (d[pfedge->dest] > d[pfedge->src] + pfedge->cost))
827 {
828 d[pfedge->dest] = d[pfedge->src] + pfedge->cost;
829 pi[pfedge->dest] = pfedge->src;
830 propagated = true;
831 }
832 }
833 if (!propagated)
834 break;
835 }
836
837 if (!propagated)
838 /* No negative cycles exist. */
839 return 0;
840
841 /* Detect. */
842 for (i = 0; i < fnum_edges; i++)
843 {
844 pfedge = fedge_list + i;
845 if (pfedge->src == new_entry_index)
846 continue;
847 if (pfedge->is_rflow_valid && pfedge->rflow
848 && d[pfedge->src] != CAP_INFINITY
849 && (d[pfedge->dest] > d[pfedge->src] + pfedge->cost))
850 {
851 found_cycle = true;
852 break;
853 }
854 }
855
856 if (!found_cycle)
857 return 0;
858
859 /* Augment the cycle with the cycle's minimum residual capacity. */
860 found_cycle = false;
861 cycle[0] = pfedge->dest;
862 j = pfedge->dest;
863
864 for (i = 1; i < fnum_vertices; i++)
865 {
866 j = pi[j];
867 cycle[i] = j;
868 for (k = 0; k < i; k++)
869 {
870 if (cycle[k] == j)
871 {
872 /* cycle[k] -> ... -> cycle[i]. */
873 cycle_start = k;
874 cycle_end = i;
875 found_cycle = true;
876 break;
877 }
878 }
879 if (found_cycle)
880 break;
881 }
882
883 gcc_assert (cycle[cycle_start] == cycle[cycle_end]);
884 if (dump_file)
885 fprintf (dump_file, "\nNegative cycle length is %d:\n",
886 cycle_end - cycle_start);
887
888 sum_cost = 0;
889 cycle_flow = CAP_INFINITY;
890 for (k = cycle_start; k < cycle_end; k++)
891 {
892 pfedge = find_fixup_edge (fixup_graph, cycle[k + 1], cycle[k]);
893 cycle_flow = MIN (cycle_flow, pfedge->rflow);
894 sum_cost += pfedge->cost;
895 if (dump_file)
896 fprintf (dump_file, "%d ", cycle[k]);
897 }
898
899 if (dump_file)
900 {
901 fprintf (dump_file, "%d", cycle[k]);
902 fprintf (dump_file,
903 ": (" HOST_WIDEST_INT_PRINT_DEC ", " HOST_WIDEST_INT_PRINT_DEC
904 ")\n", sum_cost, cycle_flow);
905 fprintf (dump_file,
906 "Augment cycle with " HOST_WIDEST_INT_PRINT_DEC "\n",
907 cycle_flow);
908 }
909
910 for (k = cycle_start; k < cycle_end; k++)
911 {
912 pfedge = find_fixup_edge (fixup_graph, cycle[k + 1], cycle[k]);
913 r_pfedge = find_fixup_edge (fixup_graph, cycle[k], cycle[k + 1]);
914 pfedge->rflow -= cycle_flow;
915 if (pfedge->type)
916 pfedge->flow += cycle_flow;
917 r_pfedge->rflow += cycle_flow;
918 if (r_pfedge->type)
919 r_pfedge->flow -= cycle_flow;
920 }
921
922 return true;
923 }
924
925
926 /* Computes the residual flow for FIXUP_GRAPH by setting the rflow field of
927 the edges. ENTRY and EXIT vertices should not be considered. */
928
929 static void
930 compute_residual_flow (fixup_graph_type *fixup_graph)
931 {
932 int i;
933 int fnum_edges;
934 fixup_edge_p fedge_list, pfedge;
935
936 gcc_assert (fixup_graph);
937
938 if (dump_file)
939 fputs ("\ncompute_residual_flow():\n", dump_file);
940
941 fnum_edges = fixup_graph->num_edges;
942 fedge_list = fixup_graph->edge_list;
943
944 for (i = 0; i < fnum_edges; i++)
945 {
946 pfedge = fedge_list + i;
947 pfedge->rflow = pfedge->max_capacity - pfedge->flow;
948 pfedge->is_rflow_valid = true;
949 add_rfixup_edge (fixup_graph, pfedge->dest, pfedge->src, pfedge->flow,
950 -pfedge->cost);
951 }
952 }
953
954
955 /* Uses Edmonds-Karp algorithm - BFS to find augmenting path from SOURCE to
956 SINK. The fields in the edge vector in the FIXUP_GRAPH are not modified by
957 this routine. The vector bb_pred in the AUGMENTING_PATH structure is updated
958 to reflect the path found.
959 Returns: 0 if no augmenting path is found, 1 otherwise. */
960
961 static int
962 find_augmenting_path (fixup_graph_type *fixup_graph,
963 augmenting_path_type *augmenting_path, int source,
964 int sink)
965 {
966 int u = 0;
967 int i;
968 fixup_vertex_p fvertex_list, pfvertex;
969 fixup_edge_p pfedge;
970 int *bb_pred, *is_visited;
971 queue_type *queue_list;
972
973 gcc_assert (augmenting_path);
974 bb_pred = augmenting_path->bb_pred;
975 gcc_assert (bb_pred);
976 is_visited = augmenting_path->is_visited;
977 gcc_assert (is_visited);
978 queue_list = &(augmenting_path->queue_list);
979
980 gcc_assert (fixup_graph);
981
982 fvertex_list = fixup_graph->vertex_list;
983
984 for (u = 0; u < fixup_graph->num_vertices; u++)
985 is_visited[u] = 0;
986
987 init_queue (queue_list);
988 enqueue (queue_list, source);
989 bb_pred[source] = -1;
990
991 while (!is_empty (queue_list))
992 {
993 u = dequeue (queue_list);
994 is_visited[u] = 1;
995 pfvertex = fvertex_list + u;
996 for (i = 0; VEC_iterate (fixup_edge_p, pfvertex->succ_edges, i, pfedge);
997 i++)
998 {
999 int dest = pfedge->dest;
1000 if ((pfedge->rflow > 0) && (is_visited[dest] == 0))
1001 {
1002 enqueue (queue_list, dest);
1003 bb_pred[dest] = u;
1004 is_visited[dest] = 1;
1005 if (dest == sink)
1006 return 1;
1007 }
1008 }
1009 }
1010
1011 return 0;
1012 }
1013
1014
1015 /* Routine to find the maximal flow:
1016 Algorithm:
1017 1. Initialize flow to 0
1018 2. Find an augmenting path form source to sink.
1019 3. Send flow equal to the path's residual capacity along the edges of this path.
1020 4. Repeat steps 2 and 3 until no new augmenting path is found.
1021
1022 Parameters:
1023 SOURCE: index of source vertex (input)
1024 SINK: index of sink vertex (input)
1025 FIXUP_GRAPH: adjacency matrix representing the graph. The flow of the edges will be
1026 set to have a valid maximal flow by this routine. (input)
1027 Return: Maximum flow possible. */
1028
1029 static gcov_type
1030 find_max_flow (fixup_graph_type *fixup_graph, int source, int sink)
1031 {
1032 int fnum_edges;
1033 augmenting_path_type augmenting_path;
1034 int *bb_pred;
1035 gcov_type max_flow = 0;
1036 int i, u;
1037 fixup_edge_p fedge_list, pfedge, r_pfedge;
1038
1039 gcc_assert (fixup_graph);
1040
1041 fnum_edges = fixup_graph->num_edges;
1042 fedge_list = fixup_graph->edge_list;
1043
1044 /* Initialize flow to 0. */
1045 for (i = 0; i < fnum_edges; i++)
1046 {
1047 pfedge = fedge_list + i;
1048 pfedge->flow = 0;
1049 }
1050
1051 compute_residual_flow (fixup_graph);
1052
1053 init_augmenting_path (&augmenting_path, fixup_graph->num_vertices);
1054
1055 bb_pred = augmenting_path.bb_pred;
1056 while (find_augmenting_path (fixup_graph, &augmenting_path, source, sink))
1057 {
1058 /* Determine the amount by which we can increment the flow. */
1059 gcov_type increment = CAP_INFINITY;
1060 for (u = sink; u != source; u = bb_pred[u])
1061 {
1062 pfedge = find_fixup_edge (fixup_graph, bb_pred[u], u);
1063 increment = MIN (increment, pfedge->rflow);
1064 }
1065 max_flow += increment;
1066
1067 /* Now increment the flow. EXIT vertex index is 1. */
1068 for (u = sink; u != source; u = bb_pred[u])
1069 {
1070 pfedge = find_fixup_edge (fixup_graph, bb_pred[u], u);
1071 r_pfedge = find_fixup_edge (fixup_graph, u, bb_pred[u]);
1072 if (pfedge->type)
1073 {
1074 /* forward edge. */
1075 pfedge->flow += increment;
1076 pfedge->rflow -= increment;
1077 r_pfedge->rflow += increment;
1078 }
1079 else
1080 {
1081 /* backward edge. */
1082 gcc_assert (r_pfedge->type);
1083 r_pfedge->rflow += increment;
1084 r_pfedge->flow -= increment;
1085 pfedge->rflow -= increment;
1086 }
1087 }
1088
1089 if (dump_file)
1090 {
1091 fprintf (dump_file, "\nDump augmenting path:\n");
1092 for (u = sink; u != source; u = bb_pred[u])
1093 {
1094 print_basic_block (dump_file, fixup_graph, u);
1095 fprintf (dump_file, "<-");
1096 }
1097 fprintf (dump_file,
1098 "ENTRY (path_capacity=" HOST_WIDEST_INT_PRINT_DEC ")\n",
1099 increment);
1100 fprintf (dump_file,
1101 "Network flow is " HOST_WIDEST_INT_PRINT_DEC ".\n",
1102 max_flow);
1103 }
1104 }
1105
1106 free_augmenting_path (&augmenting_path);
1107 if (dump_file)
1108 dump_fixup_graph (dump_file, fixup_graph, "After find_max_flow()");
1109 return max_flow;
1110 }
1111
1112
1113 /* Computes the corrected edge and basic block weights using FIXUP_GRAPH
1114 after applying the find_minimum_cost_flow() routine. */
1115
1116 static void
1117 adjust_cfg_counts (fixup_graph_type *fixup_graph)
1118 {
1119 basic_block bb;
1120 edge e;
1121 edge_iterator ei;
1122 int i, j;
1123 fixup_edge_p pfedge, pfedge_n;
1124
1125 gcc_assert (fixup_graph);
1126
1127 if (dump_file)
1128 fprintf (dump_file, "\nadjust_cfg_counts():\n");
1129
1130 FOR_BB_BETWEEN (bb, ENTRY_BLOCK_PTR, EXIT_BLOCK_PTR, next_bb)
1131 {
1132 i = 2 * bb->index;
1133
1134 /* Fixup BB. */
1135 if (dump_file)
1136 fprintf (dump_file,
1137 "BB%d: " HOST_WIDEST_INT_PRINT_DEC "", bb->index, bb->count);
1138
1139 pfedge = find_fixup_edge (fixup_graph, i, i + 1);
1140 if (pfedge->flow)
1141 {
1142 bb->count += pfedge->flow;
1143 if (dump_file)
1144 {
1145 fprintf (dump_file, " + " HOST_WIDEST_INT_PRINT_DEC "(",
1146 pfedge->flow);
1147 print_edge (dump_file, fixup_graph, i, i + 1);
1148 fprintf (dump_file, ")");
1149 }
1150 }
1151
1152 pfedge_n =
1153 find_fixup_edge (fixup_graph, i + 1, pfedge->norm_vertex_index);
1154 /* Deduct flow from normalized reverse edge. */
1155 if (pfedge->norm_vertex_index && pfedge_n->flow)
1156 {
1157 bb->count -= pfedge_n->flow;
1158 if (dump_file)
1159 {
1160 fprintf (dump_file, " - " HOST_WIDEST_INT_PRINT_DEC "(",
1161 pfedge_n->flow);
1162 print_edge (dump_file, fixup_graph, i + 1,
1163 pfedge->norm_vertex_index);
1164 fprintf (dump_file, ")");
1165 }
1166 }
1167 if (dump_file)
1168 fprintf (dump_file, " = " HOST_WIDEST_INT_PRINT_DEC "\n", bb->count);
1169
1170 /* Fixup edge. */
1171 FOR_EACH_EDGE (e, ei, bb->succs)
1172 {
1173 /* Treat edges with ignore attribute set as if they don't exist. */
1174 if (EDGE_INFO (e) && EDGE_INFO (e)->ignore)
1175 continue;
1176
1177 j = 2 * e->dest->index;
1178 if (dump_file)
1179 fprintf (dump_file, "%d->%d: " HOST_WIDEST_INT_PRINT_DEC "",
1180 bb->index, e->dest->index, e->count);
1181
1182 pfedge = find_fixup_edge (fixup_graph, i + 1, j);
1183
1184 if (bb->index != e->dest->index)
1185 {
1186 /* Non-self edge. */
1187 if (pfedge->flow)
1188 {
1189 e->count += pfedge->flow;
1190 if (dump_file)
1191 {
1192 fprintf (dump_file, " + " HOST_WIDEST_INT_PRINT_DEC "(",
1193 pfedge->flow);
1194 print_edge (dump_file, fixup_graph, i + 1, j);
1195 fprintf (dump_file, ")");
1196 }
1197 }
1198
1199 pfedge_n =
1200 find_fixup_edge (fixup_graph, j, pfedge->norm_vertex_index);
1201 /* Deduct flow from normalized reverse edge. */
1202 if (pfedge->norm_vertex_index && pfedge_n->flow)
1203 {
1204 e->count -= pfedge_n->flow;
1205 if (dump_file)
1206 {
1207 fprintf (dump_file, " - " HOST_WIDEST_INT_PRINT_DEC "(",
1208 pfedge_n->flow);
1209 print_edge (dump_file, fixup_graph, j,
1210 pfedge->norm_vertex_index);
1211 fprintf (dump_file, ")");
1212 }
1213 }
1214 }
1215 else
1216 {
1217 /* Handle self edges. Self edge is split with a normalization
1218 vertex. Here i=j. */
1219 pfedge = find_fixup_edge (fixup_graph, j, i + 1);
1220 pfedge_n =
1221 find_fixup_edge (fixup_graph, i + 1, pfedge->norm_vertex_index);
1222 e->count += pfedge_n->flow;
1223 bb->count += pfedge_n->flow;
1224 if (dump_file)
1225 {
1226 fprintf (dump_file, "(self edge)");
1227 fprintf (dump_file, " + " HOST_WIDEST_INT_PRINT_DEC "(",
1228 pfedge_n->flow);
1229 print_edge (dump_file, fixup_graph, i + 1,
1230 pfedge->norm_vertex_index);
1231 fprintf (dump_file, ")");
1232 }
1233 }
1234
1235 if (bb->count)
1236 e->probability = REG_BR_PROB_BASE * e->count / bb->count;
1237 if (dump_file)
1238 fprintf (dump_file, " = " HOST_WIDEST_INT_PRINT_DEC "\t(%.1f%%)\n",
1239 e->count, e->probability * 100.0 / REG_BR_PROB_BASE);
1240 }
1241 }
1242
1243 ENTRY_BLOCK_PTR->count = sum_edge_counts (ENTRY_BLOCK_PTR->succs);
1244 EXIT_BLOCK_PTR->count = sum_edge_counts (EXIT_BLOCK_PTR->preds);
1245
1246 /* Compute edge probabilities. */
1247 FOR_ALL_BB (bb)
1248 {
1249 if (bb->count)
1250 {
1251 FOR_EACH_EDGE (e, ei, bb->succs)
1252 e->probability = REG_BR_PROB_BASE * e->count / bb->count;
1253 }
1254 else
1255 {
1256 int total = 0;
1257 FOR_EACH_EDGE (e, ei, bb->succs)
1258 if (!(e->flags & (EDGE_COMPLEX | EDGE_FAKE)))
1259 total++;
1260 if (total)
1261 {
1262 FOR_EACH_EDGE (e, ei, bb->succs)
1263 {
1264 if (!(e->flags & (EDGE_COMPLEX | EDGE_FAKE)))
1265 e->probability = REG_BR_PROB_BASE / total;
1266 else
1267 e->probability = 0;
1268 }
1269 }
1270 else
1271 {
1272 total += EDGE_COUNT (bb->succs);
1273 FOR_EACH_EDGE (e, ei, bb->succs)
1274 e->probability = REG_BR_PROB_BASE / total;
1275 }
1276 }
1277 }
1278
1279 if (dump_file)
1280 {
1281 fprintf (dump_file, "\nCheck %s() CFG flow conservation:\n",
1282 lang_hooks.decl_printable_name (current_function_decl, 2));
1283 FOR_BB_BETWEEN (bb, ENTRY_BLOCK_PTR->next_bb, EXIT_BLOCK_PTR, next_bb)
1284 {
1285 if ((bb->count != sum_edge_counts (bb->preds))
1286 || (bb->count != sum_edge_counts (bb->succs)))
1287 {
1288 fprintf (dump_file,
1289 "BB%d(" HOST_WIDEST_INT_PRINT_DEC ") **INVALID**: ",
1290 bb->index, bb->count);
1291 fprintf (stderr,
1292 "******** BB%d(" HOST_WIDEST_INT_PRINT_DEC
1293 ") **INVALID**: \n", bb->index, bb->count);
1294 fprintf (dump_file, "in_edges=" HOST_WIDEST_INT_PRINT_DEC " ",
1295 sum_edge_counts (bb->preds));
1296 fprintf (dump_file, "out_edges=" HOST_WIDEST_INT_PRINT_DEC "\n",
1297 sum_edge_counts (bb->succs));
1298 }
1299 }
1300 }
1301 }
1302
1303
1304 /* Implements the negative cycle canceling algorithm to compute a minimum cost
1305 flow.
1306 Algorithm:
1307 1. Find maximal flow.
1308 2. Form residual network
1309 3. Repeat:
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
1313 f(u,v) = rf(v, u)
1314 Input:
1315 FIXUP_GRAPH - Initial fixup graph.
1316 The flow field is modified to represent the minimum cost flow. */
1317
1318 static void
1319 find_minimum_cost_flow (fixup_graph_type *fixup_graph)
1320 {
1321 /* Holds the index of predecessor in path. */
1322 int *pred;
1323 /* Used to hold the minimum cost cycle. */
1324 int *cycle;
1325 /* Used to record the number of iterations of cancel_negative_cycle. */
1326 int iteration;
1327 /* Vector d[i] holds the minimum cost of path from i to sink. */
1328 gcov_type *d;
1329 int fnum_vertices;
1330 int new_exit_index;
1331 int new_entry_index;
1332
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;
1337
1338 find_max_flow (fixup_graph, new_entry_index, new_exit_index);
1339
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));
1344
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. */
1348 iteration = 0;
1349 while (cancel_negative_cycle (fixup_graph, pred, d, cycle))
1350 {
1351 iteration++;
1352 if (iteration > MAX_ITER (fixup_graph->num_vertices,
1353 fixup_graph->num_edges))
1354 break;
1355 }
1356
1357 if (dump_file)
1358 dump_fixup_graph (dump_file, fixup_graph,
1359 "After find_minimum_cost_flow()");
1360
1361 /* Cleanup structures. */
1362 free (pred);
1363 free (d);
1364 free (cycle);
1365 }
1366
1367
1368 /* Compute the sum of the edge counts in TO_EDGES. */
1369
1370 gcov_type
1371 sum_edge_counts (VEC (edge, gc) *to_edges)
1372 {
1373 gcov_type sum = 0;
1374 edge e;
1375 edge_iterator ei;
1376
1377 FOR_EACH_EDGE (e, ei, to_edges)
1378 {
1379 if (EDGE_INFO (e) && EDGE_INFO (e)->ignore)
1380 continue;
1381 sum += e->count;
1382 }
1383 return sum;
1384 }
1385
1386
1387 /* Main routine. Smoothes the intial 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
1390 block. */
1391
1392 void
1393 mcf_smooth_cfg (void)
1394 {
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);
1401 }