/* Routines to implement minimum-cost maximal flow algorithm used to smooth
basic block and edge frequency counts.
Copyright (C) 2008-2014 Free Software Foundation, Inc.
Contributed by Paul Yuan (yingbo.com@gmail.com) and
Vinodha Ramasamy (vinodha@google.com).
This file is part of GCC.
GCC is free software; you can redistribute it and/or modify it under
the terms of the GNU General Public License as published by the Free
Software Foundation; either version 3, or (at your option) any later
version.
GCC is distributed in the hope that it will be useful, but WITHOUT ANY
WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
for more details.
You should have received a copy of the GNU General Public License
along with GCC; see the file COPYING3. If not see
. */
/* References:
[1] "Feedback-directed Optimizations in GCC with Estimated Edge Profiles
from Hardware Event Sampling", Vinodha Ramasamy, Paul Yuan, Dehao Chen,
and Robert Hundt; GCC Summit 2008.
[2] "Complementing Missing and Inaccurate Profiling Using a Minimum Cost
Circulation Algorithm", Roy Levin, Ilan Newman and Gadi Haber;
HiPEAC '08.
Algorithm to smooth basic block and edge counts:
1. create_fixup_graph: Create fixup graph by translating function CFG into
a graph that satisfies MCF algorithm requirements.
2. find_max_flow: Find maximal flow.
3. compute_residual_flow: Form residual network.
4. Repeat:
cancel_negative_cycle: While G contains a negative cost cycle C, reverse
the flow on the found cycle by the minimum residual capacity in that
cycle.
5. Form the minimal cost flow
f(u,v) = rf(v, u).
6. adjust_cfg_counts: Update initial edge weights with corrected weights.
delta(u.v) = f(u,v) -f(v,u).
w*(u,v) = w(u,v) + delta(u,v). */
#include "config.h"
#include "system.h"
#include "coretypes.h"
#include "basic-block.h"
#include "gcov-io.h"
#include "params.h"
#include "diagnostic-core.h"
#include "tree.h"
#include "profile.h"
#include "dumpfile.h"
/* CAP_INFINITY: Constant to represent infinite capacity. */
#define CAP_INFINITY INTTYPE_MAXIMUM (HOST_WIDEST_INT)
/* COST FUNCTION. */
#define K_POS(b) ((b))
#define K_NEG(b) (50 * (b))
#define COST(k, w) ((k) / mcf_ln ((w) + 2))
/* Limit the number of iterations for cancel_negative_cycles() to ensure
reasonable compile time. */
#define MAX_ITER(n, e) (PARAM_VALUE (PARAM_MIN_MCF_CANCEL_ITERS) + \
(1000000 / ((n) * (e))))
typedef enum
{
INVALID_EDGE = 0,
VERTEX_SPLIT_EDGE, /* Edge to represent vertex with w(e) = w(v). */
REDIRECT_EDGE, /* Edge after vertex transformation. */
REVERSE_EDGE,
SOURCE_CONNECT_EDGE, /* Single edge connecting to single source. */
SINK_CONNECT_EDGE, /* Single edge connecting to single sink. */
SINK_SOURCE_EDGE, /* Single edge connecting sink to source. */
BALANCE_EDGE, /* Edge connecting with source/sink: cp(e) = 0. */
REDIRECT_NORMALIZED_EDGE, /* Normalized edge for a redirect edge. */
REVERSE_NORMALIZED_EDGE /* Normalized edge for a reverse edge. */
} edge_type;
/* Structure to represent an edge in the fixup graph. */
typedef struct fixup_edge_d
{
int src;
int dest;
/* Flag denoting type of edge and attributes for the flow field. */
edge_type type;
bool is_rflow_valid;
/* Index to the normalization vertex added for this edge. */
int norm_vertex_index;
/* Flow for this edge. */
gcov_type flow;
/* Residual flow for this edge - used during negative cycle canceling. */
gcov_type rflow;
gcov_type weight;
gcov_type cost;
gcov_type max_capacity;
} fixup_edge_type;
typedef fixup_edge_type *fixup_edge_p;
/* Structure to represent a vertex in the fixup graph. */
typedef struct fixup_vertex_d
{
vec succ_edges;
} fixup_vertex_type;
typedef fixup_vertex_type *fixup_vertex_p;
/* Fixup graph used in the MCF algorithm. */
typedef struct fixup_graph_d
{
/* Current number of vertices for the graph. */
int num_vertices;
/* Current number of edges for the graph. */
int num_edges;
/* Index of new entry vertex. */
int new_entry_index;
/* Index of new exit vertex. */
int new_exit_index;
/* Fixup vertex list. Adjacency list for fixup graph. */
fixup_vertex_p vertex_list;
/* Fixup edge list. */
fixup_edge_p edge_list;
} fixup_graph_type;
typedef struct queue_d
{
int *queue;
int head;
int tail;
int size;
} queue_type;
/* Structure used in the maximal flow routines to find augmenting path. */
typedef struct augmenting_path_d
{
/* Queue used to hold vertex indices. */
queue_type queue_list;
/* Vector to hold chain of pred vertex indices in augmenting path. */
int *bb_pred;
/* Vector that indicates if basic block i has been visited. */
int *is_visited;
} augmenting_path_type;
/* Function definitions. */
/* Dump routines to aid debugging. */
/* Print basic block with index N for FIXUP_GRAPH in n' and n'' format. */
static void
print_basic_block (FILE *file, fixup_graph_type *fixup_graph, int n)
{
if (n == ENTRY_BLOCK)
fputs ("ENTRY", file);
else if (n == ENTRY_BLOCK + 1)
fputs ("ENTRY''", file);
else if (n == 2 * EXIT_BLOCK)
fputs ("EXIT", file);
else if (n == 2 * EXIT_BLOCK + 1)
fputs ("EXIT''", file);
else if (n == fixup_graph->new_exit_index)
fputs ("NEW_EXIT", file);
else if (n == fixup_graph->new_entry_index)
fputs ("NEW_ENTRY", file);
else
{
fprintf (file, "%d", n / 2);
if (n % 2)
fputs ("''", file);
else
fputs ("'", file);
}
}
/* Print edge S->D for given fixup_graph with n' and n'' format.
PARAMETERS:
S is the index of the source vertex of the edge (input) and
D is the index of the destination vertex of the edge (input) for the given
fixup_graph (input). */
static void
print_edge (FILE *file, fixup_graph_type *fixup_graph, int s, int d)
{
print_basic_block (file, fixup_graph, s);
fputs ("->", file);
print_basic_block (file, fixup_graph, d);
}
/* Dump out the attributes of a given edge FEDGE in the fixup_graph to a
file. */
static void
dump_fixup_edge (FILE *file, fixup_graph_type *fixup_graph, fixup_edge_p fedge)
{
if (!fedge)
{
fputs ("NULL fixup graph edge.\n", file);
return;
}
print_edge (file, fixup_graph, fedge->src, fedge->dest);
fputs (": ", file);
if (fedge->type)
{
fprintf (file, "flow/capacity=" HOST_WIDEST_INT_PRINT_DEC "/",
fedge->flow);
if (fedge->max_capacity == CAP_INFINITY)
fputs ("+oo,", file);
else
fprintf (file, "" HOST_WIDEST_INT_PRINT_DEC ",", fedge->max_capacity);
}
if (fedge->is_rflow_valid)
{
if (fedge->rflow == CAP_INFINITY)
fputs (" rflow=+oo.", file);
else
fprintf (file, " rflow=" HOST_WIDEST_INT_PRINT_DEC ",", fedge->rflow);
}
fprintf (file, " cost=" HOST_WIDEST_INT_PRINT_DEC ".", fedge->cost);
fprintf (file, "\t(%d->%d)", fedge->src, fedge->dest);
if (fedge->type)
{
switch (fedge->type)
{
case VERTEX_SPLIT_EDGE:
fputs (" @VERTEX_SPLIT_EDGE", file);
break;
case REDIRECT_EDGE:
fputs (" @REDIRECT_EDGE", file);
break;
case SOURCE_CONNECT_EDGE:
fputs (" @SOURCE_CONNECT_EDGE", file);
break;
case SINK_CONNECT_EDGE:
fputs (" @SINK_CONNECT_EDGE", file);
break;
case SINK_SOURCE_EDGE:
fputs (" @SINK_SOURCE_EDGE", file);
break;
case REVERSE_EDGE:
fputs (" @REVERSE_EDGE", file);
break;
case BALANCE_EDGE:
fputs (" @BALANCE_EDGE", file);
break;
case REDIRECT_NORMALIZED_EDGE:
case REVERSE_NORMALIZED_EDGE:
fputs (" @NORMALIZED_EDGE", file);
break;
default:
fputs (" @INVALID_EDGE", file);
break;
}
}
fputs ("\n", file);
}
/* Print out the edges and vertices of the given FIXUP_GRAPH, into the dump
file. The input string MSG is printed out as a heading. */
static void
dump_fixup_graph (FILE *file, fixup_graph_type *fixup_graph, const char *msg)
{
int i, j;
int fnum_vertices, fnum_edges;
fixup_vertex_p fvertex_list, pfvertex;
fixup_edge_p pfedge;
gcc_assert (fixup_graph);
fvertex_list = fixup_graph->vertex_list;
fnum_vertices = fixup_graph->num_vertices;
fnum_edges = fixup_graph->num_edges;
fprintf (file, "\nDump fixup graph for %s(): %s.\n",
current_function_name (), msg);
fprintf (file,
"There are %d vertices and %d edges. new_exit_index is %d.\n\n",
fnum_vertices, fnum_edges, fixup_graph->new_exit_index);
for (i = 0; i < fnum_vertices; i++)
{
pfvertex = fvertex_list + i;
fprintf (file, "vertex_list[%d]: %d succ fixup edges.\n",
i, pfvertex->succ_edges.length ());
for (j = 0; pfvertex->succ_edges.iterate (j, &pfedge);
j++)
{
/* Distinguish forward edges and backward edges in the residual flow
network. */
if (pfedge->type)
fputs ("(f) ", file);
else if (pfedge->is_rflow_valid)
fputs ("(b) ", file);
dump_fixup_edge (file, fixup_graph, pfedge);
}
}
fputs ("\n", file);
}
/* Utility routines. */
/* ln() implementation: approximate calculation. Returns ln of X. */
static double
mcf_ln (double x)
{
#define E 2.71828
int l = 1;
double m = E;
gcc_assert (x >= 0);
while (m < x)
{
m *= E;
l++;
}
return l;
}
/* sqrt() implementation: based on open source QUAKE3 code (magic sqrt
implementation) by John Carmack. Returns sqrt of X. */
static double
mcf_sqrt (double x)
{
#define MAGIC_CONST1 0x1fbcf800
#define MAGIC_CONST2 0x5f3759df
union {
int intPart;
float floatPart;
} convertor, convertor2;
gcc_assert (x >= 0);
convertor.floatPart = x;
convertor2.floatPart = x;
convertor.intPart = MAGIC_CONST1 + (convertor.intPart >> 1);
convertor2.intPart = MAGIC_CONST2 - (convertor2.intPart >> 1);
return 0.5f * (convertor.floatPart + (x * convertor2.floatPart));
}
/* Common code shared between add_fixup_edge and add_rfixup_edge. Adds an edge
(SRC->DEST) to the edge_list maintained in FIXUP_GRAPH with cost of the edge
added set to COST. */
static fixup_edge_p
add_edge (fixup_graph_type *fixup_graph, int src, int dest, gcov_type cost)
{
fixup_vertex_p curr_vertex = fixup_graph->vertex_list + src;
fixup_edge_p curr_edge = fixup_graph->edge_list + fixup_graph->num_edges;
curr_edge->src = src;
curr_edge->dest = dest;
curr_edge->cost = cost;
fixup_graph->num_edges++;
if (dump_file)
dump_fixup_edge (dump_file, fixup_graph, curr_edge);
curr_vertex->succ_edges.safe_push (curr_edge);
return curr_edge;
}
/* Add a fixup edge (src->dest) with attributes TYPE, WEIGHT, COST and
MAX_CAPACITY to the edge_list in the fixup graph. */
static void
add_fixup_edge (fixup_graph_type *fixup_graph, int src, int dest,
edge_type type, gcov_type weight, gcov_type cost,
gcov_type max_capacity)
{
fixup_edge_p curr_edge = add_edge (fixup_graph, src, dest, cost);
curr_edge->type = type;
curr_edge->weight = weight;
curr_edge->max_capacity = max_capacity;
}
/* Add a residual edge (SRC->DEST) with attributes RFLOW and COST
to the fixup graph. */
static void
add_rfixup_edge (fixup_graph_type *fixup_graph, int src, int dest,
gcov_type rflow, gcov_type cost)
{
fixup_edge_p curr_edge = add_edge (fixup_graph, src, dest, cost);
curr_edge->rflow = rflow;
curr_edge->is_rflow_valid = true;
/* This edge is not a valid edge - merely used to hold residual flow. */
curr_edge->type = INVALID_EDGE;
}
/* Return the pointer to fixup edge SRC->DEST or NULL if edge does not
exist in the FIXUP_GRAPH. */
static fixup_edge_p
find_fixup_edge (fixup_graph_type *fixup_graph, int src, int dest)
{
int j;
fixup_edge_p pfedge;
fixup_vertex_p pfvertex;
gcc_assert (src < fixup_graph->num_vertices);
pfvertex = fixup_graph->vertex_list + src;
for (j = 0; pfvertex->succ_edges.iterate (j, &pfedge);
j++)
if (pfedge->dest == dest)
return pfedge;
return NULL;
}
/* Cleanup routine to free structures in FIXUP_GRAPH. */
static void
delete_fixup_graph (fixup_graph_type *fixup_graph)
{
int i;
int fnum_vertices = fixup_graph->num_vertices;
fixup_vertex_p pfvertex = fixup_graph->vertex_list;
for (i = 0; i < fnum_vertices; i++, pfvertex++)
pfvertex->succ_edges.release ();
free (fixup_graph->vertex_list);
free (fixup_graph->edge_list);
}
/* Creates a fixup graph FIXUP_GRAPH from the function CFG. */
static void
create_fixup_graph (fixup_graph_type *fixup_graph)
{
double sqrt_avg_vertex_weight = 0;
double total_vertex_weight = 0;
double k_pos = 0;
double k_neg = 0;
/* Vector to hold D(v) = sum_out_edges(v) - sum_in_edges(v). */
gcov_type *diff_out_in = NULL;
gcov_type supply_value = 0, demand_value = 0;
gcov_type fcost = 0;
int new_entry_index = 0, new_exit_index = 0;
int i = 0, j = 0;
int new_index = 0;
basic_block bb;
edge e;
edge_iterator ei;
fixup_edge_p pfedge, r_pfedge;
fixup_edge_p fedge_list;
int fnum_edges;
/* Each basic_block will be split into 2 during vertex transformation. */
int fnum_vertices_after_transform = 2 * n_basic_blocks_for_fn (cfun);
int fnum_edges_after_transform =
n_edges_for_fn (cfun) + n_basic_blocks_for_fn (cfun);
/* Count the new SOURCE and EXIT vertices to be added. */
int fmax_num_vertices =
(fnum_vertices_after_transform + n_edges_for_fn (cfun)
+ n_basic_blocks_for_fn (cfun) + 2);
/* In create_fixup_graph: Each basic block and edge can be split into 3
edges. Number of balance edges = n_basic_blocks - 1. And there is 1 edge
connecting new_entry and new_exit, and 2 edges connecting new_entry to
entry, and exit to new_exit. So after create_fixup_graph:
max_edges = 4 * n_basic_blocks + 3 * n_edges + 2
Accounting for residual flow edges
max_edges = 2 * (4 * n_basic_blocks + 3 * n_edges)
= 8 * n_basic_blocks + 6 * n_edges
< 8 * n_basic_blocks + 8 * n_edges. */
int fmax_num_edges = 8 * (n_basic_blocks_for_fn (cfun) +
n_edges_for_fn (cfun));
/* Initial num of vertices in the fixup graph. */
fixup_graph->num_vertices = n_basic_blocks_for_fn (cfun);
/* Fixup graph vertex list. */
fixup_graph->vertex_list =
(fixup_vertex_p) xcalloc (fmax_num_vertices, sizeof (fixup_vertex_type));
/* Fixup graph edge list. */
fixup_graph->edge_list =
(fixup_edge_p) xcalloc (fmax_num_edges, sizeof (fixup_edge_type));
diff_out_in =
(gcov_type *) xcalloc (1 + fnum_vertices_after_transform,
sizeof (gcov_type));
/* Compute constants b, k_pos, k_neg used in the cost function calculation.
b = sqrt(avg_vertex_weight(cfg)); k_pos = b; k_neg = 50b. */
FOR_BB_BETWEEN (bb, ENTRY_BLOCK_PTR_FOR_FN (cfun), NULL, next_bb)
total_vertex_weight += bb->count;
sqrt_avg_vertex_weight = mcf_sqrt (total_vertex_weight /
n_basic_blocks_for_fn (cfun));
k_pos = K_POS (sqrt_avg_vertex_weight);
k_neg = K_NEG (sqrt_avg_vertex_weight);
/* 1. Vertex Transformation: Split each vertex v into two vertices v' and v'',
connected by an edge e from v' to v''. w(e) = w(v). */
if (dump_file)
fprintf (dump_file, "\nVertex transformation:\n");
FOR_BB_BETWEEN (bb, ENTRY_BLOCK_PTR_FOR_FN (cfun), NULL, next_bb)
{
/* v'->v'': index1->(index1+1). */
i = 2 * bb->index;
fcost = (gcov_type) COST (k_pos, bb->count);
add_fixup_edge (fixup_graph, i, i + 1, VERTEX_SPLIT_EDGE, bb->count,
fcost, CAP_INFINITY);
fixup_graph->num_vertices++;
FOR_EACH_EDGE (e, ei, bb->succs)
{
/* Edges with ignore attribute set should be treated like they don't
exist. */
if (EDGE_INFO (e) && EDGE_INFO (e)->ignore)
continue;
j = 2 * e->dest->index;
fcost = (gcov_type) COST (k_pos, e->count);
add_fixup_edge (fixup_graph, i + 1, j, REDIRECT_EDGE, e->count, fcost,
CAP_INFINITY);
}
}
/* After vertex transformation. */
gcc_assert (fixup_graph->num_vertices == fnum_vertices_after_transform);
/* Redirect edges are not added for edges with ignore attribute. */
gcc_assert (fixup_graph->num_edges <= fnum_edges_after_transform);
fnum_edges_after_transform = fixup_graph->num_edges;
/* 2. Initialize D(v). */
for (i = 0; i < fnum_edges_after_transform; i++)
{
pfedge = fixup_graph->edge_list + i;
diff_out_in[pfedge->src] += pfedge->weight;
diff_out_in[pfedge->dest] -= pfedge->weight;
}
/* Entry block - vertex indices 0, 1; EXIT block - vertex indices 2, 3. */
for (i = 0; i <= 3; i++)
diff_out_in[i] = 0;
/* 3. Add reverse edges: needed to decrease counts during smoothing. */
if (dump_file)
fprintf (dump_file, "\nReverse edges:\n");
for (i = 0; i < fnum_edges_after_transform; i++)
{
pfedge = fixup_graph->edge_list + i;
if ((pfedge->src == 0) || (pfedge->src == 2))
continue;
r_pfedge = find_fixup_edge (fixup_graph, pfedge->dest, pfedge->src);
if (!r_pfedge && pfedge->weight)
{
/* Skip adding reverse edges for edges with w(e) = 0, as its maximum
capacity is 0. */
fcost = (gcov_type) COST (k_neg, pfedge->weight);
add_fixup_edge (fixup_graph, pfedge->dest, pfedge->src,
REVERSE_EDGE, 0, fcost, pfedge->weight);
}
}
/* 4. Create single source and sink. Connect new source vertex s' to function
entry block. Connect sink vertex t' to function exit. */
if (dump_file)
fprintf (dump_file, "\ns'->S, T->t':\n");
new_entry_index = fixup_graph->new_entry_index = fixup_graph->num_vertices;
fixup_graph->num_vertices++;
/* Set capacity to 0 initially, it will be updated after
supply_value is computed. */
add_fixup_edge (fixup_graph, new_entry_index, ENTRY_BLOCK,
SOURCE_CONNECT_EDGE, 0 /* supply_value */, 0,
0 /* supply_value */);
add_fixup_edge (fixup_graph, ENTRY_BLOCK, new_entry_index,
SOURCE_CONNECT_EDGE, 0 /* supply_value */, 0,
0 /* supply_value */);
/* Set capacity to 0 initially, it will be updated after
demand_value is computed. */
new_exit_index = fixup_graph->new_exit_index = fixup_graph->num_vertices;
fixup_graph->num_vertices++;
add_fixup_edge (fixup_graph, 2 * EXIT_BLOCK + 1, new_exit_index,
SINK_CONNECT_EDGE,
0 /* demand_value */, 0, 0 /* demand_value */);
add_fixup_edge (fixup_graph, new_exit_index, 2 * EXIT_BLOCK + 1,
SINK_CONNECT_EDGE,
0 /* demand_value */, 0, 0 /* demand_value */);
/* Create a back edge from the new_exit to the new_entry.
Initially, its capacity will be set to 0 so that it does not
affect max flow, but later its capacity will be changed to
infinity to cancel negative cycles. */
add_fixup_edge (fixup_graph, new_exit_index, new_entry_index,
SINK_SOURCE_EDGE, 0, 0, 0);
/* Connect vertices with unbalanced D(v) to source/sink. */
if (dump_file)
fprintf (dump_file, "\nD(v) balance:\n");
/* Skip vertices for ENTRY (0, 1) and EXIT (2,3) blocks, so start
with i = 4. diff_out_in[v''] should be 0, but may not be due to
rounding error. So here we consider all vertices. */
for (i = 4; i < new_entry_index; i += 1)
{
if (diff_out_in[i] > 0)
{
add_fixup_edge (fixup_graph, i, new_exit_index, BALANCE_EDGE, 0, 0,
diff_out_in[i]);
demand_value += diff_out_in[i];
}
else if (diff_out_in[i] < 0)
{
add_fixup_edge (fixup_graph, new_entry_index, i, BALANCE_EDGE, 0, 0,
-diff_out_in[i]);
supply_value -= diff_out_in[i];
}
}
/* Set supply = demand. */
if (dump_file)
{
fprintf (dump_file, "\nAdjust supply and demand:\n");
fprintf (dump_file, "supply_value=" HOST_WIDEST_INT_PRINT_DEC "\n",
supply_value);
fprintf (dump_file, "demand_value=" HOST_WIDEST_INT_PRINT_DEC "\n",
demand_value);
}
if (demand_value > supply_value)
{
pfedge = find_fixup_edge (fixup_graph, new_entry_index, ENTRY_BLOCK);
pfedge->max_capacity += (demand_value - supply_value);
}
else
{
pfedge = find_fixup_edge (fixup_graph, 2 * EXIT_BLOCK + 1, new_exit_index);
pfedge->max_capacity += (supply_value - demand_value);
}
/* 6. Normalize edges: remove anti-parallel edges. Anti-parallel edges are
created by the vertex transformation step from self-edges in the original
CFG and by the reverse edges added earlier. */
if (dump_file)
fprintf (dump_file, "\nNormalize edges:\n");
fnum_edges = fixup_graph->num_edges;
fedge_list = fixup_graph->edge_list;
for (i = 0; i < fnum_edges; i++)
{
pfedge = fedge_list + i;
r_pfedge = find_fixup_edge (fixup_graph, pfedge->dest, pfedge->src);
if (((pfedge->type == VERTEX_SPLIT_EDGE)
|| (pfedge->type == REDIRECT_EDGE)) && r_pfedge)
{
new_index = fixup_graph->num_vertices;
fixup_graph->num_vertices++;
if (dump_file)
{
fprintf (dump_file, "\nAnti-parallel edge:\n");
dump_fixup_edge (dump_file, fixup_graph, pfedge);
dump_fixup_edge (dump_file, fixup_graph, r_pfedge);
fprintf (dump_file, "New vertex is %d.\n", new_index);
fprintf (dump_file, "------------------\n");
}
pfedge->norm_vertex_index = new_index;
if (dump_file)
{
fprintf (dump_file, "After normalization:\n");
dump_fixup_edge (dump_file, fixup_graph, pfedge);
}
/* Add a new fixup edge: new_index->src. */
add_fixup_edge (fixup_graph, new_index, pfedge->src,
REVERSE_NORMALIZED_EDGE, 0, 0,
r_pfedge->max_capacity);
gcc_assert (fixup_graph->num_vertices <= fmax_num_vertices);
/* Edge: r_pfedge->src -> r_pfedge->dest
==> r_pfedge->src -> new_index. */
r_pfedge->dest = new_index;
r_pfedge->type = REVERSE_NORMALIZED_EDGE;
r_pfedge->max_capacity = pfedge->max_capacity;
if (dump_file)
dump_fixup_edge (dump_file, fixup_graph, r_pfedge);
}
}
if (dump_file)
dump_fixup_graph (dump_file, fixup_graph, "After create_fixup_graph()");
/* Cleanup. */
free (diff_out_in);
}
/* Allocates space for the structures in AUGMENTING_PATH. The space needed is
proportional to the number of nodes in the graph, which is given by
GRAPH_SIZE. */
static void
init_augmenting_path (augmenting_path_type *augmenting_path, int graph_size)
{
augmenting_path->queue_list.queue = (int *)
xcalloc (graph_size + 2, sizeof (int));
augmenting_path->queue_list.size = graph_size + 2;
augmenting_path->bb_pred = (int *) xcalloc (graph_size, sizeof (int));
augmenting_path->is_visited = (int *) xcalloc (graph_size, sizeof (int));
}
/* Free the structures in AUGMENTING_PATH. */
static void
free_augmenting_path (augmenting_path_type *augmenting_path)
{
free (augmenting_path->queue_list.queue);
free (augmenting_path->bb_pred);
free (augmenting_path->is_visited);
}
/* Queue routines. Assumes queue will never overflow. */
static void
init_queue (queue_type *queue_list)
{
gcc_assert (queue_list);
queue_list->head = 0;
queue_list->tail = 0;
}
/* Return true if QUEUE_LIST is empty. */
static bool
is_empty (queue_type *queue_list)
{
return (queue_list->head == queue_list->tail);
}
/* Insert element X into QUEUE_LIST. */
static void
enqueue (queue_type *queue_list, int x)
{
gcc_assert (queue_list->tail < queue_list->size);
queue_list->queue[queue_list->tail] = x;
(queue_list->tail)++;
}
/* Return the first element in QUEUE_LIST. */
static int
dequeue (queue_type *queue_list)
{
int x;
gcc_assert (queue_list->head >= 0);
x = queue_list->queue[queue_list->head];
(queue_list->head)++;
return x;
}
/* Finds a negative cycle in the residual network using
the Bellman-Ford algorithm. The flow on the found cycle is reversed by the
minimum residual capacity of that cycle. ENTRY and EXIT vertices are not
considered.
Parameters:
FIXUP_GRAPH - Residual graph (input/output)
The following are allocated/freed by the caller:
PI - Vector to hold predecessors in path (pi = pred index)
D - D[I] holds minimum cost of path from i to sink
CYCLE - Vector to hold the minimum cost cycle
Return:
true if a negative cycle was found, false otherwise. */
static bool
cancel_negative_cycle (fixup_graph_type *fixup_graph,
int *pi, gcov_type *d, int *cycle)
{
int i, j, k;
int fnum_vertices, fnum_edges;
fixup_edge_p fedge_list, pfedge, r_pfedge;
bool found_cycle = false;
int cycle_start = 0, cycle_end = 0;
gcov_type sum_cost = 0, cycle_flow = 0;
bool propagated = false;
gcc_assert (fixup_graph);
fnum_vertices = fixup_graph->num_vertices;
fnum_edges = fixup_graph->num_edges;
fedge_list = fixup_graph->edge_list;
/* Initialize. */
/* Skip ENTRY. */
for (i = 1; i < fnum_vertices; i++)
{
d[i] = CAP_INFINITY;
pi[i] = -1;
cycle[i] = -1;
}
d[ENTRY_BLOCK] = 0;
/* Relax. */
for (k = 1; k < fnum_vertices; k++)
{
propagated = false;
for (i = 0; i < fnum_edges; i++)
{
pfedge = fedge_list + i;
if (pfedge->is_rflow_valid && pfedge->rflow
&& d[pfedge->src] != CAP_INFINITY
&& (d[pfedge->dest] > d[pfedge->src] + pfedge->cost))
{
d[pfedge->dest] = d[pfedge->src] + pfedge->cost;
pi[pfedge->dest] = pfedge->src;
propagated = true;
}
}
if (!propagated)
break;
}
if (!propagated)
/* No negative cycles exist. */
return 0;
/* Detect. */
for (i = 0; i < fnum_edges; i++)
{
pfedge = fedge_list + i;
if (pfedge->is_rflow_valid && pfedge->rflow
&& d[pfedge->src] != CAP_INFINITY
&& (d[pfedge->dest] > d[pfedge->src] + pfedge->cost))
{
found_cycle = true;
break;
}
}
if (!found_cycle)
return 0;
/* Augment the cycle with the cycle's minimum residual capacity. */
found_cycle = false;
cycle[0] = pfedge->dest;
j = pfedge->dest;
for (i = 1; i < fnum_vertices; i++)
{
j = pi[j];
cycle[i] = j;
for (k = 0; k < i; k++)
{
if (cycle[k] == j)
{
/* cycle[k] -> ... -> cycle[i]. */
cycle_start = k;
cycle_end = i;
found_cycle = true;
break;
}
}
if (found_cycle)
break;
}
gcc_assert (cycle[cycle_start] == cycle[cycle_end]);
if (dump_file)
fprintf (dump_file, "\nNegative cycle length is %d:\n",
cycle_end - cycle_start);
sum_cost = 0;
cycle_flow = CAP_INFINITY;
for (k = cycle_start; k < cycle_end; k++)
{
pfedge = find_fixup_edge (fixup_graph, cycle[k + 1], cycle[k]);
cycle_flow = MIN (cycle_flow, pfedge->rflow);
sum_cost += pfedge->cost;
if (dump_file)
fprintf (dump_file, "%d ", cycle[k]);
}
if (dump_file)
{
fprintf (dump_file, "%d", cycle[k]);
fprintf (dump_file,
": (" HOST_WIDEST_INT_PRINT_DEC ", " HOST_WIDEST_INT_PRINT_DEC
")\n", sum_cost, cycle_flow);
fprintf (dump_file,
"Augment cycle with " HOST_WIDEST_INT_PRINT_DEC "\n",
cycle_flow);
}
for (k = cycle_start; k < cycle_end; k++)
{
pfedge = find_fixup_edge (fixup_graph, cycle[k + 1], cycle[k]);
r_pfedge = find_fixup_edge (fixup_graph, cycle[k], cycle[k + 1]);
if (pfedge->rflow != CAP_INFINITY)
pfedge->rflow -= cycle_flow;
if (pfedge->type)
pfedge->flow += cycle_flow;
if (r_pfedge->rflow != CAP_INFINITY)
r_pfedge->rflow += cycle_flow;
if (r_pfedge->type)
r_pfedge->flow -= cycle_flow;
}
return true;
}
/* Computes the residual flow for FIXUP_GRAPH by setting the rflow field of
the edges. ENTRY and EXIT vertices should not be considered. */
static void
compute_residual_flow (fixup_graph_type *fixup_graph)
{
int i;
int fnum_edges;
fixup_edge_p fedge_list, pfedge;
gcc_assert (fixup_graph);
if (dump_file)
fputs ("\ncompute_residual_flow():\n", dump_file);
fnum_edges = fixup_graph->num_edges;
fedge_list = fixup_graph->edge_list;
for (i = 0; i < fnum_edges; i++)
{
pfedge = fedge_list + i;
pfedge->rflow = pfedge->max_capacity == CAP_INFINITY ?
CAP_INFINITY : pfedge->max_capacity - pfedge->flow;
pfedge->is_rflow_valid = true;
add_rfixup_edge (fixup_graph, pfedge->dest, pfedge->src, pfedge->flow,
-pfedge->cost);
}
}
/* Uses Edmonds-Karp algorithm - BFS to find augmenting path from SOURCE to
SINK. The fields in the edge vector in the FIXUP_GRAPH are not modified by
this routine. The vector bb_pred in the AUGMENTING_PATH structure is updated
to reflect the path found.
Returns: 0 if no augmenting path is found, 1 otherwise. */
static int
find_augmenting_path (fixup_graph_type *fixup_graph,
augmenting_path_type *augmenting_path, int source,
int sink)
{
int u = 0;
int i;
fixup_vertex_p fvertex_list, pfvertex;
fixup_edge_p pfedge;
int *bb_pred, *is_visited;
queue_type *queue_list;
gcc_assert (augmenting_path);
bb_pred = augmenting_path->bb_pred;
gcc_assert (bb_pred);
is_visited = augmenting_path->is_visited;
gcc_assert (is_visited);
queue_list = &(augmenting_path->queue_list);
gcc_assert (fixup_graph);
fvertex_list = fixup_graph->vertex_list;
for (u = 0; u < fixup_graph->num_vertices; u++)
is_visited[u] = 0;
init_queue (queue_list);
enqueue (queue_list, source);
bb_pred[source] = -1;
while (!is_empty (queue_list))
{
u = dequeue (queue_list);
is_visited[u] = 1;
pfvertex = fvertex_list + u;
for (i = 0; pfvertex->succ_edges.iterate (i, &pfedge);
i++)
{
int dest = pfedge->dest;
if ((pfedge->rflow > 0) && (is_visited[dest] == 0))
{
enqueue (queue_list, dest);
bb_pred[dest] = u;
is_visited[dest] = 1;
if (dest == sink)
return 1;
}
}
}
return 0;
}
/* Routine to find the maximal flow:
Algorithm:
1. Initialize flow to 0
2. Find an augmenting path form source to sink.
3. Send flow equal to the path's residual capacity along the edges of this path.
4. Repeat steps 2 and 3 until no new augmenting path is found.
Parameters:
SOURCE: index of source vertex (input)
SINK: index of sink vertex (input)
FIXUP_GRAPH: adjacency matrix representing the graph. The flow of the edges will be
set to have a valid maximal flow by this routine. (input)
Return: Maximum flow possible. */
static gcov_type
find_max_flow (fixup_graph_type *fixup_graph, int source, int sink)
{
int fnum_edges;
augmenting_path_type augmenting_path;
int *bb_pred;
gcov_type max_flow = 0;
int i, u;
fixup_edge_p fedge_list, pfedge, r_pfedge;
gcc_assert (fixup_graph);
fnum_edges = fixup_graph->num_edges;
fedge_list = fixup_graph->edge_list;
/* Initialize flow to 0. */
for (i = 0; i < fnum_edges; i++)
{
pfedge = fedge_list + i;
pfedge->flow = 0;
}
compute_residual_flow (fixup_graph);
init_augmenting_path (&augmenting_path, fixup_graph->num_vertices);
bb_pred = augmenting_path.bb_pred;
while (find_augmenting_path (fixup_graph, &augmenting_path, source, sink))
{
/* Determine the amount by which we can increment the flow. */
gcov_type increment = CAP_INFINITY;
for (u = sink; u != source; u = bb_pred[u])
{
pfedge = find_fixup_edge (fixup_graph, bb_pred[u], u);
increment = MIN (increment, pfedge->rflow);
}
max_flow += increment;
/* Now increment the flow. EXIT vertex index is 1. */
for (u = sink; u != source; u = bb_pred[u])
{
pfedge = find_fixup_edge (fixup_graph, bb_pred[u], u);
r_pfedge = find_fixup_edge (fixup_graph, u, bb_pred[u]);
if (pfedge->rflow != CAP_INFINITY)
pfedge->rflow -= increment;
if (r_pfedge->rflow != CAP_INFINITY)
r_pfedge->rflow += increment;
if (pfedge->type)
{
/* forward edge. */
pfedge->flow += increment;
}
else
{
/* backward edge. */
gcc_assert (r_pfedge->type);
r_pfedge->flow -= increment;
}
}
if (dump_file)
{
fprintf (dump_file, "\nDump augmenting path:\n");
for (u = sink; u != source; u = bb_pred[u])
{
print_basic_block (dump_file, fixup_graph, u);
fprintf (dump_file, "<-");
}
fprintf (dump_file,
"ENTRY (path_capacity=" HOST_WIDEST_INT_PRINT_DEC ")\n",
increment);
fprintf (dump_file,
"Network flow is " HOST_WIDEST_INT_PRINT_DEC ".\n",
max_flow);
}
}
free_augmenting_path (&augmenting_path);
if (dump_file)
dump_fixup_graph (dump_file, fixup_graph, "After find_max_flow()");
return max_flow;
}
/* Computes the corrected edge and basic block weights using FIXUP_GRAPH
after applying the find_minimum_cost_flow() routine. */
static void
adjust_cfg_counts (fixup_graph_type *fixup_graph)
{
basic_block bb;
edge e;
edge_iterator ei;
int i, j;
fixup_edge_p pfedge, pfedge_n;
gcc_assert (fixup_graph);
if (dump_file)
fprintf (dump_file, "\nadjust_cfg_counts():\n");
FOR_BB_BETWEEN (bb, ENTRY_BLOCK_PTR_FOR_FN (cfun),
EXIT_BLOCK_PTR_FOR_FN (cfun), next_bb)
{
i = 2 * bb->index;
/* Fixup BB. */
if (dump_file)
fprintf (dump_file,
"BB%d: " HOST_WIDEST_INT_PRINT_DEC "", bb->index, bb->count);
pfedge = find_fixup_edge (fixup_graph, i, i + 1);
if (pfedge->flow)
{
bb->count += pfedge->flow;
if (dump_file)
{
fprintf (dump_file, " + " HOST_WIDEST_INT_PRINT_DEC "(",
pfedge->flow);
print_edge (dump_file, fixup_graph, i, i + 1);
fprintf (dump_file, ")");
}
}
pfedge_n =
find_fixup_edge (fixup_graph, i + 1, pfedge->norm_vertex_index);
/* Deduct flow from normalized reverse edge. */
if (pfedge->norm_vertex_index && pfedge_n->flow)
{
bb->count -= pfedge_n->flow;
if (dump_file)
{
fprintf (dump_file, " - " HOST_WIDEST_INT_PRINT_DEC "(",
pfedge_n->flow);
print_edge (dump_file, fixup_graph, i + 1,
pfedge->norm_vertex_index);
fprintf (dump_file, ")");
}
}
if (dump_file)
fprintf (dump_file, " = " HOST_WIDEST_INT_PRINT_DEC "\n", bb->count);
/* Fixup edge. */
FOR_EACH_EDGE (e, ei, bb->succs)
{
/* Treat edges with ignore attribute set as if they don't exist. */
if (EDGE_INFO (e) && EDGE_INFO (e)->ignore)
continue;
j = 2 * e->dest->index;
if (dump_file)
fprintf (dump_file, "%d->%d: " HOST_WIDEST_INT_PRINT_DEC "",
bb->index, e->dest->index, e->count);
pfedge = find_fixup_edge (fixup_graph, i + 1, j);
if (bb->index != e->dest->index)
{
/* Non-self edge. */
if (pfedge->flow)
{
e->count += pfedge->flow;
if (dump_file)
{
fprintf (dump_file, " + " HOST_WIDEST_INT_PRINT_DEC "(",
pfedge->flow);
print_edge (dump_file, fixup_graph, i + 1, j);
fprintf (dump_file, ")");
}
}
pfedge_n =
find_fixup_edge (fixup_graph, j, pfedge->norm_vertex_index);
/* Deduct flow from normalized reverse edge. */
if (pfedge->norm_vertex_index && pfedge_n->flow)
{
e->count -= pfedge_n->flow;
if (dump_file)
{
fprintf (dump_file, " - " HOST_WIDEST_INT_PRINT_DEC "(",
pfedge_n->flow);
print_edge (dump_file, fixup_graph, j,
pfedge->norm_vertex_index);
fprintf (dump_file, ")");
}
}
}
else
{
/* Handle self edges. Self edge is split with a normalization
vertex. Here i=j. */
pfedge = find_fixup_edge (fixup_graph, j, i + 1);
pfedge_n =
find_fixup_edge (fixup_graph, i + 1, pfedge->norm_vertex_index);
e->count += pfedge_n->flow;
bb->count += pfedge_n->flow;
if (dump_file)
{
fprintf (dump_file, "(self edge)");
fprintf (dump_file, " + " HOST_WIDEST_INT_PRINT_DEC "(",
pfedge_n->flow);
print_edge (dump_file, fixup_graph, i + 1,
pfedge->norm_vertex_index);
fprintf (dump_file, ")");
}
}
if (bb->count)
e->probability = REG_BR_PROB_BASE * e->count / bb->count;
if (dump_file)
fprintf (dump_file, " = " HOST_WIDEST_INT_PRINT_DEC "\t(%.1f%%)\n",
e->count, e->probability * 100.0 / REG_BR_PROB_BASE);
}
}
ENTRY_BLOCK_PTR_FOR_FN (cfun)->count =
sum_edge_counts (ENTRY_BLOCK_PTR_FOR_FN (cfun)->succs);
EXIT_BLOCK_PTR_FOR_FN (cfun)->count =
sum_edge_counts (EXIT_BLOCK_PTR_FOR_FN (cfun)->preds);
/* Compute edge probabilities. */
FOR_ALL_BB_FN (bb, cfun)
{
if (bb->count)
{
FOR_EACH_EDGE (e, ei, bb->succs)
e->probability = REG_BR_PROB_BASE * e->count / bb->count;
}
else
{
int total = 0;
FOR_EACH_EDGE (e, ei, bb->succs)
if (!(e->flags & (EDGE_COMPLEX | EDGE_FAKE)))
total++;
if (total)
{
FOR_EACH_EDGE (e, ei, bb->succs)
{
if (!(e->flags & (EDGE_COMPLEX | EDGE_FAKE)))
e->probability = REG_BR_PROB_BASE / total;
else
e->probability = 0;
}
}
else
{
total += EDGE_COUNT (bb->succs);
FOR_EACH_EDGE (e, ei, bb->succs)
e->probability = REG_BR_PROB_BASE / total;
}
}
}
if (dump_file)
{
fprintf (dump_file, "\nCheck %s() CFG flow conservation:\n",
current_function_name ());
FOR_EACH_BB_FN (bb, cfun)
{
if ((bb->count != sum_edge_counts (bb->preds))
|| (bb->count != sum_edge_counts (bb->succs)))
{
fprintf (dump_file,
"BB%d(" HOST_WIDEST_INT_PRINT_DEC ") **INVALID**: ",
bb->index, bb->count);
fprintf (stderr,
"******** BB%d(" HOST_WIDEST_INT_PRINT_DEC
") **INVALID**: \n", bb->index, bb->count);
fprintf (dump_file, "in_edges=" HOST_WIDEST_INT_PRINT_DEC " ",
sum_edge_counts (bb->preds));
fprintf (dump_file, "out_edges=" HOST_WIDEST_INT_PRINT_DEC "\n",
sum_edge_counts (bb->succs));
}
}
}
}
/* Called before negative_cycle_cancellation, to form a cycle between
* new_exit to new_entry in FIXUP_GRAPH with capacity MAX_FLOW. We
* don't want the flow in the BALANCE_EDGE to be modified, so we set
* the residural flow of those edges to 0 */
static void
modify_sink_source_capacity (fixup_graph_type *fixup_graph, gcov_type max_flow)
{
fixup_edge_p edge, r_edge;
int i;
int entry = ENTRY_BLOCK;
int exit = 2 * EXIT_BLOCK + 1;
int new_entry = fixup_graph->new_entry_index;
int new_exit = fixup_graph->new_exit_index;
edge = find_fixup_edge (fixup_graph, new_entry, entry);
edge->max_capacity = CAP_INFINITY;
edge->rflow = CAP_INFINITY;
edge = find_fixup_edge (fixup_graph, entry, new_entry);
edge->max_capacity = CAP_INFINITY;
edge->rflow = CAP_INFINITY;
edge = find_fixup_edge (fixup_graph, exit, new_exit);
edge->max_capacity = CAP_INFINITY;
edge->rflow = CAP_INFINITY;
edge = find_fixup_edge (fixup_graph, new_exit, exit);
edge->max_capacity = CAP_INFINITY;
edge->rflow = CAP_INFINITY;
edge = find_fixup_edge (fixup_graph, new_exit, new_entry);
edge->max_capacity = CAP_INFINITY;
edge->flow = max_flow;
edge->rflow = CAP_INFINITY;
r_edge = find_fixup_edge (fixup_graph, new_entry, new_exit);
r_edge->rflow = max_flow;
/* Find all the backwards residual edges corresponding to
BALANCE_EDGEs and set their residual flow to 0 to enforce a
minimum flow constraint on these edges. */
for (i = 4; i < new_entry; i += 1)
{
edge = find_fixup_edge (fixup_graph, i, new_entry);
if (edge)
edge->rflow = 0;
edge = find_fixup_edge (fixup_graph, new_exit, i);
if (edge)
edge->rflow = 0;
}
}
/* Implements the negative cycle canceling algorithm to compute a minimum cost
flow.
Algorithm:
1. Find maximal flow.
2. Form residual network
3. Repeat:
While G contains a negative cost cycle C, reverse the flow on the found cycle
by the minimum residual capacity in that cycle.
4. Form the minimal cost flow
f(u,v) = rf(v, u)
Input:
FIXUP_GRAPH - Initial fixup graph.
The flow field is modified to represent the minimum cost flow. */
static void
find_minimum_cost_flow (fixup_graph_type *fixup_graph)
{
/* Holds the index of predecessor in path. */
int *pred;
/* Used to hold the minimum cost cycle. */
int *cycle;
/* Used to record the number of iterations of cancel_negative_cycle. */
int iteration;
/* Vector d[i] holds the minimum cost of path from i to sink. */
gcov_type *d;
int fnum_vertices;
int new_exit_index;
int new_entry_index;
gcov_type max_flow;
gcc_assert (fixup_graph);
fnum_vertices = fixup_graph->num_vertices;
new_exit_index = fixup_graph->new_exit_index;
new_entry_index = fixup_graph->new_entry_index;
max_flow = find_max_flow (fixup_graph, new_entry_index, new_exit_index);
/* Adjust the fixup graph to translate things into a minimum cost
circulation problem. */
modify_sink_source_capacity (fixup_graph, max_flow);
/* Initialize the structures for find_negative_cycle(). */
pred = (int *) xcalloc (fnum_vertices, sizeof (int));
d = (gcov_type *) xcalloc (fnum_vertices, sizeof (gcov_type));
cycle = (int *) xcalloc (fnum_vertices, sizeof (int));
/* Repeatedly find and cancel negative cost cycles, until
no more negative cycles exist. This also updates the flow field
to represent the minimum cost flow so far. */
iteration = 0;
while (cancel_negative_cycle (fixup_graph, pred, d, cycle))
{
iteration++;
if (iteration > MAX_ITER (fixup_graph->num_vertices,
fixup_graph->num_edges))
{
if (dump_enabled_p ())
dump_printf_loc (MSG_NOTE,
DECL_SOURCE_LOCATION (current_function_decl),
"Exiting profile correction early to avoid "
"excessive compile time");
break;
}
}
if (dump_file)
dump_fixup_graph (dump_file, fixup_graph,
"After find_minimum_cost_flow()");
/* Cleanup structures. */
free (pred);
free (d);
free (cycle);
}
/* Compute the sum of the edge counts in TO_EDGES. */
gcov_type
sum_edge_counts (vec *to_edges)
{
gcov_type sum = 0;
edge e;
edge_iterator ei;
FOR_EACH_EDGE (e, ei, to_edges)
{
if (EDGE_INFO (e) && EDGE_INFO (e)->ignore)
continue;
sum += e->count;
}
return sum;
}
/* Main routine. Smoothes the initial assigned basic block and edge counts using
a minimum cost flow algorithm, to ensure that the flow consistency rule is
obeyed: sum of outgoing edges = sum of incoming edges for each basic
block. */
void
mcf_smooth_cfg (void)
{
fixup_graph_type fixup_graph;
memset (&fixup_graph, 0, sizeof (fixup_graph));
create_fixup_graph (&fixup_graph);
find_minimum_cost_flow (&fixup_graph);
adjust_cfg_counts (&fixup_graph);
delete_fixup_graph (&fixup_graph);
}