public inbox for gcc-patches@gcc.gnu.org
 help / color / mirror / Atom feed
From: Xinliang David Li <davidxl@google.com>
To: Martin Thuresson <martint@google.com>
Cc: reply@codereview.appspotmail.com, GCC Patches <gcc-patches@gcc.gnu.org>
Subject: Re: [google] Use minimum cost circulation, not minimum cost flow to smooth profiles other minor fixes. (issue4536106)
Date: Thu, 02 Jun 2011 18:17:00 -0000	[thread overview]
Message-ID: <BANLkTinXZjRxmgsKS4XH07TVpFiR9bynGA@mail.gmail.com> (raw)
In-Reply-To: <BANLkTinmtfE=69+DJNL4Tpb482VneK7c20GSg1aKsi7TcmTN3g@mail.gmail.com>

Counter overflow?

David

On Thu, Jun 2, 2011 at 11:12 AM, Martin Thuresson <martint@google.com> wrote:
> On Thu, Jun 2, 2011 at 11:05 AM, Xinliang David Li <davidxl@google.com> wrote:
>>
>> Smoothing works for sample FDO and profile data from multi-threaded
>> programs. You won't see any difference in SPEC.
>
> Dehao reported some performance improvements from the algorithmic improvements
> he added in terms of extra fixup edges and handling of infinite capacity.
>
> Martin
>
>
>
>
>>
>> David
>>
>> On Thu, Jun 2, 2011 at 11:00 AM, Martin Thuresson <martint@google.com> wrote:
>> > This patch from Neil Vachharajani and Dehao Chen improves mcf by using
>> > minimum cost circulation instead of minimum cost flow to smooth profiles.
>> > It also introduces a parameter for controlling running time of the algorithm.
>> > This was what was originally presented in the academic work and handles
>> > certain cases where the function entry and exit have incorrect profile
>> > weights.
>> >
>> > For now, this is for google/main. Once I have collected performance results
>> > from SPEC I will propose this patch for trunk as well.
>> >
>> > Bootstraps and no test regressions. Ok for google/main?
>> >
>> > 2011-06-02  Neil Vachharajani  <nvachhar@gmail.com>, Dehao Chen
>> >        <danielcdh@gmail.com>
>> >
>> >        * gcc/doc/invoke.texi (min-mcf-cancel-iters): Document.
>> >        * gcc/mcf.c (MAX_ITER): Use new param PARAM_MIN_MCF_CANCEL_ITERS.
>> >        (edge_type): Add SINK_SOURCE_EDGE.
>> >        (dump_fixup_edge): Handle SINK_SOURCE_EDGE.
>> >        (create_fixup_graph): Make problem miminum cost circulation.
>> >        (cancel_negative_cycle): Update handling of infinite capacity.
>> >        (compute_residual_flow): Update handling of infinite capacity.
>> >        (find_max_flow): Update handling of infinite capacity.
>> >        (modify_sink_source_capacity): New function.
>> >        (find_minimum_cost_flow): Make problem miminum cost circulation.
>> >        Use param PARAM_MIN_MCF_CANCEL_ITERS.
>> >        * gcc/params.def (PARAM_MIN_MCF_CANCEL_ITERS): Define.
>> >
>> > Index: gcc/doc/invoke.texi
>> > ===================================================================
>> > --- gcc/doc/invoke.texi (revision 174456)
>> > +++ gcc/doc/invoke.texi (working copy)
>> > @@ -8341,6 +8341,12 @@ whether the result of a complex multipli
>> >
>> >  The default is @option{-fno-cx-fortran-rules}.
>> >
>> > +@item min-mcf-cancel-iters
>> > +The minimum number of iterations of negative cycle cancellation during
>> > +MCF profile correction before early termination.  This parameter is
>> > +only useful when using @option{-fprofile-correction}.
>> > +
>> > +
>> >  @end table
>> >
>> >  The following options control optimizations that may improve
>> > Index: gcc/mcf.c
>> > ===================================================================
>> > --- gcc/mcf.c   (revision 174456)
>> > +++ gcc/mcf.c   (working copy)
>> > @@ -52,6 +52,8 @@ along with GCC; see the file COPYING3.
>> >  #include "langhooks.h"
>> >  #include "tree.h"
>> >  #include "gcov-io.h"
>> > +#include "params.h"
>> > +#include "diagnostic-core.h"
>> >
>> >  #include "profile.h"
>> >
>> > @@ -64,15 +66,18 @@ along with GCC; see the file COPYING3.
>> >  #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)  10 + (1000000 / ((n) * (e)))
>> > +#define MAX_ITER(n, e)  (PARAM_VALUE (PARAM_MIN_MCF_CANCEL_ITERS) + \
>> > +                        (1000000 / ((n) * (e))))
>> > +
>> >  typedef enum
>> >  {
>> > -  INVALID_EDGE,
>> > +  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.  */
>> > @@ -250,6 +255,10 @@ dump_fixup_edge (FILE *file, fixup_graph
>> >          fputs (" @SINK_CONNECT_EDGE", file);
>> >          break;
>> >
>> > +       case SINK_SOURCE_EDGE:
>> > +         fputs (" @SINK_SOURCE_EDGE", file);
>> > +         break;
>> > +
>> >        case REVERSE_EDGE:
>> >          fputs (" @REVERSE_EDGE", file);
>> >          break;
>> > @@ -465,7 +474,7 @@ create_fixup_graph (fixup_graph_type *fi
>> >   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 = 1, demand_value = 0;
>> > +  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;
>> > @@ -486,14 +495,15 @@ create_fixup_graph (fixup_graph_type *fi
>> >     fnum_vertices_after_transform + n_edges + n_basic_blocks + 2;
>> >
>> >   /* In create_fixup_graph: Each basic block and edge can be split into 3
>> > -     edges. Number of balance edges = n_basic_blocks. So after
>> > -     create_fixup_graph:
>> > -     max_edges = 4 * n_basic_blocks + 3 * n_edges
>> > +     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 + n_edges);
>> > +     max_edges = 2 * (4 * n_basic_blocks + 3 * n_edges + 2)
>> > +     = 8 * n_basic_blocks + 6 * n_edges + 4
>> > +     < 8 * n_basic_blocks + 8 * n_edges + 8.  */
>> > +  int fmax_num_edges = 8 * (n_basic_blocks + n_edges + 1);
>> >
>> >   /* Initial num of vertices in the fixup graph.  */
>> >   fixup_graph->num_vertices = n_basic_blocks;
>> > @@ -512,7 +522,7 @@ create_fixup_graph (fixup_graph_type *fi
>> >
>> >   /* 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, NULL, next_bb)
>> > +  FOR_ALL_BB (bb)
>> >     total_vertex_weight += bb->count;
>> >
>> >   sqrt_avg_vertex_weight = mcf_sqrt (total_vertex_weight / n_basic_blocks);
>> > @@ -526,10 +536,11 @@ create_fixup_graph (fixup_graph_type *fi
>> >   if (dump_file)
>> >     fprintf (dump_file, "\nVertex transformation:\n");
>> >
>> > -  FOR_BB_BETWEEN (bb, ENTRY_BLOCK_PTR, NULL, next_bb)
>> > +  FOR_ALL_BB (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);
>> > @@ -593,23 +604,45 @@ create_fixup_graph (fixup_graph_type *fi
>> >
>> >   new_entry_index = fixup_graph->new_entry_index = fixup_graph->num_vertices;
>> >   fixup_graph->num_vertices++;
>> > -  /* Set supply_value to 1 to avoid zero count function ENTRY.  */
>> > -  add_fixup_edge (fixup_graph, new_entry_index, ENTRY_BLOCK, SOURCE_CONNECT_EDGE,
>> > -                 1 /* supply_value */, 0, 1 /* supply_value */);
>> > +  /* 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 */);
>> >
>> > -  /* Create new exit with EXIT_BLOCK as single pred.  */
>> > +
>> > +  /* 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''] will be 0, so skip v'' vertices, hence i += 2.  */
>> > -  for (i = 4; i < new_entry_index; i += 2)
>> > +
>> > +  /* 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)
>> >        {
>> > @@ -674,7 +707,6 @@ create_fixup_graph (fixup_graph_type *fi
>> >              fprintf (dump_file, "------------------\n");
>> >            }
>> >
>> > -         pfedge->cost /= 2;
>> >          pfedge->norm_vertex_index = new_index;
>> >          if (dump_file)
>> >            {
>> > @@ -684,7 +716,7 @@ create_fixup_graph (fixup_graph_type *fi
>> >
>> >          /* Add a new fixup edge: new_index->src.  */
>> >          add_fixup_edge (fixup_graph, new_index, pfedge->src,
>> > -                         REVERSE_NORMALIZED_EDGE, 0, r_pfedge->cost,
>> > +                         REVERSE_NORMALIZED_EDGE, 0, 0,
>> >                          r_pfedge->max_capacity);
>> >          gcc_assert (fixup_graph->num_vertices <= fmax_num_vertices);
>> >
>> > @@ -692,7 +724,6 @@ create_fixup_graph (fixup_graph_type *fi
>> >              ==> r_pfedge->src -> new_index.  */
>> >          r_pfedge->dest = new_index;
>> >          r_pfedge->type = REVERSE_NORMALIZED_EDGE;
>> > -         r_pfedge->cost = pfedge->cost;
>> >          r_pfedge->max_capacity = pfedge->max_capacity;
>> >          if (dump_file)
>> >            dump_fixup_edge (dump_file, fixup_graph, r_pfedge);
>> > @@ -794,14 +825,12 @@ cancel_negative_cycle (fixup_graph_type
>> >   bool found_cycle = false;
>> >   int cycle_start = 0, cycle_end = 0;
>> >   gcov_type sum_cost = 0, cycle_flow = 0;
>> > -  int new_entry_index;
>> >   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;
>> > -  new_entry_index = fixup_graph->new_entry_index;
>> >
>> >   /* Initialize.  */
>> >   /* Skip ENTRY.  */
>> > @@ -820,8 +849,6 @@ cancel_negative_cycle (fixup_graph_type
>> >     for (i = 0; i < fnum_edges; i++)
>> >       {
>> >        pfedge = fedge_list + i;
>> > -       if (pfedge->src == new_entry_index)
>> > -         continue;
>> >        if (pfedge->is_rflow_valid && pfedge->rflow
>> >             && d[pfedge->src] != CAP_INFINITY
>> >            && (d[pfedge->dest] > d[pfedge->src] + pfedge->cost))
>> > @@ -843,8 +870,6 @@ cancel_negative_cycle (fixup_graph_type
>> >   for (i = 0; i < fnum_edges; i++)
>> >     {
>> >       pfedge = fedge_list + i;
>> > -      if (pfedge->src == new_entry_index)
>> > -       continue;
>> >       if (pfedge->is_rflow_valid && pfedge->rflow
>> >           && d[pfedge->src] != CAP_INFINITY
>> >          && (d[pfedge->dest] > d[pfedge->src] + pfedge->cost))
>> > @@ -912,10 +937,12 @@ cancel_negative_cycle (fixup_graph_type
>> >     {
>> >       pfedge = find_fixup_edge (fixup_graph, cycle[k + 1], cycle[k]);
>> >       r_pfedge = find_fixup_edge (fixup_graph, cycle[k], cycle[k + 1]);
>> > -      pfedge->rflow -= cycle_flow;
>> > +      if (pfedge->rflow != CAP_INFINITY)
>> > +        pfedge->rflow -= cycle_flow;
>> >       if (pfedge->type)
>> >        pfedge->flow += cycle_flow;
>> > -      r_pfedge->rflow += cycle_flow;
>> > +      if (r_pfedge->rflow != CAP_INFINITY)
>> > +        r_pfedge->rflow += cycle_flow;
>> >       if (r_pfedge->type)
>> >        r_pfedge->flow -= cycle_flow;
>> >     }
>> > @@ -945,7 +972,8 @@ compute_residual_flow (fixup_graph_type
>> >   for (i = 0; i < fnum_edges; i++)
>> >     {
>> >       pfedge = fedge_list + i;
>> > -      pfedge->rflow = pfedge->max_capacity - pfedge->flow;
>> > +      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);
>> > @@ -1070,20 +1098,22 @@ find_max_flow (fixup_graph_type *fixup_g
>> >        {
>> >          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;
>> > -             pfedge->rflow -= increment;
>> > -             r_pfedge->rflow += increment;
>> >            }
>> >          else
>> >            {
>> >              /* backward edge.  */
>> >              gcc_assert (r_pfedge->type);
>> > -             r_pfedge->rflow += increment;
>> >              r_pfedge->flow -= increment;
>> > -             pfedge->rflow -= increment;
>> >            }
>> >        }
>> >
>> > @@ -1302,6 +1332,60 @@ adjust_cfg_counts (fixup_graph_type *fix
>> >  }
>> >
>> >
>> > +/* 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:
>> > @@ -1330,13 +1414,18 @@ find_minimum_cost_flow (fixup_graph_type
>> >   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;
>> >
>> > -  find_max_flow (fixup_graph, new_entry_index, new_exit_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));
>> > @@ -1352,7 +1441,12 @@ find_minimum_cost_flow (fixup_graph_type
>> >       iteration++;
>> >       if (iteration > MAX_ITER (fixup_graph->num_vertices,
>> >                                 fixup_graph->num_edges))
>> > -        break;
>> > +       {
>> > +         inform (DECL_SOURCE_LOCATION (current_function_decl),
>> > +                 "Exiting profile correction early to avoid excessive "
>> > +                 "compile time");
>> > +         break;
>> > +       }
>> >     }
>> >
>> >   if (dump_file)
>> > Index: gcc/params.def
>> > ===================================================================
>> > --- gcc/params.def      (revision 174456)
>> > +++ gcc/params.def      (working copy)
>> > @@ -977,6 +977,12 @@ DEFPARAM (MIN_PARTITION_SIZE,
>> >          "Size of minimal paritition for WHOPR (in estimated instructions)",
>> >          1000, 0, 0)
>> >
>> > +DEFPARAM (PARAM_MIN_MCF_CANCEL_ITERS,
>> > +         "min-mcf-cancel-iters",
>> > +         "the minimum number of iterations of negative cycle cancellation "
>> > +         "in MCF",
>> > +         10, 1, 0)
>> > +
>> >  /* Diagnostic parameters.  */
>> >
>> >  DEFPARAM (CXX_MAX_NAMESPACES_FOR_DIAGNOSTIC_HELP,
>> >
>> > --
>> > This patch is available for review at http://codereview.appspot.com/4536106
>> >
>

  reply	other threads:[~2011-06-02 18:17 UTC|newest]

Thread overview: 6+ messages / expand[flat|nested]  mbox.gz  Atom feed  top
2011-06-02 18:00 Martin Thuresson
2011-06-02 18:05 ` Xinliang David Li
2011-06-02 18:13   ` Martin Thuresson
2011-06-02 18:17     ` Xinliang David Li [this message]
2011-06-02 18:28       ` Martin Thuresson
2011-06-02 18:09 ` Xinliang David Li

Reply instructions:

You may reply publicly to this message via plain-text email
using any one of the following methods:

* Save the following mbox file, import it into your mail client,
  and reply-to-all from there: mbox

  Avoid top-posting and favor interleaved quoting:
  https://en.wikipedia.org/wiki/Posting_style#Interleaved_style

* Reply using the --to, --cc, and --in-reply-to
  switches of git-send-email(1):

  git send-email \
    --in-reply-to=BANLkTinXZjRxmgsKS4XH07TVpFiR9bynGA@mail.gmail.com \
    --to=davidxl@google.com \
    --cc=gcc-patches@gcc.gnu.org \
    --cc=martint@google.com \
    --cc=reply@codereview.appspotmail.com \
    /path/to/YOUR_REPLY

  https://kernel.org/pub/software/scm/git/docs/git-send-email.html

* If your mail client supports setting the In-Reply-To header
  via mailto: links, try the mailto: link
Be sure your reply has a Subject: header at the top and a blank line before the message body.
This is a public inbox, see mirroring instructions
for how to clone and mirror all data and code used for this inbox;
as well as URLs for read-only IMAP folder(s) and NNTP newsgroup(s).