2010-04-18 Sriraman Tallam <tmsriram@google.com>

[deliverable/binutils-gdb.git] / gold / icf.cc

// icf.cc -- Identical Code Folding.
//
// Copyright 2009, 2010 Free Software Foundation, Inc.
// Written by Sriraman Tallam <tmsriram@google.com>.

// This file is part of gold.

// This program 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 of the License, or
// (at your option) any later version.

// This program 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 this program; if not, write to the Free Software
// Foundation, Inc., 51 Franklin Street - Fifth Floor, Boston,
// MA 02110-1301, USA.

// Identical Code Folding Algorithm
// ----------------------------------
// Detecting identical functions is done here and the basic algorithm
// is as follows.  A checksum is computed on each foldable section using
// its contents and relocations.  If the symbol name corresponding to
// a relocation is known it is used to compute the checksum.  If the
// symbol name is not known the stringified name of the object and the
// section number pointed to by the relocation is used.  The checksums
// are stored as keys in a hash map and a section is identical to some
// other section if its checksum is already present in the hash map.
// Checksum collisions are handled by using a multimap and explicitly
// checking the contents when two sections have the same checksum.
//
// However, two functions A and B with identical text but with
// relocations pointing to different foldable sections can be identical if
// the corresponding foldable sections to which their relocations point to
// turn out to be identical.  Hence, this checksumming process must be
// done repeatedly until convergence is obtained.  Here is an example for
// the following case :
//
// int funcA ()               int funcB ()
// {                          {
//   return foo();              return goo();
// }                          }
//
// The functions funcA and funcB are identical if functions foo() and
// goo() are identical.
//
// Hence, as described above, we repeatedly do the checksumming,
// assigning identical functions to the same group, until convergence is
// obtained.  Now, we have two different ways to do this depending on how
// we initialize.
//
// Algorithm I :
// -----------
// We can start with marking all functions as different and repeatedly do
// the checksumming.  This has the advantage that we do not need to wait
// for convergence. We can stop at any point and correctness will be
// guaranteed although not all cases would have been found.  However, this
// has a problem that some cases can never be found even if it is run until
// convergence.  Here is an example with mutually recursive functions :
//
// int funcA (int a)            int funcB (int a)
// {                            {
//   if (a == 1)                  if (a == 1)
//     return 1;                    return 1;
//   return 1 + funcB(a - 1);     return 1 + funcA(a - 1);
// }                            }
//
// In this example funcA and funcB are identical and one of them could be
// folded into the other.  However, if we start with assuming that funcA
// and funcB are not identical, the algorithm, even after it is run to
// convergence, cannot detect that they are identical.  It should be noted
// that even if the functions were self-recursive, Algorithm I cannot catch
// that they are identical, at least as is.
//
// Algorithm II :
// ------------
// Here we start with marking all functions as identical and then repeat
// the checksumming until convergence.  This can detect the above case
// mentioned above.  It can detect all cases that Algorithm I can and more.
// However, the caveat is that it has to be run to convergence.  It cannot
// be stopped arbitrarily like Algorithm I as correctness cannot be
// guaranteed.  Algorithm II is not implemented.
//
// Algorithm I is used because experiments show that about three
// iterations are more than enough to achieve convergence. Algorithm I can
// handle recursive calls if it is changed to use a special common symbol
// for recursive relocs.  This seems to be the most common case that
// Algorithm I could not catch as is.  Mutually recursive calls are not
// frequent and Algorithm I wins because of its ability to be stopped
// arbitrarily.
//
// Caveat with using function pointers :
// ------------------------------------
//
// Programs using function pointer comparisons/checks should use function
// folding with caution as the result of such comparisons could be different
// when folding takes place.  This could lead to unexpected run-time
// behaviour.
//
// Safe Folding :
// ------------
//
// ICF in safe mode folds only ctors and dtors if their function pointers can
// never be taken.  Also, for X86-64, safe folding uses the relocation
// type to determine if a function's pointer is taken or not and only folds
// functions whose pointers are definitely not taken.
//
// Caveat with safe folding :
// ------------------------
//
// This applies only to x86_64.
//
// Position independent executables are created from PIC objects (compiled
// with -fPIC) and/or PIE objects (compiled with -fPIE).  For PIE objects, the
// relocation types for function pointer taken and a call are the same.
// Now, it is not always possible to tell if an object used in the link of
// a pie executable is a PIC object or a PIE object.  Hence, for pie
// executables, using relocation types to disambiguate function pointers is
// currently disabled.
//
// Further, it is not correct to use safe folding to build non-pie
// executables using PIC/PIE objects.  PIC/PIE objects have different
// relocation types for function pointers than non-PIC objects, and the
// current implementation of safe folding does not handle those relocation
// types.  Hence, if used, functions whose pointers are taken could still be
// folded causing unpredictable run-time behaviour if the pointers were used
// in comparisons.
//
//
//
// How to run  : --icf=[safe|all|none]
// Optional parameters : --icf-iterations <num> --print-icf-sections
//
// Performance : Less than 20 % link-time overhead on industry strength
// applications.  Up to 6 %  text size reductions.

#include "gold.h"
#include "object.h"
#include "gc.h"
#include "icf.h"
#include "symtab.h"
#include "libiberty.h"
#include "demangle.h"

namespace gold
{

// This function determines if a section or a group of identical
// sections has unique contents.  Such unique sections or groups can be
// declared final and need not be processed any further.
// Parameters :
// ID_SECTION : Vector mapping a section index to a Section_id pair.
// IS_SECN_OR_GROUP_UNIQUE : To check if a section or a group of identical
//                            sections is already known to be unique.
// SECTION_CONTENTS : Contains the section's text and relocs to sections
//                    that cannot be folded.   SECTION_CONTENTS are NULL
//                    implies that this function is being called for the
//                    first time before the first iteration of icf.

static void
preprocess_for_unique_sections(const std::vector<Section_id>& id_section,
                               std::vector<bool>* is_secn_or_group_unique,
                               std::vector<std::string>* section_contents)
{
  Unordered_map<uint32_t, unsigned int> uniq_map;
  std::pair<Unordered_map<uint32_t, unsigned int>::iterator, bool>
    uniq_map_insert;

  for (unsigned int i = 0; i < id_section.size(); i++)
    {
      if ((*is_secn_or_group_unique)[i])
        continue;

      uint32_t cksum;
      Section_id secn = id_section[i];
      section_size_type plen;
      if (section_contents == NULL)
        {
          const unsigned char* contents;
          contents = secn.first->section_contents(secn.second,
                                                  &plen,
                                                  false);
          cksum = xcrc32(contents, plen, 0xffffffff);
        }
      else
        {
          const unsigned char* contents_array = reinterpret_cast
            <const unsigned char*>((*section_contents)[i].c_str());
          cksum = xcrc32(contents_array, (*section_contents)[i].length(),
                         0xffffffff);
        }
      uniq_map_insert = uniq_map.insert(std::make_pair(cksum, i));
      if (uniq_map_insert.second)
        {
          (*is_secn_or_group_unique)[i] = true;
        }
      else
        {
          (*is_secn_or_group_unique)[i] = false;
          (*is_secn_or_group_unique)[uniq_map_insert.first->second] = false;
        }
    }
}

// This returns the buffer containing the section's contents, both
// text and relocs.  Relocs are differentiated as those pointing to
// sections that could be folded and those that cannot.  Only relocs
// pointing to sections that could be folded are recomputed on
// subsequent invocations of this function.
// Parameters  :
// FIRST_ITERATION    : true if it is the first invocation.
// SECN               : Section for which contents are desired.
// SECTION_NUM        : Unique section number of this section.
// NUM_TRACKED_RELOCS : Vector reference to store the number of relocs
//                      to ICF sections.
// KEPT_SECTION_ID    : Vector which maps folded sections to kept sections.
// SECTION_CONTENTS   : Store the section's text and relocs to non-ICF
//                      sections.

static std::string
get_section_contents(bool first_iteration,
                     const Section_id& secn,
                     unsigned int section_num,
                     unsigned int* num_tracked_relocs,
                     Symbol_table* symtab,
                     const std::vector<unsigned int>& kept_section_id,
                     std::vector<std::string>* section_contents)
{
  section_size_type plen;
  const unsigned char* contents = NULL;

  if (first_iteration)
    {
      contents = secn.first->section_contents(secn.second,
                                              &plen,
                                              false);
    }

  // The buffer to hold all the contents including relocs.  A checksum
  // is then computed on this buffer.
  std::string buffer;
  std::string icf_reloc_buffer;

  if (num_tracked_relocs)
    *num_tracked_relocs = 0;

  Icf::Reloc_info_list& reloc_info_list = 
    symtab->icf()->reloc_info_list();

  Icf::Reloc_info_list::iterator it_reloc_info_list =
    reloc_info_list.find(secn);

  buffer.clear();
  icf_reloc_buffer.clear();

  // Process relocs and put them into the buffer.

  if (it_reloc_info_list != reloc_info_list.end())
    {
      Icf::Sections_reachable_info v =
        (it_reloc_info_list->second).section_info;
      Icf::Symbol_info s = (it_reloc_info_list->second).symbol_info;
      Icf::Addend_info a = (it_reloc_info_list->second).addend_info;
      Icf::Offset_info o = (it_reloc_info_list->second).offset_info;
      Icf::Sections_reachable_info::iterator it_v = v.begin();
      Icf::Symbol_info::iterator it_s = s.begin();
      Icf::Addend_info::iterator it_a = a.begin();
      Icf::Offset_info::iterator it_o = o.begin();

      for (; it_v != v.end(); ++it_v, ++it_s, ++it_a, ++it_o)
        {
          // ADDEND_STR stores the symbol value and addend and offset,
          // each atmost 16 hex digits long.  it_a points to a pair
          // where first is the symbol value and second is the
          // addend.
          char addend_str[50];

          // It would be nice if we could use format macros in inttypes.h
          // here but there are not in ISO/IEC C++ 1998.
          snprintf(addend_str, sizeof(addend_str), "%llx %llx %llux",
                   static_cast<long long>((*it_a).first),
                   static_cast<long long>((*it_a).second),
                   static_cast<unsigned long long>(*it_o));
          Section_id reloc_secn(it_v->first, it_v->second);

          // If this reloc turns back and points to the same section,
          // like a recursive call, use a special symbol to mark this.
          if (reloc_secn.first == secn.first
              && reloc_secn.second == secn.second)
            {
              if (first_iteration)
                {
                  buffer.append("R");
                  buffer.append(addend_str);
                  buffer.append("@");
                }
              continue;
            }
          Icf::Uniq_secn_id_map& section_id_map =
            symtab->icf()->section_to_int_map();
          Icf::Uniq_secn_id_map::iterator section_id_map_it =
            section_id_map.find(reloc_secn);
          bool is_sym_preemptible = (*it_s != NULL
                                     && !(*it_s)->is_from_dynobj()
                                     && !(*it_s)->is_undefined()
                                     && (*it_s)->is_preemptible());
          if (!is_sym_preemptible
              && section_id_map_it != section_id_map.end())
            {
              // This is a reloc to a section that might be folded.
              if (num_tracked_relocs)
                (*num_tracked_relocs)++;

              char kept_section_str[10];
              unsigned int secn_id = section_id_map_it->second;
              snprintf(kept_section_str, sizeof(kept_section_str), "%u",
                       kept_section_id[secn_id]);
              if (first_iteration)
                {
                  buffer.append("ICF_R");
                  buffer.append(addend_str);
                }
              icf_reloc_buffer.append(kept_section_str);
              // Append the addend.
              icf_reloc_buffer.append(addend_str);
              icf_reloc_buffer.append("@");
            }
          else
            {
              // This is a reloc to a section that cannot be folded.
              // Process it only in the first iteration.
              if (!first_iteration)
                continue;

              uint64_t secn_flags = (it_v->first)->section_flags(it_v->second);
              // This reloc points to a merge section.  Hash the
              // contents of this section.
              if ((secn_flags & elfcpp::SHF_MERGE) != 0)
                {
                  uint64_t entsize =
                    (it_v->first)->section_entsize(it_v->second);
                  long long offset = it_a->first;

                  unsigned long long addend = it_a->second;
                  // Ignoring the addend when it is a negative value.  See the 
                  // comments in Merged_symbol_value::Value in object.h.
                  if (addend < 0xffffff00)
                    offset = offset + addend;

                  section_size_type secn_len;
                  const unsigned char* str_contents =
                  (it_v->first)->section_contents(it_v->second,
                                                  &secn_len,
                                                  false) + offset;
                  if ((secn_flags & elfcpp::SHF_STRINGS) != 0)
                    {
                      // String merge section.
                      const char* str_char =
                        reinterpret_cast<const char*>(str_contents);
                      switch(entsize)
                        {
                        case 1:
                          {
                            buffer.append(str_char);
                            break;
                          }
                        case 2:
                          {
                            const uint16_t* ptr_16 =
                              reinterpret_cast<const uint16_t*>(str_char);
                            unsigned int strlen_16 = 0;
                            // Find the NULL character.
                            while(*(ptr_16 + strlen_16) != 0)
                                strlen_16++;
                            buffer.append(str_char, strlen_16 * 2);
                          }
                          break;
                        case 4:
                          {
                            const uint32_t* ptr_32 =
                              reinterpret_cast<const uint32_t*>(str_char);
                            unsigned int strlen_32 = 0;
                            // Find the NULL character.
                            while(*(ptr_32 + strlen_32) != 0)
                                strlen_32++;
                            buffer.append(str_char, strlen_32 * 4);
                          }
                          break;
                        default:
                          gold_unreachable();
                        }
                    }
                  else
                    {
                      // Use the entsize to determine the length.
                      buffer.append(reinterpret_cast<const 
                                                     char*>(str_contents),
                                    entsize);
                    }
                  buffer.append("@");
                }
              else if ((*it_s) != NULL)
                {
                  // If symbol name is available use that.
                  const char *sym_name = (*it_s)->name();
                  buffer.append(sym_name);
                  // Append the addend.
                  buffer.append(addend_str);
                  buffer.append("@");
                }
              else
                {
                  // Symbol name is not available, like for a local symbol,
                  // use object and section id.
                  buffer.append(it_v->first->name());
                  char secn_id[10];
                  snprintf(secn_id, sizeof(secn_id), "%u",it_v->second);
                  buffer.append(secn_id);
                  // Append the addend.
                  buffer.append(addend_str);
                  buffer.append("@");
                }
            }
        }
    }

  if (first_iteration)
    {
      buffer.append("Contents = ");
      buffer.append(reinterpret_cast<const char*>(contents), plen);
      // Store the section contents that dont change to avoid recomputing
      // during the next call to this function.
      (*section_contents)[section_num] = buffer;
    }
  else
    {
      gold_assert(buffer.empty());
      // Reuse the contents computed in the previous iteration.
      buffer.append((*section_contents)[section_num]);
    }

  buffer.append(icf_reloc_buffer);
  return buffer;
}

// This function computes a checksum on each section to detect and form
// groups of identical sections.  The first iteration does this for all 
// sections.
// Further iterations do this only for the kept sections from each group to
// determine if larger groups of identical sections could be formed.  The
// first section in each group is the kept section for that group.
//
// CRC32 is the checksumming algorithm and can have collisions.  That is,
// two sections with different contents can have the same checksum. Hence,
// a multimap is used to maintain more than one group of checksum
// identical sections.  A section is added to a group only after its
// contents are explicitly compared with the kept section of the group.
//
// Parameters  :
// ITERATION_NUM           : Invocation instance of this function.
// NUM_TRACKED_RELOCS : Vector reference to store the number of relocs
//                      to ICF sections.
// KEPT_SECTION_ID    : Vector which maps folded sections to kept sections.
// ID_SECTION         : Vector mapping a section to an unique integer.
// IS_SECN_OR_GROUP_UNIQUE : To check if a section or a group of identical
//                            sectionsis already known to be unique.
// SECTION_CONTENTS   : Store the section's text and relocs to non-ICF
//                      sections.

static bool
match_sections(unsigned int iteration_num,
               Symbol_table* symtab,
               std::vector<unsigned int>* num_tracked_relocs,
               std::vector<unsigned int>* kept_section_id,
               const std::vector<Section_id>& id_section,
               std::vector<bool>* is_secn_or_group_unique,
               std::vector<std::string>* section_contents)
{
  Unordered_multimap<uint32_t, unsigned int> section_cksum;
  std::pair<Unordered_multimap<uint32_t, unsigned int>::iterator,
            Unordered_multimap<uint32_t, unsigned int>::iterator> key_range;
  bool converged = true;

  if (iteration_num == 1)
    preprocess_for_unique_sections(id_section,
                                   is_secn_or_group_unique,
                                   NULL);
  else
    preprocess_for_unique_sections(id_section,
                                   is_secn_or_group_unique,
                                   section_contents);

  std::vector<std::string> full_section_contents;

  for (unsigned int i = 0; i < id_section.size(); i++)
    {
      full_section_contents.push_back("");
      if ((*is_secn_or_group_unique)[i])
        continue;

      Section_id secn = id_section[i];
      std::string this_secn_contents;
      uint32_t cksum;
      if (iteration_num == 1)
        {
          unsigned int num_relocs = 0;
          this_secn_contents = get_section_contents(true, secn, i, &num_relocs,
                                                    symtab, (*kept_section_id),
                                                    section_contents);
          (*num_tracked_relocs)[i] = num_relocs;
        }
      else
        {
          if ((*kept_section_id)[i] != i)
            {
              // This section is already folded into something.  See
              // if it should point to a different kept section.
              unsigned int kept_section = (*kept_section_id)[i];
              if (kept_section != (*kept_section_id)[kept_section])
                {
                  (*kept_section_id)[i] = (*kept_section_id)[kept_section];
                }
              continue;
            }
          this_secn_contents = get_section_contents(false, secn, i, NULL,
                                                    symtab, (*kept_section_id),
                                                    section_contents);
        }

      const unsigned char* this_secn_contents_array =
            reinterpret_cast<const unsigned char*>(this_secn_contents.c_str());
      cksum = xcrc32(this_secn_contents_array, this_secn_contents.length(),
                     0xffffffff);
      size_t count = section_cksum.count(cksum);

      if (count == 0)
        {
          // Start a group with this cksum.
          section_cksum.insert(std::make_pair(cksum, i));
          full_section_contents[i] = this_secn_contents;
        }
      else
        {
          key_range = section_cksum.equal_range(cksum);
          Unordered_multimap<uint32_t, unsigned int>::iterator it;
          // Search all the groups with this cksum for a match.
          for (it = key_range.first; it != key_range.second; ++it)
            {
              unsigned int kept_section = it->second;
              if (full_section_contents[kept_section].length()
                  != this_secn_contents.length())
                  continue;
              if (memcmp(full_section_contents[kept_section].c_str(),
                         this_secn_contents.c_str(),
                         this_secn_contents.length()) != 0)
                  continue;
              (*kept_section_id)[i] = kept_section;
              converged = false;
              break;
            }
          if (it == key_range.second)
            {
              // Create a new group for this cksum.
              section_cksum.insert(std::make_pair(cksum, i));
              full_section_contents[i] = this_secn_contents;
            }
        }
      // If there are no relocs to foldable sections do not process
      // this section any further.
      if (iteration_num == 1 && (*num_tracked_relocs)[i] == 0)
        (*is_secn_or_group_unique)[i] = true;
    }

  return converged;
}

// During safe icf (--icf=safe), only fold functions that are ctors or dtors.
// This function returns true if the mangled function name is a ctor or a
// dtor.

static bool
is_function_ctor_or_dtor(const char* mangled_func_name)
{
  if ((is_prefix_of("_ZN", mangled_func_name)
       || is_prefix_of("_ZZ", mangled_func_name))
      && (is_gnu_v3_mangled_ctor(mangled_func_name)
          || is_gnu_v3_mangled_dtor(mangled_func_name)))
    {
      return true;
    }
  return false;
}

// This is the main ICF function called in gold.cc.  This does the
// initialization and calls match_sections repeatedly (twice by default)
// which computes the crc checksums and detects identical functions.

void
Icf::find_identical_sections(const Input_objects* input_objects,
                             Symbol_table* symtab)
{
  unsigned int section_num = 0;
  std::vector<unsigned int> num_tracked_relocs;
  std::vector<bool> is_secn_or_group_unique;
  std::vector<std::string> section_contents;
  const Target& target = parameters->target();

  // Decide which sections are possible candidates first.

  for (Input_objects::Relobj_iterator p = input_objects->relobj_begin();
       p != input_objects->relobj_end();
       ++p)
    {
      for (unsigned int i = 0;i < (*p)->shnum(); ++i)
        {
          const char* section_name = (*p)->section_name(i).c_str();
          if (!is_section_foldable_candidate(section_name))
            continue;
          if (!(*p)->is_section_included(i))
            continue;
          if (parameters->options().gc_sections()
              && symtab->gc()->is_section_garbage(*p, i))
              continue;
          const char* mangled_func_name = strrchr(section_name, '.');
          gold_assert(mangled_func_name != NULL);
          // With --icf=safe, check if the mangled function name is a ctor
          // or a dtor.  The mangled function name can be obtained from the
          // section name by stripping the section prefix.
          if (parameters->options().icf_safe_folding()
              && !is_function_ctor_or_dtor(mangled_func_name + 1)
              && (!target.can_check_for_function_pointers()
                  || section_has_function_pointers(*p, i)))
            {
              continue;
            }
          this->id_section_.push_back(Section_id(*p, i));
          this->section_id_[Section_id(*p, i)] = section_num;
          this->kept_section_id_.push_back(section_num);
          num_tracked_relocs.push_back(0);
          is_secn_or_group_unique.push_back(false);
          section_contents.push_back("");
          section_num++;
        }
    }

  unsigned int num_iterations = 0;

  // Default number of iterations to run ICF is 2.
  unsigned int max_iterations = (parameters->options().icf_iterations() > 0)
                            ? parameters->options().icf_iterations()
                            : 2;

  bool converged = false;

  while (!converged && (num_iterations < max_iterations))
    {
      num_iterations++;
      converged = match_sections(num_iterations, symtab,
                                 &num_tracked_relocs, &this->kept_section_id_,
                                 this->id_section_, &is_secn_or_group_unique,
                                 &section_contents);
    }

  if (parameters->options().print_icf_sections())
    {
      if (converged)
        gold_info(_("%s: ICF Converged after %u iteration(s)"),
                  program_name, num_iterations);
      else
        gold_info(_("%s: ICF stopped after %u iteration(s)"),
                  program_name, num_iterations);
    }

  // Unfold --keep-unique symbols.
  for (options::String_set::const_iterator p =
         parameters->options().keep_unique_begin();
       p != parameters->options().keep_unique_end();
       ++p)
    {
      const char* name = p->c_str();
      Symbol* sym = symtab->lookup(name);
      if (sym == NULL)
        {
          gold_warning(_("Could not find symbol %s to unfold\n"), name);
        }
      else if (sym->source() == Symbol::FROM_OBJECT 
               && !sym->object()->is_dynamic())
        {
          Object* obj = sym->object();
          bool is_ordinary;
          unsigned int shndx = sym->shndx(&is_ordinary);
          if (is_ordinary)
            {
              this->unfold_section(obj, shndx);
            }
        }

    }

  this->icf_ready();
}

// Unfolds the section denoted by OBJ and SHNDX if folded.

void
Icf::unfold_section(Object* obj, unsigned int shndx)
{
  Section_id secn(obj, shndx);
  Uniq_secn_id_map::iterator it = this->section_id_.find(secn);
  if (it == this->section_id_.end())
    return;
  unsigned int section_num = it->second;
  unsigned int kept_section_id = this->kept_section_id_[section_num];
  if (kept_section_id != section_num)
    this->kept_section_id_[section_num] = section_num;
}

// This function determines if the section corresponding to the
// given object and index is folded based on if the kept section
// is different from this section.

bool
Icf::is_section_folded(Object* obj, unsigned int shndx)
{
  Section_id secn(obj, shndx);
  Uniq_secn_id_map::iterator it = this->section_id_.find(secn);
  if (it == this->section_id_.end())
    return false;
  unsigned int section_num = it->second;
  unsigned int kept_section_id = this->kept_section_id_[section_num];
  return kept_section_id != section_num;
}

// This function returns the folded section for the given section.

Section_id
Icf::get_folded_section(Object* dup_obj, unsigned int dup_shndx)
{
  Section_id dup_secn(dup_obj, dup_shndx);
  Uniq_secn_id_map::iterator it = this->section_id_.find(dup_secn);
  gold_assert(it != this->section_id_.end());
  unsigned int section_num = it->second;
  unsigned int kept_section_id = this->kept_section_id_[section_num];
  Section_id folded_section = this->id_section_[kept_section_id];
  return folded_section;
}

} // End of namespace gold.