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1 // icf.cc -- Identical Code Folding.
2 //
3 // Copyright 2009, 2010 Free Software Foundation, Inc.
4 // Written by Sriraman Tallam <tmsriram@google.com>.
6 // This file is part of gold.
8 // This program is free software; you can redistribute it and/or modify
9 // it under the terms of the GNU General Public License as published by
10 // the Free Software Foundation; either version 3 of the License, or
11 // (at your option) any later version.
13 // This program is distributed in the hope that it will be useful,
14 // but WITHOUT ANY WARRANTY; without even the implied warranty of
15 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
16 // GNU General Public License for more details.
18 // You should have received a copy of the GNU General Public License
19 // along with this program; if not, write to the Free Software
20 // Foundation, Inc., 51 Franklin Street - Fifth Floor, Boston,
21 // MA 02110-1301, USA.
23 // Identical Code Folding Algorithm
24 // ----------------------------------
25 // Detecting identical functions is done here and the basic algorithm
26 // is as follows. A checksum is computed on each foldable section using
27 // its contents and relocations. If the symbol name corresponding to
28 // a relocation is known it is used to compute the checksum. If the
29 // symbol name is not known the stringified name of the object and the
30 // section number pointed to by the relocation is used. The checksums
31 // are stored as keys in a hash map and a section is identical to some
32 // other section if its checksum is already present in the hash map.
33 // Checksum collisions are handled by using a multimap and explicitly
34 // checking the contents when two sections have the same checksum.
36 // However, two functions A and B with identical text but with
37 // relocations pointing to different foldable sections can be identical if
38 // the corresponding foldable sections to which their relocations point to
39 // turn out to be identical. Hence, this checksumming process must be
40 // done repeatedly until convergence is obtained. Here is an example for
41 // the following case :
43 // int funcA () int funcB ()
44 // { {
45 // return foo(); return goo();
46 // } }
48 // The functions funcA and funcB are identical if functions foo() and
49 // goo() are identical.
51 // Hence, as described above, we repeatedly do the checksumming,
52 // assigning identical functions to the same group, until convergence is
53 // obtained. Now, we have two different ways to do this depending on how
54 // we initialize.
56 // Algorithm I :
57 // -----------
58 // We can start with marking all functions as different and repeatedly do
59 // the checksumming. This has the advantage that we do not need to wait
60 // for convergence. We can stop at any point and correctness will be
61 // guaranteed although not all cases would have been found. However, this
62 // has a problem that some cases can never be found even if it is run until
63 // convergence. Here is an example with mutually recursive functions :
65 // int funcA (int a) int funcB (int a)
66 // { {
67 // if (a == 1) if (a == 1)
68 // return 1; return 1;
69 // return 1 + funcB(a - 1); return 1 + funcA(a - 1);
70 // } }
72 // In this example funcA and funcB are identical and one of them could be
73 // folded into the other. However, if we start with assuming that funcA
74 // and funcB are not identical, the algorithm, even after it is run to
75 // convergence, cannot detect that they are identical. It should be noted
76 // that even if the functions were self-recursive, Algorithm I cannot catch
77 // that they are identical, at least as is.
79 // Algorithm II :
80 // ------------
81 // Here we start with marking all functions as identical and then repeat
82 // the checksumming until convergence. This can detect the above case
83 // mentioned above. It can detect all cases that Algorithm I can and more.
84 // However, the caveat is that it has to be run to convergence. It cannot
85 // be stopped arbitrarily like Algorithm I as correctness cannot be
86 // guaranteed. Algorithm II is not implemented.
88 // Algorithm I is used because experiments show that about three
89 // iterations are more than enough to achieve convergence. Algorithm I can
90 // handle recursive calls if it is changed to use a special common symbol
91 // for recursive relocs. This seems to be the most common case that
92 // Algorithm I could not catch as is. Mutually recursive calls are not
93 // frequent and Algorithm I wins because of its ability to be stopped
94 // arbitrarily.
96 // Caveat with using function pointers :
97 // ------------------------------------
99 // Programs using function pointer comparisons/checks should use function
100 // folding with caution as the result of such comparisons could be different
101 // when folding takes place. This could lead to unexpected run-time
102 // behaviour.
104 // Safe Folding :
105 // ------------
107 // ICF in safe mode folds only ctors and dtors if their function pointers can
108 // never be taken. Also, for X86-64, safe folding uses the relocation
109 // type to determine if a function's pointer is taken or not and only folds
110 // functions whose pointers are definitely not taken.
112 // Caveat with safe folding :
113 // ------------------------
115 // This applies only to x86_64.
117 // Position independent executables are created from PIC objects (compiled
118 // with -fPIC) and/or PIE objects (compiled with -fPIE). For PIE objects, the
119 // relocation types for function pointer taken and a call are the same.
120 // Now, it is not always possible to tell if an object used in the link of
121 // a pie executable is a PIC object or a PIE object. Hence, for pie
122 // executables, using relocation types to disambiguate function pointers is
123 // currently disabled.
125 // Further, it is not correct to use safe folding to build non-pie
126 // executables using PIC/PIE objects. PIC/PIE objects have different
127 // relocation types for function pointers than non-PIC objects, and the
128 // current implementation of safe folding does not handle those relocation
129 // types. Hence, if used, functions whose pointers are taken could still be
130 // folded causing unpredictable run-time behaviour if the pointers were used
131 // in comparisons.
135 // How to run : --icf=[safe|all|none]
136 // Optional parameters : --icf-iterations <num> --print-icf-sections
138 // Performance : Less than 20 % link-time overhead on industry strength
139 // applications. Up to 6 % text size reductions.
141 #include "gold.h"
142 #include "object.h"
143 #include "gc.h"
144 #include "icf.h"
145 #include "symtab.h"
146 #include "libiberty.h"
147 #include "demangle.h"
149 namespace gold
152 // This function determines if a section or a group of identical
153 // sections has unique contents. Such unique sections or groups can be
154 // declared final and need not be processed any further.
155 // Parameters :
156 // ID_SECTION : Vector mapping a section index to a Section_id pair.
157 // IS_SECN_OR_GROUP_UNIQUE : To check if a section or a group of identical
158 // sections is already known to be unique.
159 // SECTION_CONTENTS : Contains the section's text and relocs to sections
160 // that cannot be folded. SECTION_CONTENTS are NULL
161 // implies that this function is being called for the
162 // first time before the first iteration of icf.
164 static void
165 preprocess_for_unique_sections(const std::vector<Section_id>& id_section,
166 std::vector<bool>* is_secn_or_group_unique,
167 std::vector<std::string>* section_contents)
169 Unordered_map<uint32_t, unsigned int> uniq_map;
170 std::pair<Unordered_map<uint32_t, unsigned int>::iterator, bool>
171 uniq_map_insert;
173 for (unsigned int i = 0; i < id_section.size(); i++)
175 if ((*is_secn_or_group_unique)[i])
176 continue;
178 uint32_t cksum;
179 Section_id secn = id_section[i];
180 section_size_type plen;
181 if (section_contents == NULL)
183 const unsigned char* contents;
184 contents = secn.first->section_contents(secn.second,
185 &plen,
186 false);
187 cksum = xcrc32(contents, plen, 0xffffffff);
189 else
191 const unsigned char* contents_array = reinterpret_cast
192 <const unsigned char*>((*section_contents)[i].c_str());
193 cksum = xcrc32(contents_array, (*section_contents)[i].length(),
194 0xffffffff);
196 uniq_map_insert = uniq_map.insert(std::make_pair(cksum, i));
197 if (uniq_map_insert.second)
199 (*is_secn_or_group_unique)[i] = true;
201 else
203 (*is_secn_or_group_unique)[i] = false;
204 (*is_secn_or_group_unique)[uniq_map_insert.first->second] = false;
209 // This returns the buffer containing the section's contents, both
210 // text and relocs. Relocs are differentiated as those pointing to
211 // sections that could be folded and those that cannot. Only relocs
212 // pointing to sections that could be folded are recomputed on
213 // subsequent invocations of this function.
214 // Parameters :
215 // FIRST_ITERATION : true if it is the first invocation.
216 // SECN : Section for which contents are desired.
217 // SECTION_NUM : Unique section number of this section.
218 // NUM_TRACKED_RELOCS : Vector reference to store the number of relocs
219 // to ICF sections.
220 // KEPT_SECTION_ID : Vector which maps folded sections to kept sections.
221 // SECTION_CONTENTS : Store the section's text and relocs to non-ICF
222 // sections.
224 static std::string
225 get_section_contents(bool first_iteration,
226 const Section_id& secn,
227 unsigned int section_num,
228 unsigned int* num_tracked_relocs,
229 Symbol_table* symtab,
230 const std::vector<unsigned int>& kept_section_id,
231 std::vector<std::string>* section_contents)
233 section_size_type plen;
234 const unsigned char* contents = NULL;
236 if (first_iteration)
238 contents = secn.first->section_contents(secn.second,
239 &plen,
240 false);
243 // The buffer to hold all the contents including relocs. A checksum
244 // is then computed on this buffer.
245 std::string buffer;
246 std::string icf_reloc_buffer;
248 if (num_tracked_relocs)
249 *num_tracked_relocs = 0;
251 Icf::Reloc_info_list& reloc_info_list =
252 symtab->icf()->reloc_info_list();
254 Icf::Reloc_info_list::iterator it_reloc_info_list =
255 reloc_info_list.find(secn);
257 buffer.clear();
258 icf_reloc_buffer.clear();
260 // Process relocs and put them into the buffer.
262 if (it_reloc_info_list != reloc_info_list.end())
264 Icf::Sections_reachable_info v =
265 (it_reloc_info_list->second).section_info;
266 Icf::Symbol_info s = (it_reloc_info_list->second).symbol_info;
267 Icf::Addend_info a = (it_reloc_info_list->second).addend_info;
268 Icf::Offset_info o = (it_reloc_info_list->second).offset_info;
269 Icf::Sections_reachable_info::iterator it_v = v.begin();
270 Icf::Symbol_info::iterator it_s = s.begin();
271 Icf::Addend_info::iterator it_a = a.begin();
272 Icf::Offset_info::iterator it_o = o.begin();
274 for (; it_v != v.end(); ++it_v, ++it_s, ++it_a, ++it_o)
276 // ADDEND_STR stores the symbol value and addend and offset,
277 // each atmost 16 hex digits long. it_a points to a pair
278 // where first is the symbol value and second is the
279 // addend.
280 char addend_str[50];
282 // It would be nice if we could use format macros in inttypes.h
283 // here but there are not in ISO/IEC C++ 1998.
284 snprintf(addend_str, sizeof(addend_str), "%llx %llx %llux",
285 static_cast<long long>((*it_a).first),
286 static_cast<long long>((*it_a).second),
287 static_cast<unsigned long long>(*it_o));
288 Section_id reloc_secn(it_v->first, it_v->second);
290 // If this reloc turns back and points to the same section,
291 // like a recursive call, use a special symbol to mark this.
292 if (reloc_secn.first == secn.first
293 && reloc_secn.second == secn.second)
295 if (first_iteration)
297 buffer.append("R");
298 buffer.append(addend_str);
299 buffer.append("@");
301 continue;
303 Icf::Uniq_secn_id_map& section_id_map =
304 symtab->icf()->section_to_int_map();
305 Icf::Uniq_secn_id_map::iterator section_id_map_it =
306 section_id_map.find(reloc_secn);
307 if (section_id_map_it != section_id_map.end())
309 // This is a reloc to a section that might be folded.
310 if (num_tracked_relocs)
311 (*num_tracked_relocs)++;
313 char kept_section_str[10];
314 unsigned int secn_id = section_id_map_it->second;
315 snprintf(kept_section_str, sizeof(kept_section_str), "%u",
316 kept_section_id[secn_id]);
317 if (first_iteration)
319 buffer.append("ICF_R");
320 buffer.append(addend_str);
322 icf_reloc_buffer.append(kept_section_str);
323 // Append the addend.
324 icf_reloc_buffer.append(addend_str);
325 icf_reloc_buffer.append("@");
327 else
329 // This is a reloc to a section that cannot be folded.
330 // Process it only in the first iteration.
331 if (!first_iteration)
332 continue;
334 uint64_t secn_flags = (it_v->first)->section_flags(it_v->second);
335 // This reloc points to a merge section. Hash the
336 // contents of this section.
337 if ((secn_flags & elfcpp::SHF_MERGE) != 0)
339 uint64_t entsize =
340 (it_v->first)->section_entsize(it_v->second);
341 long long offset = it_a->first + it_a->second;
342 section_size_type secn_len;
343 const unsigned char* str_contents =
344 (it_v->first)->section_contents(it_v->second,
345 &secn_len,
346 false) + offset;
347 if ((secn_flags & elfcpp::SHF_STRINGS) != 0)
349 // String merge section.
350 const char* str_char =
351 reinterpret_cast<const char*>(str_contents);
352 switch(entsize)
354 case 1:
356 buffer.append(str_char);
357 break;
359 case 2:
361 const uint16_t* ptr_16 =
362 reinterpret_cast<const uint16_t*>(str_char);
363 unsigned int strlen_16 = 0;
364 // Find the NULL character.
365 while(*(ptr_16 + strlen_16) != 0)
366 strlen_16++;
367 buffer.append(str_char, strlen_16 * 2);
369 break;
370 case 4:
372 const uint32_t* ptr_32 =
373 reinterpret_cast<const uint32_t*>(str_char);
374 unsigned int strlen_32 = 0;
375 // Find the NULL character.
376 while(*(ptr_32 + strlen_32) != 0)
377 strlen_32++;
378 buffer.append(str_char, strlen_32 * 4);
380 break;
381 default:
382 gold_unreachable();
385 else
387 // Use the entsize to determine the length.
388 buffer.append(reinterpret_cast<const
389 char*>(str_contents),
390 entsize);
393 else if ((*it_s) != NULL)
395 // If symbol name is available use that.
396 const char *sym_name = (*it_s)->name();
397 buffer.append(sym_name);
398 // Append the addend.
399 buffer.append(addend_str);
400 buffer.append("@");
402 else
404 // Symbol name is not available, like for a local symbol,
405 // use object and section id.
406 buffer.append(it_v->first->name());
407 char secn_id[10];
408 snprintf(secn_id, sizeof(secn_id), "%u",it_v->second);
409 buffer.append(secn_id);
410 // Append the addend.
411 buffer.append(addend_str);
412 buffer.append("@");
418 if (first_iteration)
420 buffer.append("Contents = ");
421 buffer.append(reinterpret_cast<const char*>(contents), plen);
422 // Store the section contents that dont change to avoid recomputing
423 // during the next call to this function.
424 (*section_contents)[section_num] = buffer;
426 else
428 gold_assert(buffer.empty());
429 // Reuse the contents computed in the previous iteration.
430 buffer.append((*section_contents)[section_num]);
433 buffer.append(icf_reloc_buffer);
434 return buffer;
437 // This function computes a checksum on each section to detect and form
438 // groups of identical sections. The first iteration does this for all
439 // sections.
440 // Further iterations do this only for the kept sections from each group to
441 // determine if larger groups of identical sections could be formed. The
442 // first section in each group is the kept section for that group.
444 // CRC32 is the checksumming algorithm and can have collisions. That is,
445 // two sections with different contents can have the same checksum. Hence,
446 // a multimap is used to maintain more than one group of checksum
447 // identical sections. A section is added to a group only after its
448 // contents are explicitly compared with the kept section of the group.
450 // Parameters :
451 // ITERATION_NUM : Invocation instance of this function.
452 // NUM_TRACKED_RELOCS : Vector reference to store the number of relocs
453 // to ICF sections.
454 // KEPT_SECTION_ID : Vector which maps folded sections to kept sections.
455 // ID_SECTION : Vector mapping a section to an unique integer.
456 // IS_SECN_OR_GROUP_UNIQUE : To check if a section or a group of identical
457 // sectionsis already known to be unique.
458 // SECTION_CONTENTS : Store the section's text and relocs to non-ICF
459 // sections.
461 static bool
462 match_sections(unsigned int iteration_num,
463 Symbol_table* symtab,
464 std::vector<unsigned int>* num_tracked_relocs,
465 std::vector<unsigned int>* kept_section_id,
466 const std::vector<Section_id>& id_section,
467 std::vector<bool>* is_secn_or_group_unique,
468 std::vector<std::string>* section_contents)
470 Unordered_multimap<uint32_t, unsigned int> section_cksum;
471 std::pair<Unordered_multimap<uint32_t, unsigned int>::iterator,
472 Unordered_multimap<uint32_t, unsigned int>::iterator> key_range;
473 bool converged = true;
475 if (iteration_num == 1)
476 preprocess_for_unique_sections(id_section,
477 is_secn_or_group_unique,
478 NULL);
479 else
480 preprocess_for_unique_sections(id_section,
481 is_secn_or_group_unique,
482 section_contents);
484 std::vector<std::string> full_section_contents;
486 for (unsigned int i = 0; i < id_section.size(); i++)
488 full_section_contents.push_back("");
489 if ((*is_secn_or_group_unique)[i])
490 continue;
492 Section_id secn = id_section[i];
493 std::string this_secn_contents;
494 uint32_t cksum;
495 if (iteration_num == 1)
497 unsigned int num_relocs = 0;
498 this_secn_contents = get_section_contents(true, secn, i, &num_relocs,
499 symtab, (*kept_section_id),
500 section_contents);
501 (*num_tracked_relocs)[i] = num_relocs;
503 else
505 if ((*kept_section_id)[i] != i)
507 // This section is already folded into something. See
508 // if it should point to a different kept section.
509 unsigned int kept_section = (*kept_section_id)[i];
510 if (kept_section != (*kept_section_id)[kept_section])
512 (*kept_section_id)[i] = (*kept_section_id)[kept_section];
514 continue;
516 this_secn_contents = get_section_contents(false, secn, i, NULL,
517 symtab, (*kept_section_id),
518 section_contents);
521 const unsigned char* this_secn_contents_array =
522 reinterpret_cast<const unsigned char*>(this_secn_contents.c_str());
523 cksum = xcrc32(this_secn_contents_array, this_secn_contents.length(),
524 0xffffffff);
525 size_t count = section_cksum.count(cksum);
527 if (count == 0)
529 // Start a group with this cksum.
530 section_cksum.insert(std::make_pair(cksum, i));
531 full_section_contents[i] = this_secn_contents;
533 else
535 key_range = section_cksum.equal_range(cksum);
536 Unordered_multimap<uint32_t, unsigned int>::iterator it;
537 // Search all the groups with this cksum for a match.
538 for (it = key_range.first; it != key_range.second; ++it)
540 unsigned int kept_section = it->second;
541 if (full_section_contents[kept_section].length()
542 != this_secn_contents.length())
543 continue;
544 if (memcmp(full_section_contents[kept_section].c_str(),
545 this_secn_contents.c_str(),
546 this_secn_contents.length()) != 0)
547 continue;
548 (*kept_section_id)[i] = kept_section;
549 converged = false;
550 break;
552 if (it == key_range.second)
554 // Create a new group for this cksum.
555 section_cksum.insert(std::make_pair(cksum, i));
556 full_section_contents[i] = this_secn_contents;
559 // If there are no relocs to foldable sections do not process
560 // this section any further.
561 if (iteration_num == 1 && (*num_tracked_relocs)[i] == 0)
562 (*is_secn_or_group_unique)[i] = true;
565 return converged;
568 // During safe icf (--icf=safe), only fold functions that are ctors or dtors.
569 // This function returns true if the mangled function name is a ctor or a
570 // dtor.
572 static bool
573 is_function_ctor_or_dtor(const char* mangled_func_name)
575 if ((is_prefix_of("_ZN", mangled_func_name)
576 || is_prefix_of("_ZZ", mangled_func_name))
577 && (is_gnu_v3_mangled_ctor(mangled_func_name)
578 || is_gnu_v3_mangled_dtor(mangled_func_name)))
580 return true;
582 return false;
585 // This is the main ICF function called in gold.cc. This does the
586 // initialization and calls match_sections repeatedly (twice by default)
587 // which computes the crc checksums and detects identical functions.
589 void
590 Icf::find_identical_sections(const Input_objects* input_objects,
591 Symbol_table* symtab)
593 unsigned int section_num = 0;
594 std::vector<unsigned int> num_tracked_relocs;
595 std::vector<bool> is_secn_or_group_unique;
596 std::vector<std::string> section_contents;
597 const Target& target = parameters->target();
599 // Decide which sections are possible candidates first.
601 for (Input_objects::Relobj_iterator p = input_objects->relobj_begin();
602 p != input_objects->relobj_end();
603 ++p)
605 for (unsigned int i = 0;i < (*p)->shnum(); ++i)
607 const char* section_name = (*p)->section_name(i).c_str();
608 if (!is_section_foldable_candidate(section_name))
609 continue;
610 if (!(*p)->is_section_included(i))
611 continue;
612 if (parameters->options().gc_sections()
613 && symtab->gc()->is_section_garbage(*p, i))
614 continue;
615 const char* mangled_func_name = strrchr(section_name, '.');
616 gold_assert(mangled_func_name != NULL);
617 // With --icf=safe, check if the mangled function name is a ctor
618 // or a dtor. The mangled function name can be obtained from the
619 // section name by stripping the section prefix.
620 if (parameters->options().icf_safe_folding()
621 && !is_function_ctor_or_dtor(mangled_func_name + 1)
622 && (!target.can_check_for_function_pointers()
623 || section_has_function_pointers(*p, i)))
625 continue;
627 this->id_section_.push_back(Section_id(*p, i));
628 this->section_id_[Section_id(*p, i)] = section_num;
629 this->kept_section_id_.push_back(section_num);
630 num_tracked_relocs.push_back(0);
631 is_secn_or_group_unique.push_back(false);
632 section_contents.push_back("");
633 section_num++;
637 unsigned int num_iterations = 0;
639 // Default number of iterations to run ICF is 2.
640 unsigned int max_iterations = (parameters->options().icf_iterations() > 0)
641 ? parameters->options().icf_iterations()
642 : 2;
644 bool converged = false;
646 while (!converged && (num_iterations < max_iterations))
648 num_iterations++;
649 converged = match_sections(num_iterations, symtab,
650 &num_tracked_relocs, &this->kept_section_id_,
651 this->id_section_, &is_secn_or_group_unique,
652 &section_contents);
655 if (parameters->options().print_icf_sections())
657 if (converged)
658 gold_info(_("%s: ICF Converged after %u iteration(s)"),
659 program_name, num_iterations);
660 else
661 gold_info(_("%s: ICF stopped after %u iteration(s)"),
662 program_name, num_iterations);
665 // Unfold --keep-unique symbols.
666 for (options::String_set::const_iterator p =
667 parameters->options().keep_unique_begin();
668 p != parameters->options().keep_unique_end();
669 ++p)
671 const char* name = p->c_str();
672 Symbol* sym = symtab->lookup(name);
673 if (sym == NULL)
675 gold_warning(_("Could not find symbol %s to unfold\n"), name);
677 else if (sym->source() == Symbol::FROM_OBJECT
678 && !sym->object()->is_dynamic())
680 Object* obj = sym->object();
681 bool is_ordinary;
682 unsigned int shndx = sym->shndx(&is_ordinary);
683 if (is_ordinary)
685 this->unfold_section(obj, shndx);
691 this->icf_ready();
694 // Unfolds the section denoted by OBJ and SHNDX if folded.
696 void
697 Icf::unfold_section(Object* obj, unsigned int shndx)
699 Section_id secn(obj, shndx);
700 Uniq_secn_id_map::iterator it = this->section_id_.find(secn);
701 if (it == this->section_id_.end())
702 return;
703 unsigned int section_num = it->second;
704 unsigned int kept_section_id = this->kept_section_id_[section_num];
705 if (kept_section_id != section_num)
706 this->kept_section_id_[section_num] = section_num;
709 // This function determines if the section corresponding to the
710 // given object and index is folded based on if the kept section
711 // is different from this section.
713 bool
714 Icf::is_section_folded(Object* obj, unsigned int shndx)
716 Section_id secn(obj, shndx);
717 Uniq_secn_id_map::iterator it = this->section_id_.find(secn);
718 if (it == this->section_id_.end())
719 return false;
720 unsigned int section_num = it->second;
721 unsigned int kept_section_id = this->kept_section_id_[section_num];
722 return kept_section_id != section_num;
725 // This function returns the folded section for the given section.
727 Section_id
728 Icf::get_folded_section(Object* dup_obj, unsigned int dup_shndx)
730 Section_id dup_secn(dup_obj, dup_shndx);
731 Uniq_secn_id_map::iterator it = this->section_id_.find(dup_secn);
732 gold_assert(it != this->section_id_.end());
733 unsigned int section_num = it->second;
734 unsigned int kept_section_id = this->kept_section_id_[section_num];
735 Section_id folded_section = this->id_section_[kept_section_id];
736 return folded_section;
739 } // End of namespace gold.