[libc++] Avoid string reallocation in std::filesystem::path::lexically_relative (#152964)

Improves runtime by around 20 to 40%. (1.3x to 1.7x)

```
Benchmark                                                           Time             CPU      Time Old      Time New       CPU Old       CPU New
------------------------------------------------------------------------------------------------------------------------------------------------
BM_LexicallyRelative/small_path/2                                -0.2111         -0.2082           229           181           228           180
BM_LexicallyRelative/small_path/4                                -0.2579         -0.2550           455           338           452           337
BM_LexicallyRelative/small_path/8                                -0.2643         -0.2616           844           621           838           619
BM_LexicallyRelative/small_path/16                               -0.2582         -0.2556          1562          1158          1551          1155
BM_LexicallyRelative/small_path/32                               -0.2518         -0.2496          3023          2262          3004          2254
BM_LexicallyRelative/small_path/64                               -0.2806         -0.2775          6344          4564          6295          4549
BM_LexicallyRelative/small_path/128                              -0.2165         -0.2137         11762          9216         11683          9186
BM_LexicallyRelative/small_path/256                              -0.2672         -0.2645         24499         17953         24324         17891
BM_LexicallyRelative/large_path/2                                -0.3268         -0.3236           426           287           422           285
BM_LexicallyRelative/large_path/4                                -0.3274         -0.3248           734           494           729           492
BM_LexicallyRelative/large_path/8                                -0.3586         -0.3560          1409           904          1399           901
BM_LexicallyRelative/large_path/16                               -0.3978         -0.3951          2764          1665          2743          1659
BM_LexicallyRelative/large_path/32                               -0.3934         -0.3908          5323          3229          5283          3218
BM_LexicallyRelative/large_path/64                               -0.3629         -0.3605         10340          6587         10265          6564
BM_LexicallyRelative/large_path/128                              -0.3450         -0.3423         19379         12694         19233         12649
BM_LexicallyRelative/large_path/256                              -0.3097         -0.3054         36293         25052         35943         24965
```

---------

Co-authored-by: Nikolas Klauser <[email protected]>

Author: tinnamchoi

libcxx/docs/ReleaseNotes/22.rst

@@ -50,6 +50,7 @@ Improvements and New Features
 - The performance of ``unordered_set::operator=(const unordered_set&)`` has been improved by up to 5x.
 - The performance of ``map::erase`` and ``set::erase`` has been improved by up to 2x
 - The performance of ``find(key)`` in ``map``, ``set``, ``multimap`` and ``multiset`` has been improved by up to 2.3x
+- Some reallocations are now avoided in `std::filesystem::path::lexically_relative`, resulting in a performance improvement of up to 1.7x.
 
 Deprecations and Removals
 -------------------------

libcxx/src/filesystem/path.cpp

@@ -292,7 +292,9 @@ path path::lexically_relative(const path& base) const {
   // return a path constructed with 'n' dot-dot elements, followed by the
   // elements of '*this' after the mismatch.
   path Result;
-  // FIXME: Reserve enough room in Result that it won't have to re-allocate.
+  constexpr size_t ElemSize      = 2; // ".."
+  constexpr size_t SeparatorSize = 1; // separator is always a single char
+  Result.__reserve(ElemCount * (ElemSize + SeparatorSize) + SeparatorSize + PP.Path.size());
   while (ElemCount--)
     Result /= PATHSTR("..");
   for (; PP; ++PP)

libcxx/test/benchmarks/filesystem.bench.cpp

@@ -171,4 +171,24 @@ BENCHMARK_CAPTURE(BM_LexicallyNormal, large_path, getRandomPaths, /*PathLen*/ 32
     ->Range(2, 256)
     ->Complexity();
 
+template <class GenInput>
+void BM_LexicallyRelative(benchmark::State& st, GenInput gen, size_t PathLen) {
+  auto BasePath   = gen(st.range(0), PathLen);
+  auto TargetPath = gen(st.range(0), PathLen);
+  benchmark::DoNotOptimize(&BasePath);
+  benchmark::DoNotOptimize(&TargetPath);
+  for (auto _ : st) {
+    benchmark::DoNotOptimize(TargetPath.lexically_relative(BasePath));
+  }
+  st.SetComplexityN(st.range(0));
+}
+BENCHMARK_CAPTURE(BM_LexicallyRelative, small_path, getRandomPaths, /*PathLen*/ 5)
+    ->RangeMultiplier(2)
+    ->Range(2, 256)
+    ->Complexity();
+BENCHMARK_CAPTURE(BM_LexicallyRelative, large_path, getRandomPaths, /*PathLen*/ 32)
+    ->RangeMultiplier(2)
+    ->Range(2, 256)
+    ->Complexity();
+
 BENCHMARK_MAIN();