A C++ implementation of TimSort, an O(n log n) stable sorting algorithm, ported from Python's and OpenJDK's.

See also the following links for a detailed description of TimSort:

• http://svn.python.org/projects/python/trunk/Objects/listsort.txt
• http://en.wikipedia.org/wiki/Timsort

This version of the library requires at least C++20. Older versions of the library, available in different branches, offer support for older standards though implement fewer features:

• Branch 2.x.y is compatible with C++11, and is slightly more permissive in some reagard due to the lack of concepts to constrain its interface (it notaby supports iterators without postfix operator++/--).
• Branch 1.x.y is compatible with C++03. Older versions are not actively maintained anymore. If you need extended support for those, please open specific issues for the problems you want solved.

According to the benchmarks, gfx::timsort is slower than std::ranges::sort on randomized sequences, but faster on partially-sorted ones. It can be used as a drop-in replacement for std::ranges::stable_sort, with the difference that it can't fall back to a O(n log² n) algorithm when there isn't enough extra heap memory available.

Merging sorted ranges efficiently is an important part of the TimSort algorithm. This library exposes gfx::timmerge in the public API, a drop-in replacement for std::ranges::inplace_merge with the difference that it can't fall back to a O(n log n) algorithm when there isn't enough extra heap memory available. According to the benchmarks, gfx::timmerge is slower than std::ranges::inplace_merge on heavily/randomly overlapping subranges of simple elements, but it is faster for complex elements such as std::string, and on sparsely overlapping subranges.

The ibrary exposes the following functions in namespace gfx:

// timsort

template <
    std::random_access_iterator Iterator,
    std::sentinel_for<Iterator> Sentinel,
    typename Compare = std::ranges::less,
    typename Projection = std::identity
>
    requires std::sortable<Iterator, Compare, Projection>
auto timsort(Iterator first, Sentinel last,
             Compare compare={}, Projection projection={})
    -> Iterator;

template <
    std::ranges::random_access_range Range,
    typename Compare = std::ranges::less,
    typename Projection = std::identity
>
    requires std::sortable<std::ranges::iterator_t<Range>, Compare, Projection>
auto timsort(Range &range, Compare compare={}, Projection projection={})
    -> std::ranges::borrowed_iterator_t<Range>;

// timmerge

template <
    std::random_access_iterator Iterator,
    std::sentinel_for<Iterator> Sentinel,
    typename Compare = std::ranges::less,
    typename Projection = std::identity
>
    requires std::sortable<Iterator, Compare, Projection>
auto timmerge(Iterator first, Iterator middle, Sentinel last,
              Compare compare={}, Projection projection={})
    -> Iterator;

template <
    std::ranges::random_access_range Range,
    typename Compare = std::ranges::less,
    typename Projection = std::identity
>
    requires std::sortable<std::ranges::iterator_t<Range>, Compare, Projection>
auto timmerge(Range &&range, std::ranges::iterator_t<Range> middle,
              Compare compare={}, Projection projection={})
    -> std::ranges::borrowed_iterator_t<Range>;

Example of using timsort with a defaulted comparison function and a projection function to sort a vector of strings by length:

#include <string>
#include <vector>
#include <gfx/timsort.hpp>

size_t len(const std::string& str) {
    return str.size();
}

// Sort a vector of strings by length
std::vector<std::string> collection = { /* ... */ };
gfx::timsort(collection, {}, &len);

The library is tested with the following compilers:

• Ubuntu: GCC 10, Clang 11
• Windows: MSVC 19.37.32826.1, MinGW-w64 GCC 12
• MacOS: GCC 10, Clang 17

The library can be installed on the system via CMake (at least 3.14) with the following commands:

cmake -S . -B build -DCMAKE_BUILD_TYPE=Release
cmake --install build

Alternatively the library is also available Conan Center and can be directly installed in your local Conan cache with the following command:

conan install --requires=timsort/3.0.0

The following configuration macros allow gfx::timsort and gfx::timmerge to emit diagnostics, which can be helpful to diagnose issues:

• Defining GFX_TIMSORT_ENABLE_ASSERT light inserts assertions in key locations in the algorithm to avoid logic errors.
• Defining GFX_TIMSORT_ENABLE_AUDIT inserts assertions that verify pre- and postconditions. These verifications can slow the algorithm down significantly. Enable the audits only while testing or debugging. Enabling audits automatically enables lighter assertions too.
• Defining GFX_TIMSORT_ENABLE_LOG inserts logs in key locations, which allow to follow more closely the flow of the algorithm.

cpp-TimSort follows semantic versioning and provides the following macros to retrieve the current major, minor and patch versions:

GFX_TIMSORT_VERSION_MAJOR
GFX_TIMSORT_VERSION_MINOR
GFX_TIMSORT_VERSION_PATCH

The tests are written with Catch2 and can be compiled with CMake and run through CTest.

When using the project's main CMakeLists.txt, the CMake option BUILD_TESTING is ON by default unless the project is included as a subdirectory. The following CMake options are available to change the way the tests are built with CMake:

• GFX_TIMSORT_USE_VALGRIND: if ON, the tests will be run through Valgrind (OFF by default)
• GFX_TIMSORT_SANITIZE: this variable takes a comma-separated list of sanitizers options to run the tests (empty by default)

Benchmarks are available in the benchmarks subdirectory, and can be constructed directly by passing the option -DBUILD_BENCHMARKS=ON to CMake during the configuration step.

Example bench_sort output (timing scale: sec.):

c++ -v
Apple LLVM version 7.0.0 (clang-700.0.72)
Target: x86_64-apple-darwin14.5.0
Thread model: posix
c++ -I. -Wall -Wextra -g  -DNDEBUG -O2 -std=c++11 example/bench.cpp -o .bin/bench
./.bin/bench
RANDOMIZED SEQUENCE
[int]
size	100000
std::sort        0.695253
std::stable_sort 0.868916
timsort          1.255825
[std::string]
size	100000
std::sort        3.438217
std::stable_sort 4.122629
timsort          5.791845
REVERSED SEQUENCE
[int]
size	100000
std::sort        0.045461
std::stable_sort 0.575431
timsort          0.019139
[std::string]
size	100000
std::sort        0.586707
std::stable_sort 2.715778
timsort          0.345099
SORTED SEQUENCE
[int]
size	100000
std::sort        0.021876
std::stable_sort 0.087993
timsort          0.008042
[std::string]
size	100000
std::sort        0.402458
std::stable_sort 2.436326
timsort          0.298639

Example bench_merge output (timing scale: milliseconds; omitted detailed results for different middle iterator positions, reformatted to improve readability):

c++ -v
Using built-in specs.
...
Target: x86_64-pc-linux-gnu
...
gcc version 10.2.0 (GCC)
c++ -I ../include -Wall -Wextra -g -DNDEBUG -O2 -std=c++11 bench_merge.cpp -o bench_merge
./bench_merge
size	100000
element type\algorithm:      	std::inplace_merge	timmerge
RANDOMIZED SEQUENCE
[int] approx. average        	 33.404430        	 37.047990
[std::string] approx. average	324.964249        	210.297207
REVERSED SEQUENCE
[int] approx. average        	 11.441404        	  4.017482
[std::string] approx. average	305.649503        	114.773898
SORTED SEQUENCE
[int] approx. average        	  4.291098        	  0.105571
[std::string] approx. average	158.238114        	  0.273858

Detailed bench_merge results for different middle iterator positions can be found at https://github.com/timsort/cpp-TimSort/wiki/Benchmark-results