NTLib is a C++ template library containing common number theory implementations. All library types and templates are compatible to one another and can easily be combined to solve mathematical programming problems.

The main motivation for NTLib was to have a generic library for Project Euler problems. As such, most of the first 100 problems can easily solved with NTLib in just a few lines of C++ code.

Some Features of NTLib

Basic number theoretic functions such as gcd, lcm, isqrt, ...
Primality test, prime decomposition and prime generation.
Generate primitive Pythagorean triples.
Solve several kinds of Diophantine equations, i.e., Pell's equation.
Compute binomial coefficients, polygonal numbers, Euler's totient function, divisor function and Turan numbers.
...

Documentation

See here for the complete Doxygen documentation.

Getting Started

Requirements

NTLib uses up-to-date C++ features. In particular:

C++20 modules
C++23 standard library features

As a consequence (especially because of the modules), you need recent tooling to sucessfully compile the library. A working set of tools under Ubuntu 24.04 LTS is:

Clang-19.1, including Clang Tools 19
Ninja 1.11
CMake and CTest 3.28

Download NTLib

Clone NTLib into a new ntlib directory:

git clone https://github.com/pjungeblut/ntlib ntlib

There are no git submodules and no other dependencies are required to use NTLib.

Usage

TODO (pjungeblut): Document how to include NTLib using CMake.

Development

If you don't just want to use but extend/adapt NTLib, this is how to build all unit tests: Move into the ntlib directory and configure CMake using the debug preset (there is also a release preset to build everything in release mode). Then build the library and unit tests using the tests preset.

cd ntlib
cmake --preset debug            # configure the build
cmake --build --preset tests    # build the library and all unit tests
ctest --preset tests            # run all unit tests

To run the tests, navigate to build/debug/ (or build/release/) and run ctest.

Build and Run Tests for Individual Modules

Each module comes with its own unit test which can be build individually.

For example, consider the base module. The following can be used to build and run only the unit tests for the base module:

cd build/debug   # alternatively, go to `build/release`
ninja ut_base    # all unit-test targets are name with `ut_<module-name>`
./test/base      # the test executable is named like the module under test

Generate Code Coverage Reports

Note: This requires gcovr to be installed.

Note: This currently only works with clang. For other compilers, adapt the --gcov-executable flag in the root CMakeLists.txt file.

The following can be used to run all tests and execute coverage reports for the library. The report is written to build/tests/coverage/index.html.

cmake --build --preset tests --target coverage

License & Disclaimer

This software is licensed under the MIT license. See LICENSE for details. NTLib is still in development. Therefore, things will break and the API/ABI will change.

Feedback is always welcome.