Numerixx

A general-purpose, header-only numerical library for C++23, in the spirit of GSL but with a smaller scope: numerical differentiation, root finding, minimisation, polynomials, systems of nonlinear equations, quadrature and interpolation, done carefully, generically and composably.

• Solvers are values. A configured solver is a small immutable object; solvers compose (first_of tries the next solver if one fails, then stages search, solve and polish).
• No exceptions. Every result is a std::expected that carries the estimate, or the best estimate so far with the reason for the failure and the iteration and evaluation counts.
• Illegal states do not compile where the type system can express it, and are validated once at the boundary where it cannot.
• Portable. GCC, Clang, MSVC, clang-cl and Emscripten (WebAssembly). MIT licence.

Status: Numerixx 2 is being rebuilt. This branch contains the new build system and an empty library skeleton (roadmap phase 0). The modules are ported phase by phase; see the plan and the design reference. The previous API is preserved at the tags v1.0.0 (master) and v1.1.0-legacy (the last development branch); MIGRATION.md maps it to the new one.

Requirements

• A C++23 compiler: GCC ≥ 14, Clang ≥ 18 with libc++, MSVC 19.51 (/std:c++latest), clang-cl, or Emscripten ≥ 6.0.8.
• CMake ≥ 3.25 (≥ 3.30 recommended on Windows) and Ninja.

Dependencies are fetched by CPM.cmake, pinned by version and SHA256. The scalar modules need only the standard library.

Dependency	Needed by	Option (default)
FXT	numerixx::pipes (FXT pipe syntax for results)	NUMERIXX_WITH_FXT (ON)
Eigen 5.0.1	numerixx::linalg, numerixx::multiroots	NUMERIXX_WITH_LINALG (ON)
Boost.Multiprecision 1.92 (standalone)	numerixx::multiprecision adapter	NUMERIXX_WITH_MULTIPRECISION (OFF)
doctest 2.5.3, google/benchmark 1.9.5, Boost.Math 1.92	tests, benchmarks, test oracles	development only

Using Numerixx

With CPM (declare it as NAME Numerixx, so that -DCPM_Numerixx_SOURCE=<path> can substitute a local checkout):

CPMAddPackage(NAME Numerixx GITHUB_REPOSITORY troldal/Numerixx GIT_TAG <commit-or-tag>)
target_link_libraries(my_target PRIVATE numerixx::numerixx)   # every module, or link single ones: numerixx::roots

With FetchContent:

include(FetchContent)
FetchContent_Declare(numerixx GIT_REPOSITORY https://github.com/troldal/Numerixx.git GIT_TAG <commit-or-tag>)
FetchContent_MakeAvailable(numerixx)

As an installed package:

find_package(numerixx 2.0 CONFIG REQUIRED)

Each module has its own target and header: numerixx::roots and <numerixx/roots.hpp>, and so on. numerixx::numerixx links every module, including the Eigen-backed linalg and multiroots when NUMERIXX_WITH_LINALG is ON (the default), and numerixx::pipes when NUMERIXX_WITH_FXT is ON. The umbrella header <numerixx/numerixx.hpp> includes the scalar modules (and the pipes) but never the Eigen-backed ones, so Eigen's compile cost is paid only where <numerixx/linalg.hpp> or <numerixx/multiroots.hpp> is included. A user of the scalar modules only can set NUMERIXX_WITH_FXT=OFF and NUMERIXX_WITH_LINALG=OFF and downloads neither dependency.

If the parent project uses FXT or Eigen itself:

• CPM parents: declare FXT as NAME FXT (with FXT_USE_TL_EXPECTED and FXT_USE_TL_OPTIONAL OFF) and Eigen as NAME Eigen3. CPM deduplicates them in either order: declared first, Numerixx reuses the parent's fxt::fxt and Eigen3::Eigen; declared after Numerixx, the parent gets those targets from Numerixx.
• FetchContent parents: either fetch FXT and Eigen before Numerixx and define fxt::fxt and Eigen3::Eigen, which Numerixx then reuses, or add Numerixx first and use the fxt::fxt and Eigen3::Eigen targets it defines. After Numerixx, do not fetch FXT or Eigen again, define those targets again, or add FXT's or Eigen's own CMake project: that is either an error (the target already exists) or a second copy of the library.

Building and testing

Every configuration is a CMake preset; cmake --workflow --preset <name> configures, builds and tests it.

Preset	Toolchain
gcc, gcc-noexcept, gcc-multiprecision	GCC + libstdc++ with library assertions; without exceptions; with the multiprecision adapter and Boost.Math oracles
gcc-noexcept-pipes	without exceptions but with the FXT pipes; fails until the FXT pin includes FXT-1 (CI reports that failure as a warning and fails on any other error)
clang, clang-asan	Clang + libc++; with AddressSanitizer, UndefinedBehaviorSanitizer and libc++ debug hardening
msvc, clang-cl	MSVC and clang-cl (run from a Developer PowerShell)
emscripten, emscripten-jsexcept, emscripten-noexcept, emscripten-pthread	Emscripten with wasm, JavaScript or no exceptions, and with -pthread; tests run under node (activate emsdk first)
integration	the consumer-build scenarios: CPM and FetchContent parents, a scalar-only parent, an installed package

On Windows, keep the CPM cache and build directories short, because long paths lose files silently. Workflow presets accept no -D options, so set the cache location through the environment (or a CMakeUserPresets.json):

CPM_SOURCE_CACHE=C:/cpm cmake --workflow --preset gcc

Licence

MIT. See LICENSE.