Experience converting a large mathematical software package written in C++ to C++20 modules

Mathematical software has traditionally been built in the form of "packages" that build on each other. A substantial fraction of these packages is written in C++ and, as a consequence, the interface of a package is described in the form of header files that downstream packages and applications can then #include. C++ has inherited this approach towards exporting interfaces from C, but the approach is clunky, unreliable, and slow. As a consequence, C++20 has introduced a "module" system in which packages explicitly export declarations and code that compilers then store in machine-readable form and that downstream users can "import" -- a system in line with what many other programming languages have used for decades. Herein, I explore how one can convert large mathematical software packages written in C++ to this system, using the deal.II finite element library with its around 800,000 lines of code as an example. I describe an approach that allows providing both header-based and module-based interfaces from the same code base, discuss the challenges one encounters, and how modules actually work in practice in a variety of technical and human metrics. The results show that with a non-trivial, but also not prohibitive effort, the conversion to modules is possible, resulting in a reduction in compile time for the converted library itself; on the other hand, for downstream projects, compile times show no clear trend. I end with thoughts about long-term strategies for converting the entire ecosystem of mathematical software over the coming years or decades.