\section{Introduction} Fast Fourier Transform (\fft) algorithms are among the most important of the XXth Century. Applications range widely from engineering to pure science. For example: image and sound signal analysis and lossy compression. jpg and mp3 are file formats that encode the signal using its Fourier modes. In astrophysics \fft\ is used to solve the differential field equations of Newtonian Gravity and General Relativity as well, in huge N-body simulations of the cosmological evolution of the universe. While the Fourier modes of those fields, usually the matter density, encode statistical estimators that link theoretic models and observation. \cite{adamek_2016,springel_2020} are examples of some of the most recent such simulations. There are many different \fft\ algorithms as well as many implementations of those. The most notable of such implementations is the \fftw\ \cite{FFTW05} free-software library for C language, which boasts itself of being the fastest implementation at least for CPUs---note there exists implementations for GPUs such as \cufft\footnote{\url{docs.nvidia.com/cuda/pdf/CUFFT_Library.pdf}}. Despite \fft\ being well known and widely used, there is no C++ library counterpart of \fftw, and to our knowledge there is not a single \fft\ implementation templated on the type. This \gsoc\ project is aimed at the implementation of a new \fft\ library within \boostmath\footnote{\url{www.boost.org/libs/math}}---a large mathematical library that offers high-performance functions of pure and applied mathematics but no \fft\ support before this date. The work done during the last two months related to this project can be found in the dedicated git repository \url{github.com/BoostGSoC21/math/tree/develop}; all pull requests in that fork are bound to this end.