Implementing Mathematics of Arrays in Modern Fortran: Efficiency and Efficacy

Mathematics of Arrays (MoA) concerns the formal description of algorithms working on arrays of data and the efficient and effective implementation in software and hardware. Since (multidimensional) arrays are one of the most important data structures in Fortran, as witnessed by their native support in the language and the numerous operations and functions that take arrays as input and output, it is natural to examine how Fortran can be used as implementation language for MoA. This article presents the first results, both in terms of code and of performance, regarding this union. It may serve as a basis for further research, both with respect to the formal theory of MoA and to improving the practical implementation of array-based algorithms.