P3 problem and Magnolia language: Specializing array computations for emerging architectures

The problem of producing portable high-performance computing (HPC) software that is cheap to develop and maintain called the P 3 (performance, portability, productivity) problem. Good solutions have been achieved when performance profiles target machines similar. variety HPC architectures is, however, large can be expected grow larger. Software for therefore needs highly adaptable, there a pressing need provide developers with tools produce vastly different profiles. Multi-dimensional array manipulation constitutes core component numerous numerical methods, such as finite difference solvers Partial Differential Equations (PDEs). efficiency these computations tightly connected traversing distributing data in hardware-friendly way. Mathematics Arrays (MoA) allows formally reasoning about enables systematic transformations array-based programs, e.g., use layouts fit specific architecture. This paper presents programming methodology aimed tackling domains are well-explored using Magnolia, language designed embody generic programming. Magnolia programmer restrict semantic properties abstract types operations by defining so-called axioms. Axioms used tests concrete implementations specifications, formal verification, or perform semantics-preserving program transformations. We leverage Magnolia's specification facilities extend compiler term rewriting system. implement MoA's transformation rules demonstrate through case study on solver PDEs how our system exploring space possible optimizations.