ProtoX: A First Look

We present a first look at ProtoX, a code generation framework for stencil and pointwise operations that occur fre-quently in the numerical solution of partial differential equations. ProtoX has Proto as its library frontend and SPIRAL as the backend. Proto is a C++ based domain specific library which optimizes the algorithms used to compute the numerical solution of partial differential equations. Meanwhile, SPIRAL is a code generation system that focuses on generating highly optimized target code. Although the current design layout of Proto and its high level of abstractions provide a user friendly set up, there is still a room for improving it's performance by applying various techniques either at a compiler level or at an algorithmic level. Hence, in this paper we propose adding SPIRAL as the library backend for Proto enabling abstraction fusion, which is usually difficult to perform by any compiler. We demonstrate the construction of ProtoX by considering the 2D Poisson equation as a model problem from Proto. We provide the final generated code for CPU, Multi-core CPU, and GPU as well as some performance numbers for CPU.

I. Introduction

There is a myriad of application areas in the field of scientific computing and engineering where numerical solutions to partial differential equations (PDEs) are required to be computed. Numerical methods like the finite difference method (FDM), finite element method (FEM), finite volume method (FVM) and multigrid method are used to approximate the solutions to these PDEs. The key components of these algorithms are the stencil and pointwise operations. Stencils are defined as a linear transformation, $$\begin{equation*} S(x)_i=\Sigma_j \alpha_j x_{i+j},\tag{1}\end{equation*}$$ where with denoting the number of space di-mensions' denotes the weight and is the multidimensional data array.