Algebraic description and automatic generation of multigrid methods in SPIRAL

Abstract

SPIRAL is an autotuning, program generation and code synthesis system that offers a fully automatic generation of highly optimized target codes, customized for the specific execution platform at hand. Initially, SPIRAL was targeted at problem domains in digital signal processing, later also at basic linear algebra. We open SPIRAL up to a new, practically relevant and challenging domain: multigrid solvers. SPIRAL is driven by algebraic transformation rules. We specify a set of such rules for a simple multigrid solver with a Richardson smoother for a discretized square 2D Poisson equation with Dirichlet boundary conditions. We present the target code that SPIRAL generates in static single-assignment form and discuss its performance. While this example required no changes of or extensions to the SPIRAL system, more complex multigrid solvers may require small adaptations

Code generation approaches for parallel geometric multigrid solvers

“…A prominent example for an external DSL is SPIRAL [46,45,9] that was originally developed for the domain of Fast Fourier transforms. It needs to provide less functionality compared to a general purpose language and thus is easier to maintain and use.…”

Special issue: Advanced stencil‐code engineering

“…The first 2 papers follow the approach of multistage domain‐specific optimization mentioned above. The paper “Algebraic description and automatic generation of multigrid methods in SPIRAL,” authored by Matthias Bolten, Franz Franchetti, Paul H. J. Kelly, Christian Lengauer, and Marcus Mohr, opens the multistage domain‐specific optimizing program generator SPIRAL for a new domain: multigrid solvers. SPIRAL has been applied successfully in the past to linear transforms of various sorts and basic linear algebra.…”