A scalable and energy efficient GPU thread map for [formula omitted]-simplex domains

Abstract

This work proposes a new GPU thread map for m-simplex domains that improves its speedup along with the m-dimension and is energy efficient compared to other state of the art approaches. The main contributions of this work are (i) the formulation of an improved new block-space map H:Zm↦Zm for regular orthogonal simplex domains, which is analyzed in terms of resource usage, and (ii) the experimental evaluation in terms of speedup and energy efficiency with respect to a bounding box approach. Results from the analysis show that H has a potential speedup of up to 2× and 6× for 2 and 3-simplices, respectively. Experimental evaluation shows that H is competitive for 2-simplices, reaching 1.2×∼2.0× of speedup for different tests, which is on par with the fastest state of the art approaches. For 3-simplices H reaches up to 1.3×∼6.0× of speedup making it the fastest. The extension of H to higher dimensional m-simplices is feasible and has a potential speedup that scales as m! given a proper selection of parameters r,β which are the scaling and replication factors of the geometry, respectively. In terms of energy consumption, although H is among the highest in power consumption, it compensates by its short duration, making it one of the most energy efficient approaches. The results of this work show that H is a scalable and energy efficient map that improves the efficiency of GPU applications that need to process m-simplex domains, such as Cellular Automata or PDE simulations, among others.