A Scalable and Energy Efficient GPU Thread Map for Standard m-Simplex Domains

This work proposes a new GPU thread map for standard $m$-simplex domains, that scales its speedup with dimension and is energy efficient compared to other state of the art approaches. The main contributions of this work are the formulation of the new block-space map $\mathcal{H}: \mathbb{Z}^m \mapsto \mathbb{Z}^m$ which is analyzed in terms of resource usage, and its experimental evaluation in terms of speedup over a bounding box approach and energy efficiency as elements per second per Watt. Results from the analysis show that $\mathcal{H}$ has a potential speedup of up to $2\times$ and $6\times$ for $2$ and $3$-simplices, respectively. Experimental evaluation shows that $\mathcal{H}$ is competitive for $2$-simplices, reaching $1.2\times \sim 2.0\times$ of speedup for different tests, which is on par with the fastest state of the art approaches. For $3$-simplices $\mathcal{H}$ reaches up to $1.3\times \sim 6.0\times$ of speedup making it the fastest of all. The extension of $\mathcal{H}$ to higher dimensional $m$-simplices is feasible and has a potential speedup that scales as $m!$ given a proper selection of parameters $r, \beta$ which are the scaling and replication factors, respectively. In terms of energy consumption, although $\mathcal{H}$ is among the highest in power consumption, it compensates by its short duration, making it one of the most energy efficient approaches. Lastly, further improvements with Tensor and Ray Tracing Cores are analyzed, giving insights to leverage each one of them. The results obtained in this work show that $\mathcal{H}$ is a scalable and energy efficient map that can contribute to the efficiency of GPU applications when they need to process standard $m$-simplex domains, such as Cellular Automata or PDE simulations.