Analysis of a Self-Similar GPU Thread Map for Data-parallel m-Simplex Domains

This work analyzes the possible performance benefits one could obtain by employing a Self-Similar type of GPU thread map on data-parallel m-simplex domains, which is the geometrical representation of several interaction problems. The main contributions of this work are (1) the proposal of a new block-space map H: $\mathbb{Z}^{m}\mapsto \mathbb{Z}^{m}$ based on a self-similar set of sub-orthotopes, and (2) its analysis in terms of performance and thread space, from which we obtain that $\mathcal{H}(\omega)$ is time and space efficient for 2-simplices and only time efficient for 3-simplices unless the theoretical model is relaxed to allow concurrent parallel spaces. Experimental tests on a 2-simplex domain support the theoretical results, giving up to 30% of speedup over the standard approach. We also show how the map can utilize GPU tensor cores and further accelerate through fast matrix-multiply-accumulate operations. Finally, we show that extending the map to general m-simplices is a non-trivial optimization problem and depends of the choice of two parameters $r, \beta$, for which we provide some insights in order to obtain a $\mathcal{H}(\omega)$ map that can be $m!$ times more space efficient than a bounding-box approach.