arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2004.13475cs.DC
收藏

基于嵌入式二维分形的高效GPU线程映射

Efficient GPU Thread Mapping on Embedded 2D Fractals

Cristóbal A. Navarro, Felipe A. Quezada, Nancy Hitschfeld, Raimundo Vega, Benjamin Bustos

摘要:

这项工作提出了一种新的方法来映射GPU线程到一个家庭的离散嵌入式2D分形。提出了一种块空间映射$λ: \mathbb{Z}_{\mathbb{E}}^{2} \mapsto \mathbb{Z}_{\mathbb{F}}^{2}$,从欧几里得并行空间$\mathbb{E}$到嵌入式分形空间$\mathbb{F}$,该映射在$\mathcal{O}(\log_2 \log_2(n))$时间内进行,并且使用不超过$\mathcal{O}(n^\mathbb{H})$线程,其中$\mathbb{H}$是分形的Hausdorff维数,使其并行空间有效。与边界盒(BB)方法相比,$λ(ω)$在并行空间中提供了次指数级的改进,并具有单调增加的加速比$n \ge n_0$。Sierpinski垫片分形被用作一个特殊的情况下,研究和实验性能结果表明,$λ(ω)$达到$9\times$的加速比的边界框的方法。还提出了一种基于张量核的$λ(ω)$实现,用于现代GPU,提供高达$\sim40\%$的额外性能。在这项工作中获得的结果表明,在分形域上进行高效的GPU线程映射可以显着提高使用这种类型的几何图形的几个应用程序的性能。

英文摘要:

This work proposes a new approach for mapping GPU threads onto a family of discrete embedded 2D fractals. A block-space map $λ: \mathbb{Z}_{\mathbb{E}}^{2} \mapsto \mathbb{Z}_{\mathbb{F}}^{2}$ is proposed, from Euclidean parallel space $\mathbb{E}$ to embedded fractal space $\mathbb{F}$, that maps in $\mathcal{O}(\log_2 \log_2(n))$ time and uses no more than $\mathcal{O}(n^\mathbb{H})$ threads with $\mathbb{H}$ being the Hausdorff dimension of the fractal, making it parallel space efficient. When compared to a bounding-box (BB) approach, $λ(ω)$ offers a sub-exponential improvement in parallel space and a monotonically increasing speedup $n \ge n_0$. The Sierpinski gasket fractal is used as a particular case study and the experimental performance results show that $λ(ω)$ reaches up to $9\times$ of speedup over the bounding-box approach. A tensor-core based implementation of $λ(ω)$ is also proposed for modern GPUs, providing up to $\sim40\%$ of extra performance. The results obtained in this work show that doing efficient GPU thread mapping on fractal domains can significantly improve the performance of several applications that work with this type of geometry.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑