Squeeze：用于Tensor Core GPU的高效紧凑分形
Squeeze: Efficient Compact Fractals for Tensor Core GPUs
摘要：
这项工作提出了挤压，一个有效的紧凑的分形处理方案的张量核心GPU。通过结合紧凑和扩展形式之间的离散空间变换，可以在具有邻域访问的分形上进行数据并行计算，而无需在内存中扩展分形。空间变换被公式化为两个GPU张量核加速线程映射$λ(ω)$和$ν(ω)$，它们分别充当紧凑到扩展和扩展到紧凑的空间函数。映射的成本是$\mathcal{O}(\log_2 \log_s(n))$时间，$n$是扩展形式的分形的$n \times n$嵌入的边，而$s$是线性缩放因子。所提出的方法适用于任何分形，属于非重叠边界盒（NBB）类的离散分形，并可以扩展到三维。实验结果使用离散Sierpinski三角形作为案例研究显示了高达$\sim12\times$的加速比和高达$\sim 315\times$的内存减少因子相对于基于GPU的扩展空间限界框方法。这些结果表明，所提出的紧凑方法将使科学界能够有效地解决迄今为止无法适应GPU内存的问题。
英文摘要：
This work presents Squeeze, an efficient compact fractal processing scheme for tensor core GPUs. By combining discrete-space transformations between compact and expanded forms, one can do data-parallel computation on a fractal with neighborhood access without needing to expand the fractal in memory. The space transformations are formulated as two GPU tensor-core accelerated thread maps, $λ(ω)$ and $ν(ω)$, which act as compact-to-expanded and expanded-to-compact space functions, respectively. The cost of the maps is $\mathcal{O}(\log_2 \log_s(n))$ time, with $n$ being the side of a $n \times n$ embedding for the fractal in its expanded form, and $s$ the linear scaling factor. The proposed approach works for any fractal that belongs to the Non-overlapping-Bounding-Boxes (NBB) class of discrete fractals, and can be extended to three dimensions as well. Experimental results using a discrete Sierpinski Triangle as a case study shows up to $\sim12\times$ of speedup and a memory reduction factor of up to $\sim 315\times$ with respect to a GPU-based expanded-space bounding box approach. These results show that the proposed compact approach will allow the scientific community to efficiently tackle problems that up to now could not fit into GPU memory.
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。
