Squeeze: Efficient Compact Fractals for Tensor Core GPUs

TL;DR

This paper introduces Squeeze, a GPU-efficient method for processing fractals in compact form, enabling faster computation and significant memory savings for fractal-based problems.

Contribution

The paper presents a novel compact fractal processing scheme using GPU tensor-core accelerated space transformations, applicable to any NBB class fractal.

Findings

Up to 12x speedup over expanded-space methods

Memory reduction factor of up to 315x

Applicable to 3D fractals and NBB class fractals

Abstract

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, $\lambda(\omega)$ and $\nu(\omega)$, 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.