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This work presents Squeeze, an efficient compact fractal processing schemefor tensor core GPUs. By combining discrete-space transformations betweencompact and expanded forms, one can do data-parallel computation on a fractalwith neighborhood access without needing to expand the fractal in memory. Thespace transformations are formulated as two GPU tensor-core accelerated threadmaps, $\lambda(\omega)$ and $\nu(\omega)$, which act as compact-to-expanded andexpanded-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 scalingfactor. The proposed approach works for any fractal that belongs to theNon-overlapping-Bounding-Boxes (NBB) class of discrete fractals, and can beextended to three dimensions as well. Experimental results using a discreteSierpinski Triangle as a case study shows up to $\sim12\times$ of speedup and amemory reduction factor of up to $\sim 315\times$ with respect to a GPU-basedexpanded-space bounding box approach. These results show that the proposedcompact approach will allow the scientific community to efficiently tackleproblems that up to now could not fit into GPU memory.

Squeeze: Efficient Compact Fractals for Tensor Core GPUs