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This work proposes a new approach for mapping GPU threads onto a family ofdiscrete embedded 2D fractals. A block-space map $\lambda:\mathbb{Z}_{\mathbb{E}}^{2} \mapsto \mathbb{Z}_{\mathbb{F}}^{2}$ 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 nomore than $\mathcal{O}(n^\mathbb{H})$ threads with $\mathbb{H}$ being theHausdorff dimension of the fractal, making it parallel space efficient. Whencompared to a bounding-box (BB) approach, $\lambda(\omega)$ offers asub-exponential improvement in parallel space and a monotonically increasingspeedup $n \ge n_0$. The Sierpinski gasket fractal is used as a particular casestudy and the experimental performance results show that $\lambda(\omega)$reaches up to $9\times$ of speedup over the bounding-box approach. Atensor-core based implementation of $\lambda(\omega)$ is also proposed formodern GPUs, providing up to $\sim40\%$ of extra performance. The resultsobtained in this work show that doing efficient GPU thread mapping on fractaldomains can significantly improve the performance of several applications thatwork with this type of geometry.

Efficient GPU Thread Mapping on Embedded 2D Fractals