Abstract-Many general-purpose applications exploit GraphicsProcessing Units (GPUs) by executing a set of well-known dataparallel primitives. Those primitives are usually invoked from the host many times, so their throughput has a great impact on the performance of the overall system. Thus, the study of novel algorithmic strategies to optimize their implementation on current devices is an interesting topic to the GPU community. In this paper we focus on optimizing the reduction primitive, which merely reduces a data sequence into a single value using a binary associative operator. Although tree-based and sequential-based algorithms have been already implemented on GPUs, a comparison of both algorithm performance had not been carried out yet. Thus, our first contribution is to present an experimental study of state-of-the-art reduction algorithms on CUDA. Next we introduce two algorithmic optimizations that are integrated into the fastest solution (a sequential-based algorithm), improving its throughput even more. Finally, we replicate this methodology to the segmented version of the primitive, which applies when the input is composed of several independent segments. In this case, it is not clear which algorithm exhibits the best performance, since throughput deeply depends on the distribution of segments along the input. According to our results, tree-based algorithms run faster for small segments, while sequential methods are better for medium and large ones.
In this paper, we present several variants of the Surface Area Heuristics (SAH) to build kd-trees for specific sets of rays' directions. In order to cover the whole space of directions, several sets of directions are considered and each of them leads to a different specialized kd-tree. We call Multi-kd-tree to the set of these kd-trees. During rendering, each ray will traverse the kd-tree associated with the set containing its direction. In order to evaluate the efficiency of our proposal, we have implemented a Path Tracing and an Ambient Occlusion renderer on GPU with CUDA. A SAH-based kd-tree has been compared to a Multi-kd-tree and we show that all the new heuristics exhibit a better performance than SAH over usual scenes.
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