Efficient entry point encoding and decoding algorithms on 2D Hilbert space filling curve

The Hilbert curve is an important method for mapping high-dimensional spatial information into one-dimensional spatial information while preserving the locality in the high-dimensional space. Entry points of a Hilbert curve can be used for image compression, dimensionality reduction, corrupted image detection and many other applications. As far as we know, there is no specific algorithms developed for entry points. To address this issue, in this paper we present an efficient entry point encoding algorithm (EP-HE) and a corresponding decoding algorithm (EP-HD). These two algorithms are efficient by exploiting the m consecutive 0s in the rear part of an entry point. We further found that the outputs of these two algorithms are a certain multiple of a certain bit of s, where s is the starting state of these m levels. Therefore, the results of these m levels can be directly calculated without iteratively encoding and decoding. The experimental results show that these two algorithms outperform their counterparts in terms of processing entry points

Locality properties of 3D data orderings with application to parallel molecular dynamics simulations

Application performance on graphical processing units (GPUs), in terms of execution speed and memory usage, depends on the efficient use of hierarchical memory. It is expected that enhancing data locality in molecular dynamic simulations will lower the cost of data movement across the GPU memory hierarchy. The work presented in this article analyses the spatial data locality and data reuse characteristics for row-major, Hilbert and Morton orderings and the impact these have on the performance of molecular dynamics simulations. A simple cache model is presented, and this is found to give results that are consistent with the timing results for the particle force computation obtained on NVidia GeForce GTX960 and Tesla P100 GPUs. Further analysis of the observed memory use, in terms of cache hits and the number of memory transactions, provides a more detailed explanation of execution behaviour for the different orderings. To the best of our knowledge, this is the first study to investigate memory analysis and data locality issues for molecular dynamics simulations of Lennard-Jones fluids on NVidia’s Maxwell and Tesla architectures