NDPA: A generalized efficient parallel in-place N-Dimensional Permutation Algorithm

Abstract

N-dimensional transpose/permutation is a very important operation in many large-scale data intensive and scientific applications. These applications include but not limited to oil industry i.e. seismic data processing, nuclear medicine, media production, digital signal processing and business intelligence. This paper proposes an efficient in-place N-dimensional permutation algorithm. The algorithm is based on a novel 3D transpose algorithm that was published recently. The proposed algorithm has been tested on 3D, 4D, 5D, 6D and 7D data sets as a proof of concept. This is the first contribution which is breaking the dimensions’ limitation of the base algorithm. The suggested algorithm exploits the idea of mixing both logical and physical permutations together. In the logical permutation, the address map is transposed for each data unit access. In the physical permutation, actual data elements are swapped. Both permutation levels exploit the fast on-chip memory bandwidth by transferring large amount of data and allowing for fine-grain SIMD (Single Instruction, Multiple Data) operations. Thus, the performance is improved as evident from the experimental results section. The algorithm is implemented on NVidia GeForce GTS 250 GPU (Graphics Processing Unit) containing 128 cores. The rapid increase in GPUs performance coupled with the recent and continuous improvements in its programmability proved that GPUs are the right choice for computationally demanding tasks. The use of GPUs is the second contribution which reflects how strongly they fit for high performance tasks. The third contribution is improving the proposed algorithm performance to its peak as discussed in the results section.