An Empirically Optimized Radix Sort for GPU

Graphics Processing Units (GPUs) that support general purpose program are promising platforms for high performance computing. However, the fundamental architectural difference between GPU and CPU, the complexity of GPU platform and the diversity of GPU specifications have made the generation of highly efficient code for GPU increasingly difficult. Manual code generation is time consuming and the result tends to be difficult to debug and maintain. On the other hand, the code generated by today's GPU compiler often has much lower performance than the best hand-tuned codes. A promising code generation strategy, implemented by systems like ATLAS~\cite{Whaley}, FFTW~\cite{FFTW_org}, SPIRAL~\cite{Pueschel:05} and X-Sort~\cite{Li:05}, uses empirical search to find the parameter values of the implementation, such as the tile size and instruction schedules, that deliver near-optimal performance for a particular machine. However, this approach has only proved successful when applied to CPU where the performance of CPU programs has been relatively better understood. Clearly, empirical search must be extended to general purpose programs on GPU. In this paper, we propose an empirical optimization technique for one of the most important sorting routines on GPU, the radix sort, that generates highly efficient code for a number of representative NVIDIA GPUs with a wide variety of architectural specifications. Our study has been focused on the algorithmic parameters of radix sort that can be adapted to different environments and the GPU architectural factors that affect the performance of radix sort. We present a powerful empirical optimization approach that is shown to be able to find highly efficient code for different NVIDIA GPUs. Our results show that such an empirical optimization approach is quite effective at taking into account the complex interactions between architectural characteristics and that the resulting code performs significantly better than two radix sort implementations that have been shown outperforming other GPU sort routines with the maximal speedup of 33.4\%.