摘要
本文研究六边形区域上快速傅里叶变换（FFTH）的CUDA—MPI算法及其实现．首先，我们通过充分利用CUDA的层次化并行机制及其库函数，设计了FFTH的高效率的CUDA算法．对于规模为3X2048。的双精度复数类型数据，我们设计的CUDA程序与CPU串行程序相比可以达到12倍加速比，如果不计内存和显存之间的数据传输，则加速比可达40倍；其计算效率与CUFFT所提供的二维方形区域FFT程序的效率基本一致．在此基础上，我们通过研究GPU上分布式并行数据的转置与排序算法，优化设计了FFTH的CUDA-MPI算法．在3×8192^2的数据规模、10节点X6GPU的计算环境下，我们的CUDA-MPI程序与CPU串行程序相比达到了55倍的加速；其效率比MPI并行版FFTW以及基于CUFFT本地计算和FFTW并行转置的方形区域并行FFT的效率都要高出很多．FFTH的CUDA-MPI算法研究和测试为大规模CPU＋GPU异构计算机系统的可扩展新型算法的探索提供了参考．
In this paper, we study the parallel algorithm based on CUDA and MPI for the Fast Fourier Transform on the hexagon （FFTH） and its implementation. Firstly, we design a CU- DA FFTH algorithm by utilizing the hierachica! parallelization mechanism and the build-in CUFFT library for classic rectangular FFTs. With respect to the serial cpu program, our CUDA program achieves 12x speedup for 3 × 2048^2 double-precision complex-to-complex FFTH. If we ignore the PCI between main memory and GPU device memory, around 30x- 40x speedup can be even achieved. Although the non-tensorial FFTH is much more complicated than the rectangular FFT, our CUDA FFTH program gains the same efficiency as the rectangular CUFFT. Next, efforts are mainly contributed to optimization techniques for parallel array transposition and data sorting, which significantly improve the efficiency of the CUDA-MPI FFTH algorithm. On a 10-node cluster with 60 GPUs, our CUDA-MPI program achieves about 55x speedup with respect to the the serial cpu program for 3 × 8192^2 complex-to-complex double-precision FFTH, and it is more efficient than the MPI parallel FFTW. Our research on the CUDA-MPI algorithm for FFTH is beneficial to the exploration and development of new parallel algorithms on large-scale CPU-GPU heterogeneous computer systems.
出处
《数值计算与计算机应用》
CSCD
2012年第1期59-72,共14页
Journal on Numerical Methods and Computer Applications
基金
国家自然科学基金(10971212
91130014)资助项目
