Exploring parallelization strategies for NUFFT data translation

This paper introduces parallelization strategies for the Non-Uniform FFT (NUFFT) data translation on multicore architectures. The NUFFT enables the use of the celebrated FFT with un-equally spaced data in numerous situations in signal and image processing as well as in scientific computing. The critical extension lies at the translation of non-equally spaced or non-uniformly sampled data onto an equally spaced Cartesian grid or vice versa. The data translation can be made sufficiently accurate, with the arithmetic complexity linearly proportional to the size of the data ensemble. For large NUFFTs, however, the data translation is found substantially dominant in computation time on modern computers while it is expected to be dominated by the FFT. In order to match the FFT performance achieved by FFTW, data locality and parallelism in the data translation must be explored and exploited as well. We are concerned with two fundamental issues. First, the data translation can be described as a matrix-vector multiplication with a matrix of irregular sparsity. This is beyond the effective scope of the conventional tiling and parallelization schemes applied by a compiler for performance improvement on computation with dense matrices. Secondly, multicore processors exist and emerge in many different configurations, and are expected to evolve further in architectural variety. This may mean the end of performance tuning on a single type of architecture. In this paper, we introduce an automation tool that takes two specifications as input, one on an application-specific data translation algorithm, the other on a target multicore processor architecture. The tool generates a parallel code that explores the data locality and parallelism by utilizing both geometric structures in data translation and the processor-memory configurations in the target architecture. We present preliminary experimental results on both a simulator and a commercial multicore machine. The results show that our parallelization strategy brings significant performance improvement for the NUFFT data translation by efficiently exploiting the data locality and concurrency in the application.