Spherical harmonic transform with GPUs

TL;DR

This paper presents an optimized GPU-based algorithm for inverse spherical harmonic transforms, significantly accelerating computations relevant to cosmic microwave background analysis and potentially benefiting other applications.

Contribution

The authors develop a CUDA implementation of the inverse spherical harmonic transform based on S2HAT, achieving substantial speedups over CPU-based methods.

Findings

GPU acceleration up to 18 times over single-core S2HAT

Performance limited by Fast Fourier transforms

Applicable to cosmic microwave background simulations

Abstract

We describe an algorithm for computing an inverse spherical harmonic transform suitable for graphic processing units (GPU). We use CUDA and base our implementation on a Fortran90 routine included in a publicly available parallel package, S2HAT. We focus our attention on the two major sequential steps involved in the transforms computation, retaining the efficient parallel framework of the original code. We detail optimization techniques used to enhance the performance of the CUDA-based code and contrast them with those implemented in the Fortran90 version. We also present performance comparisons of a single CPU plus GPU unit with the S2HAT code running on either a single or 4 processors. In particular we find that use of the latest generation of GPUs, such as NVIDIA GF100 (Fermi), can accelerate the spherical harmonic transforms by as much as 18 times with respect to S2HAT executed on one core, and by as much as 5.5 with respect to S2HAT on 4 cores, with the overall performance being limited by the Fast Fourier transforms. The work presented here has been performed in the context of the Cosmic Microwave Background simulations and analysis. However, we expect that the developed software will be of more general interest and applicability.