Spherical harmonic transform with GPUs
Résumé
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.
Nous décrivons un algorithme de calcul d'une transformée inverse en harmoniques sphériques approprié pour des processeurs graphiques. Nous utilisons CUDA et la mise en oeuvre utilise une routine du logiciel S2hat écrit en Fortran90. Nous nous concentrons sur deux étapes séquentielles de ce calcul, tout en conservant le cadre parallele efficace du code original. Le travail présenté ici a été réalisé dans le cadre de la simulation et de l'analyse du fond difus cosmologique. Cependant, nous estimons que les techniques présentées dans ce papier sont d'un intérêt et d'une applicabilité plus générale.
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