Spherical harmonic transforms with S2HAT (Scalable Spherical Harmonic Transform library)

Giulio Fabbian (Laboratoire AstroParticule et Cosmologie), M. Szydlarski (INRIA), R. Stompor (APC), L. Grigori (INRIA), P. Esterie (LRI), J.Falcou (LRI)


Many problems in astronomy and astrophysics require a computation of the spherical harmonic transforms. This is in particular the case whenever data to be analyzed are distributed over the sphere or a set of corresponding mock data sets has to be generated. In many of those contexts, rapidly improving resolutions of both the data and simulations puts increasingly bigger emphasis on our ability to calculate the transforms quickly and reliably.

In this talk I will describe the scalable spherical harmonic transform library, S2HAT, consisting of a set of flexible, massively parallel, and scalable routines for calculating diverse (scalar, spin-weighted, etc) spherical harmonic transforms for a class of isolatitude sky grids or pixelizations. The library routines implement the standard algorithm with the complexity of O(n^3/2), where n is a number of pixels/grid points on the sphere, however, owing to their efficient parallelization and advanced numerical implementation, they achieve very competitive performance and near perfect scalability.

Here my focus will be specifically on the GPU-enabled part of the software. This includes routines coded using the CUDA language, which can run on a single, or multiple GPUs. In the latter case the inter-GPU communication is facilitated via MPI (Massage Passing Instruction) calls between the CPUs associated with the respective GPUs. I will describe in detail the implementation of the routines, discuss their performance and scalability, and provide a comparison of the many-core CPU based implementation of the routines with their GPU counterparts, highlighting advantages and shortcomings of the latter. I will illustrate the library capability and functionality with examples drawn from the cosmic microwave background studies.

The library is distributed under the GNU public license and available for download from http://www.apc.univ-paris7.fr/APC_CS/Recherche/Adamis/MIDAS09/software.html. The extensive documentation is also available.

Paper ID: P040

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