$\texttt{cunuSHT}$: GPU Accelerated Spherical Harmonic Transforms on Arbitrary Pixelizations

TL;DR

The paper introduces 'cunusht', a GPU-accelerated Python package for fast, accurate spherical harmonic transforms on arbitrary pixelizations, outperforming CPU methods significantly, especially for high-resolution problems.

Contribution

It presents a novel GPU-accelerated implementation of spherical harmonic transforms applicable to arbitrary pixelizations, with improved performance over existing CPU algorithms.

Findings

Achieves up to 5x speedup over CPU algorithms for high-resolution problems.

Supports arbitrary pixelization schemes, including nonuniform ones.

Provides a publicly available Python package with comprehensive documentation.

Abstract

We present $\texttt{cunusht}$, a general-purpose Python package that wraps a highly efficient CUDA implementation of the nonuniform spin-$0$ spherical harmonic transform. The method is applicable to arbitrary pixelization schemes, including schemes constructed from equally-spaced iso-latitude rings as well as completely nonuniform ones. The algorithm has an asymptotic scaling of $\mathrm{O}{(\ell_{\rm max}^3)}$ for maximum multipole $\ell_{\rm max}$ and achieves machine precision accuracy. While $\texttt{cunusht}$ is developed for applications in cosmology in mind, it is applicable to various other interpolation problems on the sphere. We outperform the fastest available CPU algorithm by a factor of up to 5 for problems with a nonuniform pixelization and $\ell_{\rm max}>4\cdot10^3$ when comparing a single modern GPU to a modern 32-core CPU. This performance is achieved by utilizing the double Fourier sphere method in combination with the nonuniform fast Fourier transform and by avoiding transfers between the host and device. For scenarios without GPU availability, $\texttt{cunusht}$ wraps existing CPU libraries. $\texttt{cunusht}$ is publicly available and includes tests, documentation, and demonstrations.