Wavemoth -- Fast spherical harmonic transforms by butterfly matrix compression

TL;DR

Wavemoth is an open source code that significantly accelerates spherical harmonic transforms by employing butterfly matrix compression and optimized computational techniques, outperforming existing methods especially at high resolutions.

Contribution

The paper introduces Wavemoth, a novel implementation of SHTs that uses butterfly matrix compression and optimized CPU techniques for faster performance.

Findings

Wavemoth is twice as fast as libpsht at medium resolutions.

At Planck resolution (L ~ 4000), Wavemoth is 3-6 times faster than libpsht.

Wavemoth scales as O(L^2 (log L)^2) for practical resolutions.

Abstract

We present Wavemoth, an experimental open source code for computing scalar spherical harmonic transforms (SHTs). Such transforms are ubiquitous in astronomical data analysis. Our code performs substantially better than existing publicly available codes due to improvements on two fronts. First, the computational core is made more efficient by using small amounts of precomputed data, as well as paying attention to CPU instruction pipelining and cache usage. Second, Wavemoth makes use of a fast and numerically stable algorithm based on compressing a set of linear operators in a precomputation step. The resulting SHT scales as O(L^2 (log L)^2) for the resolution range of practical interest, where L denotes the spherical harmonic truncation degree. For low and medium-range resolutions, Wavemoth tends to be twice as fast as libpsht, which is the current state of the art implementation for the HEALPix grid. At the resolution of the Planck experiment, L ~ 4000, Wavemoth is between three and six times faster than libpsht, depending on the computer architecture and the required precision. Due to the experimental nature of the project, only spherical harmonic synthesis is currently supported, although adding support or spherical harmonic analysis should be trivial.