Before revision:  This library is especially suitable for direct numerical simulations of non-linear partial differential equations in spherical geometry, like the Navier-Stokes equation. The performance of our algorithms is compared to third party SHT implementations, including fast algorithms .
After revision:  The main breakthrough is to achieve very efficient on-the-fly computations of the Legendre associated functions, even for very high resolutions, by taking advantage of the specific properties of the SHT and the advanced capabilities of current and future computers. This allows us to simultaneously and significantly reduce memory usage and computation time of the SHT. We measure the performance and accuracy of our algorithms is compared to third party SHT implementations, including fast algorithms .