Enhancing Sca/LAPACKrc with Extremely-Fast Least-Squares Solvers for Heterogeneous CPU/FPGA Supercomputers

An estimated 70% of supercomputing cycles worldwide are dedicated to solving numerical linear algebra problems, and large-scale ¿least-squares¿ computational problems are an important subset of numerical linear algebra. Sca/LAPACKrc, a multimillion dollar program to develop FPGA-accelerated linear algebra software, already has demonstrated speedups larger than 100x per commodity processor for a wide class of linear equation solvers. Despite its tremendous success, Sca/LAPACKrc still lacks a much needed functionality for least squares solvers. This project will enhance Sca/LAPACKrc with a comprehensive set of FPGA-accelerated sparse and dense least squares solvers that will be portable and easy to use and integrate. The use of these solvers within a supercomputing network will be 1 to 2 orders of magnitude less expensive than CPU-based technology with similar performance. Phase I demonstrated the world¿s first FPGA-accelerated least-squares solver, achieving speedups larger than 40x at 64-bit accuracy. Phase I also established the architectural foundations for the entire solver set. Phase II will complete the development of this solver set, which will include accelerated implementations of the QR algorithm, and most flavors of QR-based least squares solvers (in both dense and sparse direct forms), as well as large-scale sparse iterative least squares solvers of the Krylov type. Commercial Applications and other Benefits as described by the awardee: The ability to solve large least-squares problems fast and at affordable costs, has implications across a wide array of applications within the DOE mission, including energy fusion research, weather/earthquake/tsunami prediction, oil exploration, bioinformatics, geodetics, structural analysis, tomography, astrophysics, power grid control, and statistical data analysis.