Auto-tuning the Matrix Powers Kernel with SEJITS

Abstract

Abstract. The matrix powers kernel, used in communication-avoiding Krylov subspace methods, requires runtime auto-tuning for best performance. We demonstrate how the SEJITS (Selective Embedded Just-InTime Specialization) approach can be used to deliver a high-performance and performance-portable implementation of the matrix powers kernel to application authors, while separating their high-level concerns from those of auto-tuner implementers involving low-level optimizations. The benefits of delivering this kernel in the form of a specializer, rather than a traditional library, are discussed. Performance of the matrix powers kernel specializer is evaluated in the context of a communication-avoiding conjugate gradient (CA-CG) solver, which compares favorably to traditional CG.

Level-Based Blocking for Sparse Matrices: Sparse Matrix-Power-Vector Multiplication

“…Therefore, those schemes require either redundant computations (explicit schemes) and/or irregular accesses to the matrix entries with bookkeeping (implicit schemes), resulting in performance bottlenecks. In [17] a runtime auto-tuning was introduced for the MPK scheme described above to choose the appropriate parameters (e.g., explicit vs. implicit schemes) for a given matrix. This was generalized to various kernels like Jacobi and serial Gauss-Seidel iterative solvers and automated using a sparse tiling algorithm via the power of loop chain abstraction [18], [19].…”