Optimizing a Multiple Right-Hand Side Dslash Kernel for Intel Knights Corner

There is a significant interest in the computational physics community to perform lattice quantum chromodynamics (LQCD) simulations, which can run into the trillions of operations. LQCD computations solve a sparse linear system using a Wilson Dslash kernel, which has an arithmetic intensity of 0.88–2.29. This makes Dslash memory bandwidth-bound on most architectures, including Intel Xeon Phi Knights Corner (KNC). Most research optimizing the Dslash operator has been focused on single right-hand side (SRHS) linear solvers. There is a class of LQCD computations which aims to solve systems with multiple right-hand sides (MRHS), presenting additional opportunities for data reuse and vectorization. We present two approaches to MRHS Dslash: a vector register blocking approach and one using the software package QPhiX with a custom code generator for low-level intrinsics. We observed significant speedups using our approaches, with sustained performance of over 700 GFLOPS (single precision) in one instance. We achieved up to 29 % of theoretical peak performance compared to a maximum of 13 % obtained by the previous SRHS method using QPhiX.