Matrix multiplication is ubiquitous in scientific computing. From computational science to machine learning, a large and diverse set of applications rely on the performance of general matrix-matrix multiplication (GEMM) subroutines. The Intel®Math Kernel Library(R) provides highly optimized GEMM subroutines that take full advantage of the available parallelism and vectorization in both Intel®Xeon®and Intel®Xeon Phi(TM) processors. In this paper we discuss the optimization of GEMM subroutines for the Intel®Xeon PhiTMx200 (code-named Knights Landing).

Many applications, such as PDE based simulations and machine learning, apply blas/lapack routines to large groups of small matrices. While existing batched blas APIs provide meaningful speedup for this problem type, a non-canonical data layout enabling cross-matrix vectorization may provide further significant speedup. In this paper, we propose a new compact data layout that interleaves matrices in blocks according to the SIMD vector length. We combine this compact data layout with a new interface to blas/lapack routines that can be used within a hierarchical parallel application. Our layout provides up to 14X, 45X, and 27X speedup against OpenMP loops around optimized dgemm, dtrsm and dgetrf kernels, respectively, on the Intel Knights Landing architecture. We discuss the compact batched blas/lapack implementations in two libraries, KokkosKernels and Intel® Math Kernel Library. We demonstrate the APIs in a line solver for coupled PDEs. Finally, we present detailed performance analysis of our kernels.