Level-3 BLAS and LU Factorization on a Matrix Processor

Abstract

As increasing clock frequency approaches its physical limits, a good approach to enhance performance is to increase parallelism by integrating more cores as coprocessors to general-purpose processors in order to handle the different workloads in scientific, engineering, and signal processing applications. In this paper, we propose a many-core matrix processor model consisting of a scalar unit augmented with b × b simple cores tightly connected in a 2D torus matrix unit to accelerate matrix-based kernels. Data load/store is overlapped with computing using a decoupled data access unit that moves b × b blocks of data between memory and the two scalar and matrix processing units. The operation of the matrix unit is mainly processing fine-grained b × b matrix multiply-add (MMA) operations. We formulate the data alignment operations including matrix transposition and skewing as MMA operations in order to overlap them with data load/store. Two fundamental linear algebra algorithms are designed and an- alytically evaluated on the proposed matrix processor: the Level-3 BLAS kernel, GEMM, and the LU factorization with partial pivoting, the main step in solving linear systems of equa- tions. For the GEMM kernel, the maximum speed of computing measured in FLOPs/cycle is approached for different matrix sizes, n , and block sizes, b. The speed of the LU factorization for relatively large values of n ranges from around 50–90% of the maximum speed depending on the model parameters. Overall, the analytical results show the merits of using the matrix unit for accelerating the matrix-based applications.