Co-exploration of NLA kernels and specification of Compute Elements in distributed memory CGRAs

Coarse Grained Reconfigurable Architectures (CGRA) are emerging as embedded application processing units in computing platforms for Exascale computing. Such CGRAs are distributed memory multi-core compute elements on a chip that communicate over a Network-on-chip (NoC). Numerical Linear Algebra (NLA) kernels are key to several high performance computing applications. In this paper we propose a systematic methodology to obtain the specification of Compute Elements (CE) for such CGRAs. We analyze block Matrix Multiplication and block LU Decomposition algorithms in the context of a CGRA, and obtain theoretical bounds on communication requirements, and memory sizes for a CE. Support for high performance custom computations common to NLA kernels are met through custom function units (CFUs) in the CEs. We present results to justify the merits of such CFUs.