Efficient Matrix Multiplication Based on Discrete Stochastic Arithmetic

Numerical verification of industrial codes, such as those developed at Électricit e de France (EDF) R&D, requires estimating the precision and the quality of computed results, which is even more challenging for codes running in HPC environments where billions of instructions are performed each second, usually using external libraries (e.g., MPI, BLACS, BLAS, LAPACK). In this context, one needs a tool that is as nonintrusive as possible to avoid rewriting the original code. In this regard, the CADNA library, which implements the Discrete Stochastic Arithmetic, appears to be a promising approach for industrial applications. In this paper, we are interested in an efficient implementation of the BLAS routine DGEMM (General Matrix Multiply) using Discrete Stochastic Arithmetic. The implementation of the basic algorithm for a matrix product using stochastic types leads to an overhead greater than 1000 for a matrix of 1024*1024 compared to the standard version and commercial versions of xGEMM. We present details of different solutions to reduce this overhead and results we have obtained.