Matrix Multiply-Add in Min-plus Algebra on a Short-Vector SIMD Processor of Cell/B.E.

Abstract

It is well-known that the all-pairs shortest paths problem has a similar algorithmic characteristic to the classical matrix-matrix multiply-add (MMA) problem, one of the differences between the two problems is in the underlying algebra: the matrix multiply-add uses linear (+, x)-algebra whereas the all-pairs shortest paths problem uses (min, +)-algebra. This paper presents an implementation of 64×64 matrix multiply-add kernel in (min, +)-algebra on a short-vector SIMD processor, the so-called Synergistic Processing Element (SPE), of the Cell Broadband Engine (Cell/B.E.). Our implementation for the shortest paths problem adopts an existing fast algorithm of matrix multiply-add with a reduction of the number of required registers. The MMA implementation in (min, +)-algebra achieves the speed of 8.502 Gflop/s, which is about three times as low as that of the (+, x)-algebra MMA and is very close to the theoretical estimation based on the required number of instructions.