Integer and Floating Point Matrix-Vector Multiplication on the Reconfigurable Mesh

• Authors: Jerry L. Trahan;Chun-ming Lu;Ramachandran Vaidyanathan
• Venue: IPPS '96 Proceedings of the 10th International Parallel Processing Symposium
• Year: 1996

This paper presents the following results for matrix-vector multiplication on the reconfigurable mesh (R-Mesh). Multiplication of an N \times N matrix and an N \times 1 vector (each element of which is an integer of w bits) can be performed in O(\log w) time on a two-dimensional O\left(N\frac{w}{\log w}{\log^2 N}\right) \times O\left(N\frac{w}{\log w}{\log^2 N}\right) R-Mesh or a three-dimensional N\times N\times\left(\frac{w}{\log w}\log^2N\right) R-Mesh; in both cases, inputs and outputs are stored as w-bit integers. A natural extension of this problem is for floating point inputs; floating point numbers have not been handled before on any reconfigurable bus-based model. Matrix-vector multiplication with floating point inputs can be performed in O\left(\max\{\log\log N,\log w\}\right) time on an \mbox{N \times N \times \max\left\{\sqrt{\frac{N}{\log\log N}},\frac{w}{\log w} \log^{2} N\right\} } three-dimensional R-Mesh, with the inputs and outputs stored as w-bit floating point numbers.