Integer and floating point matrix-vector multiplication on the reconfigurable mesh

This paper presents the following results for matrix-vector multiplication on the reconfigurable mesh (R-Mesh). Multiplication of an N×N matrix and an N×1 vector (each element of which is an integer of w bits) can be performed in O(logw) time on a two-dimensional O(Nw/(logw)log²N)×O(Nw/(logw)log²N) R-Mesh or a three-dimensional N×N×(w/(logw)log²N) 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(max{loglogN,logw}) time on an N×N×max {√[N/(loglogN)],w/(logw)log²N} three-dimensional R-Mesh, with the inputs and outputs stored as w-bit floating point numbers