Scaling multiple addition and prefix sums on the reconfigurable mesh

Abstract

Multiple addition is the problem of adding N b-bit integers. Prefix sums and multiple addition play fundamental roles in many algorithms, particularly on the reconfigurable mesh (R-Mesh). Scaling algorithms on the R-Mesh to run with the same or increased efficiency on fewer processors is a challenging and important proposition. In this paper, we present algorithms that scale with increasing efficiency for multiple addition, prefix sums, and matrix–vector multiplication. Along the way, we obtain an improved multiple addition algorithm.