Correctly rounded architectures for Floating-Point multi-operand addition and dot-product computation

Abstract

This study presents hardware architectures performing correctly rounded Floating-Point (FP) multioperand addition and dot-product computation, both of which are widely used in various fields, such as scientific computing, digital signal processing, and 3D graphic applications. A novel realignment method is proposed to solve the catastrophic cancellation and multi-sticky bits. Only one rounding operation is performed in both of the proposed FP multi-operand adder and dot-product computation unit. Implementation results show that our architectures not only can produce correctly rounded results, whose errors are less than 0.5 ULP (Unit in the Last Place), but also have reduced delay comparing with the traditional network architecture, which uses 2-operand FP adders and multipliers to perform multi-operand addition and dot-product computation.