Unbiased Rounding for HUB Floating-point Addition

Abstract

Half-Unit-Biased (HUB) is an emerging format based on shifting the represented numbers by half Unit in the Last Place. This format simplifies two’s complement and roundto- nearest operations by preventing any carry propagation. This saves power consumption, time and area. Taking into account that the IEEE floating-point standard uses an unbiased rounding as the default mode, this feature is also desirable for HUB approaches. In this paper, we study the unbiased rounding for HUB floating-point addition in both as standalone operation and within FMA. We show two different alternatives to eliminate the bias when rounding the sum results, either partially or totally. We also present an error analysis and the implementation results of the proposed architectures to help the designers to decide what their best option are.