New Results on Non-normalized Floating-point Formats

Abstract

Compulsory normalization of the represented numbers is a key requirement of the floating-point standard. This requirement contributes to fundamental characteristics of the standard, such as taking the most of the precision available, reproducibility and facilitation of comparison and other operations. However, it also imposes a high restriction in effectiveness of basic arithmetic operation implementation. In many embedded applications may be worth to sacrifice the benefits of normalization for gaining in implementation metrics. This paper analyzes and measures the effect of removing the normalization requirement in terms of precision and implementation savings for embedded applications. We propose several adder and multiplier architectures to deal with non-normalized floating-point numbers, and quantify the accuracy loss and the improvements in hardware implementation. Our experiments show that it is possible to reduce the area and power consumption up to 78% in ASIC and 50% in FPGA implementations with a reasonable accuracy loss.