Unum: Adaptive Floating-Point Arithmetic

Usually, arithmetic units represent numeric data-types employing fixed-length representations. For instance, hardware representations of real numbers usually employ fixed-length formats defined by the IEEE Standard 754 (32-bit single-precision, 64-bit double-precision, , floating-point numbers). Fixed-length representations allow simpler and faster arithmetic units than variable-length representations. However, fixed-length representations lack the ability to adapt both their accuracy and dynamic range to the application requirements. As some variable-length representations expose this adaptivity, they allow hardware implementations to exploit this adaptivity. Recently, Unum (universal number) representation has been proposed as an extension of floating-point representations. Unum is a variable-length representation that adapts the bitsize of the representation to the actual numbers being represented and, moreover, Unum associates and propagates accuracy information through arithmetic operations. In this work we compare Unum versus the floating-point representations defined by IEEE Standard 754. We show that Unum arithmetic improves IEEE 754 arithmetic: a) results obtained using Unum arithmetic are more reliable than IEEE 754's results because Unum does not hide accuracy issues, and b) Unum arithmetic units may implement energy-efficient techniques because Unum dynamically adapts the bitsize of the representation to the actual numbers being represented.