Beyond Base-2 Logarithmic Number Systems (WiP Paper)
Syed Asad Alam, David P. Gregg · 2020
Logarithmic number systems (LNS) reduce hardware complexity for multiplication and division in embedded systems, at the cost of more complicated addition and subtraction. Existing LNS typically use base-2, meaning that representable numbers are some (often fractional) power of two. We argue that other bases should be considered. The base of the LNS determines the distribution of values and may reduce representation errors when converting inputs to LNS in domain-specific embedded hardware accelerators. Further, LNS addition and subtraction are normally implemented with lookup tables whose properties may be a function of the base.