Multidimensional Logarithmic Number System Addition and Subtraction
Vassil Dimitrov, Graham Jullien, Roberto Muscedere · 2017
This chapter describes a hardware-realizable method of performing single-digit multidimensional logarithmic number system (MDLNS) addition and subtraction that generates the same solutions as with a pure lookup table (LUT) method for any number and choice of bases, as well as exponent ranges. The simplest method to perform addition and subtraction in MDLNS is to use a pure LUT scheme. Addition and subtraction operations in the LNS have been implemented in hardware using many different number representations [4–8] (integer, fixed-point, floating point, and integer rational numbers). Depending on the method of implementation, D z and D w may be either extracted from a LU calculated exactly from the expressions, or interpolated from smaller tables. The LUT and Range-Addressable Lookup Table (RALUT) components are generated with gates, but can easily be replaced with full-custom autogenerated components. It is possible to achieve additional table reductions in the RALUT by merging adjacent table entries.