A novel algorithm for multi-operand logarithmic number system addition and subtraction using polynomial approximation

In this paper, a novel algorithm for multi-operand Logarithmic Number System (LNS) addition and subtraction is presented. In particular, the computation of the nonlinear functions required for logarithmic addition and subtraction is decomposed into computing 2^-x, log₂(1+x), some additions, and some shifts. The error behaviour of the algorithm is analyzed, upper bounds of the computational error are provided and it is shown that the introduced Propagation Error Cancellation (PEG) technique and the Error Spectrum Shaping can significantly narrow the error distribution. The inherent parallelism of the proposed algorithm and the pipelinability that exists in the computation of 2^-x and log₂(1+x) by using polynomials are exploited by simple VLSI architectures that exhibit important speed-up over the equivalent ROM-based designs. Also, a rule for the determination of the optimal number of pipeline stages is suggested