On-line high-radix exponential with selection by rounding

An on-line high-radix algorithm for computing the exponential function (e^x) with arbitrary precision n is presented. Selection by rounding and a redundant digit-set for the digits e_j are used, with selection by table in the first iteration to guarantee the convergence of the algorithm, and the on-line delay is δ = 2 cycles. A sequential architecture implementing the algorithm is proposed, and the execution times and hardware requirements are estimated for 32-bit and 64-bit computations for several radix values. An analysis of the tradeoff between area and speed shows that the most efficient implementations are obtained for radix values from r = 32 to 256, depending on the precision.