A hardware algorithm for variable-precision logarithm

This paper presents an efficient hardware algorithm for variable-precision logarithm. The algorithm uses an iterative technique that employs table lookups and polynomial approximations. Compared to similar algorithms, it reduces the number of fixed-precision operations by avoiding full precision computations and dynamically varying the precision of intermediate results. It also uses significantly smaller tables than related algorithms. For a specified hardware implementation, the algorithm requires fewer than 2L² fixed-precision multiplications to evaluate the logarithm to L words of precision. An error analysis for the algorithm is also presented