A rounding method with improved error tolerance for division by convergence

A new rounding method for division by convergence is presented. It allows twice the error tolerance of current methods, so it allows the multiplier of a 3-iteration Goldschmidt divider to be implemented using only 3 extra bits. The new rounding method applies special truncation methods at the final iteration step, and it requires a minor modification in rounding constants of the multiplier. It has been verified using a SystemC model of the Goldschmidt divider supporting variable precision. The verification consists of two parts: the maximum error of approximate quotients and the rounding result correctness. The maximum error of approximate quotients is checked by analysis and via simulation. The final rounding results are checked with both random double precision floating-point significants and exhaustive 17-bit precision test vectors.