A Rounding Method to Reduce the Required Multiplier Precision for Goldschmidt Division

A new rounding method to reduce the required precision of the multiplier for Goldschmidt division is presented. It applies special truncation methods at the final iteration step. This requires a minor modification to the rounding constants of the multiplier. It allows twice the error tolerance of conventional methods and inclusive error bounds. The proposed method further reduces the required precision of the multiplier by considering the asymmetric error bounds of Goldschmidt dividers where the factors are computed using a one´s complement operation. As a result, the proposed rounding method allows the multiplier of a three-iteration Goldschmidt divider to be implemented using only three extra bits. The proposed method has been verified using a SystemC hardware model of the divider supporting variable precision. The validity of the error analysis is also checked via simulation. The final rounding results are checked with both 10¹⁰ random double precision floating-point significands and an exhaustive suite of 17-bit test vectors.