Improved Goldschmidt division method using mapping of divisors

Abstract

To achieve high precision with fewer storage resources, an improved Goldschmidt division method of using the mapping of divisors is presented. The improved division method does not need the initial approximation, which means that the look-up table can be saved. Then a mapping method is proposed to reduce the relative errors of the iteration results through multiplying the dividends and divisors by the mapping coefficients simultaneously. Since the mapping coefficients are all fixed factors, the mapping method applies CSD coding in the multiplication with fixed factors to reduce the hardware resources. Finally, using fewer hardware resources, the proposed method can achieve smaller relative errors.