Fast additive normalisation method for exponential computation

Conventional additive normalisation methods suffer from their linear convergence rate. A new method yields the normalisation factor values directly from predetermined terms without computation. The number of normalisation factors obtained in each normalisation stage is twice the number of normalisation factors in the previous stage. As a result the number of normalisation stages needed to compute the exponential function is proportional to the logarithmic value of the operand word-length. In other words, the convergence rate of the proposed method is exponential. These two advantages of the new method significantly enhance the speed of the additive normalisation method. Based on this method, 24-bit and 53bit exponential unit architectures have been designed. Extensive 24-bit unit simulations verify the proposed algorithm and error analysis method. Based on the analysis, the hardware cost of the 53-bit unit includes 80 kbits ROM, four adders, and four multipliers.