An efficient exponential algorithm with exponential convergence rate

Abstract

This paper presents an efficient additive normalization method for exponential computation. Same as a previous additive normalization method, this new method can allow the values of the normalization factors in the normalization method be obtained directly from the remaining terms without any computation. Furthermore, the convergence rate of this method is also exponential. Instead of generating a group of logarithmic terms in each normalization stage, only one logarithmic term with large radix is generated and used as the normalization factor. This technique facilitates the computation of the partial result term in each normalization stage. The computation can then be implemented efficiently as a simple multiplication-and-add operation. Thorough simulations on the 24-bit exponential unit have verified that our proposed method is correct. From the synthesis results, the hardware cost and the delay of the proposed 53-bit exponential unit are only one-fourth and two-thirds of those of the 53-bit exponential unit in the previous design, respectively. We conclude that our proposed additive normalization method can significantly improve the performance of the exponential computation.