Efficient computation of very high effective-precision exponential function with additive normalization method

Abstract

The previously proposed fast-convergence additive normalization method with exponential convergence rate for computing the exponential function suffers from high hardware cost for obtaining the normalization factors. Furthermore, when the value of 0.v has many leading-zero bits, the hardware cost of the exponential computation will increase dramatically in order to obtain very high effective precision. In this article, we have first proposed a new method, called efficient fast-convergence additive normalization, to solve the large-hardware-cost problem present in the previous fast-convergence method. Then, leading-zero bit detection (LZD) of 0.v is applied to the new efficient fast-convergence method. With this technique, the efficient fast-convergence method can be used to obtain very high effective-precision exponential function at a low hardware cost. We have designed a 24-bit and a 53-bit effective-precision exponential unit using our proposed methods. Thorough simulations of this 24-bit unit have verified that our proposed methods are correct. From our implementation results, we have shown that the proposed efficient fast-convergence method is very effective in improving the cost and speed of the exponential units. Furthermore, we have also shown that the hardware cost of the 48-bit proposed efficient exponential unit can be reduced by about 41% by using the LZD technique. We conclude that our proposed efficient fast-convergence method with LZD technique can very effectively enhance the performance of exponential unit design.