More Efficient Radix-2 Algorithms for Some Elementary Functions

de Lugish [1] has defined efficient algorithms in radix 2 for certain elementary functions such as Y[X,Y/X^1/2, Y + lnX, Y.exp (X), etc. His technique requires a systematic 1-bit left shift of a partially converged result, together with two 4-bit comparisons to select a ternary digit for the next iteration. This selection of digits reduces the average number of full precision additions to about 1/3 of those required in conventional schemes [3]. This paper develops modified algorithms in radix 2 which are more efficient when the time for a full precision addition is comparable to the time for a shift and comparison. The modified procedure is developed for Y/X in detail where more than a 40 percent decrease in execution time is achieved for only a marginal increase in cost.