Parallel Multiplicative Algorithms for Some Elementary Functions

This correspondence presents generalized higher radix algorithms for some elementary functions which use fast parallel m-bit multipliers where radix = 2^m. These algorithms are extensions of those iterative schemes which are based on multiplications by (1 + 2^-i) and the use of prestored values of ln (1 + 2^-i) and tan-1(2^-i). The particular functions under consideration are y/x, y/x^1/2, y. exp (x), y + 1n (x), sin (x) and cos (x) [and hence tan (x)]. The extended algorithms rely on multiplication by (1 + dir-^k) where di, 0 ≤ dir, is an m-bit integer. Using a simple selection procedure for di, simulations show that p(radix r) digits of a function may be generated, on the average, in less than p + 1 iterations.