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 + d
i
r-
^k
) where d
i
, 0 ≤ d
i
r, 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.