Issue No. 10 - October (1987 vol. 36)
B. Parhami , School of Computer Science, Carleton University
We show that except for a few special cases allowing smaller tables, the lookup table used for achieving k digits of convergence after the initial multiplication (or for obtaining the approximate reciprocal of the divisor with k - 1 digits of accuracy) in iterative division methods must have at least (r--l) rk words of k + I digits, r being the number representation base. In the important special case of r = 2 with k =5, a 2k-word table with k-bit entries can be used, since the initial digit is always 1. It is also shown that a table of this optimal size can always be constructed. The special cases corresponding to r = 3 with k = 1, and r = 2 with k = 4, allow smaller tables than the general case and are thus handled separately.
table lookup, Arithmetic algorithms, computer arithmetic, division algorithm, iterative division, quadratic convergence, reciprocal approximation
B. Parhami, "On the Complexity of Table Lookup for Iterative Division," in IEEE Transactions on Computers, vol. 36, no. , pp. 1233-1236, 1987.