Division and square root in the quarter-imaginary number system

Imaginary Number Bases

“…The An alternate method for division (which produces the inverse of the divisor) is given by Nadler [6].…”

Nth ROOT COMPUTING METHODS

“…The initial random number Xo, in octal form, was 232544614, but other runs of the experiment showed, as should be the case, that the results were insensitive to x 0 after a reasonable sequence length in (8). execute, and none more than 108.…”

“…The 27-bit pseudo-random numbers used were generated in the interval (1/2, 1) by first generating a 26-bit pseudorandom number, and then putting a "1" in front of it, making a 27-bit number. The al~orithm parameters used in (8) were aull, CaI, and p.26, and the resulting serial cor-relation between two successive numbers is, from (9), .-6"2-26 (1 -2-26) 0.0005…”

“…The error of the iteration formula (10) may be estimated by considerin6 the error Ei+l= Ot -Xial the remainder of the truncated series in(8):00 Ei+ W u uk Yk (14) If f(x) is a smooth curve in the neighborhood of x ,,O., vwe may write f (cc÷+)• 0 f(() + 6 f,• where f is a small error. On the ith iteration, xz-+Gi and since f(oo) 0, f(xi) --iIf'(0c).…”