Question

Develop a method for computing \[a^x\]when \[0 \leq x < 1\] using only shifting, addition, and subtraction, similar to the following method used for division in computer hardware:

y := 0, z := x >> 1, k := 1;
L2: if x = 1 then STOP;
if x - z < 1 then
do
z := z >> 1;
k := k + 1;
while x - z < 1;
x := x - z;
z := x >> k;
y := y + log_a(2^k/(2^k - 1));
GOTO L2

Answer 1

oops it's not used for division; it's used for computing logarithms :-P

Answer 2

oh and >> is bitwise right-shift.