Prime Numbers

9.2 Enhancements to modular arithmetic 451
The reason for the particular power in the definition is to allow our
eventual general div algorithm to function. Next, we give a method for rapid
computation of R(N), based on multiplies, adds, and subtracts alone:
Algorithm 9.2.8 (Generalized reciprocation). This algorithm returns R(N)
for positive integer N.
1. [Initialize]
b = B(N − 1); r =2 b ; s = r;
2. [Perform discrete Newton iteration]
r =2r −⌊N⌊r 2 /2 b ⌋/2 b ⌋;
if(r ≤ s) goto [Adjust result];
s = r;
goto [Perform discrete Newton iteration];
3. [Adjust result]
y =4 b − Nr;
while(y