Algorithm 1. $\mathrm{Calculation} \mathrm{of} \mathrm{the} \mathrm{integer} \mathrm{square} \mathrm{root} \mathrm{of} x \mathrm{by} \mathrm{rolling} \mathrm{back} \mathrm{from} s_0$.

Input: $x,s_0$ Output: $s$$// \mathrm{integer} \mathrm{square} \mathrm{root} \mathrm{of} x$ Initialization: $s_i\leftarrow s_0$ $D\leftarrow s_i^2-x$ While $(D>0$) Do $s_i\leftarrow s_i-1$ $D\leftarrow D-(s_i\ll 1)-1$ End Do $s\leftarrow s_i$