Method for determining the square root of a long-bit number using a short-bit processor

摘要

In a method for determining the square root of a long-bit number using a short-bit processor, the long-bit number is assumed to be cx2^2K+d, where c, d<2^2k, and its solution is assumed to be (ax2^K+b)². The 'a' is determined by using a bisection method to obtain the floor value of the square root of 'c'. In order to obtained the value of 'b', there is derived a successive substitution equation: b_[n]=(c-a²)x2^2k+(d-b_[n-1]²)/2^2(k+1). An initial value is given to 'b' to execute the successive substitution equation recursively several times until the equation is convergent.