public class Sqrt {
public static void main(String[] args) {
// read in the command-line argument
double c = Double.parseDouble(args[0]);
double epsilon = 1e-15; // relative error tolerance
double t = c; // estimate of the square root of c
// repeatedly apply Newton update step until desired precision is achieved
while (Math.abs(t - c/t) > epsilon*t) {
t = (c/t + t) / 2.0;
}
// print out the estimate of the square root of c
System.out.println(t);
}
}
/*************************************************************************
* Computes the square root of a nonnegative number c using
* Newton's method:
* - initialize t = c
* - replace t with the average of c/t and t
* - repeat until desired accuracy reached
*
* % java Sqrt 2
* 1.414213562373095
*
* % java Sqrt 1000000
* 1000.0
*
* % java Sqrt 0.4
* 0.6324555320336759
*
* % java Sqrt 1048575
* 1023.9995117186336
*
* % java Sqrt 16664444
* 4082.2106756021303
*
* % java Sqrt 0
* 0.0
*
* % java Sqrt 1e-50
* 9.999999999999999E-26
*
*
* Remarks
* ----------
* - using Math.abs() is required if c < 1
*
*
* Known bugs
* ----------
* - goes into an infinite loop if the input is negative
*
*************************************************************************/
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