/******************************************************************************

* Compilation: javac Sqrt.java

* Execution: java Sqrt c

*

* 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

*

******************************************************************************/

public class Sqrt {

public static void main(String[] args) {

double c = Double.parseDouble(args[0]);

double epsilon = 1e-15;

double t = c;

if (c < 0) {

System.out.println("not support negative sqrt");

return;

}

while(Math.abs(t - c/t) > epsilon*t) {

t = (c/t + t) / 2.0;

}

System.out.println(t);

}

}