Sqrt.java

public final class Sqrt {

   public static final double EPSILON = Sqrt.getDouble ("epsilon", 1e-9);

   // Sqrt using Newton's method
   public static double sqrt (final double x) {
      assert x>=0;
      double t = 1.0D;  // a dumb guess
      for (;;) {
         // Improve the current guess, t, with a closer one
         final double t1 = (x/t + t) / 2.0;
         // For purposes of tracing the algorithm, ...
         System.out.printf ("sqrt %.2f %.6f %.6f %.2e%n", x , t1, Math.sqrt(x), Math.abs(Math.sqrt(x)-t1));
         // Stop iterating when there is little improvement
         if (Math.abs (t1-t) < EPSILON) break;
         t = t1;
      }
      return t;
   }

   public static void main (final String[] args) {
      for (String arg: args) {
         sqrt (Double.parseDouble (arg));
      }
   }

   // A function get a double from the system properites, if one is provided.
   private static double getDouble (final String name, final double defaultValue) {
      assert name!=null && name.length()>0;
      final String value = System.getProperty (name);
      if (value==null) return defaultValue;
      double d;
      try {
         d = Double.valueOf(value.trim()).doubleValue();
      } catch (final NumberFormatException ex) {
         d = defaultValue;
      }
      return d;
   }

}