/**
* Demonstrate the while statement in Java * for problems
* involving convergence, meeting/exceeding thresholds
*
* @author (Michael Branicky)
*/
public class Thresholds
{
   // How long to a billion (starting with $currentSavings at interestRate% interest)?
   public static int yearsUntilRetirement (double currentSavings, double interestRate) {
     int years = 0;
     double principal = currentSavings;
     double multiplier = 1.0 + interestRate/100.0;
     while (principal < 1E9) {
       principal = principal * multiplier;
       years = years + 1;
     }
     return years;
   }

   // Pharmacokinetics of ibuprofen
   // REF: http://www.rxlist.com/cgi/generic/ibup_cp.htm
   public static double hoursUntil1mg (double dose) {
     // peak level is up to 80% of dose after 1-2 hours
     double serumAmount = 0.8*dose;
     double hours = 1.5;
     // half-life is 1.8 to 2 hrs
     while (serumAmount>1.0) {
       serumAmount = 0.5*serumAmount;
       hours = hours + 1.9;
     } 
     return hours;
   }

   // Newton iteration for the square root function
   // REF: http://en.wikipedia.org/wiki/N-th_root_algorithm
   public static double sqrtViaNewton (double a) {
     double guess = 1.0;
     while (Math.abs(guess-a/guess)>1E-6) {
       guess = 0.5*(guess + a/guess);
     } 
     return guess;
   }

   // same method, but takes guess and tolerance as parameters
   public static double sqrtViaNewton (double a, double guess, double tol) {
     while (Math.abs(guess-a/guess)>tol) {
       guess = 0.5*(guess + a/guess);
     } 
     return guess;
   }

   public static void main(String args[])
   {
     // Test/use the yearsUntilRetirement method
     System.out.println(yearsUntilRetirement(1E6, 10.0)+" years to a billion");

     // Test/use the hoursUntil1mg method
     System.out.println("800mg ibuprofen to 1mg in ~"+hoursUntil1mg(800.)+" hours");

     // Test/use the sqrtViaNewton methods
     System.out.println("Square root of 2 ~= "+sqrtViaNewton(2.));
     System.out.println("Square root of 2 ~= "+sqrtViaNewton(2., 9., 1E-3));
     System.out.println("Square root of 3 ~= "+sqrtViaNewton(3., 2., 1E-9));

  }
}