/*
 *  ============================================================================
 *  SubtractiveCancellation.java: Simple experiments to demonstrate subtractive
 *                                cancellation...
 *  
 *  Test function is f(x) = (1.0 - cos(x))/(x*x) for values of x close to zero.
 *
 *  Written By: Mark Austin                                        February 2007
 *  ============================================================================
 */

import java.lang.Math;

public class SubtractiveCancellation {
   public static void main ( String [] args ) {

       System.out.println("");
       System.out.println("Part 1. Experiment with:  ");
       System.out.println("   f1(x) = (1-cos(x))/(x*x) ");
       System.out.println("   f2(x) = (sin(x)^2)/(x*x)(1+cos(x)) ");
       System.out.println("==================================================");
       System.out.println("              dX            f1(x)            f2(x)");
       System.out.println("==================================================");

       // Compute and print function values....

       double dX = 0.10;
       System.out.printf("%16.10f %16.8e %16.8e\n", dX, f1(dX), f2(dX) );
       dX = 0.01;
       System.out.printf("%16.10f %16.8e %16.8e\n", dX, f1(dX), f2(dX) );
       dX = 0.001;
       System.out.printf("%16.10f %16.8e %16.8e\n", dX, f1(dX), f2(dX) );
       dX = 0.0001;
       System.out.printf("%16.10f %16.8e %16.8e\n", dX, f1(dX), f2(dX) );
       dX = 0.00001;
       System.out.printf("%16.10f %16.8e %16.8e\n", dX, f1(dX), f2(dX) );
       dX = 0.000001;
       System.out.printf("%16.10f %16.8e %16.8e\n", dX, f1(dX), f2(dX) );
       dX = 0.0000001;
       System.out.printf("%16.10f %16.8e %16.8e\n", dX, f1(dX), f2(dX) );
       dX = 0.00000001;
       System.out.printf("%16.10f %16.8e %16.8e\n", dX, f1(dX), f2(dX) );
       dX = 0.000000001;
       System.out.printf("%16.10f %16.8e %16.8e\n", dX, f1(dX), f2(dX) );
       dX = 0.0000000001;
       System.out.printf("%16.10f %16.8e %16.8e\n", dX, f1(dX), f2(dX) );
       System.out.println("==================================================");

       System.out.println("");
       System.out.println("Part 2. Experiment with:            ");
       System.out.println("   f3(x) = (cosh(x)-cos(x))/(x*x*x) ");
       System.out.println("   f4(x) = 1/x                      ");
       System.out.println("==================================================");
       System.out.println("              dX            f3(x)            f4(x)");
       System.out.println("==================================================");

       // Compute and print function values....

       dX = 0.10;
       System.out.printf("%16.10f %16.8e %16.8e\n", dX, f3(dX), f4(dX) );
       dX = 0.01;
       System.out.printf("%16.10f %16.8e %16.8e\n", dX, f3(dX), f4(dX) );
       dX = 0.001;
       System.out.printf("%16.10f %16.8e %16.8e\n", dX, f3(dX), f4(dX) );
       dX = 0.0001;
       System.out.printf("%16.10f %16.8e %16.8e\n", dX, f3(dX), f4(dX) );
       dX = 0.00001;
       System.out.printf("%16.10f %16.8e %16.8e\n", dX, f3(dX), f4(dX) );
       dX = 0.000001;
       System.out.printf("%16.10f %16.8e %16.8e\n", dX, f3(dX), f4(dX) );
       dX = 0.0000001;
       System.out.printf("%16.10f %16.8e %16.8e\n", dX, f3(dX), f4(dX) );
       dX = 0.00000001;
       System.out.printf("%16.10f %16.8e %16.8e\n", dX, f3(dX), f4(dX) );
       dX = 0.000000001;
       System.out.printf("%16.10f %16.8e %16.8e\n", dX, f3(dX), f4(dX) );
       dX = 0.0000000001;
       System.out.printf("%16.10f %16.8e %16.8e\n", dX, f3(dX), f4(dX) );
       System.out.println("==================================================");
   }

   // Define mathematical functions for Part 1....

   public static double f1 ( double dX ) {
       return (1.0 - Math.cos( dX ))/( dX*dX );
   }

   public static double f2 ( double dX ) {
       return (Math.sin(dX)*Math.sin(dX))/(dX*dX*(1.0 + Math.cos( dX )));
   }

   // Define mathematical functions for Part 2....

   public static double f3 ( double dX ) {
       return (Math.cosh(dX) - Math.cos( dX ))/( dX*dX*dX );
   }

   public static double f4 ( double dX ) {
       return (1.0/dX);
   }
}