/*
      Title: Example of noise in evaluating a function.
 
      This is the program in Section 3.1.
 
      In the program, the function
         f(x) = -1 + 3*x - 3*x**2 + x**3
      is evaluated in two forms: nested and direct.
      The interval of evaluation is
         [a,b]  = [1-delta,1+delta],
      with delta specified in the data statement.
      For other computers, this value may have to be
      chosen smaller, in order to obtain the desired
      demonstration of noise in evaluating f(x).
*/

#include <stdio.h>
      
const int n=20;
const float delta = 0.001;

main()
{
	float a, b, h, x;
	float fnestd, fdirct, b1, b2;
	int j;
      	
	/* Initialization */

	a = 1.0 - delta; 
	b = 1.0 + delta;
	h = 2.0*delta/n;
	printf("\n Following are the values of x, f(x):Nested evaluation,\n");
	printf(" and f(x):Direct evaluation\n");

	for(j=0; j <= n; j++) { 
	
		/* Begin loop for evaluating function on [a,b] */

		x = a + j*h;
		b1 = -3.0 + x;
		b2 = 3.0 + x*b1;
		fnestd = -1.0 + x*b2;
		fdirct = -1.0 + 3.0*x - 3.0*x*x + x*x*x;
		printf("\t%9.6f\t%16.6e\t%16.6e\n",x, fnestd, fdirct); 
	}
	return 0;
}