#include <iostream>
#include <cmath>
using namespace std;

#include "Newton_polynomial.h"

/*
 *  This function prints out Maple code which plots
 *  the function sin(x), the polynomial interpolating
 *  sin(x) at up to five points, and the Newton
 *  polynomial evaluated at various points on the
 *  interpolated range: [low, high].
 *
 *  The output can be cut-and-pasted directly into Maple.
 */

int main() {
	Data_structures::Newton_polynomial<5> p;

	cout.precision( 20 );

	for ( double x = 1; x <= 5; ++x ) {
		p.insert( x, std::sin(x) );
	}

	double sum = 0;

	double const delta = 0.2384185791015625000e-6*0.25;

	for ( double xi = 0.5; xi <= 5.5; xi += delta ) {
		sum += p.evaluate( xi, Data_structures::BACKWARD )*delta;
	}

	cout << sum << endl;

	return 0;
}