// Bisection Version 1
#include <iostream>
#include <cmath>
using namespace std;

double f( double x )
{
    return( x * x - 2.0 );
}

int main()
{
// User input ******************************
    double x1 = 1.0;
    double x2 = 2.0;
    const double TOLERANCE = 1.0e-5;
// *****************************************

    double fx1 = f(x1), fx2 = f(x2), xp, xn, m, fm, error;
    
    if ( fx1 * fx2 >= 0.0 ) {
        cout << "STOP: Signs of f are not different at startup.\n\n";
        system( "PAUSE" );
        return( 0 );
    }
    
    if ( fx1 > 0 )
        xp = x1, xn = x2;
    else
        xp = x2, xn = x1;
    do {
        m = ( xn + xp ) / 2.0;
        fm = f(m);
        if ( fm == 0.0 ) {
            cout << "STOP: You have found the exact solution: x = " << m << "\n\n";
            system( "PAUSE" );
            return( 0 );
        }
        else if ( fm > 0.0 )
            xp = m;
        else
            xn = m;
        error = abs( xp - xn );
    } while ( error > TOLERANCE );
    cout << "The approximate solution is: x = " << ( xn + xp ) / 2.0;
    
    cout << "\n\n"; system( "PAUSE" );
    return( 0 );
}