// File: practice.cxx
// Written by Michael and Allison
// Demonstrates the bisection method to find a root to an equation.

//----------------------------------------------------------------------------
#include <cstdlib>
#include <iostream>
#include <cassert>
using namespace std;
//----------------------------------------------------------------------------

//----------------------------------------------------------------------------
// Prototypes:

// This function finds a value that is within EPSILON for a root of F.
// Preconditoin: F(low_x) <= 0 and F(high_x) >= 0.
const double EPSILON = 1e-4;
#define F(x) (3*x*x - 2*x - 9)
double bisection(double low_x, double high_x);
//----------------------------------------------------------------------------


//----------------------------------------------------------------------------
int main()
{
    cout << "One root of F is " << bisection(0.0, 1000.0) << endl;
    return EXIT_SUCCESS;
}
//----------------------------------------------------------------------------

//----------------------------------------------------------------------------
double bisection(double low_x, double high_x)
{
    double mid_x;

    assert(F(low_x) <= 0);
    assert(F(high_x) >= 0);
    
    while (abs(high_x - low_x) > EPSILON)
    {
	mid_x = (high_x + low_x)/2;
	if (F(mid_x) < 0)
	{
	    low_x = mid_x;
	}
	else
	{
	    high_x = mid_x;
	}
    }
    return (high_x + low_x)/2;
}
//----------------------------------------------------------------------------