#include "../AutomaticDifferentiation.hpp"

#include <iostream>
#include <iomanip>
using std::cout;
using std::endl;
using std::setw;
#define PRINT_VAR(x) std::cout << #x << "\t= " << std::setprecision(16) << (x) << std::endl
#define PRINT_DUAL(x) std::cout << #x << "\t= " << std::fixed << std::setprecision(4) << std::setw(10) << (x).a << ", " << std::setw(10) << (x).b << std::endl

template<typename T>
T f(const T & x)
{
    return 1 + x + x*x + 1/x + log(x);
}

template<typename T>
T df(const T & x)
{
	return 2*x + 1 + 1.0/x - 1/pow(x, 2);
}

template<typename T>
T ddf(const T & x)
{
	return 2 - 1/pow(x, 2) + 2/pow(x, 3);
}

int main()
{
	double xdbl = 1.5;
	
	{
		cout << "Analytical\n";
		cout << "f(x)      = " << f(xdbl) << endl;
		cout << "df(x)/dt  = " << df(xdbl) << endl;
		cout << "d²f(x)/dt = " << ddf(xdbl) << endl;
	}
	
	// 1st derivative forward
	{
		using Fd = Dual<double>;
		Fd x = xdbl;
		x.diff(0);
		Fd y = f(x);
		cout << "\nForward\n";
		cout << "f(x)      = " << y.a << endl;
		cout << "df(x)/dt  = " << y.d(0) << endl;
	}
	
	// 2nd derivative forward
	/*
	{
		using Fdd = Dual<Dual<double>>;
		Fdd x(xdbl);
		x.diff(0,2);
		x.x().diff(1,2);
		Fdd y = f(x);
		cout << "\nForward 2nd der\n";
		cout << "f(x)      = " << y.a.a << endl;
		cout << "df(x)/dt  = " << y.d(0).a << endl;
		cout << "d²f(x)/dt = " << y.d(0).d(1) << endl;
	}//*/

	return 0;
}