#include <iostream>
#include "mlisp.h"

double a=0.;
double b=2;
double xmin=0.;
double tolerance=0.00001;
double mphi=(3.-sqrt(5))/2.;
double xa;
double xb;
double ya;
double yb;


double fun(double x){
	x=x-105./106.;
	return (x*atan(x)-1./3.);
}

double golden__section__search(double a, double b);
double golden__start(double a,double b);
double _VVV_try(double a,double b,double xa,double ya,double xb,double yb);
double close__enough_Q(double x,double y);

double golden__start(double a,double b){
	xa=a+mphi*(b-a);
	xb=b-mphi*(b-a);
	return _VVV_try(a,b,xa,fun(xa),xb,fun(xb));
}

double golden__section__search(double a, double b){
	(a<b)? xmin=golden__start(a,b): xmin=golden__start(b,a);
	newline();
	return xmin;
}

double close__enough_Q(double x,double y){
	return abs(x-y)<tolerance;
}

double _VVV_try(double a,double b,double xa,double ya,double xb,double yb){
	close__enough_Q(a,b)? ((a+b)*0.5):(
		display("+"),
		(ya<yb)?(
			b=xb,
			xb=xa,
			yb=ya,
			xa=a+mphi*(b-a),
			_VVV_try(a,b,xa,fun(xa),xb,yb)
		):
		(
			a=xa,
			xa=xb,
			ya=yb,
			xb=b-mphi*(b-a),
			_VVV_try(a,b,xa,ya,xb,fun(xb))
		)
	);
}

int main(){
	xmin=golden__section__search(a,b);
	display("interval=\t[");
	display(a);
	display(" , ");
	display(b);
	display("]\n");
	display("xmin=\t\t");
	display(xmin);
	newline();
	display("f(xmin)=\t");
	display(fun(xmin));
}