//--------------------------------------------------------------------------//
// Interval  Class "interval.h"                                                //
//--------------------------------------------------------------------------//
#include <iostream.h>
#include <stdio.h>
#include <math.h>
#include <stdlib.h>
#include "roundvc.h"
#include <time.h>

class Interval{
	double a; //lower bound
	double b; //upper bound

public:
	Interval(void) {
	}
	Interval(double x) {
		a=x;
		b=x;
	}
	Interval(double x, double y) {
		a=x;
		b=y;
	}
	double& Inf() {
		return a;
	}
	double& Sup() {
		return b;
	}
    friend Interval operator+(const Interval& x, const Interval& y);
    friend Interval operator-(const Interval& x, const Interval& y);
    Interval operator+=(const Interval& x) {
		down;
		a += x.a;
		up;
		b += x.b;
        return (*this);
    }
    Interval operator-=(const Interval& x) {
		down;
		a -= x.b;
		up;
		b -= x.a;
        return (*this);
    }
    friend Interval operator*(const Interval& x, const Interval& y);
    friend Interval operator/(const Interval& x, const Interval& y);
	friend ostream& operator<<(ostream& s, Interval& x);
};

inline Interval operator+(const Interval& x, const Interval& y) {
	Interval z;
	down;
	z.a = x.a + y.a;
	up;
	z.b = x.b + y.b;
	return z;
}

inline Interval operator-(const Interval& x, const Interval& y) {
	Interval z;
	down;
	z.a = x.a - y.b;
	up;
	z.b = x.b - y.b;
	return z;
}

Interval operator*(const Interval& x, const Interval& y) {
	Interval z;
	double temp;
	if(x.a>=0.) {
		if(y.a>=0.) {
			down;
			z.a=x.a*y.a;
			up;
			z.b=x.b*y.b;
		} else if(y.b <=0.) {
			down;
			z.a=x.b*y.a;
			up;
			z.b=x.a*y.b;
		} else {
			down;
			z.a=x.b*y.a;
			up;
			z.b=x.b*y.b;
		}
	} else if(x.b <= 0.) {
		if(y.a>=0.) {
			down;
			z.a=x.a*y.b;
			up;
			z.b=x.b*y.a;
		} else if(y.b <=0.) {
			down;
			z.a=x.b*y.b;
			up;
			z.b=x.a*y.a;
		} else {
			down;
			z.a=x.a*y.b;
			up;
			z.b=x.a*y.a;
		}
	} else {
		if(y.a>=0.) {
			down;
			z.a=x.a*y.b;
			up;
			z.b=x.b*y.b;
		} else if(y.b <=0.) {
			down;
			z.a=x.b*y.a;
			up;
			z.b=x.a*y.a;
		} else {
			down;
			z.a=x.a*y.b;
			temp=x.b*y.a;
			if(temp < z.a) z.a=temp;
			up;
			z.b=x.a*y.a;
			temp=x.b*y.b;
			if(temp>z.b) z.b=temp;
		}
	}
	return z;
}

Interval operator/(const Interval& x, const Interval& y) {
	Interval z;
	if(y.a>=0.) {
		if(x.a>=0.) {
			down;
			z.a=x.a/y.b;
			up;
			z.b=x.b/y.a;
		} else if(x.b <=0.) {
			down;
			z.a=x.a/y.a;
			up;
			z.b=x.b/y.b;
		} else {
			down;
			z.a=x.a/y.a;
			up;
			z.b=x.b/y.a;
		}
	} else if(y.b < 0.) {
		if(x.a>=0.) {
			down;
			z.a=x.b/y.b;
			up;
			z.b=x.a/y.a;
		} else if(x.b <=0.) {
			down;
			z.a=x.b/y.a;
			up;
			z.b=x.a/y.b;
		} else {
			down;
			z.a=x.b/y.b;
			up;
			z.b=x.a/y.b;
		}
	} else {
		cout << "Division by 0\n";
		exit(1);
	}
	return z;
}

ostream& operator<<(ostream& s, Interval& x) {
	return (s<<'[' <<x.a << ',' <<x.b << ']');
}