#ifndef REAL_H

#define REAL_H

#include <utility></utility>

typedef double Real;

const Real precision = 1e-10;

const Real differential = 0.05;

const Real pi = 3.1415926535897932384626433;

inline bool equal(const Real &a, const Real &b, const Real &precision)

	{ return (a < b ? b - a : a - b) < precision; }

inline bool equal(const Real &a, const Real &b)

	{ return equal(a, b, precision); }

inline bool less(const Real &a, const Real &b)

	{ return !equal(a, b) && a < b; }

inline bool greater(const Real &a, const Real &b)

	{ return less(b, a); }

inline bool lesseq(const Real &a, const Real &b)

	{ return !less(b, a); }

inline bool greatereq(const Real &a, const Real &b)

	{ return lesseq(b, a); }

template<typename t=""></typename>

bool sort(T &a, T &b) {

	if (!(a < b)) { std::swap(a, b); return true; }

	return false;

}

template<typename t=""></typename>

bool sort(T &a, T &b, T &c) {

	bool x = false;

	if (sort(a, b)) x = true;

	if (sort(b, c)) x = true;

	if (x) sort(a, b);

	return x;

}

template<typename t=""></typename>

T merge(const Real &l, T &a, T &b)

	{ return a*(1 - l) + b*l; }

inline Real sign(const Real &x)

	{ return equal(x, 0) ? 0 : x < 0 ? -1 : 1; }

inline Real clamp(const Real &x, const Real &min, const Real &max)

	{ return x < min ? min : (max < x ? max : x); }

int solve_equation(Real *roots, const Real &k0, const Real &k1);

int solve_equation(Real *roots, const Real &k0, const Real &k1, const Real &k2);

int solve_equation(Real *roots, const Real &k0, const Real &k1, const Real &k2, const Real &k3);

#endif