#include "triangle.h"

#include <cmath>
#include <limits>
#include <stdexcept>

namespace triangle {

using namespace std;

namespace {

inline bool fuzzy_equal(double a, double b)
{
    typedef numeric_limits<double> limits_t;

    static const double &epsilon     = limits_t::epsilon();
    static const double &min         = limits_t::min();
    static const double &round_error = limits_t::round_error();


    return abs(a - b) < epsilon * abs(a + b) * round_error
        || abs(a - b) < min;
}

}


kind_t kind(double a, double b, double c)
{
    if (a > b) swap(a, b);
    if (a > c) swap(a, c);
    if (b > c) swap(b, c);

    if (a <= 0 || a + b <= c)
        throw domain_error("invalid triangle");

    if (fuzzy_equal(a, c))
        return equilateral;

    if (fuzzy_equal(a, b) || fuzzy_equal(b, c))
        return isosceles;

    return scalene;
}

}