#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;
}

inline bool is_valid(double a, double b, double c)
{
    return a > 0 && b > 0 && c > 0
        && a + b > c
        && a + c > b
        && b + c > a;
}

inline bool is_equilateral(double a, double b, double c)
{
    return fuzzy_equal(a, b)
        && fuzzy_equal(a, c)
        && fuzzy_equal(b, c);
}

inline bool is_isosceles(double a, double b, double c)
{
    return fuzzy_equal(a, b)
        || fuzzy_equal(a, c)
        || fuzzy_equal(b, c);
}

}

kind_t kind(double a, double b, double c)
{
    if (!is_valid(a, b, c))
        throw domain_error("invalid triangle");

    if (is_equilateral(a, b, c))
        return equilateral;

    if (is_isosceles(a, b, c))
        return isosceles;

    return scalene;
}

}