// Arguments: Doubles, Doubles, Doubles
#include <stan/math/prim/prob/gumbel_log.hpp>
#include <stan/math/prim/fun/log.hpp>
#include <stan/math/prim/fun/exp.hpp>

using stan::math::var;
using std::numeric_limits;
using std::vector;

class AgradDistributionGumbel : public AgradDistributionTest {
 public:
  void valid_values(vector<vector<double> >& parameters,
                    vector<double>& log_prob) {
    vector<double> param(3);

    param[0] = 0;  // y
    param[1] = 0;  // mu
    param[2] = 1;  // beta
    parameters.push_back(param);
    log_prob.push_back(-1.0);  // expected log_prob

    param[0] = 1;  // y
    param[1] = 0;  // mu
    param[2] = 1;  // beta
    parameters.push_back(param);
    log_prob.push_back(
        -1.36787944117144232159552377016146086744581113103176783450783);  // expected
                                                                          // log_prob

    param[0] = -2;  // y
    param[1] = 0;   // mu
    param[2] = 1;   // beta
    parameters.push_back(param);
    log_prob.push_back(
        -5.38905609893065022723042746057500781318031557055184732408712);  // expected
                                                                          // log_prob

    param[0] = -3.5;  // y
    param[1] = 1.9;   // mu
    param[2] = 7.2;   // beta
    parameters.push_back(param);
    log_prob.push_back(
        -3.34108104263468429556956520337231251605487161479989511157723);  // expected
                                                                          // log_prob
  }

  void invalid_values(vector<size_t>& index, vector<double>& value) {
    // y

    // mu
    index.push_back(1U);
    value.push_back(numeric_limits<double>::infinity());

    index.push_back(1U);
    value.push_back(-numeric_limits<double>::infinity());

    // beta
    index.push_back(2U);
    value.push_back(0.0);

    index.push_back(2U);
    value.push_back(-1.0);

    index.push_back(2U);
    value.push_back(-numeric_limits<double>::infinity());
  }

  template <typename T_y, typename T_loc, typename T_scale, typename T3,
            typename T4, typename T5>
  stan::return_type_t<T_y, T_loc, T_scale> log_prob(const T_y& y,
                                                    const T_loc& mu,
                                                    const T_scale& beta,
                                                    const T3&, const T4&,
                                                    const T5&) {
    return stan::math::gumbel_log(y, mu, beta);
  }

  template <bool propto, typename T_y, typename T_loc, typename T_scale,
            typename T3, typename T4, typename T5>
  stan::return_type_t<T_y, T_loc, T_scale> log_prob(const T_y& y,
                                                    const T_loc& mu,
                                                    const T_scale& beta,
                                                    const T3&, const T4&,
                                                    const T5&) {
    return stan::math::gumbel_log<propto>(y, mu, beta);
  }

  template <typename T_y, typename T_loc, typename T_scale, typename T3,
            typename T4, typename T5>
  stan::return_type_t<T_y, T_loc, T_scale> log_prob_function(
      const T_y& y, const T_loc& mu, const T_scale& beta, const T3&, const T4&,
      const T5&) {
    return -log(beta) - (y - mu) / beta - exp((mu - y) / beta);
  }
};
