#ifndef STAN_MATH_OPENCL_PRIM_CAUCHY_LPDF_HPP
#define STAN_MATH_OPENCL_PRIM_CAUCHY_LPDF_HPP
#ifdef STAN_OPENCL

#include <stan/math/prim/meta.hpp>
#include <stan/math/prim/err.hpp>
#include <stan/math/prim/fun/constants.hpp>
#include <stan/math/prim/fun/elt_divide.hpp>
#include <stan/math/prim/fun/elt_multiply.hpp>
#include <stan/math/opencl/kernel_generator.hpp>
#include <stan/math/prim/functor/partials_propagator.hpp>

namespace stan {
namespace math {

/** \ingroup opencl
 * The log of the Cauchy density for the specified scalar(s) given
 * the specified location parameter(s) and scale parameter(s). y,
 * mu, or sigma can each either be scalar a vector.  Any vector
 * inputs must be the same length.
 *
 * <p> The result log probability is defined to be the sum of
 * the log probabilities for each observation/mu/sigma triple.
 *
 * @tparam T_y_cl type of scalar outcome
 * @tparam T_loc_cl type of location
 * @tparam T_scale_cl type of scale
 * @param y (Sequence of) scalar(s).
 * @param mu (Sequence of) location(s).
 * @param sigma (Sequence of) scale(s).
 * @return The log of the product of densities.
 */
template <
    bool propto, typename T_y_cl, typename T_loc_cl, typename T_scale_cl,
    require_all_prim_or_rev_kernel_expression_t<T_y_cl, T_loc_cl,
                                                T_scale_cl>* = nullptr,
    require_any_not_stan_scalar_t<T_y_cl, T_loc_cl, T_scale_cl>* = nullptr>
return_type_t<T_y_cl, T_loc_cl, T_scale_cl> cauchy_lpdf(
    const T_y_cl& y, const T_loc_cl& mu, const T_scale_cl& sigma) {
  static const char* function = "cauchy_lpdf(OpenCL)";
  using T_partials_return = partials_return_t<T_y_cl, T_loc_cl, T_scale_cl>;
  using std::isfinite;
  using std::isnan;

  check_consistent_sizes(function, "Random variable", y, "Location parameter",
                         mu, "Scale parameter", sigma);
  const size_t N = max_size(y, mu, sigma);
  if (N == 0) {
    return 0.0;
  }
  if (!include_summand<propto, T_y_cl, T_loc_cl, T_scale_cl>::value) {
    return 0.0;
  }

  const auto& y_col = as_column_vector_or_scalar(y);
  const auto& mu_col = as_column_vector_or_scalar(mu);
  const auto& sigma_col = as_column_vector_or_scalar(sigma);

  const auto& y_val = value_of(y_col);
  const auto& mu_val = value_of(mu_col);
  const auto& sigma_val = value_of(sigma_col);

  auto check_y_not_nan
      = check_cl(function, "Random variable", y_val, "not NaN");
  auto y_not_nan_expr = !isnan(y_val);
  auto check_mu_finite
      = check_cl(function, "Location parameter", mu_val, "finite");
  auto mu_finite_expr = isfinite(mu_val);
  auto check_sigma_positive_finite
      = check_cl(function, "Scale parameter", sigma_val, "positive finite");
  auto sigma_positive_finite_expr = 0 < sigma_val && isfinite(sigma_val);

  auto inv_sigma_expr = elt_divide(1., sigma_val);
  auto y_minus_mu_expr = y_val - mu_val;
  auto logp1_expr
      = -log1p(elt_multiply(elt_multiply(y_minus_mu_expr, y_minus_mu_expr),
                            elt_multiply(inv_sigma_expr, inv_sigma_expr)));
  auto logp_expr = static_select<include_summand<propto, T_scale_cl>::value>(
      logp1_expr - log(sigma_val), logp1_expr);

  auto sigma_squared_expr = elt_multiply(sigma_val, sigma_val);
  auto y_minus_mu_squared_expr = elt_multiply(y_minus_mu_expr, y_minus_mu_expr);
  auto mu_deriv_expr = elt_divide(
      2 * y_minus_mu_expr, (sigma_squared_expr + y_minus_mu_squared_expr));
  auto sigma_deriv_expr
      = elt_divide(elt_multiply((y_minus_mu_squared_expr - sigma_squared_expr),
                                inv_sigma_expr),
                   (sigma_squared_expr + y_minus_mu_squared_expr));

  matrix_cl<double> logp_cl;
  matrix_cl<double> mu_deriv_cl;
  matrix_cl<double> y_deriv_cl;
  matrix_cl<double> sigma_deriv_cl;

  results(check_y_not_nan, check_mu_finite, check_sigma_positive_finite,
          logp_cl, mu_deriv_cl, y_deriv_cl, sigma_deriv_cl)
      = expressions(y_not_nan_expr, mu_finite_expr, sigma_positive_finite_expr,
                    logp_expr,
                    calc_if<!is_constant<T_loc_cl>::value>(mu_deriv_expr),
                    calc_if<!is_constant<T_y_cl>::value>(-mu_deriv_expr),
                    calc_if<!is_constant<T_scale_cl>::value>(sigma_deriv_expr));

  T_partials_return logp = sum(from_matrix_cl(logp_cl));
  if (include_summand<propto>::value) {
    logp -= N * LOG_PI;
  }
  auto ops_partials = make_partials_propagator(y_col, mu_col, sigma_col);

  if (!is_constant<T_y_cl>::value) {
    partials<0>(ops_partials) = std::move(y_deriv_cl);
  }
  if (!is_constant<T_loc_cl>::value) {
    partials<1>(ops_partials) = std::move(mu_deriv_cl);
  }
  if (!is_constant<T_scale_cl>::value) {
    partials<2>(ops_partials) = std::move(sigma_deriv_cl);
  }
  return ops_partials.build(logp);
}

}  // namespace math
}  // namespace stan
#endif
#endif
