text: #ifndef STAN_MATH_PRIM_SCAL_PROB_CAUCHY_LCCDF_HPP
  #define STAN_MATH_PRIM_SCAL_PROB_CAUCHY_LCCDF_HPP
  
  #include <stan/math/prim/meta.hpp>
  #include <stan/math/prim/scal/err/check_consistent_sizes.hpp>
  #include <stan/math/prim/scal/err/check_finite.hpp>
  #include <stan/math/prim/scal/err/check_not_nan.hpp>
  #include <stan/math/prim/scal/err/check_positive_finite.hpp>
  #include <stan/math/prim/scal/fun/size_zero.hpp>
  #include <stan/math/prim/scal/fun/constants.hpp>
  #include <stan/math/prim/scal/fun/value_of.hpp>
  #include <cmath>
  
  namespace stan {
  namespace math {
  
  /**
   * Returns the cauchy log complementary cumulative distribution function
   * for the given location, and scale. If given containers of matching sizes
   * returns the log sum of probabilities.
   *
   * @tparam T_y type of real parameter
   * @tparam T_loc type of location parameter
   * @tparam T_scale type of scale parameter
   * @param y real parameter
   * @param mu location parameter
   * @param sigma scale parameter
   * @return log probability or log sum of probabilities
   * @throw std::domain_error if sigma is nonpositive or y, mu are nan
   * @throw std::invalid_argument if container sizes mismatch
   */
  template <typename T_y, typename T_loc, typename T_scale>
  typename return_type<T_y, T_loc, T_scale>::type cauchy_lccdf(
      const T_y& y, const T_loc& mu, const T_scale& sigma) {
    typedef typename stan::partials_return_type<T_y, T_loc, T_scale>::type
        T_partials_return;
  
    if (size_zero(y, mu, sigma))
      return 0.0;
  
    static const char* function = "cauchy_lccdf";
  
    T_partials_return ccdf_log(0.0);
  
    check_not_nan(function, "Random variable", y);
    check_finite(function, "Location parameter", mu);
    check_positive_finite(function, "Scale parameter", sigma);
    check_consistent_sizes(function, "Random variable", y, "Location parameter",
                           mu, "Scale Parameter", sigma);
  
    scalar_seq_view<T_y> y_vec(y);
    scalar_seq_view<T_loc> mu_vec(mu);
    scalar_seq_view<T_scale> sigma_vec(sigma);
    size_t N = max_size(y, mu, sigma);
  
    operands_and_partials<T_y, T_loc, T_scale> ops_partials(y, mu, sigma);
  
    using std::atan;
    using std::log;
  
    for (size_t n = 0; n < N; n++) {
      const T_partials_return y_dbl = value_of(y_vec[n]);
      const T_partials_return mu_dbl = value_of(mu_vec[n]);
      const T_partials_return sigma_inv_dbl = 1.0 / value_of(sigma_vec[n]);
      const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
      const T_partials_return z = (y_dbl - mu_dbl) * sigma_inv_dbl;
  
      const T_partials_return Pn = 0.5 - atan(z) / pi();
      ccdf_log += log(Pn);
  
      const T_partials_return rep_deriv
          = 1.0 / (Pn * pi() * (z * z * sigma_dbl + sigma_dbl));
      if (!is_constant_all<T_y>::value)
        ops_partials.edge1_.partials_[n] -= rep_deriv;
      if (!is_constant_all<T_loc>::value)
        ops_partials.edge2_.partials_[n] += rep_deriv;
      if (!is_constant_all<T_scale>::value)
        ops_partials.edge3_.partials_[n] += rep_deriv * z;
    }
    return ops_partials.build(ccdf_log);
  }
  
  }  // namespace math
  }  // namespace stan
  #endif
  